TSTP Solution File: SYN507-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN507-1 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 23:56:02 EDT 2022
% Result : Unsatisfiable 3.09s 2.26s
% Output : Proof 3.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN507-1 : TPTP v8.1.0. Released v2.1.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n004.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Sep 5 04:44:49 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 3.09/2.26 % SZS status Unsatisfiable
% 3.09/2.26 % SZS output start Proof
% 3.09/2.26 tff(c0_1_type, type, (
% 3.09/2.26 c0_1: $i > $o)).
% 3.09/2.26 tff(a606_type, type, (
% 3.09/2.26 a606: $i)).
% 3.09/2.26 tff(c2_1_type, type, (
% 3.09/2.26 c2_1: $i > $o)).
% 3.09/2.26 tff(a604_type, type, (
% 3.09/2.26 a604: $i)).
% 3.09/2.26 tff(a599_type, type, (
% 3.09/2.26 a599: $i)).
% 3.09/2.26 tff(c3_1_type, type, (
% 3.09/2.26 c3_1: $i > $o)).
% 3.09/2.26 tff(hskp11_type, type, (
% 3.09/2.26 hskp11: $o)).
% 3.09/2.26 tff(a636_type, type, (
% 3.09/2.26 a636: $i)).
% 3.09/2.26 tff(a607_type, type, (
% 3.09/2.26 a607: $i)).
% 3.09/2.26 tff(a601_type, type, (
% 3.09/2.26 a601: $i)).
% 3.09/2.26 tff(a598_type, type, (
% 3.09/2.26 a598: $i)).
% 3.09/2.26 tff(c1_1_type, type, (
% 3.09/2.26 c1_1: $i > $o)).
% 3.09/2.26 tff(ndr1_0_type, type, (
% 3.09/2.26 ndr1_0: $o)).
% 3.09/2.26 tff(hskp10_type, type, (
% 3.09/2.26 hskp10: $o)).
% 3.09/2.26 tff(a633_type, type, (
% 3.09/2.26 a633: $i)).
% 3.09/2.26 tff(a612_type, type, (
% 3.09/2.26 a612: $i)).
% 3.09/2.26 tff(hskp17_type, type, (
% 3.09/2.26 hskp17: $o)).
% 3.09/2.26 tff(a587_type, type, (
% 3.09/2.26 a587: $i)).
% 3.09/2.26 tff(hskp3_type, type, (
% 3.09/2.26 hskp3: $o)).
% 3.09/2.26 tff(hskp22_type, type, (
% 3.09/2.26 hskp22: $o)).
% 3.09/2.26 tff(a623_type, type, (
% 3.09/2.26 a623: $i)).
% 3.09/2.26 tff(hskp6_type, type, (
% 3.09/2.26 hskp6: $o)).
% 3.09/2.26 tff(hskp20_type, type, (
% 3.09/2.26 hskp20: $o)).
% 3.09/2.26 tff(a583_type, type, (
% 3.09/2.26 a583: $i)).
% 3.09/2.26 tff(hskp26_type, type, (
% 3.09/2.26 hskp26: $o)).
% 3.09/2.26 tff(a590_type, type, (
% 3.09/2.26 a590: $i)).
% 3.09/2.26 tff(a586_type, type, (
% 3.09/2.26 a586: $i)).
% 3.09/2.26 tff(hskp4_type, type, (
% 3.09/2.26 hskp4: $o)).
% 3.09/2.26 tff(hskp2_type, type, (
% 3.09/2.26 hskp2: $o)).
% 3.09/2.26 tff(a603_type, type, (
% 3.09/2.26 a603: $i)).
% 3.09/2.26 tff(hskp14_type, type, (
% 3.09/2.26 hskp14: $o)).
% 3.09/2.26 tff(hskp29_type, type, (
% 3.09/2.26 hskp29: $o)).
% 3.09/2.26 tff(a588_type, type, (
% 3.09/2.26 a588: $i)).
% 3.09/2.26 tff(a678_type, type, (
% 3.09/2.26 a678: $i)).
% 3.09/2.26 tff(a595_type, type, (
% 3.09/2.26 a595: $i)).
% 3.09/2.26 tff(hskp9_type, type, (
% 3.09/2.26 hskp9: $o)).
% 3.09/2.26 tff(a593_type, type, (
% 3.09/2.26 a593: $i)).
% 3.09/2.26 tff(hskp8_type, type, (
% 3.09/2.26 hskp8: $o)).
% 3.09/2.26 tff(hskp23_type, type, (
% 3.09/2.26 hskp23: $o)).
% 3.09/2.26 tff(hskp27_type, type, (
% 3.09/2.26 hskp27: $o)).
% 3.09/2.26 tff(a589_type, type, (
% 3.09/2.26 a589: $i)).
% 3.09/2.26 tff(hskp5_type, type, (
% 3.09/2.26 hskp5: $o)).
% 3.09/2.26 tff(a611_type, type, (
% 3.09/2.26 a611: $i)).
% 3.09/2.26 tff(a592_type, type, (
% 3.09/2.26 a592: $i)).
% 3.09/2.26 tff(hskp7_type, type, (
% 3.09/2.26 hskp7: $o)).
% 3.09/2.26 tff(hskp12_type, type, (
% 3.09/2.26 hskp12: $o)).
% 3.09/2.26 tff(a600_type, type, (
% 3.09/2.26 a600: $i)).
% 3.09/2.26 tff(a585_type, type, (
% 3.09/2.26 a585: $i)).
% 3.09/2.26 tff(hskp1_type, type, (
% 3.09/2.26 hskp1: $o)).
% 3.09/2.26 tff(hskp16_type, type, (
% 3.09/2.26 hskp16: $o)).
% 3.09/2.26 tff(a584_type, type, (
% 3.09/2.26 a584: $i)).
% 3.09/2.26 tff(hskp0_type, type, (
% 3.09/2.26 hskp0: $o)).
% 3.09/2.26 tff(hskp28_type, type, (
% 3.09/2.26 hskp28: $o)).
% 3.09/2.26 tff(a610_type, type, (
% 3.09/2.26 a610: $i)).
% 3.09/2.26 tff(hskp18_type, type, (
% 3.09/2.26 hskp18: $o)).
% 3.09/2.26 tff(hskp15_type, type, (
% 3.09/2.26 hskp15: $o)).
% 3.09/2.26 tff(a651_type, type, (
% 3.09/2.26 a651: $i)).
% 3.09/2.26 tff(hskp25_type, type, (
% 3.09/2.26 hskp25: $o)).
% 3.09/2.26 tff(a617_type, type, (
% 3.09/2.26 a617: $i)).
% 3.09/2.26 tff(hskp19_type, type, (
% 3.09/2.26 hskp19: $o)).
% 3.09/2.26 tff(hskp13_type, type, (
% 3.09/2.26 hskp13: $o)).
% 3.09/2.26 tff(a629_type, type, (
% 3.09/2.26 a629: $i)).
% 3.09/2.26 tff(hskp21_type, type, (
% 3.09/2.26 hskp21: $o)).
% 3.09/2.26 tff(1,assumption,(~c0_1(a607)), introduced(assumption)).
% 3.09/2.26 tff(2,plain,
% 3.09/2.26 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))))),
% 3.09/2.26 inference(bind,[status(th)],[])).
% 3.09/2.26 tff(3,plain,
% 3.09/2.26 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 3.09/2.26 inference(quant_intro,[status(thm)],[2])).
% 3.09/2.26 tff(4,plain,
% 3.09/2.26 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 3.09/2.26 inference(rewrite,[status(thm)],[])).
% 3.09/2.26 tff(5,plain,
% 3.09/2.26 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))))),
% 3.09/2.26 inference(bind,[status(th)],[])).
% 3.09/2.26 tff(6,plain,
% 3.09/2.26 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 3.09/2.26 inference(quant_intro,[status(thm)],[5])).
% 3.09/2.26 tff(7,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause199')).
% 3.09/2.26 tff(8,plain,
% 3.09/2.26 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 3.09/2.26 inference(modus_ponens,[status(thm)],[7, 6])).
% 3.09/2.26 tff(9,plain,
% 3.09/2.26 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 3.09/2.26 inference(modus_ponens,[status(thm)],[8, 4])).
% 3.09/2.26 tff(10,plain,(
% 3.09/2.26 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 3.09/2.26 inference(skolemize,[status(sab)],[9])).
% 3.09/2.26 tff(11,plain,
% 3.09/2.26 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 3.09/2.26 inference(modus_ponens,[status(thm)],[10, 3])).
% 3.09/2.26 tff(12,plain,
% 3.09/2.26 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))))),
% 3.09/2.26 inference(bind,[status(th)],[])).
% 3.09/2.26 tff(13,plain,
% 3.09/2.26 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 3.09/2.26 inference(quant_intro,[status(thm)],[12])).
% 3.09/2.26 tff(14,plain,
% 3.09/2.26 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 3.09/2.26 inference(rewrite,[status(thm)],[])).
% 3.09/2.26 tff(15,plain,
% 3.09/2.26 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | hskp10) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) | hskp10))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))))),
% 3.09/2.26 inference(bind,[status(th)],[])).
% 3.09/2.26 tff(16,plain,
% 3.09/2.26 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 3.09/2.26 inference(quant_intro,[status(thm)],[15])).
% 3.09/2.26 tff(17,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause194')).
% 3.09/2.26 tff(18,plain,
% 3.09/2.26 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 3.09/2.26 inference(modus_ponens,[status(thm)],[17, 16])).
% 3.09/2.26 tff(19,plain,
% 3.09/2.26 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 3.09/2.26 inference(modus_ponens,[status(thm)],[18, 14])).
% 3.09/2.26 tff(20,plain,(
% 3.09/2.26 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 3.09/2.26 inference(skolemize,[status(sab)],[19])).
% 3.09/2.26 tff(21,plain,
% 3.09/2.26 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))),
% 3.09/2.26 inference(modus_ponens,[status(thm)],[20, 13])).
% 3.09/2.26 tff(22,assumption,(~c2_1(a607)), introduced(assumption)).
% 3.09/2.26 tff(23,plain,
% 3.09/2.26 (^[V: $i, U: $i] : refl((hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))),
% 3.09/2.26 inference(bind,[status(th)],[])).
% 3.09/2.26 tff(24,plain,
% 3.09/2.26 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 3.09/2.26 inference(quant_intro,[status(thm)],[23])).
% 3.09/2.26 tff(25,plain,
% 3.09/2.26 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 3.09/2.26 inference(rewrite,[status(thm)],[])).
% 3.09/2.26 tff(26,plain,
% 3.09/2.26 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp17) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp17))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp17) <=> (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))))),
% 3.09/2.26 inference(bind,[status(th)],[])).
% 3.09/2.26 tff(27,plain,
% 3.09/2.26 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp17) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 3.09/2.26 inference(quant_intro,[status(thm)],[26])).
% 3.09/2.26 tff(28,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause177')).
% 3.09/2.26 tff(29,plain,
% 3.09/2.26 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 3.09/2.26 inference(modus_ponens,[status(thm)],[28, 27])).
% 3.09/2.26 tff(30,plain,
% 3.09/2.26 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 3.09/2.26 inference(modus_ponens,[status(thm)],[29, 25])).
% 3.09/2.26 tff(31,plain,(
% 3.09/2.26 ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 3.09/2.26 inference(skolemize,[status(sab)],[30])).
% 3.09/2.26 tff(32,plain,
% 3.09/2.26 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 3.09/2.26 inference(modus_ponens,[status(thm)],[31, 24])).
% 3.09/2.26 tff(33,assumption,(~c3_1(a607)), introduced(assumption)).
% 3.09/2.26 tff(34,plain,
% 3.09/2.26 (^[U: $i] : refl((hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))),
% 3.09/2.26 inference(bind,[status(th)],[])).
% 3.09/2.26 tff(35,plain,
% 3.09/2.26 (![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 3.09/2.26 inference(quant_intro,[status(thm)],[34])).
% 3.09/2.26 tff(36,plain,
% 3.09/2.26 (![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 3.09/2.26 inference(rewrite,[status(thm)],[])).
% 3.09/2.26 tff(37,plain,
% 3.09/2.26 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp22) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp22))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp22) | hskp6) <=> ((hskp22 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp6))), rewrite(((hskp22 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp6) <=> (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp22) | hskp6) <=> (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))))),
% 3.09/2.26 inference(bind,[status(th)],[])).
% 3.09/2.26 tff(38,plain,
% 3.09/2.26 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp22) | hskp6) <=> ![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 3.09/2.26 inference(quant_intro,[status(thm)],[37])).
% 3.09/2.26 tff(39,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp22) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause138')).
% 3.09/2.26 tff(40,plain,
% 3.09/2.26 (![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 3.09/2.26 inference(modus_ponens,[status(thm)],[39, 38])).
% 3.09/2.26 tff(41,plain,
% 3.09/2.26 (![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 3.09/2.26 inference(modus_ponens,[status(thm)],[40, 36])).
% 3.09/2.26 tff(42,plain,(
% 3.09/2.26 ![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 3.09/2.26 inference(skolemize,[status(sab)],[41])).
% 3.09/2.26 tff(43,plain,
% 3.09/2.26 (![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 3.09/2.26 inference(modus_ponens,[status(thm)],[42, 35])).
% 3.09/2.26 tff(44,assumption,(~hskp22), introduced(assumption)).
% 3.09/2.26 tff(45,assumption,(~c0_1(a590)), introduced(assumption)).
% 3.09/2.26 tff(46,plain,
% 3.09/2.26 (^[U: $i] : refl((hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 3.09/2.26 inference(bind,[status(th)],[])).
% 3.09/2.26 tff(47,plain,
% 3.09/2.26 (![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 3.09/2.26 inference(quant_intro,[status(thm)],[46])).
% 3.09/2.26 tff(48,plain,
% 3.09/2.26 (![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 3.09/2.26 inference(rewrite,[status(thm)],[])).
% 3.09/2.26 tff(49,plain,
% 3.09/2.26 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp4) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp4))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp4) <=> (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp4) | hskp17) <=> ((hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp17))), rewrite(((hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp17) <=> (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp4) | hskp17) <=> (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 3.09/2.26 inference(bind,[status(th)],[])).
% 3.09/2.26 tff(50,plain,
% 3.09/2.26 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp4) | hskp17) <=> ![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 3.09/2.26 inference(quant_intro,[status(thm)],[49])).
% 3.09/2.26 tff(51,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp4) | hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause156')).
% 3.09/2.26 tff(52,plain,
% 3.09/2.26 (![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 3.09/2.26 inference(modus_ponens,[status(thm)],[51, 50])).
% 3.09/2.26 tff(53,plain,
% 3.09/2.26 (![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 3.09/2.26 inference(modus_ponens,[status(thm)],[52, 48])).
% 3.09/2.26 tff(54,plain,(
% 3.09/2.26 ![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 3.09/2.26 inference(skolemize,[status(sab)],[53])).
% 3.09/2.26 tff(55,plain,
% 3.09/2.26 (![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 3.09/2.26 inference(modus_ponens,[status(thm)],[54, 47])).
% 3.09/2.26 tff(56,plain,
% 3.09/2.26 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))))),
% 3.09/2.26 inference(bind,[status(th)],[])).
% 3.09/2.26 tff(57,plain,
% 3.09/2.26 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 3.09/2.26 inference(quant_intro,[status(thm)],[56])).
% 3.09/2.26 tff(58,plain,
% 3.09/2.26 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 3.09/2.26 inference(rewrite,[status(thm)],[])).
% 3.09/2.26 tff(59,plain,
% 3.09/2.26 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))))),
% 3.09/2.26 inference(bind,[status(th)],[])).
% 3.09/2.26 tff(60,plain,
% 3.09/2.26 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 3.09/2.26 inference(quant_intro,[status(thm)],[59])).
% 3.09/2.26 tff(61,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause198')).
% 3.09/2.26 tff(62,plain,
% 3.09/2.26 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 3.09/2.26 inference(modus_ponens,[status(thm)],[61, 60])).
% 3.09/2.26 tff(63,plain,
% 3.09/2.26 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 3.09/2.26 inference(modus_ponens,[status(thm)],[62, 58])).
% 3.09/2.26 tff(64,plain,(
% 3.09/2.26 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 3.09/2.26 inference(skolemize,[status(sab)],[63])).
% 3.09/2.26 tff(65,plain,
% 3.09/2.26 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 3.09/2.26 inference(modus_ponens,[status(thm)],[64, 57])).
% 3.09/2.26 tff(66,assumption,(~c1_1(a607)), introduced(assumption)).
% 3.09/2.26 tff(67,assumption,(~hskp6), introduced(assumption)).
% 3.09/2.26 tff(68,assumption,(~ndr1_0), introduced(assumption)).
% 3.09/2.26 tff(69,plain,
% 3.09/2.26 ((ndr1_0 | (~hskp17)) <=> (ndr1_0 | (~hskp17))),
% 3.09/2.26 inference(rewrite,[status(thm)],[])).
% 3.09/2.26 tff(70,plain,
% 3.09/2.26 (((~hskp17) | ndr1_0) <=> (ndr1_0 | (~hskp17))),
% 3.09/2.26 inference(rewrite,[status(thm)],[])).
% 3.09/2.26 tff(71,axiom,((~hskp17) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause14')).
% 3.09/2.26 tff(72,plain,
% 3.09/2.26 (ndr1_0 | (~hskp17)),
% 3.09/2.26 inference(modus_ponens,[status(thm)],[71, 70])).
% 3.09/2.26 tff(73,plain,
% 3.09/2.26 (ndr1_0 | (~hskp17)),
% 3.09/2.26 inference(modus_ponens,[status(thm)],[72, 69])).
% 3.09/2.26 tff(74,plain,
% 3.09/2.26 (~hskp17),
% 3.09/2.26 inference(unit_resolution,[status(thm)],[73, 68])).
% 3.09/2.26 tff(75,plain,
% 3.09/2.26 (((~hskp29) | ndr1_0) <=> ((~hskp29) | ndr1_0)),
% 3.09/2.26 inference(rewrite,[status(thm)],[])).
% 3.09/2.26 tff(76,axiom,((~hskp29) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause2')).
% 3.09/2.26 tff(77,plain,
% 3.09/2.26 ((~hskp29) | ndr1_0),
% 3.09/2.26 inference(modus_ponens,[status(thm)],[76, 75])).
% 3.09/2.26 tff(78,plain,
% 3.09/2.26 ((~hskp29) | ndr1_0),
% 3.09/2.26 inference(modus_ponens,[status(thm)],[77, 75])).
% 3.09/2.26 tff(79,plain,
% 3.09/2.26 ((~hskp29) | ndr1_0),
% 3.09/2.26 inference(modus_ponens,[status(thm)],[78, 75])).
% 3.09/2.26 tff(80,plain,
% 3.09/2.26 ((~hskp29) | ndr1_0),
% 3.09/2.26 inference(modus_ponens,[status(thm)],[79, 75])).
% 3.09/2.26 tff(81,plain,
% 3.09/2.26 ((~hskp29) | ndr1_0),
% 3.09/2.26 inference(modus_ponens,[status(thm)],[80, 75])).
% 3.09/2.26 tff(82,plain,
% 3.09/2.26 ((~hskp29) | ndr1_0),
% 3.09/2.26 inference(modus_ponens,[status(thm)],[81, 75])).
% 3.09/2.26 tff(83,plain,
% 3.09/2.26 ((~hskp29) | ndr1_0),
% 3.09/2.26 inference(modus_ponens,[status(thm)],[82, 75])).
% 3.09/2.26 tff(84,plain,
% 3.09/2.26 ((~hskp29) | ndr1_0),
% 3.09/2.26 inference(modus_ponens,[status(thm)],[83, 75])).
% 3.09/2.26 tff(85,plain,
% 3.09/2.26 (~hskp29),
% 3.09/2.26 inference(unit_resolution,[status(thm)],[84, 68])).
% 3.09/2.26 tff(86,plain,
% 3.09/2.26 ((ndr1_0 | (~hskp22)) <=> (ndr1_0 | (~hskp22))),
% 3.09/2.26 inference(rewrite,[status(thm)],[])).
% 3.09/2.26 tff(87,plain,
% 3.09/2.26 (((~hskp22) | ndr1_0) <=> (ndr1_0 | (~hskp22))),
% 3.09/2.26 inference(rewrite,[status(thm)],[])).
% 3.09/2.26 tff(88,axiom,((~hskp22) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause9')).
% 3.09/2.26 tff(89,plain,
% 3.09/2.26 (ndr1_0 | (~hskp22)),
% 3.09/2.26 inference(modus_ponens,[status(thm)],[88, 87])).
% 3.09/2.26 tff(90,plain,
% 3.09/2.26 (ndr1_0 | (~hskp22)),
% 3.09/2.26 inference(modus_ponens,[status(thm)],[89, 86])).
% 3.09/2.26 tff(91,plain,
% 3.09/2.26 (~hskp22),
% 3.09/2.26 inference(unit_resolution,[status(thm)],[90, 68])).
% 3.09/2.26 tff(92,plain,
% 3.09/2.26 ((hskp29 | hskp22 | hskp17) <=> (hskp29 | hskp22 | hskp17)),
% 3.09/2.26 inference(rewrite,[status(thm)],[])).
% 3.09/2.26 tff(93,plain,
% 3.09/2.26 (((hskp29 | hskp22) | hskp17) <=> (hskp29 | hskp22 | hskp17)),
% 3.09/2.26 inference(rewrite,[status(thm)],[])).
% 3.09/2.26 tff(94,plain,
% 3.09/2.26 ((hskp29 | hskp22) <=> (hskp29 | hskp22)),
% 3.09/2.26 inference(rewrite,[status(thm)],[])).
% 3.09/2.26 tff(95,plain,
% 3.09/2.26 (((hskp29 | hskp22) | hskp17) <=> ((hskp29 | hskp22) | hskp17)),
% 3.09/2.26 inference(monotonicity,[status(thm)],[94])).
% 3.09/2.26 tff(96,plain,
% 3.09/2.26 (((hskp29 | hskp22) | hskp17) <=> (hskp29 | hskp22 | hskp17)),
% 3.09/2.26 inference(transitivity,[status(thm)],[95, 93])).
% 3.09/2.26 tff(97,axiom,((hskp29 | hskp22) | hskp17), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause33')).
% 3.09/2.26 tff(98,plain,
% 3.09/2.26 (hskp29 | hskp22 | hskp17),
% 3.09/2.26 inference(modus_ponens,[status(thm)],[97, 96])).
% 3.09/2.26 tff(99,plain,
% 3.09/2.26 (hskp29 | hskp22 | hskp17),
% 3.09/2.26 inference(modus_ponens,[status(thm)],[98, 92])).
% 3.09/2.27 tff(100,plain,
% 3.09/2.27 (hskp29 | hskp22 | hskp17),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[99, 92])).
% 3.09/2.27 tff(101,plain,
% 3.09/2.27 (hskp29 | hskp22 | hskp17),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[100, 92])).
% 3.09/2.27 tff(102,plain,
% 3.09/2.27 (hskp29 | hskp22 | hskp17),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[101, 92])).
% 3.09/2.27 tff(103,plain,
% 3.09/2.27 (hskp29 | hskp22 | hskp17),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[102, 92])).
% 3.09/2.27 tff(104,plain,
% 3.09/2.27 (hskp29 | hskp22 | hskp17),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[103, 92])).
% 3.09/2.27 tff(105,plain,
% 3.09/2.27 (hskp29 | hskp22 | hskp17),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[104, 92])).
% 3.09/2.27 tff(106,plain,
% 3.09/2.27 ($false),
% 3.09/2.27 inference(unit_resolution,[status(thm)],[105, 91, 85, 74])).
% 3.09/2.27 tff(107,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 3.09/2.27 tff(108,plain,
% 3.09/2.27 (((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp22 | hskp6 | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)))),
% 3.09/2.27 inference(rewrite,[status(thm)],[])).
% 3.09/2.27 tff(109,plain,
% 3.09/2.27 ((hskp22 | hskp6 | (~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607))) <=> (hskp22 | hskp6 | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)))),
% 3.09/2.27 inference(rewrite,[status(thm)],[])).
% 3.09/2.27 tff(110,plain,
% 3.09/2.27 (((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | (~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607))))),
% 3.09/2.27 inference(monotonicity,[status(thm)],[109])).
% 3.09/2.27 tff(111,plain,
% 3.09/2.27 (((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | (~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp22 | hskp6 | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)))),
% 3.09/2.27 inference(transitivity,[status(thm)],[110, 108])).
% 3.09/2.27 tff(112,plain,
% 3.09/2.27 ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | (~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)))),
% 3.09/2.27 inference(quant_inst,[status(thm)],[])).
% 3.09/2.27 tff(113,plain,
% 3.09/2.27 ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp22 | hskp6 | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607))),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[112, 111])).
% 3.09/2.27 tff(114,plain,
% 3.09/2.27 (hskp6 | c1_1(a607) | (~c0_1(a607))),
% 3.09/2.27 inference(unit_resolution,[status(thm)],[113, 107, 44, 22, 43])).
% 3.09/2.27 tff(115,plain,
% 3.09/2.27 (~c0_1(a607)),
% 3.09/2.27 inference(unit_resolution,[status(thm)],[114, 67, 66])).
% 3.09/2.27 tff(116,assumption,(hskp4), introduced(assumption)).
% 3.09/2.27 tff(117,plain,
% 3.09/2.27 (((~hskp4) | (~c2_1(a588))) <=> ((~hskp4) | (~c2_1(a588)))),
% 3.09/2.27 inference(rewrite,[status(thm)],[])).
% 3.09/2.27 tff(118,plain,
% 3.09/2.27 (((~c2_1(a588)) | (~hskp4)) <=> ((~hskp4) | (~c2_1(a588)))),
% 3.09/2.27 inference(rewrite,[status(thm)],[])).
% 3.09/2.27 tff(119,axiom,((~c2_1(a588)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause120')).
% 3.09/2.27 tff(120,plain,
% 3.09/2.27 ((~hskp4) | (~c2_1(a588))),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[119, 118])).
% 3.09/2.27 tff(121,plain,
% 3.09/2.27 ((~hskp4) | (~c2_1(a588))),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[120, 117])).
% 3.09/2.27 tff(122,plain,
% 3.09/2.27 (~c2_1(a588)),
% 3.09/2.27 inference(unit_resolution,[status(thm)],[121, 116])).
% 3.09/2.27 tff(123,plain,
% 3.09/2.27 (((~hskp4) | (~c1_1(a588))) <=> ((~hskp4) | (~c1_1(a588)))),
% 3.09/2.27 inference(rewrite,[status(thm)],[])).
% 3.09/2.27 tff(124,plain,
% 3.09/2.27 (((~c1_1(a588)) | (~hskp4)) <=> ((~hskp4) | (~c1_1(a588)))),
% 3.09/2.27 inference(rewrite,[status(thm)],[])).
% 3.09/2.27 tff(125,axiom,((~c1_1(a588)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause119')).
% 3.09/2.27 tff(126,plain,
% 3.09/2.27 ((~hskp4) | (~c1_1(a588))),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[125, 124])).
% 3.09/2.27 tff(127,plain,
% 3.09/2.27 ((~hskp4) | (~c1_1(a588))),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[126, 123])).
% 3.09/2.27 tff(128,plain,
% 3.09/2.27 (~c1_1(a588)),
% 3.09/2.27 inference(unit_resolution,[status(thm)],[127, 116])).
% 3.09/2.27 tff(129,plain,
% 3.09/2.27 (((~hskp4) | c0_1(a588)) <=> ((~hskp4) | c0_1(a588))),
% 3.09/2.27 inference(rewrite,[status(thm)],[])).
% 3.09/2.27 tff(130,axiom,((~hskp4) | c0_1(a588)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause74')).
% 3.09/2.27 tff(131,plain,
% 3.09/2.27 ((~hskp4) | c0_1(a588)),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[130, 129])).
% 3.09/2.27 tff(132,plain,
% 3.09/2.27 ((~hskp4) | c0_1(a588)),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[131, 129])).
% 3.09/2.27 tff(133,plain,
% 3.09/2.27 ((~hskp4) | c0_1(a588)),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[132, 129])).
% 3.09/2.27 tff(134,plain,
% 3.09/2.27 ((~hskp4) | c0_1(a588)),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[133, 129])).
% 3.09/2.27 tff(135,plain,
% 3.09/2.27 ((~hskp4) | c0_1(a588)),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[134, 129])).
% 3.09/2.27 tff(136,plain,
% 3.09/2.27 ((~hskp4) | c0_1(a588)),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[135, 129])).
% 3.09/2.27 tff(137,plain,
% 3.09/2.27 ((~hskp4) | c0_1(a588)),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[136, 129])).
% 3.09/2.27 tff(138,plain,
% 3.09/2.27 ((~hskp4) | c0_1(a588)),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[137, 129])).
% 3.09/2.27 tff(139,plain,
% 3.09/2.27 (c0_1(a588)),
% 3.09/2.27 inference(unit_resolution,[status(thm)],[138, 116])).
% 3.09/2.27 tff(140,plain,
% 3.09/2.27 (((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)))) <=> ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp22 | hskp6 | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)))),
% 3.09/2.27 inference(rewrite,[status(thm)],[])).
% 3.09/2.27 tff(141,plain,
% 3.09/2.27 ((hskp22 | hskp6 | (~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588))) <=> (hskp22 | hskp6 | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)))),
% 3.09/2.27 inference(rewrite,[status(thm)],[])).
% 3.09/2.27 tff(142,plain,
% 3.09/2.27 (((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | (~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588)))) <=> ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588))))),
% 3.09/2.27 inference(monotonicity,[status(thm)],[141])).
% 3.09/2.27 tff(143,plain,
% 3.09/2.27 (((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | (~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588)))) <=> ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp22 | hskp6 | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)))),
% 3.09/2.27 inference(transitivity,[status(thm)],[142, 140])).
% 3.09/2.27 tff(144,plain,
% 3.09/2.27 ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | (~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588)))),
% 3.09/2.27 inference(quant_inst,[status(thm)],[])).
% 3.09/2.27 tff(145,plain,
% 3.09/2.27 ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp22 | hskp6 | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588))),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[144, 143])).
% 3.09/2.27 tff(146,plain,
% 3.09/2.27 ($false),
% 3.09/2.27 inference(unit_resolution,[status(thm)],[145, 107, 44, 67, 139, 128, 122, 43])).
% 3.09/2.27 tff(147,plain,((~hskp4) | hskp22 | hskp6), inference(lemma,lemma(discharge,[]))).
% 3.09/2.27 tff(148,plain,
% 3.09/2.27 (~hskp4),
% 3.09/2.27 inference(unit_resolution,[status(thm)],[147, 67, 44])).
% 3.09/2.27 tff(149,plain,
% 3.09/2.27 (^[U: $i] : refl((hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))),
% 3.09/2.27 inference(bind,[status(th)],[])).
% 3.09/2.27 tff(150,plain,
% 3.09/2.27 (![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 3.09/2.27 inference(quant_intro,[status(thm)],[149])).
% 3.09/2.27 tff(151,plain,
% 3.09/2.27 (![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 3.09/2.27 inference(rewrite,[status(thm)],[])).
% 3.09/2.27 tff(152,plain,
% 3.09/2.27 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp4) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp4))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp4) | hskp14) <=> ((hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp14))), rewrite(((hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp14) <=> (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp4) | hskp14) <=> (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))))),
% 3.09/2.27 inference(bind,[status(th)],[])).
% 3.09/2.27 tff(153,plain,
% 3.09/2.27 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp4) | hskp14) <=> ![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 3.09/2.27 inference(quant_intro,[status(thm)],[152])).
% 3.09/2.27 tff(154,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp4) | hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause129')).
% 3.09/2.27 tff(155,plain,
% 3.09/2.27 (![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[154, 153])).
% 3.09/2.27 tff(156,plain,
% 3.09/2.27 (![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[155, 151])).
% 3.09/2.27 tff(157,plain,(
% 3.09/2.27 ![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 3.09/2.27 inference(skolemize,[status(sab)],[156])).
% 3.09/2.27 tff(158,plain,
% 3.09/2.27 (![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[157, 150])).
% 3.09/2.27 tff(159,plain,
% 3.09/2.27 (((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp14 | hskp4 | c3_1(a607) | c2_1(a607) | (~ndr1_0) | c0_1(a607))) <=> ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp14 | hskp4 | c3_1(a607) | c2_1(a607) | (~ndr1_0) | c0_1(a607))),
% 3.09/2.27 inference(rewrite,[status(thm)],[])).
% 3.09/2.27 tff(160,plain,
% 3.09/2.27 ((hskp14 | hskp4 | (~ndr1_0) | c2_1(a607) | c0_1(a607) | c3_1(a607)) <=> (hskp14 | hskp4 | c3_1(a607) | c2_1(a607) | (~ndr1_0) | c0_1(a607))),
% 3.09/2.27 inference(rewrite,[status(thm)],[])).
% 3.09/2.27 tff(161,plain,
% 3.09/2.27 (((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp14 | hskp4 | (~ndr1_0) | c2_1(a607) | c0_1(a607) | c3_1(a607))) <=> ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp14 | hskp4 | c3_1(a607) | c2_1(a607) | (~ndr1_0) | c0_1(a607)))),
% 3.09/2.27 inference(monotonicity,[status(thm)],[160])).
% 3.09/2.27 tff(162,plain,
% 3.09/2.27 (((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp14 | hskp4 | (~ndr1_0) | c2_1(a607) | c0_1(a607) | c3_1(a607))) <=> ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp14 | hskp4 | c3_1(a607) | c2_1(a607) | (~ndr1_0) | c0_1(a607))),
% 3.09/2.27 inference(transitivity,[status(thm)],[161, 159])).
% 3.09/2.27 tff(163,plain,
% 3.09/2.27 ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp14 | hskp4 | (~ndr1_0) | c2_1(a607) | c0_1(a607) | c3_1(a607))),
% 3.09/2.27 inference(quant_inst,[status(thm)],[])).
% 3.09/2.27 tff(164,plain,
% 3.09/2.27 ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp14 | hskp4 | c3_1(a607) | c2_1(a607) | (~ndr1_0) | c0_1(a607)),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[163, 162])).
% 3.09/2.27 tff(165,plain,
% 3.09/2.27 (hskp14 | hskp4 | c3_1(a607) | c0_1(a607)),
% 3.09/2.27 inference(unit_resolution,[status(thm)],[164, 107, 22, 158])).
% 3.09/2.27 tff(166,plain,
% 3.09/2.27 (hskp14),
% 3.09/2.27 inference(unit_resolution,[status(thm)],[165, 148, 33, 115])).
% 3.09/2.27 tff(167,plain,
% 3.09/2.27 (((~hskp14) | (~c1_1(a603))) <=> ((~hskp14) | (~c1_1(a603)))),
% 3.09/2.27 inference(rewrite,[status(thm)],[])).
% 3.09/2.27 tff(168,plain,
% 3.09/2.27 (((~c1_1(a603)) | (~hskp14)) <=> ((~hskp14) | (~c1_1(a603)))),
% 3.09/2.27 inference(rewrite,[status(thm)],[])).
% 3.09/2.27 tff(169,axiom,((~c1_1(a603)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause103')).
% 3.09/2.27 tff(170,plain,
% 3.09/2.27 ((~hskp14) | (~c1_1(a603))),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[169, 168])).
% 3.09/2.27 tff(171,plain,
% 3.09/2.27 ((~hskp14) | (~c1_1(a603))),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[170, 167])).
% 3.09/2.27 tff(172,plain,
% 3.09/2.27 (~c1_1(a603)),
% 3.09/2.27 inference(unit_resolution,[status(thm)],[171, 166])).
% 3.09/2.27 tff(173,plain,
% 3.09/2.27 (((~hskp14) | c0_1(a603)) <=> ((~hskp14) | c0_1(a603))),
% 3.09/2.27 inference(rewrite,[status(thm)],[])).
% 3.09/2.27 tff(174,axiom,((~hskp14) | c0_1(a603)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause60')).
% 3.09/2.27 tff(175,plain,
% 3.09/2.27 ((~hskp14) | c0_1(a603)),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[174, 173])).
% 3.09/2.27 tff(176,plain,
% 3.09/2.27 ((~hskp14) | c0_1(a603)),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[175, 173])).
% 3.09/2.27 tff(177,plain,
% 3.09/2.27 ((~hskp14) | c0_1(a603)),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[176, 173])).
% 3.09/2.27 tff(178,plain,
% 3.09/2.27 ((~hskp14) | c0_1(a603)),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[177, 173])).
% 3.09/2.27 tff(179,plain,
% 3.09/2.27 ((~hskp14) | c0_1(a603)),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[178, 173])).
% 3.09/2.27 tff(180,plain,
% 3.09/2.27 ((~hskp14) | c0_1(a603)),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[179, 173])).
% 3.09/2.27 tff(181,plain,
% 3.09/2.27 ((~hskp14) | c0_1(a603)),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[180, 173])).
% 3.09/2.27 tff(182,plain,
% 3.09/2.27 ((~hskp14) | c0_1(a603)),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[181, 173])).
% 3.09/2.27 tff(183,plain,
% 3.09/2.27 (c0_1(a603)),
% 3.09/2.27 inference(unit_resolution,[status(thm)],[182, 166])).
% 3.09/2.27 tff(184,plain,
% 3.09/2.27 (((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)))) <=> ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp22 | hskp6 | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)))),
% 3.09/2.27 inference(rewrite,[status(thm)],[])).
% 3.09/2.27 tff(185,plain,
% 3.09/2.27 ((hskp22 | hskp6 | (~ndr1_0) | c2_1(a603) | c1_1(a603) | (~c0_1(a603))) <=> (hskp22 | hskp6 | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)))),
% 3.09/2.27 inference(rewrite,[status(thm)],[])).
% 3.09/2.27 tff(186,plain,
% 3.09/2.27 (((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | (~ndr1_0) | c2_1(a603) | c1_1(a603) | (~c0_1(a603)))) <=> ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603))))),
% 3.09/2.27 inference(monotonicity,[status(thm)],[185])).
% 3.09/2.27 tff(187,plain,
% 3.09/2.27 (((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | (~ndr1_0) | c2_1(a603) | c1_1(a603) | (~c0_1(a603)))) <=> ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp22 | hskp6 | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)))),
% 3.09/2.27 inference(transitivity,[status(thm)],[186, 184])).
% 3.09/2.27 tff(188,plain,
% 3.09/2.27 ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | (~ndr1_0) | c2_1(a603) | c1_1(a603) | (~c0_1(a603)))),
% 3.09/2.27 inference(quant_inst,[status(thm)],[])).
% 3.09/2.27 tff(189,plain,
% 3.09/2.27 ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp22 | hskp6 | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603))),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[188, 187])).
% 3.09/2.27 tff(190,plain,
% 3.09/2.27 (c2_1(a603)),
% 3.09/2.27 inference(unit_resolution,[status(thm)],[189, 107, 44, 67, 183, 172, 43])).
% 3.09/2.27 tff(191,plain,
% 3.09/2.27 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 3.09/2.27 inference(bind,[status(th)],[])).
% 3.09/2.27 tff(192,plain,
% 3.09/2.27 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 3.09/2.27 inference(quant_intro,[status(thm)],[191])).
% 3.09/2.27 tff(193,plain,
% 3.09/2.27 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 3.09/2.27 inference(rewrite,[status(thm)],[])).
% 3.09/2.27 tff(194,plain,
% 3.09/2.27 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp2))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), (((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 3.09/2.27 inference(bind,[status(th)],[])).
% 3.09/2.27 tff(195,plain,
% 3.09/2.27 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 3.09/2.27 inference(quant_intro,[status(thm)],[194])).
% 3.09/2.27 tff(196,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause166')).
% 3.09/2.27 tff(197,plain,
% 3.09/2.27 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[196, 195])).
% 3.09/2.27 tff(198,plain,
% 3.09/2.27 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[197, 193])).
% 3.09/2.27 tff(199,plain,(
% 3.09/2.27 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 3.09/2.27 inference(skolemize,[status(sab)],[198])).
% 3.09/2.27 tff(200,plain,
% 3.09/2.27 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[199, 192])).
% 3.09/2.27 tff(201,plain,
% 3.09/2.27 (((~hskp14) | (~c3_1(a603))) <=> ((~hskp14) | (~c3_1(a603)))),
% 3.09/2.27 inference(rewrite,[status(thm)],[])).
% 3.09/2.27 tff(202,plain,
% 3.09/2.27 (((~c3_1(a603)) | (~hskp14)) <=> ((~hskp14) | (~c3_1(a603)))),
% 3.09/2.27 inference(rewrite,[status(thm)],[])).
% 3.09/2.27 tff(203,axiom,((~c3_1(a603)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause104')).
% 3.09/2.27 tff(204,plain,
% 3.09/2.27 ((~hskp14) | (~c3_1(a603))),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[203, 202])).
% 3.09/2.27 tff(205,plain,
% 3.09/2.27 ((~hskp14) | (~c3_1(a603))),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[204, 201])).
% 3.09/2.27 tff(206,plain,
% 3.09/2.27 (~c3_1(a603)),
% 3.09/2.27 inference(unit_resolution,[status(thm)],[205, 166])).
% 3.09/2.27 tff(207,plain,
% 3.09/2.27 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c3_1(a607) | c1_1(a607) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a607))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c3_1(a607) | c1_1(a607) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a607))),
% 3.09/2.27 inference(rewrite,[status(thm)],[])).
% 3.09/2.27 tff(208,plain,
% 3.09/2.27 ((hskp2 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c3_1(a607) | c1_1(a607) | c0_1(a607)) <=> (hskp2 | c3_1(a607) | c1_1(a607) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a607))),
% 3.09/2.27 inference(rewrite,[status(thm)],[])).
% 3.09/2.27 tff(209,plain,
% 3.09/2.27 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c3_1(a607) | c1_1(a607) | c0_1(a607))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c3_1(a607) | c1_1(a607) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a607)))),
% 3.09/2.27 inference(monotonicity,[status(thm)],[208])).
% 3.09/2.27 tff(210,plain,
% 3.09/2.27 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c3_1(a607) | c1_1(a607) | c0_1(a607))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c3_1(a607) | c1_1(a607) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a607))),
% 3.09/2.27 inference(transitivity,[status(thm)],[209, 207])).
% 3.09/2.27 tff(211,plain,
% 3.09/2.27 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c3_1(a607) | c1_1(a607) | c0_1(a607))),
% 3.09/2.27 inference(quant_inst,[status(thm)],[])).
% 3.09/2.27 tff(212,plain,
% 3.09/2.27 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c3_1(a607) | c1_1(a607) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a607)),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[211, 210])).
% 3.09/2.27 tff(213,plain,
% 3.09/2.27 (hskp2),
% 3.09/2.27 inference(unit_resolution,[status(thm)],[212, 107, 33, 66, 172, 206, 200, 115, 190])).
% 3.09/2.27 tff(214,plain,
% 3.09/2.27 (((~hskp2) | (~c3_1(a586))) <=> ((~hskp2) | (~c3_1(a586)))),
% 3.09/2.27 inference(rewrite,[status(thm)],[])).
% 3.09/2.27 tff(215,plain,
% 3.09/2.27 (((~c3_1(a586)) | (~hskp2)) <=> ((~hskp2) | (~c3_1(a586)))),
% 3.09/2.27 inference(rewrite,[status(thm)],[])).
% 3.09/2.27 tff(216,axiom,((~c3_1(a586)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause122')).
% 3.09/2.27 tff(217,plain,
% 3.09/2.27 ((~hskp2) | (~c3_1(a586))),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[216, 215])).
% 3.09/2.27 tff(218,plain,
% 3.09/2.27 ((~hskp2) | (~c3_1(a586))),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[217, 214])).
% 3.09/2.27 tff(219,plain,
% 3.09/2.27 (~c3_1(a586)),
% 3.09/2.27 inference(unit_resolution,[status(thm)],[218, 213])).
% 3.09/2.27 tff(220,plain,
% 3.09/2.27 (((~hskp2) | c1_1(a586)) <=> ((~hskp2) | c1_1(a586))),
% 3.09/2.27 inference(rewrite,[status(thm)],[])).
% 3.09/2.27 tff(221,axiom,((~hskp2) | c1_1(a586)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause77')).
% 3.09/2.27 tff(222,plain,
% 3.09/2.27 ((~hskp2) | c1_1(a586)),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[221, 220])).
% 3.09/2.27 tff(223,plain,
% 3.09/2.27 ((~hskp2) | c1_1(a586)),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[222, 220])).
% 3.09/2.27 tff(224,plain,
% 3.09/2.27 ((~hskp2) | c1_1(a586)),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[223, 220])).
% 3.09/2.27 tff(225,plain,
% 3.09/2.27 ((~hskp2) | c1_1(a586)),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[224, 220])).
% 3.09/2.27 tff(226,plain,
% 3.09/2.27 ((~hskp2) | c1_1(a586)),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[225, 220])).
% 3.09/2.27 tff(227,plain,
% 3.09/2.27 ((~hskp2) | c1_1(a586)),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[226, 220])).
% 3.09/2.27 tff(228,plain,
% 3.09/2.27 ((~hskp2) | c1_1(a586)),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[227, 220])).
% 3.09/2.27 tff(229,plain,
% 3.09/2.27 ((~hskp2) | c1_1(a586)),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[228, 220])).
% 3.09/2.27 tff(230,plain,
% 3.09/2.27 (c1_1(a586)),
% 3.09/2.27 inference(unit_resolution,[status(thm)],[229, 213])).
% 3.09/2.27 tff(231,plain,
% 3.09/2.27 (((~hskp17) | c3_1(a607)) <=> ((~hskp17) | c3_1(a607))),
% 3.09/2.27 inference(rewrite,[status(thm)],[])).
% 3.09/2.27 tff(232,axiom,((~hskp17) | c3_1(a607)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause56')).
% 3.09/2.27 tff(233,plain,
% 3.09/2.27 ((~hskp17) | c3_1(a607)),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[232, 231])).
% 3.09/2.27 tff(234,plain,
% 3.09/2.27 ((~hskp17) | c3_1(a607)),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[233, 231])).
% 3.09/2.27 tff(235,plain,
% 3.09/2.27 ((~hskp17) | c3_1(a607)),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[234, 231])).
% 3.09/2.27 tff(236,plain,
% 3.09/2.27 ((~hskp17) | c3_1(a607)),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[235, 231])).
% 3.09/2.27 tff(237,plain,
% 3.09/2.27 ((~hskp17) | c3_1(a607)),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[236, 231])).
% 3.09/2.27 tff(238,plain,
% 3.09/2.27 ((~hskp17) | c3_1(a607)),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[237, 231])).
% 3.09/2.27 tff(239,plain,
% 3.09/2.27 ((~hskp17) | c3_1(a607)),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[238, 231])).
% 3.09/2.27 tff(240,plain,
% 3.09/2.27 ((~hskp17) | c3_1(a607)),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[239, 231])).
% 3.09/2.27 tff(241,plain,
% 3.09/2.27 (~hskp17),
% 3.09/2.27 inference(unit_resolution,[status(thm)],[240, 33])).
% 3.09/2.27 tff(242,plain,
% 3.09/2.27 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp4 | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)))),
% 3.09/2.27 inference(rewrite,[status(thm)],[])).
% 3.09/2.27 tff(243,plain,
% 3.09/2.27 ((hskp17 | hskp4 | (~ndr1_0) | c3_1(a586) | (~c1_1(a586)) | (~c0_1(a586))) <=> (hskp17 | hskp4 | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)))),
% 3.09/2.27 inference(rewrite,[status(thm)],[])).
% 3.09/2.27 tff(244,plain,
% 3.09/2.27 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c3_1(a586) | (~c1_1(a586)) | (~c0_1(a586)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586))))),
% 3.09/2.27 inference(monotonicity,[status(thm)],[243])).
% 3.09/2.27 tff(245,plain,
% 3.09/2.27 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c3_1(a586) | (~c1_1(a586)) | (~c0_1(a586)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp4 | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)))),
% 3.09/2.27 inference(transitivity,[status(thm)],[244, 242])).
% 3.09/2.27 tff(246,plain,
% 3.09/2.27 ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c3_1(a586) | (~c1_1(a586)) | (~c0_1(a586)))),
% 3.09/2.27 inference(quant_inst,[status(thm)],[])).
% 3.09/2.27 tff(247,plain,
% 3.09/2.27 ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp4 | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586))),
% 3.09/2.27 inference(modus_ponens,[status(thm)],[246, 245])).
% 3.09/2.27 tff(248,plain,
% 3.09/2.27 (~c0_1(a586)),
% 3.09/2.27 inference(unit_resolution,[status(thm)],[247, 107, 241, 148, 230, 219, 55])).
% 3.09/2.27 tff(249,plain,
% 3.09/2.27 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))))),
% 3.09/2.27 inference(bind,[status(th)],[])).
% 3.09/2.27 tff(250,plain,
% 3.09/2.27 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 3.09/2.27 inference(quant_intro,[status(thm)],[249])).
% 3.09/2.27 tff(251,plain,
% 3.09/2.27 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 3.09/2.27 inference(rewrite,[status(thm)],[])).
% 3.09/2.27 tff(252,plain,
% 3.09/2.27 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))))),
% 3.09/2.28 inference(bind,[status(th)],[])).
% 3.09/2.28 tff(253,plain,
% 3.09/2.28 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 3.09/2.28 inference(quant_intro,[status(thm)],[252])).
% 3.09/2.28 tff(254,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause197')).
% 3.09/2.28 tff(255,plain,
% 3.09/2.28 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 3.09/2.28 inference(modus_ponens,[status(thm)],[254, 253])).
% 3.09/2.28 tff(256,plain,
% 3.09/2.28 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 3.09/2.28 inference(modus_ponens,[status(thm)],[255, 251])).
% 3.09/2.28 tff(257,plain,(
% 3.09/2.28 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 3.09/2.28 inference(skolemize,[status(sab)],[256])).
% 3.09/2.28 tff(258,plain,
% 3.09/2.28 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 3.09/2.28 inference(modus_ponens,[status(thm)],[257, 250])).
% 3.09/2.28 tff(259,plain,
% 3.09/2.28 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))),
% 3.09/2.28 inference(bind,[status(th)],[])).
% 3.09/2.28 tff(260,plain,
% 3.09/2.28 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 3.09/2.28 inference(quant_intro,[status(thm)],[259])).
% 3.09/2.28 tff(261,plain,
% 3.09/2.28 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 3.09/2.28 inference(rewrite,[status(thm)],[])).
% 3.09/2.28 tff(262,plain,
% 3.09/2.28 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp11) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | hskp11))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))))),
% 3.09/2.28 inference(bind,[status(th)],[])).
% 3.09/2.28 tff(263,plain,
% 3.09/2.28 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 3.09/2.28 inference(quant_intro,[status(thm)],[262])).
% 3.09/2.28 tff(264,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause176')).
% 3.09/2.28 tff(265,plain,
% 3.09/2.28 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 3.09/2.28 inference(modus_ponens,[status(thm)],[264, 263])).
% 3.09/2.28 tff(266,plain,
% 3.09/2.28 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 3.09/2.28 inference(modus_ponens,[status(thm)],[265, 261])).
% 3.09/2.28 tff(267,plain,(
% 3.09/2.28 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 3.09/2.28 inference(skolemize,[status(sab)],[266])).
% 3.09/2.28 tff(268,plain,
% 3.09/2.28 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 3.09/2.28 inference(modus_ponens,[status(thm)],[267, 260])).
% 3.09/2.28 tff(269,assumption,(~hskp29), introduced(assumption)).
% 3.09/2.28 tff(270,plain,
% 3.09/2.28 (hskp17),
% 3.09/2.28 inference(unit_resolution,[status(thm)],[105, 269, 44])).
% 3.09/2.28 tff(271,plain,
% 3.09/2.28 (((~hskp17) | (~c2_1(a607))) <=> ((~hskp17) | (~c2_1(a607)))),
% 3.09/2.28 inference(rewrite,[status(thm)],[])).
% 3.09/2.28 tff(272,plain,
% 3.09/2.28 (((~c2_1(a607)) | (~hskp17)) <=> ((~hskp17) | (~c2_1(a607)))),
% 3.09/2.28 inference(rewrite,[status(thm)],[])).
% 3.09/2.28 tff(273,axiom,((~c2_1(a607)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause99')).
% 3.09/2.28 tff(274,plain,
% 3.09/2.28 ((~hskp17) | (~c2_1(a607))),
% 3.09/2.28 inference(modus_ponens,[status(thm)],[273, 272])).
% 3.09/2.28 tff(275,plain,
% 3.09/2.28 ((~hskp17) | (~c2_1(a607))),
% 3.09/2.28 inference(modus_ponens,[status(thm)],[274, 271])).
% 3.09/2.28 tff(276,plain,
% 3.09/2.28 (~c2_1(a607)),
% 3.09/2.28 inference(unit_resolution,[status(thm)],[275, 270])).
% 3.09/2.28 tff(277,plain,
% 3.09/2.28 (((~hskp17) | (~c1_1(a607))) <=> ((~hskp17) | (~c1_1(a607)))),
% 3.09/2.28 inference(rewrite,[status(thm)],[])).
% 3.09/2.28 tff(278,plain,
% 3.09/2.28 (((~c1_1(a607)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a607)))),
% 3.09/2.28 inference(rewrite,[status(thm)],[])).
% 3.09/2.28 tff(279,axiom,((~c1_1(a607)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause98')).
% 3.09/2.28 tff(280,plain,
% 3.09/2.28 ((~hskp17) | (~c1_1(a607))),
% 3.09/2.28 inference(modus_ponens,[status(thm)],[279, 278])).
% 3.09/2.28 tff(281,plain,
% 3.09/2.28 ((~hskp17) | (~c1_1(a607))),
% 3.09/2.28 inference(modus_ponens,[status(thm)],[280, 277])).
% 3.09/2.28 tff(282,plain,
% 3.09/2.28 (~c1_1(a607)),
% 3.09/2.28 inference(unit_resolution,[status(thm)],[281, 270])).
% 3.09/2.28 tff(283,plain,
% 3.09/2.28 (hskp6 | (~c0_1(a607))),
% 3.09/2.28 inference(unit_resolution,[status(thm)],[113, 107, 44, 282, 276, 43])).
% 3.09/2.28 tff(284,plain,
% 3.09/2.28 (~c0_1(a607)),
% 3.09/2.28 inference(unit_resolution,[status(thm)],[283, 67])).
% 3.09/2.28 tff(285,plain,
% 3.09/2.28 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 3.09/2.28 inference(bind,[status(th)],[])).
% 3.09/2.28 tff(286,plain,
% 3.09/2.28 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 3.09/2.28 inference(quant_intro,[status(thm)],[285])).
% 3.09/2.28 tff(287,plain,
% 3.09/2.28 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 3.09/2.28 inference(rewrite,[status(thm)],[])).
% 3.09/2.28 tff(288,plain,
% 3.09/2.28 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp9) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp9))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 3.09/2.28 inference(bind,[status(th)],[])).
% 3.09/2.28 tff(289,plain,
% 3.09/2.28 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 3.09/2.28 inference(quant_intro,[status(thm)],[288])).
% 3.09/2.28 tff(290,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause185')).
% 3.09/2.28 tff(291,plain,
% 3.09/2.28 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 3.09/2.28 inference(modus_ponens,[status(thm)],[290, 289])).
% 3.09/2.28 tff(292,plain,
% 3.09/2.28 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 3.09/2.28 inference(modus_ponens,[status(thm)],[291, 287])).
% 3.09/2.28 tff(293,plain,(
% 3.09/2.28 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 3.09/2.28 inference(skolemize,[status(sab)],[292])).
% 3.09/2.28 tff(294,plain,
% 3.09/2.28 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 3.09/2.28 inference(modus_ponens,[status(thm)],[293, 286])).
% 3.09/2.28 tff(295,plain,
% 3.09/2.28 (c3_1(a607)),
% 3.09/2.28 inference(unit_resolution,[status(thm)],[240, 270])).
% 3.09/2.28 tff(296,plain,
% 3.09/2.28 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))),
% 3.09/2.28 inference(bind,[status(th)],[])).
% 3.09/2.28 tff(297,plain,
% 3.09/2.28 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 3.09/2.28 inference(quant_intro,[status(thm)],[296])).
% 3.09/2.28 tff(298,plain,
% 3.09/2.28 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 3.09/2.28 inference(rewrite,[status(thm)],[])).
% 3.09/2.28 tff(299,plain,
% 3.09/2.28 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp14) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp14))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))))),
% 3.09/2.28 inference(bind,[status(th)],[])).
% 3.09/2.28 tff(300,plain,
% 3.09/2.28 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 3.09/2.28 inference(quant_intro,[status(thm)],[299])).
% 3.09/2.28 tff(301,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause172')).
% 3.09/2.28 tff(302,plain,
% 3.09/2.28 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 3.09/2.28 inference(modus_ponens,[status(thm)],[301, 300])).
% 3.09/2.28 tff(303,plain,
% 3.09/2.28 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 3.09/2.28 inference(modus_ponens,[status(thm)],[302, 298])).
% 3.09/2.28 tff(304,plain,(
% 3.09/2.28 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 3.09/2.28 inference(skolemize,[status(sab)],[303])).
% 3.09/2.28 tff(305,plain,
% 3.09/2.28 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 3.09/2.28 inference(modus_ponens,[status(thm)],[304, 297])).
% 3.09/2.28 tff(306,assumption,(~hskp3), introduced(assumption)).
% 3.09/2.28 tff(307,plain,
% 3.09/2.28 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))))),
% 3.09/2.28 inference(bind,[status(th)],[])).
% 3.09/2.28 tff(308,plain,
% 3.09/2.28 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.09/2.28 inference(quant_intro,[status(thm)],[307])).
% 3.09/2.28 tff(309,plain,
% 3.09/2.28 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.09/2.28 inference(rewrite,[status(thm)],[])).
% 3.09/2.28 tff(310,plain,
% 3.09/2.28 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp3) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | hskp3))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))))),
% 3.09/2.28 inference(bind,[status(th)],[])).
% 3.09/2.28 tff(311,plain,
% 3.09/2.28 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.09/2.28 inference(quant_intro,[status(thm)],[310])).
% 3.09/2.28 tff(312,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause174')).
% 3.09/2.28 tff(313,plain,
% 3.09/2.28 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.09/2.28 inference(modus_ponens,[status(thm)],[312, 311])).
% 3.09/2.28 tff(314,plain,
% 3.09/2.28 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.09/2.28 inference(modus_ponens,[status(thm)],[313, 309])).
% 3.09/2.28 tff(315,plain,(
% 3.09/2.28 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.09/2.28 inference(skolemize,[status(sab)],[314])).
% 3.09/2.28 tff(316,plain,
% 3.09/2.28 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.09/2.28 inference(modus_ponens,[status(thm)],[315, 308])).
% 3.09/2.28 tff(317,assumption,(hskp14), introduced(assumption)).
% 3.09/2.28 tff(318,plain,
% 3.09/2.28 (~c3_1(a603)),
% 3.09/2.28 inference(unit_resolution,[status(thm)],[205, 317])).
% 3.09/2.28 tff(319,plain,
% 3.09/2.28 (~c1_1(a603)),
% 3.09/2.28 inference(unit_resolution,[status(thm)],[171, 317])).
% 3.09/2.28 tff(320,plain,
% 3.09/2.28 (c0_1(a603)),
% 3.09/2.28 inference(unit_resolution,[status(thm)],[182, 317])).
% 3.09/2.28 tff(321,assumption,(c3_1(a607)), introduced(assumption)).
% 3.09/2.28 tff(322,plain,
% 3.09/2.28 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c1_1(a607) | c2_1(a607) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c0_1(a603)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c1_1(a607) | c2_1(a607) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c0_1(a603)) | (~c3_1(a607)))),
% 3.09/2.28 inference(rewrite,[status(thm)],[])).
% 3.09/2.28 tff(323,plain,
% 3.09/2.28 ((hskp3 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c0_1(a603)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607))) <=> (hskp3 | c1_1(a607) | c2_1(a607) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c0_1(a603)) | (~c3_1(a607)))),
% 3.09/2.28 inference(rewrite,[status(thm)],[])).
% 3.09/2.28 tff(324,plain,
% 3.09/2.28 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c0_1(a603)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c1_1(a607) | c2_1(a607) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c0_1(a603)) | (~c3_1(a607))))),
% 3.09/2.28 inference(monotonicity,[status(thm)],[323])).
% 3.09/2.28 tff(325,plain,
% 3.09/2.28 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c0_1(a603)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c1_1(a607) | c2_1(a607) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c0_1(a603)) | (~c3_1(a607)))),
% 3.09/2.28 inference(transitivity,[status(thm)],[324, 322])).
% 3.09/2.28 tff(326,plain,
% 3.09/2.28 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c0_1(a603)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)))),
% 3.09/2.28 inference(quant_inst,[status(thm)],[])).
% 3.09/2.28 tff(327,plain,
% 3.09/2.28 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c1_1(a607) | c2_1(a607) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c0_1(a603)) | (~c3_1(a607))),
% 3.09/2.28 inference(modus_ponens,[status(thm)],[326, 325])).
% 3.09/2.28 tff(328,plain,
% 3.09/2.28 ($false),
% 3.09/2.28 inference(unit_resolution,[status(thm)],[327, 107, 306, 321, 320, 66, 22, 319, 318, 316])).
% 3.09/2.28 tff(329,plain,((~hskp14) | hskp3 | (~c3_1(a607)) | c1_1(a607) | c2_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.09/2.28 tff(330,plain,
% 3.09/2.28 (~hskp14),
% 3.09/2.28 inference(unit_resolution,[status(thm)],[329, 306, 295, 282, 276])).
% 3.09/2.28 tff(331,plain,
% 3.09/2.28 (^[U: $i] : refl((hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 3.09/2.28 inference(bind,[status(th)],[])).
% 3.09/2.28 tff(332,plain,
% 3.09/2.28 (![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 3.09/2.28 inference(quant_intro,[status(thm)],[331])).
% 3.09/2.28 tff(333,plain,
% 3.09/2.28 (![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 3.09/2.28 inference(rewrite,[status(thm)],[])).
% 3.09/2.28 tff(334,plain,
% 3.09/2.28 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp29) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp29))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp29) <=> (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp29) <=> (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp29) | hskp14) <=> ((hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp14))), rewrite(((hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp14) <=> (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp29) | hskp14) <=> (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 3.09/2.28 inference(bind,[status(th)],[])).
% 3.09/2.28 tff(335,plain,
% 3.09/2.28 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp29) | hskp14) <=> ![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 3.09/2.28 inference(quant_intro,[status(thm)],[334])).
% 3.09/2.28 tff(336,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp29) | hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause162')).
% 3.09/2.28 tff(337,plain,
% 3.09/2.28 (![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 3.09/2.28 inference(modus_ponens,[status(thm)],[336, 335])).
% 3.09/2.28 tff(338,plain,
% 3.09/2.28 (![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 3.09/2.28 inference(modus_ponens,[status(thm)],[337, 333])).
% 3.09/2.28 tff(339,plain,(
% 3.09/2.28 ![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 3.09/2.28 inference(skolemize,[status(sab)],[338])).
% 3.09/2.28 tff(340,plain,
% 3.09/2.28 (![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 3.09/2.28 inference(modus_ponens,[status(thm)],[339, 332])).
% 3.09/2.28 tff(341,assumption,(hskp26), introduced(assumption)).
% 3.09/2.28 tff(342,plain,
% 3.09/2.28 (((~hskp26) | c1_1(a583)) <=> ((~hskp26) | c1_1(a583))),
% 3.09/2.28 inference(rewrite,[status(thm)],[])).
% 3.09/2.28 tff(343,axiom,((~hskp26) | c1_1(a583)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause46')).
% 3.09/2.28 tff(344,plain,
% 3.09/2.28 ((~hskp26) | c1_1(a583)),
% 3.09/2.28 inference(modus_ponens,[status(thm)],[343, 342])).
% 3.09/2.28 tff(345,plain,
% 3.09/2.28 ((~hskp26) | c1_1(a583)),
% 3.09/2.28 inference(modus_ponens,[status(thm)],[344, 342])).
% 3.09/2.28 tff(346,plain,
% 3.09/2.28 ((~hskp26) | c1_1(a583)),
% 3.09/2.28 inference(modus_ponens,[status(thm)],[345, 342])).
% 3.09/2.28 tff(347,plain,
% 3.09/2.28 ((~hskp26) | c1_1(a583)),
% 3.09/2.28 inference(modus_ponens,[status(thm)],[346, 342])).
% 3.09/2.28 tff(348,plain,
% 3.09/2.28 ((~hskp26) | c1_1(a583)),
% 3.09/2.28 inference(modus_ponens,[status(thm)],[347, 342])).
% 3.09/2.28 tff(349,plain,
% 3.09/2.28 ((~hskp26) | c1_1(a583)),
% 3.09/2.28 inference(modus_ponens,[status(thm)],[348, 342])).
% 3.09/2.28 tff(350,plain,
% 3.09/2.28 ((~hskp26) | c1_1(a583)),
% 3.09/2.28 inference(modus_ponens,[status(thm)],[349, 342])).
% 3.09/2.28 tff(351,plain,
% 3.09/2.28 ((~hskp26) | c1_1(a583)),
% 3.09/2.28 inference(modus_ponens,[status(thm)],[350, 342])).
% 3.09/2.28 tff(352,plain,
% 3.09/2.28 (c1_1(a583)),
% 3.09/2.28 inference(unit_resolution,[status(thm)],[351, 341])).
% 3.09/2.28 tff(353,plain,
% 3.09/2.28 (((~hskp26) | c0_1(a583)) <=> ((~hskp26) | c0_1(a583))),
% 3.09/2.28 inference(rewrite,[status(thm)],[])).
% 3.09/2.28 tff(354,axiom,((~hskp26) | c0_1(a583)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause45')).
% 3.09/2.28 tff(355,plain,
% 3.09/2.28 ((~hskp26) | c0_1(a583)),
% 3.09/2.28 inference(modus_ponens,[status(thm)],[354, 353])).
% 3.09/2.28 tff(356,plain,
% 3.09/2.28 ((~hskp26) | c0_1(a583)),
% 3.09/2.28 inference(modus_ponens,[status(thm)],[355, 353])).
% 3.09/2.28 tff(357,plain,
% 3.09/2.28 ((~hskp26) | c0_1(a583)),
% 3.09/2.28 inference(modus_ponens,[status(thm)],[356, 353])).
% 3.09/2.28 tff(358,plain,
% 3.09/2.28 ((~hskp26) | c0_1(a583)),
% 3.09/2.28 inference(modus_ponens,[status(thm)],[357, 353])).
% 3.09/2.28 tff(359,plain,
% 3.09/2.28 ((~hskp26) | c0_1(a583)),
% 3.09/2.28 inference(modus_ponens,[status(thm)],[358, 353])).
% 3.09/2.28 tff(360,plain,
% 3.09/2.28 ((~hskp26) | c0_1(a583)),
% 3.09/2.28 inference(modus_ponens,[status(thm)],[359, 353])).
% 3.09/2.28 tff(361,plain,
% 3.09/2.28 ((~hskp26) | c0_1(a583)),
% 3.09/2.28 inference(modus_ponens,[status(thm)],[360, 353])).
% 3.09/2.28 tff(362,plain,
% 3.09/2.28 ((~hskp26) | c0_1(a583)),
% 3.09/2.28 inference(modus_ponens,[status(thm)],[361, 353])).
% 3.09/2.28 tff(363,plain,
% 3.09/2.28 (c0_1(a583)),
% 3.09/2.28 inference(unit_resolution,[status(thm)],[362, 341])).
% 3.09/2.28 tff(364,assumption,(~hskp14), introduced(assumption)).
% 3.09/2.28 tff(365,plain,
% 3.09/2.28 (((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)))) <=> ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)))),
% 3.09/2.28 inference(rewrite,[status(thm)],[])).
% 3.09/2.28 tff(366,plain,
% 3.09/2.28 ((hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583))) <=> (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)))),
% 3.09/2.28 inference(rewrite,[status(thm)],[])).
% 3.09/2.28 tff(367,plain,
% 3.09/2.28 (((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)))) <=> ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583))))),
% 3.09/2.28 inference(monotonicity,[status(thm)],[366])).
% 3.09/2.28 tff(368,plain,
% 3.09/2.28 (((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)))) <=> ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)))),
% 3.09/2.28 inference(transitivity,[status(thm)],[367, 365])).
% 3.09/2.28 tff(369,plain,
% 3.09/2.28 ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)))),
% 3.09/2.29 inference(quant_inst,[status(thm)],[])).
% 3.09/2.29 tff(370,plain,
% 3.09/2.29 ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583))),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[369, 368])).
% 3.09/2.29 tff(371,plain,
% 3.09/2.29 (~c3_1(a583)),
% 3.09/2.29 inference(unit_resolution,[status(thm)],[370, 269, 107, 364, 363, 352, 340])).
% 3.09/2.29 tff(372,plain,
% 3.09/2.29 (^[U: $i] : refl((hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 3.09/2.29 inference(bind,[status(th)],[])).
% 3.09/2.29 tff(373,plain,
% 3.09/2.29 (![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 3.09/2.29 inference(quant_intro,[status(thm)],[372])).
% 3.09/2.29 tff(374,plain,
% 3.09/2.29 (![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 3.09/2.29 inference(rewrite,[status(thm)],[])).
% 3.09/2.29 tff(375,plain,
% 3.09/2.29 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp14))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) | hskp22) <=> ((hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp22))), rewrite(((hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp22) <=> (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) | hskp22) <=> (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 3.09/2.29 inference(bind,[status(th)],[])).
% 3.09/2.29 tff(376,plain,
% 3.09/2.29 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) | hskp22) <=> ![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 3.09/2.29 inference(quant_intro,[status(thm)],[375])).
% 3.09/2.29 tff(377,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) | hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause158')).
% 3.09/2.29 tff(378,plain,
% 3.09/2.29 (![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[377, 376])).
% 3.09/2.29 tff(379,plain,
% 3.09/2.29 (![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[378, 374])).
% 3.09/2.29 tff(380,plain,(
% 3.09/2.29 ![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 3.09/2.29 inference(skolemize,[status(sab)],[379])).
% 3.09/2.29 tff(381,plain,
% 3.09/2.29 (![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[380, 373])).
% 3.09/2.29 tff(382,plain,
% 3.09/2.29 (((~hskp26) | c2_1(a583)) <=> ((~hskp26) | c2_1(a583))),
% 3.09/2.29 inference(rewrite,[status(thm)],[])).
% 3.09/2.29 tff(383,axiom,((~hskp26) | c2_1(a583)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause47')).
% 3.09/2.29 tff(384,plain,
% 3.09/2.29 ((~hskp26) | c2_1(a583)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[383, 382])).
% 3.09/2.29 tff(385,plain,
% 3.09/2.29 ((~hskp26) | c2_1(a583)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[384, 382])).
% 3.09/2.29 tff(386,plain,
% 3.09/2.29 ((~hskp26) | c2_1(a583)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[385, 382])).
% 3.09/2.29 tff(387,plain,
% 3.09/2.29 ((~hskp26) | c2_1(a583)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[386, 382])).
% 3.09/2.29 tff(388,plain,
% 3.09/2.29 ((~hskp26) | c2_1(a583)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[387, 382])).
% 3.09/2.29 tff(389,plain,
% 3.09/2.29 ((~hskp26) | c2_1(a583)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[388, 382])).
% 3.09/2.29 tff(390,plain,
% 3.09/2.29 ((~hskp26) | c2_1(a583)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[389, 382])).
% 3.09/2.29 tff(391,plain,
% 3.09/2.29 ((~hskp26) | c2_1(a583)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[390, 382])).
% 3.09/2.29 tff(392,plain,
% 3.09/2.29 (c2_1(a583)),
% 3.09/2.29 inference(unit_resolution,[status(thm)],[391, 341])).
% 3.09/2.29 tff(393,plain,
% 3.09/2.29 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp22 | hskp14 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)))),
% 3.09/2.29 inference(rewrite,[status(thm)],[])).
% 3.09/2.29 tff(394,plain,
% 3.09/2.29 ((hskp22 | hskp14 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583))) <=> (hskp22 | hskp14 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)))),
% 3.09/2.29 inference(rewrite,[status(thm)],[])).
% 3.09/2.29 tff(395,plain,
% 3.09/2.29 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583))))),
% 3.09/2.29 inference(monotonicity,[status(thm)],[394])).
% 3.09/2.29 tff(396,plain,
% 3.09/2.29 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp22 | hskp14 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)))),
% 3.09/2.29 inference(transitivity,[status(thm)],[395, 393])).
% 3.09/2.29 tff(397,plain,
% 3.09/2.29 ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)))),
% 3.09/2.29 inference(quant_inst,[status(thm)],[])).
% 3.09/2.29 tff(398,plain,
% 3.09/2.29 ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp22 | hskp14 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583))),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[397, 396])).
% 3.09/2.29 tff(399,plain,
% 3.09/2.29 ($false),
% 3.09/2.29 inference(unit_resolution,[status(thm)],[398, 107, 44, 364, 363, 392, 381, 371])).
% 3.09/2.29 tff(400,plain,((~hskp26) | hskp22 | hskp14 | hskp29), inference(lemma,lemma(discharge,[]))).
% 3.09/2.29 tff(401,plain,
% 3.09/2.29 (~hskp26),
% 3.09/2.29 inference(unit_resolution,[status(thm)],[400, 330, 44, 269])).
% 3.09/2.29 tff(402,plain,
% 3.09/2.29 ((hskp26 | hskp11) <=> (hskp26 | hskp11)),
% 3.09/2.29 inference(rewrite,[status(thm)],[])).
% 3.09/2.29 tff(403,axiom,(hskp26 | hskp11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause1')).
% 3.09/2.29 tff(404,plain,
% 3.09/2.29 (hskp26 | hskp11),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[403, 402])).
% 3.09/2.29 tff(405,plain,
% 3.09/2.29 (hskp26 | hskp11),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[404, 402])).
% 3.09/2.29 tff(406,plain,
% 3.09/2.29 (hskp26 | hskp11),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[405, 402])).
% 3.09/2.29 tff(407,plain,
% 3.09/2.29 (hskp26 | hskp11),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[406, 402])).
% 3.09/2.29 tff(408,plain,
% 3.09/2.29 (hskp26 | hskp11),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[407, 402])).
% 3.09/2.29 tff(409,plain,
% 3.09/2.29 (hskp26 | hskp11),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[408, 402])).
% 3.09/2.29 tff(410,plain,
% 3.09/2.29 (hskp26 | hskp11),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[409, 402])).
% 3.09/2.29 tff(411,plain,
% 3.09/2.29 (hskp26 | hskp11),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[410, 402])).
% 3.09/2.29 tff(412,plain,
% 3.09/2.29 (hskp11),
% 3.09/2.29 inference(unit_resolution,[status(thm)],[411, 401])).
% 3.09/2.29 tff(413,plain,
% 3.09/2.29 (((~hskp11) | c3_1(a599)) <=> ((~hskp11) | c3_1(a599))),
% 3.09/2.29 inference(rewrite,[status(thm)],[])).
% 3.09/2.29 tff(414,axiom,((~hskp11) | c3_1(a599)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause64')).
% 3.09/2.29 tff(415,plain,
% 3.09/2.29 ((~hskp11) | c3_1(a599)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[414, 413])).
% 3.09/2.29 tff(416,plain,
% 3.09/2.29 ((~hskp11) | c3_1(a599)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[415, 413])).
% 3.09/2.29 tff(417,plain,
% 3.09/2.29 ((~hskp11) | c3_1(a599)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[416, 413])).
% 3.09/2.29 tff(418,plain,
% 3.09/2.29 ((~hskp11) | c3_1(a599)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[417, 413])).
% 3.09/2.29 tff(419,plain,
% 3.09/2.29 ((~hskp11) | c3_1(a599)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[418, 413])).
% 3.09/2.29 tff(420,plain,
% 3.09/2.29 ((~hskp11) | c3_1(a599)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[419, 413])).
% 3.09/2.29 tff(421,plain,
% 3.09/2.29 ((~hskp11) | c3_1(a599)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[420, 413])).
% 3.09/2.29 tff(422,plain,
% 3.09/2.29 ((~hskp11) | c3_1(a599)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[421, 413])).
% 3.09/2.29 tff(423,plain,
% 3.09/2.29 (c3_1(a599)),
% 3.09/2.29 inference(unit_resolution,[status(thm)],[422, 412])).
% 3.09/2.29 tff(424,plain,
% 3.09/2.29 (((~hskp11) | (~c1_1(a599))) <=> ((~hskp11) | (~c1_1(a599)))),
% 3.09/2.29 inference(rewrite,[status(thm)],[])).
% 3.09/2.29 tff(425,plain,
% 3.09/2.29 (((~c1_1(a599)) | (~hskp11)) <=> ((~hskp11) | (~c1_1(a599)))),
% 3.09/2.29 inference(rewrite,[status(thm)],[])).
% 3.09/2.29 tff(426,axiom,((~c1_1(a599)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause109')).
% 3.09/2.29 tff(427,plain,
% 3.09/2.29 ((~hskp11) | (~c1_1(a599))),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[426, 425])).
% 3.09/2.29 tff(428,plain,
% 3.09/2.29 ((~hskp11) | (~c1_1(a599))),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[427, 424])).
% 3.09/2.29 tff(429,plain,
% 3.09/2.29 (~c1_1(a599)),
% 3.09/2.29 inference(unit_resolution,[status(thm)],[428, 412])).
% 3.09/2.29 tff(430,plain,
% 3.09/2.29 (((~hskp11) | c2_1(a599)) <=> ((~hskp11) | c2_1(a599))),
% 3.09/2.29 inference(rewrite,[status(thm)],[])).
% 3.09/2.29 tff(431,axiom,((~hskp11) | c2_1(a599)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause63')).
% 3.09/2.29 tff(432,plain,
% 3.09/2.29 ((~hskp11) | c2_1(a599)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[431, 430])).
% 3.09/2.29 tff(433,plain,
% 3.09/2.29 ((~hskp11) | c2_1(a599)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[432, 430])).
% 3.09/2.29 tff(434,plain,
% 3.09/2.29 ((~hskp11) | c2_1(a599)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[433, 430])).
% 3.09/2.29 tff(435,plain,
% 3.09/2.29 ((~hskp11) | c2_1(a599)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[434, 430])).
% 3.09/2.29 tff(436,plain,
% 3.09/2.29 ((~hskp11) | c2_1(a599)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[435, 430])).
% 3.09/2.29 tff(437,plain,
% 3.09/2.29 ((~hskp11) | c2_1(a599)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[436, 430])).
% 3.09/2.29 tff(438,plain,
% 3.09/2.29 ((~hskp11) | c2_1(a599)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[437, 430])).
% 3.09/2.29 tff(439,plain,
% 3.09/2.29 ((~hskp11) | c2_1(a599)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[438, 430])).
% 3.09/2.29 tff(440,plain,
% 3.09/2.29 (c2_1(a599)),
% 3.09/2.29 inference(unit_resolution,[status(thm)],[439, 412])).
% 3.09/2.29 tff(441,plain,
% 3.09/2.29 (^[U: $i] : refl((hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))),
% 3.09/2.29 inference(bind,[status(th)],[])).
% 3.09/2.29 tff(442,plain,
% 3.09/2.29 (![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 3.09/2.29 inference(quant_intro,[status(thm)],[441])).
% 3.09/2.29 tff(443,plain,
% 3.09/2.29 (![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 3.09/2.29 inference(rewrite,[status(thm)],[])).
% 3.09/2.29 tff(444,plain,
% 3.09/2.29 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp8))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) | hskp6) <=> ((hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp6))), rewrite(((hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp6) <=> (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) | hskp6) <=> (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))))),
% 3.09/2.29 inference(bind,[status(th)],[])).
% 3.09/2.29 tff(445,plain,
% 3.09/2.29 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) | hskp6) <=> ![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 3.09/2.29 inference(quant_intro,[status(thm)],[444])).
% 3.09/2.29 tff(446,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause133')).
% 3.09/2.29 tff(447,plain,
% 3.09/2.29 (![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[446, 445])).
% 3.09/2.29 tff(448,plain,
% 3.09/2.29 (![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[447, 443])).
% 3.09/2.29 tff(449,plain,(
% 3.09/2.29 ![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 3.09/2.29 inference(skolemize,[status(sab)],[448])).
% 3.09/2.29 tff(450,plain,
% 3.09/2.29 (![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[449, 442])).
% 3.09/2.29 tff(451,plain,
% 3.09/2.29 (^[U: $i] : refl((hskp23 | hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> (hskp23 | hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))),
% 3.09/2.29 inference(bind,[status(th)],[])).
% 3.09/2.29 tff(452,plain,
% 3.09/2.29 (![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 3.09/2.29 inference(quant_intro,[status(thm)],[451])).
% 3.09/2.29 tff(453,plain,
% 3.09/2.29 (![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 3.09/2.29 inference(rewrite,[status(thm)],[])).
% 3.09/2.29 tff(454,plain,
% 3.09/2.29 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp14))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) | hskp23) <=> ((hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp23))), rewrite(((hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp23) <=> (hskp23 | hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) | hskp23) <=> (hskp23 | hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))))),
% 3.09/2.29 inference(bind,[status(th)],[])).
% 3.09/2.29 tff(455,plain,
% 3.09/2.29 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) | hskp23) <=> ![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 3.09/2.29 inference(quant_intro,[status(thm)],[454])).
% 3.09/2.29 tff(456,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) | hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause147')).
% 3.09/2.29 tff(457,plain,
% 3.09/2.29 (![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[456, 455])).
% 3.09/2.29 tff(458,plain,
% 3.09/2.29 (![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[457, 453])).
% 3.09/2.29 tff(459,plain,(
% 3.09/2.29 ![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 3.09/2.29 inference(skolemize,[status(sab)],[458])).
% 3.09/2.29 tff(460,plain,
% 3.09/2.29 (![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[459, 452])).
% 3.09/2.29 tff(461,assumption,(~c1_1(a599)), introduced(assumption)).
% 3.09/2.29 tff(462,assumption,(c3_1(a599)), introduced(assumption)).
% 3.09/2.29 tff(463,assumption,(c2_1(a599)), introduced(assumption)).
% 3.09/2.29 tff(464,plain,
% 3.09/2.29 (((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp23 | hskp14 | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)))) <=> ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp23 | hskp14 | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)))),
% 3.09/2.29 inference(rewrite,[status(thm)],[])).
% 3.09/2.29 tff(465,plain,
% 3.09/2.29 ((hskp23 | hskp14 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599))) <=> (hskp23 | hskp14 | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)))),
% 3.09/2.29 inference(rewrite,[status(thm)],[])).
% 3.09/2.29 tff(466,plain,
% 3.09/2.29 (((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp23 | hskp14 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)))) <=> ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp23 | hskp14 | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599))))),
% 3.09/2.29 inference(monotonicity,[status(thm)],[465])).
% 3.09/2.29 tff(467,plain,
% 3.09/2.29 (((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp23 | hskp14 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)))) <=> ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp23 | hskp14 | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)))),
% 3.09/2.29 inference(transitivity,[status(thm)],[466, 464])).
% 3.09/2.29 tff(468,plain,
% 3.09/2.29 ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp23 | hskp14 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)))),
% 3.09/2.29 inference(quant_inst,[status(thm)],[])).
% 3.09/2.29 tff(469,plain,
% 3.09/2.29 ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp23 | hskp14 | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599))),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[468, 467])).
% 3.09/2.29 tff(470,plain,
% 3.09/2.29 (hskp23),
% 3.09/2.29 inference(unit_resolution,[status(thm)],[469, 107, 364, 463, 462, 461, 460])).
% 3.09/2.29 tff(471,plain,
% 3.09/2.29 (((~hskp23) | (~c1_1(a636))) <=> ((~hskp23) | (~c1_1(a636)))),
% 3.09/2.29 inference(rewrite,[status(thm)],[])).
% 3.09/2.29 tff(472,plain,
% 3.09/2.29 (((~c1_1(a636)) | (~hskp23)) <=> ((~hskp23) | (~c1_1(a636)))),
% 3.09/2.29 inference(rewrite,[status(thm)],[])).
% 3.09/2.29 tff(473,axiom,((~c1_1(a636)) | (~hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause86')).
% 3.09/2.29 tff(474,plain,
% 3.09/2.29 ((~hskp23) | (~c1_1(a636))),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[473, 472])).
% 3.09/2.29 tff(475,plain,
% 3.09/2.29 ((~hskp23) | (~c1_1(a636))),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[474, 471])).
% 3.09/2.29 tff(476,plain,
% 3.09/2.29 (~c1_1(a636)),
% 3.09/2.29 inference(unit_resolution,[status(thm)],[475, 470])).
% 3.09/2.29 tff(477,plain,
% 3.09/2.29 (((~hskp23) | (~c0_1(a636))) <=> ((~hskp23) | (~c0_1(a636)))),
% 3.09/2.29 inference(rewrite,[status(thm)],[])).
% 3.09/2.29 tff(478,plain,
% 3.09/2.29 (((~c0_1(a636)) | (~hskp23)) <=> ((~hskp23) | (~c0_1(a636)))),
% 3.09/2.29 inference(rewrite,[status(thm)],[])).
% 3.09/2.29 tff(479,axiom,((~c0_1(a636)) | (~hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause85')).
% 3.09/2.29 tff(480,plain,
% 3.09/2.29 ((~hskp23) | (~c0_1(a636))),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[479, 478])).
% 3.09/2.29 tff(481,plain,
% 3.09/2.29 ((~hskp23) | (~c0_1(a636))),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[480, 477])).
% 3.09/2.29 tff(482,plain,
% 3.09/2.29 (~c0_1(a636)),
% 3.09/2.29 inference(unit_resolution,[status(thm)],[481, 470])).
% 3.09/2.29 tff(483,plain,
% 3.09/2.29 (((~hskp23) | c3_1(a636)) <=> ((~hskp23) | c3_1(a636))),
% 3.09/2.29 inference(rewrite,[status(thm)],[])).
% 3.09/2.29 tff(484,axiom,((~hskp23) | c3_1(a636)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause51')).
% 3.09/2.29 tff(485,plain,
% 3.09/2.29 ((~hskp23) | c3_1(a636)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[484, 483])).
% 3.09/2.29 tff(486,plain,
% 3.09/2.29 ((~hskp23) | c3_1(a636)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[485, 483])).
% 3.09/2.29 tff(487,plain,
% 3.09/2.29 ((~hskp23) | c3_1(a636)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[486, 483])).
% 3.09/2.29 tff(488,plain,
% 3.09/2.29 ((~hskp23) | c3_1(a636)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[487, 483])).
% 3.09/2.29 tff(489,plain,
% 3.09/2.29 ((~hskp23) | c3_1(a636)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[488, 483])).
% 3.09/2.29 tff(490,plain,
% 3.09/2.29 ((~hskp23) | c3_1(a636)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[489, 483])).
% 3.09/2.29 tff(491,plain,
% 3.09/2.29 ((~hskp23) | c3_1(a636)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[490, 483])).
% 3.09/2.29 tff(492,plain,
% 3.09/2.29 ((~hskp23) | c3_1(a636)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[491, 483])).
% 3.09/2.29 tff(493,plain,
% 3.09/2.29 (c3_1(a636)),
% 3.09/2.29 inference(unit_resolution,[status(thm)],[492, 470])).
% 3.09/2.29 tff(494,plain,
% 3.09/2.29 (((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp6 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c3_1(a636)))) <=> ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp8 | hskp6 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c3_1(a636)))),
% 3.09/2.29 inference(rewrite,[status(thm)],[])).
% 3.09/2.29 tff(495,plain,
% 3.09/2.29 ((hskp8 | hskp6 | (~ndr1_0) | c1_1(a636) | c0_1(a636) | (~c3_1(a636))) <=> (hskp8 | hskp6 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c3_1(a636)))),
% 3.09/2.29 inference(rewrite,[status(thm)],[])).
% 3.09/2.29 tff(496,plain,
% 3.09/2.29 (((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp6 | (~ndr1_0) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)))) <=> ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp6 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c3_1(a636))))),
% 3.09/2.29 inference(monotonicity,[status(thm)],[495])).
% 3.09/2.29 tff(497,plain,
% 3.09/2.29 (((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp6 | (~ndr1_0) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)))) <=> ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp8 | hskp6 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c3_1(a636)))),
% 3.09/2.29 inference(transitivity,[status(thm)],[496, 494])).
% 3.09/2.29 tff(498,plain,
% 3.09/2.29 ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp6 | (~ndr1_0) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)))),
% 3.09/2.29 inference(quant_inst,[status(thm)],[])).
% 3.09/2.29 tff(499,plain,
% 3.09/2.29 ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp8 | hskp6 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c3_1(a636))),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[498, 497])).
% 3.09/2.29 tff(500,plain,
% 3.09/2.29 (hskp8 | hskp6),
% 3.09/2.29 inference(unit_resolution,[status(thm)],[499, 107, 493, 482, 476, 450])).
% 3.09/2.29 tff(501,plain,
% 3.09/2.29 (hskp8),
% 3.09/2.29 inference(unit_resolution,[status(thm)],[500, 67])).
% 3.09/2.29 tff(502,plain,
% 3.09/2.29 (((~hskp8) | c3_1(a593)) <=> ((~hskp8) | c3_1(a593))),
% 3.09/2.29 inference(rewrite,[status(thm)],[])).
% 3.09/2.29 tff(503,axiom,((~hskp8) | c3_1(a593)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause68')).
% 3.09/2.29 tff(504,plain,
% 3.09/2.29 ((~hskp8) | c3_1(a593)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[503, 502])).
% 3.09/2.29 tff(505,plain,
% 3.09/2.29 ((~hskp8) | c3_1(a593)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[504, 502])).
% 3.09/2.29 tff(506,plain,
% 3.09/2.29 ((~hskp8) | c3_1(a593)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[505, 502])).
% 3.09/2.29 tff(507,plain,
% 3.09/2.29 ((~hskp8) | c3_1(a593)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[506, 502])).
% 3.09/2.29 tff(508,plain,
% 3.09/2.29 ((~hskp8) | c3_1(a593)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[507, 502])).
% 3.09/2.29 tff(509,plain,
% 3.09/2.29 ((~hskp8) | c3_1(a593)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[508, 502])).
% 3.09/2.29 tff(510,plain,
% 3.09/2.29 ((~hskp8) | c3_1(a593)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[509, 502])).
% 3.09/2.29 tff(511,plain,
% 3.09/2.29 ((~hskp8) | c3_1(a593)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[510, 502])).
% 3.09/2.29 tff(512,plain,
% 3.09/2.29 (c3_1(a593)),
% 3.09/2.29 inference(unit_resolution,[status(thm)],[511, 501])).
% 3.09/2.29 tff(513,plain,
% 3.09/2.29 (((~hskp8) | c1_1(a593)) <=> ((~hskp8) | c1_1(a593))),
% 3.09/2.29 inference(rewrite,[status(thm)],[])).
% 3.09/2.29 tff(514,axiom,((~hskp8) | c1_1(a593)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause67')).
% 3.09/2.29 tff(515,plain,
% 3.09/2.29 ((~hskp8) | c1_1(a593)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[514, 513])).
% 3.09/2.29 tff(516,plain,
% 3.09/2.29 ((~hskp8) | c1_1(a593)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[515, 513])).
% 3.09/2.29 tff(517,plain,
% 3.09/2.29 ((~hskp8) | c1_1(a593)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[516, 513])).
% 3.09/2.29 tff(518,plain,
% 3.09/2.29 ((~hskp8) | c1_1(a593)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[517, 513])).
% 3.09/2.29 tff(519,plain,
% 3.09/2.29 ((~hskp8) | c1_1(a593)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[518, 513])).
% 3.09/2.29 tff(520,plain,
% 3.09/2.29 ((~hskp8) | c1_1(a593)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[519, 513])).
% 3.09/2.29 tff(521,plain,
% 3.09/2.29 ((~hskp8) | c1_1(a593)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[520, 513])).
% 3.09/2.29 tff(522,plain,
% 3.09/2.29 ((~hskp8) | c1_1(a593)),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[521, 513])).
% 3.09/2.29 tff(523,plain,
% 3.09/2.29 (c1_1(a593)),
% 3.09/2.29 inference(unit_resolution,[status(thm)],[522, 501])).
% 3.09/2.29 tff(524,plain,
% 3.09/2.29 (((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)))) <=> ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp14 | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)))),
% 3.09/2.29 inference(rewrite,[status(thm)],[])).
% 3.09/2.29 tff(525,plain,
% 3.09/2.29 ((hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593))) <=> (hskp29 | hskp14 | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)))),
% 3.09/2.29 inference(rewrite,[status(thm)],[])).
% 3.09/2.29 tff(526,plain,
% 3.09/2.29 (((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)))) <=> ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593))))),
% 3.09/2.29 inference(monotonicity,[status(thm)],[525])).
% 3.09/2.29 tff(527,plain,
% 3.09/2.29 (((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)))) <=> ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp14 | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)))),
% 3.09/2.29 inference(transitivity,[status(thm)],[526, 524])).
% 3.09/2.29 tff(528,plain,
% 3.09/2.29 ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)))),
% 3.09/2.29 inference(quant_inst,[status(thm)],[])).
% 3.09/2.29 tff(529,plain,
% 3.09/2.29 ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp14 | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593))),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[528, 527])).
% 3.09/2.29 tff(530,plain,
% 3.09/2.29 (~c0_1(a593)),
% 3.09/2.29 inference(unit_resolution,[status(thm)],[529, 269, 107, 364, 523, 512, 340])).
% 3.09/2.29 tff(531,plain,
% 3.09/2.29 (^[V: $i, U: $i] : refl((hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))),
% 3.09/2.29 inference(bind,[status(th)],[])).
% 3.09/2.29 tff(532,plain,
% 3.09/2.29 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.09/2.29 inference(quant_intro,[status(thm)],[531])).
% 3.09/2.29 tff(533,plain,
% 3.09/2.29 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.09/2.29 inference(rewrite,[status(thm)],[])).
% 3.09/2.29 tff(534,plain,
% 3.09/2.29 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp27) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp27))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))))),
% 3.09/2.29 inference(bind,[status(th)],[])).
% 3.09/2.29 tff(535,plain,
% 3.09/2.29 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp27) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.09/2.29 inference(quant_intro,[status(thm)],[534])).
% 3.09/2.29 tff(536,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause178')).
% 3.09/2.29 tff(537,plain,
% 3.09/2.29 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[536, 535])).
% 3.09/2.29 tff(538,plain,
% 3.09/2.29 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[537, 533])).
% 3.09/2.29 tff(539,plain,(
% 3.09/2.29 ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.09/2.29 inference(skolemize,[status(sab)],[538])).
% 3.09/2.29 tff(540,plain,
% 3.09/2.29 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.09/2.29 inference(modus_ponens,[status(thm)],[539, 532])).
% 3.09/2.29 tff(541,plain,
% 3.09/2.29 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))))),
% 3.18/2.30 inference(bind,[status(th)],[])).
% 3.18/2.30 tff(542,plain,
% 3.18/2.30 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 3.18/2.30 inference(quant_intro,[status(thm)],[541])).
% 3.18/2.30 tff(543,plain,
% 3.18/2.30 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 3.18/2.30 inference(rewrite,[status(thm)],[])).
% 3.18/2.30 tff(544,plain,
% 3.18/2.30 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp14) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp14))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp14) <=> (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))))),
% 3.18/2.30 inference(bind,[status(th)],[])).
% 3.18/2.30 tff(545,plain,
% 3.18/2.30 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 3.18/2.30 inference(quant_intro,[status(thm)],[544])).
% 3.18/2.30 tff(546,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause192')).
% 3.18/2.30 tff(547,plain,
% 3.18/2.30 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[546, 545])).
% 3.18/2.30 tff(548,plain,
% 3.18/2.30 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[547, 543])).
% 3.18/2.30 tff(549,plain,(
% 3.18/2.30 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 3.18/2.30 inference(skolemize,[status(sab)],[548])).
% 3.18/2.30 tff(550,plain,
% 3.18/2.30 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[549, 542])).
% 3.18/2.30 tff(551,plain,
% 3.18/2.30 (((~hskp8) | (~c2_1(a593))) <=> ((~hskp8) | (~c2_1(a593)))),
% 3.18/2.30 inference(rewrite,[status(thm)],[])).
% 3.18/2.30 tff(552,plain,
% 3.18/2.30 (((~c2_1(a593)) | (~hskp8)) <=> ((~hskp8) | (~c2_1(a593)))),
% 3.18/2.30 inference(rewrite,[status(thm)],[])).
% 3.18/2.30 tff(553,axiom,((~c2_1(a593)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause114')).
% 3.18/2.30 tff(554,plain,
% 3.18/2.30 ((~hskp8) | (~c2_1(a593))),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[553, 552])).
% 3.18/2.30 tff(555,plain,
% 3.18/2.30 ((~hskp8) | (~c2_1(a593))),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[554, 551])).
% 3.18/2.30 tff(556,plain,
% 3.18/2.30 (~c2_1(a593)),
% 3.18/2.30 inference(unit_resolution,[status(thm)],[555, 501])).
% 3.18/2.30 tff(557,plain,
% 3.18/2.30 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | c2_1(a593) | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp14 | c2_1(a593) | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)))),
% 3.18/2.30 inference(rewrite,[status(thm)],[])).
% 3.18/2.30 tff(558,plain,
% 3.18/2.30 ((hskp14 | (~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a593) | (~c1_1(a593)) | (~c3_1(a593))) <=> (hskp14 | c2_1(a593) | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)))),
% 3.18/2.30 inference(rewrite,[status(thm)],[])).
% 3.18/2.30 tff(559,plain,
% 3.18/2.30 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a593) | (~c1_1(a593)) | (~c3_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | c2_1(a593) | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599))))),
% 3.18/2.30 inference(monotonicity,[status(thm)],[558])).
% 3.18/2.30 tff(560,plain,
% 3.18/2.30 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a593) | (~c1_1(a593)) | (~c3_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp14 | c2_1(a593) | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)))),
% 3.18/2.30 inference(transitivity,[status(thm)],[559, 557])).
% 3.18/2.30 tff(561,plain,
% 3.18/2.30 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a593) | (~c1_1(a593)) | (~c3_1(a593)))),
% 3.18/2.30 inference(quant_inst,[status(thm)],[])).
% 3.18/2.30 tff(562,plain,
% 3.18/2.30 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp14 | c2_1(a593) | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599))),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[561, 560])).
% 3.18/2.30 tff(563,plain,
% 3.18/2.30 (~c0_1(a599)),
% 3.18/2.30 inference(unit_resolution,[status(thm)],[562, 107, 364, 463, 462, 523, 512, 556, 550])).
% 3.18/2.30 tff(564,plain,
% 3.18/2.30 (^[U: $i] : refl((hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))),
% 3.18/2.30 inference(bind,[status(th)],[])).
% 3.18/2.30 tff(565,plain,
% 3.18/2.30 (![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 3.18/2.30 inference(quant_intro,[status(thm)],[564])).
% 3.18/2.30 tff(566,plain,
% 3.18/2.30 (![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 3.18/2.30 inference(rewrite,[status(thm)],[])).
% 3.18/2.30 tff(567,plain,
% 3.18/2.30 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp5) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp5))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp5) | hskp6) <=> ((hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp6))), rewrite(((hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp6) <=> (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp5) | hskp6) <=> (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))))),
% 3.18/2.30 inference(bind,[status(th)],[])).
% 3.18/2.30 tff(568,plain,
% 3.18/2.30 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp5) | hskp6) <=> ![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 3.18/2.30 inference(quant_intro,[status(thm)],[567])).
% 3.18/2.30 tff(569,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp5) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause131')).
% 3.18/2.30 tff(570,plain,
% 3.18/2.30 (![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[569, 568])).
% 3.18/2.30 tff(571,plain,
% 3.18/2.30 (![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[570, 566])).
% 3.18/2.30 tff(572,plain,(
% 3.18/2.30 ![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 3.18/2.30 inference(skolemize,[status(sab)],[571])).
% 3.18/2.30 tff(573,plain,
% 3.18/2.30 (![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[572, 565])).
% 3.18/2.30 tff(574,plain,
% 3.18/2.30 (((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp5 | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | c0_1(a599))) <=> ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp5 | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | c0_1(a599))),
% 3.18/2.30 inference(rewrite,[status(thm)],[])).
% 3.18/2.30 tff(575,plain,
% 3.18/2.30 ((hskp6 | hskp5 | (~ndr1_0) | c1_1(a599) | c0_1(a599) | (~c2_1(a599))) <=> (hskp6 | hskp5 | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | c0_1(a599))),
% 3.18/2.30 inference(rewrite,[status(thm)],[])).
% 3.18/2.30 tff(576,plain,
% 3.18/2.30 (((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp5 | (~ndr1_0) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))) <=> ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp5 | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | c0_1(a599)))),
% 3.18/2.30 inference(monotonicity,[status(thm)],[575])).
% 3.18/2.30 tff(577,plain,
% 3.18/2.30 (((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp5 | (~ndr1_0) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))) <=> ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp5 | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | c0_1(a599))),
% 3.18/2.30 inference(transitivity,[status(thm)],[576, 574])).
% 3.18/2.30 tff(578,plain,
% 3.18/2.30 ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp5 | (~ndr1_0) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))),
% 3.18/2.30 inference(quant_inst,[status(thm)],[])).
% 3.18/2.30 tff(579,plain,
% 3.18/2.30 ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp5 | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | c0_1(a599)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[578, 577])).
% 3.18/2.30 tff(580,plain,
% 3.18/2.30 (hskp6 | hskp5 | c0_1(a599)),
% 3.18/2.30 inference(unit_resolution,[status(thm)],[579, 107, 463, 461, 573])).
% 3.18/2.30 tff(581,plain,
% 3.18/2.30 (hskp5),
% 3.18/2.30 inference(unit_resolution,[status(thm)],[580, 563, 67])).
% 3.18/2.30 tff(582,plain,
% 3.18/2.30 (((~hskp5) | (~c2_1(a589))) <=> ((~hskp5) | (~c2_1(a589)))),
% 3.18/2.30 inference(rewrite,[status(thm)],[])).
% 3.18/2.30 tff(583,plain,
% 3.18/2.30 (((~c2_1(a589)) | (~hskp5)) <=> ((~hskp5) | (~c2_1(a589)))),
% 3.18/2.30 inference(rewrite,[status(thm)],[])).
% 3.18/2.30 tff(584,axiom,((~c2_1(a589)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause118')).
% 3.18/2.30 tff(585,plain,
% 3.18/2.30 ((~hskp5) | (~c2_1(a589))),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[584, 583])).
% 3.18/2.30 tff(586,plain,
% 3.18/2.30 ((~hskp5) | (~c2_1(a589))),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[585, 582])).
% 3.18/2.30 tff(587,plain,
% 3.18/2.30 (~c2_1(a589)),
% 3.18/2.30 inference(unit_resolution,[status(thm)],[586, 581])).
% 3.18/2.30 tff(588,plain,
% 3.18/2.30 (((~hskp5) | c1_1(a589)) <=> ((~hskp5) | c1_1(a589))),
% 3.18/2.30 inference(rewrite,[status(thm)],[])).
% 3.18/2.30 tff(589,axiom,((~hskp5) | c1_1(a589)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause73')).
% 3.18/2.30 tff(590,plain,
% 3.18/2.30 ((~hskp5) | c1_1(a589)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[589, 588])).
% 3.18/2.30 tff(591,plain,
% 3.18/2.30 ((~hskp5) | c1_1(a589)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[590, 588])).
% 3.18/2.30 tff(592,plain,
% 3.18/2.30 ((~hskp5) | c1_1(a589)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[591, 588])).
% 3.18/2.30 tff(593,plain,
% 3.18/2.30 ((~hskp5) | c1_1(a589)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[592, 588])).
% 3.18/2.30 tff(594,plain,
% 3.18/2.30 ((~hskp5) | c1_1(a589)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[593, 588])).
% 3.18/2.30 tff(595,plain,
% 3.18/2.30 ((~hskp5) | c1_1(a589)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[594, 588])).
% 3.18/2.30 tff(596,plain,
% 3.18/2.30 ((~hskp5) | c1_1(a589)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[595, 588])).
% 3.18/2.30 tff(597,plain,
% 3.18/2.30 ((~hskp5) | c1_1(a589)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[596, 588])).
% 3.18/2.30 tff(598,plain,
% 3.18/2.30 (c1_1(a589)),
% 3.18/2.30 inference(unit_resolution,[status(thm)],[597, 581])).
% 3.18/2.30 tff(599,plain,
% 3.18/2.30 (((~hskp5) | c0_1(a589)) <=> ((~hskp5) | c0_1(a589))),
% 3.18/2.30 inference(rewrite,[status(thm)],[])).
% 3.18/2.30 tff(600,axiom,((~hskp5) | c0_1(a589)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause72')).
% 3.18/2.30 tff(601,plain,
% 3.18/2.30 ((~hskp5) | c0_1(a589)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[600, 599])).
% 3.18/2.30 tff(602,plain,
% 3.18/2.30 ((~hskp5) | c0_1(a589)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[601, 599])).
% 3.18/2.30 tff(603,plain,
% 3.18/2.30 ((~hskp5) | c0_1(a589)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[602, 599])).
% 3.18/2.30 tff(604,plain,
% 3.18/2.30 ((~hskp5) | c0_1(a589)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[603, 599])).
% 3.18/2.30 tff(605,plain,
% 3.18/2.30 ((~hskp5) | c0_1(a589)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[604, 599])).
% 3.18/2.30 tff(606,plain,
% 3.18/2.30 ((~hskp5) | c0_1(a589)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[605, 599])).
% 3.18/2.30 tff(607,plain,
% 3.18/2.30 ((~hskp5) | c0_1(a589)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[606, 599])).
% 3.18/2.30 tff(608,plain,
% 3.18/2.30 ((~hskp5) | c0_1(a589)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[607, 599])).
% 3.18/2.30 tff(609,plain,
% 3.18/2.30 (c0_1(a589)),
% 3.18/2.30 inference(unit_resolution,[status(thm)],[608, 581])).
% 3.18/2.30 tff(610,assumption,(hskp27), introduced(assumption)).
% 3.18/2.30 tff(611,plain,
% 3.18/2.30 (((~hskp27) | c3_1(a611)) <=> ((~hskp27) | c3_1(a611))),
% 3.18/2.30 inference(rewrite,[status(thm)],[])).
% 3.18/2.30 tff(612,axiom,((~hskp27) | c3_1(a611)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause44')).
% 3.18/2.30 tff(613,plain,
% 3.18/2.30 ((~hskp27) | c3_1(a611)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[612, 611])).
% 3.18/2.30 tff(614,plain,
% 3.18/2.30 ((~hskp27) | c3_1(a611)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[613, 611])).
% 3.18/2.30 tff(615,plain,
% 3.18/2.30 ((~hskp27) | c3_1(a611)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[614, 611])).
% 3.18/2.30 tff(616,plain,
% 3.18/2.30 ((~hskp27) | c3_1(a611)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[615, 611])).
% 3.18/2.30 tff(617,plain,
% 3.18/2.30 ((~hskp27) | c3_1(a611)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[616, 611])).
% 3.18/2.30 tff(618,plain,
% 3.18/2.30 ((~hskp27) | c3_1(a611)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[617, 611])).
% 3.18/2.30 tff(619,plain,
% 3.18/2.30 ((~hskp27) | c3_1(a611)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[618, 611])).
% 3.18/2.30 tff(620,plain,
% 3.18/2.30 ((~hskp27) | c3_1(a611)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[619, 611])).
% 3.18/2.30 tff(621,plain,
% 3.18/2.30 (c3_1(a611)),
% 3.18/2.30 inference(unit_resolution,[status(thm)],[620, 610])).
% 3.18/2.30 tff(622,plain,
% 3.18/2.30 (((~hskp27) | c1_1(a611)) <=> ((~hskp27) | c1_1(a611))),
% 3.18/2.30 inference(rewrite,[status(thm)],[])).
% 3.18/2.30 tff(623,axiom,((~hskp27) | c1_1(a611)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause43')).
% 3.18/2.30 tff(624,plain,
% 3.18/2.30 ((~hskp27) | c1_1(a611)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[623, 622])).
% 3.18/2.30 tff(625,plain,
% 3.18/2.30 ((~hskp27) | c1_1(a611)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[624, 622])).
% 3.18/2.30 tff(626,plain,
% 3.18/2.30 ((~hskp27) | c1_1(a611)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[625, 622])).
% 3.18/2.30 tff(627,plain,
% 3.18/2.30 ((~hskp27) | c1_1(a611)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[626, 622])).
% 3.18/2.30 tff(628,plain,
% 3.18/2.30 ((~hskp27) | c1_1(a611)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[627, 622])).
% 3.18/2.30 tff(629,plain,
% 3.18/2.30 ((~hskp27) | c1_1(a611)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[628, 622])).
% 3.18/2.30 tff(630,plain,
% 3.18/2.30 ((~hskp27) | c1_1(a611)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[629, 622])).
% 3.18/2.30 tff(631,plain,
% 3.18/2.30 ((~hskp27) | c1_1(a611)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[630, 622])).
% 3.18/2.30 tff(632,plain,
% 3.18/2.30 (c1_1(a611)),
% 3.18/2.30 inference(unit_resolution,[status(thm)],[631, 610])).
% 3.18/2.30 tff(633,plain,
% 3.18/2.30 (((~hskp27) | c0_1(a611)) <=> ((~hskp27) | c0_1(a611))),
% 3.18/2.30 inference(rewrite,[status(thm)],[])).
% 3.18/2.30 tff(634,axiom,((~hskp27) | c0_1(a611)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause42')).
% 3.18/2.30 tff(635,plain,
% 3.18/2.30 ((~hskp27) | c0_1(a611)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[634, 633])).
% 3.18/2.30 tff(636,plain,
% 3.18/2.30 ((~hskp27) | c0_1(a611)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[635, 633])).
% 3.18/2.30 tff(637,plain,
% 3.18/2.30 ((~hskp27) | c0_1(a611)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[636, 633])).
% 3.18/2.30 tff(638,plain,
% 3.18/2.30 ((~hskp27) | c0_1(a611)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[637, 633])).
% 3.18/2.30 tff(639,plain,
% 3.18/2.30 ((~hskp27) | c0_1(a611)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[638, 633])).
% 3.18/2.30 tff(640,plain,
% 3.18/2.30 ((~hskp27) | c0_1(a611)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[639, 633])).
% 3.18/2.30 tff(641,plain,
% 3.18/2.30 ((~hskp27) | c0_1(a611)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[640, 633])).
% 3.18/2.30 tff(642,plain,
% 3.18/2.30 ((~hskp27) | c0_1(a611)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[641, 633])).
% 3.18/2.30 tff(643,plain,
% 3.18/2.30 (c0_1(a611)),
% 3.18/2.30 inference(unit_resolution,[status(thm)],[642, 610])).
% 3.18/2.30 tff(644,plain,
% 3.18/2.30 (((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)))) <=> ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)))),
% 3.18/2.30 inference(rewrite,[status(thm)],[])).
% 3.18/2.30 tff(645,plain,
% 3.18/2.30 ((hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611))) <=> (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)))),
% 3.18/2.30 inference(rewrite,[status(thm)],[])).
% 3.18/2.30 tff(646,plain,
% 3.18/2.30 (((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)))) <=> ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611))))),
% 3.18/2.30 inference(monotonicity,[status(thm)],[645])).
% 3.18/2.30 tff(647,plain,
% 3.18/2.30 (((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)))) <=> ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)))),
% 3.18/2.30 inference(transitivity,[status(thm)],[646, 644])).
% 3.18/2.30 tff(648,plain,
% 3.18/2.30 ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)))),
% 3.18/2.30 inference(quant_inst,[status(thm)],[])).
% 3.18/2.30 tff(649,plain,
% 3.18/2.30 ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp14 | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611))),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[648, 647])).
% 3.18/2.30 tff(650,plain,
% 3.18/2.30 ($false),
% 3.18/2.30 inference(unit_resolution,[status(thm)],[649, 269, 107, 364, 643, 632, 621, 340])).
% 3.18/2.30 tff(651,plain,((~hskp27) | hskp29 | hskp14), inference(lemma,lemma(discharge,[]))).
% 3.18/2.30 tff(652,plain,
% 3.18/2.30 (~hskp27),
% 3.18/2.30 inference(unit_resolution,[status(thm)],[651, 364, 269])).
% 3.18/2.30 tff(653,plain,
% 3.18/2.30 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | c2_1(a593) | c2_1(a589) | (~ndr1_0) | (~c0_1(a589)) | (~c1_1(a589)) | c0_1(a593) | (~c3_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | c2_1(a593) | c2_1(a589) | (~ndr1_0) | (~c0_1(a589)) | (~c1_1(a589)) | c0_1(a593) | (~c3_1(a593)))),
% 3.18/2.30 inference(rewrite,[status(thm)],[])).
% 3.18/2.30 tff(654,plain,
% 3.18/2.30 ((hskp27 | (~ndr1_0) | c2_1(a589) | (~c1_1(a589)) | (~c0_1(a589)) | c0_1(a593) | c2_1(a593) | (~c3_1(a593))) <=> (hskp27 | c2_1(a593) | c2_1(a589) | (~ndr1_0) | (~c0_1(a589)) | (~c1_1(a589)) | c0_1(a593) | (~c3_1(a593)))),
% 3.18/2.30 inference(rewrite,[status(thm)],[])).
% 3.18/2.30 tff(655,plain,
% 3.18/2.30 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a589) | (~c1_1(a589)) | (~c0_1(a589)) | c0_1(a593) | c2_1(a593) | (~c3_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | c2_1(a593) | c2_1(a589) | (~ndr1_0) | (~c0_1(a589)) | (~c1_1(a589)) | c0_1(a593) | (~c3_1(a593))))),
% 3.18/2.30 inference(monotonicity,[status(thm)],[654])).
% 3.18/2.30 tff(656,plain,
% 3.18/2.30 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a589) | (~c1_1(a589)) | (~c0_1(a589)) | c0_1(a593) | c2_1(a593) | (~c3_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | c2_1(a593) | c2_1(a589) | (~ndr1_0) | (~c0_1(a589)) | (~c1_1(a589)) | c0_1(a593) | (~c3_1(a593)))),
% 3.18/2.30 inference(transitivity,[status(thm)],[655, 653])).
% 3.18/2.30 tff(657,plain,
% 3.18/2.30 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a589) | (~c1_1(a589)) | (~c0_1(a589)) | c0_1(a593) | c2_1(a593) | (~c3_1(a593)))),
% 3.18/2.30 inference(quant_inst,[status(thm)],[])).
% 3.18/2.30 tff(658,plain,
% 3.18/2.30 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | c2_1(a593) | c2_1(a589) | (~ndr1_0) | (~c0_1(a589)) | (~c1_1(a589)) | c0_1(a593) | (~c3_1(a593))),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[657, 656])).
% 3.18/2.30 tff(659,plain,
% 3.18/2.30 ($false),
% 3.18/2.30 inference(unit_resolution,[status(thm)],[658, 107, 652, 512, 609, 598, 556, 587, 540, 530])).
% 3.18/2.30 tff(660,plain,(hskp6 | (~c2_1(a599)) | c1_1(a599) | hskp14 | (~c3_1(a599)) | hskp29), inference(lemma,lemma(discharge,[]))).
% 3.18/2.30 tff(661,plain,
% 3.18/2.30 (hskp6),
% 3.18/2.30 inference(unit_resolution,[status(thm)],[660, 440, 429, 330, 423, 269])).
% 3.18/2.30 tff(662,plain,
% 3.18/2.30 (((~hskp6) | (~c0_1(a590))) <=> ((~hskp6) | (~c0_1(a590)))),
% 3.18/2.30 inference(rewrite,[status(thm)],[])).
% 3.18/2.30 tff(663,plain,
% 3.18/2.30 (((~c0_1(a590)) | (~hskp6)) <=> ((~hskp6) | (~c0_1(a590)))),
% 3.18/2.30 inference(rewrite,[status(thm)],[])).
% 3.18/2.30 tff(664,axiom,((~c0_1(a590)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause117')).
% 3.18/2.30 tff(665,plain,
% 3.18/2.30 ((~hskp6) | (~c0_1(a590))),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[664, 663])).
% 3.18/2.30 tff(666,plain,
% 3.18/2.30 ((~hskp6) | (~c0_1(a590))),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[665, 662])).
% 3.18/2.30 tff(667,plain,
% 3.18/2.30 (~c0_1(a590)),
% 3.18/2.30 inference(unit_resolution,[status(thm)],[666, 661])).
% 3.18/2.30 tff(668,plain,
% 3.18/2.30 (((~hskp6) | c3_1(a590)) <=> ((~hskp6) | c3_1(a590))),
% 3.18/2.30 inference(rewrite,[status(thm)],[])).
% 3.18/2.30 tff(669,axiom,((~hskp6) | c3_1(a590)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause71')).
% 3.18/2.30 tff(670,plain,
% 3.18/2.30 ((~hskp6) | c3_1(a590)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[669, 668])).
% 3.18/2.30 tff(671,plain,
% 3.18/2.30 ((~hskp6) | c3_1(a590)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[670, 668])).
% 3.18/2.30 tff(672,plain,
% 3.18/2.30 ((~hskp6) | c3_1(a590)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[671, 668])).
% 3.18/2.30 tff(673,plain,
% 3.18/2.30 ((~hskp6) | c3_1(a590)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[672, 668])).
% 3.18/2.30 tff(674,plain,
% 3.18/2.30 ((~hskp6) | c3_1(a590)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[673, 668])).
% 3.18/2.30 tff(675,plain,
% 3.18/2.30 ((~hskp6) | c3_1(a590)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[674, 668])).
% 3.18/2.30 tff(676,plain,
% 3.18/2.30 ((~hskp6) | c3_1(a590)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[675, 668])).
% 3.18/2.30 tff(677,plain,
% 3.18/2.30 ((~hskp6) | c3_1(a590)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[676, 668])).
% 3.18/2.30 tff(678,plain,
% 3.18/2.30 (c3_1(a590)),
% 3.18/2.30 inference(unit_resolution,[status(thm)],[677, 661])).
% 3.18/2.30 tff(679,plain,
% 3.18/2.30 (((~hskp6) | c2_1(a590)) <=> ((~hskp6) | c2_1(a590))),
% 3.18/2.30 inference(rewrite,[status(thm)],[])).
% 3.18/2.30 tff(680,axiom,((~hskp6) | c2_1(a590)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause70')).
% 3.18/2.30 tff(681,plain,
% 3.18/2.30 ((~hskp6) | c2_1(a590)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[680, 679])).
% 3.18/2.30 tff(682,plain,
% 3.18/2.30 ((~hskp6) | c2_1(a590)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[681, 679])).
% 3.18/2.30 tff(683,plain,
% 3.18/2.30 ((~hskp6) | c2_1(a590)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[682, 679])).
% 3.18/2.30 tff(684,plain,
% 3.18/2.30 ((~hskp6) | c2_1(a590)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[683, 679])).
% 3.18/2.30 tff(685,plain,
% 3.18/2.30 ((~hskp6) | c2_1(a590)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[684, 679])).
% 3.18/2.30 tff(686,plain,
% 3.18/2.30 ((~hskp6) | c2_1(a590)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[685, 679])).
% 3.18/2.30 tff(687,plain,
% 3.18/2.30 ((~hskp6) | c2_1(a590)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[686, 679])).
% 3.18/2.30 tff(688,plain,
% 3.18/2.30 ((~hskp6) | c2_1(a590)),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[687, 679])).
% 3.18/2.30 tff(689,plain,
% 3.18/2.30 (c2_1(a590)),
% 3.18/2.30 inference(unit_resolution,[status(thm)],[688, 661])).
% 3.18/2.30 tff(690,plain,
% 3.18/2.30 (hskp23),
% 3.18/2.30 inference(unit_resolution,[status(thm)],[469, 107, 330, 440, 423, 429, 460])).
% 3.18/2.30 tff(691,plain,
% 3.18/2.30 (~c1_1(a636)),
% 3.18/2.30 inference(unit_resolution,[status(thm)],[475, 690])).
% 3.18/2.30 tff(692,plain,
% 3.18/2.30 (~c0_1(a636)),
% 3.18/2.30 inference(unit_resolution,[status(thm)],[481, 690])).
% 3.18/2.30 tff(693,plain,
% 3.18/2.30 (c3_1(a636)),
% 3.18/2.30 inference(unit_resolution,[status(thm)],[492, 690])).
% 3.18/2.30 tff(694,plain,
% 3.18/2.30 (^[V: $i, U: $i] : refl((hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))),
% 3.18/2.30 inference(bind,[status(th)],[])).
% 3.18/2.30 tff(695,plain,
% 3.18/2.30 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 3.18/2.30 inference(quant_intro,[status(thm)],[694])).
% 3.18/2.30 tff(696,plain,
% 3.18/2.30 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 3.18/2.30 inference(rewrite,[status(thm)],[])).
% 3.18/2.30 tff(697,plain,
% 3.18/2.30 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c1_1(V))), (((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c1_1(V) | c2_1(V))), (((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c1_1(V) | c2_1(V)))), ((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), ((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), (((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), (((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), ((((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), ((((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), (((((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c1_1(U)) | hskp26) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp26))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp26) <=> (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), (((((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c1_1(U)) | hskp26) <=> (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))))),
% 3.18/2.30 inference(bind,[status(th)],[])).
% 3.18/2.30 tff(698,plain,
% 3.18/2.30 (![V: $i, U: $i] : ((((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c1_1(U)) | hskp26) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 3.18/2.30 inference(quant_intro,[status(thm)],[697])).
% 3.18/2.30 tff(699,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c1_1(U)) | hskp26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause167')).
% 3.18/2.30 tff(700,plain,
% 3.18/2.30 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[699, 698])).
% 3.18/2.30 tff(701,plain,
% 3.18/2.30 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[700, 696])).
% 3.18/2.30 tff(702,plain,(
% 3.18/2.30 ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 3.18/2.30 inference(skolemize,[status(sab)],[701])).
% 3.18/2.30 tff(703,plain,
% 3.18/2.30 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[702, 695])).
% 3.18/2.30 tff(704,assumption,(hskp20), introduced(assumption)).
% 3.18/2.30 tff(705,plain,
% 3.18/2.30 (((~hskp20) | (~c3_1(a623))) <=> ((~hskp20) | (~c3_1(a623)))),
% 3.18/2.30 inference(rewrite,[status(thm)],[])).
% 3.18/2.30 tff(706,plain,
% 3.18/2.30 (((~c3_1(a623)) | (~hskp20)) <=> ((~hskp20) | (~c3_1(a623)))),
% 3.18/2.30 inference(rewrite,[status(thm)],[])).
% 3.18/2.30 tff(707,axiom,((~c3_1(a623)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause93')).
% 3.18/2.30 tff(708,plain,
% 3.18/2.30 ((~hskp20) | (~c3_1(a623))),
% 3.18/2.30 inference(modus_ponens,[status(thm)],[707, 706])).
% 3.18/2.30 tff(709,plain,
% 3.18/2.30 ((~hskp20) | (~c3_1(a623))),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[708, 705])).
% 3.18/2.31 tff(710,plain,
% 3.18/2.31 (~c3_1(a623)),
% 3.18/2.31 inference(unit_resolution,[status(thm)],[709, 704])).
% 3.18/2.31 tff(711,plain,
% 3.18/2.31 (((~hskp20) | (~c2_1(a623))) <=> ((~hskp20) | (~c2_1(a623)))),
% 3.18/2.31 inference(rewrite,[status(thm)],[])).
% 3.18/2.31 tff(712,plain,
% 3.18/2.31 (((~c2_1(a623)) | (~hskp20)) <=> ((~hskp20) | (~c2_1(a623)))),
% 3.18/2.31 inference(rewrite,[status(thm)],[])).
% 3.18/2.31 tff(713,axiom,((~c2_1(a623)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause92')).
% 3.18/2.31 tff(714,plain,
% 3.18/2.31 ((~hskp20) | (~c2_1(a623))),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[713, 712])).
% 3.18/2.31 tff(715,plain,
% 3.18/2.31 ((~hskp20) | (~c2_1(a623))),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[714, 711])).
% 3.18/2.31 tff(716,plain,
% 3.18/2.31 (~c2_1(a623)),
% 3.18/2.31 inference(unit_resolution,[status(thm)],[715, 704])).
% 3.18/2.31 tff(717,plain,
% 3.18/2.31 (((~hskp20) | (~c1_1(a623))) <=> ((~hskp20) | (~c1_1(a623)))),
% 3.18/2.31 inference(rewrite,[status(thm)],[])).
% 3.18/2.31 tff(718,plain,
% 3.18/2.31 (((~c1_1(a623)) | (~hskp20)) <=> ((~hskp20) | (~c1_1(a623)))),
% 3.18/2.31 inference(rewrite,[status(thm)],[])).
% 3.18/2.31 tff(719,axiom,((~c1_1(a623)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause91')).
% 3.18/2.31 tff(720,plain,
% 3.18/2.31 ((~hskp20) | (~c1_1(a623))),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[719, 718])).
% 3.18/2.31 tff(721,plain,
% 3.18/2.31 ((~hskp20) | (~c1_1(a623))),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[720, 717])).
% 3.18/2.31 tff(722,plain,
% 3.18/2.31 (~c1_1(a623)),
% 3.18/2.31 inference(unit_resolution,[status(thm)],[721, 704])).
% 3.18/2.31 tff(723,assumption,(~c1_1(a636)), introduced(assumption)).
% 3.18/2.31 tff(724,assumption,(~c0_1(a636)), introduced(assumption)).
% 3.18/2.31 tff(725,assumption,(c3_1(a636)), introduced(assumption)).
% 3.18/2.31 tff(726,assumption,(~hskp26), introduced(assumption)).
% 3.18/2.31 tff(727,plain,
% 3.18/2.31 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c0_1(a636) | c1_1(a636) | c1_1(a623) | c2_1(a623) | c3_1(a623) | (~ndr1_0) | (~c3_1(a636)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c0_1(a636) | c1_1(a636) | c1_1(a623) | c2_1(a623) | c3_1(a623) | (~ndr1_0) | (~c3_1(a636)))),
% 3.18/2.31 inference(rewrite,[status(thm)],[])).
% 3.18/2.31 tff(728,plain,
% 3.18/2.31 ((hskp26 | (~ndr1_0) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)) | c3_1(a623) | c1_1(a623) | c2_1(a623)) <=> (hskp26 | c0_1(a636) | c1_1(a636) | c1_1(a623) | c2_1(a623) | c3_1(a623) | (~ndr1_0) | (~c3_1(a636)))),
% 3.18/2.31 inference(rewrite,[status(thm)],[])).
% 3.18/2.31 tff(729,plain,
% 3.18/2.31 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)) | c3_1(a623) | c1_1(a623) | c2_1(a623))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c0_1(a636) | c1_1(a636) | c1_1(a623) | c2_1(a623) | c3_1(a623) | (~ndr1_0) | (~c3_1(a636))))),
% 3.18/2.31 inference(monotonicity,[status(thm)],[728])).
% 3.18/2.31 tff(730,plain,
% 3.18/2.31 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)) | c3_1(a623) | c1_1(a623) | c2_1(a623))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c0_1(a636) | c1_1(a636) | c1_1(a623) | c2_1(a623) | c3_1(a623) | (~ndr1_0) | (~c3_1(a636)))),
% 3.18/2.31 inference(transitivity,[status(thm)],[729, 727])).
% 3.18/2.31 tff(731,plain,
% 3.18/2.31 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)) | c3_1(a623) | c1_1(a623) | c2_1(a623))),
% 3.18/2.31 inference(quant_inst,[status(thm)],[])).
% 3.18/2.31 tff(732,plain,
% 3.18/2.31 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c0_1(a636) | c1_1(a636) | c1_1(a623) | c2_1(a623) | c3_1(a623) | (~ndr1_0) | (~c3_1(a636))),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[731, 730])).
% 3.18/2.31 tff(733,plain,
% 3.18/2.31 ($false),
% 3.18/2.31 inference(unit_resolution,[status(thm)],[732, 726, 107, 725, 724, 723, 722, 716, 710, 703])).
% 3.18/2.31 tff(734,plain,((~hskp20) | hskp26 | (~c3_1(a636)) | c0_1(a636) | c1_1(a636)), inference(lemma,lemma(discharge,[]))).
% 3.18/2.31 tff(735,plain,
% 3.18/2.31 (~hskp20),
% 3.18/2.31 inference(unit_resolution,[status(thm)],[734, 401, 693, 692, 691])).
% 3.18/2.31 tff(736,assumption,(hskp12), introduced(assumption)).
% 3.18/2.31 tff(737,plain,
% 3.18/2.31 (((~hskp12) | (~c3_1(a600))) <=> ((~hskp12) | (~c3_1(a600)))),
% 3.18/2.31 inference(rewrite,[status(thm)],[])).
% 3.18/2.31 tff(738,plain,
% 3.18/2.31 (((~c3_1(a600)) | (~hskp12)) <=> ((~hskp12) | (~c3_1(a600)))),
% 3.18/2.31 inference(rewrite,[status(thm)],[])).
% 3.18/2.31 tff(739,axiom,((~c3_1(a600)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause108')).
% 3.18/2.31 tff(740,plain,
% 3.18/2.31 ((~hskp12) | (~c3_1(a600))),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[739, 738])).
% 3.18/2.31 tff(741,plain,
% 3.18/2.31 ((~hskp12) | (~c3_1(a600))),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[740, 737])).
% 3.18/2.31 tff(742,plain,
% 3.18/2.31 (~c3_1(a600)),
% 3.18/2.31 inference(unit_resolution,[status(thm)],[741, 736])).
% 3.18/2.31 tff(743,plain,
% 3.18/2.31 (((~hskp12) | c2_1(a600)) <=> ((~hskp12) | c2_1(a600))),
% 3.18/2.31 inference(rewrite,[status(thm)],[])).
% 3.18/2.31 tff(744,axiom,((~hskp12) | c2_1(a600)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause62')).
% 3.18/2.31 tff(745,plain,
% 3.18/2.31 ((~hskp12) | c2_1(a600)),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[744, 743])).
% 3.18/2.31 tff(746,plain,
% 3.18/2.31 ((~hskp12) | c2_1(a600)),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[745, 743])).
% 3.18/2.31 tff(747,plain,
% 3.18/2.31 ((~hskp12) | c2_1(a600)),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[746, 743])).
% 3.18/2.31 tff(748,plain,
% 3.18/2.31 ((~hskp12) | c2_1(a600)),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[747, 743])).
% 3.18/2.31 tff(749,plain,
% 3.18/2.31 ((~hskp12) | c2_1(a600)),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[748, 743])).
% 3.18/2.31 tff(750,plain,
% 3.18/2.31 ((~hskp12) | c2_1(a600)),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[749, 743])).
% 3.18/2.31 tff(751,plain,
% 3.18/2.31 ((~hskp12) | c2_1(a600)),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[750, 743])).
% 3.18/2.31 tff(752,plain,
% 3.18/2.31 ((~hskp12) | c2_1(a600)),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[751, 743])).
% 3.18/2.31 tff(753,plain,
% 3.18/2.31 (c2_1(a600)),
% 3.18/2.31 inference(unit_resolution,[status(thm)],[752, 736])).
% 3.18/2.31 tff(754,plain,
% 3.18/2.31 (((~hskp12) | c0_1(a600)) <=> ((~hskp12) | c0_1(a600))),
% 3.18/2.31 inference(rewrite,[status(thm)],[])).
% 3.18/2.31 tff(755,axiom,((~hskp12) | c0_1(a600)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause61')).
% 3.18/2.31 tff(756,plain,
% 3.18/2.31 ((~hskp12) | c0_1(a600)),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[755, 754])).
% 3.18/2.31 tff(757,plain,
% 3.18/2.31 ((~hskp12) | c0_1(a600)),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[756, 754])).
% 3.18/2.31 tff(758,plain,
% 3.18/2.31 ((~hskp12) | c0_1(a600)),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[757, 754])).
% 3.18/2.31 tff(759,plain,
% 3.18/2.31 ((~hskp12) | c0_1(a600)),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[758, 754])).
% 3.18/2.31 tff(760,plain,
% 3.18/2.31 ((~hskp12) | c0_1(a600)),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[759, 754])).
% 3.18/2.31 tff(761,plain,
% 3.18/2.31 ((~hskp12) | c0_1(a600)),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[760, 754])).
% 3.18/2.31 tff(762,plain,
% 3.18/2.31 ((~hskp12) | c0_1(a600)),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[761, 754])).
% 3.18/2.31 tff(763,plain,
% 3.18/2.31 ((~hskp12) | c0_1(a600)),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[762, 754])).
% 3.18/2.31 tff(764,plain,
% 3.18/2.31 (c0_1(a600)),
% 3.18/2.31 inference(unit_resolution,[status(thm)],[763, 736])).
% 3.18/2.31 tff(765,plain,
% 3.18/2.31 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp14 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp22 | hskp14 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)))),
% 3.18/2.31 inference(rewrite,[status(thm)],[])).
% 3.18/2.31 tff(766,plain,
% 3.18/2.31 ((hskp22 | hskp14 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600))) <=> (hskp22 | hskp14 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)))),
% 3.18/2.31 inference(rewrite,[status(thm)],[])).
% 3.18/2.31 tff(767,plain,
% 3.18/2.31 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp14 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600))))),
% 3.18/2.31 inference(monotonicity,[status(thm)],[766])).
% 3.18/2.31 tff(768,plain,
% 3.18/2.31 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp22 | hskp14 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)))),
% 3.18/2.31 inference(transitivity,[status(thm)],[767, 765])).
% 3.18/2.31 tff(769,plain,
% 3.18/2.31 ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)))),
% 3.18/2.31 inference(quant_inst,[status(thm)],[])).
% 3.18/2.31 tff(770,plain,
% 3.18/2.31 ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp22 | hskp14 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600))),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[769, 768])).
% 3.18/2.31 tff(771,plain,
% 3.18/2.31 ($false),
% 3.18/2.31 inference(unit_resolution,[status(thm)],[770, 107, 44, 364, 764, 753, 742, 381])).
% 3.18/2.31 tff(772,plain,((~hskp12) | hskp22 | hskp14), inference(lemma,lemma(discharge,[]))).
% 3.18/2.31 tff(773,plain,
% 3.18/2.31 (~hskp12),
% 3.18/2.31 inference(unit_resolution,[status(thm)],[772, 330, 44])).
% 3.18/2.31 tff(774,plain,
% 3.18/2.31 ((hskp26 | hskp12 | hskp8) <=> (hskp26 | hskp12 | hskp8)),
% 3.18/2.31 inference(rewrite,[status(thm)],[])).
% 3.18/2.31 tff(775,plain,
% 3.18/2.31 (((hskp26 | hskp12) | hskp8) <=> (hskp26 | hskp12 | hskp8)),
% 3.18/2.31 inference(rewrite,[status(thm)],[])).
% 3.18/2.31 tff(776,plain,
% 3.18/2.31 ((hskp26 | hskp12) <=> (hskp26 | hskp12)),
% 3.18/2.31 inference(rewrite,[status(thm)],[])).
% 3.18/2.31 tff(777,plain,
% 3.18/2.31 (((hskp26 | hskp12) | hskp8) <=> ((hskp26 | hskp12) | hskp8)),
% 3.18/2.31 inference(monotonicity,[status(thm)],[776])).
% 3.18/2.31 tff(778,plain,
% 3.18/2.31 (((hskp26 | hskp12) | hskp8) <=> (hskp26 | hskp12 | hskp8)),
% 3.18/2.31 inference(transitivity,[status(thm)],[777, 775])).
% 3.18/2.31 tff(779,axiom,((hskp26 | hskp12) | hskp8), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause32')).
% 3.18/2.31 tff(780,plain,
% 3.18/2.31 (hskp26 | hskp12 | hskp8),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[779, 778])).
% 3.18/2.31 tff(781,plain,
% 3.18/2.31 (hskp26 | hskp12 | hskp8),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[780, 774])).
% 3.18/2.31 tff(782,plain,
% 3.18/2.31 (hskp26 | hskp12 | hskp8),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[781, 774])).
% 3.18/2.31 tff(783,plain,
% 3.18/2.31 (hskp26 | hskp12 | hskp8),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[782, 774])).
% 3.18/2.31 tff(784,plain,
% 3.18/2.31 (hskp26 | hskp12 | hskp8),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[783, 774])).
% 3.18/2.31 tff(785,plain,
% 3.18/2.31 (hskp26 | hskp12 | hskp8),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[784, 774])).
% 3.18/2.31 tff(786,plain,
% 3.18/2.31 (hskp26 | hskp12 | hskp8),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[785, 774])).
% 3.18/2.31 tff(787,plain,
% 3.18/2.31 (hskp26 | hskp12 | hskp8),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[786, 774])).
% 3.18/2.31 tff(788,plain,
% 3.18/2.31 (hskp8),
% 3.18/2.31 inference(unit_resolution,[status(thm)],[787, 773, 401])).
% 3.18/2.31 tff(789,plain,
% 3.18/2.31 (c3_1(a593)),
% 3.18/2.31 inference(unit_resolution,[status(thm)],[511, 788])).
% 3.18/2.31 tff(790,plain,
% 3.18/2.31 (c1_1(a593)),
% 3.18/2.31 inference(unit_resolution,[status(thm)],[522, 788])).
% 3.18/2.31 tff(791,plain,
% 3.18/2.31 (~c0_1(a593)),
% 3.18/2.31 inference(unit_resolution,[status(thm)],[529, 269, 107, 330, 790, 789, 340])).
% 3.18/2.31 tff(792,plain,
% 3.18/2.31 (^[U: $i] : refl((hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 3.18/2.31 inference(bind,[status(th)],[])).
% 3.18/2.31 tff(793,plain,
% 3.18/2.31 (![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 3.18/2.31 inference(quant_intro,[status(thm)],[792])).
% 3.18/2.31 tff(794,plain,
% 3.18/2.31 (![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 3.18/2.31 inference(rewrite,[status(thm)],[])).
% 3.18/2.31 tff(795,plain,
% 3.18/2.31 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp7) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp7))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp7) <=> (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp7) | hskp20) <=> ((hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp20))), rewrite(((hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp20) <=> (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp7) | hskp20) <=> (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 3.18/2.31 inference(bind,[status(th)],[])).
% 3.18/2.31 tff(796,plain,
% 3.18/2.31 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp7) | hskp20) <=> ![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 3.18/2.31 inference(quant_intro,[status(thm)],[795])).
% 3.18/2.31 tff(797,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp7) | hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause144')).
% 3.18/2.31 tff(798,plain,
% 3.18/2.31 (![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[797, 796])).
% 3.18/2.31 tff(799,plain,
% 3.18/2.31 (![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[798, 794])).
% 3.18/2.31 tff(800,plain,(
% 3.18/2.31 ![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 3.18/2.31 inference(skolemize,[status(sab)],[799])).
% 3.18/2.31 tff(801,plain,
% 3.18/2.31 (![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[800, 793])).
% 3.18/2.31 tff(802,plain,
% 3.18/2.31 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp7 | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)))),
% 3.18/2.31 inference(rewrite,[status(thm)],[])).
% 3.18/2.31 tff(803,plain,
% 3.18/2.31 ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)))),
% 3.18/2.31 inference(quant_inst,[status(thm)],[])).
% 3.18/2.31 tff(804,plain,
% 3.18/2.31 ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp7 | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593))),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[803, 802])).
% 3.18/2.31 tff(805,plain,
% 3.18/2.31 (hskp20 | hskp7),
% 3.18/2.31 inference(unit_resolution,[status(thm)],[804, 107, 790, 789, 801, 791])).
% 3.18/2.31 tff(806,plain,
% 3.18/2.31 (hskp7),
% 3.18/2.31 inference(unit_resolution,[status(thm)],[805, 735])).
% 3.18/2.31 tff(807,plain,
% 3.18/2.31 (((~hskp7) | (~c3_1(a592))) <=> ((~hskp7) | (~c3_1(a592)))),
% 3.18/2.31 inference(rewrite,[status(thm)],[])).
% 3.18/2.31 tff(808,plain,
% 3.18/2.31 (((~c3_1(a592)) | (~hskp7)) <=> ((~hskp7) | (~c3_1(a592)))),
% 3.18/2.31 inference(rewrite,[status(thm)],[])).
% 3.18/2.31 tff(809,axiom,((~c3_1(a592)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause116')).
% 3.18/2.31 tff(810,plain,
% 3.18/2.31 ((~hskp7) | (~c3_1(a592))),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[809, 808])).
% 3.18/2.31 tff(811,plain,
% 3.18/2.31 ((~hskp7) | (~c3_1(a592))),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[810, 807])).
% 3.18/2.31 tff(812,plain,
% 3.18/2.31 (~c3_1(a592)),
% 3.18/2.31 inference(unit_resolution,[status(thm)],[811, 806])).
% 3.18/2.31 tff(813,plain,
% 3.18/2.31 (((~hskp7) | (~c0_1(a592))) <=> ((~hskp7) | (~c0_1(a592)))),
% 3.18/2.31 inference(rewrite,[status(thm)],[])).
% 3.18/2.31 tff(814,plain,
% 3.18/2.31 (((~c0_1(a592)) | (~hskp7)) <=> ((~hskp7) | (~c0_1(a592)))),
% 3.18/2.31 inference(rewrite,[status(thm)],[])).
% 3.18/2.31 tff(815,axiom,((~c0_1(a592)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause115')).
% 3.18/2.31 tff(816,plain,
% 3.18/2.31 ((~hskp7) | (~c0_1(a592))),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[815, 814])).
% 3.18/2.31 tff(817,plain,
% 3.18/2.31 ((~hskp7) | (~c0_1(a592))),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[816, 813])).
% 3.18/2.31 tff(818,plain,
% 3.18/2.31 (~c0_1(a592)),
% 3.18/2.31 inference(unit_resolution,[status(thm)],[817, 806])).
% 3.18/2.31 tff(819,plain,
% 3.18/2.31 (((~hskp7) | c2_1(a592)) <=> ((~hskp7) | c2_1(a592))),
% 3.18/2.31 inference(rewrite,[status(thm)],[])).
% 3.18/2.31 tff(820,axiom,((~hskp7) | c2_1(a592)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause69')).
% 3.18/2.31 tff(821,plain,
% 3.18/2.31 ((~hskp7) | c2_1(a592)),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[820, 819])).
% 3.18/2.31 tff(822,plain,
% 3.18/2.31 ((~hskp7) | c2_1(a592)),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[821, 819])).
% 3.18/2.31 tff(823,plain,
% 3.18/2.31 ((~hskp7) | c2_1(a592)),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[822, 819])).
% 3.18/2.31 tff(824,plain,
% 3.18/2.31 ((~hskp7) | c2_1(a592)),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[823, 819])).
% 3.18/2.31 tff(825,plain,
% 3.18/2.31 ((~hskp7) | c2_1(a592)),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[824, 819])).
% 3.18/2.31 tff(826,plain,
% 3.18/2.31 ((~hskp7) | c2_1(a592)),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[825, 819])).
% 3.18/2.31 tff(827,plain,
% 3.18/2.31 ((~hskp7) | c2_1(a592)),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[826, 819])).
% 3.18/2.31 tff(828,plain,
% 3.18/2.31 ((~hskp7) | c2_1(a592)),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[827, 819])).
% 3.18/2.31 tff(829,plain,
% 3.18/2.31 (c2_1(a592)),
% 3.18/2.31 inference(unit_resolution,[status(thm)],[828, 806])).
% 3.18/2.31 tff(830,assumption,(~hskp4), introduced(assumption)).
% 3.18/2.31 tff(831,plain,
% 3.18/2.31 (^[U: $i] : refl((hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))),
% 3.18/2.31 inference(bind,[status(th)],[])).
% 3.18/2.31 tff(832,plain,
% 3.18/2.31 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 3.18/2.31 inference(quant_intro,[status(thm)],[831])).
% 3.18/2.31 tff(833,plain,
% 3.18/2.31 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 3.18/2.31 inference(rewrite,[status(thm)],[])).
% 3.18/2.31 tff(834,plain,
% 3.18/2.31 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp3) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp3))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp3) | hskp4) <=> ((hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp4))), rewrite(((hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp4) <=> (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp3) | hskp4) <=> (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))))),
% 3.18/2.31 inference(bind,[status(th)],[])).
% 3.18/2.31 tff(835,plain,
% 3.18/2.31 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp3) | hskp4) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 3.18/2.31 inference(quant_intro,[status(thm)],[834])).
% 3.18/2.31 tff(836,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp3) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause139')).
% 3.18/2.31 tff(837,plain,
% 3.18/2.31 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[836, 835])).
% 3.18/2.31 tff(838,plain,
% 3.18/2.31 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[837, 833])).
% 3.18/2.31 tff(839,plain,(
% 3.18/2.31 ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 3.18/2.31 inference(skolemize,[status(sab)],[838])).
% 3.18/2.31 tff(840,plain,
% 3.18/2.31 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[839, 832])).
% 3.18/2.31 tff(841,assumption,(~c3_1(a592)), introduced(assumption)).
% 3.18/2.31 tff(842,assumption,(c2_1(a592)), introduced(assumption)).
% 3.18/2.31 tff(843,plain,
% 3.18/2.31 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592))),
% 3.18/2.31 inference(rewrite,[status(thm)],[])).
% 3.18/2.31 tff(844,plain,
% 3.18/2.31 ((hskp4 | hskp3 | (~ndr1_0) | c1_1(a592) | c3_1(a592) | (~c2_1(a592))) <=> (hskp4 | hskp3 | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592))),
% 3.18/2.31 inference(rewrite,[status(thm)],[])).
% 3.18/2.31 tff(845,plain,
% 3.18/2.31 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a592) | c3_1(a592) | (~c2_1(a592)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592)))),
% 3.18/2.31 inference(monotonicity,[status(thm)],[844])).
% 3.18/2.31 tff(846,plain,
% 3.18/2.31 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a592) | c3_1(a592) | (~c2_1(a592)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592))),
% 3.18/2.31 inference(transitivity,[status(thm)],[845, 843])).
% 3.18/2.31 tff(847,plain,
% 3.18/2.31 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a592) | c3_1(a592) | (~c2_1(a592)))),
% 3.18/2.31 inference(quant_inst,[status(thm)],[])).
% 3.18/2.31 tff(848,plain,
% 3.18/2.31 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592)),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[847, 846])).
% 3.18/2.31 tff(849,plain,
% 3.18/2.31 (hskp4 | c1_1(a592)),
% 3.18/2.31 inference(unit_resolution,[status(thm)],[848, 107, 306, 842, 841, 840])).
% 3.18/2.31 tff(850,plain,
% 3.18/2.31 (c1_1(a592)),
% 3.18/2.31 inference(unit_resolution,[status(thm)],[849, 830])).
% 3.18/2.31 tff(851,assumption,(~c0_1(a592)), introduced(assumption)).
% 3.18/2.31 tff(852,plain,
% 3.18/2.31 (^[U: $i] : refl((hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))),
% 3.18/2.31 inference(bind,[status(th)],[])).
% 3.18/2.31 tff(853,plain,
% 3.18/2.31 (![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 3.18/2.31 inference(quant_intro,[status(thm)],[852])).
% 3.18/2.31 tff(854,plain,
% 3.18/2.31 (![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 3.18/2.31 inference(rewrite,[status(thm)],[])).
% 3.18/2.31 tff(855,plain,
% 3.18/2.31 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp10) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp10))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp10) <=> (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp10) <=> (hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp10) | hskp4) <=> ((hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp4))), rewrite(((hskp10 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp4) <=> (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp10) | hskp4) <=> (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))))),
% 3.18/2.31 inference(bind,[status(th)],[])).
% 3.18/2.31 tff(856,plain,
% 3.18/2.31 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp10) | hskp4) <=> ![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 3.18/2.31 inference(quant_intro,[status(thm)],[855])).
% 3.18/2.31 tff(857,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp10) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause145')).
% 3.18/2.31 tff(858,plain,
% 3.18/2.31 (![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[857, 856])).
% 3.18/2.31 tff(859,plain,
% 3.18/2.31 (![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[858, 854])).
% 3.18/2.31 tff(860,plain,(
% 3.18/2.31 ![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 3.18/2.31 inference(skolemize,[status(sab)],[859])).
% 3.18/2.31 tff(861,plain,
% 3.18/2.31 (![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[860, 853])).
% 3.18/2.31 tff(862,assumption,(c3_1(a590)), introduced(assumption)).
% 3.18/2.31 tff(863,assumption,(c2_1(a590)), introduced(assumption)).
% 3.18/2.31 tff(864,plain,
% 3.18/2.31 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp10 | hskp4 | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp10 | hskp4 | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)))),
% 3.18/2.31 inference(rewrite,[status(thm)],[])).
% 3.18/2.31 tff(865,plain,
% 3.18/2.31 ((hskp10 | hskp4 | (~ndr1_0) | c0_1(a590) | (~c2_1(a590)) | (~c3_1(a590))) <=> (hskp10 | hskp4 | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)))),
% 3.18/2.31 inference(rewrite,[status(thm)],[])).
% 3.18/2.31 tff(866,plain,
% 3.18/2.31 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c0_1(a590) | (~c2_1(a590)) | (~c3_1(a590)))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp10 | hskp4 | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590))))),
% 3.18/2.31 inference(monotonicity,[status(thm)],[865])).
% 3.18/2.31 tff(867,plain,
% 3.18/2.31 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c0_1(a590) | (~c2_1(a590)) | (~c3_1(a590)))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp10 | hskp4 | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)))),
% 3.18/2.31 inference(transitivity,[status(thm)],[866, 864])).
% 3.18/2.31 tff(868,plain,
% 3.18/2.31 ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c0_1(a590) | (~c2_1(a590)) | (~c3_1(a590)))),
% 3.18/2.31 inference(quant_inst,[status(thm)],[])).
% 3.18/2.31 tff(869,plain,
% 3.18/2.31 ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp10 | hskp4 | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590))),
% 3.18/2.31 inference(modus_ponens,[status(thm)],[868, 867])).
% 3.18/2.31 tff(870,plain,
% 3.18/2.31 (hskp10 | hskp4),
% 3.18/2.31 inference(unit_resolution,[status(thm)],[869, 107, 863, 862, 45, 861])).
% 3.18/2.31 tff(871,plain,
% 3.18/2.31 (hskp10),
% 3.18/2.31 inference(unit_resolution,[status(thm)],[870, 830])).
% 3.18/2.31 tff(872,plain,
% 3.18/2.31 (((~hskp10) | c3_1(a598)) <=> ((~hskp10) | c3_1(a598))),
% 3.18/2.31 inference(rewrite,[status(thm)],[])).
% 3.18/2.31 tff(873,axiom,((~hskp10) | c3_1(a598)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause66')).
% 3.18/2.32 tff(874,plain,
% 3.18/2.32 ((~hskp10) | c3_1(a598)),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[873, 872])).
% 3.18/2.32 tff(875,plain,
% 3.18/2.32 ((~hskp10) | c3_1(a598)),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[874, 872])).
% 3.18/2.32 tff(876,plain,
% 3.18/2.32 ((~hskp10) | c3_1(a598)),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[875, 872])).
% 3.18/2.32 tff(877,plain,
% 3.18/2.32 ((~hskp10) | c3_1(a598)),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[876, 872])).
% 3.18/2.32 tff(878,plain,
% 3.18/2.32 ((~hskp10) | c3_1(a598)),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[877, 872])).
% 3.18/2.32 tff(879,plain,
% 3.18/2.32 ((~hskp10) | c3_1(a598)),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[878, 872])).
% 3.18/2.32 tff(880,plain,
% 3.18/2.32 ((~hskp10) | c3_1(a598)),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[879, 872])).
% 3.18/2.32 tff(881,plain,
% 3.18/2.32 ((~hskp10) | c3_1(a598)),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[880, 872])).
% 3.18/2.32 tff(882,plain,
% 3.18/2.32 (c3_1(a598)),
% 3.18/2.32 inference(unit_resolution,[status(thm)],[881, 871])).
% 3.18/2.32 tff(883,plain,
% 3.18/2.32 (((~hskp10) | c0_1(a598)) <=> ((~hskp10) | c0_1(a598))),
% 3.18/2.32 inference(rewrite,[status(thm)],[])).
% 3.18/2.32 tff(884,axiom,((~hskp10) | c0_1(a598)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause65')).
% 3.18/2.32 tff(885,plain,
% 3.18/2.32 ((~hskp10) | c0_1(a598)),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[884, 883])).
% 3.18/2.32 tff(886,plain,
% 3.18/2.32 ((~hskp10) | c0_1(a598)),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[885, 883])).
% 3.18/2.32 tff(887,plain,
% 3.18/2.32 ((~hskp10) | c0_1(a598)),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[886, 883])).
% 3.18/2.32 tff(888,plain,
% 3.18/2.32 ((~hskp10) | c0_1(a598)),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[887, 883])).
% 3.18/2.32 tff(889,plain,
% 3.18/2.32 ((~hskp10) | c0_1(a598)),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[888, 883])).
% 3.18/2.32 tff(890,plain,
% 3.18/2.32 ((~hskp10) | c0_1(a598)),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[889, 883])).
% 3.18/2.32 tff(891,plain,
% 3.18/2.32 ((~hskp10) | c0_1(a598)),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[890, 883])).
% 3.18/2.32 tff(892,plain,
% 3.18/2.32 ((~hskp10) | c0_1(a598)),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[891, 883])).
% 3.18/2.32 tff(893,plain,
% 3.18/2.32 (c0_1(a598)),
% 3.18/2.32 inference(unit_resolution,[status(thm)],[892, 871])).
% 3.18/2.32 tff(894,assumption,(c2_1(a598)), introduced(assumption)).
% 3.18/2.32 tff(895,assumption,(c1_1(a592)), introduced(assumption)).
% 3.18/2.32 tff(896,assumption,(c3_1(a598)), introduced(assumption)).
% 3.18/2.32 tff(897,assumption,(c0_1(a598)), introduced(assumption)).
% 3.18/2.32 tff(898,plain,
% 3.18/2.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a607) | c2_1(a607) | c0_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c3_1(a607)))),
% 3.18/2.32 inference(rewrite,[status(thm)],[])).
% 3.18/2.32 tff(899,plain,
% 3.18/2.32 (((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a592) | (~c1_1(a592)) | (~c2_1(a592))) <=> (c1_1(a607) | c2_1(a607) | c0_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c3_1(a607)))),
% 3.18/2.32 inference(rewrite,[status(thm)],[])).
% 3.18/2.32 tff(900,plain,
% 3.18/2.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a592) | (~c1_1(a592)) | (~c2_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a607) | c2_1(a607) | c0_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c3_1(a607))))),
% 3.18/2.32 inference(monotonicity,[status(thm)],[899])).
% 3.18/2.32 tff(901,plain,
% 3.18/2.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a592) | (~c1_1(a592)) | (~c2_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c3_1(a607)))),
% 3.18/2.32 inference(transitivity,[status(thm)],[900, 898])).
% 3.18/2.32 tff(902,plain,
% 3.18/2.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a592) | (~c1_1(a592)) | (~c2_1(a592)))),
% 3.18/2.32 inference(quant_inst,[status(thm)],[])).
% 3.18/2.32 tff(903,plain,
% 3.18/2.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c3_1(a607))),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[902, 901])).
% 3.18/2.32 tff(904,plain,
% 3.18/2.32 ($false),
% 3.18/2.32 inference(unit_resolution,[status(thm)],[903, 107, 321, 897, 896, 842, 66, 22, 851, 11, 895, 894])).
% 3.18/2.32 tff(905,plain,((~c2_1(a598)) | (~c3_1(a607)) | (~c0_1(a598)) | (~c3_1(a598)) | (~c2_1(a592)) | c1_1(a607) | c2_1(a607) | c0_1(a592) | (~c1_1(a592))), inference(lemma,lemma(discharge,[]))).
% 3.18/2.32 tff(906,plain,
% 3.18/2.32 (~c2_1(a598)),
% 3.18/2.32 inference(unit_resolution,[status(thm)],[905, 893, 321, 882, 842, 66, 22, 851, 850])).
% 3.18/2.32 tff(907,plain,
% 3.18/2.32 (((~hskp10) | (~c1_1(a598))) <=> ((~hskp10) | (~c1_1(a598)))),
% 3.18/2.32 inference(rewrite,[status(thm)],[])).
% 3.18/2.32 tff(908,plain,
% 3.18/2.32 (((~c1_1(a598)) | (~hskp10)) <=> ((~hskp10) | (~c1_1(a598)))),
% 3.18/2.32 inference(rewrite,[status(thm)],[])).
% 3.18/2.32 tff(909,axiom,((~c1_1(a598)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause110')).
% 3.18/2.32 tff(910,plain,
% 3.18/2.32 ((~hskp10) | (~c1_1(a598))),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[909, 908])).
% 3.18/2.32 tff(911,plain,
% 3.18/2.32 ((~hskp10) | (~c1_1(a598))),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[910, 907])).
% 3.18/2.32 tff(912,plain,
% 3.18/2.32 (~c1_1(a598)),
% 3.18/2.32 inference(unit_resolution,[status(thm)],[911, 871])).
% 3.18/2.32 tff(913,plain,
% 3.18/2.32 (~hskp14),
% 3.18/2.32 inference(unit_resolution,[status(thm)],[329, 306, 321, 66, 22])).
% 3.18/2.32 tff(914,plain,
% 3.18/2.32 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c1_1(a598) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c2_1(a598) | (~c0_1(a598)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c1_1(a598) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c2_1(a598) | (~c0_1(a598)))),
% 3.18/2.32 inference(rewrite,[status(thm)],[])).
% 3.18/2.32 tff(915,plain,
% 3.18/2.32 ((hskp14 | (~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)) | c3_1(a592) | c0_1(a592) | (~c2_1(a592))) <=> (hskp14 | c1_1(a598) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c2_1(a598) | (~c0_1(a598)))),
% 3.18/2.32 inference(rewrite,[status(thm)],[])).
% 3.18/2.32 tff(916,plain,
% 3.18/2.32 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)) | c3_1(a592) | c0_1(a592) | (~c2_1(a592)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c1_1(a598) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c2_1(a598) | (~c0_1(a598))))),
% 3.18/2.32 inference(monotonicity,[status(thm)],[915])).
% 3.18/2.32 tff(917,plain,
% 3.18/2.32 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)) | c3_1(a592) | c0_1(a592) | (~c2_1(a592)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c1_1(a598) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c2_1(a598) | (~c0_1(a598)))),
% 3.18/2.32 inference(transitivity,[status(thm)],[916, 914])).
% 3.18/2.32 tff(918,plain,
% 3.18/2.32 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)) | c3_1(a592) | c0_1(a592) | (~c2_1(a592)))),
% 3.18/2.32 inference(quant_inst,[status(thm)],[])).
% 3.18/2.32 tff(919,plain,
% 3.18/2.32 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c1_1(a598) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c2_1(a598) | (~c0_1(a598))),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[918, 917])).
% 3.18/2.32 tff(920,plain,
% 3.18/2.32 ($false),
% 3.18/2.32 inference(unit_resolution,[status(thm)],[919, 107, 913, 893, 842, 912, 851, 841, 305, 906])).
% 3.18/2.32 tff(921,plain,(hskp4 | (~c2_1(a592)) | c0_1(a592) | c3_1(a592) | (~c3_1(a607)) | c1_1(a607) | c2_1(a607) | hskp3 | (~c2_1(a590)) | (~c3_1(a590)) | c0_1(a590)), inference(lemma,lemma(discharge,[]))).
% 3.18/2.32 tff(922,plain,
% 3.18/2.32 (hskp4),
% 3.18/2.32 inference(unit_resolution,[status(thm)],[921, 829, 818, 812, 295, 282, 276, 306, 689, 678, 667])).
% 3.18/2.32 tff(923,plain,
% 3.18/2.32 (~c2_1(a588)),
% 3.18/2.32 inference(unit_resolution,[status(thm)],[121, 922])).
% 3.18/2.32 tff(924,plain,
% 3.18/2.32 (~c1_1(a588)),
% 3.18/2.32 inference(unit_resolution,[status(thm)],[127, 922])).
% 3.18/2.32 tff(925,plain,
% 3.18/2.32 (c0_1(a588)),
% 3.18/2.32 inference(unit_resolution,[status(thm)],[138, 922])).
% 3.18/2.32 tff(926,plain,
% 3.18/2.32 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a592) | c3_1(a592) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c2_1(a592)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a592) | c3_1(a592) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c2_1(a592)))),
% 3.18/2.32 inference(rewrite,[status(thm)],[])).
% 3.18/2.32 tff(927,plain,
% 3.18/2.32 ((hskp14 | (~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588)) | c3_1(a592) | c0_1(a592) | (~c2_1(a592))) <=> (hskp14 | c0_1(a592) | c3_1(a592) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c2_1(a592)))),
% 3.18/2.32 inference(rewrite,[status(thm)],[])).
% 3.18/2.32 tff(928,plain,
% 3.18/2.32 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588)) | c3_1(a592) | c0_1(a592) | (~c2_1(a592)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a592) | c3_1(a592) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c2_1(a592))))),
% 3.18/2.32 inference(monotonicity,[status(thm)],[927])).
% 3.18/2.32 tff(929,plain,
% 3.18/2.32 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588)) | c3_1(a592) | c0_1(a592) | (~c2_1(a592)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a592) | c3_1(a592) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c2_1(a592)))),
% 3.18/2.32 inference(transitivity,[status(thm)],[928, 926])).
% 3.18/2.32 tff(930,plain,
% 3.18/2.32 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588)) | c3_1(a592) | c0_1(a592) | (~c2_1(a592)))),
% 3.18/2.32 inference(quant_inst,[status(thm)],[])).
% 3.18/2.32 tff(931,plain,
% 3.18/2.32 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a592) | c3_1(a592) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c2_1(a592))),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[930, 929])).
% 3.18/2.32 tff(932,plain,
% 3.18/2.32 ($false),
% 3.18/2.32 inference(unit_resolution,[status(thm)],[931, 107, 330, 829, 925, 818, 812, 924, 923, 305])).
% 3.18/2.32 tff(933,plain,(hskp3 | hskp29 | hskp22), inference(lemma,lemma(discharge,[]))).
% 3.18/2.32 tff(934,plain,
% 3.18/2.32 (hskp3),
% 3.18/2.32 inference(unit_resolution,[status(thm)],[933, 269, 44])).
% 3.18/2.32 tff(935,plain,
% 3.18/2.32 (((~hskp3) | (~c1_1(a587))) <=> ((~hskp3) | (~c1_1(a587)))),
% 3.18/2.32 inference(rewrite,[status(thm)],[])).
% 3.18/2.32 tff(936,plain,
% 3.18/2.32 (((~c1_1(a587)) | (~hskp3)) <=> ((~hskp3) | (~c1_1(a587)))),
% 3.18/2.32 inference(rewrite,[status(thm)],[])).
% 3.18/2.32 tff(937,axiom,((~c1_1(a587)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause121')).
% 3.18/2.32 tff(938,plain,
% 3.18/2.32 ((~hskp3) | (~c1_1(a587))),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[937, 936])).
% 3.18/2.32 tff(939,plain,
% 3.18/2.32 ((~hskp3) | (~c1_1(a587))),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[938, 935])).
% 3.18/2.32 tff(940,plain,
% 3.18/2.32 (~c1_1(a587)),
% 3.18/2.32 inference(unit_resolution,[status(thm)],[939, 934])).
% 3.18/2.32 tff(941,plain,
% 3.18/2.32 (((~hskp3) | c2_1(a587)) <=> ((~hskp3) | c2_1(a587))),
% 3.18/2.32 inference(rewrite,[status(thm)],[])).
% 3.18/2.32 tff(942,axiom,((~hskp3) | c2_1(a587)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause76')).
% 3.18/2.32 tff(943,plain,
% 3.18/2.32 ((~hskp3) | c2_1(a587)),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[942, 941])).
% 3.18/2.32 tff(944,plain,
% 3.18/2.32 ((~hskp3) | c2_1(a587)),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[943, 941])).
% 3.18/2.32 tff(945,plain,
% 3.18/2.32 ((~hskp3) | c2_1(a587)),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[944, 941])).
% 3.18/2.32 tff(946,plain,
% 3.18/2.32 ((~hskp3) | c2_1(a587)),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[945, 941])).
% 3.18/2.32 tff(947,plain,
% 3.18/2.32 ((~hskp3) | c2_1(a587)),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[946, 941])).
% 3.18/2.32 tff(948,plain,
% 3.18/2.32 ((~hskp3) | c2_1(a587)),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[947, 941])).
% 3.18/2.32 tff(949,plain,
% 3.18/2.32 ((~hskp3) | c2_1(a587)),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[948, 941])).
% 3.18/2.32 tff(950,plain,
% 3.18/2.32 ((~hskp3) | c2_1(a587)),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[949, 941])).
% 3.18/2.32 tff(951,plain,
% 3.18/2.32 (c2_1(a587)),
% 3.18/2.32 inference(unit_resolution,[status(thm)],[950, 934])).
% 3.18/2.32 tff(952,plain,
% 3.18/2.32 (((~hskp3) | c0_1(a587)) <=> ((~hskp3) | c0_1(a587))),
% 3.18/2.32 inference(rewrite,[status(thm)],[])).
% 3.18/2.32 tff(953,axiom,((~hskp3) | c0_1(a587)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause75')).
% 3.18/2.32 tff(954,plain,
% 3.18/2.32 ((~hskp3) | c0_1(a587)),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[953, 952])).
% 3.18/2.32 tff(955,plain,
% 3.18/2.32 ((~hskp3) | c0_1(a587)),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[954, 952])).
% 3.18/2.32 tff(956,plain,
% 3.18/2.32 ((~hskp3) | c0_1(a587)),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[955, 952])).
% 3.18/2.32 tff(957,plain,
% 3.18/2.32 ((~hskp3) | c0_1(a587)),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[956, 952])).
% 3.18/2.32 tff(958,plain,
% 3.18/2.32 ((~hskp3) | c0_1(a587)),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[957, 952])).
% 3.18/2.32 tff(959,plain,
% 3.18/2.32 ((~hskp3) | c0_1(a587)),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[958, 952])).
% 3.18/2.32 tff(960,plain,
% 3.18/2.32 ((~hskp3) | c0_1(a587)),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[959, 952])).
% 3.18/2.32 tff(961,plain,
% 3.18/2.32 ((~hskp3) | c0_1(a587)),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[960, 952])).
% 3.18/2.32 tff(962,plain,
% 3.18/2.32 (c0_1(a587)),
% 3.18/2.32 inference(unit_resolution,[status(thm)],[961, 934])).
% 3.18/2.32 tff(963,plain,
% 3.18/2.32 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp22 | hskp14 | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)))),
% 3.18/2.32 inference(rewrite,[status(thm)],[])).
% 3.18/2.32 tff(964,plain,
% 3.18/2.32 ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)))),
% 3.18/2.32 inference(quant_inst,[status(thm)],[])).
% 3.18/2.32 tff(965,plain,
% 3.18/2.32 ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp22 | hskp14 | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587))),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[964, 963])).
% 3.18/2.32 tff(966,plain,
% 3.18/2.32 (hskp14 | c3_1(a587)),
% 3.18/2.32 inference(unit_resolution,[status(thm)],[965, 107, 44, 962, 951, 381])).
% 3.18/2.32 tff(967,plain,
% 3.18/2.32 (c3_1(a587)),
% 3.18/2.32 inference(unit_resolution,[status(thm)],[966, 364])).
% 3.18/2.32 tff(968,plain,
% 3.18/2.32 (~hskp26),
% 3.18/2.32 inference(unit_resolution,[status(thm)],[400, 364, 44, 269])).
% 3.18/2.32 tff(969,plain,
% 3.18/2.32 (~hskp12),
% 3.18/2.32 inference(unit_resolution,[status(thm)],[772, 364, 44])).
% 3.18/2.32 tff(970,plain,
% 3.18/2.32 (hskp8),
% 3.18/2.32 inference(unit_resolution,[status(thm)],[787, 969, 968])).
% 3.18/2.32 tff(971,plain,
% 3.18/2.32 (~c2_1(a593)),
% 3.18/2.32 inference(unit_resolution,[status(thm)],[555, 970])).
% 3.18/2.32 tff(972,plain,
% 3.18/2.32 (c3_1(a593)),
% 3.18/2.32 inference(unit_resolution,[status(thm)],[511, 970])).
% 3.18/2.32 tff(973,plain,
% 3.18/2.32 (c1_1(a593)),
% 3.18/2.32 inference(unit_resolution,[status(thm)],[522, 970])).
% 3.18/2.32 tff(974,plain,
% 3.18/2.32 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | c2_1(a593) | (~ndr1_0) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a593)) | (~c1_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp14 | c2_1(a593) | (~ndr1_0) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a593)) | (~c1_1(a593)))),
% 3.18/2.32 inference(rewrite,[status(thm)],[])).
% 3.18/2.32 tff(975,plain,
% 3.18/2.32 ((hskp14 | (~ndr1_0) | (~c2_1(a587)) | (~c3_1(a587)) | (~c0_1(a587)) | c2_1(a593) | (~c1_1(a593)) | (~c3_1(a593))) <=> (hskp14 | c2_1(a593) | (~ndr1_0) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a593)) | (~c1_1(a593)))),
% 3.18/2.32 inference(rewrite,[status(thm)],[])).
% 3.18/2.32 tff(976,plain,
% 3.18/2.32 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a587)) | (~c3_1(a587)) | (~c0_1(a587)) | c2_1(a593) | (~c1_1(a593)) | (~c3_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | c2_1(a593) | (~ndr1_0) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a593)) | (~c1_1(a593))))),
% 3.18/2.32 inference(monotonicity,[status(thm)],[975])).
% 3.18/2.32 tff(977,plain,
% 3.18/2.32 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a587)) | (~c3_1(a587)) | (~c0_1(a587)) | c2_1(a593) | (~c1_1(a593)) | (~c3_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp14 | c2_1(a593) | (~ndr1_0) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a593)) | (~c1_1(a593)))),
% 3.18/2.32 inference(transitivity,[status(thm)],[976, 974])).
% 3.18/2.32 tff(978,plain,
% 3.18/2.32 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a587)) | (~c3_1(a587)) | (~c0_1(a587)) | c2_1(a593) | (~c1_1(a593)) | (~c3_1(a593)))),
% 3.18/2.32 inference(quant_inst,[status(thm)],[])).
% 3.18/2.32 tff(979,plain,
% 3.18/2.32 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp14 | c2_1(a593) | (~ndr1_0) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a593)) | (~c1_1(a593))),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[978, 977])).
% 3.18/2.32 tff(980,plain,
% 3.18/2.32 ($false),
% 3.18/2.32 inference(unit_resolution,[status(thm)],[979, 107, 364, 973, 972, 962, 951, 971, 550, 967])).
% 3.18/2.32 tff(981,plain,(hskp14 | hskp22 | hskp29), inference(lemma,lemma(discharge,[]))).
% 3.18/2.32 tff(982,plain,
% 3.18/2.32 (hskp14),
% 3.18/2.32 inference(unit_resolution,[status(thm)],[981, 269, 44])).
% 3.18/2.32 tff(983,plain,
% 3.18/2.32 (c0_1(a603)),
% 3.18/2.32 inference(unit_resolution,[status(thm)],[182, 982])).
% 3.18/2.32 tff(984,plain,
% 3.18/2.32 (~c3_1(a603)),
% 3.18/2.32 inference(unit_resolution,[status(thm)],[205, 982])).
% 3.18/2.32 tff(985,plain,
% 3.18/2.32 (~c1_1(a603)),
% 3.18/2.32 inference(unit_resolution,[status(thm)],[171, 982])).
% 3.18/2.32 tff(986,plain,
% 3.18/2.32 (^[V: $i, U: $i] : refl((hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))),
% 3.18/2.32 inference(bind,[status(th)],[])).
% 3.18/2.32 tff(987,plain,
% 3.18/2.32 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 3.18/2.32 inference(quant_intro,[status(thm)],[986])).
% 3.18/2.32 tff(988,plain,
% 3.18/2.32 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 3.18/2.32 inference(rewrite,[status(thm)],[])).
% 3.18/2.32 tff(989,plain,
% 3.18/2.32 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp26) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp26))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp26) <=> (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp26) <=> (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))))),
% 3.18/2.32 inference(bind,[status(th)],[])).
% 3.18/2.32 tff(990,plain,
% 3.18/2.32 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp26) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 3.18/2.32 inference(quant_intro,[status(thm)],[989])).
% 3.18/2.32 tff(991,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause173')).
% 3.18/2.32 tff(992,plain,
% 3.18/2.32 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[991, 990])).
% 3.18/2.32 tff(993,plain,
% 3.18/2.32 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[992, 988])).
% 3.18/2.32 tff(994,plain,(
% 3.18/2.32 ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 3.18/2.32 inference(skolemize,[status(sab)],[993])).
% 3.18/2.32 tff(995,plain,
% 3.18/2.32 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[994, 987])).
% 3.18/2.32 tff(996,assumption,(~c1_1(a587)), introduced(assumption)).
% 3.18/2.32 tff(997,assumption,(~c3_1(a603)), introduced(assumption)).
% 3.18/2.32 tff(998,assumption,(~c1_1(a603)), introduced(assumption)).
% 3.18/2.32 tff(999,assumption,(c2_1(a587)), introduced(assumption)).
% 3.18/2.32 tff(1000,assumption,(c0_1(a587)), introduced(assumption)).
% 3.18/2.32 tff(1001,plain,
% 3.18/2.32 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a603) | c3_1(a603) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a603))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a603) | c3_1(a603) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a603))),
% 3.18/2.32 inference(rewrite,[status(thm)],[])).
% 3.18/2.32 tff(1002,plain,
% 3.18/2.32 ((hskp26 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a603) | c1_1(a603) | c2_1(a603)) <=> (hskp26 | c1_1(a603) | c3_1(a603) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a603))),
% 3.18/2.32 inference(rewrite,[status(thm)],[])).
% 3.18/2.32 tff(1003,plain,
% 3.18/2.32 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a603) | c1_1(a603) | c2_1(a603))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a603) | c3_1(a603) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a603)))),
% 3.18/2.32 inference(monotonicity,[status(thm)],[1002])).
% 3.18/2.32 tff(1004,plain,
% 3.18/2.32 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a603) | c1_1(a603) | c2_1(a603))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a603) | c3_1(a603) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a603))),
% 3.18/2.32 inference(transitivity,[status(thm)],[1003, 1001])).
% 3.18/2.32 tff(1005,plain,
% 3.18/2.32 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a603) | c1_1(a603) | c2_1(a603))),
% 3.18/2.32 inference(quant_inst,[status(thm)],[])).
% 3.18/2.32 tff(1006,plain,
% 3.18/2.32 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a603) | c3_1(a603) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a603)),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[1005, 1004])).
% 3.18/2.32 tff(1007,plain,
% 3.18/2.32 (hskp26 | c2_1(a603)),
% 3.18/2.32 inference(unit_resolution,[status(thm)],[1006, 107, 1000, 999, 998, 997, 996, 995])).
% 3.18/2.32 tff(1008,plain,
% 3.18/2.32 (c2_1(a603)),
% 3.18/2.32 inference(unit_resolution,[status(thm)],[1007, 726])).
% 3.18/2.32 tff(1009,assumption,(c0_1(a603)), introduced(assumption)).
% 3.18/2.32 tff(1010,assumption,(c2_1(a603)), introduced(assumption)).
% 3.18/2.32 tff(1011,plain,
% 3.18/2.32 (hskp11),
% 3.18/2.32 inference(unit_resolution,[status(thm)],[411, 726])).
% 3.18/2.32 tff(1012,plain,
% 3.18/2.32 (~c1_1(a599)),
% 3.18/2.32 inference(unit_resolution,[status(thm)],[428, 1011])).
% 3.18/2.32 tff(1013,plain,
% 3.18/2.32 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))),
% 3.18/2.32 inference(bind,[status(th)],[])).
% 3.18/2.32 tff(1014,plain,
% 3.18/2.32 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 3.18/2.32 inference(quant_intro,[status(thm)],[1013])).
% 3.18/2.32 tff(1015,plain,
% 3.18/2.32 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 3.18/2.32 inference(rewrite,[status(thm)],[])).
% 3.18/2.32 tff(1016,plain,
% 3.18/2.32 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp16) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp16))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))))),
% 3.18/2.32 inference(bind,[status(th)],[])).
% 3.18/2.32 tff(1017,plain,
% 3.18/2.32 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 3.18/2.32 inference(quant_intro,[status(thm)],[1016])).
% 3.18/2.32 tff(1018,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause170')).
% 3.18/2.32 tff(1019,plain,
% 3.18/2.32 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[1018, 1017])).
% 3.18/2.32 tff(1020,plain,
% 3.18/2.32 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[1019, 1015])).
% 3.18/2.32 tff(1021,plain,(
% 3.18/2.32 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 3.18/2.32 inference(skolemize,[status(sab)],[1020])).
% 3.18/2.32 tff(1022,plain,
% 3.18/2.32 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 3.18/2.32 inference(modus_ponens,[status(thm)],[1021, 1014])).
% 3.18/2.32 tff(1023,plain,
% 3.18/2.32 (^[U: $i] : refl((hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))),
% 3.18/2.33 inference(bind,[status(th)],[])).
% 3.18/2.33 tff(1024,plain,
% 3.18/2.33 (![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 3.18/2.33 inference(quant_intro,[status(thm)],[1023])).
% 3.18/2.33 tff(1025,plain,
% 3.18/2.33 (![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 3.18/2.33 inference(rewrite,[status(thm)],[])).
% 3.18/2.33 tff(1026,plain,
% 3.18/2.33 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp26) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp26))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp26) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp26) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp26) | hskp0) <=> ((hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp0))), rewrite(((hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp0) <=> (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp26) | hskp0) <=> (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))))),
% 3.18/2.33 inference(bind,[status(th)],[])).
% 3.18/2.33 tff(1027,plain,
% 3.18/2.33 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp26) | hskp0) <=> ![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 3.18/2.33 inference(quant_intro,[status(thm)],[1026])).
% 3.18/2.33 tff(1028,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp26) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause126')).
% 3.18/2.33 tff(1029,plain,
% 3.18/2.33 (![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1028, 1027])).
% 3.18/2.33 tff(1030,plain,
% 3.18/2.33 (![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1029, 1025])).
% 3.18/2.33 tff(1031,plain,(
% 3.18/2.33 ![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 3.18/2.33 inference(skolemize,[status(sab)],[1030])).
% 3.18/2.33 tff(1032,plain,
% 3.18/2.33 (![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1031, 1024])).
% 3.18/2.33 tff(1033,plain,
% 3.18/2.33 (((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | c1_1(a607) | c2_1(a607) | (~ndr1_0) | c0_1(a607))) <=> ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp0 | c1_1(a607) | c2_1(a607) | (~ndr1_0) | c0_1(a607))),
% 3.18/2.33 inference(rewrite,[status(thm)],[])).
% 3.18/2.33 tff(1034,plain,
% 3.18/2.33 ((hskp26 | hskp0 | (~ndr1_0) | c2_1(a607) | c1_1(a607) | c0_1(a607)) <=> (hskp26 | hskp0 | c1_1(a607) | c2_1(a607) | (~ndr1_0) | c0_1(a607))),
% 3.18/2.33 inference(rewrite,[status(thm)],[])).
% 3.18/2.33 tff(1035,plain,
% 3.18/2.33 (((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | (~ndr1_0) | c2_1(a607) | c1_1(a607) | c0_1(a607))) <=> ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | c1_1(a607) | c2_1(a607) | (~ndr1_0) | c0_1(a607)))),
% 3.18/2.33 inference(monotonicity,[status(thm)],[1034])).
% 3.18/2.33 tff(1036,plain,
% 3.18/2.33 (((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | (~ndr1_0) | c2_1(a607) | c1_1(a607) | c0_1(a607))) <=> ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp0 | c1_1(a607) | c2_1(a607) | (~ndr1_0) | c0_1(a607))),
% 3.18/2.33 inference(transitivity,[status(thm)],[1035, 1033])).
% 3.18/2.33 tff(1037,plain,
% 3.18/2.33 ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | (~ndr1_0) | c2_1(a607) | c1_1(a607) | c0_1(a607))),
% 3.18/2.33 inference(quant_inst,[status(thm)],[])).
% 3.18/2.33 tff(1038,plain,
% 3.18/2.33 ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp0 | c1_1(a607) | c2_1(a607) | (~ndr1_0) | c0_1(a607)),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1037, 1036])).
% 3.18/2.33 tff(1039,plain,
% 3.18/2.33 (hskp26 | hskp0 | c0_1(a607)),
% 3.18/2.33 inference(unit_resolution,[status(thm)],[1038, 107, 66, 22, 1032])).
% 3.18/2.33 tff(1040,plain,
% 3.18/2.33 (hskp0),
% 3.18/2.33 inference(unit_resolution,[status(thm)],[1039, 1, 726])).
% 3.18/2.33 tff(1041,plain,
% 3.18/2.33 (((~hskp0) | (~c2_1(a584))) <=> ((~hskp0) | (~c2_1(a584)))),
% 3.18/2.33 inference(rewrite,[status(thm)],[])).
% 3.18/2.33 tff(1042,plain,
% 3.18/2.33 (((~c2_1(a584)) | (~hskp0)) <=> ((~hskp0) | (~c2_1(a584)))),
% 3.18/2.33 inference(rewrite,[status(thm)],[])).
% 3.18/2.33 tff(1043,axiom,((~c2_1(a584)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause125')).
% 3.18/2.33 tff(1044,plain,
% 3.18/2.33 ((~hskp0) | (~c2_1(a584))),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1043, 1042])).
% 3.18/2.33 tff(1045,plain,
% 3.18/2.33 ((~hskp0) | (~c2_1(a584))),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1044, 1041])).
% 3.18/2.33 tff(1046,plain,
% 3.18/2.33 (~c2_1(a584)),
% 3.18/2.33 inference(unit_resolution,[status(thm)],[1045, 1040])).
% 3.18/2.33 tff(1047,plain,
% 3.18/2.33 (((~hskp0) | (~c0_1(a584))) <=> ((~hskp0) | (~c0_1(a584)))),
% 3.18/2.33 inference(rewrite,[status(thm)],[])).
% 3.18/2.33 tff(1048,plain,
% 3.18/2.33 (((~c0_1(a584)) | (~hskp0)) <=> ((~hskp0) | (~c0_1(a584)))),
% 3.18/2.33 inference(rewrite,[status(thm)],[])).
% 3.18/2.33 tff(1049,axiom,((~c0_1(a584)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause124')).
% 3.18/2.33 tff(1050,plain,
% 3.18/2.33 ((~hskp0) | (~c0_1(a584))),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1049, 1048])).
% 3.18/2.33 tff(1051,plain,
% 3.18/2.33 ((~hskp0) | (~c0_1(a584))),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1050, 1047])).
% 3.18/2.33 tff(1052,plain,
% 3.18/2.33 (~c0_1(a584)),
% 3.18/2.33 inference(unit_resolution,[status(thm)],[1051, 1040])).
% 3.18/2.33 tff(1053,plain,
% 3.18/2.33 (((~hskp0) | c1_1(a584)) <=> ((~hskp0) | c1_1(a584))),
% 3.18/2.33 inference(rewrite,[status(thm)],[])).
% 3.18/2.33 tff(1054,axiom,((~hskp0) | c1_1(a584)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause81')).
% 3.18/2.33 tff(1055,plain,
% 3.18/2.33 ((~hskp0) | c1_1(a584)),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1054, 1053])).
% 3.18/2.33 tff(1056,plain,
% 3.18/2.33 ((~hskp0) | c1_1(a584)),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1055, 1053])).
% 3.18/2.33 tff(1057,plain,
% 3.18/2.33 ((~hskp0) | c1_1(a584)),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1056, 1053])).
% 3.18/2.33 tff(1058,plain,
% 3.18/2.33 ((~hskp0) | c1_1(a584)),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1057, 1053])).
% 3.18/2.33 tff(1059,plain,
% 3.18/2.33 ((~hskp0) | c1_1(a584)),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1058, 1053])).
% 3.18/2.33 tff(1060,plain,
% 3.18/2.33 ((~hskp0) | c1_1(a584)),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1059, 1053])).
% 3.18/2.33 tff(1061,plain,
% 3.18/2.33 ((~hskp0) | c1_1(a584)),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1060, 1053])).
% 3.18/2.33 tff(1062,plain,
% 3.18/2.33 ((~hskp0) | c1_1(a584)),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1061, 1053])).
% 3.18/2.33 tff(1063,plain,
% 3.18/2.33 (c1_1(a584)),
% 3.18/2.33 inference(unit_resolution,[status(thm)],[1062, 1040])).
% 3.18/2.33 tff(1064,plain,
% 3.18/2.33 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | c1_1(a603) | c3_1(a603) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp16 | c1_1(a603) | c3_1(a603) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a603)))),
% 3.18/2.33 inference(rewrite,[status(thm)],[])).
% 3.18/2.33 tff(1065,plain,
% 3.18/2.33 ((hskp16 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584))) <=> (hskp16 | c1_1(a603) | c3_1(a603) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a603)))),
% 3.18/2.33 inference(rewrite,[status(thm)],[])).
% 3.18/2.33 tff(1066,plain,
% 3.18/2.33 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | c1_1(a603) | c3_1(a603) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a603))))),
% 3.18/2.33 inference(monotonicity,[status(thm)],[1065])).
% 3.18/2.33 tff(1067,plain,
% 3.18/2.33 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp16 | c1_1(a603) | c3_1(a603) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a603)))),
% 3.18/2.33 inference(transitivity,[status(thm)],[1066, 1064])).
% 3.18/2.33 tff(1068,plain,
% 3.18/2.33 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584)))),
% 3.18/2.33 inference(quant_inst,[status(thm)],[])).
% 3.18/2.33 tff(1069,plain,
% 3.18/2.33 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp16 | c1_1(a603) | c3_1(a603) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a603))),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1068, 1067])).
% 3.18/2.33 tff(1070,plain,
% 3.18/2.33 (hskp16),
% 3.18/2.33 inference(unit_resolution,[status(thm)],[1069, 107, 1063, 998, 997, 1052, 1046, 1022, 1010])).
% 3.18/2.33 tff(1071,plain,
% 3.18/2.33 (((~hskp16) | (~c3_1(a606))) <=> ((~hskp16) | (~c3_1(a606)))),
% 3.18/2.33 inference(rewrite,[status(thm)],[])).
% 3.18/2.33 tff(1072,plain,
% 3.18/2.33 (((~c3_1(a606)) | (~hskp16)) <=> ((~hskp16) | (~c3_1(a606)))),
% 3.18/2.33 inference(rewrite,[status(thm)],[])).
% 3.18/2.33 tff(1073,axiom,((~c3_1(a606)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause101')).
% 3.18/2.33 tff(1074,plain,
% 3.18/2.33 ((~hskp16) | (~c3_1(a606))),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1073, 1072])).
% 3.18/2.33 tff(1075,plain,
% 3.18/2.33 ((~hskp16) | (~c3_1(a606))),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1074, 1071])).
% 3.18/2.33 tff(1076,plain,
% 3.18/2.33 (~c3_1(a606)),
% 3.18/2.33 inference(unit_resolution,[status(thm)],[1075, 1070])).
% 3.18/2.33 tff(1077,plain,
% 3.18/2.33 (c3_1(a599)),
% 3.18/2.33 inference(unit_resolution,[status(thm)],[422, 1011])).
% 3.18/2.33 tff(1078,plain,
% 3.18/2.33 (c2_1(a599)),
% 3.18/2.33 inference(unit_resolution,[status(thm)],[439, 1011])).
% 3.18/2.33 tff(1079,plain,
% 3.18/2.33 (((~hskp16) | c1_1(a606)) <=> ((~hskp16) | c1_1(a606))),
% 3.18/2.33 inference(rewrite,[status(thm)],[])).
% 3.18/2.33 tff(1080,axiom,((~hskp16) | c1_1(a606)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause57')).
% 3.18/2.33 tff(1081,plain,
% 3.18/2.33 ((~hskp16) | c1_1(a606)),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1080, 1079])).
% 3.18/2.33 tff(1082,plain,
% 3.18/2.33 ((~hskp16) | c1_1(a606)),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1081, 1079])).
% 3.18/2.33 tff(1083,plain,
% 3.18/2.33 ((~hskp16) | c1_1(a606)),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1082, 1079])).
% 3.18/2.33 tff(1084,plain,
% 3.18/2.33 ((~hskp16) | c1_1(a606)),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1083, 1079])).
% 3.18/2.33 tff(1085,plain,
% 3.18/2.33 ((~hskp16) | c1_1(a606)),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1084, 1079])).
% 3.18/2.33 tff(1086,plain,
% 3.18/2.33 ((~hskp16) | c1_1(a606)),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1085, 1079])).
% 3.18/2.33 tff(1087,plain,
% 3.18/2.33 ((~hskp16) | c1_1(a606)),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1086, 1079])).
% 3.18/2.33 tff(1088,plain,
% 3.18/2.33 ((~hskp16) | c1_1(a606)),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1087, 1079])).
% 3.18/2.33 tff(1089,plain,
% 3.18/2.33 (c1_1(a606)),
% 3.18/2.33 inference(unit_resolution,[status(thm)],[1088, 1070])).
% 3.18/2.33 tff(1090,plain,
% 3.18/2.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a606) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a606) | (~c1_1(a606)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a606) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a606) | (~c1_1(a606)))),
% 3.18/2.33 inference(rewrite,[status(thm)],[])).
% 3.18/2.33 tff(1091,plain,
% 3.18/2.33 (((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a606) | c0_1(a606) | (~c1_1(a606))) <=> (c3_1(a606) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a606) | (~c1_1(a606)))),
% 3.18/2.33 inference(rewrite,[status(thm)],[])).
% 3.18/2.33 tff(1092,plain,
% 3.18/2.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a606) | c0_1(a606) | (~c1_1(a606)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a606) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a606) | (~c1_1(a606))))),
% 3.18/2.33 inference(monotonicity,[status(thm)],[1091])).
% 3.18/2.33 tff(1093,plain,
% 3.18/2.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a606) | c0_1(a606) | (~c1_1(a606)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a606) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a606) | (~c1_1(a606)))),
% 3.18/2.33 inference(transitivity,[status(thm)],[1092, 1090])).
% 3.18/2.33 tff(1094,plain,
% 3.18/2.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a606) | c0_1(a606) | (~c1_1(a606)))),
% 3.18/2.33 inference(quant_inst,[status(thm)],[])).
% 3.18/2.33 tff(1095,plain,
% 3.18/2.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a606) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a606) | (~c1_1(a606))),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1094, 1093])).
% 3.18/2.33 tff(1096,plain,
% 3.18/2.33 (c0_1(a606)),
% 3.18/2.33 inference(unit_resolution,[status(thm)],[1095, 107, 1089, 1009, 1078, 1077, 1076, 997, 1012, 258, 1010])).
% 3.18/2.33 tff(1097,plain,
% 3.18/2.33 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W))))),
% 3.18/2.33 inference(bind,[status(th)],[])).
% 3.18/2.33 tff(1098,plain,
% 3.18/2.33 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 3.18/2.33 inference(quant_intro,[status(thm)],[1097])).
% 3.18/2.33 tff(1099,plain,
% 3.18/2.33 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 3.18/2.33 inference(rewrite,[status(thm)],[])).
% 3.18/2.33 tff(1100,plain,
% 3.18/2.33 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))))),
% 3.18/2.33 inference(bind,[status(th)],[])).
% 3.18/2.33 tff(1101,plain,
% 3.18/2.33 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 3.18/2.33 inference(quant_intro,[status(thm)],[1100])).
% 3.18/2.33 tff(1102,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause200')).
% 3.18/2.33 tff(1103,plain,
% 3.18/2.33 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1102, 1101])).
% 3.18/2.33 tff(1104,plain,
% 3.18/2.33 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1103, 1099])).
% 3.18/2.33 tff(1105,plain,(
% 3.18/2.33 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 3.18/2.33 inference(skolemize,[status(sab)],[1104])).
% 3.18/2.33 tff(1106,plain,
% 3.18/2.33 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1105, 1098])).
% 3.18/2.33 tff(1107,plain,
% 3.18/2.33 (((~hskp16) | (~c2_1(a606))) <=> ((~hskp16) | (~c2_1(a606)))),
% 3.18/2.33 inference(rewrite,[status(thm)],[])).
% 3.18/2.33 tff(1108,plain,
% 3.18/2.33 (((~c2_1(a606)) | (~hskp16)) <=> ((~hskp16) | (~c2_1(a606)))),
% 3.18/2.33 inference(rewrite,[status(thm)],[])).
% 3.18/2.33 tff(1109,axiom,((~c2_1(a606)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause100')).
% 3.18/2.33 tff(1110,plain,
% 3.18/2.33 ((~hskp16) | (~c2_1(a606))),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1109, 1108])).
% 3.18/2.33 tff(1111,plain,
% 3.18/2.33 ((~hskp16) | (~c2_1(a606))),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1110, 1107])).
% 3.18/2.33 tff(1112,plain,
% 3.18/2.33 (~c2_1(a606)),
% 3.18/2.33 inference(unit_resolution,[status(thm)],[1111, 1070])).
% 3.18/2.33 tff(1113,plain,
% 3.18/2.33 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))),
% 3.18/2.33 inference(bind,[status(th)],[])).
% 3.18/2.33 tff(1114,plain,
% 3.18/2.33 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.18/2.33 inference(quant_intro,[status(thm)],[1113])).
% 3.18/2.33 tff(1115,plain,
% 3.18/2.33 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.18/2.33 inference(rewrite,[status(thm)],[])).
% 3.18/2.33 tff(1116,plain,
% 3.18/2.33 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp28) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp28))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp28) <=> (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))))),
% 3.18/2.33 inference(bind,[status(th)],[])).
% 3.18/2.33 tff(1117,plain,
% 3.18/2.33 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.18/2.33 inference(quant_intro,[status(thm)],[1116])).
% 3.18/2.33 tff(1118,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause179')).
% 3.18/2.33 tff(1119,plain,
% 3.18/2.33 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1118, 1117])).
% 3.18/2.33 tff(1120,plain,
% 3.18/2.33 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1119, 1115])).
% 3.18/2.33 tff(1121,plain,(
% 3.18/2.33 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.18/2.33 inference(skolemize,[status(sab)],[1120])).
% 3.18/2.33 tff(1122,plain,
% 3.18/2.33 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1121, 1114])).
% 3.18/2.33 tff(1123,plain,
% 3.18/2.33 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | c2_1(a607) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp28 | c2_1(a607) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607) | (~c3_1(a607)))),
% 3.18/2.33 inference(rewrite,[status(thm)],[])).
% 3.18/2.33 tff(1124,plain,
% 3.18/2.33 ((hskp28 | (~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607) | c2_1(a607) | (~c3_1(a607))) <=> (hskp28 | c2_1(a607) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607) | (~c3_1(a607)))),
% 3.18/2.33 inference(rewrite,[status(thm)],[])).
% 3.18/2.33 tff(1125,plain,
% 3.18/2.33 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607) | c2_1(a607) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | c2_1(a607) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607) | (~c3_1(a607))))),
% 3.18/2.33 inference(monotonicity,[status(thm)],[1124])).
% 3.18/2.33 tff(1126,plain,
% 3.18/2.33 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607) | c2_1(a607) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp28 | c2_1(a607) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607) | (~c3_1(a607)))),
% 3.18/2.33 inference(transitivity,[status(thm)],[1125, 1123])).
% 3.18/2.33 tff(1127,plain,
% 3.18/2.33 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607) | c2_1(a607) | (~c3_1(a607)))),
% 3.18/2.33 inference(quant_inst,[status(thm)],[])).
% 3.18/2.33 tff(1128,plain,
% 3.18/2.33 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp28 | c2_1(a607) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607) | (~c3_1(a607))),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1127, 1126])).
% 3.18/2.33 tff(1129,plain,
% 3.18/2.33 (hskp28),
% 3.18/2.33 inference(unit_resolution,[status(thm)],[1128, 107, 321, 1009, 22, 997, 1122, 1, 1010])).
% 3.18/2.33 tff(1130,plain,
% 3.18/2.33 (((~hskp28) | c3_1(a612)) <=> ((~hskp28) | c3_1(a612))),
% 3.18/2.33 inference(rewrite,[status(thm)],[])).
% 3.18/2.33 tff(1131,axiom,((~hskp28) | c3_1(a612)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause41')).
% 3.18/2.33 tff(1132,plain,
% 3.18/2.33 ((~hskp28) | c3_1(a612)),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1131, 1130])).
% 3.18/2.33 tff(1133,plain,
% 3.18/2.33 ((~hskp28) | c3_1(a612)),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1132, 1130])).
% 3.18/2.33 tff(1134,plain,
% 3.18/2.33 ((~hskp28) | c3_1(a612)),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1133, 1130])).
% 3.18/2.33 tff(1135,plain,
% 3.18/2.33 ((~hskp28) | c3_1(a612)),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1134, 1130])).
% 3.18/2.33 tff(1136,plain,
% 3.18/2.33 ((~hskp28) | c3_1(a612)),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1135, 1130])).
% 3.18/2.33 tff(1137,plain,
% 3.18/2.33 ((~hskp28) | c3_1(a612)),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1136, 1130])).
% 3.18/2.33 tff(1138,plain,
% 3.18/2.33 ((~hskp28) | c3_1(a612)),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1137, 1130])).
% 3.18/2.33 tff(1139,plain,
% 3.18/2.33 ((~hskp28) | c3_1(a612)),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1138, 1130])).
% 3.18/2.33 tff(1140,plain,
% 3.18/2.33 (c3_1(a612)),
% 3.18/2.33 inference(unit_resolution,[status(thm)],[1139, 1129])).
% 3.18/2.33 tff(1141,plain,
% 3.18/2.33 (((~hskp28) | c2_1(a612)) <=> ((~hskp28) | c2_1(a612))),
% 3.18/2.33 inference(rewrite,[status(thm)],[])).
% 3.18/2.33 tff(1142,axiom,((~hskp28) | c2_1(a612)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause40')).
% 3.18/2.33 tff(1143,plain,
% 3.18/2.33 ((~hskp28) | c2_1(a612)),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1142, 1141])).
% 3.18/2.33 tff(1144,plain,
% 3.18/2.33 ((~hskp28) | c2_1(a612)),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1143, 1141])).
% 3.18/2.33 tff(1145,plain,
% 3.18/2.33 ((~hskp28) | c2_1(a612)),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1144, 1141])).
% 3.18/2.33 tff(1146,plain,
% 3.18/2.33 ((~hskp28) | c2_1(a612)),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1145, 1141])).
% 3.18/2.33 tff(1147,plain,
% 3.18/2.33 ((~hskp28) | c2_1(a612)),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1146, 1141])).
% 3.18/2.33 tff(1148,plain,
% 3.18/2.33 ((~hskp28) | c2_1(a612)),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1147, 1141])).
% 3.18/2.33 tff(1149,plain,
% 3.18/2.33 ((~hskp28) | c2_1(a612)),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1148, 1141])).
% 3.18/2.33 tff(1150,plain,
% 3.18/2.33 ((~hskp28) | c2_1(a612)),
% 3.18/2.33 inference(modus_ponens,[status(thm)],[1149, 1141])).
% 3.18/2.33 tff(1151,plain,
% 3.18/2.33 (c2_1(a612)),
% 3.18/2.33 inference(unit_resolution,[status(thm)],[1150, 1129])).
% 3.18/2.33 tff(1152,plain,
% 3.18/2.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a607) | c2_1(a607) | c2_1(a606) | (~ndr1_0) | (~c0_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a607) | c2_1(a607) | c2_1(a606) | (~ndr1_0) | (~c0_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a607)))),
% 3.18/2.34 inference(rewrite,[status(thm)],[])).
% 3.18/2.34 tff(1153,plain,
% 3.18/2.34 (((~ndr1_0) | (~c2_1(a612)) | (~c3_1(a612)) | (~c0_1(a612)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607))) <=> (c1_1(a607) | c2_1(a607) | c2_1(a606) | (~ndr1_0) | (~c0_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a607)))),
% 3.18/2.34 inference(rewrite,[status(thm)],[])).
% 3.18/2.34 tff(1154,plain,
% 3.18/2.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a612)) | (~c3_1(a612)) | (~c0_1(a612)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a607) | c2_1(a607) | c2_1(a606) | (~ndr1_0) | (~c0_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a607))))),
% 3.18/2.34 inference(monotonicity,[status(thm)],[1153])).
% 3.18/2.34 tff(1155,plain,
% 3.18/2.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a612)) | (~c3_1(a612)) | (~c0_1(a612)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a607) | c2_1(a607) | c2_1(a606) | (~ndr1_0) | (~c0_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a607)))),
% 3.18/2.34 inference(transitivity,[status(thm)],[1154, 1152])).
% 3.18/2.34 tff(1156,plain,
% 3.18/2.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a612)) | (~c3_1(a612)) | (~c0_1(a612)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)))),
% 3.18/2.34 inference(quant_inst,[status(thm)],[])).
% 3.18/2.34 tff(1157,plain,
% 3.18/2.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a607) | c2_1(a607) | c2_1(a606) | (~ndr1_0) | (~c0_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a607))),
% 3.18/2.34 inference(modus_ponens,[status(thm)],[1156, 1155])).
% 3.18/2.34 tff(1158,plain,
% 3.18/2.34 ((~c0_1(a612)) | (~c0_1(a606))),
% 3.18/2.34 inference(unit_resolution,[status(thm)],[1157, 107, 1151, 1140, 321, 1089, 66, 22, 1112, 1106])).
% 3.18/2.34 tff(1159,plain,
% 3.18/2.34 (~c0_1(a612)),
% 3.18/2.34 inference(unit_resolution,[status(thm)],[1158, 1096])).
% 3.18/2.34 tff(1160,plain,
% 3.18/2.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a607) | c2_1(a607) | c2_1(a606) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a607) | c2_1(a607) | c2_1(a606) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a607)))),
% 3.18/2.34 inference(rewrite,[status(thm)],[])).
% 3.18/2.34 tff(1161,plain,
% 3.18/2.34 (((~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607))) <=> (c1_1(a607) | c2_1(a607) | c2_1(a606) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a607)))),
% 3.18/2.34 inference(rewrite,[status(thm)],[])).
% 3.18/2.34 tff(1162,plain,
% 3.18/2.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a607) | c2_1(a607) | c2_1(a606) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a607))))),
% 3.18/2.34 inference(monotonicity,[status(thm)],[1161])).
% 3.18/2.34 tff(1163,plain,
% 3.18/2.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a607) | c2_1(a607) | c2_1(a606) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a607)))),
% 3.18/2.34 inference(transitivity,[status(thm)],[1162, 1160])).
% 3.18/2.34 tff(1164,plain,
% 3.18/2.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)))),
% 3.18/2.34 inference(quant_inst,[status(thm)],[])).
% 3.18/2.34 tff(1165,plain,
% 3.18/2.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a607) | c2_1(a607) | c2_1(a606) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a607))),
% 3.18/2.34 inference(modus_ponens,[status(thm)],[1164, 1163])).
% 3.18/2.34 tff(1166,plain,
% 3.18/2.34 ((~c0_1(a599)) | (~c0_1(a606))),
% 3.18/2.34 inference(unit_resolution,[status(thm)],[1165, 107, 321, 1089, 1078, 1077, 66, 22, 1112, 1106])).
% 3.18/2.34 tff(1167,plain,
% 3.18/2.34 (~c0_1(a599)),
% 3.18/2.34 inference(unit_resolution,[status(thm)],[1166, 1096])).
% 3.18/2.34 tff(1168,plain,
% 3.18/2.34 (^[V: $i, U: $i] : refl((hskp18 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp18 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))),
% 3.18/2.34 inference(bind,[status(th)],[])).
% 3.18/2.34 tff(1169,plain,
% 3.18/2.34 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.18/2.34 inference(quant_intro,[status(thm)],[1168])).
% 3.18/2.34 tff(1170,plain,
% 3.18/2.34 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.18/2.34 inference(rewrite,[status(thm)],[])).
% 3.18/2.34 tff(1171,plain,
% 3.18/2.34 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp18) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp18))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp18) <=> (hskp18 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp18) <=> (hskp18 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))))),
% 3.18/2.34 inference(bind,[status(th)],[])).
% 3.18/2.34 tff(1172,plain,
% 3.18/2.34 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp18) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.18/2.34 inference(quant_intro,[status(thm)],[1171])).
% 3.18/2.34 tff(1173,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause171')).
% 3.18/2.34 tff(1174,plain,
% 3.18/2.34 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.18/2.34 inference(modus_ponens,[status(thm)],[1173, 1172])).
% 3.18/2.34 tff(1175,plain,
% 3.18/2.34 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.18/2.34 inference(modus_ponens,[status(thm)],[1174, 1170])).
% 3.18/2.34 tff(1176,plain,(
% 3.18/2.34 ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.18/2.34 inference(skolemize,[status(sab)],[1175])).
% 3.18/2.34 tff(1177,plain,
% 3.18/2.34 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.18/2.34 inference(modus_ponens,[status(thm)],[1176, 1169])).
% 3.18/2.34 tff(1178,plain,
% 3.18/2.34 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp18 | c2_1(a607) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c0_1(a603)) | c0_1(a607) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp18 | c2_1(a607) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c0_1(a603)) | c0_1(a607) | (~c3_1(a607)))),
% 3.18/2.34 inference(rewrite,[status(thm)],[])).
% 3.18/2.34 tff(1179,plain,
% 3.18/2.34 ((hskp18 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c0_1(a603)) | c0_1(a607) | c2_1(a607) | (~c3_1(a607))) <=> (hskp18 | c2_1(a607) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c0_1(a603)) | c0_1(a607) | (~c3_1(a607)))),
% 3.18/2.34 inference(rewrite,[status(thm)],[])).
% 3.18/2.34 tff(1180,plain,
% 3.18/2.34 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c0_1(a603)) | c0_1(a607) | c2_1(a607) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp18 | c2_1(a607) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c0_1(a603)) | c0_1(a607) | (~c3_1(a607))))),
% 3.18/2.34 inference(monotonicity,[status(thm)],[1179])).
% 3.18/2.34 tff(1181,plain,
% 3.18/2.34 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c0_1(a603)) | c0_1(a607) | c2_1(a607) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp18 | c2_1(a607) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c0_1(a603)) | c0_1(a607) | (~c3_1(a607)))),
% 3.18/2.34 inference(transitivity,[status(thm)],[1180, 1178])).
% 3.18/2.34 tff(1182,plain,
% 3.18/2.34 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c0_1(a603)) | c0_1(a607) | c2_1(a607) | (~c3_1(a607)))),
% 3.18/2.34 inference(quant_inst,[status(thm)],[])).
% 3.18/2.34 tff(1183,plain,
% 3.18/2.34 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp18 | c2_1(a607) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c0_1(a603)) | c0_1(a607) | (~c3_1(a607))),
% 3.18/2.34 inference(modus_ponens,[status(thm)],[1182, 1181])).
% 3.18/2.34 tff(1184,plain,
% 3.18/2.34 (hskp18),
% 3.18/2.34 inference(unit_resolution,[status(thm)],[1183, 107, 321, 1009, 22, 998, 997, 1177, 1])).
% 3.18/2.34 tff(1185,plain,
% 3.18/2.34 (((~hskp18) | (~c2_1(a610))) <=> ((~hskp18) | (~c2_1(a610)))),
% 3.18/2.34 inference(rewrite,[status(thm)],[])).
% 3.18/2.34 tff(1186,plain,
% 3.18/2.34 (((~c2_1(a610)) | (~hskp18)) <=> ((~hskp18) | (~c2_1(a610)))),
% 3.18/2.34 inference(rewrite,[status(thm)],[])).
% 3.18/2.34 tff(1187,axiom,((~c2_1(a610)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause97')).
% 3.18/2.34 tff(1188,plain,
% 3.18/2.34 ((~hskp18) | (~c2_1(a610))),
% 3.18/2.34 inference(modus_ponens,[status(thm)],[1187, 1186])).
% 3.18/2.34 tff(1189,plain,
% 3.18/2.34 ((~hskp18) | (~c2_1(a610))),
% 3.18/2.34 inference(modus_ponens,[status(thm)],[1188, 1185])).
% 3.18/2.34 tff(1190,plain,
% 3.18/2.34 (~c2_1(a610)),
% 3.18/2.34 inference(unit_resolution,[status(thm)],[1189, 1184])).
% 3.18/2.34 tff(1191,plain,
% 3.18/2.34 (((~hskp18) | (~c0_1(a610))) <=> ((~hskp18) | (~c0_1(a610)))),
% 3.18/2.34 inference(rewrite,[status(thm)],[])).
% 3.18/2.34 tff(1192,plain,
% 3.18/2.34 (((~c0_1(a610)) | (~hskp18)) <=> ((~hskp18) | (~c0_1(a610)))),
% 3.18/2.34 inference(rewrite,[status(thm)],[])).
% 3.18/2.34 tff(1193,axiom,((~c0_1(a610)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause96')).
% 3.18/2.34 tff(1194,plain,
% 3.18/2.34 ((~hskp18) | (~c0_1(a610))),
% 3.18/2.34 inference(modus_ponens,[status(thm)],[1193, 1192])).
% 3.18/2.34 tff(1195,plain,
% 3.18/2.34 ((~hskp18) | (~c0_1(a610))),
% 3.18/2.34 inference(modus_ponens,[status(thm)],[1194, 1191])).
% 3.18/2.34 tff(1196,plain,
% 3.18/2.34 (~c0_1(a610)),
% 3.18/2.34 inference(unit_resolution,[status(thm)],[1195, 1184])).
% 3.18/2.34 tff(1197,plain,
% 3.18/2.34 (((~hskp18) | c3_1(a610)) <=> ((~hskp18) | c3_1(a610))),
% 3.18/2.34 inference(rewrite,[status(thm)],[])).
% 3.18/2.34 tff(1198,axiom,((~hskp18) | c3_1(a610)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause55')).
% 3.18/2.34 tff(1199,plain,
% 3.18/2.34 ((~hskp18) | c3_1(a610)),
% 3.18/2.34 inference(modus_ponens,[status(thm)],[1198, 1197])).
% 3.18/2.34 tff(1200,plain,
% 3.18/2.34 ((~hskp18) | c3_1(a610)),
% 3.18/2.34 inference(modus_ponens,[status(thm)],[1199, 1197])).
% 3.18/2.34 tff(1201,plain,
% 3.18/2.34 ((~hskp18) | c3_1(a610)),
% 3.18/2.34 inference(modus_ponens,[status(thm)],[1200, 1197])).
% 3.18/2.34 tff(1202,plain,
% 3.18/2.34 ((~hskp18) | c3_1(a610)),
% 3.18/2.34 inference(modus_ponens,[status(thm)],[1201, 1197])).
% 3.18/2.34 tff(1203,plain,
% 3.18/2.34 ((~hskp18) | c3_1(a610)),
% 3.18/2.34 inference(modus_ponens,[status(thm)],[1202, 1197])).
% 3.18/2.34 tff(1204,plain,
% 3.18/2.34 ((~hskp18) | c3_1(a610)),
% 3.18/2.34 inference(modus_ponens,[status(thm)],[1203, 1197])).
% 3.18/2.34 tff(1205,plain,
% 3.18/2.34 ((~hskp18) | c3_1(a610)),
% 3.18/2.34 inference(modus_ponens,[status(thm)],[1204, 1197])).
% 3.18/2.34 tff(1206,plain,
% 3.18/2.34 ((~hskp18) | c3_1(a610)),
% 3.18/2.34 inference(modus_ponens,[status(thm)],[1205, 1197])).
% 3.18/2.34 tff(1207,plain,
% 3.18/2.34 (c3_1(a610)),
% 3.18/2.34 inference(unit_resolution,[status(thm)],[1206, 1184])).
% 3.18/2.34 tff(1208,plain,
% 3.18/2.34 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | c0_1(a610) | c2_1(a610) | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | c0_1(a610) | c2_1(a610) | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a610)))),
% 3.18/2.34 inference(rewrite,[status(thm)],[])).
% 3.18/2.34 tff(1209,plain,
% 3.18/2.34 ((hskp27 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c0_1(a610) | c2_1(a610) | (~c3_1(a610))) <=> (hskp27 | c0_1(a610) | c2_1(a610) | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a610)))),
% 3.18/2.34 inference(rewrite,[status(thm)],[])).
% 3.18/2.34 tff(1210,plain,
% 3.18/2.34 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c0_1(a610) | c2_1(a610) | (~c3_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | c0_1(a610) | c2_1(a610) | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a610))))),
% 3.18/2.34 inference(monotonicity,[status(thm)],[1209])).
% 3.18/2.34 tff(1211,plain,
% 3.18/2.34 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c0_1(a610) | c2_1(a610) | (~c3_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | c0_1(a610) | c2_1(a610) | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a610)))),
% 3.18/2.34 inference(transitivity,[status(thm)],[1210, 1208])).
% 3.18/2.34 tff(1212,plain,
% 3.18/2.34 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c0_1(a610) | c2_1(a610) | (~c3_1(a610)))),
% 3.18/2.34 inference(quant_inst,[status(thm)],[])).
% 3.18/2.34 tff(1213,plain,
% 3.18/2.34 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | c0_1(a610) | c2_1(a610) | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a610))),
% 3.18/2.34 inference(modus_ponens,[status(thm)],[1212, 1211])).
% 3.18/2.34 tff(1214,plain,
% 3.18/2.34 (hskp27 | (~c0_1(a606))),
% 3.18/2.34 inference(unit_resolution,[status(thm)],[1213, 107, 1207, 1089, 1196, 1190, 1112, 540])).
% 3.18/2.34 tff(1215,plain,
% 3.18/2.34 (hskp27),
% 3.18/2.34 inference(unit_resolution,[status(thm)],[1214, 1096])).
% 3.18/2.34 tff(1216,plain,
% 3.18/2.34 (c3_1(a611)),
% 3.18/2.34 inference(unit_resolution,[status(thm)],[620, 1215])).
% 3.18/2.34 tff(1217,plain,
% 3.18/2.34 (c1_1(a611)),
% 3.18/2.34 inference(unit_resolution,[status(thm)],[631, 1215])).
% 3.18/2.34 tff(1218,plain,
% 3.18/2.34 (c0_1(a611)),
% 3.18/2.34 inference(unit_resolution,[status(thm)],[642, 1215])).
% 3.18/2.34 tff(1219,plain,
% 3.18/2.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a599) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c2_1(a599)) | c0_1(a599))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a599) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c2_1(a599)) | c0_1(a599))),
% 3.18/2.34 inference(rewrite,[status(thm)],[])).
% 3.18/2.34 tff(1220,plain,
% 3.18/2.34 (((~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599))) <=> (c1_1(a599) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c2_1(a599)) | c0_1(a599))),
% 3.18/2.34 inference(rewrite,[status(thm)],[])).
% 3.18/2.34 tff(1221,plain,
% 3.18/2.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a599) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c2_1(a599)) | c0_1(a599)))),
% 3.18/2.34 inference(monotonicity,[status(thm)],[1220])).
% 3.18/2.34 tff(1222,plain,
% 3.18/2.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a599) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c2_1(a599)) | c0_1(a599))),
% 3.18/2.34 inference(transitivity,[status(thm)],[1221, 1219])).
% 3.18/2.34 tff(1223,plain,
% 3.18/2.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))),
% 3.18/2.34 inference(quant_inst,[status(thm)],[])).
% 3.18/2.34 tff(1224,plain,
% 3.18/2.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a599) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c2_1(a599)) | c0_1(a599)),
% 3.18/2.34 inference(modus_ponens,[status(thm)],[1223, 1222])).
% 3.18/2.34 tff(1225,plain,
% 3.18/2.34 ($false),
% 3.18/2.34 inference(unit_resolution,[status(thm)],[1224, 107, 1151, 1140, 1218, 1217, 1216, 1078, 1012, 65, 1167, 1159])).
% 3.18/2.34 tff(1226,plain,(c0_1(a607) | (~c3_1(a607)) | c1_1(a607) | c2_1(a607) | (~c0_1(a603)) | c3_1(a603) | (~c2_1(a603)) | c1_1(a603) | hskp26), inference(lemma,lemma(discharge,[]))).
% 3.18/2.34 tff(1227,plain,
% 3.18/2.34 (c0_1(a607)),
% 3.18/2.34 inference(unit_resolution,[status(thm)],[1226, 1008, 66, 22, 1009, 997, 321, 998, 726])).
% 3.18/2.34 tff(1228,plain,
% 3.18/2.34 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))))),
% 3.18/2.34 inference(bind,[status(th)],[])).
% 3.18/2.34 tff(1229,plain,
% 3.18/2.34 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 3.18/2.34 inference(quant_intro,[status(thm)],[1228])).
% 3.18/2.34 tff(1230,plain,
% 3.18/2.34 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 3.18/2.34 inference(rewrite,[status(thm)],[])).
% 3.18/2.34 tff(1231,plain,
% 3.18/2.34 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp1) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) | hskp1))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))))),
% 3.18/2.34 inference(bind,[status(th)],[])).
% 3.18/2.34 tff(1232,plain,
% 3.18/2.34 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 3.18/2.34 inference(quant_intro,[status(thm)],[1231])).
% 3.18/2.34 tff(1233,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause181')).
% 3.18/2.34 tff(1234,plain,
% 3.18/2.34 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 3.18/2.34 inference(modus_ponens,[status(thm)],[1233, 1232])).
% 3.18/2.34 tff(1235,plain,
% 3.18/2.34 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 3.18/2.34 inference(modus_ponens,[status(thm)],[1234, 1230])).
% 3.18/2.34 tff(1236,plain,(
% 3.18/2.34 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 3.18/2.34 inference(skolemize,[status(sab)],[1235])).
% 3.18/2.34 tff(1237,plain,
% 3.18/2.34 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 3.18/2.34 inference(modus_ponens,[status(thm)],[1236, 1229])).
% 3.18/2.34 tff(1238,plain,
% 3.18/2.34 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | c1_1(a607) | c2_1(a607) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a607) | c2_1(a607) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c0_1(a607)))),
% 3.18/2.34 inference(rewrite,[status(thm)],[])).
% 3.18/2.34 tff(1239,plain,
% 3.18/2.34 ((hskp1 | (~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a607) | c2_1(a607) | (~c0_1(a607))) <=> (hskp1 | c1_1(a607) | c2_1(a607) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c0_1(a607)))),
% 3.18/2.34 inference(rewrite,[status(thm)],[])).
% 3.18/2.34 tff(1240,plain,
% 3.18/2.34 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a607) | c2_1(a607) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | c1_1(a607) | c2_1(a607) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c0_1(a607))))),
% 3.18/2.35 inference(monotonicity,[status(thm)],[1239])).
% 3.18/2.35 tff(1241,plain,
% 3.18/2.35 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a607) | c2_1(a607) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a607) | c2_1(a607) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c0_1(a607)))),
% 3.18/2.35 inference(transitivity,[status(thm)],[1240, 1238])).
% 3.18/2.35 tff(1242,plain,
% 3.18/2.35 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a607) | c2_1(a607) | (~c0_1(a607)))),
% 3.18/2.35 inference(quant_inst,[status(thm)],[])).
% 3.18/2.35 tff(1243,plain,
% 3.18/2.35 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a607) | c2_1(a607) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c0_1(a607))),
% 3.18/2.35 inference(modus_ponens,[status(thm)],[1242, 1241])).
% 3.18/2.35 tff(1244,plain,
% 3.18/2.35 (hskp1 | (~c2_1(a603)) | (~c0_1(a607))),
% 3.18/2.35 inference(unit_resolution,[status(thm)],[1243, 107, 1009, 66, 22, 997, 1237])).
% 3.18/2.35 tff(1245,plain,
% 3.18/2.35 (hskp1),
% 3.18/2.35 inference(unit_resolution,[status(thm)],[1244, 1227, 1008])).
% 3.18/2.35 tff(1246,plain,
% 3.18/2.35 (((~hskp1) | (~c0_1(a585))) <=> ((~hskp1) | (~c0_1(a585)))),
% 3.18/2.35 inference(rewrite,[status(thm)],[])).
% 3.18/2.35 tff(1247,plain,
% 3.18/2.35 (((~c0_1(a585)) | (~hskp1)) <=> ((~hskp1) | (~c0_1(a585)))),
% 3.18/2.35 inference(rewrite,[status(thm)],[])).
% 3.18/2.35 tff(1248,axiom,((~c0_1(a585)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause123')).
% 3.18/2.35 tff(1249,plain,
% 3.18/2.35 ((~hskp1) | (~c0_1(a585))),
% 3.18/2.35 inference(modus_ponens,[status(thm)],[1248, 1247])).
% 3.18/2.35 tff(1250,plain,
% 3.18/2.35 ((~hskp1) | (~c0_1(a585))),
% 3.18/2.35 inference(modus_ponens,[status(thm)],[1249, 1246])).
% 3.18/2.35 tff(1251,plain,
% 3.18/2.35 (~c0_1(a585)),
% 3.18/2.35 inference(unit_resolution,[status(thm)],[1250, 1245])).
% 3.18/2.35 tff(1252,plain,
% 3.18/2.35 (((~hskp1) | c2_1(a585)) <=> ((~hskp1) | c2_1(a585))),
% 3.18/2.35 inference(rewrite,[status(thm)],[])).
% 3.18/2.35 tff(1253,axiom,((~hskp1) | c2_1(a585)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause80')).
% 3.18/2.35 tff(1254,plain,
% 3.18/2.35 ((~hskp1) | c2_1(a585)),
% 3.18/2.35 inference(modus_ponens,[status(thm)],[1253, 1252])).
% 3.18/2.35 tff(1255,plain,
% 3.18/2.35 ((~hskp1) | c2_1(a585)),
% 3.18/2.35 inference(modus_ponens,[status(thm)],[1254, 1252])).
% 3.18/2.35 tff(1256,plain,
% 3.18/2.35 ((~hskp1) | c2_1(a585)),
% 3.18/2.35 inference(modus_ponens,[status(thm)],[1255, 1252])).
% 3.18/2.35 tff(1257,plain,
% 3.18/2.35 ((~hskp1) | c2_1(a585)),
% 3.18/2.35 inference(modus_ponens,[status(thm)],[1256, 1252])).
% 3.18/2.35 tff(1258,plain,
% 3.18/2.35 ((~hskp1) | c2_1(a585)),
% 3.18/2.35 inference(modus_ponens,[status(thm)],[1257, 1252])).
% 3.18/2.35 tff(1259,plain,
% 3.18/2.35 ((~hskp1) | c2_1(a585)),
% 3.18/2.35 inference(modus_ponens,[status(thm)],[1258, 1252])).
% 3.18/2.35 tff(1260,plain,
% 3.18/2.35 ((~hskp1) | c2_1(a585)),
% 3.18/2.35 inference(modus_ponens,[status(thm)],[1259, 1252])).
% 3.18/2.35 tff(1261,plain,
% 3.18/2.35 ((~hskp1) | c2_1(a585)),
% 3.18/2.35 inference(modus_ponens,[status(thm)],[1260, 1252])).
% 3.18/2.35 tff(1262,plain,
% 3.18/2.35 (c2_1(a585)),
% 3.18/2.35 inference(unit_resolution,[status(thm)],[1261, 1245])).
% 3.18/2.35 tff(1263,plain,
% 3.18/2.35 (((~hskp1) | c1_1(a585)) <=> ((~hskp1) | c1_1(a585))),
% 3.18/2.35 inference(rewrite,[status(thm)],[])).
% 3.18/2.35 tff(1264,axiom,((~hskp1) | c1_1(a585)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause79')).
% 3.18/2.35 tff(1265,plain,
% 3.18/2.35 ((~hskp1) | c1_1(a585)),
% 3.18/2.35 inference(modus_ponens,[status(thm)],[1264, 1263])).
% 3.18/2.35 tff(1266,plain,
% 3.18/2.35 ((~hskp1) | c1_1(a585)),
% 3.18/2.35 inference(modus_ponens,[status(thm)],[1265, 1263])).
% 3.18/2.35 tff(1267,plain,
% 3.18/2.35 ((~hskp1) | c1_1(a585)),
% 3.18/2.35 inference(modus_ponens,[status(thm)],[1266, 1263])).
% 3.18/2.35 tff(1268,plain,
% 3.18/2.35 ((~hskp1) | c1_1(a585)),
% 3.18/2.35 inference(modus_ponens,[status(thm)],[1267, 1263])).
% 3.18/2.35 tff(1269,plain,
% 3.18/2.35 ((~hskp1) | c1_1(a585)),
% 3.18/2.35 inference(modus_ponens,[status(thm)],[1268, 1263])).
% 3.18/2.35 tff(1270,plain,
% 3.18/2.35 ((~hskp1) | c1_1(a585)),
% 3.18/2.35 inference(modus_ponens,[status(thm)],[1269, 1263])).
% 3.18/2.35 tff(1271,plain,
% 3.18/2.35 ((~hskp1) | c1_1(a585)),
% 3.18/2.35 inference(modus_ponens,[status(thm)],[1270, 1263])).
% 3.18/2.35 tff(1272,plain,
% 3.18/2.35 ((~hskp1) | c1_1(a585)),
% 3.18/2.35 inference(modus_ponens,[status(thm)],[1271, 1263])).
% 3.18/2.35 tff(1273,plain,
% 3.18/2.35 (c1_1(a585)),
% 3.18/2.35 inference(unit_resolution,[status(thm)],[1272, 1245])).
% 3.18/2.35 tff(1274,plain,
% 3.18/2.35 (^[U: $i] : refl((hskp26 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp26 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 3.18/2.35 inference(bind,[status(th)],[])).
% 3.18/2.35 tff(1275,plain,
% 3.18/2.35 (![U: $i] : (hskp26 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp26 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 3.18/2.35 inference(quant_intro,[status(thm)],[1274])).
% 3.18/2.35 tff(1276,plain,
% 3.18/2.35 (![U: $i] : (hskp26 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp26 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 3.18/2.35 inference(rewrite,[status(thm)],[])).
% 3.18/2.35 tff(1277,plain,
% 3.18/2.35 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp26) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp26))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp26) <=> (hskp26 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp26) <=> (hskp26 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp26) | hskp28) <=> ((hskp26 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp28))), rewrite(((hskp26 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp28) <=> (hskp26 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp26) | hskp28) <=> (hskp26 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 3.18/2.35 inference(bind,[status(th)],[])).
% 3.18/2.35 tff(1278,plain,
% 3.18/2.35 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp26) | hskp28) <=> ![U: $i] : (hskp26 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 3.18/2.35 inference(quant_intro,[status(thm)],[1277])).
% 3.18/2.35 tff(1279,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp26) | hskp28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause150')).
% 3.18/2.35 tff(1280,plain,
% 3.18/2.35 (![U: $i] : (hskp26 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 3.18/2.35 inference(modus_ponens,[status(thm)],[1279, 1278])).
% 3.18/2.35 tff(1281,plain,
% 3.18/2.35 (![U: $i] : (hskp26 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 3.18/2.35 inference(modus_ponens,[status(thm)],[1280, 1276])).
% 3.18/2.35 tff(1282,plain,(
% 3.18/2.35 ![U: $i] : (hskp26 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 3.18/2.35 inference(skolemize,[status(sab)],[1281])).
% 3.18/2.35 tff(1283,plain,
% 3.18/2.35 (![U: $i] : (hskp26 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 3.18/2.35 inference(modus_ponens,[status(thm)],[1282, 1275])).
% 3.18/2.35 tff(1284,plain,
% 3.18/2.35 (((~![U: $i] : (hskp26 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp28 | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)))) <=> ((~![U: $i] : (hskp26 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp26 | hskp28 | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.18/2.35 inference(rewrite,[status(thm)],[])).
% 3.18/2.35 tff(1285,plain,
% 3.18/2.35 ((hskp26 | hskp28 | (~ndr1_0) | c2_1(a607) | (~c3_1(a607)) | (~c0_1(a607))) <=> (hskp26 | hskp28 | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.18/2.35 inference(rewrite,[status(thm)],[])).
% 3.18/2.35 tff(1286,plain,
% 3.18/2.35 (((~![U: $i] : (hskp26 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp28 | (~ndr1_0) | c2_1(a607) | (~c3_1(a607)) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp26 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp28 | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607))))),
% 3.18/2.35 inference(monotonicity,[status(thm)],[1285])).
% 3.18/2.35 tff(1287,plain,
% 3.18/2.35 (((~![U: $i] : (hskp26 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp28 | (~ndr1_0) | c2_1(a607) | (~c3_1(a607)) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp26 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp26 | hskp28 | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.18/2.35 inference(transitivity,[status(thm)],[1286, 1284])).
% 3.18/2.35 tff(1288,plain,
% 3.18/2.35 ((~![U: $i] : (hskp26 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp28 | (~ndr1_0) | c2_1(a607) | (~c3_1(a607)) | (~c0_1(a607)))),
% 3.18/2.35 inference(quant_inst,[status(thm)],[])).
% 3.18/2.35 tff(1289,plain,
% 3.18/2.35 ((~![U: $i] : (hskp26 | hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp26 | hskp28 | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607))),
% 3.18/2.35 inference(modus_ponens,[status(thm)],[1288, 1287])).
% 3.18/2.35 tff(1290,plain,
% 3.18/2.35 (hskp26 | hskp28 | (~c0_1(a607))),
% 3.18/2.35 inference(unit_resolution,[status(thm)],[1289, 107, 321, 22, 1283])).
% 3.18/2.35 tff(1291,plain,
% 3.18/2.35 (hskp28),
% 3.18/2.35 inference(unit_resolution,[status(thm)],[1290, 1227, 726])).
% 3.18/2.35 tff(1292,plain,
% 3.18/2.35 (c3_1(a612)),
% 3.18/2.35 inference(unit_resolution,[status(thm)],[1139, 1291])).
% 3.18/2.35 tff(1293,plain,
% 3.18/2.35 (c2_1(a612)),
% 3.18/2.35 inference(unit_resolution,[status(thm)],[1150, 1291])).
% 3.18/2.35 tff(1294,plain,
% 3.18/2.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c3_1(a607)))),
% 3.18/2.35 inference(rewrite,[status(thm)],[])).
% 3.18/2.35 tff(1295,plain,
% 3.18/2.35 (((~ndr1_0) | (~c2_1(a612)) | (~c3_1(a612)) | (~c0_1(a612)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585))) <=> (c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c3_1(a607)))),
% 3.18/2.35 inference(rewrite,[status(thm)],[])).
% 3.18/2.35 tff(1296,plain,
% 3.18/2.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a612)) | (~c3_1(a612)) | (~c0_1(a612)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c3_1(a607))))),
% 3.18/2.35 inference(monotonicity,[status(thm)],[1295])).
% 3.18/2.35 tff(1297,plain,
% 3.18/2.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a612)) | (~c3_1(a612)) | (~c0_1(a612)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c3_1(a607)))),
% 3.18/2.35 inference(transitivity,[status(thm)],[1296, 1294])).
% 3.18/2.35 tff(1298,plain,
% 3.18/2.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a612)) | (~c3_1(a612)) | (~c0_1(a612)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))),
% 3.18/2.35 inference(quant_inst,[status(thm)],[])).
% 3.18/2.35 tff(1299,plain,
% 3.18/2.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c3_1(a607))),
% 3.18/2.35 inference(modus_ponens,[status(thm)],[1298, 1297])).
% 3.18/2.35 tff(1300,plain,
% 3.18/2.35 (~c0_1(a612)),
% 3.18/2.35 inference(unit_resolution,[status(thm)],[1299, 107, 1293, 1292, 321, 1273, 1262, 66, 22, 1251, 11])).
% 3.18/2.35 tff(1301,plain,
% 3.18/2.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c3_1(a607)))),
% 3.18/2.35 inference(rewrite,[status(thm)],[])).
% 3.18/2.35 tff(1302,plain,
% 3.18/2.35 (((~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585))) <=> (c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c3_1(a607)))),
% 3.18/2.35 inference(rewrite,[status(thm)],[])).
% 3.18/2.35 tff(1303,plain,
% 3.18/2.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c3_1(a607))))),
% 3.18/2.35 inference(monotonicity,[status(thm)],[1302])).
% 3.18/2.35 tff(1304,plain,
% 3.18/2.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c3_1(a607)))),
% 3.18/2.35 inference(transitivity,[status(thm)],[1303, 1301])).
% 3.18/2.35 tff(1305,plain,
% 3.18/2.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))),
% 3.18/2.35 inference(quant_inst,[status(thm)],[])).
% 3.18/2.35 tff(1306,plain,
% 3.18/2.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c3_1(a607))),
% 3.18/2.35 inference(modus_ponens,[status(thm)],[1305, 1304])).
% 3.18/2.35 tff(1307,plain,
% 3.18/2.35 (~c0_1(a599)),
% 3.18/2.35 inference(unit_resolution,[status(thm)],[1306, 107, 321, 1078, 1077, 1273, 1262, 66, 22, 1251, 11])).
% 3.18/2.35 tff(1308,plain,
% 3.18/2.35 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 3.18/2.35 inference(bind,[status(th)],[])).
% 3.18/2.35 tff(1309,plain,
% 3.18/2.35 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 3.18/2.35 inference(quant_intro,[status(thm)],[1308])).
% 3.18/2.35 tff(1310,plain,
% 3.18/2.35 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 3.18/2.35 inference(rewrite,[status(thm)],[])).
% 3.18/2.35 tff(1311,plain,
% 3.18/2.35 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp8) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp8))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 3.18/2.35 inference(bind,[status(th)],[])).
% 3.18/2.35 tff(1312,plain,
% 3.18/2.35 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 3.18/2.35 inference(quant_intro,[status(thm)],[1311])).
% 3.18/2.35 tff(1313,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause175')).
% 3.18/2.35 tff(1314,plain,
% 3.18/2.35 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 3.18/2.35 inference(modus_ponens,[status(thm)],[1313, 1312])).
% 3.18/2.35 tff(1315,plain,
% 3.18/2.35 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 3.18/2.35 inference(modus_ponens,[status(thm)],[1314, 1310])).
% 3.18/2.35 tff(1316,plain,(
% 3.18/2.35 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 3.18/2.35 inference(skolemize,[status(sab)],[1315])).
% 3.18/2.35 tff(1317,plain,
% 3.18/2.35 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 3.18/2.35 inference(modus_ponens,[status(thm)],[1316, 1309])).
% 3.18/2.35 tff(1318,plain,
% 3.18/2.35 (^[V: $i, U: $i] : refl((hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))))),
% 3.18/2.35 inference(bind,[status(th)],[])).
% 3.18/2.35 tff(1319,plain,
% 3.18/2.35 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.18/2.35 inference(quant_intro,[status(thm)],[1318])).
% 3.18/2.35 tff(1320,plain,
% 3.18/2.35 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.18/2.35 inference(rewrite,[status(thm)],[])).
% 3.18/2.35 tff(1321,plain,
% 3.18/2.35 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp23) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | hskp23))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | hskp23) <=> (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp23) <=> (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))))),
% 3.18/2.35 inference(bind,[status(th)],[])).
% 3.18/2.35 tff(1322,plain,
% 3.18/2.35 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp23) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.18/2.35 inference(quant_intro,[status(thm)],[1321])).
% 3.18/2.35 tff(1323,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause182')).
% 3.18/2.35 tff(1324,plain,
% 3.18/2.35 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.18/2.35 inference(modus_ponens,[status(thm)],[1323, 1322])).
% 3.18/2.35 tff(1325,plain,
% 3.18/2.35 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.18/2.35 inference(modus_ponens,[status(thm)],[1324, 1320])).
% 3.18/2.35 tff(1326,plain,(
% 3.18/2.35 ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.18/2.35 inference(skolemize,[status(sab)],[1325])).
% 3.18/2.35 tff(1327,plain,
% 3.18/2.35 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 3.18/2.35 inference(modus_ponens,[status(thm)],[1326, 1319])).
% 3.18/2.35 tff(1328,plain,
% 3.18/2.35 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp23 | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp23 | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.18/2.35 inference(rewrite,[status(thm)],[])).
% 3.18/2.35 tff(1329,plain,
% 3.18/2.35 ((hskp23 | (~ndr1_0) | c2_1(a607) | (~c3_1(a607)) | (~c0_1(a607)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607))) <=> (hskp23 | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.18/2.35 inference(rewrite,[status(thm)],[])).
% 3.18/2.35 tff(1330,plain,
% 3.18/2.35 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a607) | (~c3_1(a607)) | (~c0_1(a607)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp23 | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607))))),
% 3.18/2.35 inference(monotonicity,[status(thm)],[1329])).
% 3.18/2.35 tff(1331,plain,
% 3.18/2.35 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a607) | (~c3_1(a607)) | (~c0_1(a607)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp23 | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.18/2.35 inference(transitivity,[status(thm)],[1330, 1328])).
% 3.18/2.35 tff(1332,plain,
% 3.18/2.35 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a607) | (~c3_1(a607)) | (~c0_1(a607)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)))),
% 3.18/2.35 inference(quant_inst,[status(thm)],[])).
% 3.18/2.35 tff(1333,plain,
% 3.18/2.35 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp23 | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607))),
% 3.18/2.35 inference(modus_ponens,[status(thm)],[1332, 1331])).
% 3.18/2.35 tff(1334,plain,
% 3.18/2.35 (hskp23 | (~c0_1(a607))),
% 3.18/2.35 inference(unit_resolution,[status(thm)],[1333, 107, 321, 66, 22, 1327])).
% 3.18/2.35 tff(1335,plain,
% 3.18/2.35 (hskp23),
% 3.18/2.35 inference(unit_resolution,[status(thm)],[1334, 1227])).
% 3.18/2.35 tff(1336,plain,
% 3.18/2.35 (~c1_1(a636)),
% 3.18/2.35 inference(unit_resolution,[status(thm)],[475, 1335])).
% 3.18/2.35 tff(1337,plain,
% 3.18/2.35 (~c0_1(a636)),
% 3.18/2.35 inference(unit_resolution,[status(thm)],[481, 1335])).
% 3.18/2.35 tff(1338,plain,
% 3.18/2.35 (c3_1(a636)),
% 3.18/2.35 inference(unit_resolution,[status(thm)],[492, 1335])).
% 3.18/2.35 tff(1339,plain,
% 3.18/2.35 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | c0_1(a636) | c1_1(a636) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a636)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a636) | c1_1(a636) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a636)))),
% 3.18/2.36 inference(rewrite,[status(thm)],[])).
% 3.18/2.36 tff(1340,plain,
% 3.18/2.36 ((hskp8 | (~ndr1_0) | c0_1(a585) | (~c2_1(a585)) | (~c1_1(a585)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636))) <=> (hskp8 | c0_1(a636) | c1_1(a636) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a636)))),
% 3.18/2.36 inference(rewrite,[status(thm)],[])).
% 3.18/2.36 tff(1341,plain,
% 3.18/2.36 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a585) | (~c2_1(a585)) | (~c1_1(a585)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | c0_1(a636) | c1_1(a636) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a636))))),
% 3.18/2.36 inference(monotonicity,[status(thm)],[1340])).
% 3.18/2.36 tff(1342,plain,
% 3.18/2.36 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a585) | (~c2_1(a585)) | (~c1_1(a585)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a636) | c1_1(a636) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a636)))),
% 3.18/2.36 inference(transitivity,[status(thm)],[1341, 1339])).
% 3.18/2.36 tff(1343,plain,
% 3.18/2.36 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a585) | (~c2_1(a585)) | (~c1_1(a585)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)))),
% 3.18/2.36 inference(quant_inst,[status(thm)],[])).
% 3.18/2.36 tff(1344,plain,
% 3.18/2.36 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a636) | c1_1(a636) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a636))),
% 3.18/2.36 inference(modus_ponens,[status(thm)],[1343, 1342])).
% 3.18/2.36 tff(1345,plain,
% 3.18/2.36 (hskp8),
% 3.18/2.36 inference(unit_resolution,[status(thm)],[1344, 107, 1338, 1273, 1262, 1337, 1336, 1251, 1317])).
% 3.18/2.36 tff(1346,plain,
% 3.18/2.36 (c3_1(a593)),
% 3.18/2.36 inference(unit_resolution,[status(thm)],[511, 1345])).
% 3.18/2.36 tff(1347,plain,
% 3.18/2.36 (c1_1(a593)),
% 3.18/2.36 inference(unit_resolution,[status(thm)],[522, 1345])).
% 3.18/2.36 tff(1348,plain,
% 3.18/2.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a599) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a599)) | c0_1(a599))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a599) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a599)) | c0_1(a599))),
% 3.18/2.36 inference(rewrite,[status(thm)],[])).
% 3.18/2.36 tff(1349,plain,
% 3.18/2.36 (((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599))) <=> (c1_1(a599) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a599)) | c0_1(a599))),
% 3.18/2.36 inference(rewrite,[status(thm)],[])).
% 3.18/2.36 tff(1350,plain,
% 3.18/2.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a599) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a599)) | c0_1(a599)))),
% 3.18/2.36 inference(monotonicity,[status(thm)],[1349])).
% 3.18/2.36 tff(1351,plain,
% 3.18/2.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a599) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a599)) | c0_1(a599))),
% 3.18/2.36 inference(transitivity,[status(thm)],[1350, 1348])).
% 3.18/2.36 tff(1352,plain,
% 3.18/2.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))),
% 3.18/2.36 inference(quant_inst,[status(thm)],[])).
% 3.18/2.36 tff(1353,plain,
% 3.18/2.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a599) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a599)) | c0_1(a599)),
% 3.18/2.36 inference(modus_ponens,[status(thm)],[1352, 1351])).
% 3.18/2.36 tff(1354,plain,
% 3.18/2.36 (~c0_1(a593)),
% 3.18/2.36 inference(unit_resolution,[status(thm)],[1353, 107, 1293, 1292, 1078, 1347, 1346, 1012, 65, 1307, 1300])).
% 3.18/2.36 tff(1355,plain,
% 3.18/2.36 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)))),
% 3.18/2.36 inference(bind,[status(th)],[])).
% 3.18/2.36 tff(1356,plain,
% 3.18/2.36 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 3.18/2.36 inference(quant_intro,[status(thm)],[1355])).
% 3.18/2.36 tff(1357,plain,
% 3.18/2.36 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 3.18/2.36 inference(rewrite,[status(thm)],[])).
% 3.18/2.36 tff(1358,plain,
% 3.18/2.36 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))))),
% 3.18/2.36 inference(bind,[status(th)],[])).
% 3.18/2.36 tff(1359,plain,
% 3.18/2.36 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 3.18/2.36 inference(quant_intro,[status(thm)],[1358])).
% 3.18/2.36 tff(1360,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause195')).
% 3.18/2.36 tff(1361,plain,
% 3.18/2.36 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 3.18/2.36 inference(modus_ponens,[status(thm)],[1360, 1359])).
% 3.18/2.36 tff(1362,plain,
% 3.18/2.36 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 3.18/2.36 inference(modus_ponens,[status(thm)],[1361, 1357])).
% 3.18/2.36 tff(1363,plain,(
% 3.18/2.36 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 3.18/2.36 inference(skolemize,[status(sab)],[1362])).
% 3.18/2.36 tff(1364,plain,
% 3.18/2.36 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 3.18/2.36 inference(modus_ponens,[status(thm)],[1363, 1356])).
% 3.18/2.36 tff(1365,plain,
% 3.18/2.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a607)))),
% 3.18/2.36 inference(rewrite,[status(thm)],[])).
% 3.18/2.36 tff(1366,plain,
% 3.18/2.36 (((~ndr1_0) | (~c2_1(a587)) | (~c3_1(a587)) | (~c0_1(a587)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585))) <=> (c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a607)))),
% 3.18/2.36 inference(rewrite,[status(thm)],[])).
% 3.18/2.36 tff(1367,plain,
% 3.18/2.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a587)) | (~c3_1(a587)) | (~c0_1(a587)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a607))))),
% 3.18/2.36 inference(monotonicity,[status(thm)],[1366])).
% 3.18/2.36 tff(1368,plain,
% 3.18/2.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a587)) | (~c3_1(a587)) | (~c0_1(a587)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a607)))),
% 3.18/2.36 inference(transitivity,[status(thm)],[1367, 1365])).
% 3.18/2.36 tff(1369,plain,
% 3.18/2.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a587)) | (~c3_1(a587)) | (~c0_1(a587)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))),
% 3.18/2.36 inference(quant_inst,[status(thm)],[])).
% 3.18/2.36 tff(1370,plain,
% 3.18/2.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a607))),
% 3.18/2.36 inference(modus_ponens,[status(thm)],[1369, 1368])).
% 3.18/2.36 tff(1371,plain,
% 3.18/2.36 (~c3_1(a587)),
% 3.18/2.36 inference(unit_resolution,[status(thm)],[1370, 107, 321, 1000, 999, 1273, 1262, 66, 22, 1251, 11])).
% 3.18/2.36 tff(1372,plain,
% 3.18/2.36 (~hskp20),
% 3.18/2.36 inference(unit_resolution,[status(thm)],[734, 1338, 726, 1337, 1336])).
% 3.18/2.36 tff(1373,plain,
% 3.18/2.36 (^[U: $i] : refl((hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 3.18/2.36 inference(bind,[status(th)],[])).
% 3.18/2.36 tff(1374,plain,
% 3.18/2.36 (![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 3.18/2.36 inference(quant_intro,[status(thm)],[1373])).
% 3.18/2.36 tff(1375,plain,
% 3.18/2.36 (![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 3.18/2.36 inference(rewrite,[status(thm)],[])).
% 3.18/2.36 tff(1376,plain,
% 3.18/2.36 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp7) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp7))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp7) <=> (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp7) | hskp20) <=> ((hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp20))), rewrite(((hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp20) <=> (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp7) | hskp20) <=> (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 3.18/2.36 inference(bind,[status(th)],[])).
% 3.18/2.36 tff(1377,plain,
% 3.18/2.36 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp7) | hskp20) <=> ![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 3.18/2.36 inference(quant_intro,[status(thm)],[1376])).
% 3.18/2.36 tff(1378,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp7) | hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause159')).
% 3.18/2.36 tff(1379,plain,
% 3.18/2.36 (![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 3.18/2.36 inference(modus_ponens,[status(thm)],[1378, 1377])).
% 3.18/2.36 tff(1380,plain,
% 3.18/2.36 (![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 3.18/2.36 inference(modus_ponens,[status(thm)],[1379, 1375])).
% 3.18/2.36 tff(1381,plain,(
% 3.18/2.36 ![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 3.18/2.36 inference(skolemize,[status(sab)],[1380])).
% 3.18/2.36 tff(1382,plain,
% 3.18/2.36 (![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 3.18/2.36 inference(modus_ponens,[status(thm)],[1381, 1374])).
% 3.18/2.36 tff(1383,plain,
% 3.18/2.36 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | hskp7 | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)))),
% 3.18/2.36 inference(rewrite,[status(thm)],[])).
% 3.18/2.36 tff(1384,plain,
% 3.18/2.36 ((hskp20 | hskp7 | (~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603))) <=> (hskp20 | hskp7 | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)))),
% 3.18/2.36 inference(rewrite,[status(thm)],[])).
% 3.18/2.36 tff(1385,plain,
% 3.18/2.36 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603))))),
% 3.18/2.36 inference(monotonicity,[status(thm)],[1384])).
% 3.18/2.36 tff(1386,plain,
% 3.18/2.36 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | hskp7 | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)))),
% 3.18/2.36 inference(transitivity,[status(thm)],[1385, 1383])).
% 3.18/2.36 tff(1387,plain,
% 3.18/2.36 ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)))),
% 3.18/2.36 inference(quant_inst,[status(thm)],[])).
% 3.18/2.36 tff(1388,plain,
% 3.18/2.36 ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | hskp7 | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603))),
% 3.18/2.36 inference(modus_ponens,[status(thm)],[1387, 1386])).
% 3.18/2.36 tff(1389,plain,
% 3.18/2.36 (hskp20 | hskp7 | (~c2_1(a603))),
% 3.18/2.36 inference(unit_resolution,[status(thm)],[1388, 107, 1009, 997, 1382])).
% 3.18/2.36 tff(1390,plain,
% 3.18/2.36 (hskp7),
% 3.18/2.36 inference(unit_resolution,[status(thm)],[1389, 1372, 1008])).
% 3.18/2.36 tff(1391,plain,
% 3.18/2.36 (~c3_1(a592)),
% 3.18/2.36 inference(unit_resolution,[status(thm)],[811, 1390])).
% 3.18/2.36 tff(1392,plain,
% 3.18/2.36 (~c0_1(a592)),
% 3.18/2.36 inference(unit_resolution,[status(thm)],[817, 1390])).
% 3.18/2.36 tff(1393,plain,
% 3.18/2.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a603) | c1_1(a599) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a603) | c1_1(a599) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)))),
% 3.18/2.36 inference(rewrite,[status(thm)],[])).
% 3.18/2.36 tff(1394,plain,
% 3.18/2.36 (((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a592) | c0_1(a592) | (~c1_1(a592))) <=> (c3_1(a603) | c1_1(a599) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)))),
% 3.18/2.36 inference(rewrite,[status(thm)],[])).
% 3.18/2.36 tff(1395,plain,
% 3.18/2.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a592) | c0_1(a592) | (~c1_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a603) | c1_1(a599) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603))))),
% 3.18/2.36 inference(monotonicity,[status(thm)],[1394])).
% 3.18/2.36 tff(1396,plain,
% 3.18/2.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a592) | c0_1(a592) | (~c1_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a603) | c1_1(a599) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)))),
% 3.18/2.36 inference(transitivity,[status(thm)],[1395, 1393])).
% 3.18/2.36 tff(1397,plain,
% 3.18/2.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a592) | c0_1(a592) | (~c1_1(a592)))),
% 3.18/2.36 inference(quant_inst,[status(thm)],[])).
% 3.18/2.36 tff(1398,plain,
% 3.18/2.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a603) | c1_1(a599) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603))),
% 3.18/2.36 inference(modus_ponens,[status(thm)],[1397, 1396])).
% 3.18/2.36 tff(1399,plain,
% 3.18/2.36 (~c1_1(a592)),
% 3.18/2.36 inference(unit_resolution,[status(thm)],[1398, 107, 1009, 1078, 1077, 997, 1012, 1392, 1391, 258, 1008])).
% 3.18/2.36 tff(1400,plain,
% 3.18/2.36 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a603) | c3_1(a603) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | (~c2_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a603) | c3_1(a603) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | (~c2_1(a603)))),
% 3.18/2.36 inference(rewrite,[status(thm)],[])).
% 3.18/2.36 tff(1401,plain,
% 3.18/2.36 ((hskp2 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c3_1(a592) | c1_1(a592) | c0_1(a592)) <=> (hskp2 | c1_1(a603) | c3_1(a603) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | (~c2_1(a603)))),
% 3.18/2.36 inference(rewrite,[status(thm)],[])).
% 3.18/2.36 tff(1402,plain,
% 3.18/2.36 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c3_1(a592) | c1_1(a592) | c0_1(a592))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a603) | c3_1(a603) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | (~c2_1(a603))))),
% 3.18/2.36 inference(monotonicity,[status(thm)],[1401])).
% 3.18/2.36 tff(1403,plain,
% 3.18/2.36 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c3_1(a592) | c1_1(a592) | c0_1(a592))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a603) | c3_1(a603) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | (~c2_1(a603)))),
% 3.18/2.36 inference(transitivity,[status(thm)],[1402, 1400])).
% 3.18/2.36 tff(1404,plain,
% 3.18/2.36 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c3_1(a592) | c1_1(a592) | c0_1(a592))),
% 3.18/2.36 inference(quant_inst,[status(thm)],[])).
% 3.18/2.36 tff(1405,plain,
% 3.18/2.36 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a603) | c3_1(a603) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | (~c2_1(a603))),
% 3.18/2.36 inference(modus_ponens,[status(thm)],[1404, 1403])).
% 3.18/2.36 tff(1406,plain,
% 3.18/2.36 (hskp2),
% 3.18/2.36 inference(unit_resolution,[status(thm)],[1405, 107, 998, 997, 1392, 1391, 200, 1399, 1008])).
% 3.18/2.36 tff(1407,plain,
% 3.18/2.36 (~c3_1(a586)),
% 3.18/2.36 inference(unit_resolution,[status(thm)],[218, 1406])).
% 3.18/2.36 tff(1408,plain,
% 3.18/2.36 (c1_1(a586)),
% 3.18/2.36 inference(unit_resolution,[status(thm)],[229, 1406])).
% 3.18/2.36 tff(1409,plain,
% 3.18/2.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a599)) | (~c2_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a599)) | (~c2_1(a599)))),
% 3.18/2.36 inference(rewrite,[status(thm)],[])).
% 3.18/2.36 tff(1410,plain,
% 3.18/2.36 (((~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586))) <=> (c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a599)) | (~c2_1(a599)))),
% 3.18/2.36 inference(rewrite,[status(thm)],[])).
% 3.18/2.36 tff(1411,plain,
% 3.18/2.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a599)) | (~c2_1(a599))))),
% 3.18/2.37 inference(monotonicity,[status(thm)],[1410])).
% 3.18/2.37 tff(1412,plain,
% 3.18/2.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a599)) | (~c2_1(a599)))),
% 3.18/2.37 inference(transitivity,[status(thm)],[1411, 1409])).
% 3.18/2.37 tff(1413,plain,
% 3.18/2.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))),
% 3.18/2.37 inference(quant_inst,[status(thm)],[])).
% 3.18/2.37 tff(1414,plain,
% 3.18/2.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a599)) | (~c2_1(a599))),
% 3.18/2.37 inference(modus_ponens,[status(thm)],[1413, 1412])).
% 3.18/2.37 tff(1415,plain,
% 3.18/2.37 (c0_1(a586)),
% 3.18/2.37 inference(unit_resolution,[status(thm)],[1414, 107, 1078, 1077, 1000, 999, 1408, 1012, 1407, 258, 1371])).
% 3.18/2.37 tff(1416,plain,
% 3.18/2.37 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))),
% 3.18/2.37 inference(bind,[status(th)],[])).
% 3.18/2.37 tff(1417,plain,
% 3.18/2.37 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 3.18/2.37 inference(quant_intro,[status(thm)],[1416])).
% 3.18/2.37 tff(1418,plain,
% 3.18/2.37 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 3.18/2.37 inference(rewrite,[status(thm)],[])).
% 3.18/2.37 tff(1419,plain,
% 3.18/2.37 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp16) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp16))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))))),
% 3.18/2.37 inference(bind,[status(th)],[])).
% 3.18/2.37 tff(1420,plain,
% 3.18/2.37 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 3.18/2.37 inference(quant_intro,[status(thm)],[1419])).
% 3.18/2.37 tff(1421,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause187')).
% 3.18/2.37 tff(1422,plain,
% 3.18/2.37 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 3.18/2.37 inference(modus_ponens,[status(thm)],[1421, 1420])).
% 3.18/2.37 tff(1423,plain,
% 3.18/2.37 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 3.18/2.37 inference(modus_ponens,[status(thm)],[1422, 1418])).
% 3.18/2.37 tff(1424,plain,(
% 3.18/2.37 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 3.18/2.37 inference(skolemize,[status(sab)],[1423])).
% 3.18/2.37 tff(1425,plain,
% 3.18/2.37 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 3.18/2.37 inference(modus_ponens,[status(thm)],[1424, 1417])).
% 3.18/2.37 tff(1426,plain,
% 3.18/2.37 (((~hskp28) | c1_1(a612)) <=> ((~hskp28) | c1_1(a612))),
% 3.18/2.37 inference(rewrite,[status(thm)],[])).
% 3.18/2.37 tff(1427,axiom,((~hskp28) | c1_1(a612)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause39')).
% 3.18/2.37 tff(1428,plain,
% 3.18/2.37 ((~hskp28) | c1_1(a612)),
% 3.18/2.37 inference(modus_ponens,[status(thm)],[1427, 1426])).
% 3.18/2.37 tff(1429,plain,
% 3.18/2.37 ((~hskp28) | c1_1(a612)),
% 3.18/2.37 inference(modus_ponens,[status(thm)],[1428, 1426])).
% 3.18/2.37 tff(1430,plain,
% 3.18/2.37 ((~hskp28) | c1_1(a612)),
% 3.18/2.37 inference(modus_ponens,[status(thm)],[1429, 1426])).
% 3.18/2.37 tff(1431,plain,
% 3.18/2.37 ((~hskp28) | c1_1(a612)),
% 3.18/2.37 inference(modus_ponens,[status(thm)],[1430, 1426])).
% 3.18/2.37 tff(1432,plain,
% 3.18/2.37 ((~hskp28) | c1_1(a612)),
% 3.18/2.37 inference(modus_ponens,[status(thm)],[1431, 1426])).
% 3.18/2.37 tff(1433,plain,
% 3.18/2.37 ((~hskp28) | c1_1(a612)),
% 3.18/2.37 inference(modus_ponens,[status(thm)],[1432, 1426])).
% 3.18/2.37 tff(1434,plain,
% 3.18/2.37 ((~hskp28) | c1_1(a612)),
% 3.18/2.37 inference(modus_ponens,[status(thm)],[1433, 1426])).
% 3.18/2.37 tff(1435,plain,
% 3.18/2.37 ((~hskp28) | c1_1(a612)),
% 3.18/2.37 inference(modus_ponens,[status(thm)],[1434, 1426])).
% 3.18/2.37 tff(1436,plain,
% 3.18/2.37 (c1_1(a612)),
% 3.18/2.37 inference(unit_resolution,[status(thm)],[1435, 1291])).
% 3.18/2.37 tff(1437,plain,
% 3.18/2.37 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp16 | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp16 | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))),
% 3.18/2.37 inference(rewrite,[status(thm)],[])).
% 3.18/2.37 tff(1438,plain,
% 3.18/2.37 ((hskp16 | (~ndr1_0) | c3_1(a586) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612))) <=> (hskp16 | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))),
% 3.18/2.37 inference(rewrite,[status(thm)],[])).
% 3.18/2.37 tff(1439,plain,
% 3.18/2.37 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a586) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp16 | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612))))),
% 3.18/2.37 inference(monotonicity,[status(thm)],[1438])).
% 3.18/2.37 tff(1440,plain,
% 3.18/2.37 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a586) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp16 | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))),
% 3.18/2.37 inference(transitivity,[status(thm)],[1439, 1437])).
% 3.18/2.37 tff(1441,plain,
% 3.18/2.37 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a586) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))),
% 3.18/2.37 inference(quant_inst,[status(thm)],[])).
% 3.18/2.37 tff(1442,plain,
% 3.18/2.37 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp16 | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612))),
% 3.18/2.37 inference(modus_ponens,[status(thm)],[1441, 1440])).
% 3.18/2.37 tff(1443,plain,
% 3.18/2.37 (hskp16 | (~c0_1(a586))),
% 3.18/2.37 inference(unit_resolution,[status(thm)],[1442, 107, 1436, 1292, 1408, 1407, 1425, 1300])).
% 3.18/2.37 tff(1444,plain,
% 3.18/2.37 (hskp16),
% 3.18/2.37 inference(unit_resolution,[status(thm)],[1443, 1415])).
% 3.18/2.37 tff(1445,plain,
% 3.18/2.37 (~c3_1(a606)),
% 3.18/2.37 inference(unit_resolution,[status(thm)],[1075, 1444])).
% 3.18/2.37 tff(1446,plain,
% 3.18/2.37 (~c2_1(a606)),
% 3.18/2.37 inference(unit_resolution,[status(thm)],[1111, 1444])).
% 3.18/2.37 tff(1447,plain,
% 3.18/2.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a607) | c2_1(a607) | c2_1(a606) | c3_1(a606) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)) | c0_1(a606) | (~c0_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a607) | c2_1(a607) | c2_1(a606) | c3_1(a606) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)) | c0_1(a606) | (~c0_1(a607)))),
% 3.18/2.37 inference(rewrite,[status(thm)],[])).
% 3.18/2.37 tff(1448,plain,
% 3.18/2.37 (((~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c0_1(a593) | (~c1_1(a593)) | (~c3_1(a593)) | c3_1(a606) | c0_1(a606) | c2_1(a606)) <=> (c1_1(a607) | c2_1(a607) | c2_1(a606) | c3_1(a606) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)) | c0_1(a606) | (~c0_1(a607)))),
% 3.18/2.37 inference(rewrite,[status(thm)],[])).
% 3.18/2.37 tff(1449,plain,
% 3.18/2.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c0_1(a593) | (~c1_1(a593)) | (~c3_1(a593)) | c3_1(a606) | c0_1(a606) | c2_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a607) | c2_1(a607) | c2_1(a606) | c3_1(a606) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)) | c0_1(a606) | (~c0_1(a607))))),
% 3.18/2.37 inference(monotonicity,[status(thm)],[1448])).
% 3.18/2.37 tff(1450,plain,
% 3.18/2.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c0_1(a593) | (~c1_1(a593)) | (~c3_1(a593)) | c3_1(a606) | c0_1(a606) | c2_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a607) | c2_1(a607) | c2_1(a606) | c3_1(a606) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)) | c0_1(a606) | (~c0_1(a607)))),
% 3.18/2.37 inference(transitivity,[status(thm)],[1449, 1447])).
% 3.18/2.37 tff(1451,plain,
% 3.18/2.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c0_1(a593) | (~c1_1(a593)) | (~c3_1(a593)) | c3_1(a606) | c0_1(a606) | c2_1(a606))),
% 3.18/2.37 inference(quant_inst,[status(thm)],[])).
% 3.18/2.37 tff(1452,plain,
% 3.18/2.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a607) | c2_1(a607) | c2_1(a606) | c3_1(a606) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)) | c0_1(a606) | (~c0_1(a607))),
% 3.18/2.37 inference(modus_ponens,[status(thm)],[1451, 1450])).
% 3.18/2.37 tff(1453,plain,
% 3.18/2.37 (c0_1(a606)),
% 3.18/2.37 inference(unit_resolution,[status(thm)],[1452, 107, 1347, 1346, 66, 22, 1446, 1445, 1364, 1227, 1354])).
% 3.18/2.37 tff(1454,plain,
% 3.18/2.37 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)))),
% 3.18/2.37 inference(bind,[status(th)],[])).
% 3.18/2.37 tff(1455,plain,
% 3.18/2.37 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 3.18/2.37 inference(quant_intro,[status(thm)],[1454])).
% 3.18/2.37 tff(1456,plain,
% 3.18/2.37 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 3.18/2.37 inference(rewrite,[status(thm)],[])).
% 3.18/2.37 tff(1457,plain,
% 3.18/2.37 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))))),
% 3.18/2.37 inference(bind,[status(th)],[])).
% 3.18/2.37 tff(1458,plain,
% 3.18/2.37 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 3.18/2.37 inference(quant_intro,[status(thm)],[1457])).
% 3.18/2.37 tff(1459,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause193')).
% 3.18/2.37 tff(1460,plain,
% 3.18/2.37 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 3.18/2.37 inference(modus_ponens,[status(thm)],[1459, 1458])).
% 3.18/2.37 tff(1461,plain,
% 3.18/2.37 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 3.18/2.37 inference(modus_ponens,[status(thm)],[1460, 1456])).
% 3.18/2.37 tff(1462,plain,(
% 3.18/2.37 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 3.18/2.37 inference(skolemize,[status(sab)],[1461])).
% 3.18/2.37 tff(1463,plain,
% 3.18/2.37 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 3.18/2.37 inference(modus_ponens,[status(thm)],[1462, 1455])).
% 3.18/2.37 tff(1464,plain,
% 3.18/2.37 (~c2_1(a593)),
% 3.18/2.37 inference(unit_resolution,[status(thm)],[555, 1345])).
% 3.18/2.37 tff(1465,plain,
% 3.18/2.37 (((~hskp2) | c2_1(a586)) <=> ((~hskp2) | c2_1(a586))),
% 3.18/2.37 inference(rewrite,[status(thm)],[])).
% 3.18/2.37 tff(1466,axiom,((~hskp2) | c2_1(a586)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause78')).
% 3.18/2.37 tff(1467,plain,
% 3.18/2.37 ((~hskp2) | c2_1(a586)),
% 3.18/2.37 inference(modus_ponens,[status(thm)],[1466, 1465])).
% 3.18/2.37 tff(1468,plain,
% 3.18/2.37 ((~hskp2) | c2_1(a586)),
% 3.18/2.37 inference(modus_ponens,[status(thm)],[1467, 1465])).
% 3.18/2.37 tff(1469,plain,
% 3.18/2.37 ((~hskp2) | c2_1(a586)),
% 3.18/2.37 inference(modus_ponens,[status(thm)],[1468, 1465])).
% 3.18/2.37 tff(1470,plain,
% 3.18/2.37 ((~hskp2) | c2_1(a586)),
% 3.18/2.37 inference(modus_ponens,[status(thm)],[1469, 1465])).
% 3.18/2.37 tff(1471,plain,
% 3.18/2.37 ((~hskp2) | c2_1(a586)),
% 3.18/2.37 inference(modus_ponens,[status(thm)],[1470, 1465])).
% 3.18/2.37 tff(1472,plain,
% 3.18/2.37 ((~hskp2) | c2_1(a586)),
% 3.18/2.37 inference(modus_ponens,[status(thm)],[1471, 1465])).
% 3.18/2.37 tff(1473,plain,
% 3.18/2.37 ((~hskp2) | c2_1(a586)),
% 3.18/2.37 inference(modus_ponens,[status(thm)],[1472, 1465])).
% 3.18/2.37 tff(1474,plain,
% 3.18/2.37 ((~hskp2) | c2_1(a586)),
% 3.18/2.37 inference(modus_ponens,[status(thm)],[1473, 1465])).
% 3.18/2.37 tff(1475,plain,
% 3.18/2.37 (c2_1(a586)),
% 3.18/2.37 inference(unit_resolution,[status(thm)],[1474, 1406])).
% 3.18/2.37 tff(1476,plain,
% 3.18/2.37 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c0_1(a586)) | (~c3_1(a636)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c0_1(a586)) | (~c3_1(a636)))),
% 3.18/2.37 inference(rewrite,[status(thm)],[])).
% 3.18/2.37 tff(1477,plain,
% 3.18/2.37 ((hskp9 | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c0_1(a586)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636))) <=> (hskp9 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c0_1(a586)) | (~c3_1(a636)))),
% 3.18/2.37 inference(rewrite,[status(thm)],[])).
% 3.18/2.37 tff(1478,plain,
% 3.18/2.37 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c0_1(a586)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c0_1(a586)) | (~c3_1(a636))))),
% 3.18/2.37 inference(monotonicity,[status(thm)],[1477])).
% 3.18/2.37 tff(1479,plain,
% 3.18/2.37 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c0_1(a586)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c0_1(a586)) | (~c3_1(a636)))),
% 3.18/2.37 inference(transitivity,[status(thm)],[1478, 1476])).
% 3.18/2.37 tff(1480,plain,
% 3.18/2.37 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c0_1(a586)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)))),
% 3.18/2.37 inference(quant_inst,[status(thm)],[])).
% 3.18/2.37 tff(1481,plain,
% 3.18/2.37 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c0_1(a586)) | (~c3_1(a636))),
% 3.18/2.37 inference(modus_ponens,[status(thm)],[1480, 1479])).
% 3.18/2.37 tff(1482,plain,
% 3.18/2.37 (hskp9),
% 3.18/2.37 inference(unit_resolution,[status(thm)],[1481, 107, 1338, 1408, 1475, 1337, 1336, 294, 1415])).
% 3.18/2.37 tff(1483,plain,
% 3.18/2.37 (((~hskp9) | (~c3_1(a595))) <=> ((~hskp9) | (~c3_1(a595)))),
% 3.18/2.37 inference(rewrite,[status(thm)],[])).
% 3.18/2.37 tff(1484,plain,
% 3.18/2.37 (((~c3_1(a595)) | (~hskp9)) <=> ((~hskp9) | (~c3_1(a595)))),
% 3.18/2.37 inference(rewrite,[status(thm)],[])).
% 3.18/2.37 tff(1485,axiom,((~c3_1(a595)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause113')).
% 3.26/2.37 tff(1486,plain,
% 3.26/2.37 ((~hskp9) | (~c3_1(a595))),
% 3.26/2.37 inference(modus_ponens,[status(thm)],[1485, 1484])).
% 3.26/2.37 tff(1487,plain,
% 3.26/2.37 ((~hskp9) | (~c3_1(a595))),
% 3.26/2.37 inference(modus_ponens,[status(thm)],[1486, 1483])).
% 3.26/2.37 tff(1488,plain,
% 3.26/2.37 (~c3_1(a595)),
% 3.26/2.37 inference(unit_resolution,[status(thm)],[1487, 1482])).
% 3.26/2.37 tff(1489,plain,
% 3.26/2.37 (((~hskp9) | (~c1_1(a595))) <=> ((~hskp9) | (~c1_1(a595)))),
% 3.26/2.37 inference(rewrite,[status(thm)],[])).
% 3.26/2.37 tff(1490,plain,
% 3.26/2.37 (((~c1_1(a595)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a595)))),
% 3.26/2.37 inference(rewrite,[status(thm)],[])).
% 3.26/2.37 tff(1491,axiom,((~c1_1(a595)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause112')).
% 3.26/2.37 tff(1492,plain,
% 3.26/2.37 ((~hskp9) | (~c1_1(a595))),
% 3.26/2.37 inference(modus_ponens,[status(thm)],[1491, 1490])).
% 3.26/2.37 tff(1493,plain,
% 3.26/2.37 ((~hskp9) | (~c1_1(a595))),
% 3.26/2.37 inference(modus_ponens,[status(thm)],[1492, 1489])).
% 3.26/2.37 tff(1494,plain,
% 3.26/2.37 (~c1_1(a595)),
% 3.26/2.37 inference(unit_resolution,[status(thm)],[1493, 1482])).
% 3.26/2.37 tff(1495,plain,
% 3.26/2.37 (((~hskp9) | (~c0_1(a595))) <=> ((~hskp9) | (~c0_1(a595)))),
% 3.26/2.37 inference(rewrite,[status(thm)],[])).
% 3.26/2.37 tff(1496,plain,
% 3.26/2.37 (((~c0_1(a595)) | (~hskp9)) <=> ((~hskp9) | (~c0_1(a595)))),
% 3.26/2.37 inference(rewrite,[status(thm)],[])).
% 3.26/2.37 tff(1497,axiom,((~c0_1(a595)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause111')).
% 3.26/2.37 tff(1498,plain,
% 3.26/2.37 ((~hskp9) | (~c0_1(a595))),
% 3.26/2.37 inference(modus_ponens,[status(thm)],[1497, 1496])).
% 3.26/2.37 tff(1499,plain,
% 3.26/2.37 ((~hskp9) | (~c0_1(a595))),
% 3.26/2.37 inference(modus_ponens,[status(thm)],[1498, 1495])).
% 3.26/2.37 tff(1500,plain,
% 3.26/2.37 (~c0_1(a595)),
% 3.26/2.37 inference(unit_resolution,[status(thm)],[1499, 1482])).
% 3.26/2.37 tff(1501,plain,
% 3.26/2.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a606) | c3_1(a606) | c0_1(a595) | c1_1(a595) | c3_1(a595) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a606)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a606) | c3_1(a606) | c0_1(a595) | c1_1(a595) | c3_1(a595) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a606)))),
% 3.26/2.37 inference(rewrite,[status(thm)],[])).
% 3.26/2.37 tff(1502,plain,
% 3.26/2.37 (((~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c0_1(a606)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a595) | c1_1(a595) | c0_1(a595)) <=> (c2_1(a606) | c3_1(a606) | c0_1(a595) | c1_1(a595) | c3_1(a595) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a606)))),
% 3.26/2.37 inference(rewrite,[status(thm)],[])).
% 3.26/2.37 tff(1503,plain,
% 3.26/2.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c0_1(a606)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a595) | c1_1(a595) | c0_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a606) | c3_1(a606) | c0_1(a595) | c1_1(a595) | c3_1(a595) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a606))))),
% 3.26/2.37 inference(monotonicity,[status(thm)],[1502])).
% 3.26/2.37 tff(1504,plain,
% 3.26/2.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c0_1(a606)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a595) | c1_1(a595) | c0_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a606) | c3_1(a606) | c0_1(a595) | c1_1(a595) | c3_1(a595) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a606)))),
% 3.26/2.37 inference(transitivity,[status(thm)],[1503, 1501])).
% 3.26/2.37 tff(1505,plain,
% 3.26/2.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c0_1(a606)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a595) | c1_1(a595) | c0_1(a595))),
% 3.26/2.37 inference(quant_inst,[status(thm)],[])).
% 3.26/2.37 tff(1506,plain,
% 3.26/2.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a606) | c3_1(a606) | c0_1(a595) | c1_1(a595) | c3_1(a595) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a606))),
% 3.26/2.37 inference(modus_ponens,[status(thm)],[1505, 1504])).
% 3.26/2.37 tff(1507,plain,
% 3.26/2.37 ($false),
% 3.26/2.37 inference(unit_resolution,[status(thm)],[1506, 107, 1347, 1446, 1445, 1500, 1494, 1488, 1464, 1463, 1354, 1453])).
% 3.26/2.37 tff(1508,plain,(hskp26 | c1_1(a607) | c2_1(a607) | (~c0_1(a587)) | (~c2_1(a587)) | c1_1(a603) | c3_1(a603) | (~c0_1(a603)) | (~c3_1(a607)) | c1_1(a587)), inference(lemma,lemma(discharge,[]))).
% 3.26/2.37 tff(1509,plain,
% 3.26/2.37 (hskp26),
% 3.26/2.37 inference(unit_resolution,[status(thm)],[1508, 282, 276, 962, 951, 985, 984, 983, 295, 940])).
% 3.26/2.37 tff(1510,plain,
% 3.26/2.37 (c2_1(a583)),
% 3.26/2.37 inference(unit_resolution,[status(thm)],[391, 1509])).
% 3.26/2.37 tff(1511,plain,
% 3.26/2.37 (c1_1(a583)),
% 3.26/2.37 inference(unit_resolution,[status(thm)],[351, 1509])).
% 3.26/2.37 tff(1512,plain,
% 3.26/2.37 (c0_1(a583)),
% 3.26/2.37 inference(unit_resolution,[status(thm)],[362, 1509])).
% 3.26/2.37 tff(1513,plain,
% 3.26/2.37 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | c1_1(a607) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c0_1(a607) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c1_1(a607) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c0_1(a607) | (~c3_1(a607)))),
% 3.26/2.37 inference(rewrite,[status(thm)],[])).
% 3.26/2.37 tff(1514,plain,
% 3.26/2.37 ((hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a607) | c0_1(a607) | (~c3_1(a607))) <=> (hskp9 | c1_1(a607) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c0_1(a607) | (~c3_1(a607)))),
% 3.26/2.37 inference(rewrite,[status(thm)],[])).
% 3.26/2.37 tff(1515,plain,
% 3.26/2.37 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a607) | c0_1(a607) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | c1_1(a607) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c0_1(a607) | (~c3_1(a607))))),
% 3.26/2.38 inference(monotonicity,[status(thm)],[1514])).
% 3.26/2.38 tff(1516,plain,
% 3.26/2.38 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a607) | c0_1(a607) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c1_1(a607) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c0_1(a607) | (~c3_1(a607)))),
% 3.26/2.38 inference(transitivity,[status(thm)],[1515, 1513])).
% 3.26/2.38 tff(1517,plain,
% 3.26/2.38 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a607) | c0_1(a607) | (~c3_1(a607)))),
% 3.26/2.38 inference(quant_inst,[status(thm)],[])).
% 3.26/2.38 tff(1518,plain,
% 3.26/2.38 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c1_1(a607) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c0_1(a607) | (~c3_1(a607))),
% 3.26/2.38 inference(modus_ponens,[status(thm)],[1517, 1516])).
% 3.26/2.38 tff(1519,plain,
% 3.26/2.38 (hskp9 | c0_1(a607)),
% 3.26/2.38 inference(unit_resolution,[status(thm)],[1518, 107, 1512, 1511, 1510, 295, 282, 294])).
% 3.26/2.38 tff(1520,plain,
% 3.26/2.38 (hskp9),
% 3.26/2.38 inference(unit_resolution,[status(thm)],[1519, 284])).
% 3.26/2.38 tff(1521,plain,
% 3.26/2.38 (~c3_1(a595)),
% 3.26/2.38 inference(unit_resolution,[status(thm)],[1487, 1520])).
% 3.26/2.38 tff(1522,plain,
% 3.26/2.38 (~c0_1(a595)),
% 3.26/2.38 inference(unit_resolution,[status(thm)],[1499, 1520])).
% 3.26/2.38 tff(1523,plain,
% 3.26/2.38 (~c1_1(a595)),
% 3.26/2.38 inference(unit_resolution,[status(thm)],[1493, 1520])).
% 3.26/2.38 tff(1524,plain,
% 3.26/2.38 (hskp6 | c2_1(a603)),
% 3.26/2.38 inference(unit_resolution,[status(thm)],[189, 107, 44, 983, 985, 43])).
% 3.26/2.38 tff(1525,plain,
% 3.26/2.38 (c2_1(a603)),
% 3.26/2.38 inference(unit_resolution,[status(thm)],[1524, 67])).
% 3.26/2.38 tff(1526,plain,
% 3.26/2.38 (hskp28),
% 3.26/2.38 inference(unit_resolution,[status(thm)],[1128, 107, 295, 983, 276, 984, 1122, 284, 1525])).
% 3.26/2.38 tff(1527,plain,
% 3.26/2.38 (c3_1(a612)),
% 3.26/2.38 inference(unit_resolution,[status(thm)],[1139, 1526])).
% 3.26/2.38 tff(1528,plain,
% 3.26/2.38 (c2_1(a612)),
% 3.26/2.38 inference(unit_resolution,[status(thm)],[1150, 1526])).
% 3.26/2.38 tff(1529,plain,
% 3.26/2.38 (c1_1(a612)),
% 3.26/2.38 inference(unit_resolution,[status(thm)],[1435, 1526])).
% 3.26/2.38 tff(1530,plain,
% 3.26/2.38 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c1_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c1_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)))),
% 3.26/2.38 inference(rewrite,[status(thm)],[])).
% 3.26/2.38 tff(1531,plain,
% 3.26/2.38 ((hskp10 | (~ndr1_0) | (~c2_1(a612)) | (~c3_1(a612)) | (~c1_1(a612)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583))) <=> (hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c1_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)))),
% 3.26/2.38 inference(rewrite,[status(thm)],[])).
% 3.26/2.38 tff(1532,plain,
% 3.26/2.38 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a612)) | (~c3_1(a612)) | (~c1_1(a612)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c1_1(a612)) | (~c3_1(a612)) | (~c2_1(a612))))),
% 3.26/2.38 inference(monotonicity,[status(thm)],[1531])).
% 3.26/2.38 tff(1533,plain,
% 3.26/2.38 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a612)) | (~c3_1(a612)) | (~c1_1(a612)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c1_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)))),
% 3.26/2.38 inference(transitivity,[status(thm)],[1532, 1530])).
% 3.26/2.38 tff(1534,plain,
% 3.26/2.38 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a612)) | (~c3_1(a612)) | (~c1_1(a612)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583)))),
% 3.26/2.38 inference(quant_inst,[status(thm)],[])).
% 3.26/2.38 tff(1535,plain,
% 3.26/2.38 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c1_1(a612)) | (~c3_1(a612)) | (~c2_1(a612))),
% 3.26/2.38 inference(modus_ponens,[status(thm)],[1534, 1533])).
% 3.26/2.38 tff(1536,plain,
% 3.26/2.38 (hskp10),
% 3.26/2.38 inference(unit_resolution,[status(thm)],[1535, 107, 1529, 1528, 1527, 1512, 1511, 1510, 21])).
% 3.26/2.38 tff(1537,plain,
% 3.26/2.38 (~c1_1(a598)),
% 3.26/2.38 inference(unit_resolution,[status(thm)],[911, 1536])).
% 3.26/2.38 tff(1538,plain,
% 3.26/2.38 (c0_1(a598)),
% 3.26/2.38 inference(unit_resolution,[status(thm)],[892, 1536])).
% 3.26/2.38 tff(1539,plain,
% 3.26/2.38 (((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | c1_1(a598) | (~ndr1_0) | c2_1(a598) | (~c0_1(a598)))) <=> ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp22 | hskp6 | c1_1(a598) | (~ndr1_0) | c2_1(a598) | (~c0_1(a598)))),
% 3.26/2.38 inference(rewrite,[status(thm)],[])).
% 3.26/2.38 tff(1540,plain,
% 3.26/2.38 ((hskp22 | hskp6 | (~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598))) <=> (hskp22 | hskp6 | c1_1(a598) | (~ndr1_0) | c2_1(a598) | (~c0_1(a598)))),
% 3.26/2.38 inference(rewrite,[status(thm)],[])).
% 3.26/2.38 tff(1541,plain,
% 3.26/2.38 (((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | (~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)))) <=> ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | c1_1(a598) | (~ndr1_0) | c2_1(a598) | (~c0_1(a598))))),
% 3.26/2.38 inference(monotonicity,[status(thm)],[1540])).
% 3.26/2.38 tff(1542,plain,
% 3.26/2.38 (((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | (~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)))) <=> ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp22 | hskp6 | c1_1(a598) | (~ndr1_0) | c2_1(a598) | (~c0_1(a598)))),
% 3.26/2.38 inference(transitivity,[status(thm)],[1541, 1539])).
% 3.26/2.38 tff(1543,plain,
% 3.26/2.38 ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | (~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)))),
% 3.26/2.38 inference(quant_inst,[status(thm)],[])).
% 3.26/2.38 tff(1544,plain,
% 3.26/2.38 ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp22 | hskp6 | c1_1(a598) | (~ndr1_0) | c2_1(a598) | (~c0_1(a598))),
% 3.26/2.38 inference(modus_ponens,[status(thm)],[1543, 1542])).
% 3.26/2.38 tff(1545,plain,
% 3.26/2.38 (c2_1(a598)),
% 3.26/2.38 inference(unit_resolution,[status(thm)],[1544, 107, 44, 67, 1538, 1537, 43])).
% 3.26/2.38 tff(1546,plain,
% 3.26/2.38 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 3.26/2.38 inference(bind,[status(th)],[])).
% 3.26/2.38 tff(1547,plain,
% 3.26/2.38 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 3.26/2.38 inference(quant_intro,[status(thm)],[1546])).
% 3.26/2.38 tff(1548,plain,
% 3.26/2.38 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 3.26/2.38 inference(rewrite,[status(thm)],[])).
% 3.26/2.38 tff(1549,plain,
% 3.26/2.38 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp1))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 3.26/2.38 inference(bind,[status(th)],[])).
% 3.26/2.38 tff(1550,plain,
% 3.26/2.38 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 3.26/2.38 inference(quant_intro,[status(thm)],[1549])).
% 3.26/2.38 tff(1551,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause169')).
% 3.26/2.38 tff(1552,plain,
% 3.26/2.38 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 3.26/2.38 inference(modus_ponens,[status(thm)],[1551, 1550])).
% 3.26/2.38 tff(1553,plain,
% 3.26/2.38 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 3.26/2.38 inference(modus_ponens,[status(thm)],[1552, 1548])).
% 3.26/2.38 tff(1554,plain,(
% 3.26/2.38 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 3.26/2.38 inference(skolemize,[status(sab)],[1553])).
% 3.26/2.38 tff(1555,plain,
% 3.26/2.38 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 3.26/2.38 inference(modus_ponens,[status(thm)],[1554, 1547])).
% 3.26/2.38 tff(1556,assumption,(~c3_1(a595)), introduced(assumption)).
% 3.26/2.38 tff(1557,assumption,(~c1_1(a595)), introduced(assumption)).
% 3.26/2.38 tff(1558,assumption,(~c0_1(a595)), introduced(assumption)).
% 3.26/2.38 tff(1559,plain,
% 3.26/2.38 (^[U: $i] : refl((hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))),
% 3.26/2.38 inference(bind,[status(th)],[])).
% 3.26/2.38 tff(1560,plain,
% 3.26/2.38 (![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 3.26/2.38 inference(quant_intro,[status(thm)],[1559])).
% 3.26/2.38 tff(1561,plain,
% 3.26/2.38 (![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 3.26/2.38 inference(rewrite,[status(thm)],[])).
% 3.26/2.38 tff(1562,plain,
% 3.26/2.38 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp29) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp29))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp29) <=> (hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp29) <=> (hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp29) | hskp15) <=> ((hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp15))), rewrite(((hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp15) <=> (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp29) | hskp15) <=> (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))))),
% 3.26/2.38 inference(bind,[status(th)],[])).
% 3.26/2.38 tff(1563,plain,
% 3.26/2.38 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp29) | hskp15) <=> ![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 3.26/2.38 inference(quant_intro,[status(thm)],[1562])).
% 3.26/2.38 tff(1564,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp29) | hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause160')).
% 3.26/2.38 tff(1565,plain,
% 3.26/2.38 (![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 3.26/2.38 inference(modus_ponens,[status(thm)],[1564, 1563])).
% 3.26/2.38 tff(1566,plain,
% 3.26/2.38 (![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 3.26/2.38 inference(modus_ponens,[status(thm)],[1565, 1561])).
% 3.26/2.38 tff(1567,plain,(
% 3.26/2.38 ![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 3.26/2.38 inference(skolemize,[status(sab)],[1566])).
% 3.26/2.38 tff(1568,plain,
% 3.26/2.38 (![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 3.26/2.38 inference(modus_ponens,[status(thm)],[1567, 1560])).
% 3.26/2.38 tff(1569,plain,
% 3.26/2.38 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a603) | c3_1(a603) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | (~c2_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a603) | c3_1(a603) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | (~c2_1(a603)))),
% 3.26/2.38 inference(rewrite,[status(thm)],[])).
% 3.26/2.38 tff(1570,plain,
% 3.26/2.38 ((hskp2 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c3_1(a595) | c1_1(a595) | c0_1(a595)) <=> (hskp2 | c1_1(a603) | c3_1(a603) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | (~c2_1(a603)))),
% 3.26/2.38 inference(rewrite,[status(thm)],[])).
% 3.26/2.38 tff(1571,plain,
% 3.26/2.38 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c3_1(a595) | c1_1(a595) | c0_1(a595))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a603) | c3_1(a603) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | (~c2_1(a603))))),
% 3.26/2.38 inference(monotonicity,[status(thm)],[1570])).
% 3.26/2.38 tff(1572,plain,
% 3.26/2.38 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c3_1(a595) | c1_1(a595) | c0_1(a595))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a603) | c3_1(a603) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | (~c2_1(a603)))),
% 3.26/2.38 inference(transitivity,[status(thm)],[1571, 1569])).
% 3.26/2.38 tff(1573,plain,
% 3.26/2.38 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c3_1(a595) | c1_1(a595) | c0_1(a595))),
% 3.26/2.38 inference(quant_inst,[status(thm)],[])).
% 3.26/2.38 tff(1574,plain,
% 3.26/2.38 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a603) | c3_1(a603) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | (~c2_1(a603))),
% 3.26/2.38 inference(modus_ponens,[status(thm)],[1573, 1572])).
% 3.26/2.38 tff(1575,plain,
% 3.26/2.38 (hskp2 | (~c2_1(a603))),
% 3.26/2.38 inference(unit_resolution,[status(thm)],[1574, 107, 985, 984, 1558, 1557, 1556, 200])).
% 3.26/2.38 tff(1576,plain,
% 3.26/2.38 (hskp2),
% 3.26/2.38 inference(unit_resolution,[status(thm)],[1575, 1525])).
% 3.26/2.38 tff(1577,plain,
% 3.26/2.38 (~c3_1(a586)),
% 3.26/2.38 inference(unit_resolution,[status(thm)],[218, 1576])).
% 3.26/2.38 tff(1578,plain,
% 3.26/2.38 (c2_1(a586)),
% 3.26/2.38 inference(unit_resolution,[status(thm)],[1474, 1576])).
% 3.26/2.38 tff(1579,plain,
% 3.26/2.38 (c1_1(a586)),
% 3.26/2.38 inference(unit_resolution,[status(thm)],[229, 1576])).
% 3.26/2.38 tff(1580,plain,
% 3.26/2.38 (((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp15 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)))) <=> ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp15 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)))),
% 3.26/2.38 inference(rewrite,[status(thm)],[])).
% 3.26/2.38 tff(1581,plain,
% 3.26/2.38 ((hskp29 | hskp15 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586))) <=> (hskp29 | hskp15 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)))),
% 3.26/2.38 inference(rewrite,[status(thm)],[])).
% 3.26/2.38 tff(1582,plain,
% 3.26/2.38 (((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp15 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)))) <=> ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp15 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586))))),
% 3.26/2.38 inference(monotonicity,[status(thm)],[1581])).
% 3.26/2.38 tff(1583,plain,
% 3.26/2.38 (((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp15 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)))) <=> ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp15 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)))),
% 3.26/2.38 inference(transitivity,[status(thm)],[1582, 1580])).
% 3.26/2.38 tff(1584,plain,
% 3.26/2.38 ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp15 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)))),
% 3.26/2.38 inference(quant_inst,[status(thm)],[])).
% 3.26/2.38 tff(1585,plain,
% 3.26/2.38 ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp15 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586))),
% 3.26/2.38 inference(modus_ponens,[status(thm)],[1584, 1583])).
% 3.26/2.38 tff(1586,plain,
% 3.26/2.38 (hskp15),
% 3.26/2.38 inference(unit_resolution,[status(thm)],[1585, 269, 107, 1579, 1578, 1577, 1568])).
% 3.26/2.38 tff(1587,plain,
% 3.26/2.38 (((~hskp15) | (~c0_1(a604))) <=> ((~hskp15) | (~c0_1(a604)))),
% 3.26/2.38 inference(rewrite,[status(thm)],[])).
% 3.26/2.38 tff(1588,plain,
% 3.26/2.38 (((~c0_1(a604)) | (~hskp15)) <=> ((~hskp15) | (~c0_1(a604)))),
% 3.26/2.38 inference(rewrite,[status(thm)],[])).
% 3.26/2.38 tff(1589,axiom,((~c0_1(a604)) | (~hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause102')).
% 3.26/2.38 tff(1590,plain,
% 3.26/2.38 ((~hskp15) | (~c0_1(a604))),
% 3.26/2.38 inference(modus_ponens,[status(thm)],[1589, 1588])).
% 3.26/2.38 tff(1591,plain,
% 3.26/2.38 ((~hskp15) | (~c0_1(a604))),
% 3.26/2.38 inference(modus_ponens,[status(thm)],[1590, 1587])).
% 3.26/2.38 tff(1592,plain,
% 3.26/2.38 (~c0_1(a604)),
% 3.26/2.38 inference(unit_resolution,[status(thm)],[1591, 1586])).
% 3.26/2.38 tff(1593,plain,
% 3.26/2.38 (((~hskp15) | c3_1(a604)) <=> ((~hskp15) | c3_1(a604))),
% 3.26/2.38 inference(rewrite,[status(thm)],[])).
% 3.26/2.38 tff(1594,axiom,((~hskp15) | c3_1(a604)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause59')).
% 3.26/2.38 tff(1595,plain,
% 3.26/2.38 ((~hskp15) | c3_1(a604)),
% 3.26/2.38 inference(modus_ponens,[status(thm)],[1594, 1593])).
% 3.26/2.38 tff(1596,plain,
% 3.26/2.38 ((~hskp15) | c3_1(a604)),
% 3.26/2.38 inference(modus_ponens,[status(thm)],[1595, 1593])).
% 3.26/2.38 tff(1597,plain,
% 3.26/2.38 ((~hskp15) | c3_1(a604)),
% 3.26/2.38 inference(modus_ponens,[status(thm)],[1596, 1593])).
% 3.26/2.38 tff(1598,plain,
% 3.26/2.38 ((~hskp15) | c3_1(a604)),
% 3.26/2.38 inference(modus_ponens,[status(thm)],[1597, 1593])).
% 3.26/2.38 tff(1599,plain,
% 3.26/2.38 ((~hskp15) | c3_1(a604)),
% 3.26/2.38 inference(modus_ponens,[status(thm)],[1598, 1593])).
% 3.26/2.38 tff(1600,plain,
% 3.26/2.38 ((~hskp15) | c3_1(a604)),
% 3.26/2.38 inference(modus_ponens,[status(thm)],[1599, 1593])).
% 3.26/2.38 tff(1601,plain,
% 3.26/2.38 ((~hskp15) | c3_1(a604)),
% 3.26/2.38 inference(modus_ponens,[status(thm)],[1600, 1593])).
% 3.26/2.38 tff(1602,plain,
% 3.26/2.38 ((~hskp15) | c3_1(a604)),
% 3.26/2.38 inference(modus_ponens,[status(thm)],[1601, 1593])).
% 3.26/2.38 tff(1603,plain,
% 3.26/2.38 (c3_1(a604)),
% 3.26/2.38 inference(unit_resolution,[status(thm)],[1602, 1586])).
% 3.26/2.38 tff(1604,plain,
% 3.26/2.38 (((~hskp15) | c1_1(a604)) <=> ((~hskp15) | c1_1(a604))),
% 3.26/2.38 inference(rewrite,[status(thm)],[])).
% 3.26/2.38 tff(1605,axiom,((~hskp15) | c1_1(a604)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause58')).
% 3.26/2.38 tff(1606,plain,
% 3.26/2.38 ((~hskp15) | c1_1(a604)),
% 3.26/2.38 inference(modus_ponens,[status(thm)],[1605, 1604])).
% 3.26/2.38 tff(1607,plain,
% 3.26/2.38 ((~hskp15) | c1_1(a604)),
% 3.26/2.38 inference(modus_ponens,[status(thm)],[1606, 1604])).
% 3.26/2.38 tff(1608,plain,
% 3.26/2.38 ((~hskp15) | c1_1(a604)),
% 3.26/2.38 inference(modus_ponens,[status(thm)],[1607, 1604])).
% 3.26/2.38 tff(1609,plain,
% 3.26/2.38 ((~hskp15) | c1_1(a604)),
% 3.26/2.38 inference(modus_ponens,[status(thm)],[1608, 1604])).
% 3.26/2.38 tff(1610,plain,
% 3.26/2.38 ((~hskp15) | c1_1(a604)),
% 3.26/2.38 inference(modus_ponens,[status(thm)],[1609, 1604])).
% 3.26/2.38 tff(1611,plain,
% 3.26/2.38 ((~hskp15) | c1_1(a604)),
% 3.26/2.38 inference(modus_ponens,[status(thm)],[1610, 1604])).
% 3.26/2.38 tff(1612,plain,
% 3.26/2.38 ((~hskp15) | c1_1(a604)),
% 3.26/2.38 inference(modus_ponens,[status(thm)],[1611, 1604])).
% 3.26/2.38 tff(1613,plain,
% 3.26/2.38 ((~hskp15) | c1_1(a604)),
% 3.26/2.38 inference(modus_ponens,[status(thm)],[1612, 1604])).
% 3.26/2.38 tff(1614,plain,
% 3.26/2.38 (c1_1(a604)),
% 3.26/2.38 inference(unit_resolution,[status(thm)],[1613, 1586])).
% 3.26/2.38 tff(1615,plain,
% 3.26/2.38 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a604) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a604) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)))),
% 3.26/2.38 inference(rewrite,[status(thm)],[])).
% 3.26/2.38 tff(1616,plain,
% 3.26/2.38 ((hskp1 | (~ndr1_0) | c0_1(a604) | (~c3_1(a604)) | (~c1_1(a604)) | c3_1(a595) | c1_1(a595) | c0_1(a595)) <=> (hskp1 | c0_1(a604) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)))),
% 3.26/2.38 inference(rewrite,[status(thm)],[])).
% 3.26/2.38 tff(1617,plain,
% 3.26/2.38 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a604) | (~c3_1(a604)) | (~c1_1(a604)) | c3_1(a595) | c1_1(a595) | c0_1(a595))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a604) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604))))),
% 3.26/2.38 inference(monotonicity,[status(thm)],[1616])).
% 3.26/2.38 tff(1618,plain,
% 3.26/2.38 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a604) | (~c3_1(a604)) | (~c1_1(a604)) | c3_1(a595) | c1_1(a595) | c0_1(a595))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a604) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)))),
% 3.26/2.38 inference(transitivity,[status(thm)],[1617, 1615])).
% 3.26/2.38 tff(1619,plain,
% 3.26/2.38 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a604) | (~c3_1(a604)) | (~c1_1(a604)) | c3_1(a595) | c1_1(a595) | c0_1(a595))),
% 3.26/2.38 inference(quant_inst,[status(thm)],[])).
% 3.26/2.38 tff(1620,plain,
% 3.26/2.38 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a604) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604))),
% 3.26/2.38 inference(modus_ponens,[status(thm)],[1619, 1618])).
% 3.26/2.38 tff(1621,plain,
% 3.26/2.38 (hskp1),
% 3.26/2.38 inference(unit_resolution,[status(thm)],[1620, 107, 1614, 1603, 1592, 1558, 1557, 1556, 1555])).
% 3.26/2.38 tff(1622,plain,
% 3.26/2.38 (~c0_1(a585)),
% 3.26/2.38 inference(unit_resolution,[status(thm)],[1250, 1621])).
% 3.26/2.38 tff(1623,plain,
% 3.26/2.38 (c2_1(a585)),
% 3.26/2.38 inference(unit_resolution,[status(thm)],[1261, 1621])).
% 3.26/2.38 tff(1624,plain,
% 3.26/2.38 (c1_1(a585)),
% 3.26/2.38 inference(unit_resolution,[status(thm)],[1272, 1621])).
% 3.26/2.38 tff(1625,plain,
% 3.26/2.38 (c3_1(a598)),
% 3.26/2.38 inference(unit_resolution,[status(thm)],[881, 1536])).
% 3.26/2.38 tff(1626,plain,
% 3.26/2.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c3_1(a607)))),
% 3.26/2.39 inference(rewrite,[status(thm)],[])).
% 3.26/2.39 tff(1627,plain,
% 3.26/2.39 (((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585))) <=> (c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c3_1(a607)))),
% 3.26/2.39 inference(rewrite,[status(thm)],[])).
% 3.26/2.39 tff(1628,plain,
% 3.26/2.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c3_1(a607))))),
% 3.26/2.39 inference(monotonicity,[status(thm)],[1627])).
% 3.26/2.39 tff(1629,plain,
% 3.26/2.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c3_1(a607)))),
% 3.26/2.39 inference(transitivity,[status(thm)],[1628, 1626])).
% 3.26/2.39 tff(1630,plain,
% 3.26/2.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))),
% 3.26/2.39 inference(quant_inst,[status(thm)],[])).
% 3.26/2.39 tff(1631,plain,
% 3.26/2.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c3_1(a607))),
% 3.26/2.39 inference(modus_ponens,[status(thm)],[1630, 1629])).
% 3.26/2.39 tff(1632,plain,
% 3.26/2.39 ($false),
% 3.26/2.39 inference(unit_resolution,[status(thm)],[1631, 107, 295, 1538, 1625, 1624, 1623, 282, 276, 1622, 11, 1545])).
% 3.26/2.39 tff(1633,plain,(hskp6 | hskp22 | c0_1(a595) | c1_1(a595) | c3_1(a595) | hskp29), inference(lemma,lemma(discharge,[]))).
% 3.26/2.39 tff(1634,plain,
% 3.26/2.39 ($false),
% 3.26/2.39 inference(unit_resolution,[status(thm)],[1633, 1523, 1522, 44, 67, 1521, 269])).
% 3.26/2.39 tff(1635,plain,(hskp6 | hskp22 | hskp29), inference(lemma,lemma(discharge,[]))).
% 3.26/2.39 tff(1636,plain,
% 3.26/2.39 (hskp6),
% 3.26/2.39 inference(unit_resolution,[status(thm)],[1635, 269, 44])).
% 3.26/2.39 tff(1637,plain,
% 3.26/2.39 (~c0_1(a590)),
% 3.26/2.39 inference(unit_resolution,[status(thm)],[666, 1636])).
% 3.26/2.39 tff(1638,assumption,(~hskp11), introduced(assumption)).
% 3.26/2.39 tff(1639,plain,
% 3.26/2.39 (^[U: $i] : refl((hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 3.26/2.39 inference(bind,[status(th)],[])).
% 3.26/2.39 tff(1640,plain,
% 3.26/2.39 (![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 3.26/2.39 inference(quant_intro,[status(thm)],[1639])).
% 3.26/2.39 tff(1641,plain,
% 3.26/2.39 (![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 3.26/2.39 inference(rewrite,[status(thm)],[])).
% 3.26/2.39 tff(1642,plain,
% 3.26/2.39 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp11) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp11))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp11) <=> (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp11) <=> (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp11) | hskp23) <=> ((hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp23))), rewrite(((hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp23) <=> (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp11) | hskp23) <=> (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 3.26/2.39 inference(bind,[status(th)],[])).
% 3.26/2.39 tff(1643,plain,
% 3.26/2.39 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp11) | hskp23) <=> ![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 3.26/2.39 inference(quant_intro,[status(thm)],[1642])).
% 3.26/2.39 tff(1644,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp11) | hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause146')).
% 3.26/2.39 tff(1645,plain,
% 3.26/2.39 (![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 3.26/2.39 inference(modus_ponens,[status(thm)],[1644, 1643])).
% 3.26/2.39 tff(1646,plain,
% 3.26/2.39 (![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 3.26/2.39 inference(modus_ponens,[status(thm)],[1645, 1641])).
% 3.26/2.39 tff(1647,plain,(
% 3.26/2.39 ![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 3.26/2.39 inference(skolemize,[status(sab)],[1646])).
% 3.26/2.39 tff(1648,plain,
% 3.26/2.39 (![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 3.26/2.39 inference(modus_ponens,[status(thm)],[1647, 1640])).
% 3.26/2.39 tff(1649,assumption,(c2_1(a583)), introduced(assumption)).
% 3.26/2.39 tff(1650,assumption,(c1_1(a583)), introduced(assumption)).
% 3.26/2.39 tff(1651,assumption,(c0_1(a583)), introduced(assumption)).
% 3.26/2.39 tff(1652,assumption,(~hskp23), introduced(assumption)).
% 3.26/2.39 tff(1653,plain,
% 3.26/2.39 (((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp23 | c1_1(a587) | (~ndr1_0) | (~c3_1(a587)) | (~c0_1(a587)))) <=> ((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp23 | c1_1(a587) | (~ndr1_0) | (~c3_1(a587)) | (~c0_1(a587)))),
% 3.26/2.39 inference(rewrite,[status(thm)],[])).
% 3.26/2.39 tff(1654,plain,
% 3.26/2.39 ((hskp11 | hskp23 | (~ndr1_0) | c1_1(a587) | (~c3_1(a587)) | (~c0_1(a587))) <=> (hskp11 | hskp23 | c1_1(a587) | (~ndr1_0) | (~c3_1(a587)) | (~c0_1(a587)))),
% 3.26/2.39 inference(rewrite,[status(thm)],[])).
% 3.26/2.39 tff(1655,plain,
% 3.26/2.39 (((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp23 | (~ndr1_0) | c1_1(a587) | (~c3_1(a587)) | (~c0_1(a587)))) <=> ((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp23 | c1_1(a587) | (~ndr1_0) | (~c3_1(a587)) | (~c0_1(a587))))),
% 3.26/2.39 inference(monotonicity,[status(thm)],[1654])).
% 3.26/2.39 tff(1656,plain,
% 3.26/2.39 (((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp23 | (~ndr1_0) | c1_1(a587) | (~c3_1(a587)) | (~c0_1(a587)))) <=> ((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp23 | c1_1(a587) | (~ndr1_0) | (~c3_1(a587)) | (~c0_1(a587)))),
% 3.26/2.39 inference(transitivity,[status(thm)],[1655, 1653])).
% 3.26/2.39 tff(1657,plain,
% 3.26/2.39 ((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp23 | (~ndr1_0) | c1_1(a587) | (~c3_1(a587)) | (~c0_1(a587)))),
% 3.26/2.39 inference(quant_inst,[status(thm)],[])).
% 3.26/2.39 tff(1658,plain,
% 3.26/2.39 ((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp23 | c1_1(a587) | (~ndr1_0) | (~c3_1(a587)) | (~c0_1(a587))),
% 3.26/2.39 inference(modus_ponens,[status(thm)],[1657, 1656])).
% 3.26/2.39 tff(1659,plain,
% 3.26/2.39 (hskp11 | hskp23 | (~c3_1(a587))),
% 3.26/2.39 inference(unit_resolution,[status(thm)],[1658, 107, 1000, 996, 1648])).
% 3.26/2.39 tff(1660,plain,
% 3.26/2.39 (~c3_1(a587)),
% 3.26/2.39 inference(unit_resolution,[status(thm)],[1659, 1652, 1638])).
% 3.26/2.39 tff(1661,plain,
% 3.26/2.39 (((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp23 | c1_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)))) <=> ((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp23 | c1_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.26/2.39 inference(rewrite,[status(thm)],[])).
% 3.26/2.39 tff(1662,plain,
% 3.26/2.39 ((hskp11 | hskp23 | (~ndr1_0) | c1_1(a607) | (~c3_1(a607)) | (~c0_1(a607))) <=> (hskp11 | hskp23 | c1_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.26/2.39 inference(rewrite,[status(thm)],[])).
% 3.26/2.39 tff(1663,plain,
% 3.26/2.39 (((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp23 | (~ndr1_0) | c1_1(a607) | (~c3_1(a607)) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp23 | c1_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607))))),
% 3.26/2.39 inference(monotonicity,[status(thm)],[1662])).
% 3.26/2.39 tff(1664,plain,
% 3.26/2.39 (((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp23 | (~ndr1_0) | c1_1(a607) | (~c3_1(a607)) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp23 | c1_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.26/2.39 inference(transitivity,[status(thm)],[1663, 1661])).
% 3.26/2.39 tff(1665,plain,
% 3.26/2.39 ((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp23 | (~ndr1_0) | c1_1(a607) | (~c3_1(a607)) | (~c0_1(a607)))),
% 3.26/2.39 inference(quant_inst,[status(thm)],[])).
% 3.26/2.39 tff(1666,plain,
% 3.26/2.39 ((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp23 | c1_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607))),
% 3.26/2.39 inference(modus_ponens,[status(thm)],[1665, 1664])).
% 3.26/2.39 tff(1667,plain,
% 3.26/2.39 (hskp11 | hskp23 | (~c0_1(a607))),
% 3.26/2.39 inference(unit_resolution,[status(thm)],[1666, 107, 321, 66, 1648])).
% 3.26/2.39 tff(1668,plain,
% 3.26/2.39 (~c0_1(a607)),
% 3.26/2.39 inference(unit_resolution,[status(thm)],[1667, 1652, 1638])).
% 3.26/2.39 tff(1669,plain,
% 3.26/2.39 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | c2_1(a607) | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a607) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp28 | c2_1(a607) | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a607) | (~c3_1(a607)))),
% 3.26/2.39 inference(rewrite,[status(thm)],[])).
% 3.26/2.39 tff(1670,plain,
% 3.26/2.39 ((hskp28 | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a607) | c2_1(a607) | (~c3_1(a607))) <=> (hskp28 | c2_1(a607) | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a607) | (~c3_1(a607)))),
% 3.26/2.39 inference(rewrite,[status(thm)],[])).
% 3.26/2.39 tff(1671,plain,
% 3.26/2.39 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a607) | c2_1(a607) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | c2_1(a607) | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a607) | (~c3_1(a607))))),
% 3.26/2.39 inference(monotonicity,[status(thm)],[1670])).
% 3.26/2.39 tff(1672,plain,
% 3.26/2.39 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a607) | c2_1(a607) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp28 | c2_1(a607) | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a607) | (~c3_1(a607)))),
% 3.26/2.39 inference(transitivity,[status(thm)],[1671, 1669])).
% 3.26/2.39 tff(1673,plain,
% 3.26/2.39 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a607) | c2_1(a607) | (~c3_1(a607)))),
% 3.26/2.39 inference(quant_inst,[status(thm)],[])).
% 3.26/2.39 tff(1674,plain,
% 3.26/2.39 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp28 | c2_1(a607) | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a607) | (~c3_1(a607))),
% 3.26/2.39 inference(modus_ponens,[status(thm)],[1673, 1672])).
% 3.26/2.39 tff(1675,plain,
% 3.26/2.39 (hskp28),
% 3.26/2.39 inference(unit_resolution,[status(thm)],[1674, 107, 321, 1000, 999, 22, 1122, 1668, 1660])).
% 3.26/2.39 tff(1676,plain,
% 3.26/2.39 (c3_1(a612)),
% 3.26/2.39 inference(unit_resolution,[status(thm)],[1139, 1675])).
% 3.26/2.39 tff(1677,plain,
% 3.26/2.39 (c2_1(a612)),
% 3.26/2.39 inference(unit_resolution,[status(thm)],[1150, 1675])).
% 3.26/2.39 tff(1678,plain,
% 3.26/2.39 (c1_1(a612)),
% 3.26/2.39 inference(unit_resolution,[status(thm)],[1435, 1675])).
% 3.26/2.39 tff(1679,plain,
% 3.26/2.39 (hskp10),
% 3.26/2.39 inference(unit_resolution,[status(thm)],[1535, 107, 1678, 1677, 1676, 1651, 1650, 1649, 21])).
% 3.26/2.39 tff(1680,plain,
% 3.26/2.39 (~c1_1(a598)),
% 3.26/2.39 inference(unit_resolution,[status(thm)],[911, 1679])).
% 3.26/2.39 tff(1681,plain,
% 3.26/2.39 (c3_1(a598)),
% 3.26/2.39 inference(unit_resolution,[status(thm)],[881, 1679])).
% 3.26/2.39 tff(1682,plain,
% 3.26/2.39 (c0_1(a598)),
% 3.26/2.39 inference(unit_resolution,[status(thm)],[892, 1679])).
% 3.26/2.39 tff(1683,plain,
% 3.26/2.39 (((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp23 | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c0_1(a598)))) <=> ((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp23 | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c0_1(a598)))),
% 3.26/2.39 inference(rewrite,[status(thm)],[])).
% 3.26/2.39 tff(1684,plain,
% 3.26/2.39 ((hskp11 | hskp23 | (~ndr1_0) | c1_1(a598) | (~c3_1(a598)) | (~c0_1(a598))) <=> (hskp11 | hskp23 | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c0_1(a598)))),
% 3.26/2.39 inference(rewrite,[status(thm)],[])).
% 3.26/2.39 tff(1685,plain,
% 3.26/2.39 (((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp23 | (~ndr1_0) | c1_1(a598) | (~c3_1(a598)) | (~c0_1(a598)))) <=> ((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp23 | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c0_1(a598))))),
% 3.26/2.39 inference(monotonicity,[status(thm)],[1684])).
% 3.26/2.39 tff(1686,plain,
% 3.26/2.39 (((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp23 | (~ndr1_0) | c1_1(a598) | (~c3_1(a598)) | (~c0_1(a598)))) <=> ((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp23 | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c0_1(a598)))),
% 3.26/2.39 inference(transitivity,[status(thm)],[1685, 1683])).
% 3.26/2.39 tff(1687,plain,
% 3.26/2.39 ((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp23 | (~ndr1_0) | c1_1(a598) | (~c3_1(a598)) | (~c0_1(a598)))),
% 3.26/2.39 inference(quant_inst,[status(thm)],[])).
% 3.26/2.39 tff(1688,plain,
% 3.26/2.39 ((~![U: $i] : (hskp11 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp23 | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c0_1(a598))),
% 3.26/2.39 inference(modus_ponens,[status(thm)],[1687, 1686])).
% 3.26/2.39 tff(1689,plain,
% 3.26/2.39 ($false),
% 3.26/2.39 inference(unit_resolution,[status(thm)],[1688, 1638, 107, 1652, 1682, 1681, 1680, 1648])).
% 3.26/2.39 tff(1690,plain,(hskp23 | hskp11 | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c3_1(a607)) | (~c0_1(a587)) | (~c2_1(a587)) | c2_1(a607) | c1_1(a587) | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.26/2.39 tff(1691,plain,
% 3.26/2.39 (hskp23),
% 3.26/2.39 inference(unit_resolution,[status(thm)],[1690, 1638, 1512, 1511, 1510, 295, 962, 951, 276, 940, 282])).
% 3.26/2.39 tff(1692,plain,
% 3.26/2.39 (~c1_1(a636)),
% 3.26/2.39 inference(unit_resolution,[status(thm)],[475, 1691])).
% 3.26/2.39 tff(1693,plain,
% 3.26/2.39 (~c0_1(a636)),
% 3.26/2.39 inference(unit_resolution,[status(thm)],[481, 1691])).
% 3.26/2.39 tff(1694,plain,
% 3.26/2.39 (c3_1(a636)),
% 3.26/2.39 inference(unit_resolution,[status(thm)],[492, 1691])).
% 3.26/2.39 tff(1695,plain,
% 3.26/2.39 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a636)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a636)))),
% 3.26/2.39 inference(rewrite,[status(thm)],[])).
% 3.26/2.39 tff(1696,plain,
% 3.26/2.39 ((hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636))) <=> (hskp9 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a636)))),
% 3.26/2.39 inference(rewrite,[status(thm)],[])).
% 3.26/2.39 tff(1697,plain,
% 3.26/2.39 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a636))))),
% 3.26/2.39 inference(monotonicity,[status(thm)],[1696])).
% 3.26/2.39 tff(1698,plain,
% 3.26/2.39 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a636)))),
% 3.26/2.39 inference(transitivity,[status(thm)],[1697, 1695])).
% 3.26/2.39 tff(1699,plain,
% 3.26/2.39 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)))),
% 3.26/2.39 inference(quant_inst,[status(thm)],[])).
% 3.26/2.39 tff(1700,plain,
% 3.26/2.39 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a636))),
% 3.26/2.39 inference(modus_ponens,[status(thm)],[1699, 1698])).
% 3.26/2.39 tff(1701,plain,
% 3.26/2.39 (hskp9),
% 3.26/2.39 inference(unit_resolution,[status(thm)],[1700, 107, 1512, 1511, 1510, 1694, 1693, 1692, 294])).
% 3.26/2.39 tff(1702,plain,
% 3.26/2.39 (~c3_1(a595)),
% 3.26/2.39 inference(unit_resolution,[status(thm)],[1487, 1701])).
% 3.26/2.39 tff(1703,plain,
% 3.26/2.39 (~c1_1(a595)),
% 3.26/2.39 inference(unit_resolution,[status(thm)],[1493, 1701])).
% 3.26/2.39 tff(1704,plain,
% 3.26/2.39 (~c0_1(a595)),
% 3.26/2.39 inference(unit_resolution,[status(thm)],[1499, 1701])).
% 3.26/2.39 tff(1705,plain,
% 3.26/2.39 (hskp6),
% 3.26/2.39 inference(unit_resolution,[status(thm)],[1633, 1704, 44, 1703, 1702, 269])).
% 3.26/2.39 tff(1706,plain,
% 3.26/2.39 (~c0_1(a590)),
% 3.26/2.39 inference(unit_resolution,[status(thm)],[666, 1705])).
% 3.26/2.39 tff(1707,plain,
% 3.26/2.39 (c3_1(a590)),
% 3.26/2.39 inference(unit_resolution,[status(thm)],[677, 1705])).
% 3.26/2.39 tff(1708,plain,
% 3.26/2.39 (c2_1(a590)),
% 3.26/2.39 inference(unit_resolution,[status(thm)],[688, 1705])).
% 3.26/2.39 tff(1709,assumption,(~hskp8), introduced(assumption)).
% 3.26/2.39 tff(1710,plain,
% 3.26/2.39 (hskp8 | hskp6),
% 3.26/2.39 inference(unit_resolution,[status(thm)],[499, 107, 725, 724, 723, 450])).
% 3.26/2.39 tff(1711,plain,
% 3.26/2.39 (hskp6),
% 3.26/2.39 inference(unit_resolution,[status(thm)],[1710, 1709])).
% 3.26/2.39 tff(1712,plain,
% 3.26/2.39 (~c0_1(a590)),
% 3.26/2.39 inference(unit_resolution,[status(thm)],[666, 1711])).
% 3.26/2.39 tff(1713,plain,
% 3.26/2.39 (c2_1(a590)),
% 3.26/2.39 inference(unit_resolution,[status(thm)],[688, 1711])).
% 3.26/2.39 tff(1714,plain,
% 3.26/2.39 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | c0_1(a636) | c1_1(a636) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a636)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a636) | c1_1(a636) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a636)))),
% 3.26/2.39 inference(rewrite,[status(thm)],[])).
% 3.26/2.39 tff(1715,plain,
% 3.26/2.39 ((hskp8 | (~ndr1_0) | c0_1(a590) | (~c2_1(a590)) | (~c1_1(a590)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636))) <=> (hskp8 | c0_1(a636) | c1_1(a636) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a636)))),
% 3.26/2.39 inference(rewrite,[status(thm)],[])).
% 3.26/2.39 tff(1716,plain,
% 3.26/2.39 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a590) | (~c2_1(a590)) | (~c1_1(a590)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | c0_1(a636) | c1_1(a636) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a636))))),
% 3.26/2.39 inference(monotonicity,[status(thm)],[1715])).
% 3.26/2.39 tff(1717,plain,
% 3.26/2.39 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a590) | (~c2_1(a590)) | (~c1_1(a590)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a636) | c1_1(a636) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a636)))),
% 3.26/2.39 inference(transitivity,[status(thm)],[1716, 1714])).
% 3.26/2.39 tff(1718,plain,
% 3.26/2.39 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a590) | (~c2_1(a590)) | (~c1_1(a590)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)))),
% 3.26/2.39 inference(quant_inst,[status(thm)],[])).
% 3.26/2.39 tff(1719,plain,
% 3.26/2.39 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a636) | c1_1(a636) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a636))),
% 3.26/2.39 inference(modus_ponens,[status(thm)],[1718, 1717])).
% 3.26/2.39 tff(1720,plain,
% 3.26/2.39 (~c1_1(a590)),
% 3.26/2.39 inference(unit_resolution,[status(thm)],[1719, 107, 1709, 725, 1713, 724, 723, 1712, 1317])).
% 3.26/2.39 tff(1721,plain,
% 3.26/2.39 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)))),
% 3.26/2.39 inference(bind,[status(th)],[])).
% 3.26/2.39 tff(1722,plain,
% 3.26/2.39 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 3.26/2.39 inference(quant_intro,[status(thm)],[1721])).
% 3.26/2.39 tff(1723,plain,
% 3.26/2.39 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 3.26/2.39 inference(rewrite,[status(thm)],[])).
% 3.26/2.39 tff(1724,plain,
% 3.26/2.39 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W)))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))))),
% 3.26/2.39 inference(bind,[status(th)],[])).
% 3.26/2.39 tff(1725,plain,
% 3.26/2.39 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 3.26/2.39 inference(quant_intro,[status(thm)],[1724])).
% 3.26/2.39 tff(1726,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause196')).
% 3.26/2.40 tff(1727,plain,
% 3.26/2.40 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 3.26/2.40 inference(modus_ponens,[status(thm)],[1726, 1725])).
% 3.26/2.40 tff(1728,plain,
% 3.26/2.40 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 3.26/2.40 inference(modus_ponens,[status(thm)],[1727, 1723])).
% 3.26/2.40 tff(1729,plain,(
% 3.26/2.40 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 3.26/2.40 inference(skolemize,[status(sab)],[1728])).
% 3.26/2.40 tff(1730,plain,
% 3.26/2.40 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))),
% 3.26/2.40 inference(modus_ponens,[status(thm)],[1729, 1722])).
% 3.26/2.40 tff(1731,plain,
% 3.26/2.40 (c3_1(a590)),
% 3.26/2.40 inference(unit_resolution,[status(thm)],[677, 1711])).
% 3.26/2.40 tff(1732,plain,
% 3.26/2.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a595) | c3_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | c2_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a595) | c3_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | c2_1(a595))),
% 3.26/2.40 inference(rewrite,[status(thm)],[])).
% 3.26/2.40 tff(1733,plain,
% 3.26/2.40 (((~ndr1_0) | c1_1(a590) | (~c2_1(a590)) | (~c3_1(a590)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a595) | c0_1(a595) | c2_1(a595)) <=> (c0_1(a595) | c3_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | c2_1(a595))),
% 3.26/2.40 inference(rewrite,[status(thm)],[])).
% 3.26/2.40 tff(1734,plain,
% 3.26/2.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a590) | (~c2_1(a590)) | (~c3_1(a590)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a595) | c0_1(a595) | c2_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a595) | c3_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | c2_1(a595)))),
% 3.26/2.40 inference(monotonicity,[status(thm)],[1733])).
% 3.26/2.40 tff(1735,plain,
% 3.26/2.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a590) | (~c2_1(a590)) | (~c3_1(a590)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a595) | c0_1(a595) | c2_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a595) | c3_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | c2_1(a595))),
% 3.26/2.40 inference(transitivity,[status(thm)],[1734, 1732])).
% 3.26/2.40 tff(1736,plain,
% 3.26/2.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a590) | (~c2_1(a590)) | (~c3_1(a590)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a595) | c0_1(a595) | c2_1(a595))),
% 3.26/2.40 inference(quant_inst,[status(thm)],[])).
% 3.26/2.40 tff(1737,plain,
% 3.26/2.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a595) | c3_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | c2_1(a595)),
% 3.26/2.40 inference(modus_ponens,[status(thm)],[1736, 1735])).
% 3.26/2.40 tff(1738,plain,
% 3.26/2.40 (c2_1(a595)),
% 3.26/2.40 inference(unit_resolution,[status(thm)],[1737, 107, 1713, 1731, 1558, 1556, 1712, 1730, 1720])).
% 3.26/2.40 tff(1739,plain,
% 3.26/2.40 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 3.28/2.40 inference(bind,[status(th)],[])).
% 3.28/2.40 tff(1740,plain,
% 3.28/2.40 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 3.28/2.40 inference(quant_intro,[status(thm)],[1739])).
% 3.28/2.40 tff(1741,plain,
% 3.28/2.40 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 3.28/2.40 inference(rewrite,[status(thm)],[])).
% 3.28/2.40 tff(1742,plain,
% 3.28/2.40 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp28) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp28))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp28) <=> (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 3.28/2.40 inference(bind,[status(th)],[])).
% 3.28/2.40 tff(1743,plain,
% 3.28/2.40 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 3.28/2.40 inference(quant_intro,[status(thm)],[1742])).
% 3.28/2.40 tff(1744,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause189')).
% 3.28/2.40 tff(1745,plain,
% 3.28/2.40 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 3.28/2.40 inference(modus_ponens,[status(thm)],[1744, 1743])).
% 3.28/2.40 tff(1746,plain,
% 3.28/2.40 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 3.28/2.40 inference(modus_ponens,[status(thm)],[1745, 1741])).
% 3.28/2.40 tff(1747,plain,(
% 3.28/2.40 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 3.28/2.40 inference(skolemize,[status(sab)],[1746])).
% 3.28/2.40 tff(1748,plain,
% 3.28/2.40 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 3.28/2.40 inference(modus_ponens,[status(thm)],[1747, 1740])).
% 3.28/2.40 tff(1749,plain,
% 3.28/2.40 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | (~c2_1(a595)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | (~c2_1(a595)))),
% 3.28/2.40 inference(rewrite,[status(thm)],[])).
% 3.28/2.40 tff(1750,plain,
% 3.28/2.40 ((hskp2 | (~ndr1_0) | c1_1(a595) | c3_1(a595) | (~c2_1(a595)) | c3_1(a595) | c1_1(a595) | c0_1(a595)) <=> (hskp2 | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | (~c2_1(a595)))),
% 3.28/2.40 inference(rewrite,[status(thm)],[])).
% 3.28/2.40 tff(1751,plain,
% 3.28/2.40 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a595) | c3_1(a595) | (~c2_1(a595)) | c3_1(a595) | c1_1(a595) | c0_1(a595))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | (~c2_1(a595))))),
% 3.28/2.40 inference(monotonicity,[status(thm)],[1750])).
% 3.28/2.40 tff(1752,plain,
% 3.28/2.40 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a595) | c3_1(a595) | (~c2_1(a595)) | c3_1(a595) | c1_1(a595) | c0_1(a595))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | (~c2_1(a595)))),
% 3.28/2.40 inference(transitivity,[status(thm)],[1751, 1749])).
% 3.28/2.40 tff(1753,plain,
% 3.28/2.40 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a595) | c3_1(a595) | (~c2_1(a595)) | c3_1(a595) | c1_1(a595) | c0_1(a595))),
% 3.28/2.40 inference(quant_inst,[status(thm)],[])).
% 3.28/2.40 tff(1754,plain,
% 3.28/2.40 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | (~c2_1(a595))),
% 3.28/2.40 inference(modus_ponens,[status(thm)],[1753, 1752])).
% 3.28/2.40 tff(1755,plain,
% 3.28/2.40 (hskp2 | (~c2_1(a595))),
% 3.28/2.40 inference(unit_resolution,[status(thm)],[1754, 107, 1558, 1557, 1556, 200])).
% 3.28/2.40 tff(1756,plain,
% 3.28/2.40 (hskp2),
% 3.28/2.40 inference(unit_resolution,[status(thm)],[1755, 1738])).
% 3.28/2.40 tff(1757,plain,
% 3.28/2.40 (~c3_1(a586)),
% 3.28/2.40 inference(unit_resolution,[status(thm)],[218, 1756])).
% 3.28/2.40 tff(1758,plain,
% 3.28/2.40 (c2_1(a586)),
% 3.28/2.40 inference(unit_resolution,[status(thm)],[1474, 1756])).
% 3.28/2.40 tff(1759,plain,
% 3.28/2.40 (c1_1(a586)),
% 3.28/2.40 inference(unit_resolution,[status(thm)],[229, 1756])).
% 3.28/2.40 tff(1760,plain,
% 3.28/2.40 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590))),
% 3.28/2.40 inference(rewrite,[status(thm)],[])).
% 3.28/2.40 tff(1761,plain,
% 3.28/2.40 ((hskp28 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c1_1(a590) | (~c3_1(a590)) | (~c2_1(a590))) <=> (hskp28 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590))),
% 3.28/2.40 inference(rewrite,[status(thm)],[])).
% 3.28/2.40 tff(1762,plain,
% 3.28/2.40 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c1_1(a590) | (~c3_1(a590)) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590)))),
% 3.28/2.40 inference(monotonicity,[status(thm)],[1761])).
% 3.28/2.40 tff(1763,plain,
% 3.28/2.40 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c1_1(a590) | (~c3_1(a590)) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590))),
% 3.28/2.40 inference(transitivity,[status(thm)],[1762, 1760])).
% 3.28/2.40 tff(1764,plain,
% 3.28/2.40 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c1_1(a590) | (~c3_1(a590)) | (~c2_1(a590)))),
% 3.28/2.40 inference(quant_inst,[status(thm)],[])).
% 3.28/2.40 tff(1765,plain,
% 3.28/2.40 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590)),
% 3.28/2.40 inference(modus_ponens,[status(thm)],[1764, 1763])).
% 3.28/2.40 tff(1766,plain,
% 3.28/2.40 (hskp28),
% 3.28/2.40 inference(unit_resolution,[status(thm)],[1765, 107, 1713, 1731, 1759, 1758, 1757, 1748, 1720])).
% 3.28/2.40 tff(1767,plain,
% 3.28/2.40 (c3_1(a612)),
% 3.28/2.40 inference(unit_resolution,[status(thm)],[1139, 1766])).
% 3.28/2.40 tff(1768,plain,
% 3.28/2.40 (c1_1(a612)),
% 3.28/2.40 inference(unit_resolution,[status(thm)],[1435, 1766])).
% 3.28/2.40 tff(1769,plain,
% 3.28/2.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a595)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a595)))),
% 3.28/2.40 inference(rewrite,[status(thm)],[])).
% 3.28/2.40 tff(1770,plain,
% 3.28/2.40 (((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595))) <=> (c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a595)))),
% 3.28/2.40 inference(rewrite,[status(thm)],[])).
% 3.28/2.40 tff(1771,plain,
% 3.28/2.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a595))))),
% 3.28/2.40 inference(monotonicity,[status(thm)],[1770])).
% 3.28/2.40 tff(1772,plain,
% 3.28/2.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a595)))),
% 3.28/2.40 inference(transitivity,[status(thm)],[1771, 1769])).
% 3.28/2.40 tff(1773,plain,
% 3.28/2.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595)))),
% 3.28/2.40 inference(quant_inst,[status(thm)],[])).
% 3.28/2.40 tff(1774,plain,
% 3.28/2.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a595))),
% 3.28/2.40 inference(modus_ponens,[status(thm)],[1773, 1772])).
% 3.28/2.40 tff(1775,plain,
% 3.28/2.40 (~c0_1(a612)),
% 3.28/2.40 inference(unit_resolution,[status(thm)],[1774, 107, 1768, 1767, 1713, 1731, 1558, 1557, 1712, 65, 1738])).
% 3.28/2.40 tff(1776,plain,
% 3.28/2.40 (c2_1(a612)),
% 3.28/2.40 inference(unit_resolution,[status(thm)],[1150, 1766])).
% 3.28/2.40 tff(1777,plain,
% 3.28/2.40 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c3_1(a636)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c3_1(a636)))),
% 3.28/2.40 inference(rewrite,[status(thm)],[])).
% 3.28/2.40 tff(1778,plain,
% 3.28/2.40 ((hskp8 | (~ndr1_0) | c0_1(a612) | (~c2_1(a612)) | (~c1_1(a612)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636))) <=> (hskp8 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c3_1(a636)))),
% 3.28/2.40 inference(rewrite,[status(thm)],[])).
% 3.28/2.40 tff(1779,plain,
% 3.28/2.40 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a612) | (~c2_1(a612)) | (~c1_1(a612)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c3_1(a636))))),
% 3.28/2.40 inference(monotonicity,[status(thm)],[1778])).
% 3.28/2.40 tff(1780,plain,
% 3.28/2.40 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a612) | (~c2_1(a612)) | (~c1_1(a612)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c3_1(a636)))),
% 3.28/2.40 inference(transitivity,[status(thm)],[1779, 1777])).
% 3.28/2.40 tff(1781,plain,
% 3.28/2.40 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a612) | (~c2_1(a612)) | (~c1_1(a612)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)))),
% 3.28/2.40 inference(quant_inst,[status(thm)],[])).
% 3.28/2.40 tff(1782,plain,
% 3.28/2.40 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c3_1(a636))),
% 3.28/2.40 inference(modus_ponens,[status(thm)],[1781, 1780])).
% 3.28/2.40 tff(1783,plain,
% 3.28/2.40 ($false),
% 3.28/2.40 inference(unit_resolution,[status(thm)],[1782, 107, 1709, 1768, 1776, 725, 724, 723, 1317, 1775])).
% 3.28/2.40 tff(1784,plain,(hskp8 | (~c3_1(a636)) | c0_1(a636) | c1_1(a636) | c0_1(a595) | c1_1(a595) | c3_1(a595)), inference(lemma,lemma(discharge,[]))).
% 3.28/2.40 tff(1785,plain,
% 3.28/2.40 (hskp8),
% 3.28/2.40 inference(unit_resolution,[status(thm)],[1784, 1694, 1693, 1692, 1704, 1703, 1702])).
% 3.28/2.40 tff(1786,plain,
% 3.28/2.40 (~c2_1(a593)),
% 3.28/2.40 inference(unit_resolution,[status(thm)],[555, 1785])).
% 3.28/2.40 tff(1787,plain,
% 3.28/2.40 (^[U: $i] : refl((hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))),
% 3.28/2.40 inference(bind,[status(th)],[])).
% 3.28/2.40 tff(1788,plain,
% 3.28/2.40 (![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 3.28/2.40 inference(quant_intro,[status(thm)],[1787])).
% 3.28/2.40 tff(1789,plain,
% 3.28/2.40 (![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 3.28/2.40 inference(rewrite,[status(thm)],[])).
% 3.28/2.40 tff(1790,plain,
% 3.28/2.40 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp29) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp29))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp29) <=> (hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp29) <=> (hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp29) | hskp18) <=> ((hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp18))), rewrite(((hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp18) <=> (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp29) | hskp18) <=> (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))))),
% 3.28/2.40 inference(bind,[status(th)],[])).
% 3.28/2.40 tff(1791,plain,
% 3.28/2.40 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp29) | hskp18) <=> ![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 3.28/2.40 inference(quant_intro,[status(thm)],[1790])).
% 3.28/2.40 tff(1792,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp29) | hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause161')).
% 3.28/2.40 tff(1793,plain,
% 3.28/2.40 (![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 3.28/2.40 inference(modus_ponens,[status(thm)],[1792, 1791])).
% 3.28/2.40 tff(1794,plain,
% 3.28/2.40 (![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 3.28/2.40 inference(modus_ponens,[status(thm)],[1793, 1789])).
% 3.28/2.40 tff(1795,plain,(
% 3.28/2.40 ![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 3.28/2.40 inference(skolemize,[status(sab)],[1794])).
% 3.28/2.40 tff(1796,plain,
% 3.28/2.40 (![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 3.28/2.40 inference(modus_ponens,[status(thm)],[1795, 1788])).
% 3.28/2.40 tff(1797,assumption,(~hskp2), introduced(assumption)).
% 3.28/2.40 tff(1798,plain,
% 3.28/2.40 (~c2_1(a595)),
% 3.28/2.40 inference(unit_resolution,[status(thm)],[1755, 1797])).
% 3.28/2.40 tff(1799,plain,
% 3.28/2.40 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a595) | c1_1(a595) | c3_1(a595) | c1_1(a587) | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a595) | c1_1(a595) | c3_1(a595) | c1_1(a587) | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)))),
% 3.28/2.40 inference(rewrite,[status(thm)],[])).
% 3.28/2.40 tff(1800,plain,
% 3.28/2.40 ((hskp2 | (~ndr1_0) | c1_1(a587) | c3_1(a587) | (~c2_1(a587)) | c3_1(a595) | c1_1(a595) | c0_1(a595)) <=> (hskp2 | c0_1(a595) | c1_1(a595) | c3_1(a595) | c1_1(a587) | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)))),
% 3.28/2.40 inference(rewrite,[status(thm)],[])).
% 3.28/2.40 tff(1801,plain,
% 3.28/2.40 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a587) | c3_1(a587) | (~c2_1(a587)) | c3_1(a595) | c1_1(a595) | c0_1(a595))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a595) | c1_1(a595) | c3_1(a595) | c1_1(a587) | (~ndr1_0) | c3_1(a587) | (~c2_1(a587))))),
% 3.28/2.40 inference(monotonicity,[status(thm)],[1800])).
% 3.28/2.40 tff(1802,plain,
% 3.28/2.40 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a587) | c3_1(a587) | (~c2_1(a587)) | c3_1(a595) | c1_1(a595) | c0_1(a595))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a595) | c1_1(a595) | c3_1(a595) | c1_1(a587) | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)))),
% 3.28/2.40 inference(transitivity,[status(thm)],[1801, 1799])).
% 3.28/2.40 tff(1803,plain,
% 3.28/2.40 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a587) | c3_1(a587) | (~c2_1(a587)) | c3_1(a595) | c1_1(a595) | c0_1(a595))),
% 3.28/2.40 inference(quant_inst,[status(thm)],[])).
% 3.28/2.40 tff(1804,plain,
% 3.28/2.40 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a595) | c1_1(a595) | c3_1(a595) | c1_1(a587) | (~ndr1_0) | c3_1(a587) | (~c2_1(a587))),
% 3.28/2.40 inference(modus_ponens,[status(thm)],[1803, 1802])).
% 3.28/2.40 tff(1805,plain,
% 3.28/2.40 (hskp2 | c3_1(a587)),
% 3.28/2.40 inference(unit_resolution,[status(thm)],[1804, 107, 999, 1558, 1557, 1556, 996, 200])).
% 3.28/2.40 tff(1806,plain,
% 3.28/2.40 (c3_1(a587)),
% 3.28/2.40 inference(unit_resolution,[status(thm)],[1805, 1797])).
% 3.28/2.40 tff(1807,plain,
% 3.28/2.40 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | c0_1(a595) | c3_1(a595) | (~ndr1_0) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a595))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | c0_1(a595) | c3_1(a595) | (~ndr1_0) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a595))),
% 3.28/2.40 inference(rewrite,[status(thm)],[])).
% 3.28/2.40 tff(1808,plain,
% 3.28/2.40 ((hskp11 | (~ndr1_0) | (~c2_1(a587)) | (~c3_1(a587)) | (~c0_1(a587)) | c3_1(a595) | c0_1(a595) | c2_1(a595)) <=> (hskp11 | c0_1(a595) | c3_1(a595) | (~ndr1_0) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a595))),
% 3.28/2.40 inference(rewrite,[status(thm)],[])).
% 3.28/2.40 tff(1809,plain,
% 3.28/2.40 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a587)) | (~c3_1(a587)) | (~c0_1(a587)) | c3_1(a595) | c0_1(a595) | c2_1(a595))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | c0_1(a595) | c3_1(a595) | (~ndr1_0) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a595)))),
% 3.28/2.40 inference(monotonicity,[status(thm)],[1808])).
% 3.28/2.40 tff(1810,plain,
% 3.28/2.40 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a587)) | (~c3_1(a587)) | (~c0_1(a587)) | c3_1(a595) | c0_1(a595) | c2_1(a595))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | c0_1(a595) | c3_1(a595) | (~ndr1_0) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a595))),
% 3.28/2.40 inference(transitivity,[status(thm)],[1809, 1807])).
% 3.28/2.40 tff(1811,plain,
% 3.28/2.40 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a587)) | (~c3_1(a587)) | (~c0_1(a587)) | c3_1(a595) | c0_1(a595) | c2_1(a595))),
% 3.28/2.40 inference(quant_inst,[status(thm)],[])).
% 3.28/2.40 tff(1812,plain,
% 3.28/2.40 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | c0_1(a595) | c3_1(a595) | (~ndr1_0) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a595)),
% 3.28/2.41 inference(modus_ponens,[status(thm)],[1811, 1810])).
% 3.28/2.41 tff(1813,plain,
% 3.28/2.41 ((~c3_1(a587)) | c2_1(a595)),
% 3.28/2.41 inference(unit_resolution,[status(thm)],[1812, 1638, 107, 1000, 999, 1558, 1556, 268])).
% 3.28/2.41 tff(1814,plain,
% 3.28/2.41 ($false),
% 3.28/2.41 inference(unit_resolution,[status(thm)],[1813, 1806, 1798])).
% 3.28/2.41 tff(1815,plain,(hskp2 | hskp11 | (~c0_1(a587)) | (~c2_1(a587)) | c0_1(a595) | c3_1(a595) | c1_1(a595) | c1_1(a587)), inference(lemma,lemma(discharge,[]))).
% 3.28/2.41 tff(1816,plain,
% 3.28/2.41 (hskp2),
% 3.28/2.41 inference(unit_resolution,[status(thm)],[1815, 1638, 962, 951, 1704, 1702, 1703, 940])).
% 3.28/2.41 tff(1817,plain,
% 3.28/2.41 (~c3_1(a586)),
% 3.28/2.41 inference(unit_resolution,[status(thm)],[218, 1816])).
% 3.28/2.41 tff(1818,plain,
% 3.28/2.41 (c2_1(a586)),
% 3.28/2.41 inference(unit_resolution,[status(thm)],[1474, 1816])).
% 3.28/2.41 tff(1819,plain,
% 3.28/2.41 (c1_1(a586)),
% 3.28/2.41 inference(unit_resolution,[status(thm)],[229, 1816])).
% 3.28/2.41 tff(1820,plain,
% 3.28/2.41 (((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp18 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)))) <=> ((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp18 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)))),
% 3.28/2.41 inference(rewrite,[status(thm)],[])).
% 3.28/2.41 tff(1821,plain,
% 3.28/2.41 ((hskp29 | hskp18 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586))) <=> (hskp29 | hskp18 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)))),
% 3.28/2.41 inference(rewrite,[status(thm)],[])).
% 3.28/2.41 tff(1822,plain,
% 3.28/2.41 (((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp18 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)))) <=> ((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp18 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586))))),
% 3.28/2.41 inference(monotonicity,[status(thm)],[1821])).
% 3.28/2.41 tff(1823,plain,
% 3.28/2.41 (((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp18 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)))) <=> ((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp18 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)))),
% 3.28/2.41 inference(transitivity,[status(thm)],[1822, 1820])).
% 3.28/2.41 tff(1824,plain,
% 3.28/2.41 ((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp18 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)))),
% 3.28/2.41 inference(quant_inst,[status(thm)],[])).
% 3.28/2.41 tff(1825,plain,
% 3.28/2.41 ((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp18 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586))),
% 3.28/2.41 inference(modus_ponens,[status(thm)],[1824, 1823])).
% 3.28/2.41 tff(1826,plain,
% 3.28/2.41 (hskp18),
% 3.28/2.41 inference(unit_resolution,[status(thm)],[1825, 269, 107, 1819, 1818, 1817, 1796])).
% 3.28/2.41 tff(1827,plain,
% 3.28/2.41 (~c2_1(a610)),
% 3.28/2.41 inference(unit_resolution,[status(thm)],[1189, 1826])).
% 3.28/2.41 tff(1828,plain,
% 3.28/2.41 (~c0_1(a610)),
% 3.28/2.41 inference(unit_resolution,[status(thm)],[1195, 1826])).
% 3.28/2.41 tff(1829,plain,
% 3.28/2.41 (hskp15),
% 3.28/2.41 inference(unit_resolution,[status(thm)],[1585, 269, 107, 1819, 1818, 1817, 1568])).
% 3.28/2.41 tff(1830,plain,
% 3.28/2.41 (~c0_1(a604)),
% 3.28/2.41 inference(unit_resolution,[status(thm)],[1591, 1829])).
% 3.28/2.41 tff(1831,plain,
% 3.28/2.41 (c3_1(a604)),
% 3.28/2.41 inference(unit_resolution,[status(thm)],[1602, 1829])).
% 3.28/2.41 tff(1832,plain,
% 3.28/2.41 (c1_1(a604)),
% 3.28/2.41 inference(unit_resolution,[status(thm)],[1613, 1829])).
% 3.28/2.41 tff(1833,plain,
% 3.28/2.41 (hskp1),
% 3.28/2.41 inference(unit_resolution,[status(thm)],[1620, 107, 1832, 1831, 1830, 1704, 1703, 1702, 1555])).
% 3.28/2.41 tff(1834,plain,
% 3.28/2.41 (~c0_1(a585)),
% 3.28/2.41 inference(unit_resolution,[status(thm)],[1250, 1833])).
% 3.28/2.41 tff(1835,plain,
% 3.28/2.41 (c2_1(a585)),
% 3.28/2.41 inference(unit_resolution,[status(thm)],[1261, 1833])).
% 3.28/2.41 tff(1836,plain,
% 3.28/2.41 (c1_1(a585)),
% 3.28/2.41 inference(unit_resolution,[status(thm)],[1272, 1833])).
% 3.28/2.41 tff(1837,plain,
% 3.28/2.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c3_1(a607)))),
% 3.28/2.41 inference(rewrite,[status(thm)],[])).
% 3.28/2.41 tff(1838,plain,
% 3.28/2.41 (((~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585))) <=> (c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c3_1(a607)))),
% 3.28/2.41 inference(rewrite,[status(thm)],[])).
% 3.28/2.41 tff(1839,plain,
% 3.28/2.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c3_1(a607))))),
% 3.28/2.41 inference(monotonicity,[status(thm)],[1838])).
% 3.28/2.41 tff(1840,plain,
% 3.28/2.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c3_1(a607)))),
% 3.28/2.41 inference(transitivity,[status(thm)],[1839, 1837])).
% 3.28/2.41 tff(1841,plain,
% 3.28/2.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))),
% 3.28/2.41 inference(quant_inst,[status(thm)],[])).
% 3.28/2.41 tff(1842,plain,
% 3.28/2.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c3_1(a607))),
% 3.28/2.41 inference(modus_ponens,[status(thm)],[1841, 1840])).
% 3.28/2.41 tff(1843,plain,
% 3.28/2.41 (~c3_1(a583)),
% 3.28/2.41 inference(unit_resolution,[status(thm)],[1842, 107, 1512, 1510, 295, 1836, 1835, 282, 276, 1834, 11])).
% 3.28/2.41 tff(1844,plain,
% 3.28/2.41 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp16 | c0_1(a604) | (~ndr1_0) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp16 | c0_1(a604) | (~ndr1_0) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c1_1(a604)))),
% 3.28/2.41 inference(rewrite,[status(thm)],[])).
% 3.28/2.41 tff(1845,plain,
% 3.28/2.41 ((hskp16 | (~ndr1_0) | c3_1(a583) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604))) <=> (hskp16 | c0_1(a604) | (~ndr1_0) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c1_1(a604)))),
% 3.28/2.41 inference(rewrite,[status(thm)],[])).
% 3.28/2.41 tff(1846,plain,
% 3.28/2.41 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a583) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp16 | c0_1(a604) | (~ndr1_0) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c1_1(a604))))),
% 3.28/2.41 inference(monotonicity,[status(thm)],[1845])).
% 3.28/2.41 tff(1847,plain,
% 3.28/2.41 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a583) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp16 | c0_1(a604) | (~ndr1_0) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c1_1(a604)))),
% 3.28/2.41 inference(transitivity,[status(thm)],[1846, 1844])).
% 3.28/2.41 tff(1848,plain,
% 3.28/2.41 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a583) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)))),
% 3.28/2.41 inference(quant_inst,[status(thm)],[])).
% 3.28/2.41 tff(1849,plain,
% 3.28/2.41 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp16 | c0_1(a604) | (~ndr1_0) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c1_1(a604))),
% 3.28/2.41 inference(modus_ponens,[status(thm)],[1848, 1847])).
% 3.28/2.41 tff(1850,plain,
% 3.28/2.41 (hskp16),
% 3.28/2.41 inference(unit_resolution,[status(thm)],[1849, 107, 1512, 1511, 1832, 1831, 1830, 1425, 1843])).
% 3.28/2.41 tff(1851,plain,
% 3.28/2.41 (c1_1(a606)),
% 3.28/2.41 inference(unit_resolution,[status(thm)],[1088, 1850])).
% 3.28/2.41 tff(1852,plain,
% 3.28/2.41 (c3_1(a610)),
% 3.28/2.41 inference(unit_resolution,[status(thm)],[1206, 1826])).
% 3.28/2.41 tff(1853,plain,
% 3.28/2.41 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | c0_1(a610) | c2_1(a610) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp28 | c0_1(a610) | c2_1(a610) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a610)))),
% 3.28/2.41 inference(rewrite,[status(thm)],[])).
% 3.28/2.41 tff(1854,plain,
% 3.28/2.41 ((hskp28 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c0_1(a610) | c2_1(a610) | (~c3_1(a610))) <=> (hskp28 | c0_1(a610) | c2_1(a610) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a610)))),
% 3.28/2.41 inference(rewrite,[status(thm)],[])).
% 3.28/2.41 tff(1855,plain,
% 3.28/2.41 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c0_1(a610) | c2_1(a610) | (~c3_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | c0_1(a610) | c2_1(a610) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a610))))),
% 3.28/2.41 inference(monotonicity,[status(thm)],[1854])).
% 3.28/2.41 tff(1856,plain,
% 3.28/2.41 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c0_1(a610) | c2_1(a610) | (~c3_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp28 | c0_1(a610) | c2_1(a610) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a610)))),
% 3.28/2.41 inference(transitivity,[status(thm)],[1855, 1853])).
% 3.28/2.41 tff(1857,plain,
% 3.28/2.41 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c0_1(a610) | c2_1(a610) | (~c3_1(a610)))),
% 3.28/2.41 inference(quant_inst,[status(thm)],[])).
% 3.28/2.41 tff(1858,plain,
% 3.28/2.41 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp28 | c0_1(a610) | c2_1(a610) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a610))),
% 3.28/2.41 inference(modus_ponens,[status(thm)],[1857, 1856])).
% 3.28/2.41 tff(1859,plain,
% 3.28/2.41 (hskp28),
% 3.28/2.41 inference(unit_resolution,[status(thm)],[1858, 107, 1512, 1510, 1852, 1828, 1827, 1122, 1843])).
% 3.28/2.41 tff(1860,plain,
% 3.28/2.41 (c3_1(a612)),
% 3.28/2.41 inference(unit_resolution,[status(thm)],[1139, 1859])).
% 3.28/2.41 tff(1861,plain,
% 3.28/2.41 (c2_1(a612)),
% 3.28/2.41 inference(unit_resolution,[status(thm)],[1150, 1859])).
% 3.28/2.41 tff(1862,plain,
% 3.28/2.41 (~c0_1(a612)),
% 3.28/2.41 inference(unit_resolution,[status(thm)],[1299, 107, 1861, 1860, 295, 1836, 1835, 282, 276, 1834, 11])).
% 3.28/2.41 tff(1863,plain,
% 3.28/2.41 (c1_1(a612)),
% 3.28/2.41 inference(unit_resolution,[status(thm)],[1435, 1859])).
% 3.28/2.41 tff(1864,plain,
% 3.28/2.41 (hskp10),
% 3.28/2.41 inference(unit_resolution,[status(thm)],[1535, 107, 1863, 1861, 1860, 1512, 1511, 1510, 21])).
% 3.28/2.41 tff(1865,plain,
% 3.28/2.41 (c3_1(a598)),
% 3.28/2.41 inference(unit_resolution,[status(thm)],[881, 1864])).
% 3.28/2.41 tff(1866,plain,
% 3.28/2.41 (~c1_1(a598)),
% 3.28/2.41 inference(unit_resolution,[status(thm)],[911, 1864])).
% 3.28/2.41 tff(1867,plain,
% 3.28/2.41 (~c3_1(a606)),
% 3.28/2.41 inference(unit_resolution,[status(thm)],[1075, 1850])).
% 3.28/2.41 tff(1868,plain,
% 3.28/2.41 (~c2_1(a606)),
% 3.28/2.41 inference(unit_resolution,[status(thm)],[1111, 1850])).
% 3.28/2.41 tff(1869,plain,
% 3.28/2.41 (c3_1(a593)),
% 3.28/2.41 inference(unit_resolution,[status(thm)],[511, 1785])).
% 3.28/2.41 tff(1870,plain,
% 3.28/2.41 (c1_1(a593)),
% 3.28/2.41 inference(unit_resolution,[status(thm)],[522, 1785])).
% 3.28/2.41 tff(1871,plain,
% 3.28/2.41 (c0_1(a598)),
% 3.28/2.41 inference(unit_resolution,[status(thm)],[892, 1864])).
% 3.28/2.41 tff(1872,assumption,(~hskp27), introduced(assumption)).
% 3.28/2.41 tff(1873,assumption,(~c2_1(a606)), introduced(assumption)).
% 3.28/2.41 tff(1874,assumption,(~c2_1(a610)), introduced(assumption)).
% 3.28/2.41 tff(1875,assumption,(~c0_1(a610)), introduced(assumption)).
% 3.28/2.41 tff(1876,assumption,(c1_1(a606)), introduced(assumption)).
% 3.28/2.41 tff(1877,assumption,(c3_1(a610)), introduced(assumption)).
% 3.28/2.41 tff(1878,plain,
% 3.28/2.41 (hskp27 | (~c0_1(a606))),
% 3.28/2.41 inference(unit_resolution,[status(thm)],[1213, 107, 1877, 1876, 1875, 1874, 1873, 540])).
% 3.28/2.41 tff(1879,plain,
% 3.28/2.41 (~c0_1(a606)),
% 3.28/2.41 inference(unit_resolution,[status(thm)],[1878, 1872])).
% 3.28/2.41 tff(1880,assumption,(~c0_1(a612)), introduced(assumption)).
% 3.28/2.41 tff(1881,assumption,(~c1_1(a598)), introduced(assumption)).
% 3.28/2.41 tff(1882,assumption,(~c3_1(a606)), introduced(assumption)).
% 3.28/2.41 tff(1883,assumption,(c3_1(a612)), introduced(assumption)).
% 3.28/2.41 tff(1884,assumption,(c2_1(a612)), introduced(assumption)).
% 3.28/2.41 tff(1885,plain,
% 3.28/2.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a606) | c3_1(a606) | c1_1(a598) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c3_1(a598)) | (~c2_1(a598)) | c0_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a606) | c3_1(a606) | c1_1(a598) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c3_1(a598)) | (~c2_1(a598)) | c0_1(a606))),
% 3.28/2.41 inference(rewrite,[status(thm)],[])).
% 3.28/2.41 tff(1886,plain,
% 3.28/2.41 (((~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c3_1(a598)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c3_1(a606) | c0_1(a606) | c2_1(a606)) <=> (c2_1(a606) | c3_1(a606) | c1_1(a598) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c3_1(a598)) | (~c2_1(a598)) | c0_1(a606))),
% 3.28/2.41 inference(rewrite,[status(thm)],[])).
% 3.28/2.41 tff(1887,plain,
% 3.28/2.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c3_1(a598)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c3_1(a606) | c0_1(a606) | c2_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a606) | c3_1(a606) | c1_1(a598) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c3_1(a598)) | (~c2_1(a598)) | c0_1(a606)))),
% 3.28/2.41 inference(monotonicity,[status(thm)],[1886])).
% 3.28/2.41 tff(1888,plain,
% 3.28/2.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c3_1(a598)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c3_1(a606) | c0_1(a606) | c2_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a606) | c3_1(a606) | c1_1(a598) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c3_1(a598)) | (~c2_1(a598)) | c0_1(a606))),
% 3.28/2.41 inference(transitivity,[status(thm)],[1887, 1885])).
% 3.28/2.41 tff(1889,plain,
% 3.28/2.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c3_1(a598)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c3_1(a606) | c0_1(a606) | c2_1(a606))),
% 3.28/2.41 inference(quant_inst,[status(thm)],[])).
% 3.28/2.41 tff(1890,plain,
% 3.28/2.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a606) | c3_1(a606) | c1_1(a598) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c3_1(a598)) | (~c2_1(a598)) | c0_1(a606)),
% 3.28/2.41 inference(modus_ponens,[status(thm)],[1889, 1888])).
% 3.28/2.41 tff(1891,plain,
% 3.28/2.41 ((~c2_1(a598)) | c0_1(a606)),
% 3.28/2.41 inference(unit_resolution,[status(thm)],[1890, 107, 1884, 1883, 896, 1873, 1882, 1881, 1730, 1880])).
% 3.28/2.41 tff(1892,plain,
% 3.28/2.41 (~c2_1(a598)),
% 3.28/2.41 inference(unit_resolution,[status(thm)],[1891, 1879])).
% 3.28/2.41 tff(1893,assumption,(~c2_1(a593)), introduced(assumption)).
% 3.28/2.41 tff(1894,assumption,(c1_1(a593)), introduced(assumption)).
% 3.28/2.41 tff(1895,plain,
% 3.28/2.41 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | c0_1(a610) | c2_1(a610) | c2_1(a593) | (~ndr1_0) | (~c0_1(a593)) | (~c1_1(a593)) | (~c3_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | c0_1(a610) | c2_1(a610) | c2_1(a593) | (~ndr1_0) | (~c0_1(a593)) | (~c1_1(a593)) | (~c3_1(a610)))),
% 3.28/2.41 inference(rewrite,[status(thm)],[])).
% 3.28/2.41 tff(1896,plain,
% 3.28/2.41 ((hskp27 | (~ndr1_0) | c2_1(a593) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a610) | c2_1(a610) | (~c3_1(a610))) <=> (hskp27 | c0_1(a610) | c2_1(a610) | c2_1(a593) | (~ndr1_0) | (~c0_1(a593)) | (~c1_1(a593)) | (~c3_1(a610)))),
% 3.28/2.41 inference(rewrite,[status(thm)],[])).
% 3.28/2.41 tff(1897,plain,
% 3.28/2.41 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a593) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a610) | c2_1(a610) | (~c3_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | c0_1(a610) | c2_1(a610) | c2_1(a593) | (~ndr1_0) | (~c0_1(a593)) | (~c1_1(a593)) | (~c3_1(a610))))),
% 3.28/2.41 inference(monotonicity,[status(thm)],[1896])).
% 3.28/2.41 tff(1898,plain,
% 3.28/2.41 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a593) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a610) | c2_1(a610) | (~c3_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | c0_1(a610) | c2_1(a610) | c2_1(a593) | (~ndr1_0) | (~c0_1(a593)) | (~c1_1(a593)) | (~c3_1(a610)))),
% 3.28/2.41 inference(transitivity,[status(thm)],[1897, 1895])).
% 3.28/2.41 tff(1899,plain,
% 3.28/2.41 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a593) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a610) | c2_1(a610) | (~c3_1(a610)))),
% 3.28/2.41 inference(quant_inst,[status(thm)],[])).
% 3.28/2.41 tff(1900,plain,
% 3.28/2.41 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | c0_1(a610) | c2_1(a610) | c2_1(a593) | (~ndr1_0) | (~c0_1(a593)) | (~c1_1(a593)) | (~c3_1(a610))),
% 3.28/2.41 inference(modus_ponens,[status(thm)],[1899, 1898])).
% 3.28/2.41 tff(1901,plain,
% 3.28/2.41 (hskp27 | (~c0_1(a593))),
% 3.28/2.41 inference(unit_resolution,[status(thm)],[1900, 107, 1877, 1894, 1875, 1874, 1893, 540])).
% 3.28/2.41 tff(1902,plain,
% 3.28/2.41 (~c0_1(a593)),
% 3.28/2.41 inference(unit_resolution,[status(thm)],[1901, 1872])).
% 3.28/2.41 tff(1903,assumption,(c3_1(a593)), introduced(assumption)).
% 3.28/2.41 tff(1904,plain,
% 3.28/2.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a606) | c3_1(a606) | c1_1(a598) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)) | c2_1(a598) | (~c0_1(a598)) | c0_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a606) | c3_1(a606) | c1_1(a598) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)) | c2_1(a598) | (~c0_1(a598)) | c0_1(a606))),
% 3.28/2.41 inference(rewrite,[status(thm)],[])).
% 3.28/2.41 tff(1905,plain,
% 3.28/2.41 (((~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)) | c0_1(a593) | (~c1_1(a593)) | (~c3_1(a593)) | c3_1(a606) | c0_1(a606) | c2_1(a606)) <=> (c2_1(a606) | c3_1(a606) | c1_1(a598) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)) | c2_1(a598) | (~c0_1(a598)) | c0_1(a606))),
% 3.28/2.41 inference(rewrite,[status(thm)],[])).
% 3.28/2.41 tff(1906,plain,
% 3.28/2.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)) | c0_1(a593) | (~c1_1(a593)) | (~c3_1(a593)) | c3_1(a606) | c0_1(a606) | c2_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a606) | c3_1(a606) | c1_1(a598) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)) | c2_1(a598) | (~c0_1(a598)) | c0_1(a606)))),
% 3.28/2.41 inference(monotonicity,[status(thm)],[1905])).
% 3.28/2.41 tff(1907,plain,
% 3.28/2.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)) | c0_1(a593) | (~c1_1(a593)) | (~c3_1(a593)) | c3_1(a606) | c0_1(a606) | c2_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a606) | c3_1(a606) | c1_1(a598) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)) | c2_1(a598) | (~c0_1(a598)) | c0_1(a606))),
% 3.28/2.41 inference(transitivity,[status(thm)],[1906, 1904])).
% 3.28/2.41 tff(1908,plain,
% 3.28/2.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)) | c0_1(a593) | (~c1_1(a593)) | (~c3_1(a593)) | c3_1(a606) | c0_1(a606) | c2_1(a606))),
% 3.28/2.41 inference(quant_inst,[status(thm)],[])).
% 3.28/2.41 tff(1909,plain,
% 3.28/2.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a606) | c3_1(a606) | c1_1(a598) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)) | c2_1(a598) | (~c0_1(a598)) | c0_1(a606)),
% 3.28/2.41 inference(modus_ponens,[status(thm)],[1908, 1907])).
% 3.28/2.41 tff(1910,plain,
% 3.28/2.41 ($false),
% 3.28/2.41 inference(unit_resolution,[status(thm)],[1909, 107, 897, 1894, 1903, 1873, 1882, 1881, 1364, 1902, 1892, 1879])).
% 3.28/2.41 tff(1911,plain,(hskp27 | (~c0_1(a598)) | (~c1_1(a593)) | (~c3_1(a593)) | c2_1(a606) | c3_1(a606) | c1_1(a598) | (~c2_1(a612)) | (~c3_1(a612)) | (~c3_1(a598)) | c0_1(a612) | (~c3_1(a610)) | (~c1_1(a606)) | c0_1(a610) | c2_1(a610) | c2_1(a593)), inference(lemma,lemma(discharge,[]))).
% 3.28/2.41 tff(1912,plain,
% 3.28/2.41 (hskp27),
% 3.28/2.41 inference(unit_resolution,[status(thm)],[1911, 1871, 1870, 1869, 1868, 1867, 1866, 1861, 1860, 1865, 1862, 1852, 1851, 1828, 1827, 1786])).
% 3.28/2.41 tff(1913,plain,
% 3.28/2.41 (c3_1(a611)),
% 3.28/2.41 inference(unit_resolution,[status(thm)],[620, 1912])).
% 3.28/2.41 tff(1914,plain,
% 3.28/2.41 (c1_1(a611)),
% 3.28/2.41 inference(unit_resolution,[status(thm)],[631, 1912])).
% 3.28/2.41 tff(1915,plain,
% 3.28/2.42 (c0_1(a611)),
% 3.28/2.42 inference(unit_resolution,[status(thm)],[642, 1912])).
% 3.28/2.42 tff(1916,plain,
% 3.28/2.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a595)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a595)))),
% 3.28/2.42 inference(rewrite,[status(thm)],[])).
% 3.28/2.42 tff(1917,plain,
% 3.28/2.42 (((~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595))) <=> (c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a595)))),
% 3.28/2.42 inference(rewrite,[status(thm)],[])).
% 3.28/2.42 tff(1918,plain,
% 3.28/2.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a595))))),
% 3.28/2.42 inference(monotonicity,[status(thm)],[1917])).
% 3.28/2.42 tff(1919,plain,
% 3.28/2.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a595)))),
% 3.28/2.42 inference(transitivity,[status(thm)],[1918, 1916])).
% 3.28/2.42 tff(1920,plain,
% 3.28/2.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595)))),
% 3.28/2.42 inference(quant_inst,[status(thm)],[])).
% 3.28/2.42 tff(1921,plain,
% 3.28/2.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a595))),
% 3.28/2.42 inference(modus_ponens,[status(thm)],[1920, 1919])).
% 3.28/2.42 tff(1922,plain,
% 3.28/2.42 (~c2_1(a595)),
% 3.28/2.42 inference(unit_resolution,[status(thm)],[1921, 107, 1915, 1914, 1913, 1708, 1707, 1704, 1703, 1706, 65])).
% 3.28/2.42 tff(1923,plain,
% 3.28/2.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a598) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c2_1(a595) | (~c3_1(a598)) | (~c2_1(a598)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a598) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c2_1(a595) | (~c3_1(a598)) | (~c2_1(a598)))),
% 3.28/2.42 inference(rewrite,[status(thm)],[])).
% 3.28/2.42 tff(1924,plain,
% 3.28/2.42 (((~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c3_1(a598)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c3_1(a595) | c0_1(a595) | c2_1(a595)) <=> (c1_1(a598) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c2_1(a595) | (~c3_1(a598)) | (~c2_1(a598)))),
% 3.28/2.42 inference(rewrite,[status(thm)],[])).
% 3.28/2.42 tff(1925,plain,
% 3.28/2.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c3_1(a598)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c3_1(a595) | c0_1(a595) | c2_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a598) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c2_1(a595) | (~c3_1(a598)) | (~c2_1(a598))))),
% 3.28/2.42 inference(monotonicity,[status(thm)],[1924])).
% 3.28/2.42 tff(1926,plain,
% 3.28/2.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c3_1(a598)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c3_1(a595) | c0_1(a595) | c2_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a598) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c2_1(a595) | (~c3_1(a598)) | (~c2_1(a598)))),
% 3.28/2.42 inference(transitivity,[status(thm)],[1925, 1923])).
% 3.28/2.42 tff(1927,plain,
% 3.28/2.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c3_1(a598)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c3_1(a595) | c0_1(a595) | c2_1(a595))),
% 3.28/2.42 inference(quant_inst,[status(thm)],[])).
% 3.28/2.42 tff(1928,plain,
% 3.28/2.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a598) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c2_1(a595) | (~c3_1(a598)) | (~c2_1(a598))),
% 3.28/2.42 inference(modus_ponens,[status(thm)],[1927, 1926])).
% 3.28/2.42 tff(1929,plain,
% 3.28/2.42 (c2_1(a595) | (~c2_1(a598))),
% 3.28/2.42 inference(unit_resolution,[status(thm)],[1928, 107, 1861, 1860, 1865, 1866, 1704, 1702, 1730, 1862])).
% 3.28/2.42 tff(1930,plain,
% 3.28/2.42 (~c2_1(a598)),
% 3.28/2.42 inference(unit_resolution,[status(thm)],[1929, 1922])).
% 3.28/2.42 tff(1931,plain,
% 3.28/2.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a604) | c1_1(a598) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a595) | c2_1(a598) | (~c0_1(a598)) | (~c3_1(a604)) | (~c1_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a604) | c1_1(a598) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a595) | c2_1(a598) | (~c0_1(a598)) | (~c3_1(a604)) | (~c1_1(a604)))),
% 3.28/2.42 inference(rewrite,[status(thm)],[])).
% 3.28/2.42 tff(1932,plain,
% 3.28/2.42 (((~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a595) | c0_1(a595) | c2_1(a595)) <=> (c0_1(a604) | c1_1(a598) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a595) | c2_1(a598) | (~c0_1(a598)) | (~c3_1(a604)) | (~c1_1(a604)))),
% 3.28/2.42 inference(rewrite,[status(thm)],[])).
% 3.28/2.42 tff(1933,plain,
% 3.28/2.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a595) | c0_1(a595) | c2_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a604) | c1_1(a598) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a595) | c2_1(a598) | (~c0_1(a598)) | (~c3_1(a604)) | (~c1_1(a604))))),
% 3.28/2.42 inference(monotonicity,[status(thm)],[1932])).
% 3.30/2.42 tff(1934,plain,
% 3.30/2.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a595) | c0_1(a595) | c2_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a604) | c1_1(a598) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a595) | c2_1(a598) | (~c0_1(a598)) | (~c3_1(a604)) | (~c1_1(a604)))),
% 3.30/2.42 inference(transitivity,[status(thm)],[1933, 1931])).
% 3.30/2.42 tff(1935,plain,
% 3.30/2.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a595) | c0_1(a595) | c2_1(a595))),
% 3.30/2.42 inference(quant_inst,[status(thm)],[])).
% 3.30/2.42 tff(1936,plain,
% 3.30/2.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a604) | c1_1(a598) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a595) | c2_1(a598) | (~c0_1(a598)) | (~c3_1(a604)) | (~c1_1(a604))),
% 3.30/2.42 inference(modus_ponens,[status(thm)],[1935, 1934])).
% 3.30/2.42 tff(1937,plain,
% 3.30/2.42 ($false),
% 3.30/2.42 inference(unit_resolution,[status(thm)],[1936, 107, 1832, 1831, 1871, 1830, 1866, 1704, 1702, 1364, 1930, 1922])).
% 3.30/2.42 tff(1938,plain,(hskp11 | hskp29 | hskp22), inference(lemma,lemma(discharge,[]))).
% 3.30/2.42 tff(1939,plain,
% 3.30/2.42 (hskp11),
% 3.30/2.42 inference(unit_resolution,[status(thm)],[1938, 269, 44])).
% 3.30/2.42 tff(1940,plain,
% 3.30/2.42 (~c1_1(a599)),
% 3.30/2.42 inference(unit_resolution,[status(thm)],[428, 1939])).
% 3.30/2.42 tff(1941,plain,
% 3.30/2.42 (c2_1(a590)),
% 3.30/2.42 inference(unit_resolution,[status(thm)],[688, 1636])).
% 3.30/2.42 tff(1942,plain,
% 3.30/2.42 (c3_1(a599)),
% 3.30/2.42 inference(unit_resolution,[status(thm)],[422, 1939])).
% 3.30/2.42 tff(1943,plain,
% 3.30/2.42 (c2_1(a599)),
% 3.30/2.42 inference(unit_resolution,[status(thm)],[439, 1939])).
% 3.30/2.42 tff(1944,plain,
% 3.30/2.42 (c3_1(a590)),
% 3.30/2.42 inference(unit_resolution,[status(thm)],[677, 1636])).
% 3.30/2.42 tff(1945,assumption,(~hskp9), introduced(assumption)).
% 3.30/2.42 tff(1946,plain,
% 3.30/2.42 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | c1_1(a599) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a599)) | c0_1(a599))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c1_1(a599) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a599)) | c0_1(a599))),
% 3.30/2.42 inference(rewrite,[status(thm)],[])).
% 3.30/2.42 tff(1947,plain,
% 3.30/2.42 ((hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a599) | c0_1(a599) | (~c3_1(a599))) <=> (hskp9 | c1_1(a599) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a599)) | c0_1(a599))),
% 3.30/2.42 inference(rewrite,[status(thm)],[])).
% 3.30/2.42 tff(1948,plain,
% 3.30/2.42 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a599) | c0_1(a599) | (~c3_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | c1_1(a599) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a599)) | c0_1(a599)))),
% 3.30/2.42 inference(monotonicity,[status(thm)],[1947])).
% 3.30/2.42 tff(1949,plain,
% 3.30/2.42 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a599) | c0_1(a599) | (~c3_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c1_1(a599) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a599)) | c0_1(a599))),
% 3.30/2.42 inference(transitivity,[status(thm)],[1948, 1946])).
% 3.30/2.42 tff(1950,plain,
% 3.30/2.42 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a599) | c0_1(a599) | (~c3_1(a599)))),
% 3.30/2.42 inference(quant_inst,[status(thm)],[])).
% 3.30/2.42 tff(1951,plain,
% 3.30/2.42 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c1_1(a599) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a599)) | c0_1(a599)),
% 3.30/2.42 inference(modus_ponens,[status(thm)],[1950, 1949])).
% 3.30/2.42 tff(1952,plain,
% 3.30/2.42 (hskp9 | c0_1(a599)),
% 3.30/2.42 inference(unit_resolution,[status(thm)],[1951, 107, 1651, 1650, 1649, 462, 461, 294])).
% 3.30/2.42 tff(1953,plain,
% 3.30/2.42 (c0_1(a599)),
% 3.30/2.42 inference(unit_resolution,[status(thm)],[1952, 1945])).
% 3.30/2.42 tff(1954,plain,
% 3.30/2.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c3_1(a607)))),
% 3.30/2.42 inference(rewrite,[status(thm)],[])).
% 3.30/2.42 tff(1955,plain,
% 3.30/2.42 (((~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a590) | (~c1_1(a590)) | (~c2_1(a590))) <=> (c1_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c3_1(a607)))),
% 3.30/2.42 inference(rewrite,[status(thm)],[])).
% 3.30/2.42 tff(1956,plain,
% 3.30/2.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a590) | (~c1_1(a590)) | (~c2_1(a590)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c3_1(a607))))),
% 3.30/2.42 inference(monotonicity,[status(thm)],[1955])).
% 3.30/2.42 tff(1957,plain,
% 3.30/2.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a590) | (~c1_1(a590)) | (~c2_1(a590)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c3_1(a607)))),
% 3.30/2.42 inference(transitivity,[status(thm)],[1956, 1954])).
% 3.30/2.42 tff(1958,plain,
% 3.30/2.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a590) | (~c1_1(a590)) | (~c2_1(a590)))),
% 3.30/2.42 inference(quant_inst,[status(thm)],[])).
% 3.30/2.42 tff(1959,plain,
% 3.30/2.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c3_1(a607))),
% 3.30/2.42 inference(modus_ponens,[status(thm)],[1958, 1957])).
% 3.30/2.42 tff(1960,plain,
% 3.30/2.42 ((~c1_1(a590)) | (~c0_1(a599))),
% 3.30/2.42 inference(unit_resolution,[status(thm)],[1959, 107, 321, 463, 462, 863, 66, 22, 45, 11])).
% 3.30/2.42 tff(1961,plain,
% 3.30/2.42 (~c1_1(a590)),
% 3.30/2.42 inference(unit_resolution,[status(thm)],[1960, 1953])).
% 3.30/2.42 tff(1962,plain,
% 3.30/2.42 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | c1_1(a590))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | c1_1(a590))),
% 3.30/2.42 inference(rewrite,[status(thm)],[])).
% 3.30/2.42 tff(1963,plain,
% 3.30/2.42 ((hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a590) | c0_1(a590) | (~c3_1(a590))) <=> (hskp9 | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | c1_1(a590))),
% 3.30/2.42 inference(rewrite,[status(thm)],[])).
% 3.30/2.42 tff(1964,plain,
% 3.30/2.42 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a590) | c0_1(a590) | (~c3_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | c1_1(a590)))),
% 3.30/2.42 inference(monotonicity,[status(thm)],[1963])).
% 3.30/2.42 tff(1965,plain,
% 3.30/2.42 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a590) | c0_1(a590) | (~c3_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | c1_1(a590))),
% 3.30/2.42 inference(transitivity,[status(thm)],[1964, 1962])).
% 3.30/2.42 tff(1966,plain,
% 3.30/2.42 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a590) | c0_1(a590) | (~c3_1(a590)))),
% 3.30/2.42 inference(quant_inst,[status(thm)],[])).
% 3.30/2.42 tff(1967,plain,
% 3.30/2.42 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | c1_1(a590)),
% 3.30/2.42 inference(modus_ponens,[status(thm)],[1966, 1965])).
% 3.30/2.42 tff(1968,plain,
% 3.30/2.42 ($false),
% 3.30/2.42 inference(unit_resolution,[status(thm)],[1967, 107, 1945, 1651, 1650, 1649, 862, 45, 294, 1961])).
% 3.30/2.42 tff(1969,plain,(hskp9 | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c3_1(a590)) | c0_1(a590) | (~c3_1(a607)) | (~c2_1(a599)) | (~c3_1(a599)) | (~c2_1(a590)) | c1_1(a607) | c2_1(a607) | c1_1(a599)), inference(lemma,lemma(discharge,[]))).
% 3.30/2.42 tff(1970,plain,
% 3.30/2.42 (hskp9),
% 3.30/2.42 inference(unit_resolution,[status(thm)],[1969, 1512, 1511, 1510, 1944, 1637, 295, 1943, 1942, 1941, 282, 276, 1940])).
% 3.30/2.42 tff(1971,plain,
% 3.30/2.42 (~c1_1(a595)),
% 3.30/2.42 inference(unit_resolution,[status(thm)],[1493, 1970])).
% 3.30/2.42 tff(1972,plain,
% 3.30/2.42 (~c0_1(a595)),
% 3.30/2.42 inference(unit_resolution,[status(thm)],[1499, 1970])).
% 3.30/2.42 tff(1973,assumption,(~hskp28), introduced(assumption)).
% 3.30/2.42 tff(1974,assumption,(~c3_1(a583)), introduced(assumption)).
% 3.30/2.42 tff(1975,plain,
% 3.30/2.42 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c1_1(a599) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)) | (~c3_1(a599)) | (~c2_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a599) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)) | (~c3_1(a599)) | (~c2_1(a599)))),
% 3.30/2.42 inference(rewrite,[status(thm)],[])).
% 3.30/2.42 tff(1976,plain,
% 3.30/2.42 ((hskp28 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c1_1(a583)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599))) <=> (hskp28 | c1_1(a599) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)) | (~c3_1(a599)) | (~c2_1(a599)))),
% 3.30/2.42 inference(rewrite,[status(thm)],[])).
% 3.30/2.42 tff(1977,plain,
% 3.30/2.42 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c1_1(a583)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c1_1(a599) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)) | (~c3_1(a599)) | (~c2_1(a599))))),
% 3.30/2.42 inference(monotonicity,[status(thm)],[1976])).
% 3.30/2.42 tff(1978,plain,
% 3.30/2.42 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c1_1(a583)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a599) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)) | (~c3_1(a599)) | (~c2_1(a599)))),
% 3.30/2.42 inference(transitivity,[status(thm)],[1977, 1975])).
% 3.30/2.42 tff(1979,plain,
% 3.30/2.42 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c1_1(a583)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)))),
% 3.30/2.42 inference(quant_inst,[status(thm)],[])).
% 3.30/2.42 tff(1980,plain,
% 3.30/2.42 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a599) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)) | (~c3_1(a599)) | (~c2_1(a599))),
% 3.30/2.42 inference(modus_ponens,[status(thm)],[1979, 1978])).
% 3.30/2.42 tff(1981,plain,
% 3.30/2.42 ($false),
% 3.30/2.42 inference(unit_resolution,[status(thm)],[1980, 107, 1973, 1650, 1649, 463, 462, 461, 1748, 1974])).
% 3.30/2.42 tff(1982,plain,(c3_1(a583) | hskp28 | (~c1_1(a583)) | (~c2_1(a583)) | (~c2_1(a599)) | (~c3_1(a599)) | c1_1(a599)), inference(lemma,lemma(discharge,[]))).
% 3.30/2.42 tff(1983,plain,
% 3.30/2.42 (c3_1(a583)),
% 3.30/2.42 inference(unit_resolution,[status(thm)],[1982, 1973, 1650, 1649, 463, 462, 461])).
% 3.30/2.42 tff(1984,plain,
% 3.30/2.42 (^[V: $i, U: $i] : refl((hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 3.30/2.42 inference(bind,[status(th)],[])).
% 3.30/2.42 tff(1985,plain,
% 3.30/2.42 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 3.30/2.42 inference(quant_intro,[status(thm)],[1984])).
% 3.30/2.42 tff(1986,plain,
% 3.30/2.42 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 3.30/2.42 inference(rewrite,[status(thm)],[])).
% 3.30/2.42 tff(1987,plain,
% 3.30/2.42 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp15) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp15))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp15) <=> (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp15) <=> (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 3.30/2.43 inference(bind,[status(th)],[])).
% 3.30/2.43 tff(1988,plain,
% 3.30/2.43 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp15) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 3.30/2.43 inference(quant_intro,[status(thm)],[1987])).
% 3.30/2.43 tff(1989,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause191')).
% 3.30/2.43 tff(1990,plain,
% 3.30/2.43 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 3.30/2.43 inference(modus_ponens,[status(thm)],[1989, 1988])).
% 3.30/2.43 tff(1991,plain,
% 3.30/2.43 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 3.30/2.43 inference(modus_ponens,[status(thm)],[1990, 1986])).
% 3.30/2.43 tff(1992,plain,(
% 3.30/2.43 ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 3.30/2.43 inference(skolemize,[status(sab)],[1991])).
% 3.30/2.43 tff(1993,plain,
% 3.30/2.43 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 3.30/2.43 inference(modus_ponens,[status(thm)],[1992, 1985])).
% 3.30/2.43 tff(1994,plain,
% 3.30/2.43 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)))),
% 3.30/2.43 inference(rewrite,[status(thm)],[])).
% 3.30/2.43 tff(1995,plain,
% 3.30/2.43 ((hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c1_1(a583)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583))) <=> (hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)))),
% 3.30/2.43 inference(rewrite,[status(thm)],[])).
% 3.30/2.43 tff(1996,plain,
% 3.30/2.43 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c1_1(a583)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583))))),
% 3.30/2.43 inference(monotonicity,[status(thm)],[1995])).
% 3.30/2.43 tff(1997,plain,
% 3.30/2.43 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c1_1(a583)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)))),
% 3.30/2.43 inference(transitivity,[status(thm)],[1996, 1994])).
% 3.30/2.43 tff(1998,plain,
% 3.30/2.43 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c1_1(a583)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583)))),
% 3.30/2.43 inference(quant_inst,[status(thm)],[])).
% 3.30/2.43 tff(1999,plain,
% 3.30/2.43 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583))),
% 3.30/2.43 inference(modus_ponens,[status(thm)],[1998, 1997])).
% 3.30/2.43 tff(2000,plain,
% 3.30/2.43 (hskp10 | (~c3_1(a583))),
% 3.30/2.43 inference(unit_resolution,[status(thm)],[1999, 107, 1651, 1650, 1649, 21])).
% 3.30/2.43 tff(2001,plain,
% 3.30/2.43 (hskp10),
% 3.30/2.43 inference(unit_resolution,[status(thm)],[2000, 1983])).
% 3.30/2.43 tff(2002,plain,
% 3.30/2.43 (~c1_1(a598)),
% 3.30/2.43 inference(unit_resolution,[status(thm)],[911, 2001])).
% 3.30/2.43 tff(2003,plain,
% 3.30/2.43 (c3_1(a598)),
% 3.30/2.43 inference(unit_resolution,[status(thm)],[881, 2001])).
% 3.30/2.43 tff(2004,plain,
% 3.30/2.43 (c0_1(a598)),
% 3.30/2.43 inference(unit_resolution,[status(thm)],[892, 2001])).
% 3.30/2.43 tff(2005,plain,
% 3.30/2.43 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | c1_1(a598) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a598)) | (~c0_1(a598)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a598) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a598)) | (~c0_1(a598)))),
% 3.30/2.43 inference(rewrite,[status(thm)],[])).
% 3.30/2.43 tff(2006,plain,
% 3.30/2.43 ((hskp15 | (~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a598) | (~c3_1(a598)) | (~c0_1(a598))) <=> (hskp15 | c1_1(a598) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a598)) | (~c0_1(a598)))),
% 3.30/2.43 inference(rewrite,[status(thm)],[])).
% 3.30/2.43 tff(2007,plain,
% 3.30/2.43 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a598) | (~c3_1(a598)) | (~c0_1(a598)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | c1_1(a598) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a598)) | (~c0_1(a598))))),
% 3.30/2.43 inference(monotonicity,[status(thm)],[2006])).
% 3.30/2.43 tff(2008,plain,
% 3.30/2.43 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a598) | (~c3_1(a598)) | (~c0_1(a598)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a598) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a598)) | (~c0_1(a598)))),
% 3.30/2.43 inference(transitivity,[status(thm)],[2007, 2005])).
% 3.30/2.43 tff(2009,plain,
% 3.30/2.43 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a598) | (~c3_1(a598)) | (~c0_1(a598)))),
% 3.30/2.43 inference(quant_inst,[status(thm)],[])).
% 3.30/2.43 tff(2010,plain,
% 3.30/2.43 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a598) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a598)) | (~c0_1(a598))),
% 3.30/2.43 inference(modus_ponens,[status(thm)],[2009, 2008])).
% 3.30/2.43 tff(2011,plain,
% 3.30/2.43 (hskp15),
% 3.30/2.43 inference(unit_resolution,[status(thm)],[2010, 107, 1651, 1650, 2004, 2003, 2002, 1993, 1983])).
% 3.30/2.43 tff(2012,plain,
% 3.30/2.43 (~c0_1(a604)),
% 3.30/2.43 inference(unit_resolution,[status(thm)],[1591, 2011])).
% 3.30/2.43 tff(2013,plain,
% 3.30/2.43 (c1_1(a604)),
% 3.30/2.43 inference(unit_resolution,[status(thm)],[1613, 2011])).
% 3.30/2.43 tff(2014,plain,
% 3.30/2.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a607) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a607)))),
% 3.30/2.43 inference(rewrite,[status(thm)],[])).
% 3.30/2.43 tff(2015,plain,
% 3.30/2.43 (((~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604))) <=> (c1_1(a607) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a607)))),
% 3.30/2.43 inference(rewrite,[status(thm)],[])).
% 3.30/2.43 tff(2016,plain,
% 3.30/2.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a607) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a607))))),
% 3.30/2.43 inference(monotonicity,[status(thm)],[2015])).
% 3.30/2.43 tff(2017,plain,
% 3.30/2.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a607)))),
% 3.30/2.43 inference(transitivity,[status(thm)],[2016, 2014])).
% 3.30/2.43 tff(2018,plain,
% 3.30/2.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))),
% 3.30/2.43 inference(quant_inst,[status(thm)],[])).
% 3.30/2.43 tff(2019,plain,
% 3.30/2.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a607))),
% 3.30/2.43 inference(modus_ponens,[status(thm)],[2018, 2017])).
% 3.30/2.43 tff(2020,plain,
% 3.30/2.43 (~c2_1(a604)),
% 3.30/2.43 inference(unit_resolution,[status(thm)],[2019, 107, 1651, 1649, 321, 2013, 66, 22, 2012, 11, 1983])).
% 3.30/2.43 tff(2021,plain,
% 3.30/2.43 (c3_1(a604)),
% 3.30/2.43 inference(unit_resolution,[status(thm)],[1602, 2011])).
% 3.30/2.43 tff(2022,plain,
% 3.30/2.43 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | c0_1(a604) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a604)) | c2_1(a604))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp28 | c0_1(a604) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a604)) | c2_1(a604))),
% 3.30/2.43 inference(rewrite,[status(thm)],[])).
% 3.30/2.43 tff(2023,plain,
% 3.30/2.43 ((hskp28 | (~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a604) | c2_1(a604) | (~c3_1(a604))) <=> (hskp28 | c0_1(a604) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a604)) | c2_1(a604))),
% 3.30/2.43 inference(rewrite,[status(thm)],[])).
% 3.30/2.43 tff(2024,plain,
% 3.30/2.43 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a604) | c2_1(a604) | (~c3_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | c0_1(a604) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a604)) | c2_1(a604)))),
% 3.30/2.43 inference(monotonicity,[status(thm)],[2023])).
% 3.30/2.43 tff(2025,plain,
% 3.30/2.43 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a604) | c2_1(a604) | (~c3_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp28 | c0_1(a604) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a604)) | c2_1(a604))),
% 3.30/2.43 inference(transitivity,[status(thm)],[2024, 2022])).
% 3.30/2.43 tff(2026,plain,
% 3.30/2.43 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a604) | c2_1(a604) | (~c3_1(a604)))),
% 3.30/2.43 inference(quant_inst,[status(thm)],[])).
% 3.30/2.43 tff(2027,plain,
% 3.30/2.43 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp28 | c0_1(a604) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a604)) | c2_1(a604)),
% 3.30/2.43 inference(modus_ponens,[status(thm)],[2026, 2025])).
% 3.30/2.43 tff(2028,plain,
% 3.30/2.43 (~c2_1(a603)),
% 3.30/2.43 inference(unit_resolution,[status(thm)],[2027, 107, 1973, 2021, 1009, 2012, 997, 1122, 2020])).
% 3.30/2.43 tff(2029,plain,
% 3.30/2.43 (hskp6 | c2_1(a603)),
% 3.30/2.43 inference(unit_resolution,[status(thm)],[189, 107, 44, 1009, 998, 43])).
% 3.30/2.43 tff(2030,plain,
% 3.30/2.43 (hskp6),
% 3.30/2.43 inference(unit_resolution,[status(thm)],[2029, 2028])).
% 3.30/2.43 tff(2031,plain,
% 3.30/2.43 (~c0_1(a590)),
% 3.30/2.43 inference(unit_resolution,[status(thm)],[666, 2030])).
% 3.30/2.43 tff(2032,plain,
% 3.30/2.43 (c2_1(a590)),
% 3.30/2.43 inference(unit_resolution,[status(thm)],[688, 2030])).
% 3.30/2.43 tff(2033,plain,
% 3.30/2.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a607)))),
% 3.30/2.43 inference(rewrite,[status(thm)],[])).
% 3.30/2.43 tff(2034,plain,
% 3.30/2.43 (((~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a590) | (~c1_1(a590)) | (~c2_1(a590))) <=> (c1_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a607)))),
% 3.30/2.43 inference(rewrite,[status(thm)],[])).
% 3.30/2.43 tff(2035,plain,
% 3.30/2.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a590) | (~c1_1(a590)) | (~c2_1(a590)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a607))))),
% 3.30/2.43 inference(monotonicity,[status(thm)],[2034])).
% 3.30/2.43 tff(2036,plain,
% 3.30/2.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a590) | (~c1_1(a590)) | (~c2_1(a590)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a607)))),
% 3.30/2.43 inference(transitivity,[status(thm)],[2035, 2033])).
% 3.30/2.43 tff(2037,plain,
% 3.30/2.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a590) | (~c1_1(a590)) | (~c2_1(a590)))),
% 3.30/2.43 inference(quant_inst,[status(thm)],[])).
% 3.30/2.43 tff(2038,plain,
% 3.30/2.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a607))),
% 3.30/2.43 inference(modus_ponens,[status(thm)],[2037, 2036])).
% 3.30/2.43 tff(2039,plain,
% 3.30/2.43 (~c1_1(a590)),
% 3.30/2.43 inference(unit_resolution,[status(thm)],[2038, 107, 1651, 1649, 321, 2032, 66, 22, 2031, 11, 1983])).
% 3.30/2.43 tff(2040,plain,
% 3.30/2.43 (c3_1(a590)),
% 3.30/2.43 inference(unit_resolution,[status(thm)],[677, 2030])).
% 3.30/2.43 tff(2041,plain,
% 3.30/2.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590))),
% 3.30/2.43 inference(rewrite,[status(thm)],[])).
% 3.30/2.43 tff(2042,plain,
% 3.30/2.43 (((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | c0_1(a590) | (~c2_1(a590))) <=> (c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590))),
% 3.30/2.43 inference(rewrite,[status(thm)],[])).
% 3.30/2.43 tff(2043,plain,
% 3.30/2.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | c0_1(a590) | (~c2_1(a590)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590)))),
% 3.30/2.43 inference(monotonicity,[status(thm)],[2042])).
% 3.30/2.43 tff(2044,plain,
% 3.30/2.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | c0_1(a590) | (~c2_1(a590)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590))),
% 3.30/2.43 inference(transitivity,[status(thm)],[2043, 2041])).
% 3.30/2.43 tff(2045,plain,
% 3.30/2.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | c0_1(a590) | (~c2_1(a590)))),
% 3.30/2.43 inference(quant_inst,[status(thm)],[])).
% 3.30/2.43 tff(2046,plain,
% 3.30/2.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590)),
% 3.30/2.43 inference(modus_ponens,[status(thm)],[2045, 2044])).
% 3.30/2.43 tff(2047,plain,
% 3.30/2.43 ($false),
% 3.30/2.43 inference(unit_resolution,[status(thm)],[2046, 107, 1651, 1650, 2032, 2040, 2031, 65, 1983, 2039])).
% 3.30/2.43 tff(2048,plain,(hskp28 | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c3_1(a607)) | c1_1(a607) | c2_1(a607) | hskp22 | (~c0_1(a603)) | c1_1(a603) | c3_1(a603) | (~c2_1(a599)) | (~c3_1(a599)) | c1_1(a599)), inference(lemma,lemma(discharge,[]))).
% 3.30/2.43 tff(2049,plain,
% 3.30/2.43 (hskp28),
% 3.30/2.43 inference(unit_resolution,[status(thm)],[2048, 1512, 1511, 1510, 295, 282, 276, 44, 983, 985, 984, 1943, 1942, 1940])).
% 3.30/2.43 tff(2050,plain,
% 3.30/2.43 (c1_1(a612)),
% 3.30/2.43 inference(unit_resolution,[status(thm)],[1435, 2049])).
% 3.30/2.43 tff(2051,plain,
% 3.30/2.43 (c2_1(a612)),
% 3.30/2.43 inference(unit_resolution,[status(thm)],[1150, 2049])).
% 3.30/2.43 tff(2052,plain,
% 3.30/2.43 (c3_1(a612)),
% 3.30/2.43 inference(unit_resolution,[status(thm)],[1139, 2049])).
% 3.30/2.43 tff(2053,plain,
% 3.30/2.43 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))),
% 3.30/2.43 inference(bind,[status(th)],[])).
% 3.30/2.43 tff(2054,plain,
% 3.30/2.43 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 3.30/2.43 inference(quant_intro,[status(thm)],[2053])).
% 3.30/2.43 tff(2055,plain,
% 3.30/2.43 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 3.30/2.43 inference(rewrite,[status(thm)],[])).
% 3.30/2.43 tff(2056,plain,
% 3.30/2.43 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp8) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp8))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))))),
% 3.30/2.43 inference(bind,[status(th)],[])).
% 3.30/2.43 tff(2057,plain,
% 3.30/2.43 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 3.30/2.43 inference(quant_intro,[status(thm)],[2056])).
% 3.30/2.43 tff(2058,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause186')).
% 3.30/2.43 tff(2059,plain,
% 3.30/2.43 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 3.30/2.43 inference(modus_ponens,[status(thm)],[2058, 2057])).
% 3.30/2.43 tff(2060,plain,
% 3.30/2.43 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 3.30/2.43 inference(modus_ponens,[status(thm)],[2059, 2055])).
% 3.30/2.43 tff(2061,plain,(
% 3.30/2.43 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 3.30/2.43 inference(skolemize,[status(sab)],[2060])).
% 3.30/2.43 tff(2062,plain,
% 3.30/2.43 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 3.30/2.43 inference(modus_ponens,[status(thm)],[2061, 2054])).
% 3.30/2.43 tff(2063,plain,
% 3.30/2.43 (hskp28),
% 3.30/2.43 inference(unit_resolution,[status(thm)],[2048, 1651, 1650, 1649, 321, 66, 22, 44, 1009, 998, 997, 463, 462, 461])).
% 3.30/2.43 tff(2064,plain,
% 3.30/2.43 (c3_1(a612)),
% 3.30/2.43 inference(unit_resolution,[status(thm)],[1139, 2063])).
% 3.30/2.43 tff(2065,plain,
% 3.30/2.43 (c2_1(a612)),
% 3.30/2.43 inference(unit_resolution,[status(thm)],[1150, 2063])).
% 3.30/2.43 tff(2066,plain,
% 3.30/2.43 (c1_1(a612)),
% 3.30/2.43 inference(unit_resolution,[status(thm)],[1435, 2063])).
% 3.30/2.43 tff(2067,plain,
% 3.30/2.43 (hskp10),
% 3.30/2.43 inference(unit_resolution,[status(thm)],[1535, 107, 2066, 2065, 2064, 1651, 1650, 1649, 21])).
% 3.30/2.43 tff(2068,plain,
% 3.30/2.43 (~c1_1(a598)),
% 3.30/2.43 inference(unit_resolution,[status(thm)],[911, 2067])).
% 3.30/2.43 tff(2069,plain,
% 3.30/2.43 (c3_1(a598)),
% 3.30/2.43 inference(unit_resolution,[status(thm)],[881, 2067])).
% 3.30/2.43 tff(2070,plain,
% 3.30/2.43 (c0_1(a598)),
% 3.30/2.43 inference(unit_resolution,[status(thm)],[892, 2067])).
% 3.30/2.43 tff(2071,plain,
% 3.30/2.43 (^[U: $i] : refl((hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 3.30/2.43 inference(bind,[status(th)],[])).
% 3.30/2.43 tff(2072,plain,
% 3.30/2.43 (![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 3.30/2.43 inference(quant_intro,[status(thm)],[2071])).
% 3.30/2.43 tff(2073,plain,
% 3.30/2.43 (![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 3.30/2.43 inference(rewrite,[status(thm)],[])).
% 3.30/2.43 tff(2074,plain,
% 3.30/2.43 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp27))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) | hskp8) <=> ((hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp8))), rewrite(((hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp8) <=> (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) | hskp8) <=> (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 3.30/2.44 inference(bind,[status(th)],[])).
% 3.30/2.44 tff(2075,plain,
% 3.30/2.44 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) | hskp8) <=> ![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 3.30/2.44 inference(quant_intro,[status(thm)],[2074])).
% 3.30/2.44 tff(2076,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause157')).
% 3.30/2.44 tff(2077,plain,
% 3.30/2.44 (![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 3.30/2.44 inference(modus_ponens,[status(thm)],[2076, 2075])).
% 3.30/2.44 tff(2078,plain,
% 3.30/2.44 (![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 3.30/2.44 inference(modus_ponens,[status(thm)],[2077, 2073])).
% 3.30/2.44 tff(2079,plain,(
% 3.30/2.44 ![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 3.30/2.44 inference(skolemize,[status(sab)],[2078])).
% 3.30/2.44 tff(2080,plain,
% 3.30/2.44 (![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 3.30/2.44 inference(modus_ponens,[status(thm)],[2079, 2072])).
% 3.30/2.44 tff(2081,plain,
% 3.30/2.44 (((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp8 | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)))) <=> ((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp27 | hskp8 | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)))),
% 3.30/2.44 inference(rewrite,[status(thm)],[])).
% 3.30/2.44 tff(2082,plain,
% 3.30/2.44 ((hskp27 | hskp8 | (~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603))) <=> (hskp27 | hskp8 | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)))),
% 3.30/2.44 inference(rewrite,[status(thm)],[])).
% 3.30/2.44 tff(2083,plain,
% 3.30/2.44 (((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp8 | (~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)))) <=> ((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp8 | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603))))),
% 3.30/2.44 inference(monotonicity,[status(thm)],[2082])).
% 3.30/2.44 tff(2084,plain,
% 3.30/2.44 (((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp8 | (~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)))) <=> ((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp27 | hskp8 | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)))),
% 3.30/2.44 inference(transitivity,[status(thm)],[2083, 2081])).
% 3.30/2.44 tff(2085,plain,
% 3.30/2.44 ((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp8 | (~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)))),
% 3.30/2.44 inference(quant_inst,[status(thm)],[])).
% 3.30/2.44 tff(2086,plain,
% 3.30/2.44 ((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp27 | hskp8 | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603))),
% 3.30/2.44 inference(modus_ponens,[status(thm)],[2085, 2084])).
% 3.30/2.44 tff(2087,plain,
% 3.30/2.44 (hskp27 | hskp8 | (~c2_1(a603))),
% 3.30/2.44 inference(unit_resolution,[status(thm)],[2086, 107, 1009, 997, 2080])).
% 3.30/2.44 tff(2088,plain,
% 3.30/2.44 (~c2_1(a603)),
% 3.30/2.44 inference(unit_resolution,[status(thm)],[2087, 1872, 1709])).
% 3.30/2.44 tff(2089,plain,
% 3.30/2.44 (((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp8 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)))) <=> ((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp27 | hskp8 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)))),
% 3.30/2.44 inference(rewrite,[status(thm)],[])).
% 3.30/2.44 tff(2090,plain,
% 3.30/2.44 ((hskp27 | hskp8 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583))) <=> (hskp27 | hskp8 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)))),
% 3.30/2.44 inference(rewrite,[status(thm)],[])).
% 3.30/2.44 tff(2091,plain,
% 3.30/2.44 (((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp8 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)))) <=> ((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp8 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583))))),
% 3.30/2.44 inference(monotonicity,[status(thm)],[2090])).
% 3.30/2.44 tff(2092,plain,
% 3.30/2.44 (((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp8 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)))) <=> ((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp27 | hskp8 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)))),
% 3.30/2.44 inference(transitivity,[status(thm)],[2091, 2089])).
% 3.30/2.44 tff(2093,plain,
% 3.30/2.44 ((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp8 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)))),
% 3.30/2.44 inference(quant_inst,[status(thm)],[])).
% 3.30/2.44 tff(2094,plain,
% 3.30/2.44 ((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp27 | hskp8 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583))),
% 3.30/2.44 inference(modus_ponens,[status(thm)],[2093, 2092])).
% 3.30/2.44 tff(2095,plain,
% 3.30/2.44 (hskp27 | hskp8 | c3_1(a583)),
% 3.30/2.44 inference(unit_resolution,[status(thm)],[2094, 107, 1651, 1649, 2080])).
% 3.30/2.44 tff(2096,plain,
% 3.30/2.44 (c3_1(a583)),
% 3.30/2.44 inference(unit_resolution,[status(thm)],[2095, 1872, 1709])).
% 3.30/2.44 tff(2097,plain,
% 3.30/2.44 (hskp6),
% 3.30/2.44 inference(unit_resolution,[status(thm)],[2029, 2088])).
% 3.30/2.44 tff(2098,plain,
% 3.30/2.44 (~c0_1(a590)),
% 3.30/2.44 inference(unit_resolution,[status(thm)],[666, 2097])).
% 3.30/2.44 tff(2099,plain,
% 3.30/2.44 (c3_1(a590)),
% 3.30/2.44 inference(unit_resolution,[status(thm)],[677, 2097])).
% 3.30/2.44 tff(2100,plain,
% 3.30/2.44 (c2_1(a590)),
% 3.30/2.44 inference(unit_resolution,[status(thm)],[688, 2097])).
% 3.30/2.44 tff(2101,plain,
% 3.30/2.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a599)) | c0_1(a599))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a599)) | c0_1(a599))),
% 3.30/2.44 inference(rewrite,[status(thm)],[])).
% 3.30/2.44 tff(2102,plain,
% 3.30/2.44 (((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599))) <=> (c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a599)) | c0_1(a599))),
% 3.30/2.44 inference(rewrite,[status(thm)],[])).
% 3.30/2.44 tff(2103,plain,
% 3.30/2.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a599)) | c0_1(a599)))),
% 3.30/2.44 inference(monotonicity,[status(thm)],[2102])).
% 3.30/2.44 tff(2104,plain,
% 3.30/2.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a599)) | c0_1(a599))),
% 3.30/2.44 inference(transitivity,[status(thm)],[2103, 2101])).
% 3.30/2.44 tff(2105,plain,
% 3.30/2.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))),
% 3.30/2.44 inference(quant_inst,[status(thm)],[])).
% 3.30/2.44 tff(2106,plain,
% 3.30/2.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a599)) | c0_1(a599)),
% 3.30/2.44 inference(modus_ponens,[status(thm)],[2105, 2104])).
% 3.30/2.44 tff(2107,plain,
% 3.30/2.44 (c0_1(a599)),
% 3.30/2.44 inference(unit_resolution,[status(thm)],[2106, 107, 1651, 1650, 463, 2100, 2099, 461, 2098, 65, 2096])).
% 3.30/2.44 tff(2108,plain,
% 3.30/2.44 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | c1_1(a599) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a599)) | (~c0_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a599) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a599)) | (~c0_1(a599)))),
% 3.30/2.44 inference(rewrite,[status(thm)],[])).
% 3.30/2.44 tff(2109,plain,
% 3.30/2.44 ((hskp15 | (~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599))) <=> (hskp15 | c1_1(a599) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a599)) | (~c0_1(a599)))),
% 3.30/2.44 inference(rewrite,[status(thm)],[])).
% 3.30/2.44 tff(2110,plain,
% 3.30/2.44 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | c1_1(a599) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a599)) | (~c0_1(a599))))),
% 3.30/2.44 inference(monotonicity,[status(thm)],[2109])).
% 3.30/2.44 tff(2111,plain,
% 3.30/2.44 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a599) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a599)) | (~c0_1(a599)))),
% 3.30/2.44 inference(transitivity,[status(thm)],[2110, 2108])).
% 3.30/2.44 tff(2112,plain,
% 3.30/2.44 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599)))),
% 3.30/2.44 inference(quant_inst,[status(thm)],[])).
% 3.30/2.44 tff(2113,plain,
% 3.30/2.44 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a599) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a599)) | (~c0_1(a599))),
% 3.30/2.44 inference(modus_ponens,[status(thm)],[2112, 2111])).
% 3.30/2.44 tff(2114,plain,
% 3.30/2.44 (hskp15),
% 3.30/2.44 inference(unit_resolution,[status(thm)],[2113, 107, 1651, 1650, 462, 461, 1993, 2096, 2107])).
% 3.30/2.44 tff(2115,plain,
% 3.30/2.44 (~c0_1(a604)),
% 3.30/2.44 inference(unit_resolution,[status(thm)],[1591, 2114])).
% 3.30/2.44 tff(2116,plain,
% 3.30/2.44 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 3.30/2.44 inference(bind,[status(th)],[])).
% 3.30/2.44 tff(2117,plain,
% 3.30/2.44 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 3.30/2.44 inference(quant_intro,[status(thm)],[2116])).
% 3.30/2.44 tff(2118,plain,
% 3.30/2.44 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 3.30/2.44 inference(rewrite,[status(thm)],[])).
% 3.30/2.44 tff(2119,plain,
% 3.30/2.44 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp16) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp16))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 3.30/2.44 inference(bind,[status(th)],[])).
% 3.30/2.44 tff(2120,plain,
% 3.30/2.44 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 3.30/2.44 inference(quant_intro,[status(thm)],[2119])).
% 3.30/2.44 tff(2121,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause180')).
% 3.30/2.44 tff(2122,plain,
% 3.30/2.44 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 3.30/2.44 inference(modus_ponens,[status(thm)],[2121, 2120])).
% 3.30/2.44 tff(2123,plain,
% 3.30/2.44 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 3.30/2.44 inference(modus_ponens,[status(thm)],[2122, 2118])).
% 3.30/2.44 tff(2124,plain,(
% 3.30/2.44 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 3.30/2.44 inference(skolemize,[status(sab)],[2123])).
% 3.30/2.44 tff(2125,plain,
% 3.30/2.44 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 3.30/2.44 inference(modus_ponens,[status(thm)],[2124, 2117])).
% 3.30/2.44 tff(2126,plain,
% 3.30/2.44 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | c3_1(a603) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c2_1(a603) | (~c0_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c3_1(a603) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c2_1(a603) | (~c0_1(a603)))),
% 3.30/2.44 inference(rewrite,[status(thm)],[])).
% 3.30/2.44 tff(2127,plain,
% 3.30/2.44 ((hskp16 | (~ndr1_0) | c2_1(a603) | c3_1(a603) | (~c0_1(a603)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590))) <=> (hskp16 | c3_1(a603) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c2_1(a603) | (~c0_1(a603)))),
% 3.30/2.44 inference(rewrite,[status(thm)],[])).
% 3.30/2.44 tff(2128,plain,
% 3.30/2.44 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a603) | c3_1(a603) | (~c0_1(a603)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | c3_1(a603) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c2_1(a603) | (~c0_1(a603))))),
% 3.30/2.44 inference(monotonicity,[status(thm)],[2127])).
% 3.30/2.44 tff(2129,plain,
% 3.30/2.44 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a603) | c3_1(a603) | (~c0_1(a603)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c3_1(a603) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c2_1(a603) | (~c0_1(a603)))),
% 3.30/2.44 inference(transitivity,[status(thm)],[2128, 2126])).
% 3.30/2.44 tff(2130,plain,
% 3.30/2.44 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a603) | c3_1(a603) | (~c0_1(a603)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)))),
% 3.30/2.44 inference(quant_inst,[status(thm)],[])).
% 3.30/2.44 tff(2131,plain,
% 3.30/2.44 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c3_1(a603) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c2_1(a603) | (~c0_1(a603))),
% 3.30/2.44 inference(modus_ponens,[status(thm)],[2130, 2129])).
% 3.30/2.44 tff(2132,plain,
% 3.30/2.44 (hskp16),
% 3.30/2.44 inference(unit_resolution,[status(thm)],[2131, 107, 1009, 2100, 2099, 997, 2098, 2125, 2088])).
% 3.30/2.44 tff(2133,plain,
% 3.30/2.44 (~c3_1(a606)),
% 3.30/2.44 inference(unit_resolution,[status(thm)],[1075, 2132])).
% 3.30/2.44 tff(2134,plain,
% 3.30/2.44 (~c2_1(a606)),
% 3.30/2.44 inference(unit_resolution,[status(thm)],[1111, 2132])).
% 3.30/2.44 tff(2135,plain,
% 3.30/2.44 (c3_1(a604)),
% 3.30/2.44 inference(unit_resolution,[status(thm)],[1602, 2114])).
% 3.30/2.44 tff(2136,plain,
% 3.30/2.44 (c1_1(a604)),
% 3.30/2.44 inference(unit_resolution,[status(thm)],[1613, 2114])).
% 3.30/2.44 tff(2137,plain,
% 3.30/2.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a606) | c3_1(a606) | c0_1(a604) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a606) | c3_1(a606) | c0_1(a604) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a606))),
% 3.30/2.44 inference(rewrite,[status(thm)],[])).
% 3.30/2.44 tff(2138,plain,
% 3.30/2.44 (((~ndr1_0) | c2_1(a603) | c1_1(a603) | (~c0_1(a603)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a606) | c0_1(a606) | c2_1(a606)) <=> (c2_1(a606) | c3_1(a606) | c0_1(a604) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a606))),
% 3.30/2.44 inference(rewrite,[status(thm)],[])).
% 3.30/2.44 tff(2139,plain,
% 3.30/2.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a603) | c1_1(a603) | (~c0_1(a603)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a606) | c0_1(a606) | c2_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a606) | c3_1(a606) | c0_1(a604) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a606)))),
% 3.30/2.44 inference(monotonicity,[status(thm)],[2138])).
% 3.30/2.44 tff(2140,plain,
% 3.30/2.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a603) | c1_1(a603) | (~c0_1(a603)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a606) | c0_1(a606) | c2_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a606) | c3_1(a606) | c0_1(a604) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a606))),
% 3.30/2.44 inference(transitivity,[status(thm)],[2139, 2137])).
% 3.30/2.44 tff(2141,plain,
% 3.30/2.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a603) | c1_1(a603) | (~c0_1(a603)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a606) | c0_1(a606) | c2_1(a606))),
% 3.30/2.44 inference(quant_inst,[status(thm)],[])).
% 3.30/2.44 tff(2142,plain,
% 3.30/2.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a606) | c3_1(a606) | c0_1(a604) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a606)),
% 3.30/2.44 inference(modus_ponens,[status(thm)],[2141, 2140])).
% 3.30/2.44 tff(2143,plain,
% 3.30/2.44 (c0_1(a606)),
% 3.30/2.44 inference(unit_resolution,[status(thm)],[2142, 107, 2136, 2135, 1009, 2134, 2133, 2115, 998, 1364, 2088])).
% 3.30/2.44 tff(2144,plain,
% 3.30/2.44 (~c2_1(a604)),
% 3.30/2.44 inference(unit_resolution,[status(thm)],[2019, 107, 1651, 1649, 321, 2136, 66, 22, 2115, 11, 2096])).
% 3.30/2.44 tff(2145,plain,
% 3.30/2.44 (c1_1(a606)),
% 3.30/2.44 inference(unit_resolution,[status(thm)],[1088, 2132])).
% 3.30/2.44 tff(2146,plain,
% 3.30/2.44 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | c2_1(a606) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c0_1(a606)) | (~c1_1(a606)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | c2_1(a606) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c0_1(a606)) | (~c1_1(a606)))),
% 3.30/2.44 inference(rewrite,[status(thm)],[])).
% 3.30/2.44 tff(2147,plain,
% 3.30/2.44 ((hskp27 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c0_1(a604) | c2_1(a604) | (~c3_1(a604))) <=> (hskp27 | c2_1(a606) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c0_1(a606)) | (~c1_1(a606)))),
% 3.30/2.44 inference(rewrite,[status(thm)],[])).
% 3.30/2.44 tff(2148,plain,
% 3.30/2.44 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c0_1(a604) | c2_1(a604) | (~c3_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | c2_1(a606) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c0_1(a606)) | (~c1_1(a606))))),
% 3.30/2.44 inference(monotonicity,[status(thm)],[2147])).
% 3.30/2.44 tff(2149,plain,
% 3.30/2.44 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c0_1(a604) | c2_1(a604) | (~c3_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | c2_1(a606) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c0_1(a606)) | (~c1_1(a606)))),
% 3.30/2.44 inference(transitivity,[status(thm)],[2148, 2146])).
% 3.30/2.44 tff(2150,plain,
% 3.30/2.44 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c0_1(a604) | c2_1(a604) | (~c3_1(a604)))),
% 3.30/2.44 inference(quant_inst,[status(thm)],[])).
% 3.30/2.44 tff(2151,plain,
% 3.30/2.44 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | c2_1(a606) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c0_1(a606)) | (~c1_1(a606))),
% 3.30/2.44 inference(modus_ponens,[status(thm)],[2150, 2149])).
% 3.30/2.44 tff(2152,plain,
% 3.30/2.44 ($false),
% 3.30/2.44 inference(unit_resolution,[status(thm)],[2151, 107, 1872, 2145, 2135, 2134, 2115, 540, 2144, 2143])).
% 3.30/2.44 tff(2153,plain,(hskp27 | (~c0_1(a603)) | c1_1(a603) | (~c0_1(a583)) | (~c2_1(a583)) | (~c3_1(a607)) | c1_1(a607) | c2_1(a607) | c3_1(a603) | (~c1_1(a583)) | (~c3_1(a599)) | c1_1(a599) | (~c2_1(a599)) | hskp22 | hskp8), inference(lemma,lemma(discharge,[]))).
% 3.30/2.44 tff(2154,plain,
% 3.30/2.44 (hskp27),
% 3.30/2.44 inference(unit_resolution,[status(thm)],[2153, 1709, 998, 1651, 1649, 321, 66, 22, 997, 1650, 462, 461, 463, 44, 1009])).
% 3.30/2.44 tff(2155,plain,
% 3.30/2.44 (c3_1(a611)),
% 3.30/2.44 inference(unit_resolution,[status(thm)],[620, 2154])).
% 3.30/2.44 tff(2156,plain,
% 3.30/2.44 (c1_1(a611)),
% 3.30/2.44 inference(unit_resolution,[status(thm)],[631, 2154])).
% 3.30/2.44 tff(2157,plain,
% 3.30/2.44 (c0_1(a611)),
% 3.30/2.44 inference(unit_resolution,[status(thm)],[642, 2154])).
% 3.30/2.44 tff(2158,plain,
% 3.30/2.44 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | c1_1(a598) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a598)) | (~c0_1(a598)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a598) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a598)) | (~c0_1(a598)))),
% 3.30/2.44 inference(rewrite,[status(thm)],[])).
% 3.30/2.44 tff(2159,plain,
% 3.30/2.44 ((hskp15 | (~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c1_1(a598) | (~c3_1(a598)) | (~c0_1(a598))) <=> (hskp15 | c1_1(a598) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a598)) | (~c0_1(a598)))),
% 3.30/2.44 inference(rewrite,[status(thm)],[])).
% 3.30/2.44 tff(2160,plain,
% 3.30/2.44 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c1_1(a598) | (~c3_1(a598)) | (~c0_1(a598)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | c1_1(a598) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a598)) | (~c0_1(a598))))),
% 3.30/2.45 inference(monotonicity,[status(thm)],[2159])).
% 3.30/2.45 tff(2161,plain,
% 3.30/2.45 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c1_1(a598) | (~c3_1(a598)) | (~c0_1(a598)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a598) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a598)) | (~c0_1(a598)))),
% 3.30/2.45 inference(transitivity,[status(thm)],[2160, 2158])).
% 3.30/2.45 tff(2162,plain,
% 3.30/2.45 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c1_1(a598) | (~c3_1(a598)) | (~c0_1(a598)))),
% 3.30/2.45 inference(quant_inst,[status(thm)],[])).
% 3.30/2.45 tff(2163,plain,
% 3.30/2.45 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a598) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a598)) | (~c0_1(a598))),
% 3.30/2.45 inference(modus_ponens,[status(thm)],[2162, 2161])).
% 3.30/2.45 tff(2164,plain,
% 3.30/2.45 (hskp15),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[2163, 107, 2157, 2156, 2155, 2070, 2069, 2068, 1993])).
% 3.30/2.45 tff(2165,plain,
% 3.30/2.45 (~c0_1(a604)),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[1591, 2164])).
% 3.30/2.45 tff(2166,plain,
% 3.30/2.45 (c3_1(a604)),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[1602, 2164])).
% 3.30/2.45 tff(2167,plain,
% 3.30/2.45 (c1_1(a604)),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[1613, 2164])).
% 3.30/2.45 tff(2168,plain,
% 3.30/2.45 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp8 | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)) | (~c0_1(a607)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp8 | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.30/2.45 inference(rewrite,[status(thm)],[])).
% 3.30/2.45 tff(2169,plain,
% 3.30/2.45 ((hskp8 | (~ndr1_0) | c2_1(a607) | (~c3_1(a607)) | (~c0_1(a607)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604))) <=> (hskp8 | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.30/2.45 inference(rewrite,[status(thm)],[])).
% 3.30/2.45 tff(2170,plain,
% 3.30/2.45 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a607) | (~c3_1(a607)) | (~c0_1(a607)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp8 | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)) | (~c0_1(a607)) | (~c3_1(a607))))),
% 3.30/2.45 inference(monotonicity,[status(thm)],[2169])).
% 3.30/2.45 tff(2171,plain,
% 3.30/2.45 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a607) | (~c3_1(a607)) | (~c0_1(a607)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp8 | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.30/2.45 inference(transitivity,[status(thm)],[2170, 2168])).
% 3.30/2.45 tff(2172,plain,
% 3.30/2.45 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a607) | (~c3_1(a607)) | (~c0_1(a607)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)))),
% 3.30/2.45 inference(quant_inst,[status(thm)],[])).
% 3.30/2.45 tff(2173,plain,
% 3.30/2.45 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp8 | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)) | (~c0_1(a607)) | (~c3_1(a607))),
% 3.30/2.45 inference(modus_ponens,[status(thm)],[2172, 2171])).
% 3.30/2.45 tff(2174,plain,
% 3.30/2.45 (~c0_1(a607)),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[2173, 107, 1709, 321, 2167, 2166, 22, 2165, 2062])).
% 3.30/2.45 tff(2175,plain,
% 3.30/2.45 (((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp6 | c1_1(a607) | (~ndr1_0) | c0_1(a607) | (~c3_1(a607)))) <=> ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp8 | hskp6 | c1_1(a607) | (~ndr1_0) | c0_1(a607) | (~c3_1(a607)))),
% 3.30/2.45 inference(rewrite,[status(thm)],[])).
% 3.30/2.45 tff(2176,plain,
% 3.30/2.45 ((hskp8 | hskp6 | (~ndr1_0) | c1_1(a607) | c0_1(a607) | (~c3_1(a607))) <=> (hskp8 | hskp6 | c1_1(a607) | (~ndr1_0) | c0_1(a607) | (~c3_1(a607)))),
% 3.30/2.45 inference(rewrite,[status(thm)],[])).
% 3.30/2.45 tff(2177,plain,
% 3.30/2.45 (((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp6 | (~ndr1_0) | c1_1(a607) | c0_1(a607) | (~c3_1(a607)))) <=> ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp6 | c1_1(a607) | (~ndr1_0) | c0_1(a607) | (~c3_1(a607))))),
% 3.30/2.45 inference(monotonicity,[status(thm)],[2176])).
% 3.30/2.45 tff(2178,plain,
% 3.30/2.45 (((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp6 | (~ndr1_0) | c1_1(a607) | c0_1(a607) | (~c3_1(a607)))) <=> ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp8 | hskp6 | c1_1(a607) | (~ndr1_0) | c0_1(a607) | (~c3_1(a607)))),
% 3.30/2.45 inference(transitivity,[status(thm)],[2177, 2175])).
% 3.30/2.45 tff(2179,plain,
% 3.30/2.45 ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp6 | (~ndr1_0) | c1_1(a607) | c0_1(a607) | (~c3_1(a607)))),
% 3.30/2.45 inference(quant_inst,[status(thm)],[])).
% 3.30/2.45 tff(2180,plain,
% 3.30/2.45 ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp8 | hskp6 | c1_1(a607) | (~ndr1_0) | c0_1(a607) | (~c3_1(a607))),
% 3.30/2.45 inference(modus_ponens,[status(thm)],[2179, 2178])).
% 3.30/2.45 tff(2181,plain,
% 3.30/2.45 (hskp8 | hskp6 | c0_1(a607)),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[2180, 107, 321, 66, 450])).
% 3.30/2.45 tff(2182,plain,
% 3.30/2.45 (hskp6),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[2181, 2174, 1709])).
% 3.30/2.45 tff(2183,plain,
% 3.30/2.45 (~c0_1(a590)),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[666, 2182])).
% 3.30/2.45 tff(2184,plain,
% 3.30/2.45 (hskp9 | c0_1(a607)),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[1518, 107, 1651, 1650, 1649, 321, 66, 294])).
% 3.30/2.45 tff(2185,plain,
% 3.30/2.45 (hskp9),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[2184, 2174])).
% 3.30/2.45 tff(2186,plain,
% 3.30/2.45 (~c1_1(a595)),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[1493, 2185])).
% 3.30/2.45 tff(2187,plain,
% 3.30/2.45 (~c0_1(a595)),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[1499, 2185])).
% 3.30/2.45 tff(2188,plain,
% 3.30/2.45 (c3_1(a590)),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[677, 2182])).
% 3.30/2.45 tff(2189,plain,
% 3.30/2.45 (c2_1(a590)),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[688, 2182])).
% 3.30/2.45 tff(2190,plain,
% 3.30/2.45 (~c2_1(a595)),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[1921, 107, 2157, 2156, 2155, 2189, 2188, 2187, 2186, 2183, 65])).
% 3.30/2.45 tff(2191,plain,
% 3.30/2.45 (~c3_1(a595)),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[1487, 2185])).
% 3.30/2.45 tff(2192,plain,
% 3.30/2.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a599) | c0_1(a595) | c3_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c2_1(a595) | (~c3_1(a599)) | (~c2_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a599) | c0_1(a595) | c3_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c2_1(a595) | (~c3_1(a599)) | (~c2_1(a599)))),
% 3.30/2.45 inference(rewrite,[status(thm)],[])).
% 3.30/2.45 tff(2193,plain,
% 3.30/2.45 (((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a595) | c0_1(a595) | c2_1(a595)) <=> (c1_1(a599) | c0_1(a595) | c3_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c2_1(a595) | (~c3_1(a599)) | (~c2_1(a599)))),
% 3.30/2.45 inference(rewrite,[status(thm)],[])).
% 3.30/2.45 tff(2194,plain,
% 3.30/2.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a595) | c0_1(a595) | c2_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a599) | c0_1(a595) | c3_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c2_1(a595) | (~c3_1(a599)) | (~c2_1(a599))))),
% 3.30/2.45 inference(monotonicity,[status(thm)],[2193])).
% 3.30/2.45 tff(2195,plain,
% 3.30/2.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a595) | c0_1(a595) | c2_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a599) | c0_1(a595) | c3_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c2_1(a595) | (~c3_1(a599)) | (~c2_1(a599)))),
% 3.30/2.45 inference(transitivity,[status(thm)],[2194, 2192])).
% 3.30/2.45 tff(2196,plain,
% 3.30/2.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a595) | c0_1(a595) | c2_1(a595))),
% 3.30/2.45 inference(quant_inst,[status(thm)],[])).
% 3.30/2.45 tff(2197,plain,
% 3.30/2.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a599) | c0_1(a595) | c3_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c2_1(a595) | (~c3_1(a599)) | (~c2_1(a599))),
% 3.30/2.45 inference(modus_ponens,[status(thm)],[2196, 2195])).
% 3.30/2.45 tff(2198,plain,
% 3.30/2.45 ($false),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[2197, 107, 463, 462, 2189, 2188, 461, 2187, 2191, 2183, 1730, 2190])).
% 3.30/2.45 tff(2199,plain,(hskp8 | (~c2_1(a599)) | (~c3_1(a599)) | c1_1(a599) | (~c3_1(a607)) | c1_1(a607) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a583)) | c2_1(a607) | c1_1(a603) | c3_1(a603) | hskp22 | (~c0_1(a603))), inference(lemma,lemma(discharge,[]))).
% 3.30/2.45 tff(2200,plain,
% 3.30/2.45 (hskp8),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[2199, 1943, 1942, 1940, 295, 282, 1512, 1511, 1510, 276, 985, 984, 44, 983])).
% 3.30/2.45 tff(2201,plain,
% 3.30/2.45 (c1_1(a593)),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[522, 2200])).
% 3.30/2.45 tff(2202,plain,
% 3.30/2.45 (~c2_1(a593)),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[555, 2200])).
% 3.30/2.45 tff(2203,plain,
% 3.30/2.45 (c3_1(a593)),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[511, 2200])).
% 3.30/2.45 tff(2204,assumption,(c1_1(a612)), introduced(assumption)).
% 3.30/2.45 tff(2205,plain,
% 3.30/2.45 (hskp10),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[1535, 107, 2204, 1884, 1883, 1651, 1650, 1649, 21])).
% 3.30/2.45 tff(2206,plain,
% 3.30/2.45 (c0_1(a598)),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[892, 2205])).
% 3.30/2.45 tff(2207,plain,
% 3.30/2.45 (c3_1(a598)),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[881, 2205])).
% 3.30/2.45 tff(2208,plain,
% 3.30/2.45 (~c1_1(a598)),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[911, 2205])).
% 3.30/2.45 tff(2209,plain,
% 3.30/2.45 (c2_1(a595)),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[2197, 107, 463, 462, 863, 862, 461, 1558, 1556, 45, 1730])).
% 3.30/2.45 tff(2210,plain,
% 3.30/2.45 (hskp2),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[1754, 107, 1558, 1557, 1556, 200, 2209])).
% 3.30/2.45 tff(2211,plain,
% 3.30/2.45 (~c3_1(a586)),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[218, 2210])).
% 3.30/2.45 tff(2212,plain,
% 3.30/2.45 (c2_1(a586)),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[1474, 2210])).
% 3.30/2.45 tff(2213,plain,
% 3.30/2.45 (c1_1(a586)),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[229, 2210])).
% 3.30/2.45 tff(2214,plain,
% 3.30/2.45 (hskp18),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[1825, 269, 107, 2213, 2212, 2211, 1796])).
% 3.30/2.45 tff(2215,plain,
% 3.30/2.45 (~c2_1(a610)),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[1189, 2214])).
% 3.30/2.45 tff(2216,plain,
% 3.30/2.45 (~c0_1(a610)),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[1195, 2214])).
% 3.30/2.45 tff(2217,plain,
% 3.30/2.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a595)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a595)))),
% 3.30/2.45 inference(rewrite,[status(thm)],[])).
% 3.30/2.45 tff(2218,plain,
% 3.30/2.45 (((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595))) <=> (c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a595)))),
% 3.30/2.45 inference(rewrite,[status(thm)],[])).
% 3.30/2.45 tff(2219,plain,
% 3.30/2.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a595))))),
% 3.30/2.45 inference(monotonicity,[status(thm)],[2218])).
% 3.30/2.45 tff(2220,plain,
% 3.30/2.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a595)))),
% 3.30/2.45 inference(transitivity,[status(thm)],[2219, 2217])).
% 3.30/2.45 tff(2221,plain,
% 3.30/2.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595)))),
% 3.30/2.45 inference(quant_inst,[status(thm)],[])).
% 3.30/2.45 tff(2222,plain,
% 3.30/2.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a595))),
% 3.30/2.45 inference(modus_ponens,[status(thm)],[2221, 2220])).
% 3.30/2.45 tff(2223,plain,
% 3.30/2.45 ((~c0_1(a593)) | (~c2_1(a595))),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[2222, 107, 1894, 1903, 863, 862, 1558, 1557, 45, 65])).
% 3.30/2.45 tff(2224,plain,
% 3.30/2.45 (~c0_1(a593)),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[2223, 2209])).
% 3.30/2.45 tff(2225,plain,
% 3.30/2.45 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | c1_1(a595) | c3_1(a595) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a595)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp16 | c1_1(a595) | c3_1(a595) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a595)))),
% 3.30/2.45 inference(rewrite,[status(thm)],[])).
% 3.30/2.45 tff(2226,plain,
% 3.30/2.45 ((hskp16 | (~ndr1_0) | c1_1(a595) | c3_1(a595) | (~c2_1(a595)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593))) <=> (hskp16 | c1_1(a595) | c3_1(a595) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a595)))),
% 3.30/2.45 inference(rewrite,[status(thm)],[])).
% 3.30/2.45 tff(2227,plain,
% 3.30/2.45 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a595) | c3_1(a595) | (~c2_1(a595)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | c1_1(a595) | c3_1(a595) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a595))))),
% 3.30/2.45 inference(monotonicity,[status(thm)],[2226])).
% 3.30/2.45 tff(2228,plain,
% 3.30/2.45 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a595) | c3_1(a595) | (~c2_1(a595)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp16 | c1_1(a595) | c3_1(a595) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a595)))),
% 3.30/2.45 inference(transitivity,[status(thm)],[2227, 2225])).
% 3.30/2.45 tff(2229,plain,
% 3.30/2.45 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a595) | c3_1(a595) | (~c2_1(a595)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)))),
% 3.30/2.45 inference(quant_inst,[status(thm)],[])).
% 3.30/2.45 tff(2230,plain,
% 3.30/2.45 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp16 | c1_1(a595) | c3_1(a595) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a595))),
% 3.30/2.45 inference(modus_ponens,[status(thm)],[2229, 2228])).
% 3.30/2.45 tff(2231,plain,
% 3.30/2.45 (hskp16),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[2230, 107, 1894, 1557, 1556, 1893, 1022, 2224, 2209])).
% 3.30/2.45 tff(2232,plain,
% 3.30/2.45 (c1_1(a606)),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[1088, 2231])).
% 3.30/2.45 tff(2233,plain,
% 3.30/2.45 (c3_1(a610)),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[1206, 2214])).
% 3.30/2.45 tff(2234,plain,
% 3.30/2.45 ((~c0_1(a612)) | (~c2_1(a595))),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[1774, 107, 2204, 1883, 863, 862, 1558, 1557, 45, 65])).
% 3.30/2.45 tff(2235,plain,
% 3.30/2.45 (~c0_1(a612)),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[2234, 2209])).
% 3.30/2.45 tff(2236,plain,
% 3.30/2.45 (~c2_1(a606)),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[1111, 2231])).
% 3.30/2.45 tff(2237,plain,
% 3.30/2.45 (~c3_1(a606)),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[1075, 2231])).
% 3.30/2.45 tff(2238,plain,
% 3.30/2.45 ($false),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[1911, 2237, 2236, 1884, 1903, 1893, 1894, 1881, 1872, 1883, 896, 2235, 2233, 2232, 2216, 2215, 897])).
% 3.30/2.45 tff(2239,plain,(c3_1(a595) | (~c2_1(a612)) | (~c3_1(a593)) | c2_1(a593) | (~c1_1(a593)) | c1_1(a598) | hskp27 | (~c3_1(a612)) | (~c3_1(a598)) | (~c0_1(a598)) | c1_1(a595) | hskp29 | (~c2_1(a590)) | (~c3_1(a590)) | c0_1(a595) | c0_1(a590) | (~c1_1(a612)) | (~c2_1(a599)) | (~c3_1(a599)) | c1_1(a599)), inference(lemma,lemma(discharge,[]))).
% 3.30/2.45 tff(2240,plain,
% 3.30/2.45 (c3_1(a595)),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[2239, 1557, 1903, 1893, 1894, 2208, 1872, 1883, 2207, 2206, 1884, 269, 863, 862, 1558, 45, 2204, 463, 462, 461])).
% 3.30/2.45 tff(2241,plain,
% 3.30/2.45 (~hskp9),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[1487, 2240])).
% 3.30/2.45 tff(2242,plain,
% 3.30/2.45 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | c0_1(a595) | c1_1(a595) | (~c3_1(a595)) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c0_1(a595) | c1_1(a595) | (~c3_1(a595)) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)))),
% 3.30/2.45 inference(rewrite,[status(thm)],[])).
% 3.30/2.45 tff(2243,plain,
% 3.30/2.45 ((hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a595) | c0_1(a595) | (~c3_1(a595))) <=> (hskp9 | c0_1(a595) | c1_1(a595) | (~c3_1(a595)) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)))),
% 3.30/2.45 inference(rewrite,[status(thm)],[])).
% 3.30/2.45 tff(2244,plain,
% 3.30/2.45 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a595) | c0_1(a595) | (~c3_1(a595)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | c0_1(a595) | c1_1(a595) | (~c3_1(a595)) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583))))),
% 3.30/2.45 inference(monotonicity,[status(thm)],[2243])).
% 3.30/2.45 tff(2245,plain,
% 3.30/2.45 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a595) | c0_1(a595) | (~c3_1(a595)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c0_1(a595) | c1_1(a595) | (~c3_1(a595)) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)))),
% 3.30/2.45 inference(transitivity,[status(thm)],[2244, 2242])).
% 3.30/2.45 tff(2246,plain,
% 3.30/2.45 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a595) | c0_1(a595) | (~c3_1(a595)))),
% 3.30/2.45 inference(quant_inst,[status(thm)],[])).
% 3.30/2.45 tff(2247,plain,
% 3.30/2.45 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c0_1(a595) | c1_1(a595) | (~c3_1(a595)) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583))),
% 3.30/2.45 inference(modus_ponens,[status(thm)],[2246, 2245])).
% 3.30/2.45 tff(2248,plain,
% 3.30/2.45 (hskp9 | (~c3_1(a595))),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[2247, 107, 1651, 1650, 1649, 1558, 1557, 294])).
% 3.30/2.45 tff(2249,plain,
% 3.30/2.45 ($false),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[2248, 2241, 2240])).
% 3.30/2.45 tff(2250,plain,(c1_1(a595) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a583)) | c0_1(a595) | (~c3_1(a593)) | c2_1(a593) | (~c1_1(a593)) | hskp27 | (~c3_1(a612)) | (~c2_1(a612)) | hskp29 | (~c2_1(a590)) | (~c3_1(a590)) | c0_1(a590) | (~c1_1(a612)) | (~c2_1(a599)) | (~c3_1(a599)) | c1_1(a599)), inference(lemma,lemma(discharge,[]))).
% 3.30/2.45 tff(2251,plain,
% 3.30/2.45 (hskp27),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[2250, 1971, 1511, 1510, 1512, 2203, 2202, 2201, 1972, 2052, 2051, 269, 1941, 1944, 1637, 2050, 1943, 1942, 1940])).
% 3.30/2.45 tff(2252,plain,
% 3.30/2.45 (c3_1(a611)),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[620, 2251])).
% 3.30/2.45 tff(2253,plain,
% 3.30/2.45 (c1_1(a611)),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[631, 2251])).
% 3.30/2.45 tff(2254,plain,
% 3.30/2.45 (c0_1(a611)),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[642, 2251])).
% 3.30/2.45 tff(2255,plain,
% 3.30/2.45 (~c2_1(a595)),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[1921, 107, 2254, 2253, 2252, 1941, 1944, 1972, 1971, 1637, 65])).
% 3.30/2.45 tff(2256,plain,
% 3.30/2.45 (~c3_1(a595)),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[1487, 1970])).
% 3.30/2.45 tff(2257,plain,
% 3.30/2.45 ($false),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[2197, 107, 1943, 1942, 1941, 1944, 1940, 1972, 2256, 1637, 1730, 2255])).
% 3.30/2.45 tff(2258,plain,(hskp29 | hskp22), inference(lemma,lemma(discharge,[]))).
% 3.30/2.45 tff(2259,plain,
% 3.30/2.45 (hskp29),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[2258, 44])).
% 3.30/2.45 tff(2260,plain,
% 3.30/2.45 (((~hskp29) | c3_1(a678)) <=> ((~hskp29) | c3_1(a678))),
% 3.30/2.45 inference(rewrite,[status(thm)],[])).
% 3.30/2.45 tff(2261,axiom,((~hskp29) | c3_1(a678)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause38')).
% 3.30/2.45 tff(2262,plain,
% 3.30/2.45 ((~hskp29) | c3_1(a678)),
% 3.30/2.45 inference(modus_ponens,[status(thm)],[2261, 2260])).
% 3.30/2.45 tff(2263,plain,
% 3.30/2.45 ((~hskp29) | c3_1(a678)),
% 3.30/2.45 inference(modus_ponens,[status(thm)],[2262, 2260])).
% 3.30/2.45 tff(2264,plain,
% 3.30/2.45 ((~hskp29) | c3_1(a678)),
% 3.30/2.45 inference(modus_ponens,[status(thm)],[2263, 2260])).
% 3.30/2.45 tff(2265,plain,
% 3.30/2.45 ((~hskp29) | c3_1(a678)),
% 3.30/2.45 inference(modus_ponens,[status(thm)],[2264, 2260])).
% 3.30/2.45 tff(2266,plain,
% 3.30/2.45 ((~hskp29) | c3_1(a678)),
% 3.30/2.45 inference(modus_ponens,[status(thm)],[2265, 2260])).
% 3.30/2.45 tff(2267,plain,
% 3.30/2.45 ((~hskp29) | c3_1(a678)),
% 3.30/2.45 inference(modus_ponens,[status(thm)],[2266, 2260])).
% 3.30/2.45 tff(2268,plain,
% 3.30/2.45 ((~hskp29) | c3_1(a678)),
% 3.30/2.45 inference(modus_ponens,[status(thm)],[2267, 2260])).
% 3.30/2.45 tff(2269,plain,
% 3.30/2.45 ((~hskp29) | c3_1(a678)),
% 3.30/2.45 inference(modus_ponens,[status(thm)],[2268, 2260])).
% 3.30/2.45 tff(2270,plain,
% 3.30/2.45 (c3_1(a678)),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[2269, 2259])).
% 3.30/2.45 tff(2271,plain,
% 3.30/2.45 (((~hskp29) | c2_1(a678)) <=> ((~hskp29) | c2_1(a678))),
% 3.30/2.45 inference(rewrite,[status(thm)],[])).
% 3.30/2.45 tff(2272,axiom,((~hskp29) | c2_1(a678)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause37')).
% 3.30/2.45 tff(2273,plain,
% 3.30/2.45 ((~hskp29) | c2_1(a678)),
% 3.30/2.45 inference(modus_ponens,[status(thm)],[2272, 2271])).
% 3.30/2.45 tff(2274,plain,
% 3.30/2.45 ((~hskp29) | c2_1(a678)),
% 3.30/2.45 inference(modus_ponens,[status(thm)],[2273, 2271])).
% 3.30/2.45 tff(2275,plain,
% 3.30/2.45 ((~hskp29) | c2_1(a678)),
% 3.30/2.45 inference(modus_ponens,[status(thm)],[2274, 2271])).
% 3.30/2.45 tff(2276,plain,
% 3.30/2.45 ((~hskp29) | c2_1(a678)),
% 3.30/2.45 inference(modus_ponens,[status(thm)],[2275, 2271])).
% 3.30/2.45 tff(2277,plain,
% 3.30/2.45 ((~hskp29) | c2_1(a678)),
% 3.30/2.45 inference(modus_ponens,[status(thm)],[2276, 2271])).
% 3.30/2.45 tff(2278,plain,
% 3.30/2.45 ((~hskp29) | c2_1(a678)),
% 3.30/2.45 inference(modus_ponens,[status(thm)],[2277, 2271])).
% 3.30/2.45 tff(2279,plain,
% 3.30/2.45 ((~hskp29) | c2_1(a678)),
% 3.30/2.45 inference(modus_ponens,[status(thm)],[2278, 2271])).
% 3.30/2.45 tff(2280,plain,
% 3.30/2.45 ((~hskp29) | c2_1(a678)),
% 3.30/2.45 inference(modus_ponens,[status(thm)],[2279, 2271])).
% 3.30/2.45 tff(2281,plain,
% 3.30/2.45 (c2_1(a678)),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[2280, 2259])).
% 3.30/2.45 tff(2282,plain,
% 3.30/2.45 (((~hskp29) | c0_1(a678)) <=> ((~hskp29) | c0_1(a678))),
% 3.30/2.45 inference(rewrite,[status(thm)],[])).
% 3.30/2.45 tff(2283,axiom,((~hskp29) | c0_1(a678)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause36')).
% 3.30/2.45 tff(2284,plain,
% 3.30/2.45 ((~hskp29) | c0_1(a678)),
% 3.30/2.45 inference(modus_ponens,[status(thm)],[2283, 2282])).
% 3.30/2.45 tff(2285,plain,
% 3.30/2.45 ((~hskp29) | c0_1(a678)),
% 3.30/2.45 inference(modus_ponens,[status(thm)],[2284, 2282])).
% 3.30/2.45 tff(2286,plain,
% 3.30/2.45 ((~hskp29) | c0_1(a678)),
% 3.30/2.45 inference(modus_ponens,[status(thm)],[2285, 2282])).
% 3.30/2.45 tff(2287,plain,
% 3.30/2.45 ((~hskp29) | c0_1(a678)),
% 3.30/2.45 inference(modus_ponens,[status(thm)],[2286, 2282])).
% 3.30/2.45 tff(2288,plain,
% 3.30/2.45 ((~hskp29) | c0_1(a678)),
% 3.30/2.45 inference(modus_ponens,[status(thm)],[2287, 2282])).
% 3.30/2.45 tff(2289,plain,
% 3.30/2.45 ((~hskp29) | c0_1(a678)),
% 3.30/2.45 inference(modus_ponens,[status(thm)],[2288, 2282])).
% 3.30/2.45 tff(2290,plain,
% 3.30/2.45 ((~hskp29) | c0_1(a678)),
% 3.30/2.45 inference(modus_ponens,[status(thm)],[2289, 2282])).
% 3.30/2.45 tff(2291,plain,
% 3.30/2.45 ((~hskp29) | c0_1(a678)),
% 3.30/2.45 inference(modus_ponens,[status(thm)],[2290, 2282])).
% 3.30/2.45 tff(2292,plain,
% 3.30/2.45 (c0_1(a678)),
% 3.30/2.45 inference(unit_resolution,[status(thm)],[2291, 2259])).
% 3.30/2.45 tff(2293,plain,
% 3.30/2.45 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | c3_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a607))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | c3_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a607))),
% 3.30/2.45 inference(rewrite,[status(thm)],[])).
% 3.30/2.45 tff(2294,plain,
% 3.30/2.45 ((hskp11 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c3_1(a607) | c0_1(a607) | c2_1(a607)) <=> (hskp11 | c3_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a607))),
% 3.30/2.45 inference(rewrite,[status(thm)],[])).
% 3.30/2.45 tff(2295,plain,
% 3.30/2.45 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c3_1(a607) | c0_1(a607) | c2_1(a607))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | c3_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a607)))),
% 3.30/2.45 inference(monotonicity,[status(thm)],[2294])).
% 3.30/2.45 tff(2296,plain,
% 3.30/2.45 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c3_1(a607) | c0_1(a607) | c2_1(a607))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | c3_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a607))),
% 3.30/2.46 inference(transitivity,[status(thm)],[2295, 2293])).
% 3.30/2.46 tff(2297,plain,
% 3.30/2.46 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c3_1(a607) | c0_1(a607) | c2_1(a607))),
% 3.30/2.46 inference(quant_inst,[status(thm)],[])).
% 3.30/2.46 tff(2298,plain,
% 3.30/2.46 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | c3_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a607)),
% 3.30/2.46 inference(modus_ponens,[status(thm)],[2297, 2296])).
% 3.30/2.46 tff(2299,plain,
% 3.30/2.46 (hskp11 | c0_1(a607)),
% 3.30/2.46 inference(unit_resolution,[status(thm)],[2298, 107, 2292, 2281, 2270, 33, 22, 268])).
% 3.30/2.46 tff(2300,plain,
% 3.30/2.46 (hskp11),
% 3.30/2.46 inference(unit_resolution,[status(thm)],[2299, 115])).
% 3.30/2.46 tff(2301,plain,
% 3.30/2.46 (~c1_1(a599)),
% 3.30/2.46 inference(unit_resolution,[status(thm)],[428, 2300])).
% 3.30/2.46 tff(2302,plain,
% 3.30/2.46 (c3_1(a599)),
% 3.30/2.46 inference(unit_resolution,[status(thm)],[422, 2300])).
% 3.30/2.46 tff(2303,plain,
% 3.30/2.46 (c2_1(a599)),
% 3.30/2.46 inference(unit_resolution,[status(thm)],[439, 2300])).
% 3.30/2.46 tff(2304,plain,
% 3.30/2.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a603) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a603) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)))),
% 3.30/2.46 inference(rewrite,[status(thm)],[])).
% 3.30/2.46 tff(2305,plain,
% 3.30/2.46 (((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586))) <=> (c3_1(a603) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)))),
% 3.30/2.46 inference(rewrite,[status(thm)],[])).
% 3.30/2.46 tff(2306,plain,
% 3.30/2.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a603) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603))))),
% 3.30/2.46 inference(monotonicity,[status(thm)],[2305])).
% 3.30/2.46 tff(2307,plain,
% 3.30/2.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a603) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)))),
% 3.30/2.46 inference(transitivity,[status(thm)],[2306, 2304])).
% 3.30/2.46 tff(2308,plain,
% 3.30/2.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))),
% 3.30/2.46 inference(quant_inst,[status(thm)],[])).
% 3.30/2.46 tff(2309,plain,
% 3.30/2.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a603) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603))),
% 3.30/2.46 inference(modus_ponens,[status(thm)],[2308, 2307])).
% 3.30/2.46 tff(2310,plain,
% 3.30/2.46 ($false),
% 3.30/2.46 inference(unit_resolution,[status(thm)],[2309, 107, 183, 2303, 2302, 230, 206, 2301, 219, 258, 190, 248])).
% 3.30/2.46 tff(2311,plain,(hskp6 | c3_1(a607) | c1_1(a607) | hskp22 | c2_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.30/2.46 tff(2312,plain,
% 3.30/2.46 (hskp6),
% 3.30/2.46 inference(unit_resolution,[status(thm)],[2311, 66, 33, 44, 22])).
% 3.30/2.46 tff(2313,plain,
% 3.30/2.46 (~c0_1(a590)),
% 3.30/2.46 inference(unit_resolution,[status(thm)],[666, 2312])).
% 3.30/2.46 tff(2314,plain,
% 3.30/2.46 (c3_1(a590)),
% 3.30/2.46 inference(unit_resolution,[status(thm)],[677, 2312])).
% 3.30/2.46 tff(2315,plain,
% 3.30/2.46 (c2_1(a590)),
% 3.30/2.46 inference(unit_resolution,[status(thm)],[688, 2312])).
% 3.30/2.46 tff(2316,assumption,(c3_1(a678)), introduced(assumption)).
% 3.30/2.46 tff(2317,assumption,(c2_1(a678)), introduced(assumption)).
% 3.30/2.46 tff(2318,assumption,(c0_1(a678)), introduced(assumption)).
% 3.30/2.46 tff(2319,plain,
% 3.30/2.46 (hskp11 | c0_1(a607)),
% 3.30/2.46 inference(unit_resolution,[status(thm)],[2298, 107, 2318, 2317, 2316, 33, 22, 268])).
% 3.30/2.46 tff(2320,plain,
% 3.30/2.46 (c0_1(a607)),
% 3.30/2.46 inference(unit_resolution,[status(thm)],[2319, 1638])).
% 3.30/2.46 tff(2321,plain,
% 3.30/2.46 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | c3_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c3_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a607)))),
% 3.30/2.46 inference(rewrite,[status(thm)],[])).
% 3.30/2.46 tff(2322,plain,
% 3.30/2.46 ((hskp16 | (~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590))) <=> (hskp16 | c3_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a607)))),
% 3.30/2.46 inference(rewrite,[status(thm)],[])).
% 3.30/2.46 tff(2323,plain,
% 3.30/2.46 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | c3_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a607))))),
% 3.30/2.46 inference(monotonicity,[status(thm)],[2322])).
% 3.30/2.46 tff(2324,plain,
% 3.30/2.46 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c3_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a607)))),
% 3.30/2.46 inference(transitivity,[status(thm)],[2323, 2321])).
% 3.30/2.46 tff(2325,plain,
% 3.30/2.46 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)))),
% 3.30/2.46 inference(quant_inst,[status(thm)],[])).
% 3.30/2.46 tff(2326,plain,
% 3.30/2.46 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c3_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a607))),
% 3.30/2.46 inference(modus_ponens,[status(thm)],[2325, 2324])).
% 3.30/2.46 tff(2327,plain,
% 3.30/2.46 (hskp16 | (~c0_1(a607))),
% 3.30/2.46 inference(unit_resolution,[status(thm)],[2326, 107, 33, 863, 862, 22, 45, 2125])).
% 3.30/2.46 tff(2328,plain,
% 3.30/2.46 (hskp16),
% 3.30/2.46 inference(unit_resolution,[status(thm)],[2327, 2320])).
% 3.30/2.46 tff(2329,plain,
% 3.30/2.46 (~c3_1(a606)),
% 3.30/2.46 inference(unit_resolution,[status(thm)],[1075, 2328])).
% 3.30/2.46 tff(2330,plain,
% 3.30/2.46 (~c2_1(a606)),
% 3.30/2.46 inference(unit_resolution,[status(thm)],[1111, 2328])).
% 3.30/2.46 tff(2331,plain,
% 3.30/2.46 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | c2_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a606))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | c2_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a606))),
% 3.30/2.46 inference(rewrite,[status(thm)],[])).
% 3.30/2.46 tff(2332,plain,
% 3.30/2.46 ((hskp11 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c3_1(a606) | c0_1(a606) | c2_1(a606)) <=> (hskp11 | c2_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a606))),
% 3.30/2.46 inference(rewrite,[status(thm)],[])).
% 3.30/2.46 tff(2333,plain,
% 3.30/2.46 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c3_1(a606) | c0_1(a606) | c2_1(a606))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | c2_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a606)))),
% 3.30/2.46 inference(monotonicity,[status(thm)],[2332])).
% 3.30/2.46 tff(2334,plain,
% 3.30/2.46 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c3_1(a606) | c0_1(a606) | c2_1(a606))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | c2_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a606))),
% 3.30/2.46 inference(transitivity,[status(thm)],[2333, 2331])).
% 3.30/2.46 tff(2335,plain,
% 3.30/2.46 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c3_1(a606) | c0_1(a606) | c2_1(a606))),
% 3.30/2.46 inference(quant_inst,[status(thm)],[])).
% 3.30/2.46 tff(2336,plain,
% 3.30/2.46 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | c2_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a606)),
% 3.30/2.46 inference(modus_ponens,[status(thm)],[2335, 2334])).
% 3.30/2.46 tff(2337,plain,
% 3.30/2.46 (c0_1(a606)),
% 3.30/2.46 inference(unit_resolution,[status(thm)],[2336, 1638, 107, 2318, 2317, 2316, 2330, 2329, 268])).
% 3.30/2.46 tff(2338,plain,
% 3.30/2.46 (^[U: $i] : refl((hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 3.30/2.46 inference(bind,[status(th)],[])).
% 3.30/2.46 tff(2339,plain,
% 3.30/2.46 (![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 3.30/2.46 inference(quant_intro,[status(thm)],[2338])).
% 3.30/2.46 tff(2340,plain,
% 3.30/2.46 (![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 3.30/2.46 inference(rewrite,[status(thm)],[])).
% 3.30/2.46 tff(2341,plain,
% 3.30/2.46 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp0) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp0))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp0) | hskp11) <=> ((hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp11))), rewrite(((hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp11) <=> (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp0) | hskp11) <=> (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 3.30/2.46 inference(bind,[status(th)],[])).
% 3.30/2.46 tff(2342,plain,
% 3.30/2.46 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp0) | hskp11) <=> ![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 3.30/2.46 inference(quant_intro,[status(thm)],[2341])).
% 3.30/2.46 tff(2343,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp0) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause149')).
% 3.30/2.46 tff(2344,plain,
% 3.30/2.46 (![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 3.30/2.46 inference(modus_ponens,[status(thm)],[2343, 2342])).
% 3.30/2.46 tff(2345,plain,
% 3.30/2.46 (![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 3.30/2.46 inference(modus_ponens,[status(thm)],[2344, 2340])).
% 3.30/2.46 tff(2346,plain,(
% 3.30/2.46 ![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 3.30/2.46 inference(skolemize,[status(sab)],[2345])).
% 3.30/2.46 tff(2347,plain,
% 3.30/2.46 (![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 3.30/2.46 inference(modus_ponens,[status(thm)],[2346, 2339])).
% 3.30/2.46 tff(2348,plain,
% 3.30/2.46 (c1_1(a606)),
% 3.30/2.46 inference(unit_resolution,[status(thm)],[1088, 2328])).
% 3.30/2.46 tff(2349,plain,
% 3.30/2.46 (((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)))) <=> ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp11 | hskp0 | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)))),
% 3.30/2.46 inference(rewrite,[status(thm)],[])).
% 3.30/2.46 tff(2350,plain,
% 3.30/2.46 ((hskp11 | hskp0 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606))) <=> (hskp11 | hskp0 | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)))),
% 3.30/2.46 inference(rewrite,[status(thm)],[])).
% 3.30/2.46 tff(2351,plain,
% 3.30/2.46 (((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)))) <=> ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606))))),
% 3.30/2.46 inference(monotonicity,[status(thm)],[2350])).
% 3.30/2.46 tff(2352,plain,
% 3.30/2.46 (((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)))) <=> ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp11 | hskp0 | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)))),
% 3.30/2.46 inference(transitivity,[status(thm)],[2351, 2349])).
% 3.30/2.46 tff(2353,plain,
% 3.30/2.46 ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)))),
% 3.30/2.46 inference(quant_inst,[status(thm)],[])).
% 3.30/2.46 tff(2354,plain,
% 3.30/2.46 ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp11 | hskp0 | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606))),
% 3.30/2.46 inference(modus_ponens,[status(thm)],[2353, 2352])).
% 3.30/2.46 tff(2355,plain,
% 3.30/2.46 (hskp0 | (~c0_1(a606))),
% 3.30/2.46 inference(unit_resolution,[status(thm)],[2354, 1638, 107, 2348, 2330, 2347])).
% 3.30/2.46 tff(2356,plain,
% 3.30/2.46 (hskp0),
% 3.30/2.46 inference(unit_resolution,[status(thm)],[2355, 2337])).
% 3.30/2.46 tff(2357,plain,
% 3.30/2.46 (~c2_1(a584)),
% 3.30/2.46 inference(unit_resolution,[status(thm)],[1045, 2356])).
% 3.30/2.46 tff(2358,plain,
% 3.30/2.46 (~c0_1(a584)),
% 3.30/2.46 inference(unit_resolution,[status(thm)],[1051, 2356])).
% 3.30/2.46 tff(2359,plain,
% 3.30/2.46 (^[U: $i] : refl((hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 3.30/2.46 inference(bind,[status(th)],[])).
% 3.30/2.46 tff(2360,plain,
% 3.30/2.46 (![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 3.30/2.46 inference(quant_intro,[status(thm)],[2359])).
% 3.30/2.46 tff(2361,plain,
% 3.30/2.46 (![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 3.30/2.46 inference(rewrite,[status(thm)],[])).
% 3.30/2.46 tff(2362,plain,
% 3.30/2.46 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp3) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp3))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp3) | hskp17) <=> ((hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp17))), rewrite(((hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp17) <=> (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp3) | hskp17) <=> (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 3.30/2.46 inference(bind,[status(th)],[])).
% 3.30/2.46 tff(2363,plain,
% 3.30/2.46 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp3) | hskp17) <=> ![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 3.30/2.46 inference(quant_intro,[status(thm)],[2362])).
% 3.30/2.46 tff(2364,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp3) | hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause155')).
% 3.30/2.46 tff(2365,plain,
% 3.30/2.46 (![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 3.30/2.46 inference(modus_ponens,[status(thm)],[2364, 2363])).
% 3.30/2.46 tff(2366,plain,
% 3.30/2.46 (![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 3.30/2.46 inference(modus_ponens,[status(thm)],[2365, 2361])).
% 3.30/2.46 tff(2367,plain,(
% 3.30/2.46 ![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 3.30/2.46 inference(skolemize,[status(sab)],[2366])).
% 3.30/2.46 tff(2368,plain,
% 3.30/2.46 (![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 3.30/2.46 inference(modus_ponens,[status(thm)],[2367, 2360])).
% 3.30/2.46 tff(2369,plain,
% 3.30/2.46 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | c3_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp3 | c3_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)))),
% 3.30/2.46 inference(rewrite,[status(thm)],[])).
% 3.30/2.46 tff(2370,plain,
% 3.30/2.46 ((hskp17 | hskp3 | (~ndr1_0) | c3_1(a606) | (~c1_1(a606)) | (~c0_1(a606))) <=> (hskp17 | hskp3 | c3_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)))),
% 3.30/2.46 inference(rewrite,[status(thm)],[])).
% 3.30/2.46 tff(2371,plain,
% 3.30/2.46 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c3_1(a606) | (~c1_1(a606)) | (~c0_1(a606)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | c3_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606))))),
% 3.30/2.46 inference(monotonicity,[status(thm)],[2370])).
% 3.30/2.46 tff(2372,plain,
% 3.30/2.46 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c3_1(a606) | (~c1_1(a606)) | (~c0_1(a606)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp3 | c3_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)))),
% 3.30/2.46 inference(transitivity,[status(thm)],[2371, 2369])).
% 3.30/2.46 tff(2373,plain,
% 3.30/2.46 ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c3_1(a606) | (~c1_1(a606)) | (~c0_1(a606)))),
% 3.30/2.46 inference(quant_inst,[status(thm)],[])).
% 3.30/2.46 tff(2374,plain,
% 3.30/2.46 ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp3 | c3_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606))),
% 3.30/2.46 inference(modus_ponens,[status(thm)],[2373, 2372])).
% 3.30/2.46 tff(2375,plain,
% 3.30/2.46 (hskp3 | (~c0_1(a606))),
% 3.30/2.46 inference(unit_resolution,[status(thm)],[2374, 107, 241, 2348, 2329, 2368])).
% 3.30/2.46 tff(2376,plain,
% 3.30/2.46 (hskp3),
% 3.30/2.46 inference(unit_resolution,[status(thm)],[2375, 2337])).
% 3.30/2.46 tff(2377,plain,
% 3.30/2.46 (~c1_1(a587)),
% 3.30/2.46 inference(unit_resolution,[status(thm)],[939, 2376])).
% 3.30/2.46 tff(2378,plain,
% 3.30/2.46 (c1_1(a584)),
% 3.30/2.46 inference(unit_resolution,[status(thm)],[1062, 2356])).
% 3.30/2.46 tff(2379,plain,
% 3.30/2.46 (c2_1(a587)),
% 3.30/2.46 inference(unit_resolution,[status(thm)],[950, 2376])).
% 3.30/2.46 tff(2380,plain,
% 3.30/2.46 (c0_1(a587)),
% 3.30/2.46 inference(unit_resolution,[status(thm)],[961, 2376])).
% 3.30/2.46 tff(2381,plain,
% 3.30/2.46 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c1_1(a587) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a587)) | (~c0_1(a587)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c1_1(a587) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a587)) | (~c0_1(a587)))),
% 3.30/2.46 inference(rewrite,[status(thm)],[])).
% 3.30/2.46 tff(2382,plain,
% 3.30/2.46 ((hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584))) <=> (hskp17 | c1_1(a587) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a587)) | (~c0_1(a587)))),
% 3.30/2.46 inference(rewrite,[status(thm)],[])).
% 3.30/2.46 tff(2383,plain,
% 3.30/2.46 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c1_1(a587) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a587)) | (~c0_1(a587))))),
% 3.30/2.46 inference(monotonicity,[status(thm)],[2382])).
% 3.30/2.46 tff(2384,plain,
% 3.30/2.46 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c1_1(a587) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a587)) | (~c0_1(a587)))),
% 3.30/2.46 inference(transitivity,[status(thm)],[2383, 2381])).
% 3.30/2.46 tff(2385,plain,
% 3.30/2.46 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584)))),
% 3.30/2.46 inference(quant_inst,[status(thm)],[])).
% 3.30/2.46 tff(2386,plain,
% 3.30/2.46 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c1_1(a587) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a587)) | (~c0_1(a587))),
% 3.30/2.46 inference(modus_ponens,[status(thm)],[2385, 2384])).
% 3.30/2.46 tff(2387,plain,
% 3.30/2.46 ($false),
% 3.30/2.46 inference(unit_resolution,[status(thm)],[2386, 107, 241, 2380, 2379, 2378, 2377, 2358, 2357, 32])).
% 3.30/2.46 tff(2388,plain,(hskp11 | (~c0_1(a678)) | (~c2_1(a678)) | (~c3_1(a678)) | c3_1(a607) | (~c2_1(a590)) | (~c3_1(a590)) | c2_1(a607) | c0_1(a590)), inference(lemma,lemma(discharge,[]))).
% 3.30/2.46 tff(2389,plain,
% 3.30/2.46 (hskp11),
% 3.30/2.46 inference(unit_resolution,[status(thm)],[2388, 2315, 2281, 2270, 33, 2292, 2314, 22, 2313])).
% 3.30/2.46 tff(2390,plain,
% 3.30/2.46 (~c1_1(a599)),
% 3.30/2.46 inference(unit_resolution,[status(thm)],[428, 2389])).
% 3.30/2.46 tff(2391,plain,
% 3.30/2.46 (c2_1(a599)),
% 3.30/2.46 inference(unit_resolution,[status(thm)],[439, 2389])).
% 3.30/2.46 tff(2392,plain,
% 3.30/2.46 (hskp11),
% 3.30/2.46 inference(unit_resolution,[status(thm)],[2388, 863, 2317, 2316, 33, 2318, 862, 22, 45])).
% 3.30/2.46 tff(2393,plain,
% 3.30/2.46 (~c1_1(a599)),
% 3.30/2.46 inference(unit_resolution,[status(thm)],[428, 2392])).
% 3.30/2.46 tff(2394,plain,
% 3.30/2.46 (c3_1(a599)),
% 3.30/2.46 inference(unit_resolution,[status(thm)],[422, 2392])).
% 3.30/2.46 tff(2395,plain,
% 3.30/2.46 (c2_1(a599)),
% 3.30/2.46 inference(unit_resolution,[status(thm)],[439, 2392])).
% 3.30/2.46 tff(2396,plain,
% 3.30/2.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a607) | c2_1(a607) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a607))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a607) | c2_1(a607) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a607))),
% 3.30/2.46 inference(rewrite,[status(thm)],[])).
% 3.30/2.46 tff(2397,plain,
% 3.30/2.46 (((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a607) | c0_1(a607) | c2_1(a607)) <=> (c3_1(a607) | c2_1(a607) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a607))),
% 3.30/2.46 inference(rewrite,[status(thm)],[])).
% 3.30/2.46 tff(2398,plain,
% 3.30/2.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a607) | c0_1(a607) | c2_1(a607))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a607) | c2_1(a607) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a607)))),
% 3.30/2.46 inference(monotonicity,[status(thm)],[2397])).
% 3.30/2.46 tff(2399,plain,
% 3.30/2.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a607) | c0_1(a607) | c2_1(a607))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a607) | c2_1(a607) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a607))),
% 3.30/2.47 inference(transitivity,[status(thm)],[2398, 2396])).
% 3.30/2.47 tff(2400,plain,
% 3.30/2.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a607) | c0_1(a607) | c2_1(a607))),
% 3.30/2.47 inference(quant_inst,[status(thm)],[])).
% 3.30/2.47 tff(2401,plain,
% 3.30/2.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a607) | c2_1(a607) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a607)),
% 3.30/2.47 inference(modus_ponens,[status(thm)],[2400, 2399])).
% 3.30/2.47 tff(2402,plain,
% 3.30/2.47 (c0_1(a607)),
% 3.30/2.47 inference(unit_resolution,[status(thm)],[2401, 107, 33, 2395, 2394, 863, 862, 22, 2393, 45, 1730])).
% 3.30/2.47 tff(2403,plain,
% 3.30/2.47 (hskp16),
% 3.30/2.47 inference(unit_resolution,[status(thm)],[2327, 2402])).
% 3.30/2.47 tff(2404,plain,
% 3.30/2.47 (~c3_1(a606)),
% 3.30/2.47 inference(unit_resolution,[status(thm)],[1075, 2403])).
% 3.30/2.47 tff(2405,plain,
% 3.30/2.47 (~c2_1(a606)),
% 3.30/2.47 inference(unit_resolution,[status(thm)],[1111, 2403])).
% 3.30/2.47 tff(2406,plain,
% 3.30/2.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a606) | c3_1(a606) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a606) | c3_1(a606) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a606))),
% 3.30/2.47 inference(rewrite,[status(thm)],[])).
% 3.30/2.47 tff(2407,plain,
% 3.30/2.47 (((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a606) | c0_1(a606) | c2_1(a606)) <=> (c2_1(a606) | c3_1(a606) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a606))),
% 3.30/2.47 inference(rewrite,[status(thm)],[])).
% 3.30/2.47 tff(2408,plain,
% 3.30/2.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a606) | c0_1(a606) | c2_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a606) | c3_1(a606) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a606)))),
% 3.30/2.47 inference(monotonicity,[status(thm)],[2407])).
% 3.30/2.47 tff(2409,plain,
% 3.30/2.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a606) | c0_1(a606) | c2_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a606) | c3_1(a606) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a606))),
% 3.30/2.47 inference(transitivity,[status(thm)],[2408, 2406])).
% 3.30/2.47 tff(2410,plain,
% 3.30/2.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a606) | c0_1(a606) | c2_1(a606))),
% 3.30/2.47 inference(quant_inst,[status(thm)],[])).
% 3.30/2.47 tff(2411,plain,
% 3.30/2.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a606) | c3_1(a606) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a606)),
% 3.30/2.47 inference(modus_ponens,[status(thm)],[2410, 2409])).
% 3.30/2.47 tff(2412,plain,
% 3.30/2.47 (c0_1(a606)),
% 3.30/2.47 inference(unit_resolution,[status(thm)],[2411, 107, 2395, 2394, 863, 862, 2405, 2404, 2393, 45, 1730])).
% 3.30/2.47 tff(2413,plain,
% 3.30/2.47 (c1_1(a606)),
% 3.30/2.47 inference(unit_resolution,[status(thm)],[1088, 2403])).
% 3.30/2.47 tff(2414,plain,
% 3.30/2.47 (hskp3 | (~c0_1(a606))),
% 3.30/2.47 inference(unit_resolution,[status(thm)],[2374, 107, 241, 2413, 2404, 2368])).
% 3.30/2.47 tff(2415,plain,
% 3.30/2.47 (hskp3),
% 3.30/2.47 inference(unit_resolution,[status(thm)],[2414, 2412])).
% 3.30/2.47 tff(2416,plain,
% 3.30/2.47 (~c1_1(a587)),
% 3.30/2.47 inference(unit_resolution,[status(thm)],[939, 2415])).
% 3.30/2.47 tff(2417,plain,
% 3.30/2.47 (c2_1(a587)),
% 3.30/2.47 inference(unit_resolution,[status(thm)],[950, 2415])).
% 3.30/2.47 tff(2418,plain,
% 3.30/2.47 (c0_1(a587)),
% 3.30/2.47 inference(unit_resolution,[status(thm)],[961, 2415])).
% 3.30/2.47 tff(2419,plain,
% 3.30/2.47 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c3_1(a607) | c1_1(a607) | c2_1(a607) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c3_1(a607) | c1_1(a607) | c2_1(a607) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)))),
% 3.30/2.47 inference(rewrite,[status(thm)],[])).
% 3.30/2.47 tff(2420,plain,
% 3.30/2.47 ((hskp26 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a607) | c1_1(a607) | c2_1(a607)) <=> (hskp26 | c3_1(a607) | c1_1(a607) | c2_1(a607) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)))),
% 3.30/2.47 inference(rewrite,[status(thm)],[])).
% 3.30/2.47 tff(2421,plain,
% 3.30/2.47 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a607) | c1_1(a607) | c2_1(a607))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c3_1(a607) | c1_1(a607) | c2_1(a607) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587))))),
% 3.30/2.47 inference(monotonicity,[status(thm)],[2420])).
% 3.30/2.47 tff(2422,plain,
% 3.30/2.47 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a607) | c1_1(a607) | c2_1(a607))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c3_1(a607) | c1_1(a607) | c2_1(a607) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)))),
% 3.30/2.47 inference(transitivity,[status(thm)],[2421, 2419])).
% 3.30/2.47 tff(2423,plain,
% 3.30/2.47 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a607) | c1_1(a607) | c2_1(a607))),
% 3.30/2.47 inference(quant_inst,[status(thm)],[])).
% 3.30/2.47 tff(2424,plain,
% 3.30/2.47 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c3_1(a607) | c1_1(a607) | c2_1(a607) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587))),
% 3.30/2.47 inference(modus_ponens,[status(thm)],[2423, 2422])).
% 3.30/2.47 tff(2425,plain,
% 3.30/2.47 (hskp26),
% 3.30/2.47 inference(unit_resolution,[status(thm)],[2424, 107, 33, 2418, 2417, 66, 22, 2416, 995])).
% 3.30/2.47 tff(2426,plain,
% 3.30/2.47 (c2_1(a583)),
% 3.30/2.47 inference(unit_resolution,[status(thm)],[391, 2425])).
% 3.30/2.47 tff(2427,plain,
% 3.30/2.47 (c1_1(a583)),
% 3.30/2.47 inference(unit_resolution,[status(thm)],[351, 2425])).
% 3.30/2.47 tff(2428,plain,
% 3.30/2.47 (c0_1(a583)),
% 3.30/2.47 inference(unit_resolution,[status(thm)],[362, 2425])).
% 3.30/2.47 tff(2429,plain,
% 3.30/2.47 (hskp9 | c0_1(a599)),
% 3.30/2.47 inference(unit_resolution,[status(thm)],[1951, 107, 2428, 2427, 2426, 2394, 2393, 294])).
% 3.30/2.47 tff(2430,plain,
% 3.30/2.47 (c0_1(a599)),
% 3.30/2.47 inference(unit_resolution,[status(thm)],[2429, 1945])).
% 3.30/2.47 tff(2431,plain,
% 3.30/2.47 (^[U: $i] : refl((hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))),
% 3.30/2.47 inference(bind,[status(th)],[])).
% 3.30/2.47 tff(2432,plain,
% 3.30/2.47 (![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 3.30/2.47 inference(quant_intro,[status(thm)],[2431])).
% 3.30/2.47 tff(2433,plain,
% 3.30/2.47 (![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 3.30/2.47 inference(rewrite,[status(thm)],[])).
% 3.30/2.47 tff(2434,plain,
% 3.30/2.47 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp25) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp25))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp25) <=> (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp25) <=> (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp25) | hskp9) <=> ((hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp9))), rewrite(((hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp9) <=> (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp25) | hskp9) <=> (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))))),
% 3.30/2.47 inference(bind,[status(th)],[])).
% 3.30/2.47 tff(2435,plain,
% 3.30/2.47 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp25) | hskp9) <=> ![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 3.30/2.47 inference(quant_intro,[status(thm)],[2434])).
% 3.30/2.47 tff(2436,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp25) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause142')).
% 3.30/2.47 tff(2437,plain,
% 3.30/2.47 (![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 3.30/2.47 inference(modus_ponens,[status(thm)],[2436, 2435])).
% 3.30/2.47 tff(2438,plain,
% 3.30/2.47 (![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 3.30/2.47 inference(modus_ponens,[status(thm)],[2437, 2433])).
% 3.30/2.47 tff(2439,plain,(
% 3.30/2.47 ![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 3.30/2.47 inference(skolemize,[status(sab)],[2438])).
% 3.30/2.47 tff(2440,plain,
% 3.30/2.47 (![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 3.30/2.47 inference(modus_ponens,[status(thm)],[2439, 2432])).
% 3.30/2.47 tff(2441,plain,
% 3.30/2.47 (((~![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | hskp9 | c2_1(a606) | c3_1(a606) | (~ndr1_0) | (~c1_1(a606)))) <=> ((~![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp25 | hskp9 | c2_1(a606) | c3_1(a606) | (~ndr1_0) | (~c1_1(a606)))),
% 3.30/2.47 inference(rewrite,[status(thm)],[])).
% 3.30/2.47 tff(2442,plain,
% 3.30/2.47 ((hskp25 | hskp9 | (~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c1_1(a606))) <=> (hskp25 | hskp9 | c2_1(a606) | c3_1(a606) | (~ndr1_0) | (~c1_1(a606)))),
% 3.30/2.47 inference(rewrite,[status(thm)],[])).
% 3.30/2.47 tff(2443,plain,
% 3.30/2.47 (((~![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | hskp9 | (~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c1_1(a606)))) <=> ((~![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | hskp9 | c2_1(a606) | c3_1(a606) | (~ndr1_0) | (~c1_1(a606))))),
% 3.30/2.47 inference(monotonicity,[status(thm)],[2442])).
% 3.30/2.47 tff(2444,plain,
% 3.30/2.47 (((~![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | hskp9 | (~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c1_1(a606)))) <=> ((~![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp25 | hskp9 | c2_1(a606) | c3_1(a606) | (~ndr1_0) | (~c1_1(a606)))),
% 3.30/2.47 inference(transitivity,[status(thm)],[2443, 2441])).
% 3.30/2.47 tff(2445,plain,
% 3.30/2.47 ((~![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | hskp9 | (~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c1_1(a606)))),
% 3.30/2.47 inference(quant_inst,[status(thm)],[])).
% 3.30/2.47 tff(2446,plain,
% 3.30/2.47 ((~![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp25 | hskp9 | c2_1(a606) | c3_1(a606) | (~ndr1_0) | (~c1_1(a606))),
% 3.30/2.47 inference(modus_ponens,[status(thm)],[2445, 2444])).
% 3.30/2.47 tff(2447,plain,
% 3.30/2.47 (hskp25 | hskp9),
% 3.30/2.47 inference(unit_resolution,[status(thm)],[2446, 107, 2413, 2405, 2404, 2440])).
% 3.30/2.47 tff(2448,plain,
% 3.30/2.47 (hskp25),
% 3.30/2.47 inference(unit_resolution,[status(thm)],[2447, 1945])).
% 3.30/2.47 tff(2449,plain,
% 3.30/2.47 (((~hskp25) | c2_1(a651)) <=> ((~hskp25) | c2_1(a651))),
% 3.30/2.47 inference(rewrite,[status(thm)],[])).
% 3.30/2.47 tff(2450,axiom,((~hskp25) | c2_1(a651)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause48')).
% 3.30/2.47 tff(2451,plain,
% 3.30/2.47 ((~hskp25) | c2_1(a651)),
% 3.30/2.47 inference(modus_ponens,[status(thm)],[2450, 2449])).
% 3.30/2.47 tff(2452,plain,
% 3.30/2.47 ((~hskp25) | c2_1(a651)),
% 3.30/2.47 inference(modus_ponens,[status(thm)],[2451, 2449])).
% 3.30/2.47 tff(2453,plain,
% 3.30/2.47 ((~hskp25) | c2_1(a651)),
% 3.30/2.47 inference(modus_ponens,[status(thm)],[2452, 2449])).
% 3.30/2.47 tff(2454,plain,
% 3.30/2.47 ((~hskp25) | c2_1(a651)),
% 3.30/2.47 inference(modus_ponens,[status(thm)],[2453, 2449])).
% 3.30/2.47 tff(2455,plain,
% 3.30/2.47 ((~hskp25) | c2_1(a651)),
% 3.30/2.47 inference(modus_ponens,[status(thm)],[2454, 2449])).
% 3.30/2.47 tff(2456,plain,
% 3.30/2.47 ((~hskp25) | c2_1(a651)),
% 3.30/2.47 inference(modus_ponens,[status(thm)],[2455, 2449])).
% 3.30/2.47 tff(2457,plain,
% 3.30/2.47 ((~hskp25) | c2_1(a651)),
% 3.30/2.47 inference(modus_ponens,[status(thm)],[2456, 2449])).
% 3.30/2.47 tff(2458,plain,
% 3.30/2.47 ((~hskp25) | c2_1(a651)),
% 3.30/2.47 inference(modus_ponens,[status(thm)],[2457, 2449])).
% 3.30/2.47 tff(2459,plain,
% 3.30/2.47 (c2_1(a651)),
% 3.30/2.47 inference(unit_resolution,[status(thm)],[2458, 2448])).
% 3.30/2.47 tff(2460,plain,
% 3.30/2.47 (((~hskp25) | (~c3_1(a651))) <=> ((~hskp25) | (~c3_1(a651)))),
% 3.30/2.47 inference(rewrite,[status(thm)],[])).
% 3.30/2.47 tff(2461,plain,
% 3.30/2.47 (((~c3_1(a651)) | (~hskp25)) <=> ((~hskp25) | (~c3_1(a651)))),
% 3.30/2.47 inference(rewrite,[status(thm)],[])).
% 3.30/2.47 tff(2462,axiom,((~c3_1(a651)) | (~hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause83')).
% 3.30/2.47 tff(2463,plain,
% 3.30/2.47 ((~hskp25) | (~c3_1(a651))),
% 3.30/2.47 inference(modus_ponens,[status(thm)],[2462, 2461])).
% 3.30/2.47 tff(2464,plain,
% 3.30/2.47 ((~hskp25) | (~c3_1(a651))),
% 3.30/2.47 inference(modus_ponens,[status(thm)],[2463, 2460])).
% 3.30/2.47 tff(2465,plain,
% 3.30/2.47 (~c3_1(a651)),
% 3.30/2.47 inference(unit_resolution,[status(thm)],[2464, 2448])).
% 3.30/2.47 tff(2466,plain,
% 3.30/2.47 (((~hskp25) | (~c1_1(a651))) <=> ((~hskp25) | (~c1_1(a651)))),
% 3.30/2.47 inference(rewrite,[status(thm)],[])).
% 3.30/2.47 tff(2467,plain,
% 3.30/2.47 (((~c1_1(a651)) | (~hskp25)) <=> ((~hskp25) | (~c1_1(a651)))),
% 3.30/2.47 inference(rewrite,[status(thm)],[])).
% 3.30/2.47 tff(2468,axiom,((~c1_1(a651)) | (~hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause82')).
% 3.30/2.47 tff(2469,plain,
% 3.30/2.47 ((~hskp25) | (~c1_1(a651))),
% 3.30/2.47 inference(modus_ponens,[status(thm)],[2468, 2467])).
% 3.30/2.47 tff(2470,plain,
% 3.30/2.47 ((~hskp25) | (~c1_1(a651))),
% 3.30/2.47 inference(modus_ponens,[status(thm)],[2469, 2466])).
% 3.30/2.47 tff(2471,plain,
% 3.30/2.47 (~c1_1(a651)),
% 3.30/2.47 inference(unit_resolution,[status(thm)],[2470, 2448])).
% 3.30/2.47 tff(2472,assumption,(c0_1(a599)), introduced(assumption)).
% 3.30/2.47 tff(2473,assumption,(~c3_1(a651)), introduced(assumption)).
% 3.30/2.47 tff(2474,assumption,(c2_1(a651)), introduced(assumption)).
% 3.30/2.47 tff(2475,assumption,(~c0_1(a604)), introduced(assumption)).
% 3.30/2.47 tff(2476,assumption,(c0_1(a651)), introduced(assumption)).
% 3.30/2.47 tff(2477,plain,
% 3.30/2.47 (((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp8 | c3_1(a651) | (~ndr1_0) | (~c2_1(a651)) | (~c0_1(a651)))) <=> ((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp27 | hskp8 | c3_1(a651) | (~ndr1_0) | (~c2_1(a651)) | (~c0_1(a651)))),
% 3.30/2.47 inference(rewrite,[status(thm)],[])).
% 3.30/2.47 tff(2478,plain,
% 3.30/2.47 ((hskp27 | hskp8 | (~ndr1_0) | c3_1(a651) | (~c2_1(a651)) | (~c0_1(a651))) <=> (hskp27 | hskp8 | c3_1(a651) | (~ndr1_0) | (~c2_1(a651)) | (~c0_1(a651)))),
% 3.30/2.47 inference(rewrite,[status(thm)],[])).
% 3.30/2.47 tff(2479,plain,
% 3.30/2.47 (((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp8 | (~ndr1_0) | c3_1(a651) | (~c2_1(a651)) | (~c0_1(a651)))) <=> ((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp8 | c3_1(a651) | (~ndr1_0) | (~c2_1(a651)) | (~c0_1(a651))))),
% 3.30/2.47 inference(monotonicity,[status(thm)],[2478])).
% 3.30/2.47 tff(2480,plain,
% 3.30/2.47 (((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp8 | (~ndr1_0) | c3_1(a651) | (~c2_1(a651)) | (~c0_1(a651)))) <=> ((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp27 | hskp8 | c3_1(a651) | (~ndr1_0) | (~c2_1(a651)) | (~c0_1(a651)))),
% 3.30/2.47 inference(transitivity,[status(thm)],[2479, 2477])).
% 3.30/2.47 tff(2481,plain,
% 3.30/2.47 ((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp8 | (~ndr1_0) | c3_1(a651) | (~c2_1(a651)) | (~c0_1(a651)))),
% 3.30/2.47 inference(quant_inst,[status(thm)],[])).
% 3.30/2.47 tff(2482,plain,
% 3.30/2.47 ((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp27 | hskp8 | c3_1(a651) | (~ndr1_0) | (~c2_1(a651)) | (~c0_1(a651))),
% 3.30/2.47 inference(modus_ponens,[status(thm)],[2481, 2480])).
% 3.30/2.47 tff(2483,plain,
% 3.30/2.47 (hskp8 | (~c0_1(a651))),
% 3.30/2.47 inference(unit_resolution,[status(thm)],[2482, 107, 1872, 2474, 2473, 2080])).
% 3.30/2.47 tff(2484,plain,
% 3.30/2.47 (hskp8),
% 3.30/2.47 inference(unit_resolution,[status(thm)],[2483, 2476])).
% 3.30/2.47 tff(2485,plain,
% 3.30/2.47 (c3_1(a593)),
% 3.30/2.47 inference(unit_resolution,[status(thm)],[511, 2484])).
% 3.30/2.47 tff(2486,assumption,(c0_1(a607)), introduced(assumption)).
% 3.30/2.47 tff(2487,plain,
% 3.30/2.47 (~c2_1(a593)),
% 3.30/2.47 inference(unit_resolution,[status(thm)],[555, 2484])).
% 3.30/2.47 tff(2488,plain,
% 3.30/2.47 (c1_1(a593)),
% 3.30/2.47 inference(unit_resolution,[status(thm)],[522, 2484])).
% 3.30/2.47 tff(2489,assumption,(~c3_1(a604)), introduced(assumption)).
% 3.30/2.47 tff(2490,plain,
% 3.30/2.47 (~hskp15),
% 3.30/2.47 inference(unit_resolution,[status(thm)],[1602, 2489])).
% 3.30/2.47 tff(2491,plain,
% 3.30/2.47 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | c1_1(a599) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a599)) | (~c0_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a599) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a599)) | (~c0_1(a599)))),
% 3.30/2.47 inference(rewrite,[status(thm)],[])).
% 3.30/2.47 tff(2492,plain,
% 3.30/2.47 ((hskp15 | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599))) <=> (hskp15 | c1_1(a599) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a599)) | (~c0_1(a599)))),
% 3.30/2.47 inference(rewrite,[status(thm)],[])).
% 3.30/2.47 tff(2493,plain,
% 3.30/2.47 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | c1_1(a599) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a599)) | (~c0_1(a599))))),
% 3.30/2.47 inference(monotonicity,[status(thm)],[2492])).
% 3.30/2.47 tff(2494,plain,
% 3.30/2.47 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a599) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a599)) | (~c0_1(a599)))),
% 3.30/2.47 inference(transitivity,[status(thm)],[2493, 2491])).
% 3.30/2.47 tff(2495,plain,
% 3.30/2.47 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599)))),
% 3.30/2.47 inference(quant_inst,[status(thm)],[])).
% 3.30/2.47 tff(2496,plain,
% 3.30/2.47 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a599) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a599)) | (~c0_1(a599))),
% 3.30/2.47 inference(modus_ponens,[status(thm)],[2495, 2494])).
% 3.30/2.47 tff(2497,plain,
% 3.30/2.47 (hskp15 | (~c0_1(a593))),
% 3.30/2.47 inference(unit_resolution,[status(thm)],[2496, 107, 462, 1894, 1903, 461, 1993, 2472])).
% 3.30/2.47 tff(2498,plain,
% 3.30/2.47 (~c0_1(a593)),
% 3.30/2.47 inference(unit_resolution,[status(thm)],[2497, 2490])).
% 3.30/2.47 tff(2499,plain,
% 3.30/2.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a604) | c3_1(a651) | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a604)) | (~c2_1(a651)) | (~c0_1(a651)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a604) | c3_1(a651) | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a604)) | (~c2_1(a651)) | (~c0_1(a651)))),
% 3.30/2.47 inference(rewrite,[status(thm)],[])).
% 3.30/2.47 tff(2500,plain,
% 3.30/2.47 (((~ndr1_0) | c3_1(a651) | (~c2_1(a651)) | (~c0_1(a651)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604))) <=> (c3_1(a604) | c3_1(a651) | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a604)) | (~c2_1(a651)) | (~c0_1(a651)))),
% 3.30/2.47 inference(rewrite,[status(thm)],[])).
% 3.30/2.47 tff(2501,plain,
% 3.30/2.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a651) | (~c2_1(a651)) | (~c0_1(a651)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a604) | c3_1(a651) | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a604)) | (~c2_1(a651)) | (~c0_1(a651))))),
% 3.30/2.47 inference(monotonicity,[status(thm)],[2500])).
% 3.30/2.47 tff(2502,plain,
% 3.30/2.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a651) | (~c2_1(a651)) | (~c0_1(a651)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a604) | c3_1(a651) | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a604)) | (~c2_1(a651)) | (~c0_1(a651)))),
% 3.30/2.47 inference(transitivity,[status(thm)],[2501, 2499])).
% 3.30/2.47 tff(2503,plain,
% 3.30/2.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a651) | (~c2_1(a651)) | (~c0_1(a651)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604)))),
% 3.30/2.47 inference(quant_inst,[status(thm)],[])).
% 3.30/2.47 tff(2504,plain,
% 3.30/2.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a604) | c3_1(a651) | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a604)) | (~c2_1(a651)) | (~c0_1(a651))),
% 3.30/2.47 inference(modus_ponens,[status(thm)],[2503, 2502])).
% 3.30/2.47 tff(2505,plain,
% 3.30/2.47 (~c1_1(a604)),
% 3.30/2.47 inference(unit_resolution,[status(thm)],[2504, 107, 2474, 2489, 463, 462, 2473, 2475, 461, 258, 2476])).
% 3.30/2.47 tff(2506,plain,
% 3.30/2.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a607) | c1_1(a604) | c3_1(a604) | c2_1(a607) | c0_1(a604) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a607) | c1_1(a604) | c3_1(a604) | c2_1(a607) | c0_1(a604) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607)))),
% 3.30/2.47 inference(rewrite,[status(thm)],[])).
% 3.30/2.47 tff(2507,plain,
% 3.30/2.47 (((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a604) | c1_1(a604) | c0_1(a604)) <=> (c3_1(a607) | c1_1(a604) | c3_1(a604) | c2_1(a607) | c0_1(a604) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607)))),
% 3.30/2.47 inference(rewrite,[status(thm)],[])).
% 3.30/2.47 tff(2508,plain,
% 3.30/2.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a604) | c1_1(a604) | c0_1(a604))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a607) | c1_1(a604) | c3_1(a604) | c2_1(a607) | c0_1(a604) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607))))),
% 3.30/2.48 inference(monotonicity,[status(thm)],[2507])).
% 3.30/2.48 tff(2509,plain,
% 3.30/2.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a604) | c1_1(a604) | c0_1(a604))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a607) | c1_1(a604) | c3_1(a604) | c2_1(a607) | c0_1(a604) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607)))),
% 3.30/2.48 inference(transitivity,[status(thm)],[2508, 2506])).
% 3.30/2.48 tff(2510,plain,
% 3.30/2.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a604) | c1_1(a604) | c0_1(a604))),
% 3.30/2.48 inference(quant_inst,[status(thm)],[])).
% 3.30/2.48 tff(2511,plain,
% 3.30/2.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a607) | c1_1(a604) | c3_1(a604) | c2_1(a607) | c0_1(a604) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607))),
% 3.30/2.48 inference(modus_ponens,[status(thm)],[2510, 2509])).
% 3.30/2.48 tff(2512,plain,
% 3.30/2.48 ($false),
% 3.30/2.48 inference(unit_resolution,[status(thm)],[2511, 107, 33, 2505, 2489, 1894, 22, 2475, 1893, 1463, 2498, 2486])).
% 3.30/2.48 tff(2513,plain,(c3_1(a604) | c3_1(a607) | (~c1_1(a593)) | c2_1(a607) | c0_1(a604) | c2_1(a593) | (~c0_1(a607)) | (~c2_1(a651)) | (~c2_1(a599)) | (~c3_1(a599)) | c3_1(a651) | c1_1(a599) | (~c0_1(a651)) | (~c3_1(a593)) | (~c0_1(a599))), inference(lemma,lemma(discharge,[]))).
% 3.30/2.48 tff(2514,plain,
% 3.30/2.48 (c3_1(a604)),
% 3.30/2.48 inference(unit_resolution,[status(thm)],[2513, 2488, 33, 22, 2475, 2487, 2486, 2474, 463, 462, 2473, 461, 2476, 2485, 2472])).
% 3.30/2.48 tff(2515,assumption,(c0_1(a606)), introduced(assumption)).
% 3.30/2.48 tff(2516,plain,
% 3.30/2.48 ((~c3_1(a604)) | c2_1(a604)),
% 3.30/2.48 inference(unit_resolution,[status(thm)],[2151, 107, 1872, 1876, 1873, 2475, 540, 2515])).
% 3.30/2.48 tff(2517,plain,
% 3.30/2.48 (c2_1(a604)),
% 3.30/2.48 inference(unit_resolution,[status(thm)],[2516, 2514])).
% 3.30/2.48 tff(2518,assumption,(hskp13), introduced(assumption)).
% 3.30/2.48 tff(2519,plain,
% 3.30/2.48 (((~hskp13) | (~c2_1(a601))) <=> ((~hskp13) | (~c2_1(a601)))),
% 3.30/2.48 inference(rewrite,[status(thm)],[])).
% 3.30/2.48 tff(2520,plain,
% 3.30/2.48 (((~c2_1(a601)) | (~hskp13)) <=> ((~hskp13) | (~c2_1(a601)))),
% 3.30/2.48 inference(rewrite,[status(thm)],[])).
% 3.30/2.48 tff(2521,axiom,((~c2_1(a601)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause107')).
% 3.30/2.48 tff(2522,plain,
% 3.30/2.48 ((~hskp13) | (~c2_1(a601))),
% 3.30/2.48 inference(modus_ponens,[status(thm)],[2521, 2520])).
% 3.30/2.48 tff(2523,plain,
% 3.30/2.48 ((~hskp13) | (~c2_1(a601))),
% 3.30/2.48 inference(modus_ponens,[status(thm)],[2522, 2519])).
% 3.30/2.48 tff(2524,plain,
% 3.30/2.48 (~c2_1(a601)),
% 3.30/2.48 inference(unit_resolution,[status(thm)],[2523, 2518])).
% 3.30/2.48 tff(2525,plain,
% 3.30/2.48 (((~hskp13) | (~c1_1(a601))) <=> ((~hskp13) | (~c1_1(a601)))),
% 3.30/2.48 inference(rewrite,[status(thm)],[])).
% 3.30/2.48 tff(2526,plain,
% 3.30/2.48 (((~c1_1(a601)) | (~hskp13)) <=> ((~hskp13) | (~c1_1(a601)))),
% 3.30/2.48 inference(rewrite,[status(thm)],[])).
% 3.30/2.48 tff(2527,axiom,((~c1_1(a601)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause106')).
% 3.30/2.48 tff(2528,plain,
% 3.30/2.48 ((~hskp13) | (~c1_1(a601))),
% 3.30/2.48 inference(modus_ponens,[status(thm)],[2527, 2526])).
% 3.30/2.48 tff(2529,plain,
% 3.30/2.48 ((~hskp13) | (~c1_1(a601))),
% 3.30/2.48 inference(modus_ponens,[status(thm)],[2528, 2525])).
% 3.30/2.48 tff(2530,plain,
% 3.30/2.48 (~c1_1(a601)),
% 3.30/2.48 inference(unit_resolution,[status(thm)],[2529, 2518])).
% 3.30/2.48 tff(2531,plain,
% 3.30/2.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a606) | c1_1(a601) | c2_1(a601) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a601)) | (~c0_1(a606)) | (~c1_1(a606)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a606) | c1_1(a601) | c2_1(a601) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a601)) | (~c0_1(a606)) | (~c1_1(a606)))),
% 3.30/2.48 inference(rewrite,[status(thm)],[])).
% 3.30/2.48 tff(2532,plain,
% 3.30/2.48 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a601) | c2_1(a601) | (~c3_1(a601))) <=> (c2_1(a606) | c1_1(a601) | c2_1(a601) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a601)) | (~c0_1(a606)) | (~c1_1(a606)))),
% 3.30/2.48 inference(rewrite,[status(thm)],[])).
% 3.30/2.48 tff(2533,plain,
% 3.30/2.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a601) | c2_1(a601) | (~c3_1(a601)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a606) | c1_1(a601) | c2_1(a601) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a601)) | (~c0_1(a606)) | (~c1_1(a606))))),
% 3.30/2.48 inference(monotonicity,[status(thm)],[2532])).
% 3.30/2.48 tff(2534,plain,
% 3.30/2.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a601) | c2_1(a601) | (~c3_1(a601)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a606) | c1_1(a601) | c2_1(a601) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a601)) | (~c0_1(a606)) | (~c1_1(a606)))),
% 3.30/2.48 inference(transitivity,[status(thm)],[2533, 2531])).
% 3.30/2.48 tff(2535,plain,
% 3.30/2.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a601) | c2_1(a601) | (~c3_1(a601)))),
% 3.30/2.48 inference(quant_inst,[status(thm)],[])).
% 3.30/2.48 tff(2536,plain,
% 3.30/2.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a606) | c1_1(a601) | c2_1(a601) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a601)) | (~c0_1(a606)) | (~c1_1(a606))),
% 3.30/2.48 inference(modus_ponens,[status(thm)],[2535, 2534])).
% 3.30/2.48 tff(2537,plain,
% 3.30/2.48 (~c3_1(a601)),
% 3.30/2.48 inference(unit_resolution,[status(thm)],[2536, 107, 2318, 2317, 2316, 1876, 1873, 2530, 2524, 1106, 2515])).
% 3.30/2.48 tff(2538,assumption,(c2_1(a604)), introduced(assumption)).
% 3.30/2.48 tff(2539,plain,
% 3.30/2.48 (((~hskp13) | (~c0_1(a601))) <=> ((~hskp13) | (~c0_1(a601)))),
% 3.30/2.48 inference(rewrite,[status(thm)],[])).
% 3.30/2.48 tff(2540,plain,
% 3.30/2.48 (((~c0_1(a601)) | (~hskp13)) <=> ((~hskp13) | (~c0_1(a601)))),
% 3.30/2.48 inference(rewrite,[status(thm)],[])).
% 3.30/2.48 tff(2541,axiom,((~c0_1(a601)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause105')).
% 3.30/2.48 tff(2542,plain,
% 3.30/2.48 ((~hskp13) | (~c0_1(a601))),
% 3.30/2.48 inference(modus_ponens,[status(thm)],[2541, 2540])).
% 3.30/2.48 tff(2543,plain,
% 3.30/2.48 ((~hskp13) | (~c0_1(a601))),
% 3.30/2.48 inference(modus_ponens,[status(thm)],[2542, 2539])).
% 3.30/2.48 tff(2544,plain,
% 3.30/2.48 (~c0_1(a601)),
% 3.30/2.48 inference(unit_resolution,[status(thm)],[2543, 2518])).
% 3.30/2.48 tff(2545,assumption,(c3_1(a604)), introduced(assumption)).
% 3.30/2.48 tff(2546,plain,
% 3.30/2.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a604) | c0_1(a601) | c2_1(a601) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a601) | (~c3_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a604) | c0_1(a601) | c2_1(a601) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a601) | (~c3_1(a604)) | (~c2_1(a604)))),
% 3.30/2.48 inference(rewrite,[status(thm)],[])).
% 3.30/2.48 tff(2547,plain,
% 3.30/2.48 (((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c3_1(a601) | c0_1(a601) | c2_1(a601)) <=> (c0_1(a604) | c0_1(a601) | c2_1(a601) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a601) | (~c3_1(a604)) | (~c2_1(a604)))),
% 3.30/2.48 inference(rewrite,[status(thm)],[])).
% 3.30/2.48 tff(2548,plain,
% 3.30/2.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c3_1(a601) | c0_1(a601) | c2_1(a601))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a604) | c0_1(a601) | c2_1(a601) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a601) | (~c3_1(a604)) | (~c2_1(a604))))),
% 3.30/2.48 inference(monotonicity,[status(thm)],[2547])).
% 3.30/2.48 tff(2549,plain,
% 3.30/2.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c3_1(a601) | c0_1(a601) | c2_1(a601))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a604) | c0_1(a601) | c2_1(a601) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a601) | (~c3_1(a604)) | (~c2_1(a604)))),
% 3.30/2.48 inference(transitivity,[status(thm)],[2548, 2546])).
% 3.30/2.48 tff(2550,plain,
% 3.30/2.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c3_1(a601) | c0_1(a601) | c2_1(a601))),
% 3.30/2.48 inference(quant_inst,[status(thm)],[])).
% 3.30/2.48 tff(2551,plain,
% 3.30/2.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a604) | c0_1(a601) | c2_1(a601) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a601) | (~c3_1(a604)) | (~c2_1(a604))),
% 3.30/2.48 inference(modus_ponens,[status(thm)],[2550, 2549])).
% 3.30/2.48 tff(2552,plain,
% 3.30/2.48 ($false),
% 3.30/2.48 inference(unit_resolution,[status(thm)],[2551, 107, 2545, 463, 462, 2475, 2544, 2524, 461, 1730, 2538, 2537])).
% 3.30/2.48 tff(2553,plain,((~hskp13) | (~c3_1(a604)) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a604) | c1_1(a599) | (~c2_1(a604)) | (~c0_1(a678)) | (~c2_1(a678)) | (~c3_1(a678)) | (~c1_1(a606)) | c2_1(a606) | (~c0_1(a606))), inference(lemma,lemma(discharge,[]))).
% 3.30/2.48 tff(2554,plain,
% 3.30/2.48 (~hskp13),
% 3.30/2.48 inference(unit_resolution,[status(thm)],[2553, 2517, 463, 462, 2475, 461, 2514, 2318, 2317, 2316, 1876, 1873, 2515])).
% 3.30/2.48 tff(2555,plain,
% 3.30/2.48 (^[U: $i] : refl((hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))),
% 3.30/2.48 inference(bind,[status(th)],[])).
% 3.30/2.48 tff(2556,plain,
% 3.30/2.48 (![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 3.30/2.48 inference(quant_intro,[status(thm)],[2555])).
% 3.30/2.48 tff(2557,plain,
% 3.30/2.48 (![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 3.30/2.48 inference(rewrite,[status(thm)],[])).
% 3.30/2.48 tff(2558,plain,
% 3.30/2.48 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp19) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp19))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp19) <=> (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp19) <=> (hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp19) | hskp13) <=> ((hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp13))), rewrite(((hskp19 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp13) <=> (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp19) | hskp13) <=> (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))))),
% 3.30/2.48 inference(bind,[status(th)],[])).
% 3.30/2.48 tff(2559,plain,
% 3.30/2.48 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp19) | hskp13) <=> ![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 3.30/2.48 inference(quant_intro,[status(thm)],[2558])).
% 3.30/2.48 tff(2560,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp19) | hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause143')).
% 3.30/2.48 tff(2561,plain,
% 3.30/2.48 (![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 3.30/2.48 inference(modus_ponens,[status(thm)],[2560, 2559])).
% 3.30/2.48 tff(2562,plain,
% 3.30/2.48 (![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 3.30/2.48 inference(modus_ponens,[status(thm)],[2561, 2557])).
% 3.30/2.48 tff(2563,plain,(
% 3.30/2.48 ![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 3.30/2.48 inference(skolemize,[status(sab)],[2562])).
% 3.30/2.48 tff(2564,plain,
% 3.30/2.48 (![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 3.30/2.48 inference(modus_ponens,[status(thm)],[2563, 2556])).
% 3.30/2.48 tff(2565,plain,
% 3.30/2.48 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | c3_1(a651) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c2_1(a651)) | (~c0_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp1 | c3_1(a651) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c2_1(a651)) | (~c0_1(a651)))),
% 3.30/2.48 inference(rewrite,[status(thm)],[])).
% 3.30/2.48 tff(2566,plain,
% 3.30/2.48 ((hskp1 | (~ndr1_0) | c3_1(a651) | (~c2_1(a651)) | (~c0_1(a651)) | c1_1(a607) | c2_1(a607) | (~c0_1(a607))) <=> (hskp1 | c3_1(a651) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c2_1(a651)) | (~c0_1(a651)))),
% 3.30/2.48 inference(rewrite,[status(thm)],[])).
% 3.30/2.48 tff(2567,plain,
% 3.30/2.48 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a651) | (~c2_1(a651)) | (~c0_1(a651)) | c1_1(a607) | c2_1(a607) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | c3_1(a651) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c2_1(a651)) | (~c0_1(a651))))),
% 3.30/2.48 inference(monotonicity,[status(thm)],[2566])).
% 3.30/2.48 tff(2568,plain,
% 3.30/2.48 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a651) | (~c2_1(a651)) | (~c0_1(a651)) | c1_1(a607) | c2_1(a607) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp1 | c3_1(a651) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c2_1(a651)) | (~c0_1(a651)))),
% 3.30/2.48 inference(transitivity,[status(thm)],[2567, 2565])).
% 3.30/2.48 tff(2569,plain,
% 3.30/2.48 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a651) | (~c2_1(a651)) | (~c0_1(a651)) | c1_1(a607) | c2_1(a607) | (~c0_1(a607)))),
% 3.30/2.48 inference(quant_inst,[status(thm)],[])).
% 3.30/2.48 tff(2570,plain,
% 3.30/2.48 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp1 | c3_1(a651) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c2_1(a651)) | (~c0_1(a651))),
% 3.30/2.48 inference(modus_ponens,[status(thm)],[2569, 2568])).
% 3.30/2.48 tff(2571,plain,
% 3.30/2.48 (hskp1 | (~c0_1(a651))),
% 3.30/2.48 inference(unit_resolution,[status(thm)],[2570, 107, 2474, 2473, 66, 22, 1237, 2486])).
% 3.30/2.48 tff(2572,plain,
% 3.30/2.48 (hskp1),
% 3.30/2.48 inference(unit_resolution,[status(thm)],[2571, 2476])).
% 3.30/2.48 tff(2573,plain,
% 3.30/2.48 (~c0_1(a585)),
% 3.30/2.48 inference(unit_resolution,[status(thm)],[1250, 2572])).
% 3.30/2.48 tff(2574,plain,
% 3.30/2.48 (c2_1(a585)),
% 3.30/2.48 inference(unit_resolution,[status(thm)],[1261, 2572])).
% 3.30/2.48 tff(2575,plain,
% 3.30/2.48 (c1_1(a585)),
% 3.30/2.48 inference(unit_resolution,[status(thm)],[1272, 2572])).
% 3.30/2.48 tff(2576,plain,
% 3.30/2.48 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp19 | hskp13 | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)))),
% 3.30/2.48 inference(rewrite,[status(thm)],[])).
% 3.30/2.48 tff(2577,plain,
% 3.30/2.48 ((hskp19 | hskp13 | (~ndr1_0) | c0_1(a585) | (~c2_1(a585)) | (~c1_1(a585))) <=> (hskp19 | hskp13 | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)))),
% 3.30/2.48 inference(rewrite,[status(thm)],[])).
% 3.30/2.48 tff(2578,plain,
% 3.30/2.48 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c0_1(a585) | (~c2_1(a585)) | (~c1_1(a585)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585))))),
% 3.30/2.48 inference(monotonicity,[status(thm)],[2577])).
% 3.30/2.48 tff(2579,plain,
% 3.30/2.48 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c0_1(a585) | (~c2_1(a585)) | (~c1_1(a585)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp19 | hskp13 | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)))),
% 3.30/2.48 inference(transitivity,[status(thm)],[2578, 2576])).
% 3.30/2.48 tff(2580,plain,
% 3.30/2.48 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c0_1(a585) | (~c2_1(a585)) | (~c1_1(a585)))),
% 3.30/2.48 inference(quant_inst,[status(thm)],[])).
% 3.30/2.48 tff(2581,plain,
% 3.30/2.48 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp19 | hskp13 | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585))),
% 3.30/2.48 inference(modus_ponens,[status(thm)],[2580, 2579])).
% 3.30/2.48 tff(2582,plain,
% 3.30/2.48 (hskp19 | hskp13),
% 3.30/2.48 inference(unit_resolution,[status(thm)],[2581, 107, 2575, 2574, 2573, 2564])).
% 3.30/2.48 tff(2583,plain,
% 3.30/2.48 (hskp19),
% 3.30/2.48 inference(unit_resolution,[status(thm)],[2582, 2554])).
% 3.30/2.48 tff(2584,plain,
% 3.30/2.48 (((~hskp19) | (~c1_1(a617))) <=> ((~hskp19) | (~c1_1(a617)))),
% 3.30/2.48 inference(rewrite,[status(thm)],[])).
% 3.30/2.48 tff(2585,plain,
% 3.30/2.48 (((~c1_1(a617)) | (~hskp19)) <=> ((~hskp19) | (~c1_1(a617)))),
% 3.30/2.48 inference(rewrite,[status(thm)],[])).
% 3.30/2.48 tff(2586,axiom,((~c1_1(a617)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause95')).
% 3.30/2.48 tff(2587,plain,
% 3.30/2.48 ((~hskp19) | (~c1_1(a617))),
% 3.30/2.48 inference(modus_ponens,[status(thm)],[2586, 2585])).
% 3.30/2.48 tff(2588,plain,
% 3.30/2.48 ((~hskp19) | (~c1_1(a617))),
% 3.30/2.48 inference(modus_ponens,[status(thm)],[2587, 2584])).
% 3.30/2.48 tff(2589,plain,
% 3.30/2.48 (~c1_1(a617)),
% 3.30/2.48 inference(unit_resolution,[status(thm)],[2588, 2583])).
% 3.30/2.48 tff(2590,plain,
% 3.30/2.48 (((~hskp19) | (~c0_1(a617))) <=> ((~hskp19) | (~c0_1(a617)))),
% 3.30/2.48 inference(rewrite,[status(thm)],[])).
% 3.30/2.48 tff(2591,plain,
% 3.30/2.48 (((~c0_1(a617)) | (~hskp19)) <=> ((~hskp19) | (~c0_1(a617)))),
% 3.30/2.48 inference(rewrite,[status(thm)],[])).
% 3.30/2.48 tff(2592,axiom,((~c0_1(a617)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause94')).
% 3.30/2.48 tff(2593,plain,
% 3.30/2.48 ((~hskp19) | (~c0_1(a617))),
% 3.30/2.48 inference(modus_ponens,[status(thm)],[2592, 2591])).
% 3.30/2.48 tff(2594,plain,
% 3.30/2.48 ((~hskp19) | (~c0_1(a617))),
% 3.30/2.48 inference(modus_ponens,[status(thm)],[2593, 2590])).
% 3.30/2.48 tff(2595,plain,
% 3.30/2.48 (~c0_1(a617)),
% 3.30/2.48 inference(unit_resolution,[status(thm)],[2594, 2583])).
% 3.30/2.48 tff(2596,plain,
% 3.30/2.48 (((~hskp19) | c2_1(a617)) <=> ((~hskp19) | c2_1(a617))),
% 3.30/2.48 inference(rewrite,[status(thm)],[])).
% 3.30/2.48 tff(2597,axiom,((~hskp19) | c2_1(a617)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause54')).
% 3.30/2.48 tff(2598,plain,
% 3.30/2.48 ((~hskp19) | c2_1(a617)),
% 3.30/2.48 inference(modus_ponens,[status(thm)],[2597, 2596])).
% 3.30/2.48 tff(2599,plain,
% 3.30/2.48 ((~hskp19) | c2_1(a617)),
% 3.30/2.48 inference(modus_ponens,[status(thm)],[2598, 2596])).
% 3.30/2.48 tff(2600,plain,
% 3.30/2.48 ((~hskp19) | c2_1(a617)),
% 3.30/2.48 inference(modus_ponens,[status(thm)],[2599, 2596])).
% 3.30/2.48 tff(2601,plain,
% 3.30/2.48 ((~hskp19) | c2_1(a617)),
% 3.30/2.48 inference(modus_ponens,[status(thm)],[2600, 2596])).
% 3.30/2.48 tff(2602,plain,
% 3.30/2.48 ((~hskp19) | c2_1(a617)),
% 3.30/2.48 inference(modus_ponens,[status(thm)],[2601, 2596])).
% 3.30/2.48 tff(2603,plain,
% 3.30/2.48 ((~hskp19) | c2_1(a617)),
% 3.30/2.48 inference(modus_ponens,[status(thm)],[2602, 2596])).
% 3.30/2.48 tff(2604,plain,
% 3.30/2.48 ((~hskp19) | c2_1(a617)),
% 3.30/2.48 inference(modus_ponens,[status(thm)],[2603, 2596])).
% 3.30/2.48 tff(2605,plain,
% 3.30/2.48 ((~hskp19) | c2_1(a617)),
% 3.30/2.48 inference(modus_ponens,[status(thm)],[2604, 2596])).
% 3.30/2.48 tff(2606,plain,
% 3.30/2.48 (c2_1(a617)),
% 3.30/2.48 inference(unit_resolution,[status(thm)],[2605, 2583])).
% 3.30/2.48 tff(2607,plain,
% 3.30/2.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617)))),
% 3.30/2.48 inference(rewrite,[status(thm)],[])).
% 3.30/2.48 tff(2608,plain,
% 3.30/2.48 (((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617))) <=> (c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617)))),
% 3.30/2.48 inference(rewrite,[status(thm)],[])).
% 3.30/2.48 tff(2609,plain,
% 3.30/2.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617))))),
% 3.30/2.48 inference(monotonicity,[status(thm)],[2608])).
% 3.30/2.48 tff(2610,plain,
% 3.30/2.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617)))),
% 3.30/2.48 inference(transitivity,[status(thm)],[2609, 2607])).
% 3.30/2.48 tff(2611,plain,
% 3.30/2.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))),
% 3.30/2.48 inference(quant_inst,[status(thm)],[])).
% 3.30/2.48 tff(2612,plain,
% 3.30/2.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617))),
% 3.30/2.48 inference(modus_ponens,[status(thm)],[2611, 2610])).
% 3.30/2.48 tff(2613,plain,
% 3.30/2.48 (~c1_1(a678)),
% 3.30/2.48 inference(unit_resolution,[status(thm)],[2612, 107, 2318, 2316, 2606, 2514, 2595, 2589, 2475, 65, 2517])).
% 3.30/2.48 tff(2614,plain,
% 3.30/2.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617)))),
% 3.30/2.48 inference(rewrite,[status(thm)],[])).
% 3.30/2.48 tff(2615,plain,
% 3.30/2.48 (((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617))) <=> (c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617)))),
% 3.30/2.48 inference(rewrite,[status(thm)],[])).
% 3.30/2.48 tff(2616,plain,
% 3.30/2.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617))))),
% 3.30/2.48 inference(monotonicity,[status(thm)],[2615])).
% 3.30/2.48 tff(2617,plain,
% 3.30/2.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617)))),
% 3.30/2.48 inference(transitivity,[status(thm)],[2616, 2614])).
% 3.30/2.48 tff(2618,plain,
% 3.30/2.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))),
% 3.30/2.48 inference(quant_inst,[status(thm)],[])).
% 3.30/2.48 tff(2619,plain,
% 3.30/2.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617))),
% 3.30/2.49 inference(modus_ponens,[status(thm)],[2618, 2617])).
% 3.30/2.49 tff(2620,plain,
% 3.30/2.49 (~c0_1(a593)),
% 3.30/2.49 inference(unit_resolution,[status(thm)],[2619, 107, 2606, 2514, 2488, 2485, 2595, 2589, 2475, 65, 2517])).
% 3.30/2.49 tff(2621,plain,
% 3.30/2.49 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c2_1(a593) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c0_1(a593) | (~c1_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c2_1(a593) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c0_1(a593) | (~c1_1(a593)))),
% 3.30/2.49 inference(rewrite,[status(thm)],[])).
% 3.30/2.49 tff(2622,plain,
% 3.30/2.49 ((hskp17 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593))) <=> (hskp17 | c2_1(a593) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c0_1(a593) | (~c1_1(a593)))),
% 3.30/2.49 inference(rewrite,[status(thm)],[])).
% 3.30/2.49 tff(2623,plain,
% 3.30/2.49 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c2_1(a593) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c0_1(a593) | (~c1_1(a593))))),
% 3.30/2.49 inference(monotonicity,[status(thm)],[2622])).
% 3.30/2.49 tff(2624,plain,
% 3.30/2.49 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c2_1(a593) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c0_1(a593) | (~c1_1(a593)))),
% 3.30/2.49 inference(transitivity,[status(thm)],[2623, 2621])).
% 3.30/2.49 tff(2625,plain,
% 3.30/2.49 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)))),
% 3.30/2.49 inference(quant_inst,[status(thm)],[])).
% 3.30/2.49 tff(2626,plain,
% 3.30/2.49 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c2_1(a593) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c0_1(a593) | (~c1_1(a593))),
% 3.30/2.49 inference(modus_ponens,[status(thm)],[2625, 2624])).
% 3.30/2.49 tff(2627,plain,
% 3.30/2.49 ($false),
% 3.30/2.49 inference(unit_resolution,[status(thm)],[2626, 107, 241, 2318, 2317, 2488, 2487, 32, 2620, 2613])).
% 3.30/2.49 tff(2628,plain,((~c0_1(a651)) | (~c0_1(a678)) | (~c2_1(a678)) | c0_1(a604) | (~c3_1(a678)) | (~c2_1(a599)) | (~c3_1(a599)) | c1_1(a599) | (~c1_1(a606)) | c2_1(a606) | (~c0_1(a606)) | hskp27 | c3_1(a607) | c2_1(a607) | (~c0_1(a607)) | (~c2_1(a651)) | c3_1(a651) | (~c0_1(a599)) | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.30/2.49 tff(2629,plain,
% 3.30/2.49 (~c0_1(a651)),
% 3.30/2.49 inference(unit_resolution,[status(thm)],[2628, 2475, 2317, 2318, 2316, 2395, 2394, 2393, 2413, 2405, 2412, 1872, 33, 22, 2402, 2474, 2473, 2472, 66])).
% 3.30/2.49 tff(2630,assumption,(~c1_1(a651)), introduced(assumption)).
% 3.30/2.49 tff(2631,plain,
% 3.30/2.49 (c3_1(a583)),
% 3.30/2.49 inference(unit_resolution,[status(thm)],[1982, 1973, 461, 1649, 463, 462, 1650])).
% 3.30/2.49 tff(2632,plain,
% 3.30/2.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a651) | c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a651)) | c0_1(a651))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a651) | c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a651)) | c0_1(a651))),
% 3.30/2.49 inference(rewrite,[status(thm)],[])).
% 3.30/2.49 tff(2633,plain,
% 3.30/2.49 (((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a651) | c0_1(a651) | (~c2_1(a651))) <=> (c1_1(a651) | c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a651)) | c0_1(a651))),
% 3.30/2.49 inference(rewrite,[status(thm)],[])).
% 3.30/2.49 tff(2634,plain,
% 3.30/2.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a651) | c0_1(a651) | (~c2_1(a651)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a651) | c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a651)) | c0_1(a651)))),
% 3.30/2.49 inference(monotonicity,[status(thm)],[2633])).
% 3.30/2.49 tff(2635,plain,
% 3.30/2.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a651) | c0_1(a651) | (~c2_1(a651)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a651) | c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a651)) | c0_1(a651))),
% 3.30/2.49 inference(transitivity,[status(thm)],[2634, 2632])).
% 3.30/2.49 tff(2636,plain,
% 3.30/2.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a651) | c0_1(a651) | (~c2_1(a651)))),
% 3.30/2.49 inference(quant_inst,[status(thm)],[])).
% 3.30/2.49 tff(2637,plain,
% 3.30/2.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a651) | c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a651)) | c0_1(a651)),
% 3.30/2.49 inference(modus_ponens,[status(thm)],[2636, 2635])).
% 3.30/2.49 tff(2638,plain,
% 3.30/2.49 (c0_1(a651)),
% 3.30/2.49 inference(unit_resolution,[status(thm)],[2637, 107, 1651, 1650, 2474, 863, 862, 2630, 45, 65, 2631])).
% 3.30/2.49 tff(2639,plain,
% 3.30/2.49 (hskp15),
% 3.30/2.49 inference(unit_resolution,[status(thm)],[2113, 107, 1651, 1650, 462, 461, 1993, 2631, 2472])).
% 3.30/2.49 tff(2640,plain,
% 3.30/2.49 (~c0_1(a604)),
% 3.30/2.49 inference(unit_resolution,[status(thm)],[1591, 2639])).
% 3.30/2.49 tff(2641,plain,
% 3.30/2.49 (c3_1(a604)),
% 3.30/2.49 inference(unit_resolution,[status(thm)],[1602, 2639])).
% 3.30/2.49 tff(2642,plain,
% 3.30/2.49 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | c3_1(a651) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c2_1(a651)) | (~c0_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp28 | c3_1(a651) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c2_1(a651)) | (~c0_1(a651)))),
% 3.30/2.49 inference(rewrite,[status(thm)],[])).
% 3.30/2.49 tff(2643,plain,
% 3.30/2.49 ((hskp28 | (~ndr1_0) | c3_1(a651) | (~c2_1(a651)) | (~c0_1(a651)) | c0_1(a604) | c2_1(a604) | (~c3_1(a604))) <=> (hskp28 | c3_1(a651) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c2_1(a651)) | (~c0_1(a651)))),
% 3.30/2.49 inference(rewrite,[status(thm)],[])).
% 3.30/2.49 tff(2644,plain,
% 3.30/2.49 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a651) | (~c2_1(a651)) | (~c0_1(a651)) | c0_1(a604) | c2_1(a604) | (~c3_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | c3_1(a651) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c2_1(a651)) | (~c0_1(a651))))),
% 3.30/2.49 inference(monotonicity,[status(thm)],[2643])).
% 3.30/2.49 tff(2645,plain,
% 3.30/2.49 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a651) | (~c2_1(a651)) | (~c0_1(a651)) | c0_1(a604) | c2_1(a604) | (~c3_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp28 | c3_1(a651) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c2_1(a651)) | (~c0_1(a651)))),
% 3.30/2.49 inference(transitivity,[status(thm)],[2644, 2642])).
% 3.30/2.49 tff(2646,plain,
% 3.30/2.49 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a651) | (~c2_1(a651)) | (~c0_1(a651)) | c0_1(a604) | c2_1(a604) | (~c3_1(a604)))),
% 3.30/2.49 inference(quant_inst,[status(thm)],[])).
% 3.30/2.49 tff(2647,plain,
% 3.30/2.49 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp28 | c3_1(a651) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c2_1(a651)) | (~c0_1(a651))),
% 3.30/2.49 inference(modus_ponens,[status(thm)],[2646, 2645])).
% 3.30/2.49 tff(2648,plain,
% 3.30/2.49 (c2_1(a604)),
% 3.30/2.49 inference(unit_resolution,[status(thm)],[2647, 107, 1973, 2474, 2641, 2473, 2640, 1122, 2638])).
% 3.30/2.49 tff(2649,plain,
% 3.30/2.49 (~hskp13),
% 3.30/2.49 inference(unit_resolution,[status(thm)],[2553, 2641, 463, 462, 2640, 461, 2648, 2318, 2317, 2316, 1876, 1873, 2515])).
% 3.30/2.49 tff(2650,plain,
% 3.30/2.49 (c1_1(a604)),
% 3.30/2.49 inference(unit_resolution,[status(thm)],[1613, 2639])).
% 3.30/2.49 tff(2651,plain,
% 3.30/2.49 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c1_1(a604)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp19 | hskp13 | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c1_1(a604)))),
% 3.30/2.49 inference(rewrite,[status(thm)],[])).
% 3.30/2.49 tff(2652,plain,
% 3.30/2.49 ((hskp19 | hskp13 | (~ndr1_0) | c0_1(a604) | (~c2_1(a604)) | (~c1_1(a604))) <=> (hskp19 | hskp13 | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c1_1(a604)))),
% 3.30/2.49 inference(rewrite,[status(thm)],[])).
% 3.30/2.49 tff(2653,plain,
% 3.30/2.49 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c0_1(a604) | (~c2_1(a604)) | (~c1_1(a604)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c1_1(a604))))),
% 3.30/2.49 inference(monotonicity,[status(thm)],[2652])).
% 3.30/2.49 tff(2654,plain,
% 3.30/2.49 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c0_1(a604) | (~c2_1(a604)) | (~c1_1(a604)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp19 | hskp13 | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c1_1(a604)))),
% 3.30/2.49 inference(transitivity,[status(thm)],[2653, 2651])).
% 3.30/2.49 tff(2655,plain,
% 3.30/2.49 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c0_1(a604) | (~c2_1(a604)) | (~c1_1(a604)))),
% 3.30/2.49 inference(quant_inst,[status(thm)],[])).
% 3.30/2.49 tff(2656,plain,
% 3.30/2.49 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp19 | hskp13 | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c1_1(a604))),
% 3.30/2.49 inference(modus_ponens,[status(thm)],[2655, 2654])).
% 3.30/2.49 tff(2657,plain,
% 3.30/2.49 (hskp19 | hskp13),
% 3.30/2.49 inference(unit_resolution,[status(thm)],[2656, 107, 2650, 2640, 2564, 2648])).
% 3.30/2.49 tff(2658,plain,
% 3.30/2.49 (hskp19),
% 3.30/2.49 inference(unit_resolution,[status(thm)],[2657, 2649])).
% 3.30/2.49 tff(2659,plain,
% 3.30/2.49 (~c1_1(a617)),
% 3.30/2.49 inference(unit_resolution,[status(thm)],[2588, 2658])).
% 3.30/2.49 tff(2660,plain,
% 3.30/2.49 (~c0_1(a617)),
% 3.30/2.49 inference(unit_resolution,[status(thm)],[2594, 2658])).
% 3.30/2.49 tff(2661,plain,
% 3.30/2.49 (c2_1(a617)),
% 3.30/2.49 inference(unit_resolution,[status(thm)],[2605, 2658])).
% 3.30/2.49 tff(2662,plain,
% 3.30/2.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617)))),
% 3.30/2.49 inference(rewrite,[status(thm)],[])).
% 3.30/2.49 tff(2663,plain,
% 3.30/2.49 (((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617))) <=> (c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617)))),
% 3.30/2.49 inference(rewrite,[status(thm)],[])).
% 3.30/2.49 tff(2664,plain,
% 3.30/2.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617))))),
% 3.30/2.49 inference(monotonicity,[status(thm)],[2663])).
% 3.30/2.49 tff(2665,plain,
% 3.30/2.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617)))),
% 3.30/2.49 inference(transitivity,[status(thm)],[2664, 2662])).
% 3.30/2.49 tff(2666,plain,
% 3.30/2.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))),
% 3.30/2.49 inference(quant_inst,[status(thm)],[])).
% 3.30/2.49 tff(2667,plain,
% 3.30/2.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617))),
% 3.30/2.49 inference(modus_ponens,[status(thm)],[2666, 2665])).
% 3.30/2.49 tff(2668,plain,
% 3.30/2.49 ($false),
% 3.30/2.49 inference(unit_resolution,[status(thm)],[2667, 107, 1651, 1650, 2661, 2641, 2660, 2659, 2640, 65, 2631, 2648])).
% 3.30/2.49 tff(2669,plain,(hskp28 | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a599)) | (~c3_1(a599)) | c1_1(a599) | (~c0_1(a678)) | (~c2_1(a678)) | (~c3_1(a678)) | (~c1_1(a606)) | c2_1(a606) | (~c0_1(a606)) | (~c2_1(a651)) | c3_1(a651) | (~c0_1(a599)) | (~c2_1(a590)) | (~c3_1(a590)) | c1_1(a651) | c0_1(a590) | (~c2_1(a583))), inference(lemma,lemma(discharge,[]))).
% 3.30/2.49 tff(2670,plain,
% 3.30/2.49 (hskp28),
% 3.30/2.49 inference(unit_resolution,[status(thm)],[2669, 2474, 2427, 2395, 2394, 2393, 2318, 2317, 2316, 2413, 2405, 2412, 2428, 2473, 2472, 863, 862, 2630, 45, 2426])).
% 3.30/2.49 tff(2671,plain,
% 3.30/2.49 (c3_1(a612)),
% 3.30/2.49 inference(unit_resolution,[status(thm)],[1139, 2670])).
% 3.30/2.49 tff(2672,plain,
% 3.30/2.49 (c1_1(a612)),
% 3.30/2.49 inference(unit_resolution,[status(thm)],[1435, 2670])).
% 3.30/2.49 tff(2673,plain,
% 3.30/2.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a651) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a651)) | c0_1(a651))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a651) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a651)) | c0_1(a651))),
% 3.30/2.49 inference(rewrite,[status(thm)],[])).
% 3.30/2.49 tff(2674,plain,
% 3.30/2.49 (((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a651) | c0_1(a651) | (~c2_1(a651))) <=> (c1_1(a651) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a651)) | c0_1(a651))),
% 3.30/2.49 inference(rewrite,[status(thm)],[])).
% 3.30/2.49 tff(2675,plain,
% 3.30/2.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a651) | c0_1(a651) | (~c2_1(a651)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a651) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a651)) | c0_1(a651)))),
% 3.30/2.49 inference(monotonicity,[status(thm)],[2674])).
% 3.30/2.49 tff(2676,plain,
% 3.30/2.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a651) | c0_1(a651) | (~c2_1(a651)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a651) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a651)) | c0_1(a651))),
% 3.30/2.49 inference(transitivity,[status(thm)],[2675, 2673])).
% 3.30/2.49 tff(2677,plain,
% 3.30/2.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a651) | c0_1(a651) | (~c2_1(a651)))),
% 3.30/2.49 inference(quant_inst,[status(thm)],[])).
% 3.30/2.49 tff(2678,plain,
% 3.30/2.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a651) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a651)) | c0_1(a651)),
% 3.30/2.49 inference(modus_ponens,[status(thm)],[2677, 2676])).
% 3.30/2.49 tff(2679,plain,
% 3.30/2.49 ((~c0_1(a612)) | c0_1(a651)),
% 3.30/2.49 inference(unit_resolution,[status(thm)],[2678, 107, 2672, 2671, 2474, 863, 862, 2630, 45, 65])).
% 3.30/2.49 tff(2680,plain,
% 3.30/2.49 (~c0_1(a612)),
% 3.30/2.49 inference(unit_resolution,[status(thm)],[2679, 2629])).
% 3.30/2.49 tff(2681,plain,
% 3.30/2.49 (^[V: $i, U: $i] : refl((hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))),
% 3.30/2.49 inference(bind,[status(th)],[])).
% 3.30/2.49 tff(2682,plain,
% 3.30/2.49 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 3.30/2.49 inference(quant_intro,[status(thm)],[2681])).
% 3.30/2.49 tff(2683,plain,
% 3.30/2.49 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 3.30/2.49 inference(rewrite,[status(thm)],[])).
% 3.30/2.49 tff(2684,plain,
% 3.30/2.49 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp15) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp15))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp15) <=> (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp15) <=> (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))))),
% 3.30/2.49 inference(bind,[status(th)],[])).
% 3.30/2.49 tff(2685,plain,
% 3.30/2.49 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp15) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 3.30/2.49 inference(quant_intro,[status(thm)],[2684])).
% 3.30/2.49 tff(2686,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause188')).
% 3.30/2.49 tff(2687,plain,
% 3.30/2.49 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 3.30/2.49 inference(modus_ponens,[status(thm)],[2686, 2685])).
% 3.30/2.49 tff(2688,plain,
% 3.30/2.49 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 3.30/2.49 inference(modus_ponens,[status(thm)],[2687, 2683])).
% 3.30/2.49 tff(2689,plain,(
% 3.30/2.49 ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 3.30/2.49 inference(skolemize,[status(sab)],[2688])).
% 3.30/2.49 tff(2690,plain,
% 3.30/2.49 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 3.30/2.49 inference(modus_ponens,[status(thm)],[2689, 2682])).
% 3.30/2.49 tff(2691,plain,
% 3.30/2.49 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a651) | c3_1(a651) | (~ndr1_0) | (~c2_1(a651)) | c0_1(a651))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a651) | c3_1(a651) | (~ndr1_0) | (~c2_1(a651)) | c0_1(a651))),
% 3.30/2.50 inference(rewrite,[status(thm)],[])).
% 3.30/2.50 tff(2692,plain,
% 3.30/2.50 ((hskp2 | (~ndr1_0) | c1_1(a651) | c3_1(a651) | (~c2_1(a651)) | c3_1(a651) | c1_1(a651) | c0_1(a651)) <=> (hskp2 | c1_1(a651) | c3_1(a651) | (~ndr1_0) | (~c2_1(a651)) | c0_1(a651))),
% 3.30/2.50 inference(rewrite,[status(thm)],[])).
% 3.30/2.50 tff(2693,plain,
% 3.30/2.50 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a651) | c3_1(a651) | (~c2_1(a651)) | c3_1(a651) | c1_1(a651) | c0_1(a651))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a651) | c3_1(a651) | (~ndr1_0) | (~c2_1(a651)) | c0_1(a651)))),
% 3.30/2.50 inference(monotonicity,[status(thm)],[2692])).
% 3.30/2.50 tff(2694,plain,
% 3.30/2.50 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a651) | c3_1(a651) | (~c2_1(a651)) | c3_1(a651) | c1_1(a651) | c0_1(a651))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a651) | c3_1(a651) | (~ndr1_0) | (~c2_1(a651)) | c0_1(a651))),
% 3.30/2.50 inference(transitivity,[status(thm)],[2693, 2691])).
% 3.30/2.50 tff(2695,plain,
% 3.30/2.50 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a651) | c3_1(a651) | (~c2_1(a651)) | c3_1(a651) | c1_1(a651) | c0_1(a651))),
% 3.30/2.50 inference(quant_inst,[status(thm)],[])).
% 3.30/2.50 tff(2696,plain,
% 3.30/2.50 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a651) | c3_1(a651) | (~ndr1_0) | (~c2_1(a651)) | c0_1(a651)),
% 3.30/2.50 inference(modus_ponens,[status(thm)],[2695, 2694])).
% 3.30/2.50 tff(2697,plain,
% 3.30/2.50 (hskp2 | c0_1(a651)),
% 3.30/2.50 inference(unit_resolution,[status(thm)],[2696, 107, 2474, 2630, 2473, 200])).
% 3.30/2.50 tff(2698,plain,
% 3.30/2.50 (hskp2),
% 3.30/2.50 inference(unit_resolution,[status(thm)],[2697, 2629])).
% 3.30/2.50 tff(2699,plain,
% 3.30/2.50 (~c3_1(a586)),
% 3.30/2.50 inference(unit_resolution,[status(thm)],[218, 2698])).
% 3.30/2.50 tff(2700,plain,
% 3.30/2.50 (c2_1(a586)),
% 3.30/2.50 inference(unit_resolution,[status(thm)],[1474, 2698])).
% 3.30/2.50 tff(2701,plain,
% 3.30/2.50 (c1_1(a586)),
% 3.30/2.50 inference(unit_resolution,[status(thm)],[229, 2698])).
% 3.30/2.50 tff(2702,plain,
% 3.30/2.50 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))),
% 3.30/2.50 inference(rewrite,[status(thm)],[])).
% 3.30/2.50 tff(2703,plain,
% 3.30/2.50 ((hskp15 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612))) <=> (hskp15 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))),
% 3.30/2.50 inference(rewrite,[status(thm)],[])).
% 3.30/2.50 tff(2704,plain,
% 3.30/2.50 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612))))),
% 3.30/2.50 inference(monotonicity,[status(thm)],[2703])).
% 3.30/2.50 tff(2705,plain,
% 3.30/2.50 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))),
% 3.30/2.50 inference(transitivity,[status(thm)],[2704, 2702])).
% 3.30/2.50 tff(2706,plain,
% 3.30/2.50 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))),
% 3.30/2.50 inference(quant_inst,[status(thm)],[])).
% 3.30/2.50 tff(2707,plain,
% 3.30/2.50 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612))),
% 3.30/2.50 inference(modus_ponens,[status(thm)],[2706, 2705])).
% 3.30/2.50 tff(2708,plain,
% 3.30/2.50 (hskp15),
% 3.30/2.50 inference(unit_resolution,[status(thm)],[2707, 107, 2672, 2671, 2701, 2700, 2699, 2690, 2680])).
% 3.30/2.50 tff(2709,plain,
% 3.30/2.50 (c1_1(a604)),
% 3.30/2.50 inference(unit_resolution,[status(thm)],[1613, 2708])).
% 3.30/2.50 tff(2710,plain,
% 3.30/2.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a607) | c1_1(a651) | c3_1(a651) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a607)) | c0_1(a651))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a607) | c1_1(a651) | c3_1(a651) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a607)) | c0_1(a651))),
% 3.30/2.50 inference(rewrite,[status(thm)],[])).
% 3.30/2.50 tff(2711,plain,
% 3.30/2.50 (((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)) | c3_1(a651) | c1_1(a651) | c0_1(a651)) <=> (c3_1(a607) | c1_1(a651) | c3_1(a651) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a607)) | c0_1(a651))),
% 3.30/2.50 inference(rewrite,[status(thm)],[])).
% 3.30/2.50 tff(2712,plain,
% 3.30/2.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)) | c3_1(a651) | c1_1(a651) | c0_1(a651))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a607) | c1_1(a651) | c3_1(a651) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a607)) | c0_1(a651)))),
% 3.30/2.50 inference(monotonicity,[status(thm)],[2711])).
% 3.30/2.50 tff(2713,plain,
% 3.30/2.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)) | c3_1(a651) | c1_1(a651) | c0_1(a651))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a607) | c1_1(a651) | c3_1(a651) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a607)) | c0_1(a651))),
% 3.30/2.50 inference(transitivity,[status(thm)],[2712, 2710])).
% 3.30/2.50 tff(2714,plain,
% 3.30/2.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)) | c3_1(a651) | c1_1(a651) | c0_1(a651))),
% 3.30/2.50 inference(quant_inst,[status(thm)],[])).
% 3.30/2.50 tff(2715,plain,
% 3.30/2.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a607) | c1_1(a651) | c3_1(a651) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a607)) | c0_1(a651)),
% 3.30/2.50 inference(modus_ponens,[status(thm)],[2714, 2713])).
% 3.30/2.50 tff(2716,plain,
% 3.30/2.50 (c2_1(a604) | (~c1_1(a604)) | c0_1(a651)),
% 3.30/2.50 inference(unit_resolution,[status(thm)],[2715, 107, 33, 2630, 2473, 22, 2475, 1463, 2402])).
% 3.30/2.50 tff(2717,plain,
% 3.30/2.50 (c2_1(a604)),
% 3.30/2.50 inference(unit_resolution,[status(thm)],[2716, 2709, 2629])).
% 3.30/2.50 tff(2718,plain,
% 3.30/2.50 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 3.30/2.50 inference(bind,[status(th)],[])).
% 3.30/2.50 tff(2719,plain,
% 3.30/2.50 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 3.30/2.50 inference(quant_intro,[status(thm)],[2718])).
% 3.30/2.50 tff(2720,plain,
% 3.30/2.50 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 3.30/2.50 inference(rewrite,[status(thm)],[])).
% 3.30/2.50 tff(2721,plain,
% 3.30/2.50 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | hskp12) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp12))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 3.30/2.50 inference(bind,[status(th)],[])).
% 3.30/2.50 tff(2722,plain,
% 3.30/2.50 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 3.30/2.50 inference(quant_intro,[status(thm)],[2721])).
% 3.30/2.50 tff(2723,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause190')).
% 3.30/2.50 tff(2724,plain,
% 3.30/2.50 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 3.30/2.50 inference(modus_ponens,[status(thm)],[2723, 2722])).
% 3.30/2.50 tff(2725,plain,
% 3.30/2.50 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 3.30/2.50 inference(modus_ponens,[status(thm)],[2724, 2720])).
% 3.30/2.50 tff(2726,plain,(
% 3.30/2.50 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 3.30/2.50 inference(skolemize,[status(sab)],[2725])).
% 3.30/2.50 tff(2727,plain,
% 3.30/2.50 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 3.30/2.50 inference(modus_ponens,[status(thm)],[2726, 2719])).
% 3.30/2.50 tff(2728,plain,
% 3.30/2.50 (c2_1(a612)),
% 3.30/2.50 inference(unit_resolution,[status(thm)],[1150, 2670])).
% 3.30/2.50 tff(2729,plain,
% 3.30/2.50 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))),
% 3.30/2.50 inference(rewrite,[status(thm)],[])).
% 3.30/2.50 tff(2730,plain,
% 3.30/2.50 ((hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612))) <=> (hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))),
% 3.30/2.50 inference(rewrite,[status(thm)],[])).
% 3.30/2.50 tff(2731,plain,
% 3.30/2.50 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612))))),
% 3.30/2.50 inference(monotonicity,[status(thm)],[2730])).
% 3.30/2.50 tff(2732,plain,
% 3.30/2.50 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))),
% 3.30/2.50 inference(transitivity,[status(thm)],[2731, 2729])).
% 3.30/2.50 tff(2733,plain,
% 3.30/2.50 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))),
% 3.30/2.50 inference(quant_inst,[status(thm)],[])).
% 3.30/2.50 tff(2734,plain,
% 3.30/2.50 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612))),
% 3.30/2.50 inference(modus_ponens,[status(thm)],[2733, 2732])).
% 3.30/2.50 tff(2735,plain,
% 3.30/2.50 (hskp12),
% 3.30/2.50 inference(unit_resolution,[status(thm)],[2734, 107, 2672, 2728, 2428, 2427, 2426, 2727, 2680])).
% 3.30/2.50 tff(2736,plain,
% 3.30/2.50 (~c3_1(a600)),
% 3.30/2.50 inference(unit_resolution,[status(thm)],[741, 2735])).
% 3.30/2.50 tff(2737,plain,
% 3.30/2.50 (c2_1(a600)),
% 3.30/2.50 inference(unit_resolution,[status(thm)],[752, 2735])).
% 3.30/2.50 tff(2738,plain,
% 3.30/2.50 (c0_1(a600)),
% 3.30/2.50 inference(unit_resolution,[status(thm)],[763, 2735])).
% 3.30/2.50 tff(2739,plain,
% 3.30/2.50 (((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp8 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)))) <=> ((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp27 | hskp8 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)))),
% 3.30/2.50 inference(rewrite,[status(thm)],[])).
% 3.30/2.50 tff(2740,plain,
% 3.30/2.50 ((hskp27 | hskp8 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600))) <=> (hskp27 | hskp8 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)))),
% 3.30/2.50 inference(rewrite,[status(thm)],[])).
% 3.30/2.50 tff(2741,plain,
% 3.30/2.50 (((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp8 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)))) <=> ((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp8 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600))))),
% 3.30/2.50 inference(monotonicity,[status(thm)],[2740])).
% 3.30/2.50 tff(2742,plain,
% 3.30/2.50 (((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp8 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)))) <=> ((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp27 | hskp8 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)))),
% 3.30/2.50 inference(transitivity,[status(thm)],[2741, 2739])).
% 3.30/2.50 tff(2743,plain,
% 3.30/2.50 ((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp8 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)))),
% 3.30/2.50 inference(quant_inst,[status(thm)],[])).
% 3.30/2.50 tff(2744,plain,
% 3.30/2.50 ((~![U: $i] : (hskp27 | hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp27 | hskp8 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600))),
% 3.30/2.50 inference(modus_ponens,[status(thm)],[2743, 2742])).
% 3.30/2.50 tff(2745,plain,
% 3.30/2.50 (hskp8),
% 3.30/2.50 inference(unit_resolution,[status(thm)],[2744, 107, 1872, 2738, 2737, 2736, 2080])).
% 3.30/2.50 tff(2746,plain,
% 3.30/2.50 (c3_1(a593)),
% 3.30/2.50 inference(unit_resolution,[status(thm)],[511, 2745])).
% 3.30/2.50 tff(2747,plain,
% 3.30/2.50 (c1_1(a593)),
% 3.30/2.50 inference(unit_resolution,[status(thm)],[522, 2745])).
% 3.30/2.50 tff(2748,plain,
% 3.30/2.50 (c3_1(a604)),
% 3.30/2.50 inference(unit_resolution,[status(thm)],[1602, 2708])).
% 3.30/2.50 tff(2749,plain,
% 3.30/2.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a651) | c0_1(a604) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a651)) | c0_1(a651))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a651) | c0_1(a604) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a651)) | c0_1(a651))),
% 3.30/2.50 inference(rewrite,[status(thm)],[])).
% 3.30/2.50 tff(2750,plain,
% 3.30/2.50 (((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a651) | c0_1(a651) | (~c2_1(a651))) <=> (c1_1(a651) | c0_1(a604) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a651)) | c0_1(a651))),
% 3.30/2.50 inference(rewrite,[status(thm)],[])).
% 3.30/2.50 tff(2751,plain,
% 3.30/2.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a651) | c0_1(a651) | (~c2_1(a651)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a651) | c0_1(a604) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a651)) | c0_1(a651)))),
% 3.30/2.50 inference(monotonicity,[status(thm)],[2750])).
% 3.30/2.50 tff(2752,plain,
% 3.30/2.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a651) | c0_1(a651) | (~c2_1(a651)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a651) | c0_1(a604) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a651)) | c0_1(a651))),
% 3.30/2.50 inference(transitivity,[status(thm)],[2751, 2749])).
% 3.30/2.50 tff(2753,plain,
% 3.30/2.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a651) | c0_1(a651) | (~c2_1(a651)))),
% 3.30/2.50 inference(quant_inst,[status(thm)],[])).
% 3.30/2.50 tff(2754,plain,
% 3.30/2.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a651) | c0_1(a604) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a651)) | c0_1(a651)),
% 3.30/2.50 inference(modus_ponens,[status(thm)],[2753, 2752])).
% 3.30/2.50 tff(2755,plain,
% 3.30/2.50 (~c0_1(a593)),
% 3.30/2.50 inference(unit_resolution,[status(thm)],[2754, 107, 2474, 2748, 2747, 2746, 2630, 2475, 65, 2629, 2717])).
% 3.30/2.50 tff(2756,plain,
% 3.30/2.50 (~c2_1(a593)),
% 3.30/2.50 inference(unit_resolution,[status(thm)],[555, 2745])).
% 3.30/2.50 tff(2757,plain,
% 3.30/2.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a607) | c1_1(a651) | c3_1(a651) | c2_1(a607) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607)) | c0_1(a651))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a607) | c1_1(a651) | c3_1(a651) | c2_1(a607) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607)) | c0_1(a651))),
% 3.30/2.50 inference(rewrite,[status(thm)],[])).
% 3.30/2.50 tff(2758,plain,
% 3.30/2.50 (((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a651) | c1_1(a651) | c0_1(a651)) <=> (c3_1(a607) | c1_1(a651) | c3_1(a651) | c2_1(a607) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607)) | c0_1(a651))),
% 3.30/2.50 inference(rewrite,[status(thm)],[])).
% 3.30/2.50 tff(2759,plain,
% 3.30/2.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a651) | c1_1(a651) | c0_1(a651))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a607) | c1_1(a651) | c3_1(a651) | c2_1(a607) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607)) | c0_1(a651)))),
% 3.30/2.50 inference(monotonicity,[status(thm)],[2758])).
% 3.30/2.50 tff(2760,plain,
% 3.30/2.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a651) | c1_1(a651) | c0_1(a651))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a607) | c1_1(a651) | c3_1(a651) | c2_1(a607) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607)) | c0_1(a651))),
% 3.30/2.50 inference(transitivity,[status(thm)],[2759, 2757])).
% 3.30/2.50 tff(2761,plain,
% 3.30/2.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a651) | c1_1(a651) | c0_1(a651))),
% 3.30/2.50 inference(quant_inst,[status(thm)],[])).
% 3.30/2.50 tff(2762,plain,
% 3.30/2.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a607) | c1_1(a651) | c3_1(a651) | c2_1(a607) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607)) | c0_1(a651)),
% 3.30/2.50 inference(modus_ponens,[status(thm)],[2761, 2760])).
% 3.30/2.50 tff(2763,plain,
% 3.30/2.50 ($false),
% 3.30/2.50 inference(unit_resolution,[status(thm)],[2762, 107, 33, 2747, 2630, 2473, 22, 2756, 1463, 2755, 2402, 2629])).
% 3.30/2.50 tff(2764,plain,(c0_1(a604) | c3_1(a607) | c1_1(a651) | c3_1(a651) | c2_1(a607) | (~c2_1(a651)) | hskp27 | (~c2_1(a590)) | (~c3_1(a590)) | c0_1(a590) | (~c2_1(a678)) | (~c0_1(a678)) | (~c3_1(a678)) | (~c0_1(a599)) | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.30/2.50 tff(2765,plain,
% 3.30/2.50 (c0_1(a604)),
% 3.30/2.50 inference(unit_resolution,[status(thm)],[2764, 2471, 33, 2465, 22, 2459, 1872, 863, 862, 45, 2317, 2318, 2316, 2430, 66])).
% 3.30/2.50 tff(2766,plain,
% 3.30/2.50 (~hskp15),
% 3.30/2.50 inference(unit_resolution,[status(thm)],[1591, 2765])).
% 3.30/2.50 tff(2767,plain,
% 3.30/2.50 (hskp28),
% 3.30/2.50 inference(unit_resolution,[status(thm)],[2669, 2459, 2427, 2395, 2394, 2393, 2318, 2317, 2316, 2413, 2405, 2412, 2428, 2465, 2430, 863, 862, 2471, 45, 2426])).
% 3.30/2.50 tff(2768,plain,
% 3.30/2.50 (c3_1(a612)),
% 3.30/2.50 inference(unit_resolution,[status(thm)],[1139, 2767])).
% 3.30/2.50 tff(2769,plain,
% 3.30/2.50 (c1_1(a612)),
% 3.30/2.50 inference(unit_resolution,[status(thm)],[1435, 2767])).
% 3.30/2.50 tff(2770,plain,
% 3.30/2.50 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | c1_1(a599) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a599)) | (~c0_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a599) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a599)) | (~c0_1(a599)))),
% 3.30/2.50 inference(rewrite,[status(thm)],[])).
% 3.30/2.50 tff(2771,plain,
% 3.30/2.50 ((hskp15 | (~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599))) <=> (hskp15 | c1_1(a599) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a599)) | (~c0_1(a599)))),
% 3.30/2.50 inference(rewrite,[status(thm)],[])).
% 3.30/2.50 tff(2772,plain,
% 3.30/2.50 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | c1_1(a599) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a599)) | (~c0_1(a599))))),
% 3.30/2.50 inference(monotonicity,[status(thm)],[2771])).
% 3.30/2.50 tff(2773,plain,
% 3.30/2.50 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a599) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a599)) | (~c0_1(a599)))),
% 3.30/2.50 inference(transitivity,[status(thm)],[2772, 2770])).
% 3.30/2.50 tff(2774,plain,
% 3.30/2.50 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599)))),
% 3.30/2.50 inference(quant_inst,[status(thm)],[])).
% 3.30/2.50 tff(2775,plain,
% 3.30/2.50 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a599) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a599)) | (~c0_1(a599))),
% 3.30/2.50 inference(modus_ponens,[status(thm)],[2774, 2773])).
% 3.30/2.50 tff(2776,plain,
% 3.30/2.50 (hskp15 | (~c0_1(a612))),
% 3.30/2.50 inference(unit_resolution,[status(thm)],[2775, 107, 2769, 2768, 2394, 2393, 1993, 2430])).
% 3.30/2.51 tff(2777,plain,
% 3.30/2.51 (~c0_1(a612)),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[2776, 2766])).
% 3.30/2.51 tff(2778,plain,
% 3.30/2.51 (c2_1(a612)),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[1150, 2767])).
% 3.30/2.51 tff(2779,plain,
% 3.30/2.51 (hskp12),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[2734, 107, 2769, 2778, 2428, 2427, 2426, 2727, 2777])).
% 3.30/2.51 tff(2780,plain,
% 3.30/2.51 (~c3_1(a600)),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[741, 2779])).
% 3.30/2.51 tff(2781,plain,
% 3.30/2.51 (c2_1(a600)),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[752, 2779])).
% 3.30/2.51 tff(2782,plain,
% 3.30/2.51 (c0_1(a600)),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[763, 2779])).
% 3.30/2.51 tff(2783,plain,
% 3.30/2.51 (hskp8),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[2744, 107, 1872, 2782, 2781, 2780, 2080])).
% 3.30/2.51 tff(2784,plain,
% 3.30/2.51 (c3_1(a593)),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[511, 2783])).
% 3.30/2.51 tff(2785,plain,
% 3.30/2.51 (c1_1(a593)),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[522, 2783])).
% 3.30/2.51 tff(2786,plain,
% 3.30/2.51 (~c0_1(a593)),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[2496, 107, 2766, 2394, 2785, 2784, 2393, 1993, 2430])).
% 3.30/2.51 tff(2787,plain,
% 3.30/2.51 (~c2_1(a593)),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[555, 2783])).
% 3.30/2.51 tff(2788,plain,
% 3.30/2.51 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | c2_1(a606) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c0_1(a606)) | (~c1_1(a606)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | c2_1(a606) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c0_1(a606)) | (~c1_1(a606)))),
% 3.30/2.51 inference(rewrite,[status(thm)],[])).
% 3.30/2.51 tff(2789,plain,
% 3.30/2.51 ((hskp27 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c0_1(a593) | c2_1(a593) | (~c3_1(a593))) <=> (hskp27 | c2_1(a606) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c0_1(a606)) | (~c1_1(a606)))),
% 3.30/2.51 inference(rewrite,[status(thm)],[])).
% 3.30/2.51 tff(2790,plain,
% 3.30/2.51 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c0_1(a593) | c2_1(a593) | (~c3_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | c2_1(a606) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c0_1(a606)) | (~c1_1(a606))))),
% 3.30/2.51 inference(monotonicity,[status(thm)],[2789])).
% 3.30/2.51 tff(2791,plain,
% 3.30/2.51 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c0_1(a593) | c2_1(a593) | (~c3_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | c2_1(a606) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c0_1(a606)) | (~c1_1(a606)))),
% 3.30/2.51 inference(transitivity,[status(thm)],[2790, 2788])).
% 3.30/2.51 tff(2792,plain,
% 3.30/2.51 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c0_1(a593) | c2_1(a593) | (~c3_1(a593)))),
% 3.30/2.51 inference(quant_inst,[status(thm)],[])).
% 3.30/2.51 tff(2793,plain,
% 3.30/2.51 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | c2_1(a606) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c0_1(a606)) | (~c1_1(a606))),
% 3.30/2.51 inference(modus_ponens,[status(thm)],[2792, 2791])).
% 3.30/2.51 tff(2794,plain,
% 3.30/2.51 ($false),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[2793, 107, 1872, 2413, 2784, 2405, 2787, 540, 2786, 2412])).
% 3.30/2.51 tff(2795,plain,(hskp9 | hskp27 | c3_1(a607) | c2_1(a607) | (~c2_1(a590)) | (~c3_1(a590)) | c0_1(a590) | (~c2_1(a678)) | (~c0_1(a678)) | (~c3_1(a678)) | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.30/2.51 tff(2796,plain,
% 3.30/2.51 (hskp9),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[2795, 1872, 33, 22, 863, 862, 45, 2317, 2318, 2316, 66])).
% 3.30/2.51 tff(2797,plain,
% 3.30/2.51 (~c3_1(a595)),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[1487, 2796])).
% 3.30/2.51 tff(2798,plain,
% 3.30/2.51 (~c0_1(a595)),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[1499, 2796])).
% 3.30/2.51 tff(2799,plain,
% 3.30/2.51 (~c1_1(a595)),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[1493, 2796])).
% 3.30/2.51 tff(2800,plain,
% 3.30/2.51 (c0_1(a595) | c2_1(a595)),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[2197, 107, 2395, 2394, 863, 862, 2393, 1556, 45, 1730])).
% 3.30/2.51 tff(2801,plain,
% 3.30/2.51 (c2_1(a595)),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[2800, 1558])).
% 3.30/2.51 tff(2802,plain,
% 3.30/2.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a595)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a595)))),
% 3.30/2.51 inference(rewrite,[status(thm)],[])).
% 3.30/2.51 tff(2803,plain,
% 3.30/2.51 (((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595))) <=> (c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a595)))),
% 3.30/2.51 inference(rewrite,[status(thm)],[])).
% 3.30/2.51 tff(2804,plain,
% 3.30/2.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a595))))),
% 3.30/2.51 inference(monotonicity,[status(thm)],[2803])).
% 3.30/2.51 tff(2805,plain,
% 3.30/2.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a595)))),
% 3.30/2.51 inference(transitivity,[status(thm)],[2804, 2802])).
% 3.30/2.51 tff(2806,plain,
% 3.30/2.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595)))),
% 3.30/2.51 inference(quant_inst,[status(thm)],[])).
% 3.30/2.51 tff(2807,plain,
% 3.30/2.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a595) | c1_1(a595) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a595))),
% 3.30/2.51 inference(modus_ponens,[status(thm)],[2806, 2805])).
% 3.30/2.51 tff(2808,plain,
% 3.30/2.51 (c0_1(a595) | (~c1_1(a678)) | (~c2_1(a595))),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[2807, 107, 2318, 2316, 863, 862, 1557, 45, 65])).
% 3.30/2.51 tff(2809,plain,
% 3.30/2.51 (~c1_1(a678)),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[2808, 1558, 2801])).
% 3.30/2.51 tff(2810,plain,
% 3.30/2.51 (hskp2 | c0_1(a595) | (~c2_1(a595))),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[1754, 107, 1557, 1556, 200])).
% 3.30/2.51 tff(2811,plain,
% 3.30/2.51 (hskp2),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[2810, 1558, 2801])).
% 3.30/2.51 tff(2812,plain,
% 3.30/2.51 (~c3_1(a586)),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[218, 2811])).
% 3.30/2.51 tff(2813,plain,
% 3.30/2.51 (c2_1(a586)),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[1474, 2811])).
% 3.30/2.51 tff(2814,plain,
% 3.30/2.51 (c1_1(a586)),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[229, 2811])).
% 3.30/2.51 tff(2815,plain,
% 3.30/2.51 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c3_1(a586) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c2_1(a586)) | (~c1_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c3_1(a586) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c2_1(a586)) | (~c1_1(a586)))),
% 3.30/2.51 inference(rewrite,[status(thm)],[])).
% 3.30/2.51 tff(2816,plain,
% 3.30/2.51 ((hskp28 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c1_1(a678) | (~c3_1(a678)) | (~c2_1(a678))) <=> (hskp28 | c3_1(a586) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c2_1(a586)) | (~c1_1(a586)))),
% 3.30/2.51 inference(rewrite,[status(thm)],[])).
% 3.30/2.51 tff(2817,plain,
% 3.30/2.51 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c1_1(a678) | (~c3_1(a678)) | (~c2_1(a678)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c3_1(a586) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c2_1(a586)) | (~c1_1(a586))))),
% 3.30/2.51 inference(monotonicity,[status(thm)],[2816])).
% 3.30/2.51 tff(2818,plain,
% 3.30/2.51 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c1_1(a678) | (~c3_1(a678)) | (~c2_1(a678)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c3_1(a586) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c2_1(a586)) | (~c1_1(a586)))),
% 3.30/2.51 inference(transitivity,[status(thm)],[2817, 2815])).
% 3.30/2.51 tff(2819,plain,
% 3.30/2.51 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c1_1(a678) | (~c3_1(a678)) | (~c2_1(a678)))),
% 3.30/2.51 inference(quant_inst,[status(thm)],[])).
% 3.30/2.51 tff(2820,plain,
% 3.30/2.51 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c3_1(a586) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c2_1(a586)) | (~c1_1(a586))),
% 3.30/2.51 inference(modus_ponens,[status(thm)],[2819, 2818])).
% 3.30/2.51 tff(2821,plain,
% 3.30/2.51 (hskp28),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[2820, 107, 2317, 2316, 2814, 2813, 2812, 1748, 2809])).
% 3.30/2.51 tff(2822,plain,
% 3.30/2.51 (c3_1(a612)),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[1139, 2821])).
% 3.30/2.51 tff(2823,plain,
% 3.30/2.51 (c1_1(a612)),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[1435, 2821])).
% 3.30/2.51 tff(2824,plain,
% 3.30/2.51 (~c0_1(a612)),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[1774, 107, 2823, 2822, 863, 862, 1558, 1557, 45, 65, 2801])).
% 3.30/2.51 tff(2825,plain,
% 3.30/2.51 (hskp15),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[2707, 107, 2823, 2822, 2814, 2813, 2812, 2690, 2824])).
% 3.30/2.51 tff(2826,plain,
% 3.30/2.51 (~c0_1(a604)),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[1591, 2825])).
% 3.30/2.51 tff(2827,plain,
% 3.30/2.51 (c1_1(a604)),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[1613, 2825])).
% 3.30/2.51 tff(2828,plain,
% 3.30/2.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a607) | c2_1(a607) | c0_1(a604) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a607) | c2_1(a607) | c0_1(a604) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a607)))),
% 3.30/2.51 inference(rewrite,[status(thm)],[])).
% 3.30/2.51 tff(2829,plain,
% 3.30/2.51 (((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)) | c3_1(a595) | c1_1(a595) | c0_1(a595)) <=> (c3_1(a607) | c2_1(a607) | c0_1(a604) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a607)))),
% 3.30/2.51 inference(rewrite,[status(thm)],[])).
% 3.30/2.51 tff(2830,plain,
% 3.30/2.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)) | c3_1(a595) | c1_1(a595) | c0_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a607) | c2_1(a607) | c0_1(a604) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a607))))),
% 3.30/2.51 inference(monotonicity,[status(thm)],[2829])).
% 3.30/2.51 tff(2831,plain,
% 3.30/2.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)) | c3_1(a595) | c1_1(a595) | c0_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a607) | c2_1(a607) | c0_1(a604) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a607)))),
% 3.30/2.51 inference(transitivity,[status(thm)],[2830, 2828])).
% 3.30/2.51 tff(2832,plain,
% 3.30/2.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)) | c3_1(a595) | c1_1(a595) | c0_1(a595))),
% 3.30/2.51 inference(quant_inst,[status(thm)],[])).
% 3.30/2.51 tff(2833,plain,
% 3.30/2.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a607) | c2_1(a607) | c0_1(a604) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a607))),
% 3.30/2.51 inference(modus_ponens,[status(thm)],[2832, 2831])).
% 3.30/2.51 tff(2834,plain,
% 3.30/2.51 (c2_1(a604)),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[2833, 107, 33, 2827, 22, 2826, 1558, 1557, 1556, 1463, 2402])).
% 3.30/2.51 tff(2835,plain,
% 3.30/2.51 (c2_1(a612)),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[1150, 2821])).
% 3.30/2.51 tff(2836,plain,
% 3.30/2.51 (hskp12),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[2734, 107, 2823, 2835, 1651, 1650, 1649, 2727, 2824])).
% 3.30/2.51 tff(2837,plain,
% 3.30/2.51 (~c3_1(a600)),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[741, 2836])).
% 3.30/2.51 tff(2838,plain,
% 3.30/2.51 (c2_1(a600)),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[752, 2836])).
% 3.30/2.51 tff(2839,plain,
% 3.30/2.51 (c0_1(a600)),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[763, 2836])).
% 3.30/2.51 tff(2840,plain,
% 3.30/2.51 (hskp8),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[2744, 107, 1872, 2839, 2838, 2837, 2080])).
% 3.30/2.51 tff(2841,plain,
% 3.30/2.51 (c3_1(a593)),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[511, 2840])).
% 3.30/2.51 tff(2842,plain,
% 3.30/2.51 (c1_1(a593)),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[522, 2840])).
% 3.30/2.51 tff(2843,plain,
% 3.30/2.51 (c3_1(a604)),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[1602, 2825])).
% 3.30/2.51 tff(2844,plain,
% 3.30/2.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a604) | c0_1(a595) | c1_1(a595) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a595)) | (~c3_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a604) | c0_1(a595) | c1_1(a595) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a595)) | (~c3_1(a604)) | (~c2_1(a604)))),
% 3.30/2.51 inference(rewrite,[status(thm)],[])).
% 3.30/2.51 tff(2845,plain,
% 3.30/2.51 (((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595))) <=> (c0_1(a604) | c0_1(a595) | c1_1(a595) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a595)) | (~c3_1(a604)) | (~c2_1(a604)))),
% 3.30/2.51 inference(rewrite,[status(thm)],[])).
% 3.30/2.51 tff(2846,plain,
% 3.30/2.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a604) | c0_1(a595) | c1_1(a595) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a595)) | (~c3_1(a604)) | (~c2_1(a604))))),
% 3.30/2.51 inference(monotonicity,[status(thm)],[2845])).
% 3.30/2.51 tff(2847,plain,
% 3.30/2.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a604) | c0_1(a595) | c1_1(a595) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a595)) | (~c3_1(a604)) | (~c2_1(a604)))),
% 3.30/2.51 inference(transitivity,[status(thm)],[2846, 2844])).
% 3.30/2.51 tff(2848,plain,
% 3.30/2.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595)))),
% 3.30/2.51 inference(quant_inst,[status(thm)],[])).
% 3.30/2.51 tff(2849,plain,
% 3.30/2.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a604) | c0_1(a595) | c1_1(a595) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a595)) | (~c3_1(a604)) | (~c2_1(a604))),
% 3.30/2.51 inference(modus_ponens,[status(thm)],[2848, 2847])).
% 3.30/2.51 tff(2850,plain,
% 3.30/2.51 (~c0_1(a593)),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[2849, 107, 2843, 2842, 2841, 2826, 1558, 1557, 65, 2801, 2834])).
% 3.30/2.51 tff(2851,plain,
% 3.30/2.51 (~c2_1(a593)),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[555, 2840])).
% 3.30/2.51 tff(2852,plain,
% 3.30/2.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a607) | c2_1(a607) | c0_1(a595) | c1_1(a595) | c3_1(a595) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a607) | c2_1(a607) | c0_1(a595) | c1_1(a595) | c3_1(a595) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607)))),
% 3.30/2.51 inference(rewrite,[status(thm)],[])).
% 3.30/2.51 tff(2853,plain,
% 3.30/2.51 (((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a595) | c1_1(a595) | c0_1(a595)) <=> (c3_1(a607) | c2_1(a607) | c0_1(a595) | c1_1(a595) | c3_1(a595) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607)))),
% 3.30/2.51 inference(rewrite,[status(thm)],[])).
% 3.30/2.51 tff(2854,plain,
% 3.30/2.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a595) | c1_1(a595) | c0_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a607) | c2_1(a607) | c0_1(a595) | c1_1(a595) | c3_1(a595) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607))))),
% 3.30/2.51 inference(monotonicity,[status(thm)],[2853])).
% 3.30/2.51 tff(2855,plain,
% 3.30/2.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a595) | c1_1(a595) | c0_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a607) | c2_1(a607) | c0_1(a595) | c1_1(a595) | c3_1(a595) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607)))),
% 3.30/2.51 inference(transitivity,[status(thm)],[2854, 2852])).
% 3.30/2.51 tff(2856,plain,
% 3.30/2.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a595) | c1_1(a595) | c0_1(a595))),
% 3.30/2.51 inference(quant_inst,[status(thm)],[])).
% 3.30/2.51 tff(2857,plain,
% 3.30/2.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a607) | c2_1(a607) | c0_1(a595) | c1_1(a595) | c3_1(a595) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607))),
% 3.30/2.51 inference(modus_ponens,[status(thm)],[2856, 2855])).
% 3.30/2.51 tff(2858,plain,
% 3.30/2.51 ($false),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[2857, 107, 33, 2842, 22, 1558, 1557, 1556, 2851, 1463, 2850, 2402])).
% 3.30/2.51 tff(2859,plain,(c0_1(a595) | c3_1(a607) | c2_1(a607) | c1_1(a595) | c3_1(a595) | hskp27 | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c2_1(a590)) | (~c3_1(a590)) | c0_1(a590) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678))), inference(lemma,lemma(discharge,[]))).
% 3.30/2.51 tff(2860,plain,
% 3.30/2.51 ($false),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[2859, 2799, 2798, 22, 33, 2797, 1872, 2428, 2427, 2426, 863, 862, 45, 2317, 2316, 2318])).
% 3.30/2.51 tff(2861,plain,(hskp27 | c2_1(a607) | c3_1(a607) | (~c2_1(a590)) | (~c3_1(a590)) | c0_1(a590) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.30/2.51 tff(2862,plain,
% 3.30/2.51 (hskp27),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[2861, 2315, 33, 22, 2314, 2313, 2281, 2270, 2292, 66])).
% 3.30/2.51 tff(2863,plain,
% 3.30/2.51 (c3_1(a611)),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[620, 2862])).
% 3.30/2.51 tff(2864,plain,
% 3.30/2.51 (c1_1(a611)),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[631, 2862])).
% 3.30/2.51 tff(2865,plain,
% 3.30/2.51 (c0_1(a611)),
% 3.30/2.51 inference(unit_resolution,[status(thm)],[642, 2862])).
% 3.30/2.51 tff(2866,plain,
% 3.30/2.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a599)) | c0_1(a599))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a599)) | c0_1(a599))),
% 3.30/2.51 inference(rewrite,[status(thm)],[])).
% 3.30/2.51 tff(2867,plain,
% 3.30/2.51 (((~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599))) <=> (c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a599)) | c0_1(a599))),
% 3.30/2.51 inference(rewrite,[status(thm)],[])).
% 3.30/2.51 tff(2868,plain,
% 3.30/2.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a599)) | c0_1(a599)))),
% 3.30/2.52 inference(monotonicity,[status(thm)],[2867])).
% 3.30/2.52 tff(2869,plain,
% 3.30/2.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a599)) | c0_1(a599))),
% 3.30/2.52 inference(transitivity,[status(thm)],[2868, 2866])).
% 3.30/2.52 tff(2870,plain,
% 3.30/2.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))),
% 3.30/2.52 inference(quant_inst,[status(thm)],[])).
% 3.30/2.52 tff(2871,plain,
% 3.30/2.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a599)) | c0_1(a599)),
% 3.30/2.52 inference(modus_ponens,[status(thm)],[2870, 2869])).
% 3.30/2.52 tff(2872,plain,
% 3.30/2.52 (c0_1(a599)),
% 3.30/2.52 inference(unit_resolution,[status(thm)],[2871, 107, 2865, 2864, 2863, 2391, 2315, 2314, 2390, 2313, 65])).
% 3.30/2.52 tff(2873,plain,
% 3.30/2.52 (c3_1(a599)),
% 3.30/2.52 inference(unit_resolution,[status(thm)],[422, 2389])).
% 3.30/2.52 tff(2874,plain,
% 3.30/2.52 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | c1_1(a599) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a599)) | (~c0_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a599) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a599)) | (~c0_1(a599)))),
% 3.30/2.52 inference(rewrite,[status(thm)],[])).
% 3.30/2.52 tff(2875,plain,
% 3.30/2.52 ((hskp15 | (~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599))) <=> (hskp15 | c1_1(a599) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a599)) | (~c0_1(a599)))),
% 3.30/2.52 inference(rewrite,[status(thm)],[])).
% 3.30/2.52 tff(2876,plain,
% 3.30/2.52 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | c1_1(a599) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a599)) | (~c0_1(a599))))),
% 3.30/2.52 inference(monotonicity,[status(thm)],[2875])).
% 3.30/2.52 tff(2877,plain,
% 3.30/2.52 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a599) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a599)) | (~c0_1(a599)))),
% 3.30/2.52 inference(transitivity,[status(thm)],[2876, 2874])).
% 3.30/2.52 tff(2878,plain,
% 3.30/2.52 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599)))),
% 3.30/2.52 inference(quant_inst,[status(thm)],[])).
% 3.30/2.52 tff(2879,plain,
% 3.30/2.52 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a599) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a599)) | (~c0_1(a599))),
% 3.30/2.52 inference(modus_ponens,[status(thm)],[2878, 2877])).
% 3.30/2.52 tff(2880,plain,
% 3.30/2.52 (hskp15),
% 3.30/2.52 inference(unit_resolution,[status(thm)],[2879, 107, 2865, 2864, 2863, 2873, 2390, 1993, 2872])).
% 3.30/2.52 tff(2881,plain,
% 3.30/2.52 (~c0_1(a604)),
% 3.30/2.52 inference(unit_resolution,[status(thm)],[1591, 2880])).
% 3.30/2.52 tff(2882,plain,
% 3.30/2.52 (c1_1(a604)),
% 3.30/2.52 inference(unit_resolution,[status(thm)],[1613, 2880])).
% 3.30/2.52 tff(2883,plain,
% 3.30/2.52 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c2_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c2_1(a604) | (~c1_1(a604)))),
% 3.30/2.52 inference(rewrite,[status(thm)],[])).
% 3.30/2.52 tff(2884,plain,
% 3.30/2.52 ((hskp17 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c0_1(a599)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604))) <=> (hskp17 | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c2_1(a604) | (~c1_1(a604)))),
% 3.30/2.52 inference(rewrite,[status(thm)],[])).
% 3.30/2.52 tff(2885,plain,
% 3.30/2.52 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c0_1(a599)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c2_1(a604) | (~c1_1(a604))))),
% 3.30/2.52 inference(monotonicity,[status(thm)],[2884])).
% 3.30/2.52 tff(2886,plain,
% 3.30/2.52 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c0_1(a599)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c2_1(a604) | (~c1_1(a604)))),
% 3.30/2.52 inference(transitivity,[status(thm)],[2885, 2883])).
% 3.30/2.52 tff(2887,plain,
% 3.30/2.52 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c0_1(a599)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)))),
% 3.30/2.52 inference(quant_inst,[status(thm)],[])).
% 3.30/2.52 tff(2888,plain,
% 3.30/2.52 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c2_1(a604) | (~c1_1(a604))),
% 3.30/2.52 inference(modus_ponens,[status(thm)],[2887, 2886])).
% 3.30/2.52 tff(2889,plain,
% 3.30/2.52 (c2_1(a604)),
% 3.30/2.52 inference(unit_resolution,[status(thm)],[2888, 107, 241, 2882, 2391, 2881, 2390, 32, 2872])).
% 3.30/2.52 tff(2890,plain,
% 3.30/2.52 (c0_1(a607)),
% 3.30/2.52 inference(unit_resolution,[status(thm)],[2401, 107, 33, 2391, 2873, 2315, 2314, 22, 2390, 2313, 1730])).
% 3.30/2.52 tff(2891,plain,
% 3.30/2.52 (hskp16 | (~c0_1(a607))),
% 3.30/2.52 inference(unit_resolution,[status(thm)],[2326, 107, 33, 2315, 2314, 22, 2313, 2125])).
% 3.30/2.52 tff(2892,plain,
% 3.30/2.52 (hskp16),
% 3.30/2.52 inference(unit_resolution,[status(thm)],[2891, 2890])).
% 3.30/2.52 tff(2893,plain,
% 3.30/2.52 (~c3_1(a606)),
% 3.30/2.52 inference(unit_resolution,[status(thm)],[1075, 2892])).
% 3.30/2.52 tff(2894,plain,
% 3.30/2.52 (~c2_1(a606)),
% 3.30/2.52 inference(unit_resolution,[status(thm)],[1111, 2892])).
% 3.30/2.52 tff(2895,plain,
% 3.30/2.52 (c0_1(a606)),
% 3.30/2.52 inference(unit_resolution,[status(thm)],[2411, 107, 2391, 2873, 2315, 2314, 2894, 2893, 2390, 2313, 1730])).
% 3.30/2.52 tff(2896,plain,
% 3.30/2.52 (c1_1(a606)),
% 3.30/2.52 inference(unit_resolution,[status(thm)],[1088, 2892])).
% 3.40/2.52 tff(2897,plain,
% 3.40/2.52 (c3_1(a604)),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[1602, 2880])).
% 3.40/2.52 tff(2898,plain,
% 3.40/2.52 (~hskp13),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[2553, 2889, 2391, 2873, 2881, 2390, 2897, 2292, 2281, 2270, 2896, 2894, 2895])).
% 3.40/2.52 tff(2899,plain,
% 3.40/2.52 (hskp19 | hskp13),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[2656, 107, 2882, 2881, 2564, 2889])).
% 3.40/2.52 tff(2900,plain,
% 3.40/2.52 (hskp19),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[2899, 2898])).
% 3.40/2.52 tff(2901,plain,
% 3.40/2.52 (~c1_1(a617)),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[2588, 2900])).
% 3.40/2.52 tff(2902,plain,
% 3.40/2.52 (~c0_1(a617)),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[2594, 2900])).
% 3.40/2.52 tff(2903,plain,
% 3.40/2.52 (c2_1(a617)),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[2605, 2900])).
% 3.40/2.52 tff(2904,plain,
% 3.40/2.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617)))),
% 3.40/2.52 inference(rewrite,[status(thm)],[])).
% 3.40/2.52 tff(2905,plain,
% 3.40/2.52 (((~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617))) <=> (c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617)))),
% 3.40/2.52 inference(rewrite,[status(thm)],[])).
% 3.40/2.52 tff(2906,plain,
% 3.40/2.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617))))),
% 3.40/2.52 inference(monotonicity,[status(thm)],[2905])).
% 3.40/2.52 tff(2907,plain,
% 3.40/2.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617)))),
% 3.40/2.52 inference(transitivity,[status(thm)],[2906, 2904])).
% 3.40/2.52 tff(2908,plain,
% 3.40/2.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))),
% 3.40/2.52 inference(quant_inst,[status(thm)],[])).
% 3.40/2.52 tff(2909,plain,
% 3.40/2.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617))),
% 3.40/2.52 inference(modus_ponens,[status(thm)],[2908, 2907])).
% 3.40/2.52 tff(2910,plain,
% 3.40/2.52 ($false),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[2909, 107, 2865, 2864, 2863, 2903, 2897, 2902, 2901, 2881, 65, 2889])).
% 3.40/2.52 tff(2911,plain,(c1_1(a607) | c3_1(a607) | c2_1(a607) | hskp22), inference(lemma,lemma(discharge,[]))).
% 3.40/2.52 tff(2912,plain,
% 3.40/2.52 (c1_1(a607)),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[2911, 33, 22, 44])).
% 3.40/2.52 tff(2913,plain,
% 3.40/2.52 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | c3_1(a607) | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp4 | c3_1(a607) | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607)))),
% 3.40/2.52 inference(rewrite,[status(thm)],[])).
% 3.40/2.52 tff(2914,plain,
% 3.40/2.52 ((hskp17 | hskp4 | (~ndr1_0) | c3_1(a607) | (~c1_1(a607)) | (~c0_1(a607))) <=> (hskp17 | hskp4 | c3_1(a607) | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607)))),
% 3.40/2.52 inference(rewrite,[status(thm)],[])).
% 3.40/2.52 tff(2915,plain,
% 3.40/2.52 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c3_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | c3_1(a607) | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607))))),
% 3.40/2.52 inference(monotonicity,[status(thm)],[2914])).
% 3.40/2.52 tff(2916,plain,
% 3.40/2.52 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c3_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp4 | c3_1(a607) | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607)))),
% 3.40/2.52 inference(transitivity,[status(thm)],[2915, 2913])).
% 3.40/2.52 tff(2917,plain,
% 3.40/2.52 ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c3_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))),
% 3.40/2.52 inference(quant_inst,[status(thm)],[])).
% 3.40/2.52 tff(2918,plain,
% 3.40/2.52 ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp4 | c3_1(a607) | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607))),
% 3.40/2.52 inference(modus_ponens,[status(thm)],[2917, 2916])).
% 3.40/2.52 tff(2919,plain,
% 3.40/2.52 (hskp4 | (~c1_1(a607)) | (~c0_1(a607))),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[2918, 107, 241, 33, 55])).
% 3.40/2.52 tff(2920,plain,
% 3.40/2.52 (~c0_1(a607)),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[2919, 148, 2912])).
% 3.40/2.52 tff(2921,plain,
% 3.40/2.52 (hskp14),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[165, 2920, 33, 148])).
% 3.40/2.52 tff(2922,plain,
% 3.40/2.52 (~c1_1(a603)),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[171, 2921])).
% 3.40/2.52 tff(2923,plain,
% 3.40/2.52 (c0_1(a603)),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[182, 2921])).
% 3.40/2.52 tff(2924,plain,
% 3.40/2.52 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~c1_1(a607)) | c2_1(a607) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | (~c1_1(a607)) | c2_1(a607) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607))),
% 3.40/2.52 inference(rewrite,[status(thm)],[])).
% 3.40/2.52 tff(2925,plain,
% 3.40/2.52 ((hskp17 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607) | c2_1(a607) | (~c1_1(a607))) <=> (hskp17 | (~c1_1(a607)) | c2_1(a607) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607))),
% 3.40/2.52 inference(rewrite,[status(thm)],[])).
% 3.40/2.52 tff(2926,plain,
% 3.40/2.52 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607) | c2_1(a607) | (~c1_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~c1_1(a607)) | c2_1(a607) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607)))),
% 3.40/2.52 inference(monotonicity,[status(thm)],[2925])).
% 3.40/2.52 tff(2927,plain,
% 3.40/2.52 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607) | c2_1(a607) | (~c1_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | (~c1_1(a607)) | c2_1(a607) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607))),
% 3.40/2.52 inference(transitivity,[status(thm)],[2926, 2924])).
% 3.40/2.52 tff(2928,plain,
% 3.40/2.52 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607) | c2_1(a607) | (~c1_1(a607)))),
% 3.40/2.52 inference(quant_inst,[status(thm)],[])).
% 3.40/2.52 tff(2929,plain,
% 3.40/2.52 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | (~c1_1(a607)) | c2_1(a607) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607)),
% 3.40/2.52 inference(modus_ponens,[status(thm)],[2928, 2927])).
% 3.40/2.52 tff(2930,plain,
% 3.40/2.52 (~c2_1(a603)),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[2929, 107, 241, 2923, 2912, 22, 2922, 32, 2920])).
% 3.40/2.52 tff(2931,plain,
% 3.40/2.52 ($false),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[189, 107, 44, 67, 2923, 2922, 43, 2930])).
% 3.40/2.52 tff(2932,plain,(hskp6 | hskp22 | c2_1(a607) | c3_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.40/2.52 tff(2933,plain,
% 3.40/2.52 (hskp6),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[2932, 33, 22, 44])).
% 3.40/2.52 tff(2934,plain,
% 3.40/2.52 (~c0_1(a590)),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[666, 2933])).
% 3.40/2.52 tff(2935,plain,
% 3.40/2.52 (c0_1(a607)),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[2299, 1638])).
% 3.40/2.52 tff(2936,plain,
% 3.40/2.52 (hskp4),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[2919, 2935, 2912])).
% 3.40/2.52 tff(2937,plain,
% 3.40/2.52 (hskp6),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[147, 2936, 44])).
% 3.40/2.52 tff(2938,plain,
% 3.40/2.52 (~c0_1(a590)),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[666, 2937])).
% 3.40/2.52 tff(2939,plain,
% 3.40/2.52 (c2_1(a590)),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[688, 2937])).
% 3.40/2.52 tff(2940,plain,
% 3.40/2.52 (c3_1(a590)),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[677, 2937])).
% 3.40/2.52 tff(2941,plain,
% 3.40/2.52 ($false),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[2388, 2940, 2939, 2281, 2270, 33, 2292, 1638, 22, 2938])).
% 3.40/2.52 tff(2942,plain,(hskp11 | c3_1(a607) | c2_1(a607) | hskp22), inference(lemma,lemma(discharge,[]))).
% 3.40/2.52 tff(2943,plain,
% 3.40/2.52 (hskp11),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[2942, 33, 22, 44])).
% 3.40/2.52 tff(2944,plain,
% 3.40/2.52 (~c1_1(a599)),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[428, 2943])).
% 3.40/2.52 tff(2945,plain,
% 3.40/2.52 (c3_1(a590)),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[677, 2933])).
% 3.40/2.52 tff(2946,plain,
% 3.40/2.52 (c2_1(a590)),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[688, 2933])).
% 3.40/2.52 tff(2947,plain,
% 3.40/2.52 (c2_1(a599)),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[439, 2943])).
% 3.40/2.52 tff(2948,plain,
% 3.40/2.52 (c3_1(a599)),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[422, 2943])).
% 3.40/2.52 tff(2949,plain,
% 3.40/2.52 (c0_1(a607)),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[2401, 107, 33, 2947, 2948, 2946, 2945, 22, 2944, 2934, 1730])).
% 3.40/2.52 tff(2950,plain,
% 3.40/2.52 (hskp4),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[2919, 2949, 2912])).
% 3.40/2.52 tff(2951,plain,
% 3.40/2.52 (~c2_1(a588)),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[121, 2950])).
% 3.40/2.52 tff(2952,plain,
% 3.40/2.52 (~c1_1(a588)),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[127, 2950])).
% 3.40/2.52 tff(2953,plain,
% 3.40/2.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~c1_1(a607)) | c2_1(a607) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a588)) | (~c0_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (~c1_1(a607)) | c2_1(a607) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a588)) | (~c0_1(a607)))),
% 3.40/2.52 inference(rewrite,[status(thm)],[])).
% 3.40/2.52 tff(2954,plain,
% 3.40/2.52 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a588) | c2_1(a588) | (~c3_1(a588))) <=> ((~c1_1(a607)) | c2_1(a607) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a588)) | (~c0_1(a607)))),
% 3.40/2.52 inference(rewrite,[status(thm)],[])).
% 3.40/2.52 tff(2955,plain,
% 3.40/2.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a588) | c2_1(a588) | (~c3_1(a588)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~c1_1(a607)) | c2_1(a607) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a588)) | (~c0_1(a607))))),
% 3.40/2.52 inference(monotonicity,[status(thm)],[2954])).
% 3.40/2.52 tff(2956,plain,
% 3.40/2.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a588) | c2_1(a588) | (~c3_1(a588)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (~c1_1(a607)) | c2_1(a607) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a588)) | (~c0_1(a607)))),
% 3.40/2.52 inference(transitivity,[status(thm)],[2955, 2953])).
% 3.40/2.52 tff(2957,plain,
% 3.40/2.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a588) | c2_1(a588) | (~c3_1(a588)))),
% 3.40/2.52 inference(quant_inst,[status(thm)],[])).
% 3.40/2.52 tff(2958,plain,
% 3.40/2.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (~c1_1(a607)) | c2_1(a607) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a588)) | (~c0_1(a607))),
% 3.40/2.52 inference(modus_ponens,[status(thm)],[2957, 2956])).
% 3.40/2.52 tff(2959,plain,
% 3.40/2.52 (~c3_1(a588)),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[2958, 107, 2292, 2281, 2270, 2912, 22, 2952, 2951, 1106, 2949])).
% 3.40/2.52 tff(2960,plain,
% 3.40/2.52 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | c3_1(a607) | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp3 | c3_1(a607) | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607)))),
% 3.40/2.52 inference(rewrite,[status(thm)],[])).
% 3.40/2.52 tff(2961,plain,
% 3.40/2.52 ((hskp17 | hskp3 | (~ndr1_0) | c3_1(a607) | (~c1_1(a607)) | (~c0_1(a607))) <=> (hskp17 | hskp3 | c3_1(a607) | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607)))),
% 3.40/2.52 inference(rewrite,[status(thm)],[])).
% 3.40/2.52 tff(2962,plain,
% 3.40/2.52 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c3_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | c3_1(a607) | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607))))),
% 3.40/2.52 inference(monotonicity,[status(thm)],[2961])).
% 3.40/2.52 tff(2963,plain,
% 3.40/2.52 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c3_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp3 | c3_1(a607) | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607)))),
% 3.40/2.52 inference(transitivity,[status(thm)],[2962, 2960])).
% 3.40/2.52 tff(2964,plain,
% 3.40/2.52 ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c3_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))),
% 3.40/2.52 inference(quant_inst,[status(thm)],[])).
% 3.40/2.52 tff(2965,plain,
% 3.40/2.52 ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp3 | c3_1(a607) | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607))),
% 3.40/2.52 inference(modus_ponens,[status(thm)],[2964, 2963])).
% 3.40/2.52 tff(2966,plain,
% 3.40/2.52 (hskp3 | (~c1_1(a607)) | (~c0_1(a607))),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[2965, 107, 241, 33, 2368])).
% 3.40/2.52 tff(2967,plain,
% 3.40/2.52 (hskp3),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[2966, 2949, 2912])).
% 3.40/2.52 tff(2968,plain,
% 3.40/2.52 (~c1_1(a587)),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[939, 2967])).
% 3.40/2.52 tff(2969,plain,
% 3.40/2.52 (c2_1(a587)),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[950, 2967])).
% 3.40/2.52 tff(2970,plain,
% 3.40/2.52 (c0_1(a587)),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[961, 2967])).
% 3.40/2.52 tff(2971,plain,
% 3.40/2.52 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a588) | c2_1(a588) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a588))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a588) | c2_1(a588) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a588))),
% 3.40/2.52 inference(rewrite,[status(thm)],[])).
% 3.40/2.52 tff(2972,plain,
% 3.40/2.52 ((hskp26 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a588) | c1_1(a588) | c2_1(a588)) <=> (hskp26 | c1_1(a588) | c2_1(a588) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a588))),
% 3.40/2.52 inference(rewrite,[status(thm)],[])).
% 3.40/2.52 tff(2973,plain,
% 3.40/2.52 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a588) | c1_1(a588) | c2_1(a588))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a588) | c2_1(a588) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a588)))),
% 3.40/2.52 inference(monotonicity,[status(thm)],[2972])).
% 3.40/2.52 tff(2974,plain,
% 3.40/2.52 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a588) | c1_1(a588) | c2_1(a588))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a588) | c2_1(a588) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a588))),
% 3.40/2.52 inference(transitivity,[status(thm)],[2973, 2971])).
% 3.40/2.52 tff(2975,plain,
% 3.40/2.52 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a588) | c1_1(a588) | c2_1(a588))),
% 3.40/2.52 inference(quant_inst,[status(thm)],[])).
% 3.40/2.52 tff(2976,plain,
% 3.40/2.52 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a588) | c2_1(a588) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a588)),
% 3.40/2.52 inference(modus_ponens,[status(thm)],[2975, 2974])).
% 3.40/2.52 tff(2977,plain,
% 3.40/2.52 (hskp26),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[2976, 107, 2970, 2969, 2952, 2951, 2968, 995, 2959])).
% 3.40/2.52 tff(2978,plain,
% 3.40/2.52 (c2_1(a583)),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[391, 2977])).
% 3.40/2.52 tff(2979,plain,
% 3.40/2.52 (c1_1(a583)),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[351, 2977])).
% 3.40/2.52 tff(2980,plain,
% 3.40/2.52 (c0_1(a583)),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[362, 2977])).
% 3.40/2.52 tff(2981,plain,
% 3.40/2.52 (hskp16),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[2326, 107, 33, 2946, 2945, 22, 2934, 2125, 2949])).
% 3.40/2.52 tff(2982,plain,
% 3.40/2.52 (~c2_1(a606)),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[1111, 2981])).
% 3.40/2.52 tff(2983,plain,
% 3.40/2.52 (c1_1(a606)),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[1088, 2981])).
% 3.40/2.52 tff(2984,plain,
% 3.40/2.52 (~c3_1(a606)),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[1075, 2981])).
% 3.40/2.52 tff(2985,plain,
% 3.40/2.52 (c0_1(a606)),
% 3.40/2.52 inference(unit_resolution,[status(thm)],[2411, 107, 2947, 2948, 2946, 2945, 2982, 2984, 2944, 2934, 1730])).
% 3.40/2.52 tff(2986,assumption,(c1_1(a607)), introduced(assumption)).
% 3.40/2.52 tff(2987,assumption,(~hskp17), introduced(assumption)).
% 3.40/2.52 tff(2988,plain,
% 3.40/2.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a604) | c0_1(a604) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c2_1(a604))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a604) | c0_1(a604) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c2_1(a604))),
% 3.40/2.53 inference(rewrite,[status(thm)],[])).
% 3.40/2.53 tff(2989,plain,
% 3.40/2.53 (((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a604) | c0_1(a604) | c2_1(a604)) <=> (c3_1(a604) | c0_1(a604) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c2_1(a604))),
% 3.40/2.53 inference(rewrite,[status(thm)],[])).
% 3.40/2.53 tff(2990,plain,
% 3.40/2.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a604) | c0_1(a604) | c2_1(a604))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a604) | c0_1(a604) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c2_1(a604)))),
% 3.40/2.53 inference(monotonicity,[status(thm)],[2989])).
% 3.40/2.53 tff(2991,plain,
% 3.40/2.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a604) | c0_1(a604) | c2_1(a604))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a604) | c0_1(a604) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c2_1(a604))),
% 3.40/2.53 inference(transitivity,[status(thm)],[2990, 2988])).
% 3.40/2.53 tff(2992,plain,
% 3.40/2.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a604) | c0_1(a604) | c2_1(a604))),
% 3.40/2.53 inference(quant_inst,[status(thm)],[])).
% 3.40/2.53 tff(2993,plain,
% 3.40/2.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a604) | c0_1(a604) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c2_1(a604)),
% 3.40/2.53 inference(modus_ponens,[status(thm)],[2992, 2991])).
% 3.40/2.53 tff(2994,plain,
% 3.40/2.53 (c2_1(a604)),
% 3.40/2.53 inference(unit_resolution,[status(thm)],[2993, 107, 2489, 463, 462, 863, 862, 2475, 461, 45, 1730])).
% 3.40/2.53 tff(2995,plain,
% 3.40/2.53 (^[U: $i] : refl((hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 3.40/2.53 inference(bind,[status(th)],[])).
% 3.40/2.53 tff(2996,plain,
% 3.40/2.53 (![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 3.40/2.53 inference(quant_intro,[status(thm)],[2995])).
% 3.40/2.53 tff(2997,plain,
% 3.40/2.53 (![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 3.40/2.53 inference(rewrite,[status(thm)],[])).
% 3.40/2.53 tff(2998,plain,
% 3.40/2.53 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp15))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) | hskp25) <=> ((hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp25))), rewrite(((hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp25) <=> (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) | hskp25) <=> (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 3.40/2.53 inference(bind,[status(th)],[])).
% 3.40/2.53 tff(2999,plain,
% 3.40/2.53 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) | hskp25) <=> ![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 3.40/2.53 inference(quant_intro,[status(thm)],[2998])).
% 3.40/2.53 tff(3000,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) | hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause148')).
% 3.40/2.53 tff(3001,plain,
% 3.40/2.53 (![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 3.40/2.53 inference(modus_ponens,[status(thm)],[3000, 2999])).
% 3.40/2.53 tff(3002,plain,
% 3.40/2.53 (![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 3.40/2.53 inference(modus_ponens,[status(thm)],[3001, 2997])).
% 3.40/2.53 tff(3003,plain,(
% 3.40/2.53 ![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 3.40/2.53 inference(skolemize,[status(sab)],[3002])).
% 3.40/2.53 tff(3004,plain,
% 3.40/2.53 (![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 3.40/2.53 inference(modus_ponens,[status(thm)],[3003, 2996])).
% 3.40/2.53 tff(3005,plain,
% 3.40/2.53 (((~![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp15 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp15 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)))),
% 3.40/2.53 inference(rewrite,[status(thm)],[])).
% 3.40/2.53 tff(3006,plain,
% 3.40/2.53 ((hskp25 | hskp15 | (~ndr1_0) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607))) <=> (hskp25 | hskp15 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)))),
% 3.40/2.53 inference(rewrite,[status(thm)],[])).
% 3.40/2.53 tff(3007,plain,
% 3.40/2.53 (((~![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp15 | (~ndr1_0) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp15 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607))))),
% 3.40/2.53 inference(monotonicity,[status(thm)],[3006])).
% 3.40/2.53 tff(3008,plain,
% 3.40/2.53 (((~![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp15 | (~ndr1_0) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp15 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)))),
% 3.40/2.53 inference(transitivity,[status(thm)],[3007, 3005])).
% 3.40/2.53 tff(3009,plain,
% 3.40/2.53 ((~![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp15 | (~ndr1_0) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))),
% 3.40/2.53 inference(quant_inst,[status(thm)],[])).
% 3.40/2.53 tff(3010,plain,
% 3.40/2.53 ((~![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp15 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607))),
% 3.40/2.53 inference(modus_ponens,[status(thm)],[3009, 3008])).
% 3.40/2.53 tff(3011,plain,
% 3.40/2.53 (hskp25 | hskp15 | (~c1_1(a607)) | (~c0_1(a607))),
% 3.40/2.53 inference(unit_resolution,[status(thm)],[3010, 107, 22, 3004])).
% 3.40/2.53 tff(3012,plain,
% 3.40/2.53 (hskp25),
% 3.40/2.53 inference(unit_resolution,[status(thm)],[3011, 2490, 2986, 2486])).
% 3.40/2.53 tff(3013,plain,
% 3.40/2.53 (~c3_1(a651)),
% 3.40/2.53 inference(unit_resolution,[status(thm)],[2464, 3012])).
% 3.40/2.53 tff(3014,plain,
% 3.40/2.53 (~c1_1(a651)),
% 3.40/2.53 inference(unit_resolution,[status(thm)],[2470, 3012])).
% 3.40/2.53 tff(3015,plain,
% 3.40/2.53 (c2_1(a651)),
% 3.40/2.53 inference(unit_resolution,[status(thm)],[2458, 3012])).
% 3.40/2.53 tff(3016,plain,
% 3.40/2.53 (~c0_1(a651)),
% 3.40/2.53 inference(unit_resolution,[status(thm)],[2483, 1709])).
% 3.40/2.53 tff(3017,plain,
% 3.40/2.53 (c3_1(a583)),
% 3.40/2.53 inference(unit_resolution,[status(thm)],[2095, 1709, 1872])).
% 3.40/2.53 tff(3018,plain,
% 3.40/2.53 ($false),
% 3.40/2.53 inference(unit_resolution,[status(thm)],[2637, 107, 1651, 1650, 2474, 863, 862, 2630, 45, 65, 3017, 3016])).
% 3.40/2.53 tff(3019,plain,(hskp8 | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a651)) | (~c2_1(a590)) | (~c3_1(a590)) | c1_1(a651) | c0_1(a590) | hskp27 | c3_1(a651) | (~c2_1(a583))), inference(lemma,lemma(discharge,[]))).
% 3.40/2.53 tff(3020,plain,
% 3.40/2.53 (hskp8),
% 3.40/2.53 inference(unit_resolution,[status(thm)],[3019, 3015, 1650, 1651, 863, 862, 3014, 45, 1872, 3013, 1649])).
% 3.40/2.53 tff(3021,plain,
% 3.40/2.53 (c3_1(a593)),
% 3.40/2.53 inference(unit_resolution,[status(thm)],[511, 3020])).
% 3.40/2.53 tff(3022,plain,
% 3.40/2.53 (~c2_1(a593)),
% 3.40/2.53 inference(unit_resolution,[status(thm)],[555, 3020])).
% 3.40/2.53 tff(3023,plain,
% 3.40/2.53 (c1_1(a593)),
% 3.40/2.53 inference(unit_resolution,[status(thm)],[522, 3020])).
% 3.40/2.53 tff(3024,assumption,(~c1_1(a604)), introduced(assumption)).
% 3.40/2.53 tff(3025,plain,
% 3.40/2.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a604) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a604) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a604)))),
% 3.40/2.53 inference(rewrite,[status(thm)],[])).
% 3.40/2.53 tff(3026,plain,
% 3.40/2.53 (((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a604) | c0_1(a604) | (~c2_1(a604))) <=> (c1_1(a604) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a604)))),
% 3.40/2.53 inference(rewrite,[status(thm)],[])).
% 3.40/2.53 tff(3027,plain,
% 3.40/2.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a604) | c0_1(a604) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a604) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a604))))),
% 3.40/2.53 inference(monotonicity,[status(thm)],[3026])).
% 3.40/2.53 tff(3028,plain,
% 3.40/2.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a604) | c0_1(a604) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a604) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a604)))),
% 3.40/2.53 inference(transitivity,[status(thm)],[3027, 3025])).
% 3.40/2.53 tff(3029,plain,
% 3.40/2.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a604) | c0_1(a604) | (~c2_1(a604)))),
% 3.40/2.53 inference(quant_inst,[status(thm)],[])).
% 3.40/2.53 tff(3030,plain,
% 3.40/2.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a604) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a604))),
% 3.40/2.53 inference(modus_ponens,[status(thm)],[3029, 3028])).
% 3.40/2.53 tff(3031,plain,
% 3.40/2.53 (~c1_1(a678)),
% 3.40/2.53 inference(unit_resolution,[status(thm)],[3030, 107, 2318, 2316, 3024, 863, 862, 2475, 45, 65, 2538])).
% 3.40/2.53 tff(3032,plain,
% 3.40/2.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a604) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a604) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a604)))),
% 3.40/2.53 inference(rewrite,[status(thm)],[])).
% 3.40/2.53 tff(3033,plain,
% 3.40/2.53 (((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a604) | c0_1(a604) | (~c2_1(a604))) <=> (c1_1(a604) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a604)))),
% 3.40/2.53 inference(rewrite,[status(thm)],[])).
% 3.40/2.53 tff(3034,plain,
% 3.40/2.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a604) | c0_1(a604) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a604) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a604))))),
% 3.40/2.53 inference(monotonicity,[status(thm)],[3033])).
% 3.40/2.53 tff(3035,plain,
% 3.40/2.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a604) | c0_1(a604) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a604) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a604)))),
% 3.40/2.53 inference(transitivity,[status(thm)],[3034, 3032])).
% 3.40/2.53 tff(3036,plain,
% 3.40/2.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a604) | c0_1(a604) | (~c2_1(a604)))),
% 3.40/2.53 inference(quant_inst,[status(thm)],[])).
% 3.40/2.53 tff(3037,plain,
% 3.40/2.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a604) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a604))),
% 3.40/2.53 inference(modus_ponens,[status(thm)],[3036, 3035])).
% 3.40/2.53 tff(3038,plain,
% 3.40/2.53 (~c0_1(a593)),
% 3.40/2.53 inference(unit_resolution,[status(thm)],[3037, 107, 3024, 1894, 1903, 863, 862, 2475, 45, 65, 2538])).
% 3.40/2.53 tff(3039,plain,
% 3.40/2.53 ($false),
% 3.40/2.53 inference(unit_resolution,[status(thm)],[2626, 107, 2987, 2318, 2317, 1894, 1893, 32, 3038, 3031])).
% 3.40/2.53 tff(3040,plain,(c1_1(a604) | hskp17 | (~c0_1(a678)) | (~c2_1(a678)) | (~c1_1(a593)) | c2_1(a593) | (~c3_1(a593)) | (~c2_1(a590)) | (~c3_1(a590)) | c0_1(a604) | c0_1(a590) | (~c2_1(a604)) | (~c3_1(a678))), inference(lemma,lemma(discharge,[]))).
% 3.40/2.53 tff(3041,plain,
% 3.40/2.53 (c1_1(a604)),
% 3.40/2.53 inference(unit_resolution,[status(thm)],[3040, 3023, 2318, 2317, 2987, 3022, 3021, 863, 862, 2475, 45, 2994, 2316])).
% 3.40/2.53 tff(3042,plain,
% 3.40/2.53 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | c3_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c1_1(a590)) | (~c2_1(a604)) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c3_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c1_1(a590)) | (~c2_1(a604)) | (~c1_1(a604)))),
% 3.40/2.53 inference(rewrite,[status(thm)],[])).
% 3.40/2.53 tff(3043,plain,
% 3.40/2.53 ((hskp15 | (~ndr1_0) | c3_1(a604) | (~c2_1(a604)) | (~c1_1(a604)) | c0_1(a590) | (~c1_1(a590)) | (~c3_1(a590))) <=> (hskp15 | c3_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c1_1(a590)) | (~c2_1(a604)) | (~c1_1(a604)))),
% 3.40/2.53 inference(rewrite,[status(thm)],[])).
% 3.40/2.53 tff(3044,plain,
% 3.40/2.53 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a604) | (~c2_1(a604)) | (~c1_1(a604)) | c0_1(a590) | (~c1_1(a590)) | (~c3_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | c3_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c1_1(a590)) | (~c2_1(a604)) | (~c1_1(a604))))),
% 3.40/2.53 inference(monotonicity,[status(thm)],[3043])).
% 3.40/2.53 tff(3045,plain,
% 3.40/2.53 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a604) | (~c2_1(a604)) | (~c1_1(a604)) | c0_1(a590) | (~c1_1(a590)) | (~c3_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c3_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c1_1(a590)) | (~c2_1(a604)) | (~c1_1(a604)))),
% 3.40/2.53 inference(transitivity,[status(thm)],[3044, 3042])).
% 3.40/2.53 tff(3046,plain,
% 3.40/2.53 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a604) | (~c2_1(a604)) | (~c1_1(a604)) | c0_1(a590) | (~c1_1(a590)) | (~c3_1(a590)))),
% 3.40/2.53 inference(quant_inst,[status(thm)],[])).
% 3.40/2.53 tff(3047,plain,
% 3.40/2.53 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c3_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c1_1(a590)) | (~c2_1(a604)) | (~c1_1(a604))),
% 3.40/2.53 inference(modus_ponens,[status(thm)],[3046, 3045])).
% 3.40/2.53 tff(3048,plain,
% 3.40/2.53 ((~c1_1(a590)) | (~c1_1(a604))),
% 3.40/2.53 inference(unit_resolution,[status(thm)],[3047, 107, 2490, 2489, 862, 45, 2690, 2994])).
% 3.40/2.53 tff(3049,plain,
% 3.40/2.53 (~c1_1(a590)),
% 3.40/2.53 inference(unit_resolution,[status(thm)],[3048, 3041])).
% 3.40/2.53 tff(3050,plain,
% 3.40/2.53 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | c0_1(a604) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a604)) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | c0_1(a604) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a604)) | (~c1_1(a604)))),
% 3.40/2.53 inference(rewrite,[status(thm)],[])).
% 3.40/2.53 tff(3051,plain,
% 3.40/2.53 ((hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604))) <=> (hskp12 | c0_1(a604) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a604)) | (~c1_1(a604)))),
% 3.40/2.53 inference(rewrite,[status(thm)],[])).
% 3.40/2.53 tff(3052,plain,
% 3.40/2.53 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | c0_1(a604) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a604)) | (~c1_1(a604))))),
% 3.40/2.53 inference(monotonicity,[status(thm)],[3051])).
% 3.40/2.53 tff(3053,plain,
% 3.40/2.53 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | c0_1(a604) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a604)) | (~c1_1(a604)))),
% 3.40/2.53 inference(transitivity,[status(thm)],[3052, 3050])).
% 3.40/2.53 tff(3054,plain,
% 3.40/2.53 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))),
% 3.40/2.53 inference(quant_inst,[status(thm)],[])).
% 3.40/2.53 tff(3055,plain,
% 3.40/2.53 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | c0_1(a604) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a604)) | (~c1_1(a604))),
% 3.40/2.53 inference(modus_ponens,[status(thm)],[3054, 3053])).
% 3.40/2.53 tff(3056,plain,
% 3.40/2.53 (hskp12 | (~c2_1(a604)) | (~c1_1(a604))),
% 3.40/2.53 inference(unit_resolution,[status(thm)],[3055, 107, 1651, 1650, 1649, 2475, 2727])).
% 3.40/2.53 tff(3057,plain,
% 3.40/2.53 (hskp12),
% 3.40/2.53 inference(unit_resolution,[status(thm)],[3056, 3041, 2994])).
% 3.40/2.53 tff(3058,plain,
% 3.40/2.53 (~c3_1(a600)),
% 3.40/2.53 inference(unit_resolution,[status(thm)],[741, 3057])).
% 3.40/2.53 tff(3059,plain,
% 3.40/2.53 (c2_1(a600)),
% 3.40/2.53 inference(unit_resolution,[status(thm)],[752, 3057])).
% 3.40/2.53 tff(3060,plain,
% 3.40/2.53 (c0_1(a600)),
% 3.40/2.53 inference(unit_resolution,[status(thm)],[763, 3057])).
% 3.40/2.53 tff(3061,plain,
% 3.40/2.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a604) | c0_1(a604) | c3_1(a600) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | (~c2_1(a600)) | (~c0_1(a600)) | (~c1_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a604) | c0_1(a604) | c3_1(a600) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | (~c2_1(a600)) | (~c0_1(a600)) | (~c1_1(a604)))),
% 3.40/2.53 inference(rewrite,[status(thm)],[])).
% 3.40/2.53 tff(3062,plain,
% 3.40/2.53 (((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604))) <=> (c3_1(a604) | c0_1(a604) | c3_1(a600) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | (~c2_1(a600)) | (~c0_1(a600)) | (~c1_1(a604)))),
% 3.40/2.53 inference(rewrite,[status(thm)],[])).
% 3.40/2.53 tff(3063,plain,
% 3.40/2.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a604) | c0_1(a604) | c3_1(a600) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | (~c2_1(a600)) | (~c0_1(a600)) | (~c1_1(a604))))),
% 3.40/2.53 inference(monotonicity,[status(thm)],[3062])).
% 3.40/2.53 tff(3064,plain,
% 3.40/2.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a604) | c0_1(a604) | c3_1(a600) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | (~c2_1(a600)) | (~c0_1(a600)) | (~c1_1(a604)))),
% 3.40/2.54 inference(transitivity,[status(thm)],[3063, 3061])).
% 3.40/2.54 tff(3065,plain,
% 3.40/2.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604)))),
% 3.40/2.54 inference(quant_inst,[status(thm)],[])).
% 3.40/2.54 tff(3066,plain,
% 3.40/2.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a604) | c0_1(a604) | c3_1(a600) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | (~c2_1(a600)) | (~c0_1(a600)) | (~c1_1(a604))),
% 3.40/2.54 inference(modus_ponens,[status(thm)],[3065, 3064])).
% 3.40/2.54 tff(3067,plain,
% 3.40/2.54 ($false),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[3066, 107, 3041, 2489, 3060, 3059, 863, 862, 2475, 3058, 258, 3049])).
% 3.40/2.54 tff(3068,plain,(c3_1(a604) | (~c2_1(a590)) | (~c3_1(a590)) | c0_1(a604) | c0_1(a590) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a678)) | (~c2_1(a678)) | hskp17 | (~c3_1(a678)) | hskp27 | (~c2_1(a599)) | (~c3_1(a599)) | c1_1(a599) | (~c1_1(a607)) | (~c0_1(a607)) | c2_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.40/2.54 tff(3069,plain,
% 3.40/2.54 (c3_1(a604)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[3068, 1872, 862, 2475, 45, 1651, 1650, 1649, 2318, 2317, 2987, 2316, 863, 463, 462, 461, 2986, 2486, 22])).
% 3.40/2.54 tff(3070,plain,
% 3.40/2.54 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~c1_1(a607)) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | (~c1_1(a607)) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c0_1(a607)))),
% 3.40/2.54 inference(rewrite,[status(thm)],[])).
% 3.40/2.54 tff(3071,plain,
% 3.40/2.54 ((hskp27 | (~ndr1_0) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a604) | c2_1(a604) | (~c3_1(a604))) <=> (hskp27 | (~c1_1(a607)) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c0_1(a607)))),
% 3.40/2.54 inference(rewrite,[status(thm)],[])).
% 3.40/2.54 tff(3072,plain,
% 3.40/2.54 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a604) | c2_1(a604) | (~c3_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~c1_1(a607)) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c0_1(a607))))),
% 3.40/2.54 inference(monotonicity,[status(thm)],[3071])).
% 3.40/2.54 tff(3073,plain,
% 3.40/2.54 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a604) | c2_1(a604) | (~c3_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | (~c1_1(a607)) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c0_1(a607)))),
% 3.40/2.54 inference(transitivity,[status(thm)],[3072, 3070])).
% 3.40/2.54 tff(3074,plain,
% 3.40/2.54 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a604) | c2_1(a604) | (~c3_1(a604)))),
% 3.40/2.54 inference(quant_inst,[status(thm)],[])).
% 3.40/2.54 tff(3075,plain,
% 3.40/2.54 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | (~c1_1(a607)) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c0_1(a607))),
% 3.40/2.54 inference(modus_ponens,[status(thm)],[3074, 3073])).
% 3.40/2.54 tff(3076,plain,
% 3.40/2.54 (hskp27 | (~c3_1(a604)) | c2_1(a604)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[3075, 107, 2986, 22, 2475, 540, 2486])).
% 3.40/2.54 tff(3077,plain,
% 3.40/2.54 (c2_1(a604)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[3076, 3069, 1872])).
% 3.40/2.54 tff(3078,plain,
% 3.40/2.54 (~hskp13),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[2553, 3069, 463, 462, 2515, 461, 2475, 2318, 2317, 2316, 1876, 1873, 3077])).
% 3.40/2.54 tff(3079,plain,
% 3.40/2.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a599)) | c0_1(a599) | (~c3_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a599)) | c0_1(a599) | (~c3_1(a604)) | (~c2_1(a604)))),
% 3.40/2.54 inference(rewrite,[status(thm)],[])).
% 3.40/2.54 tff(3080,plain,
% 3.40/2.54 (((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599))) <=> (c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a599)) | c0_1(a599) | (~c3_1(a604)) | (~c2_1(a604)))),
% 3.40/2.54 inference(rewrite,[status(thm)],[])).
% 3.40/2.54 tff(3081,plain,
% 3.40/2.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a599)) | c0_1(a599) | (~c3_1(a604)) | (~c2_1(a604))))),
% 3.40/2.54 inference(monotonicity,[status(thm)],[3080])).
% 3.40/2.54 tff(3082,plain,
% 3.40/2.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a599)) | c0_1(a599) | (~c3_1(a604)) | (~c2_1(a604)))),
% 3.40/2.54 inference(transitivity,[status(thm)],[3081, 3079])).
% 3.40/2.54 tff(3083,plain,
% 3.40/2.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))),
% 3.40/2.54 inference(quant_inst,[status(thm)],[])).
% 3.40/2.54 tff(3084,plain,
% 3.40/2.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a599)) | c0_1(a599) | (~c3_1(a604)) | (~c2_1(a604))),
% 3.40/2.54 inference(modus_ponens,[status(thm)],[3083, 3082])).
% 3.40/2.54 tff(3085,plain,
% 3.40/2.54 (c0_1(a599)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[3084, 107, 1651, 1650, 2545, 463, 2475, 461, 65, 3017, 2538])).
% 3.40/2.54 tff(3086,plain,
% 3.40/2.54 (hskp15),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[2113, 107, 1651, 1650, 462, 461, 1993, 3017, 3085])).
% 3.40/2.54 tff(3087,plain,
% 3.40/2.54 (c1_1(a604)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[1613, 3086])).
% 3.40/2.54 tff(3088,plain,
% 3.40/2.54 (hskp12),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[3056, 3087, 2538])).
% 3.40/2.54 tff(3089,plain,
% 3.40/2.54 (~c3_1(a600)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[741, 3088])).
% 3.40/2.54 tff(3090,plain,
% 3.40/2.54 (c2_1(a600)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[752, 3088])).
% 3.40/2.54 tff(3091,plain,
% 3.40/2.54 (c0_1(a600)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[763, 3088])).
% 3.40/2.54 tff(3092,plain,
% 3.40/2.54 ($false),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[2744, 107, 1872, 1709, 3091, 3090, 3089, 2080])).
% 3.40/2.54 tff(3093,plain,(hskp8 | hskp27 | (~c2_1(a604)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a583)) | c0_1(a604) | (~c3_1(a599)) | c1_1(a599) | (~c3_1(a604)) | (~c2_1(a599))), inference(lemma,lemma(discharge,[]))).
% 3.40/2.54 tff(3094,plain,
% 3.40/2.54 (hskp8),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[3093, 1872, 3077, 1651, 1650, 1649, 2475, 462, 461, 3069, 463])).
% 3.40/2.54 tff(3095,plain,
% 3.40/2.54 (c3_1(a593)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[511, 3094])).
% 3.40/2.54 tff(3096,plain,
% 3.40/2.54 (~c2_1(a593)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[555, 3094])).
% 3.40/2.54 tff(3097,plain,
% 3.40/2.54 (c1_1(a593)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[522, 3094])).
% 3.40/2.54 tff(3098,plain,
% 3.40/2.54 (c1_1(a604)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[3040, 3097, 2318, 2317, 2987, 3096, 3095, 863, 862, 2475, 45, 3077, 2316])).
% 3.40/2.54 tff(3099,plain,
% 3.40/2.54 (hskp19 | hskp13 | (~c2_1(a604)) | (~c1_1(a604))),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[2656, 107, 2475, 2564])).
% 3.40/2.54 tff(3100,plain,
% 3.40/2.54 (hskp19),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[3099, 3098, 3078, 3077])).
% 3.40/2.54 tff(3101,plain,
% 3.40/2.54 (~c1_1(a617)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[2588, 3100])).
% 3.40/2.54 tff(3102,plain,
% 3.40/2.54 (~c0_1(a617)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[2594, 3100])).
% 3.40/2.54 tff(3103,plain,
% 3.40/2.54 (c2_1(a617)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[2605, 3100])).
% 3.40/2.54 tff(3104,plain,
% 3.40/2.54 (~c1_1(a678)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[2612, 107, 2318, 2316, 3103, 3069, 3102, 3101, 2475, 65, 3077])).
% 3.40/2.54 tff(3105,plain,
% 3.40/2.54 (~c0_1(a593)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[2619, 107, 3103, 3069, 3097, 3095, 3102, 3101, 2475, 65, 3077])).
% 3.40/2.54 tff(3106,plain,
% 3.40/2.54 ($false),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[2626, 107, 2987, 2318, 2317, 3097, 3096, 32, 3105, 3104])).
% 3.40/2.54 tff(3107,plain,(hskp27 | hskp17 | (~c0_1(a678)) | (~c2_1(a678)) | c0_1(a604) | (~c3_1(a678)) | (~c2_1(a590)) | (~c3_1(a590)) | c0_1(a590) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c3_1(a599)) | c1_1(a599) | (~c2_1(a599)) | (~c0_1(a606)) | (~c1_1(a606)) | c2_1(a606) | (~c1_1(a607)) | c2_1(a607) | (~c0_1(a607))), inference(lemma,lemma(discharge,[]))).
% 3.40/2.54 tff(3108,plain,
% 3.40/2.54 (hskp27),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[3107, 2475, 2318, 2317, 2987, 2316, 863, 862, 45, 1651, 1650, 1649, 462, 461, 463, 2515, 1876, 1873, 2986, 22, 2486])).
% 3.40/2.54 tff(3109,plain,
% 3.40/2.54 (c3_1(a611)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[620, 3108])).
% 3.40/2.54 tff(3110,plain,
% 3.40/2.54 (c1_1(a611)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[631, 3108])).
% 3.40/2.54 tff(3111,plain,
% 3.40/2.54 (c0_1(a611)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[642, 3108])).
% 3.40/2.54 tff(3112,plain,
% 3.40/2.54 (c0_1(a599)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[2871, 107, 3111, 3110, 3109, 463, 863, 862, 461, 45, 65])).
% 3.40/2.54 tff(3113,plain,
% 3.40/2.54 (hskp15),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[2879, 107, 3111, 3110, 3109, 462, 461, 1993, 3112])).
% 3.40/2.54 tff(3114,plain,
% 3.40/2.54 (c1_1(a604)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[1613, 3113])).
% 3.40/2.54 tff(3115,plain,
% 3.40/2.54 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a604) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a604) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a604) | (~c1_1(a604)))),
% 3.40/2.54 inference(rewrite,[status(thm)],[])).
% 3.40/2.54 tff(3116,plain,
% 3.40/2.54 ((hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604))) <=> (hskp17 | c0_1(a604) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a604) | (~c1_1(a604)))),
% 3.40/2.54 inference(rewrite,[status(thm)],[])).
% 3.40/2.54 tff(3117,plain,
% 3.40/2.54 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a604) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a604) | (~c1_1(a604))))),
% 3.40/2.54 inference(monotonicity,[status(thm)],[3116])).
% 3.40/2.54 tff(3118,plain,
% 3.40/2.54 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a604) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a604) | (~c1_1(a604)))),
% 3.40/2.54 inference(transitivity,[status(thm)],[3117, 3115])).
% 3.40/2.54 tff(3119,plain,
% 3.40/2.54 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)))),
% 3.40/2.54 inference(quant_inst,[status(thm)],[])).
% 3.40/2.54 tff(3120,plain,
% 3.40/2.54 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a604) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a604) | (~c1_1(a604))),
% 3.40/2.54 inference(modus_ponens,[status(thm)],[3119, 3118])).
% 3.40/2.54 tff(3121,plain,
% 3.40/2.54 (c2_1(a604) | (~c1_1(a604))),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[3120, 107, 2987, 1000, 999, 2475, 996, 32])).
% 3.40/2.54 tff(3122,plain,
% 3.40/2.54 (c2_1(a604)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[3121, 3114])).
% 3.40/2.54 tff(3123,plain,
% 3.40/2.54 (c3_1(a604)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[1602, 3113])).
% 3.40/2.54 tff(3124,plain,
% 3.40/2.54 (~hskp13),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[2553, 3123, 463, 462, 2515, 461, 2475, 2318, 2317, 2316, 1876, 1873, 3122])).
% 3.40/2.54 tff(3125,plain,
% 3.40/2.54 (hskp19),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[3099, 3124, 3114, 3122])).
% 3.40/2.54 tff(3126,plain,
% 3.40/2.54 (~c1_1(a617)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[2588, 3125])).
% 3.40/2.54 tff(3127,plain,
% 3.40/2.54 (~c0_1(a617)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[2594, 3125])).
% 3.40/2.54 tff(3128,plain,
% 3.40/2.54 (c2_1(a617)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[2605, 3125])).
% 3.40/2.54 tff(3129,plain,
% 3.40/2.54 ($false),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[2909, 107, 3111, 3110, 3109, 3128, 3123, 3127, 3126, 2475, 65, 3122])).
% 3.40/2.54 tff(3130,plain,(c0_1(a604) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a606)) | c1_1(a599) | (~c0_1(a678)) | (~c2_1(a678)) | (~c3_1(a678)) | (~c1_1(a606)) | c2_1(a606) | hskp17 | (~c0_1(a587)) | (~c2_1(a587)) | c1_1(a587) | (~c2_1(a590)) | (~c3_1(a590)) | c0_1(a590) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c1_1(a607)) | c2_1(a607) | (~c0_1(a607))), inference(lemma,lemma(discharge,[]))).
% 3.40/2.54 tff(3131,plain,
% 3.40/2.54 (c0_1(a604)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[3130, 2947, 2948, 2985, 2944, 2292, 2281, 2270, 2983, 2982, 241, 2970, 2969, 2968, 2946, 2945, 2934, 2980, 2979, 2978, 2912, 22, 2949])).
% 3.40/2.54 tff(3132,plain,
% 3.40/2.54 (~hskp15),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[1591, 3131])).
% 3.40/2.54 tff(3133,plain,
% 3.40/2.54 (hskp4),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[2919, 2486, 2986])).
% 3.40/2.54 tff(3134,plain,
% 3.40/2.54 (~c2_1(a588)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[121, 3133])).
% 3.40/2.54 tff(3135,plain,
% 3.40/2.54 (~c1_1(a588)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[127, 3133])).
% 3.40/2.54 tff(3136,plain,
% 3.40/2.54 (~c3_1(a588)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[2958, 107, 2318, 2317, 2316, 2986, 22, 3135, 3134, 1106, 2486])).
% 3.40/2.54 tff(3137,plain,
% 3.40/2.54 (hskp3),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[2966, 2486, 2986])).
% 3.40/2.54 tff(3138,plain,
% 3.40/2.54 (~c1_1(a587)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[939, 3137])).
% 3.40/2.54 tff(3139,plain,
% 3.40/2.54 (c2_1(a587)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[950, 3137])).
% 3.40/2.54 tff(3140,plain,
% 3.40/2.54 (c0_1(a587)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[961, 3137])).
% 3.40/2.54 tff(3141,plain,
% 3.40/2.54 (hskp26),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[2976, 107, 3140, 3139, 3135, 3134, 3138, 995, 3136])).
% 3.40/2.54 tff(3142,plain,
% 3.40/2.54 (c2_1(a583)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[391, 3141])).
% 3.40/2.54 tff(3143,plain,
% 3.40/2.54 (c1_1(a583)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[351, 3141])).
% 3.40/2.54 tff(3144,plain,
% 3.40/2.54 (c0_1(a583)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[362, 3141])).
% 3.40/2.54 tff(3145,assumption,(hskp9), introduced(assumption)).
% 3.40/2.54 tff(3146,plain,
% 3.40/2.54 (~c3_1(a595)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[1487, 3145])).
% 3.40/2.54 tff(3147,plain,
% 3.40/2.54 (~c0_1(a595)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[1499, 3145])).
% 3.40/2.54 tff(3148,plain,
% 3.40/2.54 (~c1_1(a595)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[1493, 3145])).
% 3.40/2.54 tff(3149,plain,
% 3.40/2.54 ($false),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[2859, 3148, 3147, 22, 33, 3146, 1872, 1651, 1650, 1649, 863, 862, 45, 2317, 2316, 2318])).
% 3.40/2.54 tff(3150,plain,((~hskp9) | c2_1(a607) | c3_1(a607) | hskp27 | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c2_1(a590)) | (~c3_1(a590)) | c0_1(a590) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678))), inference(lemma,lemma(discharge,[]))).
% 3.40/2.54 tff(3151,plain,
% 3.40/2.54 (~hskp9),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[3150, 1872, 33, 22, 3144, 3143, 3142, 863, 862, 45, 2317, 2316, 2318])).
% 3.40/2.54 tff(3152,plain,
% 3.40/2.54 (hskp9 | c0_1(a599)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[1951, 107, 3144, 3143, 3142, 462, 461, 294])).
% 3.40/2.54 tff(3153,plain,
% 3.40/2.54 (c0_1(a599)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[3152, 3151])).
% 3.40/2.54 tff(3154,assumption,(~hskp15), introduced(assumption)).
% 3.40/2.54 tff(3155,plain,
% 3.40/2.54 (hskp25),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[3011, 3154, 2986, 2486])).
% 3.40/2.54 tff(3156,plain,
% 3.40/2.54 (~c3_1(a651)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[2464, 3155])).
% 3.40/2.54 tff(3157,plain,
% 3.40/2.54 (~c1_1(a651)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[2470, 3155])).
% 3.40/2.54 tff(3158,plain,
% 3.40/2.54 (c2_1(a651)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[2458, 3155])).
% 3.40/2.54 tff(3159,plain,
% 3.40/2.54 (hskp8),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[3019, 1872, 3143, 3144, 863, 862, 3158, 45, 3157, 3156, 3142])).
% 3.40/2.54 tff(3160,plain,
% 3.40/2.54 (c3_1(a593)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[511, 3159])).
% 3.40/2.54 tff(3161,plain,
% 3.40/2.54 (c1_1(a593)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[522, 3159])).
% 3.40/2.54 tff(3162,plain,
% 3.40/2.54 ((~c0_1(a593)) | (~c0_1(a599))),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[2496, 107, 3154, 462, 3161, 3160, 461, 1993])).
% 3.40/2.54 tff(3163,plain,
% 3.40/2.54 (~c0_1(a593)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[3162, 3153])).
% 3.40/2.54 tff(3164,plain,
% 3.40/2.54 (~c2_1(a593)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[555, 3159])).
% 3.40/2.54 tff(3165,plain,
% 3.40/2.54 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~c1_1(a607)) | c2_1(a607) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | (~c1_1(a607)) | c2_1(a607) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c0_1(a607)))),
% 3.40/2.54 inference(rewrite,[status(thm)],[])).
% 3.40/2.54 tff(3166,plain,
% 3.40/2.54 ((hskp27 | (~ndr1_0) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a593) | c2_1(a593) | (~c3_1(a593))) <=> (hskp27 | (~c1_1(a607)) | c2_1(a607) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c0_1(a607)))),
% 3.40/2.54 inference(rewrite,[status(thm)],[])).
% 3.40/2.54 tff(3167,plain,
% 3.40/2.54 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a593) | c2_1(a593) | (~c3_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~c1_1(a607)) | c2_1(a607) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c0_1(a607))))),
% 3.40/2.54 inference(monotonicity,[status(thm)],[3166])).
% 3.40/2.54 tff(3168,plain,
% 3.40/2.54 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a593) | c2_1(a593) | (~c3_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | (~c1_1(a607)) | c2_1(a607) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c0_1(a607)))),
% 3.40/2.54 inference(transitivity,[status(thm)],[3167, 3165])).
% 3.40/2.54 tff(3169,plain,
% 3.40/2.54 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a593) | c2_1(a593) | (~c3_1(a593)))),
% 3.40/2.54 inference(quant_inst,[status(thm)],[])).
% 3.40/2.54 tff(3170,plain,
% 3.40/2.54 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | (~c1_1(a607)) | c2_1(a607) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c0_1(a607))),
% 3.40/2.54 inference(modus_ponens,[status(thm)],[3169, 3168])).
% 3.40/2.54 tff(3171,plain,
% 3.40/2.54 ($false),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[3170, 107, 1872, 3160, 2986, 22, 3164, 540, 3163, 2486])).
% 3.40/2.54 tff(3172,plain,(hskp27 | (~c1_1(a607)) | c2_1(a607) | (~c0_1(a607)) | hskp15 | (~c3_1(a599)) | c1_1(a599) | c3_1(a607) | (~c2_1(a590)) | (~c3_1(a590)) | c0_1(a590) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678))), inference(lemma,lemma(discharge,[]))).
% 3.40/2.54 tff(3173,plain,
% 3.40/2.54 (hskp27),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[3172, 2912, 22, 2949, 3132, 2948, 2944, 33, 2946, 2945, 2934, 2281, 2270, 2292])).
% 3.40/2.54 tff(3174,plain,
% 3.40/2.54 (c3_1(a611)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[620, 3173])).
% 3.40/2.54 tff(3175,plain,
% 3.40/2.54 (c1_1(a611)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[631, 3173])).
% 3.40/2.54 tff(3176,plain,
% 3.40/2.54 (c0_1(a611)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[642, 3173])).
% 3.40/2.54 tff(3177,plain,
% 3.40/2.54 (c0_1(a599)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[2871, 107, 3176, 3175, 3174, 2947, 2946, 2945, 2944, 2934, 65])).
% 3.40/2.54 tff(3178,plain,
% 3.40/2.54 ($false),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[2879, 107, 3132, 3176, 3175, 3174, 2948, 2944, 1993, 3177])).
% 3.40/2.54 tff(3179,plain,(c3_1(a607) | c2_1(a607) | hskp22), inference(lemma,lemma(discharge,[]))).
% 3.40/2.54 tff(3180,plain,
% 3.40/2.54 (c3_1(a607)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[3179, 22, 44])).
% 3.40/2.54 tff(3181,assumption,(~c3_1(a590)), introduced(assumption)).
% 3.40/2.54 tff(3182,plain,
% 3.40/2.54 (~hskp6),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[677, 3181])).
% 3.40/2.54 tff(3183,plain,
% 3.40/2.54 (~hskp4),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[147, 3182, 44])).
% 3.40/2.54 tff(3184,assumption,(~c2_1(a590)), introduced(assumption)).
% 3.40/2.54 tff(3185,plain,
% 3.40/2.54 (((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp14 | hskp4 | c2_1(a590) | c3_1(a590) | c0_1(a590) | (~ndr1_0))) <=> ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp14 | hskp4 | c2_1(a590) | c3_1(a590) | c0_1(a590) | (~ndr1_0))),
% 3.40/2.54 inference(rewrite,[status(thm)],[])).
% 3.40/2.54 tff(3186,plain,
% 3.40/2.54 ((hskp14 | hskp4 | (~ndr1_0) | c2_1(a590) | c0_1(a590) | c3_1(a590)) <=> (hskp14 | hskp4 | c2_1(a590) | c3_1(a590) | c0_1(a590) | (~ndr1_0))),
% 3.40/2.54 inference(rewrite,[status(thm)],[])).
% 3.40/2.54 tff(3187,plain,
% 3.40/2.54 (((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp14 | hskp4 | (~ndr1_0) | c2_1(a590) | c0_1(a590) | c3_1(a590))) <=> ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp14 | hskp4 | c2_1(a590) | c3_1(a590) | c0_1(a590) | (~ndr1_0)))),
% 3.40/2.54 inference(monotonicity,[status(thm)],[3186])).
% 3.40/2.54 tff(3188,plain,
% 3.40/2.54 (((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp14 | hskp4 | (~ndr1_0) | c2_1(a590) | c0_1(a590) | c3_1(a590))) <=> ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp14 | hskp4 | c2_1(a590) | c3_1(a590) | c0_1(a590) | (~ndr1_0))),
% 3.40/2.54 inference(transitivity,[status(thm)],[3187, 3185])).
% 3.40/2.54 tff(3189,plain,
% 3.40/2.54 ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp14 | hskp4 | (~ndr1_0) | c2_1(a590) | c0_1(a590) | c3_1(a590))),
% 3.40/2.54 inference(quant_inst,[status(thm)],[])).
% 3.40/2.54 tff(3190,plain,
% 3.40/2.54 ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp14 | hskp4 | c2_1(a590) | c3_1(a590) | c0_1(a590) | (~ndr1_0)),
% 3.40/2.54 inference(modus_ponens,[status(thm)],[3189, 3188])).
% 3.40/2.54 tff(3191,plain,
% 3.40/2.54 (hskp14 | hskp4 | c2_1(a590) | c3_1(a590)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[3190, 107, 45, 158])).
% 3.40/2.54 tff(3192,plain,
% 3.40/2.54 (hskp14),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[3191, 3184, 3183, 3181])).
% 3.40/2.54 tff(3193,plain,
% 3.40/2.54 (~c1_1(a603)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[171, 3192])).
% 3.40/2.54 tff(3194,plain,
% 3.40/2.54 (c0_1(a603)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[182, 3192])).
% 3.40/2.54 tff(3195,plain,
% 3.40/2.54 (c2_1(a603)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[189, 107, 44, 3182, 3194, 3193, 43])).
% 3.40/2.54 tff(3196,plain,
% 3.40/2.54 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | c2_1(a590) | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | c2_1(a590) | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)))),
% 3.40/2.54 inference(rewrite,[status(thm)],[])).
% 3.40/2.54 tff(3197,plain,
% 3.40/2.54 ((hskp11 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c3_1(a590) | c0_1(a590) | c2_1(a590)) <=> (hskp11 | c2_1(a590) | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)))),
% 3.40/2.54 inference(rewrite,[status(thm)],[])).
% 3.40/2.54 tff(3198,plain,
% 3.40/2.54 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c3_1(a590) | c0_1(a590) | c2_1(a590))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | c2_1(a590) | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678))))),
% 3.40/2.54 inference(monotonicity,[status(thm)],[3197])).
% 3.40/2.54 tff(3199,plain,
% 3.40/2.54 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c3_1(a590) | c0_1(a590) | c2_1(a590))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | c2_1(a590) | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)))),
% 3.40/2.54 inference(transitivity,[status(thm)],[3198, 3196])).
% 3.40/2.54 tff(3200,plain,
% 3.40/2.54 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c3_1(a590) | c0_1(a590) | c2_1(a590))),
% 3.40/2.54 inference(quant_inst,[status(thm)],[])).
% 3.40/2.54 tff(3201,plain,
% 3.40/2.54 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | c2_1(a590) | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678))),
% 3.40/2.54 inference(modus_ponens,[status(thm)],[3200, 3199])).
% 3.40/2.54 tff(3202,plain,
% 3.40/2.54 (hskp11 | c2_1(a590)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[3201, 107, 2292, 2281, 2270, 3181, 45, 268])).
% 3.40/2.54 tff(3203,plain,
% 3.40/2.54 (hskp11),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[3202, 3184])).
% 3.40/2.54 tff(3204,plain,
% 3.40/2.54 (~c1_1(a599)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[428, 3203])).
% 3.40/2.54 tff(3205,plain,
% 3.40/2.54 (~c3_1(a603)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[205, 3192])).
% 3.40/2.54 tff(3206,plain,
% 3.40/2.54 (c3_1(a599)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[422, 3203])).
% 3.40/2.54 tff(3207,plain,
% 3.40/2.54 (c2_1(a599)),
% 3.40/2.54 inference(unit_resolution,[status(thm)],[439, 3203])).
% 3.40/2.54 tff(3208,plain,
% 3.40/2.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a590) | c3_1(a603) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c1_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a590) | c3_1(a603) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c1_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)))),
% 3.40/2.55 inference(rewrite,[status(thm)],[])).
% 3.40/2.55 tff(3209,plain,
% 3.40/2.55 (((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a590) | c0_1(a590) | (~c1_1(a590))) <=> (c3_1(a590) | c3_1(a603) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c1_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)))),
% 3.40/2.55 inference(rewrite,[status(thm)],[])).
% 3.40/2.55 tff(3210,plain,
% 3.40/2.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a590) | c0_1(a590) | (~c1_1(a590)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a590) | c3_1(a603) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c1_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603))))),
% 3.40/2.55 inference(monotonicity,[status(thm)],[3209])).
% 3.40/2.55 tff(3211,plain,
% 3.40/2.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a590) | c0_1(a590) | (~c1_1(a590)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a590) | c3_1(a603) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c1_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)))),
% 3.40/2.55 inference(transitivity,[status(thm)],[3210, 3208])).
% 3.40/2.55 tff(3212,plain,
% 3.40/2.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a590) | c0_1(a590) | (~c1_1(a590)))),
% 3.40/2.55 inference(quant_inst,[status(thm)],[])).
% 3.40/2.55 tff(3213,plain,
% 3.40/2.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a590) | c3_1(a603) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c1_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603))),
% 3.40/2.55 inference(modus_ponens,[status(thm)],[3212, 3211])).
% 3.40/2.55 tff(3214,plain,
% 3.40/2.55 (~c1_1(a590)),
% 3.40/2.55 inference(unit_resolution,[status(thm)],[3213, 107, 3194, 3207, 3206, 3181, 3205, 3204, 45, 258, 3195])).
% 3.40/2.55 tff(3215,plain,
% 3.40/2.55 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c2_1(a590) | c3_1(a590) | c1_1(a603) | (~ndr1_0) | c1_1(a590) | (~c2_1(a603)) | (~c0_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c2_1(a590) | c3_1(a590) | c1_1(a603) | (~ndr1_0) | c1_1(a590) | (~c2_1(a603)) | (~c0_1(a603)))),
% 3.40/2.55 inference(rewrite,[status(thm)],[])).
% 3.40/2.55 tff(3216,plain,
% 3.40/2.55 ((hskp26 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c3_1(a590) | c1_1(a590) | c2_1(a590)) <=> (hskp26 | c2_1(a590) | c3_1(a590) | c1_1(a603) | (~ndr1_0) | c1_1(a590) | (~c2_1(a603)) | (~c0_1(a603)))),
% 3.40/2.55 inference(rewrite,[status(thm)],[])).
% 3.40/2.55 tff(3217,plain,
% 3.40/2.55 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c3_1(a590) | c1_1(a590) | c2_1(a590))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c2_1(a590) | c3_1(a590) | c1_1(a603) | (~ndr1_0) | c1_1(a590) | (~c2_1(a603)) | (~c0_1(a603))))),
% 3.40/2.55 inference(monotonicity,[status(thm)],[3216])).
% 3.40/2.55 tff(3218,plain,
% 3.40/2.55 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c3_1(a590) | c1_1(a590) | c2_1(a590))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c2_1(a590) | c3_1(a590) | c1_1(a603) | (~ndr1_0) | c1_1(a590) | (~c2_1(a603)) | (~c0_1(a603)))),
% 3.40/2.55 inference(transitivity,[status(thm)],[3217, 3215])).
% 3.40/2.55 tff(3219,plain,
% 3.40/2.55 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c3_1(a590) | c1_1(a590) | c2_1(a590))),
% 3.40/2.55 inference(quant_inst,[status(thm)],[])).
% 3.40/2.55 tff(3220,plain,
% 3.40/2.55 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c2_1(a590) | c3_1(a590) | c1_1(a603) | (~ndr1_0) | c1_1(a590) | (~c2_1(a603)) | (~c0_1(a603))),
% 3.40/2.55 inference(modus_ponens,[status(thm)],[3219, 3218])).
% 3.40/2.55 tff(3221,plain,
% 3.40/2.55 (hskp26),
% 3.40/2.55 inference(unit_resolution,[status(thm)],[3220, 107, 3194, 3184, 3181, 3193, 995, 3195, 3214])).
% 3.40/2.55 tff(3222,plain,
% 3.40/2.55 (c2_1(a583)),
% 3.40/2.55 inference(unit_resolution,[status(thm)],[391, 3221])).
% 3.40/2.55 tff(3223,plain,
% 3.40/2.55 (c1_1(a583)),
% 3.40/2.55 inference(unit_resolution,[status(thm)],[351, 3221])).
% 3.40/2.55 tff(3224,plain,
% 3.40/2.55 (c0_1(a583)),
% 3.40/2.55 inference(unit_resolution,[status(thm)],[362, 3221])).
% 3.40/2.55 tff(3225,plain,
% 3.40/2.55 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c3_1(a590) | c1_1(a603) | c3_1(a603) | c0_1(a590) | (~ndr1_0) | c1_1(a590) | (~c2_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c3_1(a590) | c1_1(a603) | c3_1(a603) | c0_1(a590) | (~ndr1_0) | c1_1(a590) | (~c2_1(a603)))),
% 3.40/2.55 inference(rewrite,[status(thm)],[])).
% 3.40/2.55 tff(3226,plain,
% 3.40/2.55 ((hskp2 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c3_1(a590) | c1_1(a590) | c0_1(a590)) <=> (hskp2 | c3_1(a590) | c1_1(a603) | c3_1(a603) | c0_1(a590) | (~ndr1_0) | c1_1(a590) | (~c2_1(a603)))),
% 3.40/2.55 inference(rewrite,[status(thm)],[])).
% 3.40/2.55 tff(3227,plain,
% 3.40/2.55 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c3_1(a590) | c1_1(a590) | c0_1(a590))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c3_1(a590) | c1_1(a603) | c3_1(a603) | c0_1(a590) | (~ndr1_0) | c1_1(a590) | (~c2_1(a603))))),
% 3.40/2.55 inference(monotonicity,[status(thm)],[3226])).
% 3.40/2.55 tff(3228,plain,
% 3.40/2.55 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c3_1(a590) | c1_1(a590) | c0_1(a590))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c3_1(a590) | c1_1(a603) | c3_1(a603) | c0_1(a590) | (~ndr1_0) | c1_1(a590) | (~c2_1(a603)))),
% 3.40/2.55 inference(transitivity,[status(thm)],[3227, 3225])).
% 3.40/2.55 tff(3229,plain,
% 3.40/2.55 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c3_1(a590) | c1_1(a590) | c0_1(a590))),
% 3.40/2.55 inference(quant_inst,[status(thm)],[])).
% 3.40/2.55 tff(3230,plain,
% 3.40/2.55 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c3_1(a590) | c1_1(a603) | c3_1(a603) | c0_1(a590) | (~ndr1_0) | c1_1(a590) | (~c2_1(a603))),
% 3.40/2.55 inference(modus_ponens,[status(thm)],[3229, 3228])).
% 3.40/2.55 tff(3231,plain,
% 3.40/2.55 (hskp2),
% 3.40/2.55 inference(unit_resolution,[status(thm)],[3230, 107, 3181, 3193, 3205, 45, 200, 3195, 3214])).
% 3.40/2.55 tff(3232,plain,
% 3.40/2.55 (~c3_1(a586)),
% 3.40/2.55 inference(unit_resolution,[status(thm)],[218, 3231])).
% 3.40/2.55 tff(3233,plain,
% 3.40/2.55 (c2_1(a586)),
% 3.40/2.55 inference(unit_resolution,[status(thm)],[1474, 3231])).
% 3.40/2.55 tff(3234,plain,
% 3.40/2.55 (c1_1(a586)),
% 3.40/2.55 inference(unit_resolution,[status(thm)],[229, 3231])).
% 3.40/2.55 tff(3235,plain,
% 3.40/2.55 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c3_1(a599)) | (~c2_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c3_1(a599)) | (~c2_1(a599)))),
% 3.40/2.55 inference(rewrite,[status(thm)],[])).
% 3.40/2.55 tff(3236,plain,
% 3.40/2.55 ((hskp28 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599))) <=> (hskp28 | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c3_1(a599)) | (~c2_1(a599)))),
% 3.40/2.55 inference(rewrite,[status(thm)],[])).
% 3.40/2.55 tff(3237,plain,
% 3.40/2.55 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c3_1(a599)) | (~c2_1(a599))))),
% 3.40/2.55 inference(monotonicity,[status(thm)],[3236])).
% 3.40/2.55 tff(3238,plain,
% 3.40/2.55 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c3_1(a599)) | (~c2_1(a599)))),
% 3.40/2.55 inference(transitivity,[status(thm)],[3237, 3235])).
% 3.40/2.55 tff(3239,plain,
% 3.40/2.55 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)))),
% 3.40/2.55 inference(quant_inst,[status(thm)],[])).
% 3.40/2.55 tff(3240,plain,
% 3.40/2.55 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c3_1(a599)) | (~c2_1(a599))),
% 3.40/2.55 inference(modus_ponens,[status(thm)],[3239, 3238])).
% 3.40/2.55 tff(3241,plain,
% 3.40/2.55 (hskp28),
% 3.40/2.55 inference(unit_resolution,[status(thm)],[3240, 107, 3207, 3206, 3234, 3233, 3204, 3232, 1748])).
% 3.40/2.55 tff(3242,plain,
% 3.40/2.55 (c3_1(a612)),
% 3.40/2.55 inference(unit_resolution,[status(thm)],[1139, 3241])).
% 3.40/2.55 tff(3243,plain,
% 3.40/2.55 (c2_1(a612)),
% 3.40/2.55 inference(unit_resolution,[status(thm)],[1150, 3241])).
% 3.40/2.55 tff(3244,plain,
% 3.40/2.55 (c1_1(a612)),
% 3.40/2.55 inference(unit_resolution,[status(thm)],[1435, 3241])).
% 3.40/2.55 tff(3245,plain,
% 3.40/2.55 (hskp10),
% 3.40/2.55 inference(unit_resolution,[status(thm)],[1535, 107, 3244, 3243, 3242, 3224, 3223, 3222, 21])).
% 3.40/2.55 tff(3246,plain,
% 3.40/2.55 (~c1_1(a598)),
% 3.40/2.55 inference(unit_resolution,[status(thm)],[911, 3245])).
% 3.40/2.55 tff(3247,plain,
% 3.40/2.55 (c0_1(a598)),
% 3.40/2.55 inference(unit_resolution,[status(thm)],[892, 3245])).
% 3.40/2.55 tff(3248,plain,
% 3.40/2.55 (c2_1(a598)),
% 3.40/2.55 inference(unit_resolution,[status(thm)],[1544, 107, 44, 3182, 3247, 3246, 43])).
% 3.40/2.55 tff(3249,plain,
% 3.40/2.55 (c0_1(a586)),
% 3.40/2.55 inference(unit_resolution,[status(thm)],[2309, 107, 3194, 3207, 3206, 3234, 3205, 3204, 3232, 258, 3195])).
% 3.40/2.55 tff(3250,plain,
% 3.40/2.55 (hskp17 | (~c0_1(a586))),
% 3.40/2.55 inference(unit_resolution,[status(thm)],[247, 107, 3183, 3234, 3232, 55])).
% 3.40/2.55 tff(3251,plain,
% 3.40/2.55 (hskp17),
% 3.40/2.55 inference(unit_resolution,[status(thm)],[3250, 3249])).
% 3.40/2.55 tff(3252,plain,
% 3.40/2.55 (~c1_1(a607)),
% 3.40/2.55 inference(unit_resolution,[status(thm)],[281, 3251])).
% 3.40/2.55 tff(3253,plain,
% 3.40/2.55 (~c0_1(a607)),
% 3.40/2.55 inference(unit_resolution,[status(thm)],[114, 3252, 3182])).
% 3.40/2.55 tff(3254,plain,
% 3.40/2.55 (hskp8 | hskp6 | c1_1(a607) | c0_1(a607)),
% 3.40/2.55 inference(unit_resolution,[status(thm)],[2180, 107, 3180, 450])).
% 3.40/2.55 tff(3255,plain,
% 3.40/2.55 (hskp8),
% 3.40/2.55 inference(unit_resolution,[status(thm)],[3254, 3252, 3182, 3253])).
% 3.40/2.55 tff(3256,plain,
% 3.40/2.55 (~c2_1(a593)),
% 3.40/2.55 inference(unit_resolution,[status(thm)],[555, 3255])).
% 3.40/2.55 tff(3257,plain,
% 3.40/2.55 (c1_1(a593)),
% 3.40/2.55 inference(unit_resolution,[status(thm)],[522, 3255])).
% 3.40/2.55 tff(3258,plain,
% 3.40/2.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a607) | c2_1(a607) | c2_1(a593) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c0_1(a593)) | (~c1_1(a593)) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a607) | c2_1(a607) | c2_1(a593) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c0_1(a593)) | (~c1_1(a593)) | (~c3_1(a607)))),
% 3.40/2.55 inference(rewrite,[status(thm)],[])).
% 3.40/2.55 tff(3259,plain,
% 3.40/2.55 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a593) | (~c1_1(a593)) | (~c0_1(a593)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607))) <=> (c1_1(a607) | c2_1(a607) | c2_1(a593) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c0_1(a593)) | (~c1_1(a593)) | (~c3_1(a607)))),
% 3.40/2.55 inference(rewrite,[status(thm)],[])).
% 3.40/2.55 tff(3260,plain,
% 3.40/2.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a593) | (~c1_1(a593)) | (~c0_1(a593)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a607) | c2_1(a607) | c2_1(a593) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c0_1(a593)) | (~c1_1(a593)) | (~c3_1(a607))))),
% 3.40/2.55 inference(monotonicity,[status(thm)],[3259])).
% 3.40/2.55 tff(3261,plain,
% 3.40/2.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a593) | (~c1_1(a593)) | (~c0_1(a593)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a607) | c2_1(a607) | c2_1(a593) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c0_1(a593)) | (~c1_1(a593)) | (~c3_1(a607)))),
% 3.40/2.55 inference(transitivity,[status(thm)],[3260, 3258])).
% 3.40/2.55 tff(3262,plain,
% 3.40/2.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a593) | (~c1_1(a593)) | (~c0_1(a593)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)))),
% 3.40/2.55 inference(quant_inst,[status(thm)],[])).
% 3.40/2.55 tff(3263,plain,
% 3.40/2.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a607) | c2_1(a607) | c2_1(a593) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c0_1(a593)) | (~c1_1(a593)) | (~c3_1(a607))),
% 3.40/2.55 inference(modus_ponens,[status(thm)],[3262, 3261])).
% 3.40/2.55 tff(3264,plain,
% 3.40/2.55 (~c0_1(a593)),
% 3.40/2.55 inference(unit_resolution,[status(thm)],[3263, 107, 2292, 2281, 2270, 3180, 3257, 3252, 22, 3256, 1106])).
% 3.40/2.55 tff(3265,plain,
% 3.40/2.55 (c3_1(a593)),
% 3.40/2.55 inference(unit_resolution,[status(thm)],[511, 3255])).
% 3.40/2.55 tff(3266,plain,
% 3.40/2.55 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c3_1(a590) | c0_1(a590) | (~ndr1_0) | c1_1(a590) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c3_1(a590) | c0_1(a590) | (~ndr1_0) | c1_1(a590) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)))),
% 3.40/2.55 inference(rewrite,[status(thm)],[])).
% 3.40/2.55 tff(3267,plain,
% 3.40/2.55 ((hskp1 | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)) | c3_1(a590) | c1_1(a590) | c0_1(a590)) <=> (hskp1 | c3_1(a590) | c0_1(a590) | (~ndr1_0) | c1_1(a590) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)))),
% 3.40/2.55 inference(rewrite,[status(thm)],[])).
% 3.40/2.55 tff(3268,plain,
% 3.40/2.55 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)) | c3_1(a590) | c1_1(a590) | c0_1(a590))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c3_1(a590) | c0_1(a590) | (~ndr1_0) | c1_1(a590) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593))))),
% 3.40/2.55 inference(monotonicity,[status(thm)],[3267])).
% 3.40/2.55 tff(3269,plain,
% 3.40/2.55 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)) | c3_1(a590) | c1_1(a590) | c0_1(a590))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c3_1(a590) | c0_1(a590) | (~ndr1_0) | c1_1(a590) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)))),
% 3.40/2.55 inference(transitivity,[status(thm)],[3268, 3266])).
% 3.40/2.55 tff(3270,plain,
% 3.40/2.55 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)) | c3_1(a590) | c1_1(a590) | c0_1(a590))),
% 3.40/2.55 inference(quant_inst,[status(thm)],[])).
% 3.40/2.55 tff(3271,plain,
% 3.40/2.55 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c3_1(a590) | c0_1(a590) | (~ndr1_0) | c1_1(a590) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593))),
% 3.40/2.55 inference(modus_ponens,[status(thm)],[3270, 3269])).
% 3.40/2.55 tff(3272,plain,
% 3.40/2.55 (hskp1),
% 3.40/2.55 inference(unit_resolution,[status(thm)],[3271, 107, 3257, 3265, 3181, 45, 1555, 3264, 3214])).
% 3.40/2.55 tff(3273,plain,
% 3.40/2.55 (~c0_1(a585)),
% 3.40/2.55 inference(unit_resolution,[status(thm)],[1250, 3272])).
% 3.40/2.55 tff(3274,plain,
% 3.40/2.55 (c2_1(a585)),
% 3.40/2.55 inference(unit_resolution,[status(thm)],[1261, 3272])).
% 3.40/2.55 tff(3275,plain,
% 3.40/2.55 (c1_1(a585)),
% 3.40/2.55 inference(unit_resolution,[status(thm)],[1272, 3272])).
% 3.40/2.55 tff(3276,plain,
% 3.40/2.55 (c3_1(a598)),
% 3.40/2.55 inference(unit_resolution,[status(thm)],[881, 3245])).
% 3.40/2.55 tff(3277,plain,
% 3.40/2.55 ($false),
% 3.40/2.55 inference(unit_resolution,[status(thm)],[1631, 107, 3180, 3247, 3276, 3275, 3274, 3252, 22, 3273, 11, 3248])).
% 3.40/2.55 tff(3278,plain,(c2_1(a590) | c2_1(a607) | hskp22 | c3_1(a590) | c0_1(a590)), inference(lemma,lemma(discharge,[]))).
% 3.40/2.55 tff(3279,plain,
% 3.40/2.55 (c2_1(a590)),
% 3.40/2.55 inference(unit_resolution,[status(thm)],[3278, 3181, 44, 22, 45])).
% 3.40/2.55 tff(3280,plain,
% 3.40/2.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a607)))),
% 3.40/2.55 inference(rewrite,[status(thm)],[])).
% 3.40/2.55 tff(3281,plain,
% 3.40/2.55 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a590) | (~c1_1(a590)) | (~c2_1(a590))) <=> (c1_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a607)))),
% 3.40/2.55 inference(rewrite,[status(thm)],[])).
% 3.40/2.55 tff(3282,plain,
% 3.40/2.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a590) | (~c1_1(a590)) | (~c2_1(a590)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a607))))),
% 3.40/2.55 inference(monotonicity,[status(thm)],[3281])).
% 3.40/2.55 tff(3283,plain,
% 3.40/2.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a590) | (~c1_1(a590)) | (~c2_1(a590)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a607)))),
% 3.40/2.55 inference(transitivity,[status(thm)],[3282, 3280])).
% 3.40/2.55 tff(3284,plain,
% 3.40/2.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a590) | (~c1_1(a590)) | (~c2_1(a590)))),
% 3.40/2.55 inference(quant_inst,[status(thm)],[])).
% 3.40/2.55 tff(3285,plain,
% 3.40/2.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a607))),
% 3.40/2.55 inference(modus_ponens,[status(thm)],[3284, 3283])).
% 3.40/2.55 tff(3286,plain,
% 3.40/2.55 (~c1_1(a590)),
% 3.40/2.55 inference(unit_resolution,[status(thm)],[3285, 107, 2318, 2317, 2316, 321, 863, 66, 22, 45, 11])).
% 3.40/2.55 tff(3287,plain,
% 3.40/2.55 (((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp5 | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | c1_1(a590))) <=> ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp5 | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | c1_1(a590))),
% 3.40/2.55 inference(rewrite,[status(thm)],[])).
% 3.40/2.55 tff(3288,plain,
% 3.40/2.55 ((hskp6 | hskp5 | (~ndr1_0) | c1_1(a590) | c0_1(a590) | (~c2_1(a590))) <=> (hskp6 | hskp5 | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | c1_1(a590))),
% 3.40/2.55 inference(rewrite,[status(thm)],[])).
% 3.40/2.55 tff(3289,plain,
% 3.40/2.55 (((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp5 | (~ndr1_0) | c1_1(a590) | c0_1(a590) | (~c2_1(a590)))) <=> ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp5 | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | c1_1(a590)))),
% 3.40/2.55 inference(monotonicity,[status(thm)],[3288])).
% 3.40/2.55 tff(3290,plain,
% 3.40/2.55 (((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp5 | (~ndr1_0) | c1_1(a590) | c0_1(a590) | (~c2_1(a590)))) <=> ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp5 | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | c1_1(a590))),
% 3.40/2.55 inference(transitivity,[status(thm)],[3289, 3287])).
% 3.40/2.55 tff(3291,plain,
% 3.40/2.55 ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp5 | (~ndr1_0) | c1_1(a590) | c0_1(a590) | (~c2_1(a590)))),
% 3.40/2.55 inference(quant_inst,[status(thm)],[])).
% 3.40/2.55 tff(3292,plain,
% 3.40/2.55 ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp5 | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | c1_1(a590)),
% 3.40/2.55 inference(modus_ponens,[status(thm)],[3291, 3290])).
% 3.40/2.55 tff(3293,plain,
% 3.40/2.55 (hskp6 | hskp5 | (~c2_1(a590)) | c1_1(a590)),
% 3.40/2.55 inference(unit_resolution,[status(thm)],[3292, 107, 45, 573])).
% 3.40/2.55 tff(3294,plain,
% 3.40/2.55 (hskp5),
% 3.40/2.55 inference(unit_resolution,[status(thm)],[3293, 3286, 67, 863])).
% 3.40/2.55 tff(3295,plain,
% 3.40/2.55 (~c2_1(a589)),
% 3.40/2.55 inference(unit_resolution,[status(thm)],[586, 3294])).
% 3.40/2.55 tff(3296,plain,
% 3.40/2.55 (c1_1(a589)),
% 3.40/2.55 inference(unit_resolution,[status(thm)],[597, 3294])).
% 3.40/2.55 tff(3297,plain,
% 3.40/2.55 (c0_1(a589)),
% 3.40/2.55 inference(unit_resolution,[status(thm)],[608, 3294])).
% 3.40/2.55 tff(3298,plain,
% 3.40/2.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a607) | c2_1(a607) | c2_1(a589) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c0_1(a589)) | (~c1_1(a589)) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a607) | c2_1(a607) | c2_1(a589) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c0_1(a589)) | (~c1_1(a589)) | (~c3_1(a607)))),
% 3.40/2.55 inference(rewrite,[status(thm)],[])).
% 3.40/2.55 tff(3299,plain,
% 3.40/2.55 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a589) | (~c1_1(a589)) | (~c0_1(a589)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607))) <=> (c1_1(a607) | c2_1(a607) | c2_1(a589) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c0_1(a589)) | (~c1_1(a589)) | (~c3_1(a607)))),
% 3.40/2.55 inference(rewrite,[status(thm)],[])).
% 3.40/2.55 tff(3300,plain,
% 3.40/2.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a589) | (~c1_1(a589)) | (~c0_1(a589)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a607) | c2_1(a607) | c2_1(a589) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c0_1(a589)) | (~c1_1(a589)) | (~c3_1(a607))))),
% 3.40/2.55 inference(monotonicity,[status(thm)],[3299])).
% 3.40/2.55 tff(3301,plain,
% 3.40/2.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a589) | (~c1_1(a589)) | (~c0_1(a589)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a607) | c2_1(a607) | c2_1(a589) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c0_1(a589)) | (~c1_1(a589)) | (~c3_1(a607)))),
% 3.40/2.55 inference(transitivity,[status(thm)],[3300, 3298])).
% 3.40/2.55 tff(3302,plain,
% 3.40/2.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a589) | (~c1_1(a589)) | (~c0_1(a589)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)))),
% 3.40/2.55 inference(quant_inst,[status(thm)],[])).
% 3.40/2.55 tff(3303,plain,
% 3.40/2.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a607) | c2_1(a607) | c2_1(a589) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c0_1(a589)) | (~c1_1(a589)) | (~c3_1(a607))),
% 3.40/2.55 inference(modus_ponens,[status(thm)],[3302, 3301])).
% 3.40/2.55 tff(3304,plain,
% 3.40/2.55 ($false),
% 3.40/2.55 inference(unit_resolution,[status(thm)],[3303, 107, 2318, 2317, 2316, 321, 3297, 3296, 66, 22, 3295, 1106])).
% 3.40/2.55 tff(3305,plain,(c1_1(a607) | (~c0_1(a678)) | (~c2_1(a678)) | (~c3_1(a678)) | (~c3_1(a607)) | c2_1(a607) | hskp6 | (~c2_1(a590)) | c0_1(a590)), inference(lemma,lemma(discharge,[]))).
% 3.40/2.55 tff(3306,plain,
% 3.40/2.55 (c1_1(a607)),
% 3.40/2.55 inference(unit_resolution,[status(thm)],[3305, 3182, 2281, 2270, 3180, 22, 2292, 3279, 45])).
% 3.40/2.55 tff(3307,plain,
% 3.40/2.55 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp14 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a607)))),
% 3.40/2.56 inference(rewrite,[status(thm)],[])).
% 3.40/2.56 tff(3308,plain,
% 3.40/2.56 ((hskp14 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a607) | (~c1_1(a607)) | (~c3_1(a607))) <=> (hskp14 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a607)))),
% 3.40/2.56 inference(rewrite,[status(thm)],[])).
% 3.40/2.56 tff(3309,plain,
% 3.40/2.56 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a607) | (~c1_1(a607)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a607))))),
% 3.40/2.56 inference(monotonicity,[status(thm)],[3308])).
% 3.40/2.56 tff(3310,plain,
% 3.40/2.56 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a607) | (~c1_1(a607)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp14 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a607)))),
% 3.40/2.56 inference(transitivity,[status(thm)],[3309, 3307])).
% 3.40/2.56 tff(3311,plain,
% 3.40/2.56 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a607) | (~c1_1(a607)) | (~c3_1(a607)))),
% 3.40/2.56 inference(quant_inst,[status(thm)],[])).
% 3.40/2.56 tff(3312,plain,
% 3.40/2.56 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp14 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a607))),
% 3.40/2.56 inference(modus_ponens,[status(thm)],[3311, 3310])).
% 3.40/2.56 tff(3313,plain,
% 3.40/2.56 (hskp14 | (~c1_1(a607)) | (~c3_1(a607))),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[3312, 107, 2292, 2281, 2270, 22, 550])).
% 3.40/2.56 tff(3314,plain,
% 3.40/2.56 (hskp14),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[3313, 3306, 3180])).
% 3.40/2.56 tff(3315,plain,
% 3.40/2.56 (~c1_1(a603)),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[171, 3314])).
% 3.40/2.56 tff(3316,plain,
% 3.40/2.56 (c0_1(a603)),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[182, 3314])).
% 3.40/2.56 tff(3317,plain,
% 3.40/2.56 (c2_1(a603)),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[189, 107, 44, 3182, 3316, 3315, 43])).
% 3.40/2.56 tff(3318,plain,
% 3.40/2.56 (~hskp17),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[281, 3306])).
% 3.40/2.56 tff(3319,plain,
% 3.40/2.56 (~c3_1(a603)),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[205, 3314])).
% 3.40/2.56 tff(3320,plain,
% 3.40/2.56 (hskp26),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[411, 1638])).
% 3.40/2.56 tff(3321,plain,
% 3.40/2.56 (c0_1(a583)),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[362, 3320])).
% 3.40/2.56 tff(3322,plain,
% 3.40/2.56 (c1_1(a583)),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[351, 3320])).
% 3.40/2.56 tff(3323,plain,
% 3.40/2.56 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a583)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp4 | (~ndr1_0) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a583)))),
% 3.40/2.56 inference(rewrite,[status(thm)],[])).
% 3.40/2.56 tff(3324,plain,
% 3.40/2.56 ((hskp17 | hskp4 | (~ndr1_0) | c3_1(a583) | (~c1_1(a583)) | (~c0_1(a583))) <=> (hskp17 | hskp4 | (~ndr1_0) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a583)))),
% 3.40/2.56 inference(rewrite,[status(thm)],[])).
% 3.40/2.56 tff(3325,plain,
% 3.40/2.56 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c3_1(a583) | (~c1_1(a583)) | (~c0_1(a583)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a583))))),
% 3.40/2.56 inference(monotonicity,[status(thm)],[3324])).
% 3.40/2.56 tff(3326,plain,
% 3.40/2.56 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c3_1(a583) | (~c1_1(a583)) | (~c0_1(a583)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp4 | (~ndr1_0) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a583)))),
% 3.40/2.56 inference(transitivity,[status(thm)],[3325, 3323])).
% 3.40/2.56 tff(3327,plain,
% 3.40/2.56 ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c3_1(a583) | (~c1_1(a583)) | (~c0_1(a583)))),
% 3.40/2.56 inference(quant_inst,[status(thm)],[])).
% 3.40/2.56 tff(3328,plain,
% 3.40/2.56 ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp4 | (~ndr1_0) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a583))),
% 3.40/2.56 inference(modus_ponens,[status(thm)],[3327, 3326])).
% 3.40/2.56 tff(3329,plain,
% 3.40/2.56 (c3_1(a583)),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[3328, 107, 2987, 3183, 3321, 3322, 55])).
% 3.40/2.56 tff(3330,plain,
% 3.40/2.56 (c2_1(a583)),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[391, 3320])).
% 3.40/2.56 tff(3331,plain,
% 3.40/2.56 (hskp10),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[1999, 107, 3321, 3322, 3330, 21, 3329])).
% 3.40/2.56 tff(3332,plain,
% 3.40/2.56 (~c1_1(a598)),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[911, 3331])).
% 3.40/2.56 tff(3333,plain,
% 3.40/2.56 (c3_1(a598)),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[881, 3331])).
% 3.40/2.56 tff(3334,plain,
% 3.40/2.56 (c0_1(a598)),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[892, 3331])).
% 3.40/2.56 tff(3335,plain,
% 3.40/2.56 (hskp23),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[1688, 1638, 107, 3334, 3333, 3332, 1648])).
% 3.40/2.56 tff(3336,plain,
% 3.40/2.56 (~c1_1(a636)),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[475, 3335])).
% 3.40/2.56 tff(3337,plain,
% 3.40/2.56 (~c0_1(a636)),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[481, 3335])).
% 3.40/2.56 tff(3338,plain,
% 3.40/2.56 (c3_1(a636)),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[492, 3335])).
% 3.40/2.56 tff(3339,assumption,(c2_1(a636)), introduced(assumption)).
% 3.40/2.56 tff(3340,assumption,(c3_1(a583)), introduced(assumption)).
% 3.40/2.56 tff(3341,plain,
% 3.40/2.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a636)) | (~c2_1(a636)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a636)) | (~c2_1(a636)))),
% 3.40/2.56 inference(rewrite,[status(thm)],[])).
% 3.40/2.56 tff(3342,plain,
% 3.40/2.56 (((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a636) | (~c3_1(a636)) | (~c2_1(a636)) | c1_1(a636) | c0_1(a636) | (~c2_1(a636))) <=> (c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a636)) | (~c2_1(a636)))),
% 3.40/2.56 inference(rewrite,[status(thm)],[])).
% 3.40/2.56 tff(3343,plain,
% 3.40/2.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a636) | (~c3_1(a636)) | (~c2_1(a636)) | c1_1(a636) | c0_1(a636) | (~c2_1(a636)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a636)) | (~c2_1(a636))))),
% 3.40/2.56 inference(monotonicity,[status(thm)],[3342])).
% 3.40/2.56 tff(3344,plain,
% 3.40/2.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a636) | (~c3_1(a636)) | (~c2_1(a636)) | c1_1(a636) | c0_1(a636) | (~c2_1(a636)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a636)) | (~c2_1(a636)))),
% 3.40/2.56 inference(transitivity,[status(thm)],[3343, 3341])).
% 3.40/2.56 tff(3345,plain,
% 3.40/2.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a636) | (~c3_1(a636)) | (~c2_1(a636)) | c1_1(a636) | c0_1(a636) | (~c2_1(a636)))),
% 3.40/2.56 inference(quant_inst,[status(thm)],[])).
% 3.40/2.56 tff(3346,plain,
% 3.40/2.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a636) | c1_1(a636) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a636)) | (~c2_1(a636))),
% 3.40/2.56 inference(modus_ponens,[status(thm)],[3345, 3344])).
% 3.40/2.56 tff(3347,plain,
% 3.40/2.56 ($false),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[3346, 107, 1651, 1650, 725, 724, 723, 65, 3340, 3339])).
% 3.40/2.56 tff(3348,plain,(c1_1(a636) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a636)) | c0_1(a636) | (~c3_1(a583)) | (~c2_1(a636))), inference(lemma,lemma(discharge,[]))).
% 3.40/2.56 tff(3349,plain,
% 3.40/2.56 (~c2_1(a636)),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[3348, 3338, 3322, 3329, 3337, 3336, 3321])).
% 3.40/2.56 tff(3350,plain,
% 3.40/2.56 (c2_1(a598)),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[1544, 107, 44, 3182, 3334, 3332, 43])).
% 3.40/2.56 tff(3351,plain,
% 3.40/2.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a590) | c3_1(a603) | c1_1(a598) | c0_1(a590) | (~ndr1_0) | (~c1_1(a590)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c2_1(a603)) | (~c0_1(a603)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a590) | c3_1(a603) | c1_1(a598) | c0_1(a590) | (~ndr1_0) | (~c1_1(a590)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c2_1(a603)) | (~c0_1(a603)))),
% 3.40/2.56 inference(rewrite,[status(thm)],[])).
% 3.40/2.56 tff(3352,plain,
% 3.40/2.56 (((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a598) | (~c3_1(a598)) | (~c2_1(a598)) | c3_1(a590) | c0_1(a590) | (~c1_1(a590))) <=> (c3_1(a590) | c3_1(a603) | c1_1(a598) | c0_1(a590) | (~ndr1_0) | (~c1_1(a590)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c2_1(a603)) | (~c0_1(a603)))),
% 3.40/2.56 inference(rewrite,[status(thm)],[])).
% 3.40/2.56 tff(3353,plain,
% 3.40/2.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a598) | (~c3_1(a598)) | (~c2_1(a598)) | c3_1(a590) | c0_1(a590) | (~c1_1(a590)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a590) | c3_1(a603) | c1_1(a598) | c0_1(a590) | (~ndr1_0) | (~c1_1(a590)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c2_1(a603)) | (~c0_1(a603))))),
% 3.40/2.56 inference(monotonicity,[status(thm)],[3352])).
% 3.40/2.56 tff(3354,plain,
% 3.40/2.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a598) | (~c3_1(a598)) | (~c2_1(a598)) | c3_1(a590) | c0_1(a590) | (~c1_1(a590)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a590) | c3_1(a603) | c1_1(a598) | c0_1(a590) | (~ndr1_0) | (~c1_1(a590)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c2_1(a603)) | (~c0_1(a603)))),
% 3.40/2.56 inference(transitivity,[status(thm)],[3353, 3351])).
% 3.40/2.56 tff(3355,plain,
% 3.40/2.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a598) | (~c3_1(a598)) | (~c2_1(a598)) | c3_1(a590) | c0_1(a590) | (~c1_1(a590)))),
% 3.40/2.56 inference(quant_inst,[status(thm)],[])).
% 3.40/2.56 tff(3356,plain,
% 3.40/2.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a590) | c3_1(a603) | c1_1(a598) | c0_1(a590) | (~ndr1_0) | (~c1_1(a590)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c2_1(a603)) | (~c0_1(a603))),
% 3.40/2.56 inference(modus_ponens,[status(thm)],[3355, 3354])).
% 3.40/2.56 tff(3357,plain,
% 3.40/2.56 (~c1_1(a590)),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[3356, 107, 1009, 3333, 3181, 997, 3332, 45, 258, 3350, 1010])).
% 3.40/2.56 tff(3358,plain,
% 3.40/2.56 (hskp5),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[3293, 3357, 3182, 863])).
% 3.40/2.56 tff(3359,plain,
% 3.40/2.56 (~c2_1(a589)),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[586, 3358])).
% 3.40/2.56 tff(3360,plain,
% 3.40/2.56 (c1_1(a589)),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[597, 3358])).
% 3.40/2.56 tff(3361,plain,
% 3.40/2.56 (c0_1(a589)),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[608, 3358])).
% 3.40/2.56 tff(3362,plain,
% 3.40/2.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a636) | c2_1(a589) | (~ndr1_0) | (~c0_1(a589)) | (~c1_1(a589)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c3_1(a636)) | c2_1(a636))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a636) | c2_1(a589) | (~ndr1_0) | (~c0_1(a589)) | (~c1_1(a589)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c3_1(a636)) | c2_1(a636))),
% 3.40/2.56 inference(rewrite,[status(thm)],[])).
% 3.40/2.56 tff(3363,plain,
% 3.40/2.56 (((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c2_1(a589) | (~c1_1(a589)) | (~c0_1(a589)) | c1_1(a636) | c2_1(a636) | (~c3_1(a636))) <=> (c1_1(a636) | c2_1(a589) | (~ndr1_0) | (~c0_1(a589)) | (~c1_1(a589)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c3_1(a636)) | c2_1(a636))),
% 3.40/2.56 inference(rewrite,[status(thm)],[])).
% 3.40/2.56 tff(3364,plain,
% 3.40/2.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c2_1(a589) | (~c1_1(a589)) | (~c0_1(a589)) | c1_1(a636) | c2_1(a636) | (~c3_1(a636)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a636) | c2_1(a589) | (~ndr1_0) | (~c0_1(a589)) | (~c1_1(a589)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c3_1(a636)) | c2_1(a636)))),
% 3.40/2.56 inference(monotonicity,[status(thm)],[3363])).
% 3.40/2.56 tff(3365,plain,
% 3.40/2.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c2_1(a589) | (~c1_1(a589)) | (~c0_1(a589)) | c1_1(a636) | c2_1(a636) | (~c3_1(a636)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a636) | c2_1(a589) | (~ndr1_0) | (~c0_1(a589)) | (~c1_1(a589)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c3_1(a636)) | c2_1(a636))),
% 3.40/2.56 inference(transitivity,[status(thm)],[3364, 3362])).
% 3.40/2.56 tff(3366,plain,
% 3.40/2.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c2_1(a589) | (~c1_1(a589)) | (~c0_1(a589)) | c1_1(a636) | c2_1(a636) | (~c3_1(a636)))),
% 3.40/2.56 inference(quant_inst,[status(thm)],[])).
% 3.40/2.56 tff(3367,plain,
% 3.40/2.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a636) | c2_1(a589) | (~ndr1_0) | (~c0_1(a589)) | (~c1_1(a589)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c3_1(a636)) | c2_1(a636)),
% 3.40/2.56 inference(modus_ponens,[status(thm)],[3366, 3365])).
% 3.40/2.56 tff(3368,plain,
% 3.40/2.56 ($false),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[3367, 107, 3338, 3334, 3333, 3361, 3360, 3336, 3359, 1106, 3350, 3349])).
% 3.40/2.56 tff(3369,plain,(hskp11 | (~c2_1(a590)) | c0_1(a590) | (~c0_1(a603)) | c3_1(a590) | c3_1(a603) | (~c2_1(a603)) | hskp22 | hskp17), inference(lemma,lemma(discharge,[]))).
% 3.40/2.56 tff(3370,plain,
% 3.40/2.56 (hskp11),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[3369, 3279, 45, 3316, 3181, 3319, 3317, 44, 3318])).
% 3.40/2.56 tff(3371,plain,
% 3.40/2.56 (~c1_1(a599)),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[428, 3370])).
% 3.40/2.56 tff(3372,plain,
% 3.40/2.56 (c3_1(a599)),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[422, 3370])).
% 3.40/2.56 tff(3373,plain,
% 3.40/2.56 (c2_1(a599)),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[439, 3370])).
% 3.40/2.56 tff(3374,plain,
% 3.40/2.56 (~c1_1(a590)),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[3213, 107, 3316, 3373, 3372, 3181, 3319, 3371, 45, 258, 3317])).
% 3.40/2.56 tff(3375,plain,
% 3.40/2.56 (hskp2 | c1_1(a590) | (~c2_1(a603))),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[3230, 107, 3181, 3315, 3319, 45, 200])).
% 3.40/2.56 tff(3376,plain,
% 3.40/2.56 (hskp2),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[3375, 3374, 3317])).
% 3.40/2.56 tff(3377,plain,
% 3.40/2.56 (~c3_1(a586)),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[218, 3376])).
% 3.40/2.56 tff(3378,plain,
% 3.40/2.56 (c1_1(a586)),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[229, 3376])).
% 3.40/2.56 tff(3379,plain,
% 3.40/2.56 (~c0_1(a586)),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[247, 107, 3318, 3183, 3378, 3377, 55])).
% 3.40/2.56 tff(3380,plain,
% 3.40/2.56 ($false),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[2309, 107, 3316, 3373, 3372, 3378, 3319, 3371, 3377, 258, 3317, 3379])).
% 3.40/2.56 tff(3381,plain,(c3_1(a590) | c0_1(a590) | hskp22 | c2_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.40/2.56 tff(3382,plain,
% 3.40/2.56 (c3_1(a590)),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[3381, 45, 44, 22])).
% 3.40/2.56 tff(3383,plain,
% 3.40/2.56 (~hskp6),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[688, 3184])).
% 3.40/2.56 tff(3384,plain,
% 3.40/2.56 (~c0_1(a607)),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[114, 66, 67])).
% 3.40/2.56 tff(3385,plain,
% 3.40/2.56 (hskp8),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[3254, 66, 67, 3384])).
% 3.40/2.56 tff(3386,plain,
% 3.40/2.56 (~c2_1(a593)),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[555, 3385])).
% 3.40/2.56 tff(3387,plain,
% 3.40/2.56 (c3_1(a593)),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[511, 3385])).
% 3.40/2.56 tff(3388,plain,
% 3.40/2.56 (c1_1(a593)),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[522, 3385])).
% 3.40/2.56 tff(3389,plain,
% 3.40/2.56 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | c2_1(a593) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a593)) | (~c1_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp14 | c2_1(a593) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a593)) | (~c1_1(a593)))),
% 3.40/2.56 inference(rewrite,[status(thm)],[])).
% 3.40/2.56 tff(3390,plain,
% 3.40/2.56 ((hskp14 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a593) | (~c1_1(a593)) | (~c3_1(a593))) <=> (hskp14 | c2_1(a593) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a593)) | (~c1_1(a593)))),
% 3.40/2.56 inference(rewrite,[status(thm)],[])).
% 3.40/2.56 tff(3391,plain,
% 3.40/2.56 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a593) | (~c1_1(a593)) | (~c3_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | c2_1(a593) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a593)) | (~c1_1(a593))))),
% 3.40/2.56 inference(monotonicity,[status(thm)],[3390])).
% 3.40/2.56 tff(3392,plain,
% 3.40/2.56 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a593) | (~c1_1(a593)) | (~c3_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp14 | c2_1(a593) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a593)) | (~c1_1(a593)))),
% 3.40/2.56 inference(transitivity,[status(thm)],[3391, 3389])).
% 3.40/2.56 tff(3393,plain,
% 3.40/2.56 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a593) | (~c1_1(a593)) | (~c3_1(a593)))),
% 3.40/2.56 inference(quant_inst,[status(thm)],[])).
% 3.40/2.56 tff(3394,plain,
% 3.40/2.56 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp14 | c2_1(a593) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a593)) | (~c1_1(a593))),
% 3.40/2.56 inference(modus_ponens,[status(thm)],[3393, 3392])).
% 3.40/2.56 tff(3395,plain,
% 3.40/2.56 (hskp14),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[3394, 107, 2292, 2281, 2270, 3388, 3387, 3386, 550])).
% 3.40/2.56 tff(3396,plain,
% 3.40/2.56 (hskp3),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[329, 3395, 3180, 66, 22])).
% 3.40/2.56 tff(3397,plain,
% 3.40/2.56 (~c1_1(a587)),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[939, 3396])).
% 3.40/2.56 tff(3398,plain,
% 3.40/2.56 (~c1_1(a603)),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[171, 3395])).
% 3.40/2.56 tff(3399,plain,
% 3.40/2.56 (c0_1(a603)),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[182, 3395])).
% 3.40/2.56 tff(3400,plain,
% 3.40/2.56 (~c3_1(a603)),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[205, 3395])).
% 3.40/2.56 tff(3401,plain,
% 3.40/2.56 (c0_1(a587)),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[961, 3396])).
% 3.40/2.56 tff(3402,plain,
% 3.40/2.56 (c2_1(a587)),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[950, 3396])).
% 3.40/2.56 tff(3403,plain,
% 3.40/2.56 ($false),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[1508, 3402, 3401, 22, 3180, 726, 66, 3400, 3399, 3398, 3397])).
% 3.40/2.56 tff(3404,plain,(c1_1(a607) | c2_1(a607) | hskp26 | hskp6 | hskp22), inference(lemma,lemma(discharge,[]))).
% 3.40/2.56 tff(3405,plain,
% 3.40/2.56 (c1_1(a607)),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[3404, 726, 22, 3383, 44])).
% 3.40/2.56 tff(3406,plain,
% 3.40/2.56 (hskp14),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[3313, 3405, 3180])).
% 3.40/2.56 tff(3407,plain,
% 3.40/2.56 (~c1_1(a603)),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[171, 3406])).
% 3.40/2.56 tff(3408,plain,
% 3.40/2.56 (c0_1(a603)),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[182, 3406])).
% 3.40/2.56 tff(3409,plain,
% 3.40/2.56 (c2_1(a603)),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[189, 107, 44, 3383, 3408, 3407, 43])).
% 3.40/2.56 tff(3410,plain,
% 3.40/2.56 (~hskp17),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[281, 3405])).
% 3.40/2.56 tff(3411,plain,
% 3.40/2.56 (^[U: $i] : refl((hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 3.40/2.56 inference(bind,[status(th)],[])).
% 3.40/2.56 tff(3412,plain,
% 3.40/2.56 (![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 3.40/2.56 inference(quant_intro,[status(thm)],[3411])).
% 3.40/2.56 tff(3413,plain,
% 3.40/2.56 (![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 3.40/2.56 inference(rewrite,[status(thm)],[])).
% 3.40/2.56 tff(3414,plain,
% 3.40/2.56 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp3) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp3))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp3) | hskp17) <=> ((hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp17))), rewrite(((hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp17) <=> (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp3) | hskp17) <=> (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 3.40/2.56 inference(bind,[status(th)],[])).
% 3.40/2.56 tff(3415,plain,
% 3.40/2.56 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp3) | hskp17) <=> ![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 3.40/2.56 inference(quant_intro,[status(thm)],[3414])).
% 3.40/2.56 tff(3416,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp3) | hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause154')).
% 3.40/2.56 tff(3417,plain,
% 3.40/2.56 (![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 3.40/2.56 inference(modus_ponens,[status(thm)],[3416, 3415])).
% 3.40/2.56 tff(3418,plain,
% 3.40/2.56 (![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 3.40/2.56 inference(modus_ponens,[status(thm)],[3417, 3413])).
% 3.40/2.56 tff(3419,plain,(
% 3.40/2.56 ![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 3.40/2.56 inference(skolemize,[status(sab)],[3418])).
% 3.40/2.56 tff(3420,plain,
% 3.40/2.56 (![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 3.40/2.56 inference(modus_ponens,[status(thm)],[3419, 3412])).
% 3.40/2.56 tff(3421,plain,
% 3.40/2.56 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp3 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c3_1(a607)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp3 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c3_1(a607)))),
% 3.40/2.56 inference(rewrite,[status(thm)],[])).
% 3.40/2.56 tff(3422,plain,
% 3.40/2.56 ((hskp17 | hskp3 | (~ndr1_0) | c2_1(a607) | (~c3_1(a607)) | (~c1_1(a607))) <=> (hskp17 | hskp3 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c3_1(a607)))),
% 3.40/2.56 inference(rewrite,[status(thm)],[])).
% 3.40/2.56 tff(3423,plain,
% 3.40/2.56 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c2_1(a607) | (~c3_1(a607)) | (~c1_1(a607)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp3 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c3_1(a607))))),
% 3.40/2.56 inference(monotonicity,[status(thm)],[3422])).
% 3.40/2.56 tff(3424,plain,
% 3.40/2.56 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c2_1(a607) | (~c3_1(a607)) | (~c1_1(a607)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp3 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c3_1(a607)))),
% 3.40/2.56 inference(transitivity,[status(thm)],[3423, 3421])).
% 3.40/2.56 tff(3425,plain,
% 3.40/2.56 ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c2_1(a607) | (~c3_1(a607)) | (~c1_1(a607)))),
% 3.40/2.56 inference(quant_inst,[status(thm)],[])).
% 3.40/2.56 tff(3426,plain,
% 3.40/2.56 ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp3 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c3_1(a607))),
% 3.40/2.56 inference(modus_ponens,[status(thm)],[3425, 3424])).
% 3.40/2.56 tff(3427,plain,
% 3.40/2.56 (hskp17 | hskp3 | (~c1_1(a607)) | (~c3_1(a607))),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[3426, 107, 22, 3420])).
% 3.40/2.56 tff(3428,plain,
% 3.40/2.56 (hskp3),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[3427, 3410, 3180, 3405])).
% 3.40/2.56 tff(3429,plain,
% 3.40/2.56 (~c1_1(a587)),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[939, 3428])).
% 3.40/2.56 tff(3430,plain,
% 3.40/2.56 (c2_1(a587)),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[950, 3428])).
% 3.40/2.56 tff(3431,plain,
% 3.40/2.56 (c0_1(a587)),
% 3.40/2.56 inference(unit_resolution,[status(thm)],[961, 3428])).
% 3.40/2.56 tff(3432,plain,
% 3.40/2.56 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c2_1(a590) | c0_1(a590) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | (~c1_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c2_1(a590) | c0_1(a590) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | (~c1_1(a590)))),
% 3.40/2.57 inference(rewrite,[status(thm)],[])).
% 3.40/2.57 tff(3433,plain,
% 3.40/2.57 ((hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a590) | c2_1(a590) | (~c1_1(a590))) <=> (hskp17 | c2_1(a590) | c0_1(a590) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | (~c1_1(a590)))),
% 3.40/2.57 inference(rewrite,[status(thm)],[])).
% 3.40/2.57 tff(3434,plain,
% 3.40/2.57 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a590) | c2_1(a590) | (~c1_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c2_1(a590) | c0_1(a590) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | (~c1_1(a590))))),
% 3.40/2.57 inference(monotonicity,[status(thm)],[3433])).
% 3.40/2.57 tff(3435,plain,
% 3.40/2.57 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a590) | c2_1(a590) | (~c1_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c2_1(a590) | c0_1(a590) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | (~c1_1(a590)))),
% 3.40/2.57 inference(transitivity,[status(thm)],[3434, 3432])).
% 3.40/2.57 tff(3436,plain,
% 3.40/2.57 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a590) | c2_1(a590) | (~c1_1(a590)))),
% 3.40/2.57 inference(quant_inst,[status(thm)],[])).
% 3.40/2.57 tff(3437,plain,
% 3.40/2.57 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c2_1(a590) | c0_1(a590) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | (~c1_1(a590))),
% 3.40/2.57 inference(modus_ponens,[status(thm)],[3436, 3435])).
% 3.40/2.57 tff(3438,plain,
% 3.40/2.57 (~c1_1(a590)),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[3437, 107, 3410, 3184, 3431, 3430, 45, 3429, 32])).
% 3.40/2.57 tff(3439,plain,
% 3.40/2.57 (((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | c2_1(a590) | c0_1(a590) | (~ndr1_0) | c1_1(a590))) <=> ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp0 | c2_1(a590) | c0_1(a590) | (~ndr1_0) | c1_1(a590))),
% 3.40/2.57 inference(rewrite,[status(thm)],[])).
% 3.40/2.57 tff(3440,plain,
% 3.40/2.57 ((hskp26 | hskp0 | (~ndr1_0) | c2_1(a590) | c1_1(a590) | c0_1(a590)) <=> (hskp26 | hskp0 | c2_1(a590) | c0_1(a590) | (~ndr1_0) | c1_1(a590))),
% 3.40/2.57 inference(rewrite,[status(thm)],[])).
% 3.40/2.57 tff(3441,plain,
% 3.40/2.57 (((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | (~ndr1_0) | c2_1(a590) | c1_1(a590) | c0_1(a590))) <=> ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | c2_1(a590) | c0_1(a590) | (~ndr1_0) | c1_1(a590)))),
% 3.40/2.57 inference(monotonicity,[status(thm)],[3440])).
% 3.40/2.57 tff(3442,plain,
% 3.40/2.57 (((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | (~ndr1_0) | c2_1(a590) | c1_1(a590) | c0_1(a590))) <=> ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp0 | c2_1(a590) | c0_1(a590) | (~ndr1_0) | c1_1(a590))),
% 3.40/2.57 inference(transitivity,[status(thm)],[3441, 3439])).
% 3.40/2.57 tff(3443,plain,
% 3.40/2.57 ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | (~ndr1_0) | c2_1(a590) | c1_1(a590) | c0_1(a590))),
% 3.40/2.57 inference(quant_inst,[status(thm)],[])).
% 3.40/2.57 tff(3444,plain,
% 3.40/2.57 ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp0 | c2_1(a590) | c0_1(a590) | (~ndr1_0) | c1_1(a590)),
% 3.40/2.57 inference(modus_ponens,[status(thm)],[3443, 3442])).
% 3.40/2.57 tff(3445,plain,
% 3.40/2.57 (hskp26 | hskp0 | c2_1(a590) | c1_1(a590)),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[3444, 107, 45, 1032])).
% 3.40/2.57 tff(3446,plain,
% 3.40/2.57 (hskp0),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[3445, 3438, 3184, 726])).
% 3.40/2.57 tff(3447,plain,
% 3.40/2.57 (~c2_1(a584)),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[1045, 3446])).
% 3.40/2.57 tff(3448,plain,
% 3.40/2.57 (~c0_1(a584)),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[1051, 3446])).
% 3.40/2.57 tff(3449,plain,
% 3.40/2.57 (c1_1(a584)),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[1062, 3446])).
% 3.40/2.57 tff(3450,plain,
% 3.40/2.57 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c1_1(a603) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a603)) | (~c0_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c1_1(a603) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a603)) | (~c0_1(a603)))),
% 3.40/2.57 inference(rewrite,[status(thm)],[])).
% 3.40/2.57 tff(3451,plain,
% 3.40/2.57 ((hskp17 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584))) <=> (hskp17 | c1_1(a603) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a603)) | (~c0_1(a603)))),
% 3.40/2.57 inference(rewrite,[status(thm)],[])).
% 3.40/2.57 tff(3452,plain,
% 3.40/2.57 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c1_1(a603) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a603)) | (~c0_1(a603))))),
% 3.40/2.57 inference(monotonicity,[status(thm)],[3451])).
% 3.40/2.57 tff(3453,plain,
% 3.40/2.57 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c1_1(a603) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a603)) | (~c0_1(a603)))),
% 3.40/2.57 inference(transitivity,[status(thm)],[3452, 3450])).
% 3.40/2.57 tff(3454,plain,
% 3.40/2.57 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584)))),
% 3.40/2.57 inference(quant_inst,[status(thm)],[])).
% 3.40/2.57 tff(3455,plain,
% 3.40/2.57 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c1_1(a603) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a603)) | (~c0_1(a603))),
% 3.40/2.57 inference(modus_ponens,[status(thm)],[3454, 3453])).
% 3.40/2.57 tff(3456,plain,
% 3.40/2.57 ($false),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[3455, 107, 3410, 3408, 3449, 3407, 3448, 3447, 32, 3409])).
% 3.40/2.57 tff(3457,plain,(hskp26 | c2_1(a590) | c0_1(a590) | hskp22 | c2_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.40/2.57 tff(3458,plain,
% 3.40/2.57 (hskp26),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[3457, 3184, 45, 44, 22])).
% 3.40/2.57 tff(3459,plain,
% 3.40/2.57 (c2_1(a583)),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[391, 3458])).
% 3.40/2.57 tff(3460,plain,
% 3.40/2.57 (c1_1(a583)),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[351, 3458])).
% 3.40/2.57 tff(3461,plain,
% 3.40/2.57 (c0_1(a583)),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[362, 3458])).
% 3.40/2.57 tff(3462,plain,
% 3.40/2.57 (c2_1(a603)),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[189, 107, 44, 67, 3399, 3398, 43])).
% 3.40/2.57 tff(3463,plain,
% 3.40/2.57 (hskp9),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[1518, 107, 1651, 1650, 1649, 3180, 66, 294, 3384])).
% 3.40/2.57 tff(3464,plain,
% 3.40/2.57 (~c3_1(a595)),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[1487, 3463])).
% 3.40/2.57 tff(3465,plain,
% 3.40/2.57 (~c1_1(a595)),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[1493, 3463])).
% 3.40/2.57 tff(3466,plain,
% 3.40/2.57 (~c0_1(a595)),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[1499, 3463])).
% 3.40/2.57 tff(3467,plain,
% 3.40/2.57 (hskp2),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[1574, 107, 3398, 3400, 3466, 3465, 3464, 200, 3462])).
% 3.40/2.57 tff(3468,plain,
% 3.40/2.57 (~c3_1(a586)),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[218, 3467])).
% 3.40/2.57 tff(3469,plain,
% 3.40/2.57 (hskp9),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[1518, 107, 3321, 3322, 3330, 3180, 66, 294, 3384])).
% 3.40/2.57 tff(3470,plain,
% 3.40/2.57 (~c3_1(a595)),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[1487, 3469])).
% 3.40/2.57 tff(3471,plain,
% 3.40/2.57 (~c0_1(a595)),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[1499, 3469])).
% 3.40/2.57 tff(3472,plain,
% 3.40/2.57 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | c0_1(a595) | c3_1(a595) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a595))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | c0_1(a595) | c3_1(a595) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a595))),
% 3.40/2.57 inference(rewrite,[status(thm)],[])).
% 3.40/2.57 tff(3473,plain,
% 3.40/2.57 ((hskp11 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c3_1(a595) | c0_1(a595) | c2_1(a595)) <=> (hskp11 | c0_1(a595) | c3_1(a595) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a595))),
% 3.40/2.57 inference(rewrite,[status(thm)],[])).
% 3.40/2.57 tff(3474,plain,
% 3.40/2.57 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c3_1(a595) | c0_1(a595) | c2_1(a595))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | c0_1(a595) | c3_1(a595) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a595)))),
% 3.40/2.57 inference(monotonicity,[status(thm)],[3473])).
% 3.40/2.57 tff(3475,plain,
% 3.40/2.57 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c3_1(a595) | c0_1(a595) | c2_1(a595))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | c0_1(a595) | c3_1(a595) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a595))),
% 3.40/2.57 inference(transitivity,[status(thm)],[3474, 3472])).
% 3.40/2.57 tff(3476,plain,
% 3.40/2.57 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c3_1(a595) | c0_1(a595) | c2_1(a595))),
% 3.40/2.57 inference(quant_inst,[status(thm)],[])).
% 3.40/2.57 tff(3477,plain,
% 3.40/2.57 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | c0_1(a595) | c3_1(a595) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a595)),
% 3.40/2.57 inference(modus_ponens,[status(thm)],[3476, 3475])).
% 3.40/2.57 tff(3478,plain,
% 3.40/2.57 (c2_1(a595)),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[3477, 1638, 107, 2292, 2281, 2270, 3471, 3470, 268])).
% 3.40/2.57 tff(3479,plain,
% 3.40/2.57 (~c1_1(a595)),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[1493, 3469])).
% 3.40/2.57 tff(3480,plain,
% 3.40/2.57 (((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp5 | c0_1(a595) | c1_1(a595) | (~ndr1_0) | (~c2_1(a595)))) <=> ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp5 | c0_1(a595) | c1_1(a595) | (~ndr1_0) | (~c2_1(a595)))),
% 3.40/2.57 inference(rewrite,[status(thm)],[])).
% 3.40/2.57 tff(3481,plain,
% 3.40/2.57 ((hskp6 | hskp5 | (~ndr1_0) | c1_1(a595) | c0_1(a595) | (~c2_1(a595))) <=> (hskp6 | hskp5 | c0_1(a595) | c1_1(a595) | (~ndr1_0) | (~c2_1(a595)))),
% 3.40/2.57 inference(rewrite,[status(thm)],[])).
% 3.40/2.57 tff(3482,plain,
% 3.40/2.57 (((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp5 | (~ndr1_0) | c1_1(a595) | c0_1(a595) | (~c2_1(a595)))) <=> ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp5 | c0_1(a595) | c1_1(a595) | (~ndr1_0) | (~c2_1(a595))))),
% 3.40/2.57 inference(monotonicity,[status(thm)],[3481])).
% 3.40/2.57 tff(3483,plain,
% 3.40/2.57 (((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp5 | (~ndr1_0) | c1_1(a595) | c0_1(a595) | (~c2_1(a595)))) <=> ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp5 | c0_1(a595) | c1_1(a595) | (~ndr1_0) | (~c2_1(a595)))),
% 3.40/2.57 inference(transitivity,[status(thm)],[3482, 3480])).
% 3.40/2.57 tff(3484,plain,
% 3.40/2.57 ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp5 | (~ndr1_0) | c1_1(a595) | c0_1(a595) | (~c2_1(a595)))),
% 3.40/2.57 inference(quant_inst,[status(thm)],[])).
% 3.40/2.57 tff(3485,plain,
% 3.40/2.57 ((~![U: $i] : (hskp6 | hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp5 | c0_1(a595) | c1_1(a595) | (~ndr1_0) | (~c2_1(a595))),
% 3.40/2.57 inference(modus_ponens,[status(thm)],[3484, 3483])).
% 3.40/2.57 tff(3486,plain,
% 3.40/2.57 (hskp5 | (~c2_1(a595))),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[3485, 107, 67, 3471, 3479, 573])).
% 3.40/2.57 tff(3487,plain,
% 3.40/2.57 (hskp5),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[3486, 3478])).
% 3.40/2.57 tff(3488,plain,
% 3.40/2.57 (~c2_1(a589)),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[586, 3487])).
% 3.40/2.57 tff(3489,plain,
% 3.40/2.57 (c1_1(a589)),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[597, 3487])).
% 3.40/2.57 tff(3490,plain,
% 3.40/2.57 (c0_1(a589)),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[608, 3487])).
% 3.40/2.57 tff(3491,plain,
% 3.40/2.57 ($false),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[3303, 107, 2292, 2281, 2270, 3180, 3490, 3489, 66, 22, 3488, 1106])).
% 3.40/2.57 tff(3492,plain,(c1_1(a607) | c2_1(a607) | hskp6 | hskp11 | hskp22), inference(lemma,lemma(discharge,[]))).
% 3.40/2.57 tff(3493,plain,
% 3.40/2.57 (c1_1(a607)),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[3492, 1638, 67, 22, 44])).
% 3.40/2.57 tff(3494,plain,
% 3.40/2.57 (~hskp17),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[281, 3493])).
% 3.40/2.57 tff(3495,plain,
% 3.40/2.57 (hskp17 | c3_1(a583)),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[3328, 107, 148, 3321, 3322, 55])).
% 3.40/2.57 tff(3496,plain,
% 3.40/2.57 (c3_1(a583)),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[3495, 3494])).
% 3.40/2.57 tff(3497,plain,
% 3.40/2.57 (hskp10 | (~c3_1(a583))),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[1999, 107, 3321, 3322, 3330, 21])).
% 3.40/2.57 tff(3498,plain,
% 3.40/2.57 (hskp10),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[3497, 3496])).
% 3.40/2.57 tff(3499,plain,
% 3.40/2.57 (~c1_1(a598)),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[911, 3498])).
% 3.40/2.57 tff(3500,plain,
% 3.40/2.57 (c3_1(a598)),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[881, 3498])).
% 3.40/2.57 tff(3501,plain,
% 3.40/2.57 (c0_1(a598)),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[892, 3498])).
% 3.40/2.57 tff(3502,plain,
% 3.40/2.57 (hskp23),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[1688, 1638, 107, 3501, 3500, 3499, 1648])).
% 3.40/2.57 tff(3503,plain,
% 3.40/2.57 (~c1_1(a636)),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[475, 3502])).
% 3.40/2.57 tff(3504,plain,
% 3.40/2.57 (~c0_1(a636)),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[481, 3502])).
% 3.40/2.57 tff(3505,plain,
% 3.40/2.57 (c3_1(a636)),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[492, 3502])).
% 3.40/2.57 tff(3506,plain,
% 3.40/2.57 (~c2_1(a636)),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[3348, 3505, 3322, 3496, 3504, 3503, 3321])).
% 3.40/2.57 tff(3507,plain,
% 3.40/2.57 (c2_1(a598)),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[1544, 107, 44, 67, 3501, 3499, 43])).
% 3.40/2.57 tff(3508,plain,
% 3.40/2.57 (hskp15),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[2010, 107, 3321, 3322, 3501, 3500, 3499, 1993, 3496])).
% 3.40/2.57 tff(3509,plain,
% 3.40/2.57 (~c0_1(a604)),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[1591, 3508])).
% 3.40/2.57 tff(3510,plain,
% 3.40/2.57 (c1_1(a604)),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[1613, 3508])).
% 3.40/2.57 tff(3511,plain,
% 3.40/2.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a636) | c0_1(a604) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a636)) | c2_1(a636))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a636) | c0_1(a604) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a636)) | c2_1(a636))),
% 3.40/2.57 inference(rewrite,[status(thm)],[])).
% 3.40/2.57 tff(3512,plain,
% 3.40/2.57 (((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c1_1(a636) | c2_1(a636) | (~c3_1(a636)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604))) <=> (c1_1(a636) | c0_1(a604) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a636)) | c2_1(a636))),
% 3.40/2.57 inference(rewrite,[status(thm)],[])).
% 3.40/2.57 tff(3513,plain,
% 3.40/2.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c1_1(a636) | c2_1(a636) | (~c3_1(a636)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a636) | c0_1(a604) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a636)) | c2_1(a636)))),
% 3.40/2.57 inference(monotonicity,[status(thm)],[3512])).
% 3.40/2.57 tff(3514,plain,
% 3.40/2.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c1_1(a636) | c2_1(a636) | (~c3_1(a636)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a636) | c0_1(a604) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a636)) | c2_1(a636))),
% 3.40/2.57 inference(transitivity,[status(thm)],[3513, 3511])).
% 3.40/2.57 tff(3515,plain,
% 3.40/2.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c1_1(a636) | c2_1(a636) | (~c3_1(a636)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))),
% 3.40/2.57 inference(quant_inst,[status(thm)],[])).
% 3.40/2.57 tff(3516,plain,
% 3.40/2.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a636) | c0_1(a604) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a636)) | c2_1(a636)),
% 3.40/2.57 inference(modus_ponens,[status(thm)],[3515, 3514])).
% 3.40/2.57 tff(3517,plain,
% 3.40/2.57 (~c2_1(a604)),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[3516, 107, 3505, 3510, 3501, 3500, 3503, 3509, 11, 3507, 3506])).
% 3.40/2.57 tff(3518,plain,
% 3.40/2.57 (hskp14),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[3313, 3493, 3180])).
% 3.40/2.57 tff(3519,plain,
% 3.40/2.57 (~c1_1(a603)),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[171, 3518])).
% 3.40/2.57 tff(3520,plain,
% 3.40/2.57 (c0_1(a603)),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[182, 3518])).
% 3.40/2.57 tff(3521,plain,
% 3.40/2.57 (c2_1(a603)),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[189, 107, 44, 67, 3520, 3519, 43])).
% 3.40/2.57 tff(3522,plain,
% 3.40/2.57 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a604) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | c2_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a604) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | c2_1(a604) | (~c1_1(a604)))),
% 3.40/2.57 inference(rewrite,[status(thm)],[])).
% 3.40/2.57 tff(3523,plain,
% 3.40/2.57 ((hskp17 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604))) <=> (hskp17 | c0_1(a604) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | c2_1(a604) | (~c1_1(a604)))),
% 3.40/2.57 inference(rewrite,[status(thm)],[])).
% 3.40/2.57 tff(3524,plain,
% 3.40/2.57 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a604) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | c2_1(a604) | (~c1_1(a604))))),
% 3.40/2.57 inference(monotonicity,[status(thm)],[3523])).
% 3.40/2.57 tff(3525,plain,
% 3.40/2.57 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a604) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | c2_1(a604) | (~c1_1(a604)))),
% 3.40/2.57 inference(transitivity,[status(thm)],[3524, 3522])).
% 3.40/2.57 tff(3526,plain,
% 3.40/2.57 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)))),
% 3.40/2.57 inference(quant_inst,[status(thm)],[])).
% 3.40/2.57 tff(3527,plain,
% 3.40/2.57 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a604) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | c2_1(a604) | (~c1_1(a604))),
% 3.40/2.57 inference(modus_ponens,[status(thm)],[3526, 3525])).
% 3.40/2.57 tff(3528,plain,
% 3.40/2.57 ($false),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[3527, 107, 3494, 3510, 3520, 3509, 3519, 32, 3521, 3517])).
% 3.40/2.57 tff(3529,plain,(hskp11 | hskp22 | hskp6 | c2_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.40/2.57 tff(3530,plain,
% 3.40/2.57 (hskp11),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[3529, 67, 44, 22])).
% 3.40/2.57 tff(3531,plain,
% 3.40/2.57 (~c1_1(a599)),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[428, 3530])).
% 3.40/2.57 tff(3532,plain,
% 3.40/2.57 (c1_1(a586)),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[229, 3467])).
% 3.40/2.57 tff(3533,plain,
% 3.40/2.57 (c3_1(a599)),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[422, 3530])).
% 3.40/2.57 tff(3534,plain,
% 3.40/2.57 (c2_1(a599)),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[439, 3530])).
% 3.40/2.57 tff(3535,plain,
% 3.40/2.57 (c0_1(a586)),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[2309, 107, 3399, 3534, 3533, 3532, 3400, 3531, 3468, 258, 3462])).
% 3.40/2.57 tff(3536,plain,
% 3.40/2.57 (~c0_1(a593)),
% 3.40/2.57 inference(unit_resolution,[status(thm)],[3263, 107, 2292, 2281, 2270, 3180, 3388, 66, 22, 3386, 1106])).
% 3.40/2.57 tff(3537,plain,
% 3.40/2.57 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | c1_1(a603) | c3_1(a603) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp16 | c1_1(a603) | c3_1(a603) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a603)))),
% 3.40/2.57 inference(rewrite,[status(thm)],[])).
% 3.40/2.57 tff(3538,plain,
% 3.40/2.57 ((hskp16 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593))) <=> (hskp16 | c1_1(a603) | c3_1(a603) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a603)))),
% 3.40/2.57 inference(rewrite,[status(thm)],[])).
% 3.40/2.57 tff(3539,plain,
% 3.40/2.57 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | c1_1(a603) | c3_1(a603) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a603))))),
% 3.40/2.57 inference(monotonicity,[status(thm)],[3538])).
% 3.40/2.57 tff(3540,plain,
% 3.40/2.57 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp16 | c1_1(a603) | c3_1(a603) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a603)))),
% 3.40/2.58 inference(transitivity,[status(thm)],[3539, 3537])).
% 3.40/2.58 tff(3541,plain,
% 3.40/2.58 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)))),
% 3.40/2.58 inference(quant_inst,[status(thm)],[])).
% 3.40/2.58 tff(3542,plain,
% 3.40/2.58 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp16 | c1_1(a603) | c3_1(a603) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a603))),
% 3.40/2.58 inference(modus_ponens,[status(thm)],[3541, 3540])).
% 3.40/2.58 tff(3543,plain,
% 3.40/2.58 (hskp16 | (~c2_1(a603))),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[3542, 107, 3388, 3398, 3400, 3386, 1022, 3536])).
% 3.40/2.58 tff(3544,plain,
% 3.40/2.58 (hskp16),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[3543, 3462])).
% 3.40/2.58 tff(3545,plain,
% 3.40/2.58 (~c2_1(a606)),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[1111, 3544])).
% 3.40/2.58 tff(3546,plain,
% 3.40/2.58 (c1_1(a606)),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[1088, 3544])).
% 3.40/2.58 tff(3547,plain,
% 3.40/2.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a607) | c2_1(a607) | c2_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a607) | c2_1(a607) | c2_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a607)))),
% 3.40/2.58 inference(rewrite,[status(thm)],[])).
% 3.40/2.58 tff(3548,plain,
% 3.40/2.58 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607))) <=> (c1_1(a607) | c2_1(a607) | c2_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a607)))),
% 3.40/2.58 inference(rewrite,[status(thm)],[])).
% 3.40/2.58 tff(3549,plain,
% 3.40/2.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a607) | c2_1(a607) | c2_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a607))))),
% 3.40/2.58 inference(monotonicity,[status(thm)],[3548])).
% 3.40/2.58 tff(3550,plain,
% 3.40/2.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a607) | c2_1(a607) | c2_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a607)))),
% 3.40/2.58 inference(transitivity,[status(thm)],[3549, 3547])).
% 3.40/2.58 tff(3551,plain,
% 3.40/2.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)))),
% 3.40/2.58 inference(quant_inst,[status(thm)],[])).
% 3.40/2.58 tff(3552,plain,
% 3.40/2.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a607) | c2_1(a607) | c2_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a607))),
% 3.40/2.58 inference(modus_ponens,[status(thm)],[3551, 3550])).
% 3.40/2.58 tff(3553,plain,
% 3.40/2.58 (~c0_1(a606)),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[3552, 107, 2292, 2281, 2270, 3180, 3546, 66, 22, 3545, 1106])).
% 3.40/2.58 tff(3554,plain,
% 3.40/2.58 (~c3_1(a606)),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[1075, 3544])).
% 3.40/2.58 tff(3555,plain,
% 3.40/2.58 (c2_1(a586)),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[1474, 3467])).
% 3.40/2.58 tff(3556,plain,
% 3.40/2.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a606) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a606) | (~c1_1(a606)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a606) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a606) | (~c1_1(a606)))),
% 3.40/2.58 inference(rewrite,[status(thm)],[])).
% 3.40/2.58 tff(3557,plain,
% 3.40/2.58 (((~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a606) | c0_1(a606) | (~c1_1(a606))) <=> (c3_1(a606) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a606) | (~c1_1(a606)))),
% 3.40/2.58 inference(rewrite,[status(thm)],[])).
% 3.40/2.58 tff(3558,plain,
% 3.40/2.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a606) | c0_1(a606) | (~c1_1(a606)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a606) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a606) | (~c1_1(a606))))),
% 3.40/2.58 inference(monotonicity,[status(thm)],[3557])).
% 3.40/2.58 tff(3559,plain,
% 3.40/2.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a606) | c0_1(a606) | (~c1_1(a606)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a606) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a606) | (~c1_1(a606)))),
% 3.40/2.58 inference(transitivity,[status(thm)],[3558, 3556])).
% 3.40/2.58 tff(3560,plain,
% 3.40/2.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a606) | c0_1(a606) | (~c1_1(a606)))),
% 3.40/2.58 inference(quant_inst,[status(thm)],[])).
% 3.40/2.58 tff(3561,plain,
% 3.40/2.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a606) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a606) | (~c1_1(a606))),
% 3.40/2.58 inference(modus_ponens,[status(thm)],[3560, 3559])).
% 3.40/2.58 tff(3562,plain,
% 3.40/2.58 ($false),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[3561, 107, 3546, 3534, 3533, 3555, 3554, 3531, 3468, 258, 3553, 3535])).
% 3.40/2.58 tff(3563,plain,(c1_1(a607) | c2_1(a607) | hskp22 | hskp6 | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a583))), inference(lemma,lemma(discharge,[]))).
% 3.40/2.58 tff(3564,plain,
% 3.40/2.58 (c1_1(a607)),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[3563, 3383, 44, 22, 3461, 3460, 3459])).
% 3.40/2.58 tff(3565,plain,
% 3.40/2.58 (~hskp17),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[281, 3564])).
% 3.40/2.58 tff(3566,plain,
% 3.40/2.58 (hskp3),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[3427, 3565, 3180, 3564])).
% 3.40/2.58 tff(3567,plain,
% 3.40/2.58 (~c1_1(a587)),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[939, 3566])).
% 3.40/2.58 tff(3568,plain,
% 3.40/2.58 (c2_1(a587)),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[950, 3566])).
% 3.40/2.58 tff(3569,plain,
% 3.40/2.58 (c0_1(a587)),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[961, 3566])).
% 3.40/2.58 tff(3570,plain,
% 3.40/2.58 (~c1_1(a590)),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[3437, 107, 3565, 3184, 3569, 3568, 45, 3567, 32])).
% 3.40/2.58 tff(3571,plain,
% 3.40/2.58 (~hskp4),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[147, 3383, 44])).
% 3.40/2.58 tff(3572,plain,
% 3.40/2.58 (hskp17 | c3_1(a583)),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[3328, 107, 3571, 3461, 3460, 55])).
% 3.40/2.58 tff(3573,plain,
% 3.40/2.58 (c3_1(a583)),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[3572, 3565])).
% 3.40/2.58 tff(3574,plain,
% 3.40/2.58 (hskp10 | (~c3_1(a583))),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[1999, 107, 3461, 3460, 3459, 21])).
% 3.40/2.58 tff(3575,plain,
% 3.40/2.58 (hskp10),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[3574, 3573])).
% 3.40/2.58 tff(3576,plain,
% 3.40/2.58 (~c1_1(a598)),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[911, 3575])).
% 3.40/2.58 tff(3577,plain,
% 3.40/2.58 (c0_1(a598)),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[892, 3575])).
% 3.40/2.58 tff(3578,plain,
% 3.40/2.58 (c2_1(a598)),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[1544, 107, 44, 3383, 3577, 3576, 43])).
% 3.40/2.58 tff(3579,plain,
% 3.40/2.58 (c3_1(a598)),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[881, 3575])).
% 3.40/2.58 tff(3580,plain,
% 3.40/2.58 (hskp15),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[2010, 107, 3461, 3460, 3577, 3579, 3576, 1993, 3573])).
% 3.40/2.58 tff(3581,plain,
% 3.40/2.58 (~c0_1(a604)),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[1591, 3580])).
% 3.40/2.58 tff(3582,plain,
% 3.40/2.58 (c1_1(a604)),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[1613, 3580])).
% 3.40/2.58 tff(3583,plain,
% 3.40/2.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c2_1(a590) | c0_1(a604) | (~ndr1_0) | (~c3_1(a590)) | c1_1(a590) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c2_1(a604)) | (~c1_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a590) | c0_1(a604) | (~ndr1_0) | (~c3_1(a590)) | c1_1(a590) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c2_1(a604)) | (~c1_1(a604)))),
% 3.40/2.58 inference(rewrite,[status(thm)],[])).
% 3.40/2.58 tff(3584,plain,
% 3.40/2.58 (((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c1_1(a590) | c2_1(a590) | (~c3_1(a590)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604))) <=> (c2_1(a590) | c0_1(a604) | (~ndr1_0) | (~c3_1(a590)) | c1_1(a590) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c2_1(a604)) | (~c1_1(a604)))),
% 3.40/2.58 inference(rewrite,[status(thm)],[])).
% 3.40/2.58 tff(3585,plain,
% 3.40/2.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c1_1(a590) | c2_1(a590) | (~c3_1(a590)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c2_1(a590) | c0_1(a604) | (~ndr1_0) | (~c3_1(a590)) | c1_1(a590) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c2_1(a604)) | (~c1_1(a604))))),
% 3.40/2.58 inference(monotonicity,[status(thm)],[3584])).
% 3.40/2.58 tff(3586,plain,
% 3.40/2.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c1_1(a590) | c2_1(a590) | (~c3_1(a590)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a590) | c0_1(a604) | (~ndr1_0) | (~c3_1(a590)) | c1_1(a590) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c2_1(a604)) | (~c1_1(a604)))),
% 3.40/2.58 inference(transitivity,[status(thm)],[3585, 3583])).
% 3.40/2.58 tff(3587,plain,
% 3.40/2.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c1_1(a590) | c2_1(a590) | (~c3_1(a590)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))),
% 3.40/2.58 inference(quant_inst,[status(thm)],[])).
% 3.40/2.58 tff(3588,plain,
% 3.40/2.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a590) | c0_1(a604) | (~ndr1_0) | (~c3_1(a590)) | c1_1(a590) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c2_1(a604)) | (~c1_1(a604))),
% 3.40/2.58 inference(modus_ponens,[status(thm)],[3587, 3586])).
% 3.40/2.58 tff(3589,plain,
% 3.40/2.58 (~c2_1(a604)),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[3588, 107, 3582, 3577, 3579, 3184, 3382, 3581, 11, 3578, 3570])).
% 3.40/2.58 tff(3590,plain,
% 3.40/2.58 (hskp14),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[3313, 3564, 3180])).
% 3.40/2.58 tff(3591,plain,
% 3.40/2.58 (~c1_1(a603)),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[171, 3590])).
% 3.40/2.58 tff(3592,plain,
% 3.40/2.58 (c0_1(a603)),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[182, 3590])).
% 3.40/2.58 tff(3593,plain,
% 3.40/2.58 (c2_1(a603)),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[189, 107, 44, 3383, 3592, 3591, 43])).
% 3.40/2.58 tff(3594,plain,
% 3.40/2.58 ($false),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[3527, 107, 3565, 3582, 3592, 3581, 3591, 32, 3593, 3589])).
% 3.40/2.58 tff(3595,plain,(c2_1(a590) | hskp22 | c0_1(a590) | c2_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.40/2.58 tff(3596,plain,
% 3.40/2.58 (c2_1(a590)),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[3595, 45, 44, 22])).
% 3.40/2.58 tff(3597,plain,
% 3.40/2.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590))),
% 3.40/2.58 inference(rewrite,[status(thm)],[])).
% 3.40/2.58 tff(3598,plain,
% 3.40/2.58 (((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | c0_1(a590) | (~c2_1(a590))) <=> (c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590))),
% 3.40/2.58 inference(rewrite,[status(thm)],[])).
% 3.40/2.58 tff(3599,plain,
% 3.40/2.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | c0_1(a590) | (~c2_1(a590)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590)))),
% 3.40/2.58 inference(monotonicity,[status(thm)],[3598])).
% 3.40/2.58 tff(3600,plain,
% 3.40/2.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | c0_1(a590) | (~c2_1(a590)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590))),
% 3.40/2.58 inference(transitivity,[status(thm)],[3599, 3597])).
% 3.40/2.58 tff(3601,plain,
% 3.40/2.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | c0_1(a590) | (~c2_1(a590)))),
% 3.40/2.58 inference(quant_inst,[status(thm)],[])).
% 3.40/2.58 tff(3602,plain,
% 3.40/2.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590)),
% 3.40/2.58 inference(modus_ponens,[status(thm)],[3601, 3600])).
% 3.40/2.58 tff(3603,plain,
% 3.40/2.58 (~c1_1(a678)),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[3602, 107, 2318, 2316, 863, 862, 45, 65, 3286])).
% 3.40/2.58 tff(3604,assumption,(~hskp0), introduced(assumption)).
% 3.40/2.58 tff(3605,plain,
% 3.40/2.58 (hskp26 | hskp0 | c1_1(a607) | c0_1(a607)),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[1038, 107, 22, 1032])).
% 3.40/2.58 tff(3606,plain,
% 3.40/2.58 (c0_1(a607)),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[3605, 3604, 66, 726])).
% 3.40/2.58 tff(3607,plain,
% 3.40/2.58 (hskp23),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[1334, 3606])).
% 3.40/2.58 tff(3608,plain,
% 3.40/2.58 (~c1_1(a636)),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[475, 3607])).
% 3.40/2.58 tff(3609,plain,
% 3.40/2.58 (~c0_1(a636)),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[481, 3607])).
% 3.40/2.58 tff(3610,plain,
% 3.40/2.58 (((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | c2_1(a636))) <=> ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp0 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | c2_1(a636))),
% 3.40/2.58 inference(rewrite,[status(thm)],[])).
% 3.40/2.58 tff(3611,plain,
% 3.40/2.58 ((hskp26 | hskp0 | (~ndr1_0) | c2_1(a636) | c1_1(a636) | c0_1(a636)) <=> (hskp26 | hskp0 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | c2_1(a636))),
% 3.40/2.58 inference(rewrite,[status(thm)],[])).
% 3.40/2.58 tff(3612,plain,
% 3.40/2.58 (((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | (~ndr1_0) | c2_1(a636) | c1_1(a636) | c0_1(a636))) <=> ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | c2_1(a636)))),
% 3.40/2.58 inference(monotonicity,[status(thm)],[3611])).
% 3.40/2.58 tff(3613,plain,
% 3.40/2.58 (((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | (~ndr1_0) | c2_1(a636) | c1_1(a636) | c0_1(a636))) <=> ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp0 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | c2_1(a636))),
% 3.40/2.58 inference(transitivity,[status(thm)],[3612, 3610])).
% 3.40/2.58 tff(3614,plain,
% 3.40/2.58 ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | (~ndr1_0) | c2_1(a636) | c1_1(a636) | c0_1(a636))),
% 3.40/2.58 inference(quant_inst,[status(thm)],[])).
% 3.40/2.58 tff(3615,plain,
% 3.40/2.58 ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp0 | c0_1(a636) | c1_1(a636) | (~ndr1_0) | c2_1(a636)),
% 3.40/2.58 inference(modus_ponens,[status(thm)],[3614, 3613])).
% 3.40/2.58 tff(3616,plain,
% 3.40/2.58 (c2_1(a636)),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[3615, 726, 107, 3604, 3609, 3608, 1032])).
% 3.40/2.58 tff(3617,plain,
% 3.40/2.58 (hskp26 | hskp28 | (~c0_1(a607)) | (~c3_1(a607))),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[1289, 107, 22, 1283])).
% 3.40/2.58 tff(3618,plain,
% 3.40/2.58 (hskp28),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[3617, 3606, 321, 726])).
% 3.40/2.58 tff(3619,plain,
% 3.40/2.58 (c3_1(a612)),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[1139, 3618])).
% 3.40/2.58 tff(3620,plain,
% 3.40/2.58 (c1_1(a612)),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[1435, 3618])).
% 3.40/2.58 tff(3621,plain,
% 3.40/2.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a636) | c1_1(a636) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a636)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a636) | c1_1(a636) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a636)))),
% 3.40/2.58 inference(rewrite,[status(thm)],[])).
% 3.40/2.58 tff(3622,plain,
% 3.40/2.58 (((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a636) | c0_1(a636) | (~c2_1(a636))) <=> (c0_1(a636) | c1_1(a636) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a636)))),
% 3.40/2.58 inference(rewrite,[status(thm)],[])).
% 3.40/2.58 tff(3623,plain,
% 3.40/2.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a636) | c0_1(a636) | (~c2_1(a636)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a636) | c1_1(a636) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a636))))),
% 3.40/2.58 inference(monotonicity,[status(thm)],[3622])).
% 3.40/2.58 tff(3624,plain,
% 3.40/2.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a636) | c0_1(a636) | (~c2_1(a636)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a636) | c1_1(a636) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a636)))),
% 3.40/2.58 inference(transitivity,[status(thm)],[3623, 3621])).
% 3.40/2.58 tff(3625,plain,
% 3.40/2.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a636) | c0_1(a636) | (~c2_1(a636)))),
% 3.40/2.58 inference(quant_inst,[status(thm)],[])).
% 3.40/2.58 tff(3626,plain,
% 3.40/2.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a636) | c1_1(a636) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a636))),
% 3.40/2.58 inference(modus_ponens,[status(thm)],[3625, 3624])).
% 3.40/2.58 tff(3627,plain,
% 3.40/2.58 (~c0_1(a612)),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[3626, 107, 3620, 3619, 863, 862, 3609, 3608, 45, 65, 3616])).
% 3.40/2.58 tff(3628,plain,
% 3.40/2.58 (c2_1(a612)),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[1150, 3618])).
% 3.40/2.58 tff(3629,plain,
% 3.40/2.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c3_1(a607)))),
% 3.40/2.58 inference(rewrite,[status(thm)],[])).
% 3.40/2.58 tff(3630,plain,
% 3.40/2.58 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612))) <=> (c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c3_1(a607)))),
% 3.40/2.58 inference(rewrite,[status(thm)],[])).
% 3.40/2.58 tff(3631,plain,
% 3.40/2.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c3_1(a607))))),
% 3.40/2.58 inference(monotonicity,[status(thm)],[3630])).
% 3.40/2.58 tff(3632,plain,
% 3.40/2.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c3_1(a607)))),
% 3.40/2.58 inference(transitivity,[status(thm)],[3631, 3629])).
% 3.40/2.58 tff(3633,plain,
% 3.40/2.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))),
% 3.40/2.58 inference(quant_inst,[status(thm)],[])).
% 3.40/2.58 tff(3634,plain,
% 3.40/2.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c3_1(a607))),
% 3.40/2.58 inference(modus_ponens,[status(thm)],[3633, 3632])).
% 3.40/2.58 tff(3635,plain,
% 3.40/2.58 ($false),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[3634, 107, 2318, 2317, 2316, 3620, 3628, 321, 66, 22, 11, 3627])).
% 3.40/2.58 tff(3636,plain,(hskp0 | (~c0_1(a678)) | (~c2_1(a678)) | (~c3_1(a678)) | (~c3_1(a607)) | c1_1(a607) | c2_1(a607) | (~c2_1(a590)) | (~c3_1(a590)) | c0_1(a590) | hskp26), inference(lemma,lemma(discharge,[]))).
% 3.40/2.58 tff(3637,plain,
% 3.40/2.58 (hskp0),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[3636, 726, 2317, 2316, 321, 66, 22, 863, 862, 45, 2318])).
% 3.40/2.58 tff(3638,plain,
% 3.40/2.58 (~c2_1(a584)),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[1045, 3637])).
% 3.40/2.58 tff(3639,plain,
% 3.40/2.58 (~c0_1(a584)),
% 3.40/2.58 inference(unit_resolution,[status(thm)],[1051, 3637])).
% 3.40/2.58 tff(3640,assumption,(~c3_1(a584)), introduced(assumption)).
% 3.40/2.58 tff(3641,assumption,(~c2_1(a584)), introduced(assumption)).
% 3.40/2.58 tff(3642,assumption,(~c0_1(a584)), introduced(assumption)).
% 3.40/2.58 tff(3643,plain,
% 3.40/2.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a599) | c0_1(a590) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | c3_1(a584) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a599) | c0_1(a590) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | c3_1(a584) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)))),
% 3.40/2.58 inference(rewrite,[status(thm)],[])).
% 3.40/2.58 tff(3644,plain,
% 3.40/2.58 (((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a584) | c0_1(a584) | c2_1(a584)) <=> (c1_1(a599) | c0_1(a590) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | c3_1(a584) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)))),
% 3.40/2.58 inference(rewrite,[status(thm)],[])).
% 3.40/2.58 tff(3645,plain,
% 3.40/2.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a584) | c0_1(a584) | c2_1(a584))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a599) | c0_1(a590) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | c3_1(a584) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599))))),
% 3.40/2.59 inference(monotonicity,[status(thm)],[3644])).
% 3.40/2.59 tff(3646,plain,
% 3.40/2.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a584) | c0_1(a584) | c2_1(a584))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a599) | c0_1(a590) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | c3_1(a584) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)))),
% 3.40/2.59 inference(transitivity,[status(thm)],[3645, 3643])).
% 3.40/2.59 tff(3647,plain,
% 3.40/2.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a584) | c0_1(a584) | c2_1(a584))),
% 3.40/2.59 inference(quant_inst,[status(thm)],[])).
% 3.40/2.59 tff(3648,plain,
% 3.40/2.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a599) | c0_1(a590) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | c3_1(a584) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599))),
% 3.40/2.59 inference(modus_ponens,[status(thm)],[3647, 3646])).
% 3.40/2.59 tff(3649,plain,
% 3.40/2.59 ($false),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[3648, 107, 463, 462, 863, 862, 461, 45, 3642, 3641, 1730, 3640])).
% 3.40/2.59 tff(3650,plain,(c3_1(a584) | (~c2_1(a599)) | (~c3_1(a599)) | (~c2_1(a590)) | (~c3_1(a590)) | c1_1(a599) | c0_1(a590) | c0_1(a584) | c2_1(a584)), inference(lemma,lemma(discharge,[]))).
% 3.40/2.59 tff(3651,plain,
% 3.40/2.59 (c3_1(a584)),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[3650, 1078, 1077, 863, 862, 1012, 45, 3639, 3638])).
% 3.40/2.59 tff(3652,plain,
% 3.40/2.59 (c1_1(a584)),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[1062, 3637])).
% 3.40/2.59 tff(3653,plain,
% 3.40/2.59 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | c2_1(a584) | (~ndr1_0) | (~c3_1(a584)) | (~c1_1(a584)) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp14 | c2_1(a584) | (~ndr1_0) | (~c3_1(a584)) | (~c1_1(a584)) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)))),
% 3.40/2.59 inference(rewrite,[status(thm)],[])).
% 3.40/2.59 tff(3654,plain,
% 3.40/2.59 ((hskp14 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a584) | (~c1_1(a584)) | (~c3_1(a584))) <=> (hskp14 | c2_1(a584) | (~ndr1_0) | (~c3_1(a584)) | (~c1_1(a584)) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)))),
% 3.40/2.59 inference(rewrite,[status(thm)],[])).
% 3.40/2.59 tff(3655,plain,
% 3.40/2.59 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a584) | (~c1_1(a584)) | (~c3_1(a584)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | c2_1(a584) | (~ndr1_0) | (~c3_1(a584)) | (~c1_1(a584)) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678))))),
% 3.40/2.59 inference(monotonicity,[status(thm)],[3654])).
% 3.40/2.59 tff(3656,plain,
% 3.40/2.59 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a584) | (~c1_1(a584)) | (~c3_1(a584)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp14 | c2_1(a584) | (~ndr1_0) | (~c3_1(a584)) | (~c1_1(a584)) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)))),
% 3.40/2.59 inference(transitivity,[status(thm)],[3655, 3653])).
% 3.40/2.59 tff(3657,plain,
% 3.40/2.59 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a584) | (~c1_1(a584)) | (~c3_1(a584)))),
% 3.40/2.59 inference(quant_inst,[status(thm)],[])).
% 3.40/2.59 tff(3658,plain,
% 3.40/2.59 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp14 | c2_1(a584) | (~ndr1_0) | (~c3_1(a584)) | (~c1_1(a584)) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678))),
% 3.40/2.59 inference(modus_ponens,[status(thm)],[3657, 3656])).
% 3.40/2.59 tff(3659,plain,
% 3.40/2.59 (hskp14 | (~c3_1(a584))),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[3658, 107, 2318, 2317, 2316, 3652, 3638, 550])).
% 3.40/2.59 tff(3660,plain,
% 3.40/2.59 (hskp14),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[3659, 3651])).
% 3.40/2.59 tff(3661,plain,
% 3.40/2.59 (hskp3),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[329, 3660, 321, 66, 22])).
% 3.40/2.59 tff(3662,plain,
% 3.40/2.59 (~c1_1(a587)),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[939, 3661])).
% 3.40/2.59 tff(3663,plain,
% 3.40/2.59 (~c1_1(a603)),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[171, 3660])).
% 3.40/2.59 tff(3664,plain,
% 3.40/2.59 (c0_1(a603)),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[182, 3660])).
% 3.40/2.59 tff(3665,plain,
% 3.40/2.59 (~c3_1(a603)),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[205, 3660])).
% 3.40/2.59 tff(3666,plain,
% 3.40/2.59 (c0_1(a587)),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[961, 3661])).
% 3.40/2.59 tff(3667,plain,
% 3.40/2.59 (c2_1(a587)),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[950, 3661])).
% 3.40/2.59 tff(3668,plain,
% 3.40/2.59 ($false),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[1508, 3667, 3666, 22, 321, 66, 726, 3665, 3664, 3663, 3662])).
% 3.40/2.59 tff(3669,plain,(hskp26 | c2_1(a607) | (~c3_1(a607)) | c1_1(a607) | (~c0_1(a678)) | (~c2_1(a678)) | (~c3_1(a678)) | (~c2_1(a590)) | (~c3_1(a590)) | c0_1(a590)), inference(lemma,lemma(discharge,[]))).
% 3.40/2.59 tff(3670,plain,
% 3.40/2.59 (hskp26),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[3669, 66, 321, 22, 2318, 2317, 2316, 863, 862, 45])).
% 3.40/2.59 tff(3671,plain,
% 3.40/2.59 (c2_1(a583)),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[391, 3670])).
% 3.40/2.59 tff(3672,plain,
% 3.40/2.59 (c1_1(a583)),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[351, 3670])).
% 3.40/2.59 tff(3673,plain,
% 3.40/2.59 (c0_1(a583)),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[362, 3670])).
% 3.40/2.59 tff(3674,plain,
% 3.40/2.59 (hskp9),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[1967, 107, 3673, 3672, 3671, 862, 45, 294, 3286])).
% 3.40/2.59 tff(3675,plain,
% 3.40/2.59 (~c3_1(a595)),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[1487, 3674])).
% 3.40/2.59 tff(3676,plain,
% 3.40/2.59 (~c0_1(a595)),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[1499, 3674])).
% 3.40/2.59 tff(3677,plain,
% 3.40/2.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a595) | c3_1(a595) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c3_1(a590)) | (~c2_1(a590)) | c2_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a595) | c3_1(a595) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c3_1(a590)) | (~c2_1(a590)) | c2_1(a595))),
% 3.40/2.59 inference(rewrite,[status(thm)],[])).
% 3.40/2.59 tff(3678,plain,
% 3.40/2.59 (((~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c3_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a595) | c0_1(a595) | c2_1(a595)) <=> (c0_1(a595) | c3_1(a595) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c3_1(a590)) | (~c2_1(a590)) | c2_1(a595))),
% 3.40/2.59 inference(rewrite,[status(thm)],[])).
% 3.40/2.59 tff(3679,plain,
% 3.40/2.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c3_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a595) | c0_1(a595) | c2_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a595) | c3_1(a595) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c3_1(a590)) | (~c2_1(a590)) | c2_1(a595)))),
% 3.40/2.59 inference(monotonicity,[status(thm)],[3678])).
% 3.40/2.59 tff(3680,plain,
% 3.40/2.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c3_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a595) | c0_1(a595) | c2_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a595) | c3_1(a595) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c3_1(a590)) | (~c2_1(a590)) | c2_1(a595))),
% 3.40/2.59 inference(transitivity,[status(thm)],[3679, 3677])).
% 3.40/2.59 tff(3681,plain,
% 3.40/2.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c3_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a595) | c0_1(a595) | c2_1(a595))),
% 3.40/2.59 inference(quant_inst,[status(thm)],[])).
% 3.40/2.59 tff(3682,plain,
% 3.40/2.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a595) | c3_1(a595) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c3_1(a590)) | (~c2_1(a590)) | c2_1(a595)),
% 3.40/2.59 inference(modus_ponens,[status(thm)],[3681, 3680])).
% 3.40/2.59 tff(3683,plain,
% 3.40/2.59 (c2_1(a595)),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[3682, 107, 2317, 2316, 863, 862, 3676, 3675, 45, 1730, 3603])).
% 3.40/2.59 tff(3684,plain,
% 3.40/2.59 (~c1_1(a595)),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[1493, 3674])).
% 3.40/2.59 tff(3685,plain,
% 3.40/2.59 (hskp2 | (~c2_1(a595))),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[1754, 107, 3676, 3684, 3675, 200])).
% 3.40/2.59 tff(3686,plain,
% 3.40/2.59 (hskp2),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[3685, 3683])).
% 3.40/2.59 tff(3687,plain,
% 3.40/2.59 (~c3_1(a586)),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[218, 3686])).
% 3.40/2.59 tff(3688,plain,
% 3.40/2.59 (c2_1(a586)),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[1474, 3686])).
% 3.40/2.59 tff(3689,plain,
% 3.40/2.59 (c1_1(a586)),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[229, 3686])).
% 3.40/2.59 tff(3690,plain,
% 3.40/2.59 (hskp28),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[2820, 107, 2317, 2316, 3689, 3688, 3687, 1748, 3603])).
% 3.40/2.59 tff(3691,plain,
% 3.40/2.59 (c3_1(a612)),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[1139, 3690])).
% 3.40/2.59 tff(3692,plain,
% 3.40/2.59 (c1_1(a612)),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[1435, 3690])).
% 3.40/2.59 tff(3693,plain,
% 3.40/2.59 (~c0_1(a612)),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[1774, 107, 3692, 3691, 863, 862, 3676, 3684, 45, 65, 3683])).
% 3.40/2.59 tff(3694,plain,
% 3.40/2.59 (c2_1(a612)),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[1150, 3690])).
% 3.40/2.59 tff(3695,plain,
% 3.40/2.59 ($false),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[3634, 107, 2318, 2317, 2316, 3692, 3694, 321, 66, 22, 11, 3693])).
% 3.40/2.59 tff(3696,plain,(c1_1(a607) | (~c0_1(a678)) | (~c2_1(a678)) | (~c3_1(a678)) | (~c3_1(a607)) | c2_1(a607) | (~c2_1(a590)) | (~c3_1(a590)) | c0_1(a590)), inference(lemma,lemma(discharge,[]))).
% 3.40/2.59 tff(3697,plain,
% 3.40/2.59 (c1_1(a607)),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[3696, 3596, 2281, 2270, 3180, 22, 2292, 3382, 45])).
% 3.40/2.59 tff(3698,plain,
% 3.40/2.59 (~hskp17),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[281, 3697])).
% 3.40/2.59 tff(3699,plain,
% 3.40/2.59 (hskp3),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[3427, 3697, 3180, 3698])).
% 3.40/2.59 tff(3700,plain,
% 3.40/2.59 (~c1_1(a587)),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[939, 3699])).
% 3.40/2.59 tff(3701,plain,
% 3.40/2.59 (c2_1(a587)),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[950, 3699])).
% 3.40/2.59 tff(3702,plain,
% 3.40/2.59 (c0_1(a587)),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[961, 3699])).
% 3.40/2.59 tff(3703,plain,
% 3.40/2.59 (~hskp17),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[281, 2986])).
% 3.40/2.59 tff(3704,plain,
% 3.40/2.59 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~c1_1(a607)) | c2_1(a607) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a607))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | (~c1_1(a607)) | c2_1(a607) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a607))),
% 3.40/2.59 inference(rewrite,[status(thm)],[])).
% 3.40/2.59 tff(3705,plain,
% 3.40/2.59 ((hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a607) | c2_1(a607) | (~c1_1(a607))) <=> (hskp17 | (~c1_1(a607)) | c2_1(a607) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a607))),
% 3.40/2.59 inference(rewrite,[status(thm)],[])).
% 3.40/2.59 tff(3706,plain,
% 3.40/2.59 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a607) | c2_1(a607) | (~c1_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~c1_1(a607)) | c2_1(a607) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a607)))),
% 3.40/2.59 inference(monotonicity,[status(thm)],[3705])).
% 3.40/2.59 tff(3707,plain,
% 3.40/2.59 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a607) | c2_1(a607) | (~c1_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | (~c1_1(a607)) | c2_1(a607) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a607))),
% 3.40/2.59 inference(transitivity,[status(thm)],[3706, 3704])).
% 3.40/2.59 tff(3708,plain,
% 3.40/2.59 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a607) | c2_1(a607) | (~c1_1(a607)))),
% 3.40/2.59 inference(quant_inst,[status(thm)],[])).
% 3.40/2.59 tff(3709,plain,
% 3.40/2.59 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | (~c1_1(a607)) | c2_1(a607) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a607)),
% 3.40/2.59 inference(modus_ponens,[status(thm)],[3708, 3707])).
% 3.40/2.59 tff(3710,plain,
% 3.40/2.59 ($false),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[3709, 107, 3703, 1000, 999, 2986, 22, 996, 32, 1])).
% 3.40/2.59 tff(3711,plain,(c0_1(a607) | (~c0_1(a587)) | (~c2_1(a587)) | (~c1_1(a607)) | c2_1(a607) | c1_1(a587)), inference(lemma,lemma(discharge,[]))).
% 3.40/2.59 tff(3712,plain,
% 3.40/2.59 (c0_1(a607)),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[3711, 3702, 3701, 3697, 22, 3700])).
% 3.40/2.59 tff(3713,plain,
% 3.40/2.59 (hskp14),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[3313, 3697, 3180])).
% 3.40/2.59 tff(3714,plain,
% 3.40/2.59 (~c3_1(a603)),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[205, 3713])).
% 3.40/2.59 tff(3715,plain,
% 3.40/2.59 (~c1_1(a603)),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[171, 3713])).
% 3.40/2.59 tff(3716,plain,
% 3.40/2.59 (c0_1(a603)),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[182, 3713])).
% 3.40/2.59 tff(3717,plain,
% 3.40/2.59 (hskp3),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[3427, 2986, 321, 3703])).
% 3.40/2.59 tff(3718,plain,
% 3.40/2.59 (~c1_1(a587)),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[939, 3717])).
% 3.40/2.59 tff(3719,plain,
% 3.40/2.59 (c2_1(a587)),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[950, 3717])).
% 3.40/2.59 tff(3720,plain,
% 3.40/2.59 (c0_1(a587)),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[961, 3717])).
% 3.40/2.59 tff(3721,plain,
% 3.40/2.59 (hskp26 | c2_1(a603)),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[1006, 107, 3720, 3719, 998, 997, 3718, 995])).
% 3.40/2.59 tff(3722,plain,
% 3.40/2.59 (c2_1(a603)),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[3721, 726])).
% 3.40/2.59 tff(3723,plain,
% 3.40/2.59 ($false),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[2929, 107, 3703, 1009, 2986, 22, 998, 32, 1, 1010])).
% 3.40/2.59 tff(3724,plain,(c0_1(a607) | (~c0_1(a603)) | (~c1_1(a607)) | c2_1(a607) | c1_1(a603) | (~c2_1(a603))), inference(lemma,lemma(discharge,[]))).
% 3.40/2.59 tff(3725,plain,
% 3.40/2.59 (c0_1(a607)),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[3724, 3722, 2986, 22, 998, 1009])).
% 3.40/2.59 tff(3726,plain,
% 3.40/2.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~c1_1(a607)) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a599)) | c0_1(a599) | (~c0_1(a607)) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (~c1_1(a607)) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a599)) | c0_1(a599) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.40/2.59 inference(rewrite,[status(thm)],[])).
% 3.40/2.59 tff(3727,plain,
% 3.40/2.59 (((~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599))) <=> ((~c1_1(a607)) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a599)) | c0_1(a599) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.40/2.59 inference(rewrite,[status(thm)],[])).
% 3.40/2.59 tff(3728,plain,
% 3.40/2.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~c1_1(a607)) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a599)) | c0_1(a599) | (~c0_1(a607)) | (~c3_1(a607))))),
% 3.40/2.59 inference(monotonicity,[status(thm)],[3727])).
% 3.40/2.59 tff(3729,plain,
% 3.40/2.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (~c1_1(a607)) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a599)) | c0_1(a599) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.40/2.59 inference(transitivity,[status(thm)],[3728, 3726])).
% 3.40/2.59 tff(3730,plain,
% 3.40/2.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))),
% 3.40/2.59 inference(quant_inst,[status(thm)],[])).
% 3.40/2.59 tff(3731,plain,
% 3.40/2.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (~c1_1(a607)) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a599)) | c0_1(a599) | (~c0_1(a607)) | (~c3_1(a607))),
% 3.40/2.59 inference(modus_ponens,[status(thm)],[3730, 3729])).
% 3.40/2.59 tff(3732,plain,
% 3.40/2.59 (c0_1(a599) | (~c0_1(a607))),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[3731, 107, 321, 1078, 863, 862, 2986, 1012, 45, 65])).
% 3.40/2.59 tff(3733,plain,
% 3.40/2.59 (c0_1(a599)),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[3732, 3725])).
% 3.40/2.59 tff(3734,plain,
% 3.40/2.59 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~c1_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c0_1(a599)) | (~c0_1(a607)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | (~c1_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c0_1(a599)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.40/2.59 inference(rewrite,[status(thm)],[])).
% 3.40/2.59 tff(3735,plain,
% 3.40/2.59 ((hskp15 | (~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599))) <=> (hskp15 | (~c1_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c0_1(a599)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.40/2.59 inference(rewrite,[status(thm)],[])).
% 3.40/2.59 tff(3736,plain,
% 3.40/2.59 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~c1_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c0_1(a599)) | (~c0_1(a607)) | (~c3_1(a607))))),
% 3.40/2.59 inference(monotonicity,[status(thm)],[3735])).
% 3.40/2.59 tff(3737,plain,
% 3.40/2.59 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | (~c1_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c0_1(a599)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.40/2.59 inference(transitivity,[status(thm)],[3736, 3734])).
% 3.40/2.59 tff(3738,plain,
% 3.40/2.59 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599)))),
% 3.40/2.59 inference(quant_inst,[status(thm)],[])).
% 3.40/2.59 tff(3739,plain,
% 3.40/2.59 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | (~c1_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c0_1(a599)) | (~c0_1(a607)) | (~c3_1(a607))),
% 3.40/2.59 inference(modus_ponens,[status(thm)],[3738, 3737])).
% 3.40/2.59 tff(3740,plain,
% 3.40/2.59 (hskp15 | (~c0_1(a599)) | (~c0_1(a607))),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[3739, 107, 321, 1077, 2986, 1012, 1993])).
% 3.40/2.59 tff(3741,plain,
% 3.40/2.59 (hskp15),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[3740, 3725, 3733])).
% 3.40/2.59 tff(3742,plain,
% 3.40/2.59 (~c0_1(a604)),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[1591, 3741])).
% 3.40/2.59 tff(3743,plain,
% 3.40/2.59 (c1_1(a604)),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[1613, 3741])).
% 3.40/2.59 tff(3744,plain,
% 3.40/2.59 (c2_1(a604)),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[3527, 107, 3703, 3743, 1009, 3742, 998, 32, 3722])).
% 3.40/2.59 tff(3745,plain,
% 3.40/2.59 (c3_1(a604)),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[1602, 3741])).
% 3.40/2.59 tff(3746,assumption,(hskp19), introduced(assumption)).
% 3.40/2.59 tff(3747,plain,
% 3.40/2.59 (~c1_1(a617)),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[2588, 3746])).
% 3.40/2.59 tff(3748,plain,
% 3.40/2.59 (~c0_1(a617)),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[2594, 3746])).
% 3.40/2.59 tff(3749,plain,
% 3.40/2.59 (c2_1(a617)),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[2605, 3746])).
% 3.40/2.59 tff(3750,plain,
% 3.40/2.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a617) | c1_1(a617) | (~c1_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c0_1(a607)) | (~c3_1(a607)) | (~c2_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a617) | c1_1(a617) | (~c1_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c0_1(a607)) | (~c3_1(a607)) | (~c2_1(a617)))),
% 3.40/2.59 inference(rewrite,[status(thm)],[])).
% 3.40/2.59 tff(3751,plain,
% 3.40/2.59 (((~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617))) <=> (c0_1(a617) | c1_1(a617) | (~c1_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c0_1(a607)) | (~c3_1(a607)) | (~c2_1(a617)))),
% 3.40/2.59 inference(rewrite,[status(thm)],[])).
% 3.40/2.59 tff(3752,plain,
% 3.40/2.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a617) | c1_1(a617) | (~c1_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c0_1(a607)) | (~c3_1(a607)) | (~c2_1(a617))))),
% 3.40/2.59 inference(monotonicity,[status(thm)],[3751])).
% 3.40/2.59 tff(3753,plain,
% 3.40/2.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a617) | c1_1(a617) | (~c1_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c0_1(a607)) | (~c3_1(a607)) | (~c2_1(a617)))),
% 3.40/2.59 inference(transitivity,[status(thm)],[3752, 3750])).
% 3.40/2.59 tff(3754,plain,
% 3.40/2.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))),
% 3.40/2.59 inference(quant_inst,[status(thm)],[])).
% 3.40/2.59 tff(3755,plain,
% 3.40/2.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a617) | c1_1(a617) | (~c1_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c0_1(a607)) | (~c3_1(a607)) | (~c2_1(a617))),
% 3.40/2.59 inference(modus_ponens,[status(thm)],[3754, 3753])).
% 3.40/2.59 tff(3756,plain,
% 3.40/2.59 ($false),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[3755, 107, 3749, 321, 2545, 3748, 3747, 2986, 2475, 65, 2486, 2538])).
% 3.40/2.59 tff(3757,plain,((~hskp19) | (~c3_1(a607)) | (~c3_1(a604)) | (~c1_1(a607)) | c0_1(a604) | (~c0_1(a607)) | (~c2_1(a604))), inference(lemma,lemma(discharge,[]))).
% 3.40/2.59 tff(3758,plain,
% 3.40/2.59 (~hskp19),
% 3.40/2.59 inference(unit_resolution,[status(thm)],[3757, 3745, 321, 2986, 3742, 3725, 3744])).
% 3.40/2.59 tff(3759,plain,
% 3.40/2.59 (^[U: $i] : refl((hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 3.40/2.59 inference(bind,[status(th)],[])).
% 3.40/2.59 tff(3760,plain,
% 3.40/2.59 (![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 3.40/2.59 inference(quant_intro,[status(thm)],[3759])).
% 3.40/2.59 tff(3761,plain,
% 3.40/2.59 (![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 3.40/2.59 inference(rewrite,[status(thm)],[])).
% 3.40/2.59 tff(3762,plain,
% 3.40/2.59 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp19) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp19))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp19) <=> (hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp19) <=> (hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp19) | hskp20) <=> ((hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp20))), rewrite(((hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp20) <=> (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp19) | hskp20) <=> (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 3.40/2.59 inference(bind,[status(th)],[])).
% 3.48/2.60 tff(3763,plain,
% 3.48/2.60 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp19) | hskp20) <=> ![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 3.48/2.60 inference(quant_intro,[status(thm)],[3762])).
% 3.48/2.60 tff(3764,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp19) | hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause163')).
% 3.48/2.60 tff(3765,plain,
% 3.48/2.60 (![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 3.48/2.60 inference(modus_ponens,[status(thm)],[3764, 3763])).
% 3.48/2.60 tff(3766,plain,
% 3.48/2.60 (![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 3.48/2.60 inference(modus_ponens,[status(thm)],[3765, 3761])).
% 3.48/2.60 tff(3767,plain,(
% 3.48/2.60 ![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 3.48/2.60 inference(skolemize,[status(sab)],[3766])).
% 3.48/2.60 tff(3768,plain,
% 3.48/2.60 (![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 3.48/2.60 inference(modus_ponens,[status(thm)],[3767, 3760])).
% 3.48/2.60 tff(3769,plain,
% 3.48/2.60 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp19 | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp20 | hskp19 | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.48/2.60 inference(rewrite,[status(thm)],[])).
% 3.48/2.60 tff(3770,plain,
% 3.48/2.60 ((hskp20 | hskp19 | (~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607))) <=> (hskp20 | hskp19 | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.48/2.60 inference(rewrite,[status(thm)],[])).
% 3.48/2.60 tff(3771,plain,
% 3.48/2.60 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp19 | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607))))),
% 3.48/2.60 inference(monotonicity,[status(thm)],[3770])).
% 3.48/2.60 tff(3772,plain,
% 3.48/2.60 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp20 | hskp19 | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.48/2.60 inference(transitivity,[status(thm)],[3771, 3769])).
% 3.48/2.60 tff(3773,plain,
% 3.48/2.60 ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)))),
% 3.48/2.60 inference(quant_inst,[status(thm)],[])).
% 3.48/2.60 tff(3774,plain,
% 3.48/2.60 ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp20 | hskp19 | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607))),
% 3.48/2.60 inference(modus_ponens,[status(thm)],[3773, 3772])).
% 3.48/2.60 tff(3775,plain,
% 3.48/2.60 (hskp20 | hskp19 | (~c1_1(a607)) | (~c0_1(a607))),
% 3.48/2.60 inference(unit_resolution,[status(thm)],[3774, 107, 321, 3768])).
% 3.48/2.60 tff(3776,plain,
% 3.48/2.60 (hskp20),
% 3.48/2.60 inference(unit_resolution,[status(thm)],[3775, 3758, 2986, 3725])).
% 3.48/2.60 tff(3777,plain,
% 3.48/2.60 (~c3_1(a623)),
% 3.48/2.60 inference(unit_resolution,[status(thm)],[709, 3776])).
% 3.48/2.60 tff(3778,plain,
% 3.48/2.60 (~c2_1(a623)),
% 3.48/2.60 inference(unit_resolution,[status(thm)],[715, 3776])).
% 3.48/2.60 tff(3779,plain,
% 3.48/2.60 (~c1_1(a623)),
% 3.48/2.60 inference(unit_resolution,[status(thm)],[721, 3776])).
% 3.48/2.60 tff(3780,plain,
% 3.48/2.60 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a623) | c2_1(a623) | c3_1(a623) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a623) | c2_1(a623) | c3_1(a623) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)))),
% 3.48/2.60 inference(rewrite,[status(thm)],[])).
% 3.48/2.60 tff(3781,plain,
% 3.48/2.60 ((hskp26 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c3_1(a623) | c1_1(a623) | c2_1(a623)) <=> (hskp26 | c1_1(a623) | c2_1(a623) | c3_1(a623) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)))),
% 3.48/2.60 inference(rewrite,[status(thm)],[])).
% 3.48/2.60 tff(3782,plain,
% 3.48/2.60 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c3_1(a623) | c1_1(a623) | c2_1(a623))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a623) | c2_1(a623) | c3_1(a623) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603))))),
% 3.48/2.60 inference(monotonicity,[status(thm)],[3781])).
% 3.48/2.60 tff(3783,plain,
% 3.48/2.60 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c3_1(a623) | c1_1(a623) | c2_1(a623))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a623) | c2_1(a623) | c3_1(a623) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)))),
% 3.48/2.60 inference(transitivity,[status(thm)],[3782, 3780])).
% 3.48/2.60 tff(3784,plain,
% 3.48/2.60 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c3_1(a623) | c1_1(a623) | c2_1(a623))),
% 3.48/2.60 inference(quant_inst,[status(thm)],[])).
% 3.48/2.60 tff(3785,plain,
% 3.48/2.60 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a623) | c2_1(a623) | c3_1(a623) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603))),
% 3.48/2.60 inference(modus_ponens,[status(thm)],[3784, 3783])).
% 3.48/2.60 tff(3786,plain,
% 3.48/2.60 ($false),
% 3.48/2.60 inference(unit_resolution,[status(thm)],[3785, 726, 107, 1009, 3779, 3778, 3777, 998, 995, 3722])).
% 3.48/2.60 tff(3787,plain,(hskp26 | (~c0_1(a603)) | c1_1(a603) | (~c1_1(a607)) | (~c3_1(a607)) | (~c2_1(a590)) | (~c3_1(a590)) | c0_1(a590) | c2_1(a607) | c3_1(a603)), inference(lemma,lemma(discharge,[]))).
% 3.48/2.60 tff(3788,plain,
% 3.48/2.60 (hskp26),
% 3.48/2.60 inference(unit_resolution,[status(thm)],[3787, 3716, 3715, 3697, 3180, 3596, 3382, 45, 22, 3714])).
% 3.48/2.60 tff(3789,plain,
% 3.48/2.60 (c2_1(a583)),
% 3.48/2.60 inference(unit_resolution,[status(thm)],[391, 3788])).
% 3.48/2.60 tff(3790,plain,
% 3.48/2.60 (c1_1(a583)),
% 3.48/2.60 inference(unit_resolution,[status(thm)],[351, 3788])).
% 3.48/2.60 tff(3791,plain,
% 3.48/2.60 (c0_1(a583)),
% 3.48/2.60 inference(unit_resolution,[status(thm)],[362, 3788])).
% 3.48/2.60 tff(3792,assumption,(hskp0), introduced(assumption)).
% 3.48/2.60 tff(3793,assumption,(~c1_1(a678)), introduced(assumption)).
% 3.48/2.60 tff(3794,plain,
% 3.48/2.60 (~c2_1(a584)),
% 3.48/2.60 inference(unit_resolution,[status(thm)],[1045, 3792])).
% 3.48/2.60 tff(3795,plain,
% 3.48/2.60 (~c0_1(a584)),
% 3.48/2.60 inference(unit_resolution,[status(thm)],[1051, 3792])).
% 3.48/2.60 tff(3796,plain,
% 3.48/2.60 (c1_1(a584)),
% 3.48/2.60 inference(unit_resolution,[status(thm)],[1062, 3792])).
% 3.48/2.60 tff(3797,plain,
% 3.48/2.60 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)))),
% 3.48/2.60 inference(rewrite,[status(thm)],[])).
% 3.48/2.60 tff(3798,plain,
% 3.48/2.60 ((hskp17 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584))) <=> (hskp17 | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)))),
% 3.48/2.60 inference(rewrite,[status(thm)],[])).
% 3.48/2.60 tff(3799,plain,
% 3.48/2.60 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678))))),
% 3.48/2.60 inference(monotonicity,[status(thm)],[3798])).
% 3.48/2.60 tff(3800,plain,
% 3.48/2.60 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)))),
% 3.48/2.60 inference(transitivity,[status(thm)],[3799, 3797])).
% 3.48/2.60 tff(3801,plain,
% 3.48/2.60 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584)))),
% 3.48/2.60 inference(quant_inst,[status(thm)],[])).
% 3.48/2.60 tff(3802,plain,
% 3.48/2.60 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678))),
% 3.48/2.60 inference(modus_ponens,[status(thm)],[3801, 3800])).
% 3.48/2.60 tff(3803,plain,
% 3.48/2.60 ($false),
% 3.48/2.60 inference(unit_resolution,[status(thm)],[3802, 107, 2987, 2318, 2317, 3796, 3795, 3794, 32, 3793])).
% 3.48/2.60 tff(3804,plain,((~hskp0) | hskp17 | (~c0_1(a678)) | (~c2_1(a678)) | c1_1(a678)), inference(lemma,lemma(discharge,[]))).
% 3.48/2.60 tff(3805,plain,
% 3.48/2.60 (c1_1(a678)),
% 3.48/2.60 inference(unit_resolution,[status(thm)],[3804, 3792, 2318, 2317, 3703])).
% 3.48/2.60 tff(3806,plain,
% 3.48/2.60 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c1_1(a678)) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c1_1(a678)) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)))),
% 3.48/2.60 inference(rewrite,[status(thm)],[])).
% 3.48/2.60 tff(3807,plain,
% 3.48/2.60 ((hskp10 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c1_1(a678)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583))) <=> (hskp10 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c1_1(a678)) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)))),
% 3.48/2.60 inference(rewrite,[status(thm)],[])).
% 3.48/2.60 tff(3808,plain,
% 3.48/2.60 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c1_1(a678)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c1_1(a678)) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583))))),
% 3.48/2.60 inference(monotonicity,[status(thm)],[3807])).
% 3.48/2.60 tff(3809,plain,
% 3.48/2.60 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c1_1(a678)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c1_1(a678)) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)))),
% 3.48/2.60 inference(transitivity,[status(thm)],[3808, 3806])).
% 3.48/2.60 tff(3810,plain,
% 3.48/2.60 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c1_1(a678)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583)))),
% 3.48/2.60 inference(quant_inst,[status(thm)],[])).
% 3.48/2.60 tff(3811,plain,
% 3.48/2.60 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c1_1(a678)) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583))),
% 3.48/2.60 inference(modus_ponens,[status(thm)],[3810, 3809])).
% 3.48/2.60 tff(3812,plain,
% 3.48/2.60 (hskp10 | (~c1_1(a678))),
% 3.48/2.60 inference(unit_resolution,[status(thm)],[3811, 107, 2317, 2316, 1651, 1650, 1649, 21])).
% 3.48/2.60 tff(3813,plain,
% 3.48/2.60 (hskp10),
% 3.48/2.60 inference(unit_resolution,[status(thm)],[3812, 3805])).
% 3.48/2.60 tff(3814,plain,
% 3.48/2.60 (~c1_1(a598)),
% 3.48/2.60 inference(unit_resolution,[status(thm)],[911, 3813])).
% 3.48/2.60 tff(3815,plain,
% 3.48/2.60 (c3_1(a598)),
% 3.48/2.60 inference(unit_resolution,[status(thm)],[881, 3813])).
% 3.48/2.60 tff(3816,plain,
% 3.48/2.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~c1_1(a607)) | c2_1(a607) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | (~c0_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (~c1_1(a607)) | c2_1(a607) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | (~c0_1(a607)))),
% 3.48/2.60 inference(rewrite,[status(thm)],[])).
% 3.48/2.60 tff(3817,plain,
% 3.48/2.60 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598))) <=> ((~c1_1(a607)) | c2_1(a607) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | (~c0_1(a607)))),
% 3.48/2.60 inference(rewrite,[status(thm)],[])).
% 3.48/2.60 tff(3818,plain,
% 3.48/2.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~c1_1(a607)) | c2_1(a607) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | (~c0_1(a607))))),
% 3.48/2.60 inference(monotonicity,[status(thm)],[3817])).
% 3.48/2.60 tff(3819,plain,
% 3.48/2.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (~c1_1(a607)) | c2_1(a607) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | (~c0_1(a607)))),
% 3.48/2.60 inference(transitivity,[status(thm)],[3818, 3816])).
% 3.48/2.60 tff(3820,plain,
% 3.48/2.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)))),
% 3.48/2.60 inference(quant_inst,[status(thm)],[])).
% 3.48/2.60 tff(3821,plain,
% 3.48/2.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (~c1_1(a607)) | c2_1(a607) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | (~c0_1(a607))),
% 3.48/2.60 inference(modus_ponens,[status(thm)],[3820, 3819])).
% 3.48/2.60 tff(3822,plain,
% 3.48/2.60 (c2_1(a598)),
% 3.48/2.60 inference(unit_resolution,[status(thm)],[3821, 107, 2318, 2317, 2316, 3815, 2986, 22, 3814, 1106, 2486])).
% 3.48/2.60 tff(3823,plain,
% 3.48/2.60 (c0_1(a598)),
% 3.48/2.60 inference(unit_resolution,[status(thm)],[892, 3813])).
% 3.48/2.60 tff(3824,plain,
% 3.48/2.60 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c1_1(a598) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a598)) | (~c0_1(a598)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c1_1(a598) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a598)) | (~c0_1(a598)))),
% 3.48/2.60 inference(rewrite,[status(thm)],[])).
% 3.48/2.60 tff(3825,plain,
% 3.48/2.60 ((hskp17 | (~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c0_1(a598)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584))) <=> (hskp17 | c1_1(a598) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a598)) | (~c0_1(a598)))),
% 3.48/2.60 inference(rewrite,[status(thm)],[])).
% 3.48/2.60 tff(3826,plain,
% 3.48/2.60 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c0_1(a598)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c1_1(a598) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a598)) | (~c0_1(a598))))),
% 3.48/2.60 inference(monotonicity,[status(thm)],[3825])).
% 3.48/2.60 tff(3827,plain,
% 3.48/2.60 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c0_1(a598)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c1_1(a598) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a598)) | (~c0_1(a598)))),
% 3.48/2.60 inference(transitivity,[status(thm)],[3826, 3824])).
% 3.48/2.60 tff(3828,plain,
% 3.48/2.60 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c0_1(a598)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584)))),
% 3.48/2.60 inference(quant_inst,[status(thm)],[])).
% 3.48/2.60 tff(3829,plain,
% 3.48/2.60 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c1_1(a598) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c2_1(a598)) | (~c0_1(a598))),
% 3.48/2.60 inference(modus_ponens,[status(thm)],[3828, 3827])).
% 3.48/2.60 tff(3830,plain,
% 3.48/2.60 ($false),
% 3.48/2.60 inference(unit_resolution,[status(thm)],[3829, 107, 3703, 3823, 3796, 3814, 3795, 3794, 32, 3822])).
% 3.48/2.60 tff(3831,plain,((~hskp0) | (~c0_1(a678)) | (~c2_1(a678)) | (~c3_1(a678)) | (~c1_1(a607)) | c2_1(a607) | (~c0_1(a607)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a583))), inference(lemma,lemma(discharge,[]))).
% 3.48/2.60 tff(3832,plain,
% 3.48/2.60 (~hskp0),
% 3.48/2.60 inference(unit_resolution,[status(thm)],[3831, 3697, 2281, 2270, 2292, 22, 3712, 3791, 3790, 3789])).
% 3.48/2.60 tff(3833,plain,
% 3.48/2.60 (((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp11 | hskp0 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)))),
% 3.48/2.60 inference(rewrite,[status(thm)],[])).
% 3.48/2.60 tff(3834,plain,
% 3.48/2.60 ((hskp11 | hskp0 | (~ndr1_0) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607))) <=> (hskp11 | hskp0 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)))),
% 3.48/2.60 inference(rewrite,[status(thm)],[])).
% 3.48/2.60 tff(3835,plain,
% 3.48/2.60 (((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | (~ndr1_0) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607))))),
% 3.48/2.60 inference(monotonicity,[status(thm)],[3834])).
% 3.48/2.60 tff(3836,plain,
% 3.48/2.60 (((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | (~ndr1_0) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp11 | hskp0 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)))),
% 3.48/2.60 inference(transitivity,[status(thm)],[3835, 3833])).
% 3.48/2.60 tff(3837,plain,
% 3.48/2.60 ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | (~ndr1_0) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))),
% 3.48/2.60 inference(quant_inst,[status(thm)],[])).
% 3.48/2.60 tff(3838,plain,
% 3.48/2.60 ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp11 | hskp0 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607))),
% 3.48/2.60 inference(modus_ponens,[status(thm)],[3837, 3836])).
% 3.48/2.60 tff(3839,plain,
% 3.48/2.60 (hskp11 | hskp0 | (~c1_1(a607)) | (~c0_1(a607))),
% 3.48/2.60 inference(unit_resolution,[status(thm)],[3838, 107, 22, 2347])).
% 3.48/2.60 tff(3840,plain,
% 3.48/2.60 (hskp11),
% 3.48/2.60 inference(unit_resolution,[status(thm)],[3839, 3832, 3697, 3712])).
% 3.48/2.60 tff(3841,plain,
% 3.48/2.60 (~c1_1(a599)),
% 3.48/2.60 inference(unit_resolution,[status(thm)],[428, 3840])).
% 3.48/2.60 tff(3842,plain,
% 3.48/2.60 (c2_1(a599)),
% 3.48/2.60 inference(unit_resolution,[status(thm)],[439, 3840])).
% 3.48/2.60 tff(3843,plain,
% 3.48/2.60 (c0_1(a599)),
% 3.48/2.60 inference(unit_resolution,[status(thm)],[3731, 107, 3180, 3842, 3596, 3382, 3697, 3841, 45, 65, 3712])).
% 3.48/2.60 tff(3844,plain,
% 3.48/2.60 (c3_1(a599)),
% 3.48/2.60 inference(unit_resolution,[status(thm)],[422, 3840])).
% 3.48/2.60 tff(3845,plain,
% 3.48/2.60 (hskp15),
% 3.48/2.60 inference(unit_resolution,[status(thm)],[3739, 107, 3180, 3844, 3697, 3841, 1993, 3712, 3843])).
% 3.48/2.60 tff(3846,plain,
% 3.48/2.60 (c3_1(a604)),
% 3.48/2.60 inference(unit_resolution,[status(thm)],[1602, 3845])).
% 3.48/2.60 tff(3847,plain,
% 3.48/2.60 (~c0_1(a604)),
% 3.48/2.60 inference(unit_resolution,[status(thm)],[1591, 3845])).
% 3.48/2.60 tff(3848,plain,
% 3.48/2.60 (c1_1(a604)),
% 3.48/2.60 inference(unit_resolution,[status(thm)],[1613, 3845])).
% 3.48/2.60 tff(3849,plain,
% 3.48/2.60 (c2_1(a604)),
% 3.48/2.60 inference(unit_resolution,[status(thm)],[2888, 107, 3698, 3848, 3842, 3847, 3841, 32, 3843])).
% 3.48/2.60 tff(3850,assumption,(~c1_1(a590)), introduced(assumption)).
% 3.48/2.60 tff(3851,plain,
% 3.48/2.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~c1_1(a607)) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | c1_1(a590) | (~c3_1(a604)) | (~c2_1(a604)) | (~c0_1(a607)) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (~c1_1(a607)) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | c1_1(a590) | (~c3_1(a604)) | (~c2_1(a604)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.48/2.60 inference(rewrite,[status(thm)],[])).
% 3.48/2.60 tff(3852,plain,
% 3.48/2.60 (((~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a590) | c0_1(a590) | (~c2_1(a590))) <=> ((~c1_1(a607)) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | c1_1(a590) | (~c3_1(a604)) | (~c2_1(a604)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.48/2.60 inference(rewrite,[status(thm)],[])).
% 3.48/2.60 tff(3853,plain,
% 3.48/2.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a590) | c0_1(a590) | (~c2_1(a590)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~c1_1(a607)) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | c1_1(a590) | (~c3_1(a604)) | (~c2_1(a604)) | (~c0_1(a607)) | (~c3_1(a607))))),
% 3.48/2.60 inference(monotonicity,[status(thm)],[3852])).
% 3.48/2.60 tff(3854,plain,
% 3.48/2.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a590) | c0_1(a590) | (~c2_1(a590)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (~c1_1(a607)) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | c1_1(a590) | (~c3_1(a604)) | (~c2_1(a604)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.48/2.60 inference(transitivity,[status(thm)],[3853, 3851])).
% 3.48/2.61 tff(3855,plain,
% 3.48/2.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a590) | c0_1(a590) | (~c2_1(a590)))),
% 3.48/2.61 inference(quant_inst,[status(thm)],[])).
% 3.48/2.61 tff(3856,plain,
% 3.48/2.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (~c1_1(a607)) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | c1_1(a590) | (~c3_1(a604)) | (~c2_1(a604)) | (~c0_1(a607)) | (~c3_1(a607))),
% 3.48/2.61 inference(modus_ponens,[status(thm)],[3855, 3854])).
% 3.48/2.61 tff(3857,plain,
% 3.48/2.61 ($false),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[3856, 107, 321, 2545, 863, 2986, 2475, 45, 65, 2486, 2538, 3850])).
% 3.48/2.61 tff(3858,plain,(c1_1(a590) | (~c3_1(a607)) | (~c3_1(a604)) | (~c2_1(a590)) | (~c1_1(a607)) | c0_1(a604) | c0_1(a590) | (~c0_1(a607)) | (~c2_1(a604))), inference(lemma,lemma(discharge,[]))).
% 3.48/2.61 tff(3859,plain,
% 3.48/2.61 (c1_1(a590)),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[3858, 3849, 3180, 3596, 3697, 3847, 45, 3712, 3846])).
% 3.48/2.61 tff(3860,plain,
% 3.48/2.61 (~hskp19),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[3757, 3849, 3180, 3697, 3847, 3712, 3846])).
% 3.48/2.61 tff(3861,plain,
% 3.48/2.61 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c1_1(a590)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp19 | hskp13 | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c1_1(a590)))),
% 3.48/2.61 inference(rewrite,[status(thm)],[])).
% 3.48/2.61 tff(3862,plain,
% 3.48/2.61 ((hskp19 | hskp13 | (~ndr1_0) | c0_1(a590) | (~c2_1(a590)) | (~c1_1(a590))) <=> (hskp19 | hskp13 | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c1_1(a590)))),
% 3.48/2.61 inference(rewrite,[status(thm)],[])).
% 3.48/2.61 tff(3863,plain,
% 3.48/2.61 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c0_1(a590) | (~c2_1(a590)) | (~c1_1(a590)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c1_1(a590))))),
% 3.48/2.61 inference(monotonicity,[status(thm)],[3862])).
% 3.48/2.61 tff(3864,plain,
% 3.48/2.61 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c0_1(a590) | (~c2_1(a590)) | (~c1_1(a590)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp19 | hskp13 | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c1_1(a590)))),
% 3.48/2.61 inference(transitivity,[status(thm)],[3863, 3861])).
% 3.48/2.61 tff(3865,plain,
% 3.48/2.61 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c0_1(a590) | (~c2_1(a590)) | (~c1_1(a590)))),
% 3.48/2.61 inference(quant_inst,[status(thm)],[])).
% 3.48/2.61 tff(3866,plain,
% 3.48/2.61 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp19 | hskp13 | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | (~c1_1(a590))),
% 3.48/2.61 inference(modus_ponens,[status(thm)],[3865, 3864])).
% 3.48/2.61 tff(3867,plain,
% 3.48/2.61 (hskp19 | hskp13 | (~c2_1(a590)) | (~c1_1(a590))),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[3866, 107, 45, 2564])).
% 3.48/2.61 tff(3868,plain,
% 3.48/2.61 (hskp13),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[3867, 3860, 3596, 3859])).
% 3.48/2.61 tff(3869,plain,
% 3.48/2.61 (~c2_1(a601)),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[2523, 3868])).
% 3.48/2.61 tff(3870,plain,
% 3.48/2.61 (~c1_1(a601)),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[2529, 3868])).
% 3.48/2.61 tff(3871,plain,
% 3.48/2.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~c1_1(a607)) | c2_1(a607) | c1_1(a601) | c2_1(a601) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a601)) | (~c0_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (~c1_1(a607)) | c2_1(a607) | c1_1(a601) | c2_1(a601) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a601)) | (~c0_1(a607)))),
% 3.48/2.61 inference(rewrite,[status(thm)],[])).
% 3.48/2.61 tff(3872,plain,
% 3.48/2.61 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a601) | c2_1(a601) | (~c3_1(a601))) <=> ((~c1_1(a607)) | c2_1(a607) | c1_1(a601) | c2_1(a601) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a601)) | (~c0_1(a607)))),
% 3.48/2.61 inference(rewrite,[status(thm)],[])).
% 3.48/2.61 tff(3873,plain,
% 3.48/2.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a601) | c2_1(a601) | (~c3_1(a601)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~c1_1(a607)) | c2_1(a607) | c1_1(a601) | c2_1(a601) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a601)) | (~c0_1(a607))))),
% 3.48/2.61 inference(monotonicity,[status(thm)],[3872])).
% 3.48/2.61 tff(3874,plain,
% 3.48/2.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a601) | c2_1(a601) | (~c3_1(a601)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (~c1_1(a607)) | c2_1(a607) | c1_1(a601) | c2_1(a601) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a601)) | (~c0_1(a607)))),
% 3.48/2.61 inference(transitivity,[status(thm)],[3873, 3871])).
% 3.48/2.61 tff(3875,plain,
% 3.48/2.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a601) | c2_1(a601) | (~c3_1(a601)))),
% 3.48/2.61 inference(quant_inst,[status(thm)],[])).
% 3.48/2.61 tff(3876,plain,
% 3.48/2.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (~c1_1(a607)) | c2_1(a607) | c1_1(a601) | c2_1(a601) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a601)) | (~c0_1(a607))),
% 3.48/2.61 inference(modus_ponens,[status(thm)],[3875, 3874])).
% 3.48/2.61 tff(3877,plain,
% 3.48/2.61 (~c3_1(a601)),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[3876, 107, 2292, 2281, 2270, 3697, 22, 3870, 3869, 1106, 3712])).
% 3.48/2.61 tff(3878,plain,
% 3.48/2.61 (~c0_1(a601)),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[2543, 3868])).
% 3.48/2.61 tff(3879,plain,
% 3.48/2.61 ($false),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[2551, 107, 3846, 3842, 3844, 3847, 3878, 3869, 3841, 1730, 3849, 3877])).
% 3.48/2.61 tff(3880,plain,(c0_1(a590) | c2_1(a607) | hskp22), inference(lemma,lemma(discharge,[]))).
% 3.48/2.61 tff(3881,plain,
% 3.48/2.61 (c0_1(a590)),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[3880, 22, 44])).
% 3.48/2.61 tff(3882,plain,
% 3.48/2.61 (~hskp6),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[666, 3881])).
% 3.48/2.61 tff(3883,plain,
% 3.48/2.61 (hskp26),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[3404, 66, 22, 3882, 44])).
% 3.48/2.61 tff(3884,plain,
% 3.48/2.61 (c2_1(a583)),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[391, 3883])).
% 3.48/2.61 tff(3885,plain,
% 3.48/2.61 (c0_1(a583)),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[362, 3883])).
% 3.48/2.61 tff(3886,plain,
% 3.48/2.61 (c1_1(a583)),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[351, 3883])).
% 3.48/2.61 tff(3887,plain,
% 3.48/2.61 ($false),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[3563, 3886, 3885, 44, 22, 3882, 66, 3884])).
% 3.48/2.61 tff(3888,plain,(c1_1(a607) | hskp22 | c2_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.48/2.61 tff(3889,plain,
% 3.48/2.61 (c1_1(a607)),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[3888, 22, 44])).
% 3.48/2.61 tff(3890,plain,
% 3.48/2.61 (~hskp17),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[281, 3889])).
% 3.48/2.61 tff(3891,plain,
% 3.48/2.61 (hskp3),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[3427, 3889, 3180, 3890])).
% 3.48/2.61 tff(3892,plain,
% 3.48/2.61 (~c1_1(a587)),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[939, 3891])).
% 3.48/2.61 tff(3893,plain,
% 3.48/2.61 (c0_1(a587)),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[961, 3891])).
% 3.48/2.61 tff(3894,plain,
% 3.48/2.61 (c2_1(a587)),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[950, 3891])).
% 3.48/2.61 tff(3895,plain,
% 3.48/2.61 (c0_1(a607)),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[3711, 3894, 3893, 3889, 22, 3892])).
% 3.48/2.61 tff(3896,plain,
% 3.48/2.61 (hskp11),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[3529, 3882, 44, 22])).
% 3.48/2.61 tff(3897,plain,
% 3.48/2.61 (~c1_1(a599)),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[428, 3896])).
% 3.48/2.61 tff(3898,plain,
% 3.48/2.61 (c3_1(a599)),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[422, 3896])).
% 3.48/2.61 tff(3899,plain,
% 3.48/2.61 (c2_1(a599)),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[439, 3896])).
% 3.48/2.61 tff(3900,assumption,(~c0_1(a599)), introduced(assumption)).
% 3.48/2.61 tff(3901,plain,
% 3.48/2.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~c1_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599) | (~c0_1(a607)) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (~c1_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.48/2.61 inference(rewrite,[status(thm)],[])).
% 3.48/2.61 tff(3902,plain,
% 3.48/2.61 (((~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599))) <=> ((~c1_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.48/2.61 inference(rewrite,[status(thm)],[])).
% 3.48/2.61 tff(3903,plain,
% 3.48/2.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~c1_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599) | (~c0_1(a607)) | (~c3_1(a607))))),
% 3.48/2.61 inference(monotonicity,[status(thm)],[3902])).
% 3.48/2.61 tff(3904,plain,
% 3.48/2.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (~c1_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.48/2.61 inference(transitivity,[status(thm)],[3903, 3901])).
% 3.48/2.61 tff(3905,plain,
% 3.48/2.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))),
% 3.48/2.61 inference(quant_inst,[status(thm)],[])).
% 3.48/2.61 tff(3906,plain,
% 3.48/2.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (~c1_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599) | (~c0_1(a607)) | (~c3_1(a607))),
% 3.48/2.61 inference(modus_ponens,[status(thm)],[3905, 3904])).
% 3.48/2.61 tff(3907,plain,
% 3.48/2.61 ($false),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[3906, 107, 321, 463, 462, 2986, 461, 65, 2486, 3900])).
% 3.48/2.61 tff(3908,plain,(c0_1(a599) | (~c3_1(a607)) | (~c2_1(a599)) | (~c3_1(a599)) | (~c1_1(a607)) | c1_1(a599) | (~c0_1(a607))), inference(lemma,lemma(discharge,[]))).
% 3.48/2.61 tff(3909,plain,
% 3.48/2.61 (c0_1(a599)),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[3908, 3180, 3899, 3898, 3889, 3897, 3895])).
% 3.48/2.61 tff(3910,plain,
% 3.48/2.61 (hskp15 | (~c1_1(a607)) | (~c0_1(a599)) | (~c0_1(a607))),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[3739, 107, 3180, 3898, 3897, 1993])).
% 3.48/2.61 tff(3911,plain,
% 3.48/2.61 (hskp15),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[3910, 3909, 3889, 3895])).
% 3.48/2.61 tff(3912,plain,
% 3.48/2.61 (c3_1(a604)),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[1602, 3911])).
% 3.48/2.61 tff(3913,plain,
% 3.48/2.61 (~c0_1(a604)),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[1591, 3911])).
% 3.48/2.61 tff(3914,plain,
% 3.48/2.61 (hskp14),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[3313, 3889, 3180])).
% 3.48/2.61 tff(3915,plain,
% 3.48/2.61 (~c1_1(a603)),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[171, 3914])).
% 3.48/2.61 tff(3916,plain,
% 3.48/2.61 (c0_1(a603)),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[182, 3914])).
% 3.48/2.61 tff(3917,plain,
% 3.48/2.61 (c2_1(a603)),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[189, 107, 44, 3882, 3916, 3915, 43])).
% 3.48/2.61 tff(3918,plain,
% 3.48/2.61 (c1_1(a604)),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[1613, 3911])).
% 3.48/2.61 tff(3919,plain,
% 3.48/2.61 (c2_1(a604)),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[3527, 107, 3890, 3918, 3916, 3913, 3915, 32, 3917])).
% 3.48/2.61 tff(3920,plain,
% 3.48/2.61 (~hskp19),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[3757, 3919, 3180, 3889, 3913, 3895, 3912])).
% 3.48/2.61 tff(3921,plain,
% 3.48/2.61 (hskp20 | hskp19 | (~c1_1(a607)) | (~c0_1(a607))),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[3774, 107, 3180, 3768])).
% 3.48/2.61 tff(3922,plain,
% 3.48/2.61 (hskp20),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[3921, 3920, 3889, 3895])).
% 3.48/2.61 tff(3923,plain,
% 3.48/2.61 (~c2_1(a623)),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[715, 3922])).
% 3.48/2.61 tff(3924,plain,
% 3.48/2.61 (~c1_1(a623)),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[721, 3922])).
% 3.48/2.61 tff(3925,plain,
% 3.48/2.61 (((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | c1_1(a623) | c2_1(a623) | (~ndr1_0) | (~c0_1(a623)))) <=> ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp22 | hskp6 | c1_1(a623) | c2_1(a623) | (~ndr1_0) | (~c0_1(a623)))),
% 3.48/2.61 inference(rewrite,[status(thm)],[])).
% 3.48/2.61 tff(3926,plain,
% 3.48/2.61 ((hskp22 | hskp6 | (~ndr1_0) | c2_1(a623) | c1_1(a623) | (~c0_1(a623))) <=> (hskp22 | hskp6 | c1_1(a623) | c2_1(a623) | (~ndr1_0) | (~c0_1(a623)))),
% 3.48/2.61 inference(rewrite,[status(thm)],[])).
% 3.48/2.61 tff(3927,plain,
% 3.48/2.61 (((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | (~ndr1_0) | c2_1(a623) | c1_1(a623) | (~c0_1(a623)))) <=> ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | c1_1(a623) | c2_1(a623) | (~ndr1_0) | (~c0_1(a623))))),
% 3.48/2.61 inference(monotonicity,[status(thm)],[3926])).
% 3.48/2.61 tff(3928,plain,
% 3.48/2.61 (((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | (~ndr1_0) | c2_1(a623) | c1_1(a623) | (~c0_1(a623)))) <=> ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp22 | hskp6 | c1_1(a623) | c2_1(a623) | (~ndr1_0) | (~c0_1(a623)))),
% 3.48/2.61 inference(transitivity,[status(thm)],[3927, 3925])).
% 3.48/2.61 tff(3929,plain,
% 3.48/2.61 ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp22 | hskp6 | (~ndr1_0) | c2_1(a623) | c1_1(a623) | (~c0_1(a623)))),
% 3.48/2.61 inference(quant_inst,[status(thm)],[])).
% 3.48/2.61 tff(3930,plain,
% 3.48/2.61 ((~![U: $i] : (hskp22 | hskp6 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp22 | hskp6 | c1_1(a623) | c2_1(a623) | (~ndr1_0) | (~c0_1(a623))),
% 3.48/2.61 inference(modus_ponens,[status(thm)],[3929, 3928])).
% 3.48/2.61 tff(3931,plain,
% 3.48/2.61 (~c0_1(a623)),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[3930, 107, 44, 3882, 3924, 3923, 43])).
% 3.48/2.61 tff(3932,plain,
% 3.48/2.61 (~hskp4),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[147, 3882, 44])).
% 3.48/2.61 tff(3933,plain,
% 3.48/2.61 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp10 | hskp4 | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp10 | hskp4 | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)))),
% 3.48/2.61 inference(rewrite,[status(thm)],[])).
% 3.48/2.61 tff(3934,plain,
% 3.48/2.61 ((hskp10 | hskp4 | (~ndr1_0) | c0_1(a604) | (~c2_1(a604)) | (~c3_1(a604))) <=> (hskp10 | hskp4 | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)))),
% 3.48/2.61 inference(rewrite,[status(thm)],[])).
% 3.48/2.61 tff(3935,plain,
% 3.48/2.61 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c0_1(a604) | (~c2_1(a604)) | (~c3_1(a604)))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp10 | hskp4 | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604))))),
% 3.48/2.61 inference(monotonicity,[status(thm)],[3934])).
% 3.48/2.61 tff(3936,plain,
% 3.48/2.61 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c0_1(a604) | (~c2_1(a604)) | (~c3_1(a604)))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp10 | hskp4 | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)))),
% 3.48/2.61 inference(transitivity,[status(thm)],[3935, 3933])).
% 3.48/2.61 tff(3937,plain,
% 3.48/2.61 ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c0_1(a604) | (~c2_1(a604)) | (~c3_1(a604)))),
% 3.48/2.61 inference(quant_inst,[status(thm)],[])).
% 3.48/2.61 tff(3938,plain,
% 3.48/2.61 ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp10 | hskp4 | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604))),
% 3.48/2.61 inference(modus_ponens,[status(thm)],[3937, 3936])).
% 3.48/2.61 tff(3939,plain,
% 3.48/2.61 (hskp10),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[3938, 107, 3932, 3912, 3913, 861, 3919])).
% 3.48/2.61 tff(3940,plain,
% 3.48/2.61 (~c1_1(a598)),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[911, 3939])).
% 3.48/2.61 tff(3941,plain,
% 3.48/2.61 (c3_1(a598)),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[881, 3939])).
% 3.48/2.61 tff(3942,plain,
% 3.48/2.61 (c2_1(a598)),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[3821, 107, 2292, 2281, 2270, 3941, 3889, 22, 3940, 1106, 3895])).
% 3.48/2.61 tff(3943,plain,
% 3.48/2.61 (~c3_1(a623)),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[709, 3922])).
% 3.48/2.61 tff(3944,plain,
% 3.48/2.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a623) | c3_1(a623) | c0_1(a604) | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c3_1(a604)) | (~c2_1(a604)) | c0_1(a623))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a623) | c3_1(a623) | c0_1(a604) | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c3_1(a604)) | (~c2_1(a604)) | c0_1(a623))),
% 3.48/2.61 inference(rewrite,[status(thm)],[])).
% 3.48/2.61 tff(3945,plain,
% 3.48/2.61 (((~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c3_1(a598)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c3_1(a623) | c0_1(a623) | c2_1(a623)) <=> (c2_1(a623) | c3_1(a623) | c0_1(a604) | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c3_1(a604)) | (~c2_1(a604)) | c0_1(a623))),
% 3.48/2.61 inference(rewrite,[status(thm)],[])).
% 3.48/2.61 tff(3946,plain,
% 3.48/2.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c3_1(a598)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c3_1(a623) | c0_1(a623) | c2_1(a623))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a623) | c3_1(a623) | c0_1(a604) | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c3_1(a604)) | (~c2_1(a604)) | c0_1(a623)))),
% 3.48/2.61 inference(monotonicity,[status(thm)],[3945])).
% 3.48/2.61 tff(3947,plain,
% 3.48/2.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c3_1(a598)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c3_1(a623) | c0_1(a623) | c2_1(a623))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a623) | c3_1(a623) | c0_1(a604) | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c3_1(a604)) | (~c2_1(a604)) | c0_1(a623))),
% 3.48/2.61 inference(transitivity,[status(thm)],[3946, 3944])).
% 3.48/2.61 tff(3948,plain,
% 3.48/2.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c3_1(a598)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c3_1(a623) | c0_1(a623) | c2_1(a623))),
% 3.48/2.61 inference(quant_inst,[status(thm)],[])).
% 3.48/2.61 tff(3949,plain,
% 3.48/2.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a623) | c3_1(a623) | c0_1(a604) | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c3_1(a604)) | (~c2_1(a604)) | c0_1(a623)),
% 3.48/2.61 inference(modus_ponens,[status(thm)],[3948, 3947])).
% 3.48/2.61 tff(3950,plain,
% 3.48/2.61 ($false),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[3949, 107, 3912, 3941, 3923, 3943, 3913, 3940, 1730, 3942, 3919, 3931])).
% 3.48/2.61 tff(3951,plain,(c2_1(a607) | hskp22), inference(lemma,lemma(discharge,[]))).
% 3.48/2.61 tff(3952,plain,
% 3.48/2.61 (hskp22),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[3951, 22])).
% 3.48/2.61 tff(3953,plain,
% 3.48/2.61 (((~hskp22) | c1_1(a633)) <=> ((~hskp22) | c1_1(a633))),
% 3.48/2.61 inference(rewrite,[status(thm)],[])).
% 3.48/2.61 tff(3954,axiom,((~hskp22) | c1_1(a633)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause52')).
% 3.48/2.61 tff(3955,plain,
% 3.48/2.61 ((~hskp22) | c1_1(a633)),
% 3.48/2.61 inference(modus_ponens,[status(thm)],[3954, 3953])).
% 3.48/2.61 tff(3956,plain,
% 3.48/2.61 ((~hskp22) | c1_1(a633)),
% 3.48/2.61 inference(modus_ponens,[status(thm)],[3955, 3953])).
% 3.48/2.61 tff(3957,plain,
% 3.48/2.61 ((~hskp22) | c1_1(a633)),
% 3.48/2.61 inference(modus_ponens,[status(thm)],[3956, 3953])).
% 3.48/2.61 tff(3958,plain,
% 3.48/2.61 ((~hskp22) | c1_1(a633)),
% 3.48/2.61 inference(modus_ponens,[status(thm)],[3957, 3953])).
% 3.48/2.61 tff(3959,plain,
% 3.48/2.61 ((~hskp22) | c1_1(a633)),
% 3.48/2.61 inference(modus_ponens,[status(thm)],[3958, 3953])).
% 3.48/2.61 tff(3960,plain,
% 3.48/2.61 ((~hskp22) | c1_1(a633)),
% 3.48/2.61 inference(modus_ponens,[status(thm)],[3959, 3953])).
% 3.48/2.61 tff(3961,plain,
% 3.48/2.61 ((~hskp22) | c1_1(a633)),
% 3.48/2.61 inference(modus_ponens,[status(thm)],[3960, 3953])).
% 3.48/2.61 tff(3962,plain,
% 3.48/2.61 ((~hskp22) | c1_1(a633)),
% 3.48/2.61 inference(modus_ponens,[status(thm)],[3961, 3953])).
% 3.48/2.61 tff(3963,plain,
% 3.48/2.61 (c1_1(a633)),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[3962, 3952])).
% 3.48/2.61 tff(3964,plain,
% 3.48/2.61 (((~hskp22) | (~c0_1(a633))) <=> ((~hskp22) | (~c0_1(a633)))),
% 3.48/2.61 inference(rewrite,[status(thm)],[])).
% 3.48/2.61 tff(3965,plain,
% 3.48/2.61 (((~c0_1(a633)) | (~hskp22)) <=> ((~hskp22) | (~c0_1(a633)))),
% 3.48/2.61 inference(rewrite,[status(thm)],[])).
% 3.48/2.61 tff(3966,axiom,((~c0_1(a633)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause87')).
% 3.48/2.61 tff(3967,plain,
% 3.48/2.61 ((~hskp22) | (~c0_1(a633))),
% 3.48/2.61 inference(modus_ponens,[status(thm)],[3966, 3965])).
% 3.48/2.61 tff(3968,plain,
% 3.48/2.61 ((~hskp22) | (~c0_1(a633))),
% 3.48/2.61 inference(modus_ponens,[status(thm)],[3967, 3964])).
% 3.48/2.61 tff(3969,plain,
% 3.48/2.61 (~c0_1(a633)),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[3968, 3952])).
% 3.48/2.61 tff(3970,plain,
% 3.48/2.61 (((~hskp22) | (~c3_1(a633))) <=> ((~hskp22) | (~c3_1(a633)))),
% 3.48/2.61 inference(rewrite,[status(thm)],[])).
% 3.48/2.61 tff(3971,plain,
% 3.48/2.61 (((~c3_1(a633)) | (~hskp22)) <=> ((~hskp22) | (~c3_1(a633)))),
% 3.48/2.61 inference(rewrite,[status(thm)],[])).
% 3.48/2.61 tff(3972,axiom,((~c3_1(a633)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause88')).
% 3.48/2.61 tff(3973,plain,
% 3.48/2.61 ((~hskp22) | (~c3_1(a633))),
% 3.48/2.61 inference(modus_ponens,[status(thm)],[3972, 3971])).
% 3.48/2.61 tff(3974,plain,
% 3.48/2.61 ((~hskp22) | (~c3_1(a633))),
% 3.48/2.61 inference(modus_ponens,[status(thm)],[3973, 3970])).
% 3.48/2.61 tff(3975,plain,
% 3.48/2.61 (~c3_1(a633)),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[3974, 3952])).
% 3.48/2.61 tff(3976,plain,
% 3.48/2.61 (hskp22),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[3888, 22, 66])).
% 3.48/2.61 tff(3977,plain,
% 3.48/2.61 (c1_1(a633)),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[3962, 3976])).
% 3.48/2.61 tff(3978,plain,
% 3.48/2.61 (~c3_1(a633)),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[3974, 3976])).
% 3.48/2.61 tff(3979,plain,
% 3.48/2.61 (~c0_1(a633)),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[3968, 3976])).
% 3.48/2.61 tff(3980,assumption,(~c3_1(a633)), introduced(assumption)).
% 3.48/2.61 tff(3981,assumption,(~c0_1(a633)), introduced(assumption)).
% 3.48/2.61 tff(3982,plain,
% 3.48/2.61 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | c0_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c2_1(a633))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | c0_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c2_1(a633))),
% 3.48/2.61 inference(rewrite,[status(thm)],[])).
% 3.48/2.61 tff(3983,plain,
% 3.48/2.61 ((hskp11 | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c3_1(a633) | c0_1(a633) | c2_1(a633)) <=> (hskp11 | c0_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c2_1(a633))),
% 3.48/2.61 inference(rewrite,[status(thm)],[])).
% 3.48/2.61 tff(3984,plain,
% 3.48/2.61 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c3_1(a633) | c0_1(a633) | c2_1(a633))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | c0_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c2_1(a633)))),
% 3.48/2.61 inference(monotonicity,[status(thm)],[3983])).
% 3.48/2.61 tff(3985,plain,
% 3.48/2.61 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c3_1(a633) | c0_1(a633) | c2_1(a633))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | c0_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c2_1(a633))),
% 3.48/2.61 inference(transitivity,[status(thm)],[3984, 3982])).
% 3.48/2.61 tff(3986,plain,
% 3.48/2.61 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c3_1(a633) | c0_1(a633) | c2_1(a633))),
% 3.48/2.61 inference(quant_inst,[status(thm)],[])).
% 3.48/2.61 tff(3987,plain,
% 3.48/2.61 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | c0_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c2_1(a633)),
% 3.48/2.61 inference(modus_ponens,[status(thm)],[3986, 3985])).
% 3.48/2.61 tff(3988,plain,
% 3.48/2.61 ((~c3_1(a583)) | c2_1(a633)),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[3987, 1638, 107, 3321, 3330, 3981, 3980, 268])).
% 3.48/2.61 tff(3989,plain,
% 3.48/2.61 (c2_1(a633)),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[3988, 3340])).
% 3.48/2.61 tff(3990,plain,
% 3.48/2.61 (hskp10),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[3497, 3340])).
% 3.48/2.61 tff(3991,plain,
% 3.48/2.61 (~c1_1(a598)),
% 3.48/2.61 inference(unit_resolution,[status(thm)],[911, 3990])).
% 3.48/2.61 tff(3992,assumption,(c1_1(a633)), introduced(assumption)).
% 3.48/2.61 tff(3993,plain,
% 3.48/2.61 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | c0_1(a633) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a633)) | (~c1_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | c0_1(a633) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a633)) | (~c1_1(a633)))),
% 3.48/2.61 inference(rewrite,[status(thm)],[])).
% 3.48/2.61 tff(3994,plain,
% 3.48/2.61 ((hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633))) <=> (hskp12 | c0_1(a633) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a633)) | (~c1_1(a633)))),
% 3.48/2.61 inference(rewrite,[status(thm)],[])).
% 3.48/2.61 tff(3995,plain,
% 3.48/2.61 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | c0_1(a633) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a633)) | (~c1_1(a633))))),
% 3.48/2.62 inference(monotonicity,[status(thm)],[3994])).
% 3.48/2.62 tff(3996,plain,
% 3.48/2.62 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | c0_1(a633) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a633)) | (~c1_1(a633)))),
% 3.48/2.62 inference(transitivity,[status(thm)],[3995, 3993])).
% 3.48/2.62 tff(3997,plain,
% 3.48/2.62 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633)))),
% 3.48/2.62 inference(quant_inst,[status(thm)],[])).
% 3.48/2.62 tff(3998,plain,
% 3.48/2.62 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | c0_1(a633) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a633)) | (~c1_1(a633))),
% 3.48/2.62 inference(modus_ponens,[status(thm)],[3997, 3996])).
% 3.48/2.62 tff(3999,plain,
% 3.48/2.62 (hskp12 | (~c2_1(a633))),
% 3.48/2.62 inference(unit_resolution,[status(thm)],[3998, 107, 3321, 3322, 3330, 3992, 3981, 2727])).
% 3.48/2.62 tff(4000,plain,
% 3.48/2.62 (hskp12),
% 3.48/2.62 inference(unit_resolution,[status(thm)],[3999, 3989])).
% 3.48/2.62 tff(4001,plain,
% 3.48/2.62 (~c3_1(a600)),
% 3.48/2.62 inference(unit_resolution,[status(thm)],[741, 4000])).
% 3.48/2.62 tff(4002,plain,
% 3.48/2.62 (c3_1(a598)),
% 3.48/2.62 inference(unit_resolution,[status(thm)],[881, 3990])).
% 3.48/2.62 tff(4003,plain,
% 3.48/2.62 (c2_1(a600)),
% 3.48/2.62 inference(unit_resolution,[status(thm)],[752, 4000])).
% 3.48/2.62 tff(4004,plain,
% 3.48/2.62 (c0_1(a600)),
% 3.48/2.62 inference(unit_resolution,[status(thm)],[763, 4000])).
% 3.48/2.62 tff(4005,plain,
% 3.48/2.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a633) | c3_1(a633) | c3_1(a600) | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c2_1(a600)) | (~c0_1(a600)) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a633) | c3_1(a633) | c3_1(a600) | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c2_1(a600)) | (~c0_1(a600)) | (~c1_1(a633)))),
% 3.48/2.62 inference(rewrite,[status(thm)],[])).
% 3.48/2.62 tff(4006,plain,
% 3.48/2.62 (((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a598) | (~c3_1(a598)) | (~c2_1(a598)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633))) <=> (c0_1(a633) | c3_1(a633) | c3_1(a600) | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c2_1(a600)) | (~c0_1(a600)) | (~c1_1(a633)))),
% 3.48/2.62 inference(rewrite,[status(thm)],[])).
% 3.48/2.62 tff(4007,plain,
% 3.48/2.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a598) | (~c3_1(a598)) | (~c2_1(a598)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a633) | c3_1(a633) | c3_1(a600) | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c2_1(a600)) | (~c0_1(a600)) | (~c1_1(a633))))),
% 3.48/2.62 inference(monotonicity,[status(thm)],[4006])).
% 3.48/2.62 tff(4008,plain,
% 3.48/2.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a598) | (~c3_1(a598)) | (~c2_1(a598)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a633) | c3_1(a633) | c3_1(a600) | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c2_1(a600)) | (~c0_1(a600)) | (~c1_1(a633)))),
% 3.48/2.62 inference(transitivity,[status(thm)],[4007, 4005])).
% 3.48/2.62 tff(4009,plain,
% 3.48/2.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a598) | (~c3_1(a598)) | (~c2_1(a598)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))),
% 3.48/2.62 inference(quant_inst,[status(thm)],[])).
% 3.48/2.62 tff(4010,plain,
% 3.48/2.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a633) | c3_1(a633) | c3_1(a600) | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c2_1(a600)) | (~c0_1(a600)) | (~c1_1(a633))),
% 3.48/2.62 inference(modus_ponens,[status(thm)],[4009, 4008])).
% 3.48/2.62 tff(4011,plain,
% 3.48/2.62 (~c2_1(a598)),
% 3.48/2.62 inference(unit_resolution,[status(thm)],[4010, 107, 3992, 4004, 4003, 4002, 3981, 3980, 4001, 3991, 258])).
% 3.48/2.62 tff(4012,plain,
% 3.48/2.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a633) | c1_1(a598) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c3_1(a598)) | c2_1(a598) | (~c2_1(a633)) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a633) | c1_1(a598) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c3_1(a598)) | c2_1(a598) | (~c2_1(a633)) | (~c1_1(a633)))),
% 3.48/2.62 inference(rewrite,[status(thm)],[])).
% 3.48/2.62 tff(4013,plain,
% 3.48/2.62 (((~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633))) <=> (c0_1(a633) | c1_1(a598) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c3_1(a598)) | c2_1(a598) | (~c2_1(a633)) | (~c1_1(a633)))),
% 3.48/2.62 inference(rewrite,[status(thm)],[])).
% 3.48/2.62 tff(4014,plain,
% 3.48/2.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a633) | c1_1(a598) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c3_1(a598)) | c2_1(a598) | (~c2_1(a633)) | (~c1_1(a633))))),
% 3.48/2.62 inference(monotonicity,[status(thm)],[4013])).
% 3.48/2.62 tff(4015,plain,
% 3.48/2.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a633) | c1_1(a598) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c3_1(a598)) | c2_1(a598) | (~c2_1(a633)) | (~c1_1(a633)))),
% 3.48/2.62 inference(transitivity,[status(thm)],[4014, 4012])).
% 3.48/2.62 tff(4016,plain,
% 3.48/2.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633)))),
% 3.48/2.62 inference(quant_inst,[status(thm)],[])).
% 3.48/2.62 tff(4017,plain,
% 3.48/2.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a633) | c1_1(a598) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c3_1(a598)) | c2_1(a598) | (~c2_1(a633)) | (~c1_1(a633))),
% 3.48/2.62 inference(modus_ponens,[status(thm)],[4016, 4015])).
% 3.48/2.62 tff(4018,plain,
% 3.48/2.62 ($false),
% 3.48/2.62 inference(unit_resolution,[status(thm)],[4017, 107, 3321, 3330, 3992, 4002, 3981, 3991, 11, 4011, 3340, 3989])).
% 3.48/2.62 tff(4019,plain,((~c3_1(a583)) | (~c1_1(a633)) | c0_1(a633) | c3_1(a633) | hskp11), inference(lemma,lemma(discharge,[]))).
% 3.48/2.62 tff(4020,plain,
% 3.48/2.62 (~c3_1(a583)),
% 3.48/2.62 inference(unit_resolution,[status(thm)],[4019, 1638, 3979, 3978, 3977])).
% 3.48/2.62 tff(4021,plain,
% 3.48/2.62 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a583)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp3 | (~ndr1_0) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a583)))),
% 3.48/2.62 inference(rewrite,[status(thm)],[])).
% 3.48/2.62 tff(4022,plain,
% 3.48/2.62 ((hskp17 | hskp3 | (~ndr1_0) | c3_1(a583) | (~c1_1(a583)) | (~c0_1(a583))) <=> (hskp17 | hskp3 | (~ndr1_0) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a583)))),
% 3.48/2.62 inference(rewrite,[status(thm)],[])).
% 3.48/2.62 tff(4023,plain,
% 3.48/2.62 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c3_1(a583) | (~c1_1(a583)) | (~c0_1(a583)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a583))))),
% 3.48/2.62 inference(monotonicity,[status(thm)],[4022])).
% 3.48/2.62 tff(4024,plain,
% 3.48/2.62 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c3_1(a583) | (~c1_1(a583)) | (~c0_1(a583)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp3 | (~ndr1_0) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a583)))),
% 3.48/2.62 inference(transitivity,[status(thm)],[4023, 4021])).
% 3.48/2.62 tff(4025,plain,
% 3.48/2.62 ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c3_1(a583) | (~c1_1(a583)) | (~c0_1(a583)))),
% 3.48/2.62 inference(quant_inst,[status(thm)],[])).
% 3.48/2.62 tff(4026,plain,
% 3.48/2.62 ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp3 | (~ndr1_0) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a583))),
% 3.48/2.62 inference(modus_ponens,[status(thm)],[4025, 4024])).
% 3.48/2.62 tff(4027,plain,
% 3.48/2.62 (hskp3 | c3_1(a583)),
% 3.48/2.62 inference(unit_resolution,[status(thm)],[4026, 107, 241, 3321, 3322, 2368])).
% 3.48/2.62 tff(4028,plain,
% 3.48/2.62 (hskp3),
% 3.48/2.62 inference(unit_resolution,[status(thm)],[4027, 4020])).
% 3.48/2.62 tff(4029,plain,
% 3.48/2.62 (~c1_1(a587)),
% 3.48/2.62 inference(unit_resolution,[status(thm)],[939, 4028])).
% 3.48/2.62 tff(4030,plain,
% 3.48/2.62 (((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp18 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)))) <=> ((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp18 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)))),
% 3.48/2.62 inference(rewrite,[status(thm)],[])).
% 3.48/2.62 tff(4031,plain,
% 3.48/2.62 ((hskp29 | hskp18 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c1_1(a583))) <=> (hskp29 | hskp18 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)))),
% 3.48/2.62 inference(rewrite,[status(thm)],[])).
% 3.48/2.62 tff(4032,plain,
% 3.48/2.62 (((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp18 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c1_1(a583)))) <=> ((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp18 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583))))),
% 3.48/2.62 inference(monotonicity,[status(thm)],[4031])).
% 3.48/2.62 tff(4033,plain,
% 3.48/2.62 (((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp18 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c1_1(a583)))) <=> ((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp18 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)))),
% 3.48/2.62 inference(transitivity,[status(thm)],[4032, 4030])).
% 3.48/2.62 tff(4034,plain,
% 3.48/2.62 ((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp18 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c1_1(a583)))),
% 3.48/2.62 inference(quant_inst,[status(thm)],[])).
% 3.48/2.62 tff(4035,plain,
% 3.48/2.62 ((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp18 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583))),
% 3.48/2.62 inference(modus_ponens,[status(thm)],[4034, 4033])).
% 3.48/2.62 tff(4036,plain,
% 3.48/2.62 (hskp18 | c3_1(a583)),
% 3.48/2.62 inference(unit_resolution,[status(thm)],[4035, 269, 107, 3322, 3330, 1796])).
% 3.48/2.62 tff(4037,plain,
% 3.48/2.62 (hskp18),
% 3.48/2.62 inference(unit_resolution,[status(thm)],[4036, 4020])).
% 3.48/2.62 tff(4038,plain,
% 3.48/2.62 (~c2_1(a610)),
% 3.48/2.62 inference(unit_resolution,[status(thm)],[1189, 4037])).
% 3.48/2.62 tff(4039,plain,
% 3.48/2.62 (~c0_1(a610)),
% 3.48/2.62 inference(unit_resolution,[status(thm)],[1195, 4037])).
% 3.48/2.62 tff(4040,plain,
% 3.48/2.62 (c2_1(a587)),
% 3.48/2.62 inference(unit_resolution,[status(thm)],[950, 4028])).
% 3.48/2.62 tff(4041,plain,
% 3.48/2.62 (c0_1(a587)),
% 3.48/2.62 inference(unit_resolution,[status(thm)],[961, 4028])).
% 3.48/2.62 tff(4042,plain,
% 3.48/2.62 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a610) | c2_1(a610) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | (~c1_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a610) | c2_1(a610) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | (~c1_1(a610)))),
% 3.48/2.62 inference(rewrite,[status(thm)],[])).
% 3.48/2.62 tff(4043,plain,
% 3.48/2.62 ((hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a610) | c2_1(a610) | (~c1_1(a610))) <=> (hskp17 | c0_1(a610) | c2_1(a610) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | (~c1_1(a610)))),
% 3.48/2.62 inference(rewrite,[status(thm)],[])).
% 3.48/2.62 tff(4044,plain,
% 3.48/2.62 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a610) | c2_1(a610) | (~c1_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a610) | c2_1(a610) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | (~c1_1(a610))))),
% 3.48/2.62 inference(monotonicity,[status(thm)],[4043])).
% 3.48/2.62 tff(4045,plain,
% 3.48/2.62 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a610) | c2_1(a610) | (~c1_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a610) | c2_1(a610) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | (~c1_1(a610)))),
% 3.48/2.62 inference(transitivity,[status(thm)],[4044, 4042])).
% 3.48/2.62 tff(4046,plain,
% 3.48/2.62 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a610) | c2_1(a610) | (~c1_1(a610)))),
% 3.48/2.62 inference(quant_inst,[status(thm)],[])).
% 3.48/2.62 tff(4047,plain,
% 3.48/2.62 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a610) | c2_1(a610) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | (~c1_1(a610))),
% 3.48/2.62 inference(modus_ponens,[status(thm)],[4046, 4045])).
% 3.48/2.62 tff(4048,plain,
% 3.48/2.62 (~c1_1(a610)),
% 3.48/2.62 inference(unit_resolution,[status(thm)],[4047, 107, 241, 4041, 4040, 4039, 4038, 4029, 32])).
% 3.48/2.62 tff(4049,plain,
% 3.48/2.62 (hskp4 | c3_1(a583)),
% 3.48/2.62 inference(unit_resolution,[status(thm)],[3328, 107, 241, 3321, 3322, 55])).
% 3.48/2.62 tff(4050,plain,
% 3.48/2.62 (hskp4),
% 3.48/2.62 inference(unit_resolution,[status(thm)],[4049, 4020])).
% 3.48/2.62 tff(4051,plain,
% 3.48/2.62 (~c2_1(a588)),
% 3.48/2.62 inference(unit_resolution,[status(thm)],[121, 4050])).
% 3.48/2.62 tff(4052,plain,
% 3.48/2.62 (~c1_1(a588)),
% 3.48/2.62 inference(unit_resolution,[status(thm)],[127, 4050])).
% 3.48/2.62 tff(4053,plain,
% 3.48/2.62 (((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp15 | c3_1(a633) | (~ndr1_0) | (~c2_1(a633)) | (~c1_1(a633)))) <=> ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp15 | c3_1(a633) | (~ndr1_0) | (~c2_1(a633)) | (~c1_1(a633)))),
% 3.48/2.62 inference(rewrite,[status(thm)],[])).
% 3.48/2.62 tff(4054,plain,
% 3.48/2.62 ((hskp29 | hskp15 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c1_1(a633))) <=> (hskp29 | hskp15 | c3_1(a633) | (~ndr1_0) | (~c2_1(a633)) | (~c1_1(a633)))),
% 3.48/2.62 inference(rewrite,[status(thm)],[])).
% 3.48/2.62 tff(4055,plain,
% 3.48/2.62 (((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp15 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c1_1(a633)))) <=> ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp15 | c3_1(a633) | (~ndr1_0) | (~c2_1(a633)) | (~c1_1(a633))))),
% 3.48/2.62 inference(monotonicity,[status(thm)],[4054])).
% 3.48/2.62 tff(4056,plain,
% 3.48/2.62 (((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp15 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c1_1(a633)))) <=> ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp15 | c3_1(a633) | (~ndr1_0) | (~c2_1(a633)) | (~c1_1(a633)))),
% 3.48/2.62 inference(transitivity,[status(thm)],[4055, 4053])).
% 3.48/2.62 tff(4057,plain,
% 3.48/2.62 ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp15 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c1_1(a633)))),
% 3.48/2.62 inference(quant_inst,[status(thm)],[])).
% 3.48/2.62 tff(4058,plain,
% 3.48/2.62 ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp15 | c3_1(a633) | (~ndr1_0) | (~c2_1(a633)) | (~c1_1(a633))),
% 3.48/2.62 inference(modus_ponens,[status(thm)],[4057, 4056])).
% 3.48/2.62 tff(4059,plain,
% 3.48/2.62 (hskp29 | hskp15 | (~c2_1(a633))),
% 3.48/2.62 inference(unit_resolution,[status(thm)],[4058, 107, 3992, 3980, 1568])).
% 3.48/2.62 tff(4060,plain,
% 3.48/2.62 (~c2_1(a633)),
% 3.48/2.62 inference(unit_resolution,[status(thm)],[4059, 3154, 269])).
% 3.48/2.62 tff(4061,plain,
% 3.48/2.62 (((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp15 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)))) <=> ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp15 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)))),
% 3.48/2.62 inference(rewrite,[status(thm)],[])).
% 3.48/2.62 tff(4062,plain,
% 3.48/2.62 ((hskp29 | hskp15 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c1_1(a583))) <=> (hskp29 | hskp15 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)))),
% 3.48/2.62 inference(rewrite,[status(thm)],[])).
% 3.48/2.62 tff(4063,plain,
% 3.48/2.62 (((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp15 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c1_1(a583)))) <=> ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp15 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583))))),
% 3.48/2.62 inference(monotonicity,[status(thm)],[4062])).
% 3.48/2.62 tff(4064,plain,
% 3.48/2.62 (((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp15 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c1_1(a583)))) <=> ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp15 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)))),
% 3.48/2.62 inference(transitivity,[status(thm)],[4063, 4061])).
% 3.48/2.62 tff(4065,plain,
% 3.48/2.62 ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp15 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c1_1(a583)))),
% 3.48/2.62 inference(quant_inst,[status(thm)],[])).
% 3.48/2.62 tff(4066,plain,
% 3.48/2.62 ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp15 | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583))),
% 3.48/2.62 inference(modus_ponens,[status(thm)],[4065, 4064])).
% 3.48/2.62 tff(4067,plain,
% 3.48/2.62 (hskp15 | c3_1(a583)),
% 3.48/2.62 inference(unit_resolution,[status(thm)],[4066, 269, 107, 3322, 3330, 1568])).
% 3.48/2.62 tff(4068,plain,
% 3.48/2.62 (c3_1(a583)),
% 3.48/2.62 inference(unit_resolution,[status(thm)],[4067, 3154])).
% 3.48/2.62 tff(4069,plain,
% 3.48/2.62 ($false),
% 3.48/2.62 inference(unit_resolution,[status(thm)],[3988, 4068, 4060])).
% 3.48/2.62 tff(4070,plain,(hskp15 | hskp11 | c0_1(a633) | c3_1(a633) | hskp29 | (~c1_1(a633))), inference(lemma,lemma(discharge,[]))).
% 3.48/2.62 tff(4071,plain,
% 3.48/2.62 (hskp15),
% 3.48/2.62 inference(unit_resolution,[status(thm)],[4070, 1638, 3979, 3978, 269, 3977])).
% 3.48/2.62 tff(4072,plain,
% 3.48/2.62 (~c0_1(a604)),
% 3.48/2.62 inference(unit_resolution,[status(thm)],[1591, 4071])).
% 3.48/2.62 tff(4073,plain,
% 3.48/2.62 (c0_1(a588)),
% 3.48/2.62 inference(unit_resolution,[status(thm)],[138, 4050])).
% 3.48/2.62 tff(4074,plain,
% 3.48/2.62 (c3_1(a604)),
% 3.48/2.62 inference(unit_resolution,[status(thm)],[1602, 4071])).
% 3.48/2.62 tff(4075,plain,
% 3.48/2.62 (c1_1(a604)),
% 3.48/2.62 inference(unit_resolution,[status(thm)],[1613, 4071])).
% 3.48/2.62 tff(4076,plain,
% 3.48/2.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a607) | c2_1(a607) | c0_1(a604) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a607))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a607) | c2_1(a607) | c0_1(a604) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a607))),
% 3.48/2.62 inference(rewrite,[status(thm)],[])).
% 3.48/2.62 tff(4077,plain,
% 3.48/2.62 (((~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a607) | c0_1(a607) | c2_1(a607)) <=> (c3_1(a607) | c2_1(a607) | c0_1(a604) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a607))),
% 3.48/2.62 inference(rewrite,[status(thm)],[])).
% 3.48/2.62 tff(4078,plain,
% 3.48/2.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a607) | c0_1(a607) | c2_1(a607))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a607) | c2_1(a607) | c0_1(a604) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a607)))),
% 3.48/2.62 inference(monotonicity,[status(thm)],[4077])).
% 3.48/2.62 tff(4079,plain,
% 3.48/2.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a607) | c0_1(a607) | c2_1(a607))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a607) | c2_1(a607) | c0_1(a604) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a607))),
% 3.48/2.62 inference(transitivity,[status(thm)],[4078, 4076])).
% 3.48/2.62 tff(4080,plain,
% 3.48/2.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a607) | c0_1(a607) | c2_1(a607))),
% 3.48/2.62 inference(quant_inst,[status(thm)],[])).
% 3.48/2.62 tff(4081,plain,
% 3.48/2.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a607) | c2_1(a607) | c0_1(a604) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a607)),
% 3.48/2.62 inference(modus_ponens,[status(thm)],[4080, 4079])).
% 3.48/2.62 tff(4082,plain,
% 3.48/2.62 (c0_1(a607)),
% 3.48/2.62 inference(unit_resolution,[status(thm)],[4081, 107, 33, 4075, 4074, 4073, 22, 4072, 4052, 4051, 1364])).
% 3.48/2.62 tff(4083,plain,
% 3.48/2.63 (hskp16),
% 3.48/2.63 inference(unit_resolution,[status(thm)],[1849, 107, 3321, 3322, 4075, 4074, 4072, 1425, 4020])).
% 3.48/2.63 tff(4084,plain,
% 3.48/2.63 (~c3_1(a606)),
% 3.48/2.63 inference(unit_resolution,[status(thm)],[1075, 4083])).
% 3.48/2.63 tff(4085,plain,
% 3.48/2.63 (~c2_1(a606)),
% 3.48/2.63 inference(unit_resolution,[status(thm)],[1111, 4083])).
% 3.48/2.63 tff(4086,plain,
% 3.48/2.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a607) | c2_1(a607) | c2_1(a606) | c3_1(a606) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a606) | (~c0_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a607) | c2_1(a607) | c2_1(a606) | c3_1(a606) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a606) | (~c0_1(a607)))),
% 3.48/2.63 inference(rewrite,[status(thm)],[])).
% 3.48/2.63 tff(4087,plain,
% 3.48/2.63 (((~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a606) | c0_1(a606) | c2_1(a606)) <=> (c1_1(a607) | c2_1(a607) | c2_1(a606) | c3_1(a606) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a606) | (~c0_1(a607)))),
% 3.48/2.63 inference(rewrite,[status(thm)],[])).
% 3.48/2.63 tff(4088,plain,
% 3.48/2.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a606) | c0_1(a606) | c2_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a607) | c2_1(a607) | c2_1(a606) | c3_1(a606) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a606) | (~c0_1(a607))))),
% 3.48/2.63 inference(monotonicity,[status(thm)],[4087])).
% 3.48/2.63 tff(4089,plain,
% 3.48/2.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a606) | c0_1(a606) | c2_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a607) | c2_1(a607) | c2_1(a606) | c3_1(a606) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a606) | (~c0_1(a607)))),
% 3.48/2.63 inference(transitivity,[status(thm)],[4088, 4086])).
% 3.48/2.63 tff(4090,plain,
% 3.48/2.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a606) | c0_1(a606) | c2_1(a606))),
% 3.48/2.63 inference(quant_inst,[status(thm)],[])).
% 3.48/2.63 tff(4091,plain,
% 3.48/2.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a607) | c2_1(a607) | c2_1(a606) | c3_1(a606) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a606) | (~c0_1(a607))),
% 3.48/2.63 inference(modus_ponens,[status(thm)],[4090, 4089])).
% 3.48/2.63 tff(4092,plain,
% 3.48/2.63 (c0_1(a606)),
% 3.48/2.63 inference(unit_resolution,[status(thm)],[4091, 107, 4075, 4074, 66, 22, 4085, 4084, 4072, 1364, 4082])).
% 3.48/2.63 tff(4093,plain,
% 3.48/2.63 (c1_1(a606)),
% 3.48/2.63 inference(unit_resolution,[status(thm)],[1088, 4083])).
% 3.48/2.63 tff(4094,plain,
% 3.48/2.63 (c3_1(a610)),
% 3.48/2.63 inference(unit_resolution,[status(thm)],[1206, 4037])).
% 3.48/2.63 tff(4095,plain,
% 3.48/2.63 (hskp28),
% 3.48/2.63 inference(unit_resolution,[status(thm)],[1858, 107, 3321, 3330, 4094, 4039, 4038, 1122, 4020])).
% 3.48/2.63 tff(4096,plain,
% 3.48/2.63 (c3_1(a612)),
% 3.48/2.63 inference(unit_resolution,[status(thm)],[1139, 4095])).
% 3.48/2.63 tff(4097,plain,
% 3.48/2.63 (c2_1(a612)),
% 3.48/2.63 inference(unit_resolution,[status(thm)],[1150, 4095])).
% 3.48/2.63 tff(4098,plain,
% 3.48/2.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a610) | c2_1(a606) | (~ndr1_0) | (~c0_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a606)) | (~c1_1(a606)) | c1_1(a610) | (~c3_1(a610)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a610) | c2_1(a606) | (~ndr1_0) | (~c0_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a606)) | (~c1_1(a606)) | c1_1(a610) | (~c3_1(a610)))),
% 3.48/2.63 inference(rewrite,[status(thm)],[])).
% 3.48/2.63 tff(4099,plain,
% 3.48/2.63 (((~ndr1_0) | (~c2_1(a612)) | (~c3_1(a612)) | (~c0_1(a612)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610))) <=> (c2_1(a610) | c2_1(a606) | (~ndr1_0) | (~c0_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a606)) | (~c1_1(a606)) | c1_1(a610) | (~c3_1(a610)))),
% 3.48/2.63 inference(rewrite,[status(thm)],[])).
% 3.48/2.63 tff(4100,plain,
% 3.48/2.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a612)) | (~c3_1(a612)) | (~c0_1(a612)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a610) | c2_1(a606) | (~ndr1_0) | (~c0_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a606)) | (~c1_1(a606)) | c1_1(a610) | (~c3_1(a610))))),
% 3.48/2.63 inference(monotonicity,[status(thm)],[4099])).
% 3.48/2.63 tff(4101,plain,
% 3.48/2.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a612)) | (~c3_1(a612)) | (~c0_1(a612)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a610) | c2_1(a606) | (~ndr1_0) | (~c0_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a606)) | (~c1_1(a606)) | c1_1(a610) | (~c3_1(a610)))),
% 3.48/2.63 inference(transitivity,[status(thm)],[4100, 4098])).
% 3.48/2.63 tff(4102,plain,
% 3.48/2.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a612)) | (~c3_1(a612)) | (~c0_1(a612)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610)))),
% 3.48/2.63 inference(quant_inst,[status(thm)],[])).
% 3.48/2.63 tff(4103,plain,
% 3.48/2.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a610) | c2_1(a606) | (~ndr1_0) | (~c0_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a606)) | (~c1_1(a606)) | c1_1(a610) | (~c3_1(a610))),
% 3.48/2.63 inference(modus_ponens,[status(thm)],[4102, 4101])).
% 3.48/2.63 tff(4104,plain,
% 3.48/2.63 (~c0_1(a612)),
% 3.48/2.63 inference(unit_resolution,[status(thm)],[4103, 107, 4097, 4096, 4094, 4093, 4038, 4085, 1106, 4092, 4048])).
% 3.48/2.63 tff(4105,plain,
% 3.48/2.63 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | c0_1(a610) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c1_1(a610) | (~c3_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c0_1(a610) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c1_1(a610) | (~c3_1(a610)))),
% 3.48/2.63 inference(rewrite,[status(thm)],[])).
% 3.48/2.63 tff(4106,plain,
% 3.48/2.63 ((hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a610) | c0_1(a610) | (~c3_1(a610))) <=> (hskp9 | c0_1(a610) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c1_1(a610) | (~c3_1(a610)))),
% 3.48/2.63 inference(rewrite,[status(thm)],[])).
% 3.48/2.63 tff(4107,plain,
% 3.48/2.63 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a610) | c0_1(a610) | (~c3_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | c0_1(a610) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c1_1(a610) | (~c3_1(a610))))),
% 3.48/2.63 inference(monotonicity,[status(thm)],[4106])).
% 3.48/2.63 tff(4108,plain,
% 3.48/2.63 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a610) | c0_1(a610) | (~c3_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c0_1(a610) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c1_1(a610) | (~c3_1(a610)))),
% 3.48/2.63 inference(transitivity,[status(thm)],[4107, 4105])).
% 3.48/2.63 tff(4109,plain,
% 3.48/2.63 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c1_1(a610) | c0_1(a610) | (~c3_1(a610)))),
% 3.48/2.63 inference(quant_inst,[status(thm)],[])).
% 3.48/2.63 tff(4110,plain,
% 3.48/2.63 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c0_1(a610) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c1_1(a610) | (~c3_1(a610))),
% 3.48/2.63 inference(modus_ponens,[status(thm)],[4109, 4108])).
% 3.48/2.63 tff(4111,plain,
% 3.48/2.63 (hskp9),
% 3.48/2.63 inference(unit_resolution,[status(thm)],[4110, 107, 3321, 3322, 3330, 4094, 4039, 294, 4048])).
% 3.48/2.63 tff(4112,plain,
% 3.48/2.63 (~c1_1(a595)),
% 3.48/2.63 inference(unit_resolution,[status(thm)],[1493, 4111])).
% 3.48/2.63 tff(4113,plain,
% 3.48/2.63 (~c0_1(a595)),
% 3.48/2.63 inference(unit_resolution,[status(thm)],[1499, 4111])).
% 3.48/2.63 tff(4114,plain,
% 3.48/2.63 (hskp27),
% 3.48/2.63 inference(unit_resolution,[status(thm)],[1213, 107, 4094, 4093, 4039, 4038, 4085, 540, 4092])).
% 3.48/2.63 tff(4115,plain,
% 3.48/2.63 (c3_1(a611)),
% 3.48/2.63 inference(unit_resolution,[status(thm)],[620, 4114])).
% 3.48/2.63 tff(4116,plain,
% 3.48/2.63 (c1_1(a611)),
% 3.48/2.63 inference(unit_resolution,[status(thm)],[631, 4114])).
% 3.48/2.63 tff(4117,plain,
% 3.48/2.63 (c0_1(a611)),
% 3.48/2.63 inference(unit_resolution,[status(thm)],[642, 4114])).
% 3.48/2.63 tff(4118,plain,
% 3.48/2.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a595) | c1_1(a595) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c2_1(a595)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a595) | c1_1(a595) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c2_1(a595)))),
% 3.48/2.63 inference(rewrite,[status(thm)],[])).
% 3.48/2.63 tff(4119,plain,
% 3.48/2.63 (((~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595))) <=> (c0_1(a595) | c1_1(a595) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c2_1(a595)))),
% 3.48/2.63 inference(rewrite,[status(thm)],[])).
% 3.48/2.63 tff(4120,plain,
% 3.48/2.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a595) | c1_1(a595) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c2_1(a595))))),
% 3.48/2.63 inference(monotonicity,[status(thm)],[4119])).
% 3.48/2.63 tff(4121,plain,
% 3.48/2.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a595) | c1_1(a595) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c2_1(a595)))),
% 3.48/2.63 inference(transitivity,[status(thm)],[4120, 4118])).
% 3.48/2.63 tff(4122,plain,
% 3.48/2.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c1_1(a595) | c0_1(a595) | (~c2_1(a595)))),
% 3.48/2.63 inference(quant_inst,[status(thm)],[])).
% 3.48/2.63 tff(4123,plain,
% 3.48/2.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a595) | c1_1(a595) | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c2_1(a595))),
% 3.48/2.63 inference(modus_ponens,[status(thm)],[4122, 4121])).
% 3.48/2.63 tff(4124,plain,
% 3.48/2.63 (~c2_1(a595)),
% 3.48/2.63 inference(unit_resolution,[status(thm)],[4123, 107, 4097, 4096, 4117, 4116, 4115, 4113, 4112, 65, 4104])).
% 3.48/2.63 tff(4125,plain,
% 3.48/2.63 (~c3_1(a595)),
% 3.48/2.63 inference(unit_resolution,[status(thm)],[1487, 4111])).
% 3.48/2.63 tff(4126,plain,
% 3.48/2.63 (c1_1(a612)),
% 3.48/2.63 inference(unit_resolution,[status(thm)],[1435, 4095])).
% 3.48/2.63 tff(4127,plain,
% 3.48/2.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a607) | c2_1(a607) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)) | c2_1(a595) | (~c0_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a607) | c2_1(a607) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)) | c2_1(a595) | (~c0_1(a607)))),
% 3.48/2.63 inference(rewrite,[status(thm)],[])).
% 3.48/2.63 tff(4128,plain,
% 3.48/2.63 (((~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)) | c3_1(a595) | c0_1(a595) | c2_1(a595)) <=> (c1_1(a607) | c2_1(a607) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)) | c2_1(a595) | (~c0_1(a607)))),
% 3.48/2.63 inference(rewrite,[status(thm)],[])).
% 3.48/2.63 tff(4129,plain,
% 3.48/2.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)) | c3_1(a595) | c0_1(a595) | c2_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a607) | c2_1(a607) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)) | c2_1(a595) | (~c0_1(a607))))),
% 3.48/2.63 inference(monotonicity,[status(thm)],[4128])).
% 3.48/2.63 tff(4130,plain,
% 3.48/2.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)) | c3_1(a595) | c0_1(a595) | c2_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a607) | c2_1(a607) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)) | c2_1(a595) | (~c0_1(a607)))),
% 3.48/2.63 inference(transitivity,[status(thm)],[4129, 4127])).
% 3.48/2.63 tff(4131,plain,
% 3.48/2.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)) | c3_1(a595) | c0_1(a595) | c2_1(a595))),
% 3.48/2.63 inference(quant_inst,[status(thm)],[])).
% 3.48/2.63 tff(4132,plain,
% 3.48/2.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a607) | c2_1(a607) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)) | c2_1(a595) | (~c0_1(a607))),
% 3.48/2.63 inference(modus_ponens,[status(thm)],[4131, 4130])).
% 3.48/2.63 tff(4133,plain,
% 3.48/2.63 ($false),
% 3.48/2.63 inference(unit_resolution,[status(thm)],[4132, 107, 4126, 4096, 66, 22, 4113, 4125, 1364, 4082, 4104, 4124])).
% 3.48/2.63 tff(4134,plain,(hskp11 | c1_1(a607) | c2_1(a607) | c3_1(a607) | hskp29), inference(lemma,lemma(discharge,[]))).
% 3.48/2.63 tff(4135,plain,
% 3.48/2.63 (hskp11),
% 3.48/2.63 inference(unit_resolution,[status(thm)],[4134, 269, 22, 33, 66])).
% 3.48/2.63 tff(4136,plain,
% 3.48/2.63 (~c1_1(a599)),
% 3.48/2.63 inference(unit_resolution,[status(thm)],[428, 4135])).
% 3.48/2.63 tff(4137,plain,
% 3.48/2.63 ((hskp29 | hskp17 | hskp7) <=> (hskp29 | hskp17 | hskp7)),
% 3.48/2.63 inference(rewrite,[status(thm)],[])).
% 3.48/2.63 tff(4138,plain,
% 3.48/2.63 (((hskp29 | hskp7) | hskp17) <=> (hskp29 | hskp17 | hskp7)),
% 3.48/2.63 inference(rewrite,[status(thm)],[])).
% 3.48/2.63 tff(4139,axiom,((hskp29 | hskp7) | hskp17), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause34')).
% 3.48/2.63 tff(4140,plain,
% 3.48/2.63 (hskp29 | hskp17 | hskp7),
% 3.48/2.63 inference(modus_ponens,[status(thm)],[4139, 4138])).
% 3.48/2.63 tff(4141,plain,
% 3.48/2.63 (hskp29 | hskp17 | hskp7),
% 3.48/2.63 inference(modus_ponens,[status(thm)],[4140, 4137])).
% 3.48/2.63 tff(4142,plain,
% 3.48/2.63 (hskp29 | hskp17 | hskp7),
% 3.48/2.63 inference(modus_ponens,[status(thm)],[4141, 4137])).
% 3.48/2.63 tff(4143,plain,
% 3.48/2.63 (hskp29 | hskp17 | hskp7),
% 3.48/2.63 inference(modus_ponens,[status(thm)],[4142, 4137])).
% 3.48/2.63 tff(4144,plain,
% 3.48/2.63 (hskp29 | hskp17 | hskp7),
% 3.48/2.63 inference(modus_ponens,[status(thm)],[4143, 4137])).
% 3.48/2.63 tff(4145,plain,
% 3.48/2.63 (hskp29 | hskp17 | hskp7),
% 3.48/2.63 inference(modus_ponens,[status(thm)],[4144, 4137])).
% 3.48/2.63 tff(4146,plain,
% 3.48/2.63 (hskp29 | hskp17 | hskp7),
% 3.48/2.63 inference(modus_ponens,[status(thm)],[4145, 4137])).
% 3.48/2.63 tff(4147,plain,
% 3.48/2.63 (hskp29 | hskp17 | hskp7),
% 3.48/2.63 inference(modus_ponens,[status(thm)],[4146, 4137])).
% 3.48/2.63 tff(4148,plain,
% 3.48/2.63 (hskp7),
% 3.48/2.63 inference(unit_resolution,[status(thm)],[4147, 269, 241])).
% 3.48/2.63 tff(4149,plain,
% 3.48/2.63 (~c3_1(a592)),
% 3.48/2.63 inference(unit_resolution,[status(thm)],[811, 4148])).
% 3.48/2.63 tff(4150,plain,
% 3.48/2.63 (~c0_1(a592)),
% 3.48/2.63 inference(unit_resolution,[status(thm)],[817, 4148])).
% 3.48/2.63 tff(4151,plain,
% 3.48/2.63 (c2_1(a592)),
% 3.48/2.63 inference(unit_resolution,[status(thm)],[828, 4148])).
% 3.48/2.63 tff(4152,plain,
% 3.48/2.63 (c3_1(a599)),
% 3.48/2.63 inference(unit_resolution,[status(thm)],[422, 4135])).
% 3.48/2.63 tff(4153,plain,
% 3.48/2.63 (c2_1(a599)),
% 3.48/2.63 inference(unit_resolution,[status(thm)],[439, 4135])).
% 3.48/2.63 tff(4154,plain,
% 3.48/2.63 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a633) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c2_1(a633) | (~c1_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a633) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c2_1(a633) | (~c1_1(a633)))),
% 3.48/2.63 inference(rewrite,[status(thm)],[])).
% 3.48/2.63 tff(4155,plain,
% 3.48/2.63 ((hskp17 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c0_1(a599)) | c0_1(a633) | c2_1(a633) | (~c1_1(a633))) <=> (hskp17 | c0_1(a633) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c2_1(a633) | (~c1_1(a633)))),
% 3.48/2.63 inference(rewrite,[status(thm)],[])).
% 3.48/2.63 tff(4156,plain,
% 3.48/2.63 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c0_1(a599)) | c0_1(a633) | c2_1(a633) | (~c1_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a633) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c2_1(a633) | (~c1_1(a633))))),
% 3.48/2.63 inference(monotonicity,[status(thm)],[4155])).
% 3.48/2.63 tff(4157,plain,
% 3.48/2.63 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c0_1(a599)) | c0_1(a633) | c2_1(a633) | (~c1_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a633) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c2_1(a633) | (~c1_1(a633)))),
% 3.48/2.63 inference(transitivity,[status(thm)],[4156, 4154])).
% 3.48/2.63 tff(4158,plain,
% 3.48/2.63 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c0_1(a599)) | c0_1(a633) | c2_1(a633) | (~c1_1(a633)))),
% 3.48/2.63 inference(quant_inst,[status(thm)],[])).
% 3.48/2.63 tff(4159,plain,
% 3.48/2.63 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a633) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c2_1(a633) | (~c1_1(a633))),
% 3.48/2.63 inference(modus_ponens,[status(thm)],[4158, 4157])).
% 3.48/2.63 tff(4160,plain,
% 3.48/2.63 ((~c0_1(a599)) | c2_1(a633)),
% 3.48/2.63 inference(unit_resolution,[status(thm)],[4159, 107, 241, 3992, 463, 3981, 461, 32])).
% 3.48/2.63 tff(4161,plain,
% 3.48/2.63 (~c0_1(a599)),
% 3.48/2.63 inference(unit_resolution,[status(thm)],[4160, 4060])).
% 3.48/2.63 tff(4162,plain,
% 3.48/2.63 (((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp15 | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592)))) <=> ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp15 | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592)))),
% 3.48/2.63 inference(rewrite,[status(thm)],[])).
% 3.48/2.63 tff(4163,plain,
% 3.48/2.63 ((hskp29 | hskp15 | (~ndr1_0) | c3_1(a592) | (~c2_1(a592)) | (~c1_1(a592))) <=> (hskp29 | hskp15 | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592)))),
% 3.48/2.63 inference(rewrite,[status(thm)],[])).
% 3.48/2.63 tff(4164,plain,
% 3.48/2.63 (((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp15 | (~ndr1_0) | c3_1(a592) | (~c2_1(a592)) | (~c1_1(a592)))) <=> ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp15 | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592))))),
% 3.48/2.63 inference(monotonicity,[status(thm)],[4163])).
% 3.48/2.63 tff(4165,plain,
% 3.48/2.63 (((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp15 | (~ndr1_0) | c3_1(a592) | (~c2_1(a592)) | (~c1_1(a592)))) <=> ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp15 | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592)))),
% 3.48/2.63 inference(transitivity,[status(thm)],[4164, 4162])).
% 3.48/2.63 tff(4166,plain,
% 3.48/2.63 ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp15 | (~ndr1_0) | c3_1(a592) | (~c2_1(a592)) | (~c1_1(a592)))),
% 3.48/2.63 inference(quant_inst,[status(thm)],[])).
% 3.48/2.63 tff(4167,plain,
% 3.48/2.63 ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp15 | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592))),
% 3.48/2.63 inference(modus_ponens,[status(thm)],[4166, 4165])).
% 3.48/2.63 tff(4168,plain,
% 3.48/2.63 (hskp15 | (~c1_1(a592))),
% 3.48/2.63 inference(unit_resolution,[status(thm)],[4167, 269, 107, 4151, 4149, 1568])).
% 3.48/2.63 tff(4169,plain,
% 3.48/2.63 (~c1_1(a592)),
% 3.48/2.63 inference(unit_resolution,[status(thm)],[4168, 3154])).
% 3.48/2.63 tff(4170,plain,
% 3.48/2.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a607) | c0_1(a633) | c2_1(a607) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | (~c0_1(a607)) | c2_1(a633) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a607) | c0_1(a633) | c2_1(a607) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | (~c0_1(a607)) | c2_1(a633) | (~c1_1(a633)))),
% 3.48/2.63 inference(rewrite,[status(thm)],[])).
% 3.48/2.63 tff(4171,plain,
% 3.48/2.63 (((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a633) | c2_1(a633) | (~c1_1(a633)) | c3_1(a592) | c1_1(a592) | c0_1(a592)) <=> (c3_1(a607) | c0_1(a633) | c2_1(a607) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | (~c0_1(a607)) | c2_1(a633) | (~c1_1(a633)))),
% 3.48/2.64 inference(rewrite,[status(thm)],[])).
% 3.48/2.64 tff(4172,plain,
% 3.48/2.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a633) | c2_1(a633) | (~c1_1(a633)) | c3_1(a592) | c1_1(a592) | c0_1(a592))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a607) | c0_1(a633) | c2_1(a607) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | (~c0_1(a607)) | c2_1(a633) | (~c1_1(a633))))),
% 3.48/2.64 inference(monotonicity,[status(thm)],[4171])).
% 3.48/2.64 tff(4173,plain,
% 3.48/2.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a633) | c2_1(a633) | (~c1_1(a633)) | c3_1(a592) | c1_1(a592) | c0_1(a592))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a607) | c0_1(a633) | c2_1(a607) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | (~c0_1(a607)) | c2_1(a633) | (~c1_1(a633)))),
% 3.48/2.64 inference(transitivity,[status(thm)],[4172, 4170])).
% 3.48/2.64 tff(4174,plain,
% 3.48/2.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a607) | c3_1(a607) | (~c0_1(a607)) | c0_1(a633) | c2_1(a633) | (~c1_1(a633)) | c3_1(a592) | c1_1(a592) | c0_1(a592))),
% 3.48/2.64 inference(quant_inst,[status(thm)],[])).
% 3.48/2.64 tff(4175,plain,
% 3.48/2.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a607) | c0_1(a633) | c2_1(a607) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | (~c0_1(a607)) | c2_1(a633) | (~c1_1(a633))),
% 3.48/2.64 inference(modus_ponens,[status(thm)],[4174, 4173])).
% 3.48/2.64 tff(4176,plain,
% 3.48/2.64 (c1_1(a592) | (~c0_1(a607)) | c2_1(a633)),
% 3.48/2.64 inference(unit_resolution,[status(thm)],[4175, 107, 3992, 33, 3981, 22, 4150, 4149, 1463])).
% 3.48/2.64 tff(4177,plain,
% 3.48/2.64 (~c0_1(a607)),
% 3.48/2.64 inference(unit_resolution,[status(thm)],[4176, 4169, 4060])).
% 3.48/2.64 tff(4178,plain,
% 3.48/2.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a607) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599) | c0_1(a607))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a607) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599) | c0_1(a607))),
% 3.48/2.64 inference(rewrite,[status(thm)],[])).
% 3.48/2.64 tff(4179,plain,
% 3.48/2.64 (((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a607) | c0_1(a607) | c2_1(a607)) <=> (c3_1(a607) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599) | c0_1(a607))),
% 3.48/2.64 inference(rewrite,[status(thm)],[])).
% 3.48/2.64 tff(4180,plain,
% 3.48/2.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a607) | c0_1(a607) | c2_1(a607))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a607) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599) | c0_1(a607)))),
% 3.48/2.64 inference(monotonicity,[status(thm)],[4179])).
% 3.48/2.64 tff(4181,plain,
% 3.48/2.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a607) | c0_1(a607) | c2_1(a607))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a607) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599) | c0_1(a607))),
% 3.48/2.64 inference(transitivity,[status(thm)],[4180, 4178])).
% 3.48/2.64 tff(4182,plain,
% 3.48/2.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a607) | c0_1(a607) | c2_1(a607))),
% 3.48/2.64 inference(quant_inst,[status(thm)],[])).
% 3.48/2.64 tff(4183,plain,
% 3.48/2.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c3_1(a607) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599) | c0_1(a607)),
% 3.48/2.64 inference(modus_ponens,[status(thm)],[4182, 4181])).
% 3.48/2.64 tff(4184,plain,
% 3.48/2.64 ($false),
% 3.48/2.64 inference(unit_resolution,[status(thm)],[4183, 107, 33, 463, 462, 22, 461, 1730, 4177, 4161])).
% 3.48/2.64 tff(4185,plain,(hskp15 | c3_1(a607) | (~c2_1(a599)) | (~c3_1(a599)) | c2_1(a607) | c1_1(a599) | (~c1_1(a633)) | c0_1(a633) | hskp29 | c3_1(a633)), inference(lemma,lemma(discharge,[]))).
% 3.48/2.64 tff(4186,plain,
% 3.48/2.64 (hskp15),
% 3.48/2.64 inference(unit_resolution,[status(thm)],[4185, 4153, 33, 4152, 22, 4136, 3977, 3979, 269, 3978])).
% 3.48/2.64 tff(4187,plain,
% 3.48/2.64 (~c0_1(a604)),
% 3.48/2.64 inference(unit_resolution,[status(thm)],[1591, 4186])).
% 3.48/2.64 tff(4188,plain,
% 3.48/2.64 (c3_1(a604)),
% 3.48/2.64 inference(unit_resolution,[status(thm)],[1602, 4186])).
% 3.48/2.64 tff(4189,plain,
% 3.48/2.64 (c1_1(a604)),
% 3.48/2.64 inference(unit_resolution,[status(thm)],[1613, 4186])).
% 3.48/2.64 tff(4190,plain,
% 3.48/2.64 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c1_1(a607) | c2_1(a607) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c1_1(a607) | c2_1(a607) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c0_1(a607)))),
% 3.48/2.64 inference(rewrite,[status(thm)],[])).
% 3.48/2.64 tff(4191,plain,
% 3.48/2.64 ((hskp14 | (~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c3_1(a592) | c0_1(a592) | (~c2_1(a592))) <=> (hskp14 | c1_1(a607) | c2_1(a607) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c0_1(a607)))),
% 3.48/2.64 inference(rewrite,[status(thm)],[])).
% 3.48/2.64 tff(4192,plain,
% 3.48/2.64 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c3_1(a592) | c0_1(a592) | (~c2_1(a592)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c1_1(a607) | c2_1(a607) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c0_1(a607))))),
% 3.48/2.64 inference(monotonicity,[status(thm)],[4191])).
% 3.48/2.64 tff(4193,plain,
% 3.48/2.64 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c3_1(a592) | c0_1(a592) | (~c2_1(a592)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c1_1(a607) | c2_1(a607) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c0_1(a607)))),
% 3.48/2.64 inference(transitivity,[status(thm)],[4192, 4190])).
% 3.48/2.64 tff(4194,plain,
% 3.48/2.64 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c3_1(a592) | c0_1(a592) | (~c2_1(a592)))),
% 3.48/2.64 inference(quant_inst,[status(thm)],[])).
% 3.48/2.64 tff(4195,plain,
% 3.48/2.64 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c1_1(a607) | c2_1(a607) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c0_1(a607))),
% 3.48/2.64 inference(modus_ponens,[status(thm)],[4194, 4193])).
% 3.48/2.64 tff(4196,plain,
% 3.48/2.64 (hskp14 | (~c0_1(a607))),
% 3.48/2.64 inference(unit_resolution,[status(thm)],[4195, 107, 842, 66, 22, 851, 841, 305])).
% 3.48/2.64 tff(4197,plain,
% 3.48/2.64 (~c0_1(a607)),
% 3.48/2.64 inference(unit_resolution,[status(thm)],[4196, 364])).
% 3.48/2.64 tff(4198,plain,
% 3.48/2.64 (hskp4),
% 3.48/2.64 inference(unit_resolution,[status(thm)],[165, 4197, 33, 364])).
% 3.48/2.64 tff(4199,plain,
% 3.48/2.64 (~c2_1(a588)),
% 3.48/2.64 inference(unit_resolution,[status(thm)],[121, 4198])).
% 3.48/2.64 tff(4200,plain,
% 3.48/2.64 (~c1_1(a588)),
% 3.48/2.64 inference(unit_resolution,[status(thm)],[127, 4198])).
% 3.48/2.64 tff(4201,plain,
% 3.48/2.64 (c0_1(a588)),
% 3.48/2.64 inference(unit_resolution,[status(thm)],[138, 4198])).
% 3.48/2.64 tff(4202,assumption,(c1_1(a604)), introduced(assumption)).
% 3.48/2.64 tff(4203,plain,
% 3.48/2.64 ($false),
% 3.48/2.64 inference(unit_resolution,[status(thm)],[4081, 107, 33, 4202, 2545, 4201, 22, 2475, 4200, 4199, 1364, 4197])).
% 3.48/2.64 tff(4204,plain,(hskp14 | c3_1(a607) | (~c1_1(a604)) | (~c3_1(a604)) | c2_1(a607) | c0_1(a604) | (~c2_1(a592)) | c1_1(a607) | c0_1(a592) | c3_1(a592)), inference(lemma,lemma(discharge,[]))).
% 3.48/2.64 tff(4205,plain,
% 3.48/2.64 (hskp14),
% 3.48/2.64 inference(unit_resolution,[status(thm)],[4204, 4189, 33, 4188, 22, 4187, 4151, 66, 4150, 4149])).
% 3.48/2.64 tff(4206,plain,
% 3.48/2.64 (~c3_1(a603)),
% 3.48/2.64 inference(unit_resolution,[status(thm)],[205, 4205])).
% 3.48/2.64 tff(4207,plain,
% 3.48/2.64 (c0_1(a603)),
% 3.48/2.64 inference(unit_resolution,[status(thm)],[182, 4205])).
% 3.48/2.64 tff(4208,plain,
% 3.48/2.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a633) | c3_1(a633) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a633) | c3_1(a633) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)) | (~c1_1(a633)))),
% 3.48/2.64 inference(rewrite,[status(thm)],[])).
% 3.48/2.64 tff(4209,plain,
% 3.48/2.64 (((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633))) <=> (c0_1(a633) | c3_1(a633) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)) | (~c1_1(a633)))),
% 3.48/2.64 inference(rewrite,[status(thm)],[])).
% 3.48/2.64 tff(4210,plain,
% 3.48/2.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a633) | c3_1(a633) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)) | (~c1_1(a633))))),
% 3.48/2.64 inference(monotonicity,[status(thm)],[4209])).
% 3.48/2.64 tff(4211,plain,
% 3.48/2.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a633) | c3_1(a633) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)) | (~c1_1(a633)))),
% 3.48/2.64 inference(transitivity,[status(thm)],[4210, 4208])).
% 3.48/2.64 tff(4212,plain,
% 3.48/2.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))),
% 3.48/2.64 inference(quant_inst,[status(thm)],[])).
% 3.48/2.64 tff(4213,plain,
% 3.48/2.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a633) | c3_1(a633) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)) | (~c1_1(a633))),
% 3.48/2.64 inference(modus_ponens,[status(thm)],[4212, 4211])).
% 3.48/2.64 tff(4214,plain,
% 3.48/2.64 (~c2_1(a603)),
% 3.48/2.64 inference(unit_resolution,[status(thm)],[4213, 107, 3977, 4207, 4153, 4152, 3979, 3978, 4206, 4136, 258])).
% 3.48/2.64 tff(4215,plain,
% 3.48/2.64 (~c1_1(a603)),
% 3.48/2.64 inference(unit_resolution,[status(thm)],[171, 4205])).
% 3.48/2.64 tff(4216,plain,
% 3.48/2.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a633) | c3_1(a633) | c0_1(a604) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a604)) | (~c1_1(a604)) | c2_1(a633))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a633) | c3_1(a633) | c0_1(a604) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a604)) | (~c1_1(a604)) | c2_1(a633))),
% 3.48/2.64 inference(rewrite,[status(thm)],[])).
% 3.48/2.64 tff(4217,plain,
% 3.48/2.64 (((~ndr1_0) | c2_1(a603) | c1_1(a603) | (~c0_1(a603)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a633) | c0_1(a633) | c2_1(a633)) <=> (c0_1(a633) | c3_1(a633) | c0_1(a604) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a604)) | (~c1_1(a604)) | c2_1(a633))),
% 3.48/2.64 inference(rewrite,[status(thm)],[])).
% 3.48/2.64 tff(4218,plain,
% 3.48/2.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a603) | c1_1(a603) | (~c0_1(a603)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a633) | c0_1(a633) | c2_1(a633))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a633) | c3_1(a633) | c0_1(a604) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a604)) | (~c1_1(a604)) | c2_1(a633)))),
% 3.48/2.64 inference(monotonicity,[status(thm)],[4217])).
% 3.48/2.64 tff(4219,plain,
% 3.48/2.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a603) | c1_1(a603) | (~c0_1(a603)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a633) | c0_1(a633) | c2_1(a633))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a633) | c3_1(a633) | c0_1(a604) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a604)) | (~c1_1(a604)) | c2_1(a633))),
% 3.48/2.64 inference(transitivity,[status(thm)],[4218, 4216])).
% 3.48/2.64 tff(4220,plain,
% 3.48/2.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a603) | c1_1(a603) | (~c0_1(a603)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a633) | c0_1(a633) | c2_1(a633))),
% 3.48/2.64 inference(quant_inst,[status(thm)],[])).
% 3.48/2.64 tff(4221,plain,
% 3.48/2.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a633) | c3_1(a633) | c0_1(a604) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a604)) | (~c1_1(a604)) | c2_1(a633)),
% 3.48/2.64 inference(modus_ponens,[status(thm)],[4220, 4219])).
% 3.48/2.64 tff(4222,plain,
% 3.48/2.64 (c2_1(a633)),
% 3.48/2.64 inference(unit_resolution,[status(thm)],[4221, 107, 4189, 4188, 4207, 3979, 3978, 4187, 4215, 1364, 4214])).
% 3.48/2.64 tff(4223,plain,
% 3.48/2.64 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c3_1(a607) | c1_1(a607) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c3_1(a607) | c1_1(a607) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)))),
% 3.48/2.64 inference(rewrite,[status(thm)],[])).
% 3.48/2.64 tff(4224,plain,
% 3.48/2.64 ((hskp26 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c0_1(a599)) | c3_1(a607) | c1_1(a607) | c2_1(a607)) <=> (hskp26 | c3_1(a607) | c1_1(a607) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)))),
% 3.48/2.64 inference(rewrite,[status(thm)],[])).
% 3.48/2.64 tff(4225,plain,
% 3.48/2.64 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c0_1(a599)) | c3_1(a607) | c1_1(a607) | c2_1(a607))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c3_1(a607) | c1_1(a607) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599))))),
% 3.48/2.64 inference(monotonicity,[status(thm)],[4224])).
% 3.48/2.64 tff(4226,plain,
% 3.48/2.64 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c0_1(a599)) | c3_1(a607) | c1_1(a607) | c2_1(a607))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c3_1(a607) | c1_1(a607) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)))),
% 3.48/2.64 inference(transitivity,[status(thm)],[4225, 4223])).
% 3.48/2.64 tff(4227,plain,
% 3.48/2.64 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c0_1(a599)) | c3_1(a607) | c1_1(a607) | c2_1(a607))),
% 3.48/2.64 inference(quant_inst,[status(thm)],[])).
% 3.48/2.64 tff(4228,plain,
% 3.48/2.64 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c3_1(a607) | c1_1(a607) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599))),
% 3.48/2.64 inference(modus_ponens,[status(thm)],[4227, 4226])).
% 3.48/2.64 tff(4229,plain,
% 3.48/2.64 (hskp26 | (~c0_1(a599))),
% 3.48/2.64 inference(unit_resolution,[status(thm)],[4228, 107, 33, 463, 66, 22, 461, 995])).
% 3.48/2.64 tff(4230,plain,
% 3.48/2.64 (~c0_1(a599)),
% 3.48/2.64 inference(unit_resolution,[status(thm)],[4229, 726])).
% 3.48/2.64 tff(4231,plain,
% 3.48/2.64 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c3_1(a607) | c1_1(a607) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | c0_1(a599))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c3_1(a607) | c1_1(a607) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | c0_1(a599))),
% 3.48/2.64 inference(rewrite,[status(thm)],[])).
% 3.48/2.64 tff(4232,plain,
% 3.48/2.64 ((hskp26 | (~ndr1_0) | c1_1(a599) | c0_1(a599) | (~c3_1(a599)) | c3_1(a607) | c1_1(a607) | c2_1(a607)) <=> (hskp26 | c3_1(a607) | c1_1(a607) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | c0_1(a599))),
% 3.48/2.64 inference(rewrite,[status(thm)],[])).
% 3.48/2.64 tff(4233,plain,
% 3.48/2.64 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a599) | c0_1(a599) | (~c3_1(a599)) | c3_1(a607) | c1_1(a607) | c2_1(a607))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c3_1(a607) | c1_1(a607) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | c0_1(a599)))),
% 3.48/2.64 inference(monotonicity,[status(thm)],[4232])).
% 3.48/2.64 tff(4234,plain,
% 3.48/2.64 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a599) | c0_1(a599) | (~c3_1(a599)) | c3_1(a607) | c1_1(a607) | c2_1(a607))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c3_1(a607) | c1_1(a607) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | c0_1(a599))),
% 3.48/2.64 inference(transitivity,[status(thm)],[4233, 4231])).
% 3.48/2.64 tff(4235,plain,
% 3.48/2.64 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a599) | c0_1(a599) | (~c3_1(a599)) | c3_1(a607) | c1_1(a607) | c2_1(a607))),
% 3.48/2.64 inference(quant_inst,[status(thm)],[])).
% 3.48/2.64 tff(4236,plain,
% 3.48/2.64 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c3_1(a607) | c1_1(a607) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | c0_1(a599)),
% 3.48/2.64 inference(modus_ponens,[status(thm)],[4235, 4234])).
% 3.48/2.64 tff(4237,plain,
% 3.48/2.64 (hskp26 | c0_1(a599)),
% 3.48/2.64 inference(unit_resolution,[status(thm)],[4236, 107, 33, 462, 66, 22, 461, 703])).
% 3.48/2.64 tff(4238,plain,
% 3.48/2.64 ($false),
% 3.48/2.64 inference(unit_resolution,[status(thm)],[4237, 4230, 726])).
% 3.48/2.64 tff(4239,plain,(hskp26 | c3_1(a607) | (~c3_1(a599)) | c1_1(a607) | c2_1(a607) | c1_1(a599) | (~c2_1(a599))), inference(lemma,lemma(discharge,[]))).
% 3.48/2.64 tff(4240,plain,
% 3.48/2.64 (hskp26),
% 3.48/2.64 inference(unit_resolution,[status(thm)],[4239, 4152, 33, 66, 22, 4136, 4153])).
% 3.48/2.64 tff(4241,plain,
% 3.48/2.64 (c2_1(a583)),
% 3.48/2.64 inference(unit_resolution,[status(thm)],[391, 4240])).
% 3.48/2.64 tff(4242,plain,
% 3.48/2.64 (c1_1(a583)),
% 3.48/2.64 inference(unit_resolution,[status(thm)],[351, 4240])).
% 3.48/2.64 tff(4243,plain,
% 3.48/2.64 (c0_1(a583)),
% 3.48/2.64 inference(unit_resolution,[status(thm)],[362, 4240])).
% 3.48/2.64 tff(4244,plain,
% 3.48/2.64 (hskp12),
% 3.48/2.64 inference(unit_resolution,[status(thm)],[3998, 107, 4243, 4242, 4241, 3977, 3979, 2727, 4222])).
% 3.48/2.64 tff(4245,plain,
% 3.48/2.64 (~c3_1(a600)),
% 3.48/2.64 inference(unit_resolution,[status(thm)],[741, 4244])).
% 3.48/2.64 tff(4246,plain,
% 3.48/2.64 (c2_1(a600)),
% 3.48/2.64 inference(unit_resolution,[status(thm)],[752, 4244])).
% 3.48/2.64 tff(4247,plain,
% 3.48/2.64 (c0_1(a600)),
% 3.48/2.64 inference(unit_resolution,[status(thm)],[763, 4244])).
% 3.48/2.64 tff(4248,plain,
% 3.48/2.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a633) | c3_1(a633) | c3_1(a600) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a600)) | (~c0_1(a600)) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a633) | c3_1(a633) | c3_1(a600) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a600)) | (~c0_1(a600)) | (~c1_1(a633)))),
% 3.48/2.64 inference(rewrite,[status(thm)],[])).
% 3.48/2.64 tff(4249,plain,
% 3.48/2.64 (((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633))) <=> (c0_1(a633) | c3_1(a633) | c3_1(a600) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a600)) | (~c0_1(a600)) | (~c1_1(a633)))),
% 3.48/2.64 inference(rewrite,[status(thm)],[])).
% 3.48/2.64 tff(4250,plain,
% 3.48/2.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a633) | c3_1(a633) | c3_1(a600) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a600)) | (~c0_1(a600)) | (~c1_1(a633))))),
% 3.48/2.64 inference(monotonicity,[status(thm)],[4249])).
% 3.48/2.64 tff(4251,plain,
% 3.48/2.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a633) | c3_1(a633) | c3_1(a600) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a600)) | (~c0_1(a600)) | (~c1_1(a633)))),
% 3.48/2.64 inference(transitivity,[status(thm)],[4250, 4248])).
% 3.48/2.64 tff(4252,plain,
% 3.48/2.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))),
% 3.48/2.64 inference(quant_inst,[status(thm)],[])).
% 3.48/2.64 tff(4253,plain,
% 3.48/2.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a633) | c3_1(a633) | c3_1(a600) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a600)) | (~c0_1(a600)) | (~c1_1(a633))),
% 3.48/2.64 inference(modus_ponens,[status(thm)],[4252, 4251])).
% 3.48/2.64 tff(4254,plain,
% 3.48/2.64 ($false),
% 3.48/2.64 inference(unit_resolution,[status(thm)],[4253, 107, 3977, 4247, 4246, 4153, 4152, 3979, 3978, 4245, 4136, 258])).
% 3.48/2.64 tff(4255,plain,(hskp29 | c3_1(a607) | c1_1(a607) | c2_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.48/2.64 tff(4256,plain,
% 3.48/2.64 (hskp29),
% 3.48/2.64 inference(unit_resolution,[status(thm)],[4255, 33, 66, 22])).
% 3.48/2.64 tff(4257,plain,
% 3.48/2.64 (c3_1(a678)),
% 3.48/2.64 inference(unit_resolution,[status(thm)],[2269, 4256])).
% 3.48/2.64 tff(4258,plain,
% 3.48/2.64 (c2_1(a678)),
% 3.48/2.64 inference(unit_resolution,[status(thm)],[2280, 4256])).
% 3.48/2.64 tff(4259,plain,
% 3.48/2.64 (c0_1(a678)),
% 3.48/2.64 inference(unit_resolution,[status(thm)],[2291, 4256])).
% 3.48/2.64 tff(4260,plain,
% 3.48/2.64 (hskp11 | c0_1(a607)),
% 3.48/2.64 inference(unit_resolution,[status(thm)],[2298, 107, 4259, 4258, 4257, 33, 22, 268])).
% 3.48/2.64 tff(4261,plain,
% 3.48/2.64 (c0_1(a607)),
% 3.48/2.64 inference(unit_resolution,[status(thm)],[4260, 1638])).
% 3.48/2.64 tff(4262,plain,
% 3.48/2.64 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))))),
% 3.48/2.64 inference(bind,[status(th)],[])).
% 3.48/2.64 tff(4263,plain,
% 3.48/2.64 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 3.48/2.64 inference(quant_intro,[status(thm)],[4262])).
% 3.48/2.64 tff(4264,plain,
% 3.48/2.64 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 3.48/2.64 inference(rewrite,[status(thm)],[])).
% 3.48/2.64 tff(4265,plain,
% 3.48/2.64 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp8) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) | hskp8))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))))),
% 3.48/2.65 inference(bind,[status(th)],[])).
% 3.48/2.65 tff(4266,plain,
% 3.48/2.65 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 3.48/2.65 inference(quant_intro,[status(thm)],[4265])).
% 3.48/2.65 tff(4267,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause183')).
% 3.48/2.65 tff(4268,plain,
% 3.48/2.65 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 3.48/2.65 inference(modus_ponens,[status(thm)],[4267, 4266])).
% 3.48/2.65 tff(4269,plain,
% 3.48/2.65 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 3.48/2.65 inference(modus_ponens,[status(thm)],[4268, 4264])).
% 3.48/2.65 tff(4270,plain,(
% 3.48/2.65 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 3.48/2.65 inference(skolemize,[status(sab)],[4269])).
% 3.48/2.65 tff(4271,plain,
% 3.48/2.65 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 3.48/2.65 inference(modus_ponens,[status(thm)],[4270, 4263])).
% 3.48/2.65 tff(4272,plain,
% 3.48/2.65 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | c3_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c3_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c0_1(a607)))),
% 3.48/2.65 inference(rewrite,[status(thm)],[])).
% 3.48/2.65 tff(4273,plain,
% 3.48/2.65 ((hskp8 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c3_1(a607) | c2_1(a607) | (~c0_1(a607))) <=> (hskp8 | c3_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c0_1(a607)))),
% 3.48/2.65 inference(rewrite,[status(thm)],[])).
% 3.48/2.65 tff(4274,plain,
% 3.48/2.65 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c3_1(a607) | c2_1(a607) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | c3_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c0_1(a607))))),
% 3.48/2.65 inference(monotonicity,[status(thm)],[4273])).
% 3.48/2.65 tff(4275,plain,
% 3.48/2.65 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c3_1(a607) | c2_1(a607) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c3_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c0_1(a607)))),
% 3.48/2.65 inference(transitivity,[status(thm)],[4274, 4272])).
% 3.48/2.65 tff(4276,plain,
% 3.48/2.65 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c3_1(a607) | c2_1(a607) | (~c0_1(a607)))),
% 3.48/2.65 inference(quant_inst,[status(thm)],[])).
% 3.48/2.65 tff(4277,plain,
% 3.48/2.65 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c3_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c0_1(a607))),
% 3.48/2.65 inference(modus_ponens,[status(thm)],[4276, 4275])).
% 3.48/2.65 tff(4278,plain,
% 3.48/2.65 (hskp8),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[4277, 107, 3321, 3330, 33, 22, 4271, 4261, 4020])).
% 3.48/2.65 tff(4279,plain,
% 3.48/2.65 (~c2_1(a593)),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[555, 4278])).
% 3.48/2.65 tff(4280,plain,
% 3.48/2.65 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | c0_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a633))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | c0_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a633))),
% 3.48/2.65 inference(rewrite,[status(thm)],[])).
% 3.48/2.65 tff(4281,plain,
% 3.48/2.65 ((hskp11 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c3_1(a633) | c0_1(a633) | c2_1(a633)) <=> (hskp11 | c0_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a633))),
% 3.48/2.65 inference(rewrite,[status(thm)],[])).
% 3.48/2.65 tff(4282,plain,
% 3.48/2.65 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c3_1(a633) | c0_1(a633) | c2_1(a633))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | c0_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a633)))),
% 3.48/2.65 inference(monotonicity,[status(thm)],[4281])).
% 3.48/2.65 tff(4283,plain,
% 3.48/2.65 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c3_1(a633) | c0_1(a633) | c2_1(a633))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | c0_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a633))),
% 3.48/2.65 inference(transitivity,[status(thm)],[4282, 4280])).
% 3.48/2.65 tff(4284,plain,
% 3.48/2.65 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c3_1(a633) | c0_1(a633) | c2_1(a633))),
% 3.48/2.65 inference(quant_inst,[status(thm)],[])).
% 3.48/2.65 tff(4285,plain,
% 3.48/2.65 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | c0_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a633)),
% 3.48/2.65 inference(modus_ponens,[status(thm)],[4284, 4283])).
% 3.48/2.65 tff(4286,plain,
% 3.48/2.65 (hskp11 | c2_1(a633)),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[4285, 107, 4259, 4258, 4257, 3979, 3978, 268])).
% 3.48/2.65 tff(4287,plain,
% 3.48/2.65 (c2_1(a633)),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[4286, 1638])).
% 3.48/2.65 tff(4288,plain,
% 3.48/2.65 (c3_1(a593)),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[511, 4278])).
% 3.48/2.65 tff(4289,plain,
% 3.48/2.65 (c1_1(a593)),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[522, 4278])).
% 3.48/2.65 tff(4290,assumption,(c2_1(a633)), introduced(assumption)).
% 3.48/2.65 tff(4291,plain,
% 3.48/2.65 (^[U: $i] : refl((hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 3.48/2.65 inference(bind,[status(th)],[])).
% 3.48/2.65 tff(4292,plain,
% 3.48/2.65 (![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 3.48/2.65 inference(quant_intro,[status(thm)],[4291])).
% 3.48/2.65 tff(4293,plain,
% 3.48/2.65 (![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 3.48/2.65 inference(rewrite,[status(thm)],[])).
% 3.48/2.65 tff(4294,plain,
% 3.48/2.65 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp15))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) | hskp11) <=> ((hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp11))), rewrite(((hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp11) <=> (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) | hskp11) <=> (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 3.48/2.65 inference(bind,[status(th)],[])).
% 3.48/2.65 tff(4295,plain,
% 3.48/2.65 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) | hskp11) <=> ![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 3.48/2.65 inference(quant_intro,[status(thm)],[4294])).
% 3.48/2.65 tff(4296,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause153')).
% 3.48/2.65 tff(4297,plain,
% 3.48/2.65 (![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 3.48/2.65 inference(modus_ponens,[status(thm)],[4296, 4295])).
% 3.48/2.65 tff(4298,plain,
% 3.48/2.65 (![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 3.48/2.65 inference(modus_ponens,[status(thm)],[4297, 4293])).
% 3.48/2.65 tff(4299,plain,(
% 3.48/2.65 ![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 3.48/2.65 inference(skolemize,[status(sab)],[4298])).
% 3.48/2.65 tff(4300,plain,
% 3.48/2.65 (![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 3.48/2.65 inference(modus_ponens,[status(thm)],[4299, 4292])).
% 3.48/2.65 tff(4301,plain,
% 3.48/2.65 (((~![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp15 | c2_1(a593) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)))) <=> ((~![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp15 | c2_1(a593) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)))),
% 3.48/2.65 inference(rewrite,[status(thm)],[])).
% 3.48/2.65 tff(4302,plain,
% 3.48/2.65 ((hskp11 | hskp15 | (~ndr1_0) | c2_1(a593) | (~c3_1(a593)) | (~c0_1(a593))) <=> (hskp11 | hskp15 | c2_1(a593) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)))),
% 3.48/2.65 inference(rewrite,[status(thm)],[])).
% 3.48/2.65 tff(4303,plain,
% 3.48/2.65 (((~![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp15 | (~ndr1_0) | c2_1(a593) | (~c3_1(a593)) | (~c0_1(a593)))) <=> ((~![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp15 | c2_1(a593) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593))))),
% 3.48/2.65 inference(monotonicity,[status(thm)],[4302])).
% 3.48/2.65 tff(4304,plain,
% 3.48/2.65 (((~![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp15 | (~ndr1_0) | c2_1(a593) | (~c3_1(a593)) | (~c0_1(a593)))) <=> ((~![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp15 | c2_1(a593) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)))),
% 3.48/2.65 inference(transitivity,[status(thm)],[4303, 4301])).
% 3.48/2.65 tff(4305,plain,
% 3.48/2.65 ((~![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp15 | (~ndr1_0) | c2_1(a593) | (~c3_1(a593)) | (~c0_1(a593)))),
% 3.48/2.65 inference(quant_inst,[status(thm)],[])).
% 3.48/2.65 tff(4306,plain,
% 3.48/2.65 ((~![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp15 | c2_1(a593) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593))),
% 3.48/2.65 inference(modus_ponens,[status(thm)],[4305, 4304])).
% 3.48/2.65 tff(4307,plain,
% 3.48/2.65 (hskp15 | (~c0_1(a593))),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[4306, 1638, 107, 1903, 1893, 4300])).
% 3.48/2.65 tff(4308,plain,
% 3.48/2.65 (~c0_1(a593)),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[4307, 3154])).
% 3.48/2.65 tff(4309,plain,
% 3.48/2.65 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | c3_1(a633) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a633)) | (~c1_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c3_1(a633) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a633)) | (~c1_1(a633)))),
% 3.48/2.65 inference(rewrite,[status(thm)],[])).
% 3.48/2.65 tff(4310,plain,
% 3.48/2.65 ((hskp15 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c1_1(a633)) | c0_1(a593) | (~c1_1(a593)) | (~c3_1(a593))) <=> (hskp15 | c3_1(a633) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a633)) | (~c1_1(a633)))),
% 3.48/2.65 inference(rewrite,[status(thm)],[])).
% 3.48/2.65 tff(4311,plain,
% 3.48/2.65 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c1_1(a633)) | c0_1(a593) | (~c1_1(a593)) | (~c3_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | c3_1(a633) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a633)) | (~c1_1(a633))))),
% 3.48/2.65 inference(monotonicity,[status(thm)],[4310])).
% 3.48/2.65 tff(4312,plain,
% 3.48/2.65 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c1_1(a633)) | c0_1(a593) | (~c1_1(a593)) | (~c3_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c3_1(a633) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a633)) | (~c1_1(a633)))),
% 3.48/2.65 inference(transitivity,[status(thm)],[4311, 4309])).
% 3.48/2.65 tff(4313,plain,
% 3.48/2.65 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c1_1(a633)) | c0_1(a593) | (~c1_1(a593)) | (~c3_1(a593)))),
% 3.48/2.65 inference(quant_inst,[status(thm)],[])).
% 3.48/2.65 tff(4314,plain,
% 3.48/2.65 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c3_1(a633) | (~ndr1_0) | c0_1(a593) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a633)) | (~c1_1(a633))),
% 3.48/2.65 inference(modus_ponens,[status(thm)],[4313, 4312])).
% 3.48/2.65 tff(4315,plain,
% 3.48/2.65 ($false),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[4314, 107, 3154, 3992, 1894, 1903, 3980, 2690, 4308, 4290])).
% 3.48/2.65 tff(4316,plain,(hskp15 | (~c1_1(a633)) | (~c1_1(a593)) | (~c3_1(a593)) | c3_1(a633) | (~c2_1(a633)) | hskp11 | c2_1(a593)), inference(lemma,lemma(discharge,[]))).
% 3.48/2.65 tff(4317,plain,
% 3.48/2.65 (hskp15),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[4316, 4289, 3977, 4288, 3978, 4287, 1638, 4279])).
% 3.48/2.65 tff(4318,plain,
% 3.48/2.65 (~c0_1(a604)),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[1591, 4317])).
% 3.48/2.65 tff(4319,plain,
% 3.48/2.65 (c3_1(a604)),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[1602, 4317])).
% 3.48/2.65 tff(4320,plain,
% 3.48/2.65 (c1_1(a604)),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[1613, 4317])).
% 3.48/2.65 tff(4321,plain,
% 3.48/2.65 (hskp16),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[1849, 107, 3321, 3322, 4320, 4319, 4318, 1425, 4020])).
% 3.48/2.65 tff(4322,plain,
% 3.48/2.65 (~c3_1(a606)),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[1075, 4321])).
% 3.48/2.65 tff(4323,plain,
% 3.48/2.65 (~c2_1(a606)),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[1111, 4321])).
% 3.48/2.65 tff(4324,plain,
% 3.48/2.65 (c0_1(a606)),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[4091, 107, 4320, 4319, 66, 22, 4323, 4322, 4318, 1364, 4261])).
% 3.48/2.65 tff(4325,plain,
% 3.48/2.65 (c1_1(a606)),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[1088, 4321])).
% 3.48/2.65 tff(4326,plain,
% 3.48/2.65 (hskp0 | (~c0_1(a606))),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[2354, 1638, 107, 4325, 4323, 2347])).
% 3.48/2.65 tff(4327,plain,
% 3.48/2.65 (hskp0),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[4326, 4324])).
% 3.48/2.65 tff(4328,plain,
% 3.48/2.65 (~c2_1(a584)),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[1045, 4327])).
% 3.48/2.65 tff(4329,plain,
% 3.48/2.65 (~c0_1(a584)),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[1051, 4327])).
% 3.48/2.65 tff(4330,plain,
% 3.48/2.65 (hskp3),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[4026, 107, 241, 3321, 3322, 2368, 4020])).
% 3.48/2.65 tff(4331,plain,
% 3.48/2.65 (~c1_1(a587)),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[939, 4330])).
% 3.48/2.65 tff(4332,plain,
% 3.48/2.65 (c1_1(a584)),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[1062, 4327])).
% 3.48/2.65 tff(4333,plain,
% 3.48/2.65 (c2_1(a587)),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[950, 4330])).
% 3.48/2.65 tff(4334,plain,
% 3.48/2.65 (c0_1(a587)),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[961, 4330])).
% 3.48/2.65 tff(4335,plain,
% 3.48/2.65 ($false),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[2386, 107, 241, 4334, 4333, 4332, 4331, 4329, 4328, 32])).
% 3.48/2.65 tff(4336,plain,(hskp11 | c1_1(a607) | c2_1(a607) | c3_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.48/2.65 tff(4337,plain,
% 3.48/2.65 (hskp11),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[4336, 33, 22, 66])).
% 3.48/2.65 tff(4338,plain,
% 3.48/2.65 (~c1_1(a599)),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[428, 4337])).
% 3.48/2.65 tff(4339,plain,
% 3.48/2.65 (c3_1(a599)),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[422, 4337])).
% 3.48/2.65 tff(4340,plain,
% 3.48/2.65 (c2_1(a599)),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[439, 4337])).
% 3.48/2.65 tff(4341,plain,
% 3.48/2.65 ($false),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[4253, 107, 3992, 764, 753, 463, 462, 3981, 3980, 742, 461, 258])).
% 3.48/2.65 tff(4342,plain,((~hskp12) | (~c1_1(a633)) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a633) | c3_1(a633) | c1_1(a599)), inference(lemma,lemma(discharge,[]))).
% 3.48/2.65 tff(4343,plain,
% 3.48/2.65 (~hskp12),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[4342, 4340, 3977, 4339, 3979, 3978, 4338])).
% 3.48/2.65 tff(4344,plain,
% 3.48/2.65 (hskp26),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[4239, 4339, 33, 66, 22, 4338, 4340])).
% 3.48/2.65 tff(4345,plain,
% 3.48/2.65 (c2_1(a583)),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[391, 4344])).
% 3.48/2.65 tff(4346,plain,
% 3.48/2.65 (c1_1(a583)),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[351, 4344])).
% 3.48/2.65 tff(4347,plain,
% 3.48/2.65 (c0_1(a583)),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[362, 4344])).
% 3.48/2.65 tff(4348,plain,
% 3.48/2.65 (hskp12 | (~c2_1(a633))),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[3998, 107, 4347, 4346, 4345, 3977, 3979, 2727])).
% 3.48/2.65 tff(4349,plain,
% 3.48/2.65 (~c2_1(a633)),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[4348, 4343])).
% 3.48/2.65 tff(4350,plain,
% 3.48/2.65 ((~c0_1(a599)) | c2_1(a633)),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[4159, 107, 241, 3977, 4340, 3979, 4338, 32])).
% 3.48/2.65 tff(4351,plain,
% 3.48/2.65 (~c0_1(a599)),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[4350, 4349])).
% 3.48/2.65 tff(4352,plain,
% 3.48/2.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a633) | c3_1(a633) | c1_1(a599) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a633) | c3_1(a633) | c1_1(a599) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a633)))),
% 3.48/2.65 inference(rewrite,[status(thm)],[])).
% 3.48/2.65 tff(4353,plain,
% 3.48/2.65 (((~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633))) <=> (c0_1(a633) | c3_1(a633) | c1_1(a599) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a633)))),
% 3.48/2.65 inference(rewrite,[status(thm)],[])).
% 3.48/2.65 tff(4354,plain,
% 3.48/2.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a633) | c3_1(a633) | c1_1(a599) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a633))))),
% 3.48/2.65 inference(monotonicity,[status(thm)],[4353])).
% 3.48/2.65 tff(4355,plain,
% 3.48/2.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a633) | c3_1(a633) | c1_1(a599) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a633)))),
% 3.48/2.65 inference(transitivity,[status(thm)],[4354, 4352])).
% 3.48/2.65 tff(4356,plain,
% 3.48/2.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))),
% 3.48/2.65 inference(quant_inst,[status(thm)],[])).
% 3.48/2.65 tff(4357,plain,
% 3.48/2.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a633) | c3_1(a633) | c1_1(a599) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a633))),
% 3.48/2.65 inference(modus_ponens,[status(thm)],[4356, 4355])).
% 3.48/2.65 tff(4358,plain,
% 3.48/2.65 ($false),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[4357, 107, 1651, 1649, 3992, 463, 462, 3981, 3980, 461, 258, 1974])).
% 3.48/2.65 tff(4359,plain,(c3_1(a583) | (~c0_1(a583)) | (~c2_1(a583)) | (~c1_1(a633)) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a633) | c3_1(a633) | c1_1(a599)), inference(lemma,lemma(discharge,[]))).
% 3.48/2.65 tff(4360,plain,
% 3.48/2.65 (c3_1(a583)),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[4359, 4347, 4345, 3977, 4340, 4339, 3979, 3978, 4338])).
% 3.48/2.65 tff(4361,plain,
% 3.48/2.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a599) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a599) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599))),
% 3.48/2.65 inference(rewrite,[status(thm)],[])).
% 3.48/2.65 tff(4362,plain,
% 3.48/2.65 (((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599))) <=> (c1_1(a599) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599))),
% 3.48/2.65 inference(rewrite,[status(thm)],[])).
% 3.48/2.65 tff(4363,plain,
% 3.48/2.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a599) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599)))),
% 3.48/2.65 inference(monotonicity,[status(thm)],[4362])).
% 3.48/2.65 tff(4364,plain,
% 3.48/2.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a599) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599))),
% 3.48/2.65 inference(transitivity,[status(thm)],[4363, 4361])).
% 3.48/2.65 tff(4365,plain,
% 3.48/2.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))),
% 3.48/2.65 inference(quant_inst,[status(thm)],[])).
% 3.48/2.65 tff(4366,plain,
% 3.48/2.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a599) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599)),
% 3.48/2.65 inference(modus_ponens,[status(thm)],[4365, 4364])).
% 3.48/2.65 tff(4367,plain,
% 3.48/2.65 ($false),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[4366, 107, 4347, 4346, 4340, 4339, 4338, 65, 4360, 4351])).
% 3.48/2.65 tff(4368,plain,(c3_1(a607) | c1_1(a607) | c2_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.48/2.65 tff(4369,plain,
% 3.48/2.65 (c3_1(a607)),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[4368, 22, 66])).
% 3.48/2.65 tff(4370,assumption,(hskp29), introduced(assumption)).
% 3.48/2.65 tff(4371,plain,
% 3.48/2.65 (c3_1(a678)),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[2269, 4370])).
% 3.48/2.65 tff(4372,plain,
% 3.48/2.65 (c2_1(a678)),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[2280, 4370])).
% 3.48/2.65 tff(4373,plain,
% 3.48/2.65 (c0_1(a678)),
% 3.48/2.65 inference(unit_resolution,[status(thm)],[2291, 4370])).
% 3.48/2.65 tff(4374,plain,
% 3.48/2.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a607)) | (~c2_1(a633)) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a607)) | (~c2_1(a633)) | (~c1_1(a633)))),
% 3.48/2.65 inference(rewrite,[status(thm)],[])).
% 3.48/2.65 tff(4375,plain,
% 3.48/2.65 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633))) <=> (c0_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a607)) | (~c2_1(a633)) | (~c1_1(a633)))),
% 3.48/2.65 inference(rewrite,[status(thm)],[])).
% 3.48/2.65 tff(4376,plain,
% 3.48/2.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a607)) | (~c2_1(a633)) | (~c1_1(a633))))),
% 3.48/2.65 inference(monotonicity,[status(thm)],[4375])).
% 3.48/2.65 tff(4377,plain,
% 3.48/2.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a607)) | (~c2_1(a633)) | (~c1_1(a633)))),
% 3.48/2.66 inference(transitivity,[status(thm)],[4376, 4374])).
% 3.48/2.66 tff(4378,plain,
% 3.48/2.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633)))),
% 3.48/2.66 inference(quant_inst,[status(thm)],[])).
% 3.48/2.66 tff(4379,plain,
% 3.48/2.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a607)) | (~c2_1(a633)) | (~c1_1(a633))),
% 3.48/2.66 inference(modus_ponens,[status(thm)],[4378, 4377])).
% 3.48/2.66 tff(4380,plain,
% 3.48/2.66 (~c2_1(a633)),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[4379, 107, 4373, 4372, 4371, 3977, 4369, 3979, 66, 22, 11])).
% 3.48/2.66 tff(4381,plain,
% 3.48/2.66 ($false),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[4285, 1638, 107, 4373, 4372, 4371, 3979, 3978, 268, 4380])).
% 3.48/2.66 tff(4382,plain,((~hskp29) | hskp11 | c1_1(a607) | c2_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.48/2.66 tff(4383,plain,
% 3.48/2.66 (~hskp29),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[4382, 1638, 66, 22])).
% 3.48/2.66 tff(4384,plain,
% 3.48/2.66 (hskp29 | hskp18),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[4035, 107, 3322, 3330, 1796, 4020])).
% 3.48/2.66 tff(4385,plain,
% 3.48/2.66 (hskp18),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[4384, 4383])).
% 3.48/2.66 tff(4386,plain,
% 3.48/2.66 (~c2_1(a610)),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[1189, 4385])).
% 3.48/2.66 tff(4387,plain,
% 3.48/2.66 (~c0_1(a610)),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[1195, 4385])).
% 3.48/2.66 tff(4388,plain,
% 3.48/2.66 (c3_1(a610)),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[1206, 4385])).
% 3.48/2.66 tff(4389,plain,
% 3.48/2.66 (hskp28),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[1858, 107, 3321, 3330, 4388, 4387, 4386, 1122, 4020])).
% 3.48/2.66 tff(4390,plain,
% 3.48/2.66 (c3_1(a612)),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[1139, 4389])).
% 3.48/2.66 tff(4391,plain,
% 3.48/2.66 (c2_1(a612)),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[1150, 4389])).
% 3.48/2.66 tff(4392,plain,
% 3.48/2.66 (c1_1(a612)),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[1435, 4389])).
% 3.48/2.66 tff(4393,plain,
% 3.48/2.66 (hskp10),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[1535, 107, 4392, 4391, 4390, 3321, 3322, 3330, 21])).
% 3.48/2.66 tff(4394,plain,
% 3.48/2.66 (~c1_1(a598)),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[911, 4393])).
% 3.48/2.66 tff(4395,plain,
% 3.48/2.66 (c3_1(a598)),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[881, 4393])).
% 3.48/2.66 tff(4396,plain,
% 3.48/2.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a633) | c3_1(a633) | c1_1(a598) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a633) | c3_1(a633) | c1_1(a598) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c1_1(a633)))),
% 3.48/2.66 inference(rewrite,[status(thm)],[])).
% 3.48/2.66 tff(4397,plain,
% 3.48/2.66 (((~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a598) | (~c3_1(a598)) | (~c2_1(a598)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633))) <=> (c0_1(a633) | c3_1(a633) | c1_1(a598) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c1_1(a633)))),
% 3.48/2.66 inference(rewrite,[status(thm)],[])).
% 3.48/2.66 tff(4398,plain,
% 3.48/2.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a598) | (~c3_1(a598)) | (~c2_1(a598)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a633) | c3_1(a633) | c1_1(a598) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c1_1(a633))))),
% 3.48/2.66 inference(monotonicity,[status(thm)],[4397])).
% 3.48/2.66 tff(4399,plain,
% 3.48/2.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a598) | (~c3_1(a598)) | (~c2_1(a598)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a633) | c3_1(a633) | c1_1(a598) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c1_1(a633)))),
% 3.48/2.66 inference(transitivity,[status(thm)],[4398, 4396])).
% 3.48/2.66 tff(4400,plain,
% 3.48/2.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a598) | (~c3_1(a598)) | (~c2_1(a598)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))),
% 3.48/2.66 inference(quant_inst,[status(thm)],[])).
% 3.48/2.66 tff(4401,plain,
% 3.48/2.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a633) | c3_1(a633) | c1_1(a598) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c1_1(a633))),
% 3.48/2.66 inference(modus_ponens,[status(thm)],[4400, 4399])).
% 3.48/2.66 tff(4402,plain,
% 3.48/2.66 (~c2_1(a598)),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[4401, 107, 3321, 3330, 3977, 4395, 3979, 3978, 4394, 258, 4020])).
% 3.48/2.66 tff(4403,plain,
% 3.48/2.66 (c0_1(a598)),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[892, 4393])).
% 3.48/2.66 tff(4404,plain,
% 3.48/2.66 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | c1_1(a598) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | c2_1(a598) | (~c0_1(a598)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a598) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | c2_1(a598) | (~c0_1(a598)))),
% 3.48/2.66 inference(rewrite,[status(thm)],[])).
% 3.48/2.66 tff(4405,plain,
% 3.48/2.66 ((hskp1 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a598) | c2_1(a598) | (~c0_1(a598))) <=> (hskp1 | c1_1(a598) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | c2_1(a598) | (~c0_1(a598)))),
% 3.48/2.66 inference(rewrite,[status(thm)],[])).
% 3.48/2.66 tff(4406,plain,
% 3.48/2.66 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a598) | c2_1(a598) | (~c0_1(a598)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | c1_1(a598) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | c2_1(a598) | (~c0_1(a598))))),
% 3.48/2.66 inference(monotonicity,[status(thm)],[4405])).
% 3.48/2.66 tff(4407,plain,
% 3.48/2.66 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a598) | c2_1(a598) | (~c0_1(a598)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a598) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | c2_1(a598) | (~c0_1(a598)))),
% 3.48/2.66 inference(transitivity,[status(thm)],[4406, 4404])).
% 3.48/2.66 tff(4408,plain,
% 3.48/2.66 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a598) | c2_1(a598) | (~c0_1(a598)))),
% 3.48/2.66 inference(quant_inst,[status(thm)],[])).
% 3.48/2.66 tff(4409,plain,
% 3.48/2.66 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a598) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | c2_1(a598) | (~c0_1(a598))),
% 3.48/2.66 inference(modus_ponens,[status(thm)],[4408, 4407])).
% 3.48/2.66 tff(4410,plain,
% 3.48/2.66 (hskp1),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[4409, 107, 3321, 3330, 4403, 4394, 1237, 4402, 4020])).
% 3.48/2.66 tff(4411,plain,
% 3.48/2.66 (~c0_1(a585)),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[1250, 4410])).
% 3.48/2.66 tff(4412,plain,
% 3.48/2.66 (c2_1(a585)),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[1261, 4410])).
% 3.48/2.66 tff(4413,plain,
% 3.48/2.66 (c1_1(a585)),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[1272, 4410])).
% 3.48/2.66 tff(4414,plain,
% 3.48/2.66 (~c0_1(a612)),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[1299, 107, 4391, 4390, 4369, 4413, 4412, 66, 22, 4411, 11])).
% 3.48/2.66 tff(4415,plain,
% 3.48/2.66 (hskp23),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[1688, 1638, 107, 4403, 4395, 4394, 1648])).
% 3.48/2.66 tff(4416,plain,
% 3.48/2.66 (~c1_1(a636)),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[475, 4415])).
% 3.48/2.66 tff(4417,plain,
% 3.48/2.66 (~c0_1(a636)),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[481, 4415])).
% 3.48/2.66 tff(4418,plain,
% 3.48/2.66 (c3_1(a636)),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[492, 4415])).
% 3.48/2.66 tff(4419,plain,
% 3.48/2.66 (hskp9),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[1700, 107, 3321, 3322, 3330, 4418, 4417, 4416, 294])).
% 3.48/2.66 tff(4420,plain,
% 3.48/2.66 (~c1_1(a595)),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[1493, 4419])).
% 3.48/2.66 tff(4421,plain,
% 3.48/2.66 (~c0_1(a595)),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[1499, 4419])).
% 3.48/2.66 tff(4422,plain,
% 3.48/2.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a636) | c0_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a633)) | (~c3_1(a636)) | (~c2_1(a636)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a636) | c0_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a633)) | (~c3_1(a636)) | (~c2_1(a636)))),
% 3.48/2.66 inference(rewrite,[status(thm)],[])).
% 3.48/2.66 tff(4423,plain,
% 3.48/2.66 (((~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a636) | (~c3_1(a636)) | (~c2_1(a636)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633))) <=> (c1_1(a636) | c0_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a633)) | (~c3_1(a636)) | (~c2_1(a636)))),
% 3.48/2.66 inference(rewrite,[status(thm)],[])).
% 3.48/2.66 tff(4424,plain,
% 3.48/2.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a636) | (~c3_1(a636)) | (~c2_1(a636)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a636) | c0_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a633)) | (~c3_1(a636)) | (~c2_1(a636))))),
% 3.48/2.66 inference(monotonicity,[status(thm)],[4423])).
% 3.48/2.66 tff(4425,plain,
% 3.48/2.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a636) | (~c3_1(a636)) | (~c2_1(a636)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a636) | c0_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a633)) | (~c3_1(a636)) | (~c2_1(a636)))),
% 3.48/2.66 inference(transitivity,[status(thm)],[4424, 4422])).
% 3.48/2.66 tff(4426,plain,
% 3.48/2.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a636) | (~c3_1(a636)) | (~c2_1(a636)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))),
% 3.48/2.66 inference(quant_inst,[status(thm)],[])).
% 3.48/2.66 tff(4427,plain,
% 3.48/2.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a636) | c0_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c1_1(a633)) | (~c3_1(a636)) | (~c2_1(a636))),
% 3.48/2.66 inference(modus_ponens,[status(thm)],[4426, 4425])).
% 3.48/2.66 tff(4428,plain,
% 3.48/2.66 (~c2_1(a636)),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[4427, 107, 3321, 3330, 4418, 3977, 4416, 3979, 3978, 258, 4020])).
% 3.48/2.66 tff(4429,plain,
% 3.48/2.66 (hskp15),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[4070, 4383, 3979, 3978, 1638, 3977])).
% 3.48/2.66 tff(4430,plain,
% 3.48/2.66 (~c0_1(a604)),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[1591, 4429])).
% 3.48/2.66 tff(4431,plain,
% 3.48/2.66 (c3_1(a604)),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[1602, 4429])).
% 3.48/2.66 tff(4432,plain,
% 3.48/2.66 (c1_1(a604)),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[1613, 4429])).
% 3.48/2.66 tff(4433,plain,
% 3.48/2.66 (hskp16),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[1849, 107, 3321, 3322, 4432, 4431, 4430, 1425, 4020])).
% 3.48/2.66 tff(4434,plain,
% 3.48/2.66 (~c3_1(a606)),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[1075, 4433])).
% 3.48/2.66 tff(4435,plain,
% 3.48/2.66 (~c2_1(a606)),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[1111, 4433])).
% 3.48/2.66 tff(4436,plain,
% 3.48/2.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a606) | c3_1(a606) | c0_1(a604) | c1_1(a598) | (~ndr1_0) | c2_1(a598) | (~c0_1(a598)) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a606) | c3_1(a606) | c0_1(a604) | c1_1(a598) | (~ndr1_0) | c2_1(a598) | (~c0_1(a598)) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a606))),
% 3.48/2.66 inference(rewrite,[status(thm)],[])).
% 3.48/2.66 tff(4437,plain,
% 3.48/2.66 (((~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a606) | c0_1(a606) | c2_1(a606)) <=> (c2_1(a606) | c3_1(a606) | c0_1(a604) | c1_1(a598) | (~ndr1_0) | c2_1(a598) | (~c0_1(a598)) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a606))),
% 3.48/2.66 inference(rewrite,[status(thm)],[])).
% 3.48/2.66 tff(4438,plain,
% 3.48/2.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a606) | c0_1(a606) | c2_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a606) | c3_1(a606) | c0_1(a604) | c1_1(a598) | (~ndr1_0) | c2_1(a598) | (~c0_1(a598)) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a606)))),
% 3.48/2.66 inference(monotonicity,[status(thm)],[4437])).
% 3.48/2.66 tff(4439,plain,
% 3.48/2.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a606) | c0_1(a606) | c2_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a606) | c3_1(a606) | c0_1(a604) | c1_1(a598) | (~ndr1_0) | c2_1(a598) | (~c0_1(a598)) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a606))),
% 3.48/2.66 inference(transitivity,[status(thm)],[4438, 4436])).
% 3.48/2.66 tff(4440,plain,
% 3.48/2.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a606) | c0_1(a606) | c2_1(a606))),
% 3.48/2.66 inference(quant_inst,[status(thm)],[])).
% 3.48/2.66 tff(4441,plain,
% 3.48/2.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a606) | c3_1(a606) | c0_1(a604) | c1_1(a598) | (~ndr1_0) | c2_1(a598) | (~c0_1(a598)) | (~c3_1(a604)) | (~c1_1(a604)) | c0_1(a606)),
% 3.48/2.66 inference(modus_ponens,[status(thm)],[4440, 4439])).
% 3.48/2.66 tff(4442,plain,
% 3.48/2.66 (c0_1(a606)),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[4441, 107, 4432, 4431, 4403, 4435, 4434, 4430, 4394, 1364, 4402])).
% 3.48/2.66 tff(4443,plain,
% 3.48/2.66 (c1_1(a606)),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[1088, 4433])).
% 3.48/2.66 tff(4444,plain,
% 3.48/2.66 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | c0_1(a636) | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a636)) | c2_1(a636))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | c0_1(a636) | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a636)) | c2_1(a636))),
% 3.48/2.66 inference(rewrite,[status(thm)],[])).
% 3.48/2.66 tff(4445,plain,
% 3.48/2.66 ((hskp27 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c0_1(a636) | c2_1(a636) | (~c3_1(a636))) <=> (hskp27 | c0_1(a636) | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a636)) | c2_1(a636))),
% 3.48/2.66 inference(rewrite,[status(thm)],[])).
% 3.48/2.66 tff(4446,plain,
% 3.48/2.66 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c0_1(a636) | c2_1(a636) | (~c3_1(a636)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | c0_1(a636) | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a636)) | c2_1(a636)))),
% 3.48/2.66 inference(monotonicity,[status(thm)],[4445])).
% 3.48/2.66 tff(4447,plain,
% 3.48/2.66 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c0_1(a636) | c2_1(a636) | (~c3_1(a636)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | c0_1(a636) | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a636)) | c2_1(a636))),
% 3.48/2.66 inference(transitivity,[status(thm)],[4446, 4444])).
% 3.48/2.66 tff(4448,plain,
% 3.48/2.66 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c0_1(a636) | c2_1(a636) | (~c3_1(a636)))),
% 3.48/2.66 inference(quant_inst,[status(thm)],[])).
% 3.48/2.66 tff(4449,plain,
% 3.48/2.66 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp27 | c0_1(a636) | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)) | (~c3_1(a636)) | c2_1(a636)),
% 3.48/2.66 inference(modus_ponens,[status(thm)],[4448, 4447])).
% 3.48/2.66 tff(4450,plain,
% 3.48/2.66 (hskp27),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[4449, 107, 4418, 4443, 4417, 4435, 540, 4442, 4428])).
% 3.48/2.66 tff(4451,plain,
% 3.48/2.66 (c3_1(a611)),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[620, 4450])).
% 3.48/2.66 tff(4452,plain,
% 3.48/2.66 (c1_1(a611)),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[631, 4450])).
% 3.48/2.66 tff(4453,plain,
% 3.48/2.66 (c0_1(a611)),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[642, 4450])).
% 3.48/2.66 tff(4454,plain,
% 3.48/2.66 (~c2_1(a595)),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[4123, 107, 4391, 4390, 4453, 4452, 4451, 4421, 4420, 65, 4414])).
% 3.48/2.66 tff(4455,plain,
% 3.48/2.66 (~c3_1(a595)),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[1487, 4419])).
% 3.48/2.66 tff(4456,plain,
% 3.48/2.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a598) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)) | c2_1(a595) | c2_1(a598) | (~c0_1(a598)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a598) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)) | c2_1(a595) | c2_1(a598) | (~c0_1(a598)))),
% 3.48/2.66 inference(rewrite,[status(thm)],[])).
% 3.48/2.66 tff(4457,plain,
% 3.48/2.66 (((~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)) | c3_1(a595) | c0_1(a595) | c2_1(a595)) <=> (c1_1(a598) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)) | c2_1(a595) | c2_1(a598) | (~c0_1(a598)))),
% 3.48/2.66 inference(rewrite,[status(thm)],[])).
% 3.48/2.66 tff(4458,plain,
% 3.48/2.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)) | c3_1(a595) | c0_1(a595) | c2_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a598) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)) | c2_1(a595) | c2_1(a598) | (~c0_1(a598))))),
% 3.48/2.66 inference(monotonicity,[status(thm)],[4457])).
% 3.48/2.66 tff(4459,plain,
% 3.48/2.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)) | c3_1(a595) | c0_1(a595) | c2_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a598) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)) | c2_1(a595) | c2_1(a598) | (~c0_1(a598)))),
% 3.48/2.66 inference(transitivity,[status(thm)],[4458, 4456])).
% 3.48/2.66 tff(4460,plain,
% 3.48/2.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)) | c3_1(a595) | c0_1(a595) | c2_1(a595))),
% 3.48/2.66 inference(quant_inst,[status(thm)],[])).
% 3.48/2.66 tff(4461,plain,
% 3.48/2.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a598) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)) | c2_1(a595) | c2_1(a598) | (~c0_1(a598))),
% 3.48/2.66 inference(modus_ponens,[status(thm)],[4460, 4459])).
% 3.48/2.66 tff(4462,plain,
% 3.48/2.66 ($false),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[4461, 107, 4392, 4390, 4403, 4394, 4421, 4455, 1364, 4402, 4414, 4454])).
% 3.48/2.66 tff(4463,plain,(hskp11 | c1_1(a607) | c2_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.48/2.66 tff(4464,plain,
% 3.48/2.66 (hskp11),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[4463, 22, 66])).
% 3.48/2.66 tff(4465,plain,
% 3.48/2.66 (~c1_1(a599)),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[428, 4464])).
% 3.48/2.66 tff(4466,plain,
% 3.48/2.66 (c2_1(a599)),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[439, 4464])).
% 3.48/2.66 tff(4467,plain,
% 3.48/2.66 (c3_1(a599)),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[422, 4464])).
% 3.48/2.66 tff(4468,plain,
% 3.48/2.66 (hskp3),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[329, 317, 4369, 66, 22])).
% 3.48/2.66 tff(4469,plain,
% 3.48/2.66 (~c1_1(a587)),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[939, 4468])).
% 3.48/2.66 tff(4470,plain,
% 3.48/2.66 (c0_1(a587)),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[961, 4468])).
% 3.48/2.66 tff(4471,plain,
% 3.48/2.66 (c2_1(a587)),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[950, 4468])).
% 3.48/2.66 tff(4472,plain,
% 3.48/2.66 ($false),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[1508, 4471, 4470, 66, 22, 4369, 726, 320, 318, 319, 4469])).
% 3.48/2.66 tff(4473,plain,((~hskp14) | c1_1(a607) | c2_1(a607) | hskp26), inference(lemma,lemma(discharge,[]))).
% 3.48/2.66 tff(4474,plain,
% 3.48/2.66 (~hskp14),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[4473, 726, 22, 66])).
% 3.48/2.66 tff(4475,plain,
% 3.48/2.66 (~hskp12),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[4342, 4467, 3977, 4466, 3979, 3978, 4465])).
% 3.48/2.66 tff(4476,plain,
% 3.48/2.66 (hskp8),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[787, 726, 4475])).
% 3.48/2.66 tff(4477,plain,
% 3.48/2.66 (~c2_1(a593)),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[555, 4476])).
% 3.48/2.66 tff(4478,plain,
% 3.48/2.66 (c3_1(a593)),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[511, 4476])).
% 3.48/2.66 tff(4479,plain,
% 3.48/2.66 (c1_1(a593)),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[522, 4476])).
% 3.48/2.66 tff(4480,plain,
% 3.48/2.66 (hskp14 | (~c0_1(a599))),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[562, 107, 4466, 4467, 4479, 4478, 4477, 550])).
% 3.48/2.66 tff(4481,plain,
% 3.48/2.66 (~c0_1(a599)),
% 3.48/2.66 inference(unit_resolution,[status(thm)],[4480, 4474])).
% 3.48/2.66 tff(4482,assumption,(~c2_1(a633)), introduced(assumption)).
% 3.48/2.66 tff(4483,plain,
% 3.48/2.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a633) | c3_1(a633) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599) | c2_1(a633))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a633) | c3_1(a633) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599) | c2_1(a633))),
% 3.48/2.66 inference(rewrite,[status(thm)],[])).
% 3.48/2.66 tff(4484,plain,
% 3.48/2.66 (((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | c2_1(a633)) <=> (c0_1(a633) | c3_1(a633) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599) | c2_1(a633))),
% 3.48/2.66 inference(rewrite,[status(thm)],[])).
% 3.48/2.66 tff(4485,plain,
% 3.48/2.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | c2_1(a633))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a633) | c3_1(a633) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599) | c2_1(a633)))),
% 3.48/2.66 inference(monotonicity,[status(thm)],[4484])).
% 3.48/2.66 tff(4486,plain,
% 3.48/2.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | c2_1(a633))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a633) | c3_1(a633) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599) | c2_1(a633))),
% 3.48/2.67 inference(transitivity,[status(thm)],[4485, 4483])).
% 3.48/2.67 tff(4487,plain,
% 3.48/2.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | c2_1(a633))),
% 3.48/2.67 inference(quant_inst,[status(thm)],[])).
% 3.48/2.67 tff(4488,plain,
% 3.48/2.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a633) | c3_1(a633) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599) | c2_1(a633)),
% 3.48/2.67 inference(modus_ponens,[status(thm)],[4487, 4486])).
% 3.48/2.67 tff(4489,plain,
% 3.48/2.67 ($false),
% 3.48/2.67 inference(unit_resolution,[status(thm)],[4488, 107, 463, 462, 3981, 3980, 461, 1730, 3900, 4482])).
% 3.48/2.67 tff(4490,plain,(c0_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a633) | c3_1(a633) | c1_1(a599) | c2_1(a633)), inference(lemma,lemma(discharge,[]))).
% 3.48/2.67 tff(4491,plain,
% 3.48/2.67 (c2_1(a633)),
% 3.48/2.67 inference(unit_resolution,[status(thm)],[4490, 4481, 4467, 3979, 3978, 4465, 4466])).
% 3.48/2.67 tff(4492,plain,
% 3.48/2.67 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c3_1(a633) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a633)) | (~c1_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c3_1(a633) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a633)) | (~c1_1(a633)))),
% 3.48/2.67 inference(rewrite,[status(thm)],[])).
% 3.48/2.67 tff(4493,plain,
% 3.48/2.67 ((hskp28 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c1_1(a633)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599))) <=> (hskp28 | c3_1(a633) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a633)) | (~c1_1(a633)))),
% 3.48/2.67 inference(rewrite,[status(thm)],[])).
% 3.48/2.67 tff(4494,plain,
% 3.48/2.67 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c1_1(a633)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c3_1(a633) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a633)) | (~c1_1(a633))))),
% 3.48/2.67 inference(monotonicity,[status(thm)],[4493])).
% 3.48/2.67 tff(4495,plain,
% 3.48/2.67 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c1_1(a633)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c3_1(a633) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a633)) | (~c1_1(a633)))),
% 3.48/2.67 inference(transitivity,[status(thm)],[4494, 4492])).
% 3.48/2.67 tff(4496,plain,
% 3.48/2.67 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c1_1(a633)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)))),
% 3.48/2.67 inference(quant_inst,[status(thm)],[])).
% 3.48/2.67 tff(4497,plain,
% 3.48/2.67 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c3_1(a633) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a633)) | (~c1_1(a633))),
% 3.48/2.67 inference(modus_ponens,[status(thm)],[4496, 4495])).
% 3.48/2.67 tff(4498,plain,
% 3.48/2.67 (hskp28 | (~c2_1(a633))),
% 3.48/2.67 inference(unit_resolution,[status(thm)],[4497, 107, 3977, 4466, 4467, 3978, 4465, 1748])).
% 3.48/2.67 tff(4499,plain,
% 3.48/2.67 (hskp28),
% 3.48/2.67 inference(unit_resolution,[status(thm)],[4498, 4491])).
% 3.48/2.67 tff(4500,plain,
% 3.48/2.67 (c3_1(a612)),
% 3.48/2.67 inference(unit_resolution,[status(thm)],[1139, 4499])).
% 3.48/2.67 tff(4501,plain,
% 3.48/2.67 (c1_1(a612)),
% 3.48/2.67 inference(unit_resolution,[status(thm)],[1435, 4499])).
% 3.48/2.67 tff(4502,plain,
% 3.48/2.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a599) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a599) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599))),
% 3.48/2.67 inference(rewrite,[status(thm)],[])).
% 3.48/2.67 tff(4503,plain,
% 3.48/2.67 (((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599))) <=> (c1_1(a599) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599))),
% 3.48/2.67 inference(rewrite,[status(thm)],[])).
% 3.48/2.67 tff(4504,plain,
% 3.48/2.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a599) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599)))),
% 3.48/2.67 inference(monotonicity,[status(thm)],[4503])).
% 3.48/2.67 tff(4505,plain,
% 3.48/2.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a599) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599))),
% 3.48/2.67 inference(transitivity,[status(thm)],[4504, 4502])).
% 3.48/2.67 tff(4506,plain,
% 3.48/2.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c1_1(a599) | c0_1(a599) | (~c2_1(a599)))),
% 3.48/2.67 inference(quant_inst,[status(thm)],[])).
% 3.48/2.67 tff(4507,plain,
% 3.48/2.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a599) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599)),
% 3.48/2.67 inference(modus_ponens,[status(thm)],[4506, 4505])).
% 3.48/2.67 tff(4508,plain,
% 3.48/2.67 (~c0_1(a612)),
% 3.48/2.67 inference(unit_resolution,[status(thm)],[4507, 107, 4501, 4500, 4466, 4467, 4465, 65, 4481])).
% 3.48/2.67 tff(4509,plain,
% 3.48/2.67 (hskp23 | hskp14),
% 3.48/2.67 inference(unit_resolution,[status(thm)],[469, 107, 4466, 4467, 4465, 460])).
% 3.48/2.67 tff(4510,plain,
% 3.48/2.67 (hskp23),
% 3.48/2.67 inference(unit_resolution,[status(thm)],[4509, 4474])).
% 3.48/2.67 tff(4511,plain,
% 3.48/2.67 (c3_1(a636)),
% 3.48/2.67 inference(unit_resolution,[status(thm)],[492, 4510])).
% 3.48/2.67 tff(4512,plain,
% 3.48/2.67 (~c0_1(a636)),
% 3.48/2.67 inference(unit_resolution,[status(thm)],[481, 4510])).
% 3.48/2.67 tff(4513,plain,
% 3.48/2.67 (~c1_1(a636)),
% 3.48/2.67 inference(unit_resolution,[status(thm)],[475, 4510])).
% 3.48/2.67 tff(4514,plain,
% 3.48/2.67 (~hskp20),
% 3.48/2.67 inference(unit_resolution,[status(thm)],[734, 4513, 726, 4512, 4511])).
% 3.48/2.67 tff(4515,plain,
% 3.48/2.67 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp7 | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))),
% 3.48/2.67 inference(rewrite,[status(thm)],[])).
% 3.48/2.67 tff(4516,plain,
% 3.48/2.67 ((hskp20 | hskp7 | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c1_1(a612))) <=> (hskp20 | hskp7 | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))),
% 3.48/2.67 inference(rewrite,[status(thm)],[])).
% 3.48/2.67 tff(4517,plain,
% 3.48/2.67 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c1_1(a612)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612))))),
% 3.48/2.67 inference(monotonicity,[status(thm)],[4516])).
% 3.48/2.67 tff(4518,plain,
% 3.48/2.67 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c1_1(a612)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp7 | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))),
% 3.48/2.67 inference(transitivity,[status(thm)],[4517, 4515])).
% 3.48/2.67 tff(4519,plain,
% 3.48/2.67 ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c1_1(a612)))),
% 3.48/2.67 inference(quant_inst,[status(thm)],[])).
% 3.48/2.67 tff(4520,plain,
% 3.48/2.67 ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp7 | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612))),
% 3.48/2.67 inference(modus_ponens,[status(thm)],[4519, 4518])).
% 3.48/2.67 tff(4521,plain,
% 3.48/2.67 (hskp7),
% 3.48/2.67 inference(unit_resolution,[status(thm)],[4520, 107, 4514, 4501, 4500, 801, 4508])).
% 3.48/2.67 tff(4522,plain,
% 3.48/2.67 (~c0_1(a592)),
% 3.48/2.67 inference(unit_resolution,[status(thm)],[817, 4521])).
% 3.48/2.67 tff(4523,plain,
% 3.48/2.67 (c2_1(a592)),
% 3.48/2.67 inference(unit_resolution,[status(thm)],[828, 4521])).
% 3.48/2.67 tff(4524,plain,
% 3.48/2.67 (~c3_1(a592)),
% 3.48/2.67 inference(unit_resolution,[status(thm)],[811, 4521])).
% 3.48/2.67 tff(4525,plain,
% 3.48/2.67 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a633) | c3_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c2_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a633) | c3_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c2_1(a633)))),
% 3.48/2.67 inference(rewrite,[status(thm)],[])).
% 3.48/2.67 tff(4526,plain,
% 3.48/2.67 ((hskp14 | (~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c3_1(a633) | c0_1(a633) | (~c2_1(a633))) <=> (hskp14 | c0_1(a633) | c3_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c2_1(a633)))),
% 3.48/2.67 inference(rewrite,[status(thm)],[])).
% 3.48/2.67 tff(4527,plain,
% 3.48/2.67 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c3_1(a633) | c0_1(a633) | (~c2_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a633) | c3_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c2_1(a633))))),
% 3.48/2.67 inference(monotonicity,[status(thm)],[4526])).
% 3.48/2.67 tff(4528,plain,
% 3.48/2.67 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c3_1(a633) | c0_1(a633) | (~c2_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a633) | c3_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c2_1(a633)))),
% 3.48/2.67 inference(transitivity,[status(thm)],[4527, 4525])).
% 3.48/2.67 tff(4529,plain,
% 3.48/2.67 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c3_1(a633) | c0_1(a633) | (~c2_1(a633)))),
% 3.48/2.67 inference(quant_inst,[status(thm)],[])).
% 3.48/2.67 tff(4530,plain,
% 3.48/2.67 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a633) | c3_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c2_1(a633))),
% 3.48/2.67 inference(modus_ponens,[status(thm)],[4529, 4528])).
% 3.48/2.67 tff(4531,plain,
% 3.48/2.67 (hskp14 | (~c0_1(a607)) | (~c2_1(a633))),
% 3.48/2.67 inference(unit_resolution,[status(thm)],[4530, 107, 3979, 3978, 66, 22, 305])).
% 3.48/2.67 tff(4532,plain,
% 3.48/2.67 (~c0_1(a607)),
% 3.48/2.67 inference(unit_resolution,[status(thm)],[4531, 4491, 4474])).
% 3.48/2.67 tff(4533,plain,
% 3.48/2.67 (hskp26 | hskp0 | c2_1(a607) | c0_1(a607)),
% 3.48/2.67 inference(unit_resolution,[status(thm)],[1038, 107, 66, 1032])).
% 3.48/2.67 tff(4534,plain,
% 3.48/2.67 (hskp0),
% 3.48/2.67 inference(unit_resolution,[status(thm)],[4533, 4532, 22, 726])).
% 3.48/2.67 tff(4535,plain,
% 3.48/2.67 (~c2_1(a584)),
% 3.48/2.67 inference(unit_resolution,[status(thm)],[1045, 4534])).
% 3.48/2.67 tff(4536,plain,
% 3.48/2.67 (~c0_1(a584)),
% 3.48/2.67 inference(unit_resolution,[status(thm)],[1051, 4534])).
% 3.48/2.67 tff(4537,plain,
% 3.48/2.67 (c1_1(a584)),
% 3.48/2.67 inference(unit_resolution,[status(thm)],[1062, 4534])).
% 3.48/2.67 tff(4538,plain,
% 3.48/2.67 (hskp14 | (~c0_1(a599))),
% 3.48/2.67 inference(unit_resolution,[status(thm)],[562, 107, 4466, 4467, 1894, 1903, 1893, 550])).
% 3.48/2.67 tff(4539,plain,
% 3.48/2.67 (~c0_1(a599)),
% 3.48/2.67 inference(unit_resolution,[status(thm)],[4538, 364])).
% 3.48/2.67 tff(4540,plain,
% 3.48/2.67 (c2_1(a633)),
% 3.48/2.67 inference(unit_resolution,[status(thm)],[4490, 4539, 4467, 3979, 3978, 4465, 4466])).
% 3.48/2.67 tff(4541,plain,
% 3.48/2.67 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a633) | c3_1(a633) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c2_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a633) | c3_1(a633) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c2_1(a633)))),
% 3.48/2.67 inference(rewrite,[status(thm)],[])).
% 3.48/2.67 tff(4542,plain,
% 3.48/2.67 ((hskp14 | (~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588)) | c3_1(a633) | c0_1(a633) | (~c2_1(a633))) <=> (hskp14 | c0_1(a633) | c3_1(a633) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c2_1(a633)))),
% 3.48/2.67 inference(rewrite,[status(thm)],[])).
% 3.48/2.67 tff(4543,plain,
% 3.48/2.67 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588)) | c3_1(a633) | c0_1(a633) | (~c2_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c0_1(a633) | c3_1(a633) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c2_1(a633))))),
% 3.48/2.67 inference(monotonicity,[status(thm)],[4542])).
% 3.48/2.67 tff(4544,plain,
% 3.48/2.67 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588)) | c3_1(a633) | c0_1(a633) | (~c2_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a633) | c3_1(a633) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c2_1(a633)))),
% 3.48/2.67 inference(transitivity,[status(thm)],[4543, 4541])).
% 3.48/2.67 tff(4545,plain,
% 3.48/2.67 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588)) | c3_1(a633) | c0_1(a633) | (~c2_1(a633)))),
% 3.48/2.67 inference(quant_inst,[status(thm)],[])).
% 3.48/2.67 tff(4546,plain,
% 3.48/2.67 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c0_1(a633) | c3_1(a633) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c2_1(a633))),
% 3.48/2.67 inference(modus_ponens,[status(thm)],[4545, 4544])).
% 3.48/2.67 tff(4547,plain,
% 3.48/2.67 ($false),
% 3.48/2.67 inference(unit_resolution,[status(thm)],[4546, 107, 364, 139, 3981, 3980, 128, 122, 305, 4290])).
% 3.48/2.67 tff(4548,plain,((~hskp4) | hskp14 | c0_1(a633) | c3_1(a633) | (~c2_1(a633))), inference(lemma,lemma(discharge,[]))).
% 3.48/2.67 tff(4549,plain,
% 3.48/2.67 (~hskp4),
% 3.48/2.67 inference(unit_resolution,[status(thm)],[4548, 364, 3979, 3978, 4540])).
% 3.48/2.67 tff(4550,plain,
% 3.48/2.67 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp10 | hskp4 | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599))),
% 3.48/2.67 inference(rewrite,[status(thm)],[])).
% 3.48/2.67 tff(4551,plain,
% 3.48/2.67 ((hskp10 | hskp4 | (~ndr1_0) | c0_1(a599) | (~c2_1(a599)) | (~c3_1(a599))) <=> (hskp10 | hskp4 | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599))),
% 3.48/2.67 inference(rewrite,[status(thm)],[])).
% 3.48/2.67 tff(4552,plain,
% 3.48/2.67 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c0_1(a599) | (~c2_1(a599)) | (~c3_1(a599)))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599)))),
% 3.48/2.67 inference(monotonicity,[status(thm)],[4551])).
% 3.48/2.67 tff(4553,plain,
% 3.48/2.67 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c0_1(a599) | (~c2_1(a599)) | (~c3_1(a599)))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp10 | hskp4 | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599))),
% 3.48/2.67 inference(transitivity,[status(thm)],[4552, 4550])).
% 3.48/2.67 tff(4554,plain,
% 3.48/2.67 ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c0_1(a599) | (~c2_1(a599)) | (~c3_1(a599)))),
% 3.48/2.67 inference(quant_inst,[status(thm)],[])).
% 3.48/2.67 tff(4555,plain,
% 3.48/2.67 ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp10 | hskp4 | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | c0_1(a599)),
% 3.56/2.67 inference(modus_ponens,[status(thm)],[4554, 4553])).
% 3.56/2.67 tff(4556,plain,
% 3.56/2.67 (hskp10 | hskp4 | c0_1(a599)),
% 3.56/2.67 inference(unit_resolution,[status(thm)],[4555, 107, 4466, 4467, 861])).
% 3.56/2.67 tff(4557,plain,
% 3.56/2.67 (hskp10),
% 3.56/2.67 inference(unit_resolution,[status(thm)],[4556, 4549, 4539])).
% 3.56/2.67 tff(4558,plain,
% 3.56/2.67 (c0_1(a598)),
% 3.56/2.67 inference(unit_resolution,[status(thm)],[892, 4557])).
% 3.56/2.67 tff(4559,plain,
% 3.56/2.67 (((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp18 | c3_1(a633) | (~ndr1_0) | (~c2_1(a633)) | (~c1_1(a633)))) <=> ((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp18 | c3_1(a633) | (~ndr1_0) | (~c2_1(a633)) | (~c1_1(a633)))),
% 3.56/2.67 inference(rewrite,[status(thm)],[])).
% 3.56/2.67 tff(4560,plain,
% 3.56/2.67 ((hskp29 | hskp18 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c1_1(a633))) <=> (hskp29 | hskp18 | c3_1(a633) | (~ndr1_0) | (~c2_1(a633)) | (~c1_1(a633)))),
% 3.56/2.67 inference(rewrite,[status(thm)],[])).
% 3.56/2.67 tff(4561,plain,
% 3.56/2.67 (((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp18 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c1_1(a633)))) <=> ((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp18 | c3_1(a633) | (~ndr1_0) | (~c2_1(a633)) | (~c1_1(a633))))),
% 3.56/2.67 inference(monotonicity,[status(thm)],[4560])).
% 3.56/2.67 tff(4562,plain,
% 3.56/2.67 (((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp18 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c1_1(a633)))) <=> ((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp18 | c3_1(a633) | (~ndr1_0) | (~c2_1(a633)) | (~c1_1(a633)))),
% 3.56/2.67 inference(transitivity,[status(thm)],[4561, 4559])).
% 3.56/2.67 tff(4563,plain,
% 3.56/2.67 ((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp18 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c1_1(a633)))),
% 3.56/2.67 inference(quant_inst,[status(thm)],[])).
% 3.56/2.67 tff(4564,plain,
% 3.56/2.67 ((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp18 | c3_1(a633) | (~ndr1_0) | (~c2_1(a633)) | (~c1_1(a633))),
% 3.56/2.67 inference(modus_ponens,[status(thm)],[4563, 4562])).
% 3.56/2.67 tff(4565,plain,
% 3.56/2.67 (hskp29 | hskp18 | (~c2_1(a633))),
% 3.56/2.67 inference(unit_resolution,[status(thm)],[4564, 107, 3977, 3978, 1796])).
% 3.56/2.67 tff(4566,plain,
% 3.56/2.67 (hskp18),
% 3.56/2.67 inference(unit_resolution,[status(thm)],[4565, 269, 4540])).
% 3.56/2.67 tff(4567,plain,
% 3.56/2.67 (~c2_1(a610)),
% 3.56/2.67 inference(unit_resolution,[status(thm)],[1189, 4566])).
% 3.56/2.67 tff(4568,plain,
% 3.56/2.67 (~c0_1(a610)),
% 3.56/2.67 inference(unit_resolution,[status(thm)],[1195, 4566])).
% 3.56/2.67 tff(4569,plain,
% 3.56/2.67 (hskp6),
% 3.56/2.67 inference(unit_resolution,[status(thm)],[660, 269, 364, 4465, 4467, 4466])).
% 3.56/2.67 tff(4570,plain,
% 3.56/2.67 (~c0_1(a590)),
% 3.56/2.67 inference(unit_resolution,[status(thm)],[666, 4569])).
% 3.56/2.67 tff(4571,plain,
% 3.56/2.67 (c3_1(a590)),
% 3.56/2.67 inference(unit_resolution,[status(thm)],[677, 4569])).
% 3.56/2.67 tff(4572,plain,
% 3.56/2.67 (c2_1(a590)),
% 3.56/2.67 inference(unit_resolution,[status(thm)],[688, 4569])).
% 3.56/2.67 tff(4573,plain,
% 3.56/2.67 (hskp3),
% 3.56/2.67 inference(unit_resolution,[status(thm)],[921, 4572, 4369, 841, 842, 66, 22, 851, 4549, 4571, 4570])).
% 3.56/2.67 tff(4574,plain,
% 3.56/2.67 (c2_1(a587)),
% 3.56/2.67 inference(unit_resolution,[status(thm)],[950, 4573])).
% 3.56/2.67 tff(4575,plain,
% 3.56/2.67 (c0_1(a587)),
% 3.56/2.67 inference(unit_resolution,[status(thm)],[961, 4573])).
% 3.56/2.67 tff(4576,plain,
% 3.56/2.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a607)) | (~c2_1(a633)) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a607)) | (~c2_1(a633)) | (~c1_1(a633)))),
% 3.56/2.67 inference(rewrite,[status(thm)],[])).
% 3.56/2.67 tff(4577,plain,
% 3.56/2.67 (((~ndr1_0) | (~c2_1(a587)) | (~c3_1(a587)) | (~c0_1(a587)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633))) <=> (c0_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a607)) | (~c2_1(a633)) | (~c1_1(a633)))),
% 3.56/2.67 inference(rewrite,[status(thm)],[])).
% 3.56/2.67 tff(4578,plain,
% 3.56/2.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a587)) | (~c3_1(a587)) | (~c0_1(a587)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a607)) | (~c2_1(a633)) | (~c1_1(a633))))),
% 3.56/2.67 inference(monotonicity,[status(thm)],[4577])).
% 3.56/2.67 tff(4579,plain,
% 3.56/2.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a587)) | (~c3_1(a587)) | (~c0_1(a587)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a607)) | (~c2_1(a633)) | (~c1_1(a633)))),
% 3.56/2.67 inference(transitivity,[status(thm)],[4578, 4576])).
% 3.56/2.67 tff(4580,plain,
% 3.56/2.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a587)) | (~c3_1(a587)) | (~c0_1(a587)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633)))),
% 3.56/2.67 inference(quant_inst,[status(thm)],[])).
% 3.56/2.67 tff(4581,plain,
% 3.56/2.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c3_1(a587)) | (~c2_1(a587)) | (~c0_1(a587)) | (~c3_1(a607)) | (~c2_1(a633)) | (~c1_1(a633))),
% 3.56/2.67 inference(modus_ponens,[status(thm)],[4580, 4579])).
% 3.56/2.67 tff(4582,plain,
% 3.56/2.67 (~c3_1(a587)),
% 3.56/2.67 inference(unit_resolution,[status(thm)],[4581, 107, 3977, 4369, 4575, 4574, 3979, 66, 22, 11, 4540])).
% 3.56/2.67 tff(4583,plain,
% 3.56/2.67 (~c1_1(a587)),
% 3.56/2.67 inference(unit_resolution,[status(thm)],[939, 4573])).
% 3.56/2.67 tff(4584,assumption,(c1_1(a584)), introduced(assumption)).
% 3.56/2.67 tff(4585,plain,
% 3.56/2.67 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | c1_1(a587) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | c3_1(a587) | (~c2_1(a587)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp16 | c1_1(a587) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | c3_1(a587) | (~c2_1(a587)))),
% 3.56/2.67 inference(rewrite,[status(thm)],[])).
% 3.56/2.67 tff(4586,plain,
% 3.56/2.67 ((hskp16 | (~ndr1_0) | c1_1(a587) | c3_1(a587) | (~c2_1(a587)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584))) <=> (hskp16 | c1_1(a587) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | c3_1(a587) | (~c2_1(a587)))),
% 3.56/2.67 inference(rewrite,[status(thm)],[])).
% 3.56/2.67 tff(4587,plain,
% 3.56/2.67 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a587) | c3_1(a587) | (~c2_1(a587)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | c1_1(a587) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | c3_1(a587) | (~c2_1(a587))))),
% 3.56/2.67 inference(monotonicity,[status(thm)],[4586])).
% 3.56/2.67 tff(4588,plain,
% 3.56/2.67 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a587) | c3_1(a587) | (~c2_1(a587)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp16 | c1_1(a587) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | c3_1(a587) | (~c2_1(a587)))),
% 3.56/2.68 inference(transitivity,[status(thm)],[4587, 4585])).
% 3.56/2.68 tff(4589,plain,
% 3.56/2.68 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a587) | c3_1(a587) | (~c2_1(a587)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584)))),
% 3.56/2.68 inference(quant_inst,[status(thm)],[])).
% 3.56/2.68 tff(4590,plain,
% 3.56/2.68 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp16 | c1_1(a587) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | c3_1(a587) | (~c2_1(a587))),
% 3.56/2.68 inference(modus_ponens,[status(thm)],[4589, 4588])).
% 3.56/2.68 tff(4591,plain,
% 3.56/2.68 (hskp16),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[4590, 107, 4574, 4584, 4583, 3642, 3641, 1022, 4582])).
% 3.56/2.68 tff(4592,plain,
% 3.56/2.68 (c1_1(a606)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[1088, 4591])).
% 3.56/2.68 tff(4593,plain,
% 3.56/2.68 (c3_1(a610)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[1206, 4566])).
% 3.56/2.68 tff(4594,plain,
% 3.56/2.68 (hskp28),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[4498, 4540])).
% 3.56/2.68 tff(4595,plain,
% 3.56/2.68 (c3_1(a612)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[1139, 4594])).
% 3.56/2.68 tff(4596,plain,
% 3.56/2.68 (c1_1(a612)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[1435, 4594])).
% 3.56/2.68 tff(4597,plain,
% 3.56/2.68 (~c0_1(a612)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[4507, 107, 4596, 4595, 4466, 4467, 4465, 65, 4539])).
% 3.56/2.68 tff(4598,plain,
% 3.56/2.68 (c3_1(a598)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[881, 4557])).
% 3.56/2.68 tff(4599,plain,
% 3.56/2.68 (~c1_1(a598)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[911, 4557])).
% 3.56/2.68 tff(4600,plain,
% 3.56/2.68 (~hskp27),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[651, 269, 364])).
% 3.56/2.68 tff(4601,plain,
% 3.56/2.68 (c2_1(a612)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[1150, 4594])).
% 3.56/2.68 tff(4602,plain,
% 3.56/2.68 (~c2_1(a606)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[1111, 4591])).
% 3.56/2.68 tff(4603,plain,
% 3.56/2.68 (~c3_1(a606)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[1075, 4591])).
% 3.56/2.68 tff(4604,plain,
% 3.56/2.68 ($false),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[1911, 4603, 4602, 1894, 4601, 4600, 1893, 1903, 4599, 4595, 4598, 4597, 4593, 4592, 4568, 4567, 4558])).
% 3.56/2.68 tff(4605,plain,(hskp29 | (~c1_1(a593)) | c2_1(a593) | (~c3_1(a593)) | (~c1_1(a584)) | c0_1(a584) | c2_1(a584) | c1_1(a607) | c2_1(a607) | c3_1(a592) | (~c2_1(a592)) | c0_1(a592) | hskp14), inference(lemma,lemma(discharge,[]))).
% 3.56/2.68 tff(4606,plain,
% 3.56/2.68 (hskp29),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[4605, 4479, 4477, 4478, 4537, 4536, 4535, 66, 22, 4524, 4523, 4522, 4474])).
% 3.56/2.68 tff(4607,plain,
% 3.56/2.68 (c3_1(a678)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[2269, 4606])).
% 3.56/2.68 tff(4608,plain,
% 3.56/2.68 (c2_1(a678)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[2280, 4606])).
% 3.56/2.68 tff(4609,plain,
% 3.56/2.68 (c0_1(a678)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[2291, 4606])).
% 3.56/2.68 tff(4610,plain,
% 3.56/2.68 ($false),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[4379, 107, 4609, 4608, 4607, 3977, 4369, 3979, 66, 22, 11, 4491])).
% 3.56/2.68 tff(4611,plain,(hskp26 | c1_1(a607) | c2_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.56/2.68 tff(4612,plain,
% 3.56/2.68 (hskp26),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[4611, 22, 66])).
% 3.56/2.68 tff(4613,plain,
% 3.56/2.68 (c0_1(a583)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[362, 4612])).
% 3.56/2.68 tff(4614,plain,
% 3.56/2.68 (c2_1(a583)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[391, 4612])).
% 3.56/2.68 tff(4615,plain,
% 3.56/2.68 (c3_1(a583)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[4359, 4614, 4466, 3977, 4467, 4613, 3979, 3978, 4465])).
% 3.56/2.68 tff(4616,plain,
% 3.56/2.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c3_1(a607)) | (~c2_1(a633)) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c3_1(a607)) | (~c2_1(a633)) | (~c1_1(a633)))),
% 3.56/2.68 inference(rewrite,[status(thm)],[])).
% 3.56/2.68 tff(4617,plain,
% 3.56/2.68 (((~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633))) <=> (c0_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c3_1(a607)) | (~c2_1(a633)) | (~c1_1(a633)))),
% 3.56/2.68 inference(rewrite,[status(thm)],[])).
% 3.56/2.68 tff(4618,plain,
% 3.56/2.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c3_1(a607)) | (~c2_1(a633)) | (~c1_1(a633))))),
% 3.56/2.68 inference(monotonicity,[status(thm)],[4617])).
% 3.56/2.68 tff(4619,plain,
% 3.56/2.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c3_1(a607)) | (~c2_1(a633)) | (~c1_1(a633)))),
% 3.56/2.68 inference(transitivity,[status(thm)],[4618, 4616])).
% 3.56/2.68 tff(4620,plain,
% 3.56/2.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | c1_1(a607) | c2_1(a607) | (~c3_1(a607)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633)))),
% 3.56/2.68 inference(quant_inst,[status(thm)],[])).
% 3.56/2.68 tff(4621,plain,
% 3.56/2.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a633) | c1_1(a607) | c2_1(a607) | (~ndr1_0) | (~c2_1(a583)) | (~c3_1(a583)) | (~c0_1(a583)) | (~c3_1(a607)) | (~c2_1(a633)) | (~c1_1(a633))),
% 3.56/2.68 inference(modus_ponens,[status(thm)],[4620, 4619])).
% 3.56/2.68 tff(4622,plain,
% 3.56/2.68 (~c2_1(a633)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[4621, 107, 4613, 4614, 3977, 4369, 3979, 66, 22, 11, 4615])).
% 3.56/2.68 tff(4623,plain,
% 3.56/2.68 (c1_1(a583)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[351, 4612])).
% 3.56/2.68 tff(4624,plain,
% 3.56/2.68 (hskp10),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[2000, 3340])).
% 3.56/2.68 tff(4625,plain,
% 3.56/2.68 (~c1_1(a598)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[911, 4624])).
% 3.56/2.68 tff(4626,plain,
% 3.56/2.68 (c3_1(a598)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[881, 4624])).
% 3.56/2.68 tff(4627,plain,
% 3.56/2.68 (c0_1(a598)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[892, 4624])).
% 3.56/2.68 tff(4628,plain,
% 3.56/2.68 ($false),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[2010, 107, 3154, 1651, 1650, 4627, 4626, 4625, 1993, 3340])).
% 3.56/2.68 tff(4629,plain,((~c3_1(a583)) | hskp15 | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a583))), inference(lemma,lemma(discharge,[]))).
% 3.56/2.68 tff(4630,plain,
% 3.56/2.68 (hskp15),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[4629, 4615, 4613, 4623, 4614])).
% 3.56/2.68 tff(4631,plain,
% 3.56/2.68 (~c0_1(a604)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[1591, 4630])).
% 3.56/2.68 tff(4632,plain,
% 3.56/2.68 (c3_1(a604)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[1602, 4630])).
% 3.56/2.68 tff(4633,plain,
% 3.56/2.68 (c1_1(a604)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[1613, 4630])).
% 3.56/2.68 tff(4634,plain,
% 3.56/2.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a633) | c3_1(a633) | c1_1(a607) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)) | (~c0_1(a607)) | c2_1(a633))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a633) | c3_1(a633) | c1_1(a607) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)) | (~c0_1(a607)) | c2_1(a633))),
% 3.56/2.68 inference(rewrite,[status(thm)],[])).
% 3.56/2.68 tff(4635,plain,
% 3.56/2.68 (((~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a633) | c0_1(a633) | c2_1(a633)) <=> (c0_1(a633) | c3_1(a633) | c1_1(a607) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)) | (~c0_1(a607)) | c2_1(a633))),
% 3.56/2.68 inference(rewrite,[status(thm)],[])).
% 3.56/2.68 tff(4636,plain,
% 3.56/2.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a633) | c0_1(a633) | c2_1(a633))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a633) | c3_1(a633) | c1_1(a607) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)) | (~c0_1(a607)) | c2_1(a633)))),
% 3.56/2.68 inference(monotonicity,[status(thm)],[4635])).
% 3.56/2.68 tff(4637,plain,
% 3.56/2.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a633) | c0_1(a633) | c2_1(a633))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a633) | c3_1(a633) | c1_1(a607) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)) | (~c0_1(a607)) | c2_1(a633))),
% 3.56/2.68 inference(transitivity,[status(thm)],[4636, 4634])).
% 3.56/2.68 tff(4638,plain,
% 3.56/2.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a607) | c1_1(a607) | (~c0_1(a607)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)) | c3_1(a633) | c0_1(a633) | c2_1(a633))),
% 3.56/2.68 inference(quant_inst,[status(thm)],[])).
% 3.56/2.68 tff(4639,plain,
% 3.56/2.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a633) | c3_1(a633) | c1_1(a607) | c2_1(a607) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)) | (~c0_1(a607)) | c2_1(a633)),
% 3.56/2.68 inference(modus_ponens,[status(thm)],[4638, 4637])).
% 3.56/2.68 tff(4640,plain,
% 3.56/2.68 ((~c0_1(a607)) | c2_1(a633)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[4639, 107, 4633, 4632, 3979, 3978, 66, 22, 4631, 1364])).
% 3.56/2.68 tff(4641,plain,
% 3.56/2.68 (~c0_1(a607)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[4640, 4622])).
% 3.56/2.68 tff(4642,plain,
% 3.56/2.68 (hskp9 | c0_1(a607)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[1518, 107, 4613, 4623, 4614, 4369, 66, 294])).
% 3.56/2.68 tff(4643,plain,
% 3.56/2.68 (hskp9),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[4642, 4641])).
% 3.56/2.68 tff(4644,plain,
% 3.56/2.68 (~c3_1(a595)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[1487, 4643])).
% 3.56/2.68 tff(4645,plain,
% 3.56/2.68 (~c1_1(a595)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[1493, 4643])).
% 3.56/2.68 tff(4646,plain,
% 3.56/2.68 (~c0_1(a595)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[1499, 4643])).
% 3.56/2.68 tff(4647,plain,
% 3.56/2.68 (hskp1),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[1620, 107, 4633, 4632, 4631, 4646, 4645, 4644, 1555])).
% 3.56/2.68 tff(4648,plain,
% 3.56/2.68 (~c0_1(a585)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[1250, 4647])).
% 3.56/2.68 tff(4649,plain,
% 3.56/2.68 (c2_1(a585)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[1261, 4647])).
% 3.56/2.68 tff(4650,plain,
% 3.56/2.68 (c1_1(a585)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[1272, 4647])).
% 3.56/2.68 tff(4651,plain,
% 3.56/2.68 ($false),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[1842, 107, 4613, 4614, 4369, 4650, 4649, 66, 22, 4648, 11, 4615])).
% 3.56/2.68 tff(4652,plain,(c2_1(a607) | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.56/2.68 tff(4653,plain,
% 3.56/2.68 (c2_1(a607)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[4652, 66])).
% 3.56/2.68 tff(4654,plain,
% 3.56/2.68 (~hskp17),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[275, 4653])).
% 3.56/2.68 tff(4655,assumption,(~c1_1(a633)), introduced(assumption)).
% 3.56/2.68 tff(4656,plain,
% 3.56/2.68 (~hskp22),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[3962, 4655])).
% 3.56/2.68 tff(4657,plain,
% 3.56/2.68 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a633) | c3_1(a607) | c0_1(a633) | c3_1(a633) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a633) | c3_1(a607) | c0_1(a633) | c3_1(a633) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0))),
% 3.56/2.68 inference(rewrite,[status(thm)],[])).
% 3.56/2.68 tff(4658,plain,
% 3.56/2.68 ((hskp2 | (~ndr1_0) | c1_1(a607) | c3_1(a607) | (~c2_1(a607)) | c3_1(a633) | c1_1(a633) | c0_1(a633)) <=> (hskp2 | c1_1(a633) | c3_1(a607) | c0_1(a633) | c3_1(a633) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0))),
% 3.56/2.68 inference(rewrite,[status(thm)],[])).
% 3.56/2.68 tff(4659,plain,
% 3.56/2.68 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a607) | c3_1(a607) | (~c2_1(a607)) | c3_1(a633) | c1_1(a633) | c0_1(a633))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a633) | c3_1(a607) | c0_1(a633) | c3_1(a633) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0)))),
% 3.56/2.68 inference(monotonicity,[status(thm)],[4658])).
% 3.56/2.68 tff(4660,plain,
% 3.56/2.68 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a607) | c3_1(a607) | (~c2_1(a607)) | c3_1(a633) | c1_1(a633) | c0_1(a633))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a633) | c3_1(a607) | c0_1(a633) | c3_1(a633) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0))),
% 3.56/2.68 inference(transitivity,[status(thm)],[4659, 4657])).
% 3.56/2.68 tff(4661,plain,
% 3.56/2.68 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a607) | c3_1(a607) | (~c2_1(a607)) | c3_1(a633) | c1_1(a633) | c0_1(a633))),
% 3.56/2.68 inference(quant_inst,[status(thm)],[])).
% 3.56/2.68 tff(4662,plain,
% 3.56/2.68 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a633) | c3_1(a607) | c0_1(a633) | c3_1(a633) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0)),
% 3.56/2.68 inference(modus_ponens,[status(thm)],[4661, 4660])).
% 3.56/2.68 tff(4663,plain,
% 3.56/2.68 (hskp2 | c1_1(a633) | c0_1(a633)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[4662, 107, 33, 3980, 66, 4653, 200])).
% 3.56/2.68 tff(4664,plain,
% 3.56/2.68 (hskp2),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[4663, 4655, 3981])).
% 3.56/2.68 tff(4665,plain,
% 3.56/2.68 (~c3_1(a586)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[218, 4664])).
% 3.56/2.68 tff(4666,plain,
% 3.56/2.68 (hskp29),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[2258, 4656])).
% 3.56/2.68 tff(4667,plain,
% 3.56/2.68 (c3_1(a678)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[2269, 4666])).
% 3.56/2.68 tff(4668,plain,
% 3.56/2.68 (c2_1(a678)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[2280, 4666])).
% 3.56/2.68 tff(4669,plain,
% 3.56/2.68 (c0_1(a678)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[2291, 4666])).
% 3.56/2.68 tff(4670,plain,
% 3.56/2.68 (hskp11 | c2_1(a633)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[4285, 107, 4669, 4668, 4667, 3981, 3980, 268])).
% 3.56/2.68 tff(4671,plain,
% 3.56/2.68 (c2_1(a633)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[4670, 1638])).
% 3.56/2.68 tff(4672,plain,
% 3.56/2.68 (~c3_1(a583)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[4629, 3154, 3321, 3322, 3330])).
% 3.56/2.68 tff(4673,plain,
% 3.56/2.68 (hskp4 | c3_1(a583)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[3328, 107, 2987, 3321, 3322, 55])).
% 3.56/2.68 tff(4674,plain,
% 3.56/2.68 (hskp4),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[4673, 4672])).
% 3.56/2.68 tff(4675,plain,
% 3.56/2.68 (hskp6),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[147, 4674, 4656])).
% 3.56/2.68 tff(4676,plain,
% 3.56/2.68 (~c0_1(a590)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[666, 4675])).
% 3.56/2.68 tff(4677,plain,
% 3.56/2.68 (c3_1(a590)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[677, 4675])).
% 3.56/2.68 tff(4678,plain,
% 3.56/2.68 (c2_1(a590)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[688, 4675])).
% 3.56/2.68 tff(4679,plain,
% 3.56/2.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a633) | c0_1(a633) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a633) | c0_1(a633) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a633)))),
% 3.56/2.68 inference(rewrite,[status(thm)],[])).
% 3.56/2.68 tff(4680,plain,
% 3.56/2.68 (((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a633) | c0_1(a633) | (~c2_1(a633))) <=> (c1_1(a633) | c0_1(a633) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a633)))),
% 3.56/2.68 inference(rewrite,[status(thm)],[])).
% 3.56/2.68 tff(4681,plain,
% 3.56/2.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a633) | c0_1(a633) | (~c2_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a633) | c0_1(a633) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a633))))),
% 3.56/2.68 inference(monotonicity,[status(thm)],[4680])).
% 3.56/2.68 tff(4682,plain,
% 3.56/2.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a633) | c0_1(a633) | (~c2_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a633) | c0_1(a633) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a633)))),
% 3.56/2.68 inference(transitivity,[status(thm)],[4681, 4679])).
% 3.56/2.68 tff(4683,plain,
% 3.56/2.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a633) | c0_1(a633) | (~c2_1(a633)))),
% 3.56/2.68 inference(quant_inst,[status(thm)],[])).
% 3.56/2.68 tff(4684,plain,
% 3.56/2.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a633) | c0_1(a633) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a633))),
% 3.56/2.68 inference(modus_ponens,[status(thm)],[4683, 4682])).
% 3.56/2.68 tff(4685,plain,
% 3.56/2.68 (~c1_1(a678)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[4684, 107, 4669, 4667, 4655, 4678, 4677, 3981, 4676, 65, 4290])).
% 3.56/2.68 tff(4686,plain,
% 3.56/2.68 (~c2_1(a588)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[121, 4674])).
% 3.56/2.68 tff(4687,plain,
% 3.56/2.68 (c0_1(a588)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[138, 4674])).
% 3.56/2.68 tff(4688,plain,
% 3.56/2.68 (((~![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp15 | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c3_1(a588)))) <=> ((~![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp15 | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c3_1(a588)))),
% 3.56/2.68 inference(rewrite,[status(thm)],[])).
% 3.56/2.68 tff(4689,plain,
% 3.56/2.68 ((hskp11 | hskp15 | (~ndr1_0) | c2_1(a588) | (~c3_1(a588)) | (~c0_1(a588))) <=> (hskp11 | hskp15 | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c3_1(a588)))),
% 3.56/2.68 inference(rewrite,[status(thm)],[])).
% 3.56/2.68 tff(4690,plain,
% 3.56/2.68 (((~![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp15 | (~ndr1_0) | c2_1(a588) | (~c3_1(a588)) | (~c0_1(a588)))) <=> ((~![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp15 | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c3_1(a588))))),
% 3.56/2.68 inference(monotonicity,[status(thm)],[4689])).
% 3.56/2.68 tff(4691,plain,
% 3.56/2.68 (((~![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp15 | (~ndr1_0) | c2_1(a588) | (~c3_1(a588)) | (~c0_1(a588)))) <=> ((~![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp15 | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c3_1(a588)))),
% 3.56/2.68 inference(transitivity,[status(thm)],[4690, 4688])).
% 3.56/2.68 tff(4692,plain,
% 3.56/2.68 ((~![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp15 | (~ndr1_0) | c2_1(a588) | (~c3_1(a588)) | (~c0_1(a588)))),
% 3.56/2.68 inference(quant_inst,[status(thm)],[])).
% 3.56/2.68 tff(4693,plain,
% 3.56/2.68 ((~![U: $i] : (hskp11 | hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp15 | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c3_1(a588))),
% 3.56/2.68 inference(modus_ponens,[status(thm)],[4692, 4691])).
% 3.56/2.68 tff(4694,plain,
% 3.56/2.68 (~c3_1(a588)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[4693, 1638, 107, 3154, 4687, 4686, 4300])).
% 3.56/2.68 tff(4695,plain,
% 3.56/2.68 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | c0_1(a590) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c3_1(a590)) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c0_1(a590) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c3_1(a590)) | (~c2_1(a590)))),
% 3.56/2.68 inference(rewrite,[status(thm)],[])).
% 3.56/2.68 tff(4696,plain,
% 3.56/2.68 ((hskp16 | (~ndr1_0) | c2_1(a588) | c3_1(a588) | (~c0_1(a588)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590))) <=> (hskp16 | c0_1(a590) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c3_1(a590)) | (~c2_1(a590)))),
% 3.56/2.68 inference(rewrite,[status(thm)],[])).
% 3.56/2.68 tff(4697,plain,
% 3.56/2.68 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a588) | c3_1(a588) | (~c0_1(a588)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | c0_1(a590) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c3_1(a590)) | (~c2_1(a590))))),
% 3.56/2.68 inference(monotonicity,[status(thm)],[4696])).
% 3.56/2.68 tff(4698,plain,
% 3.56/2.68 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a588) | c3_1(a588) | (~c0_1(a588)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c0_1(a590) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c3_1(a590)) | (~c2_1(a590)))),
% 3.56/2.68 inference(transitivity,[status(thm)],[4697, 4695])).
% 3.56/2.68 tff(4699,plain,
% 3.56/2.68 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a588) | c3_1(a588) | (~c0_1(a588)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)))),
% 3.56/2.68 inference(quant_inst,[status(thm)],[])).
% 3.56/2.68 tff(4700,plain,
% 3.56/2.68 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c0_1(a590) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c3_1(a590)) | (~c2_1(a590))),
% 3.56/2.68 inference(modus_ponens,[status(thm)],[4699, 4698])).
% 3.56/2.68 tff(4701,plain,
% 3.56/2.68 (hskp16),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[4700, 107, 4678, 4677, 4687, 4676, 4686, 2125, 4694])).
% 3.56/2.68 tff(4702,plain,
% 3.56/2.68 (~c3_1(a606)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[1075, 4701])).
% 3.56/2.68 tff(4703,plain,
% 3.56/2.68 (c1_1(a606)),
% 3.56/2.68 inference(unit_resolution,[status(thm)],[1088, 4701])).
% 3.56/2.68 tff(4704,plain,
% 3.56/2.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | c0_1(a606) | (~c1_1(a606)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | c0_1(a606) | (~c1_1(a606)))),
% 3.56/2.68 inference(rewrite,[status(thm)],[])).
% 3.56/2.68 tff(4705,plain,
% 3.56/2.68 (((~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a678) | (~c3_1(a678)) | (~c2_1(a678)) | c3_1(a606) | c0_1(a606) | (~c1_1(a606))) <=> (c3_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | c0_1(a606) | (~c1_1(a606)))),
% 3.56/2.68 inference(rewrite,[status(thm)],[])).
% 3.56/2.68 tff(4706,plain,
% 3.56/2.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a678) | (~c3_1(a678)) | (~c2_1(a678)) | c3_1(a606) | c0_1(a606) | (~c1_1(a606)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | c0_1(a606) | (~c1_1(a606))))),
% 3.56/2.68 inference(monotonicity,[status(thm)],[4705])).
% 3.56/2.68 tff(4707,plain,
% 3.56/2.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a678) | (~c3_1(a678)) | (~c2_1(a678)) | c3_1(a606) | c0_1(a606) | (~c1_1(a606)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | c0_1(a606) | (~c1_1(a606)))),
% 3.56/2.68 inference(transitivity,[status(thm)],[4706, 4704])).
% 3.56/2.68 tff(4708,plain,
% 3.56/2.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a678) | (~c3_1(a678)) | (~c2_1(a678)) | c3_1(a606) | c0_1(a606) | (~c1_1(a606)))),
% 3.56/2.69 inference(quant_inst,[status(thm)],[])).
% 3.56/2.69 tff(4709,plain,
% 3.56/2.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | c0_1(a606) | (~c1_1(a606))),
% 3.56/2.69 inference(modus_ponens,[status(thm)],[4708, 4707])).
% 3.56/2.69 tff(4710,plain,
% 3.56/2.69 (c0_1(a606)),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[4709, 107, 4668, 4667, 3321, 3330, 4703, 4702, 258, 4672, 4685])).
% 3.56/2.69 tff(4711,plain,
% 3.56/2.69 (~c2_1(a606)),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[1111, 4701])).
% 3.56/2.69 tff(4712,plain,
% 3.56/2.69 (~hskp0),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[3804, 4685, 2987, 4668, 4669])).
% 3.56/2.69 tff(4713,plain,
% 3.56/2.69 ($false),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[2354, 1638, 107, 4712, 4703, 4711, 2347, 4710])).
% 3.56/2.69 tff(4714,plain,(hskp15 | hskp11 | hskp17 | c1_1(a633) | c0_1(a633) | (~c2_1(a633))), inference(lemma,lemma(discharge,[]))).
% 3.56/2.69 tff(4715,plain,
% 3.56/2.69 (hskp15),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[4714, 1638, 2987, 4655, 3981, 4671])).
% 3.56/2.69 tff(4716,plain,
% 3.56/2.69 (~c0_1(a604)),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[1591, 4715])).
% 3.56/2.69 tff(4717,plain,
% 3.56/2.69 (c3_1(a604)),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[1602, 4715])).
% 3.56/2.69 tff(4718,plain,
% 3.56/2.69 (c1_1(a604)),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[1613, 4715])).
% 3.56/2.69 tff(4719,plain,
% 3.56/2.69 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a633) | c0_1(a633) | c3_1(a633) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a633) | c0_1(a633) | c3_1(a633) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)))),
% 3.56/2.69 inference(rewrite,[status(thm)],[])).
% 3.56/2.69 tff(4720,plain,
% 3.56/2.69 ((hskp1 | (~ndr1_0) | c0_1(a604) | (~c3_1(a604)) | (~c1_1(a604)) | c3_1(a633) | c1_1(a633) | c0_1(a633)) <=> (hskp1 | c1_1(a633) | c0_1(a633) | c3_1(a633) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)))),
% 3.56/2.69 inference(rewrite,[status(thm)],[])).
% 3.56/2.69 tff(4721,plain,
% 3.56/2.69 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a604) | (~c3_1(a604)) | (~c1_1(a604)) | c3_1(a633) | c1_1(a633) | c0_1(a633))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a633) | c0_1(a633) | c3_1(a633) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604))))),
% 3.56/2.69 inference(monotonicity,[status(thm)],[4720])).
% 3.56/2.69 tff(4722,plain,
% 3.56/2.69 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a604) | (~c3_1(a604)) | (~c1_1(a604)) | c3_1(a633) | c1_1(a633) | c0_1(a633))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a633) | c0_1(a633) | c3_1(a633) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)))),
% 3.56/2.69 inference(transitivity,[status(thm)],[4721, 4719])).
% 3.56/2.69 tff(4723,plain,
% 3.56/2.69 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a604) | (~c3_1(a604)) | (~c1_1(a604)) | c3_1(a633) | c1_1(a633) | c0_1(a633))),
% 3.56/2.69 inference(quant_inst,[status(thm)],[])).
% 3.56/2.69 tff(4724,plain,
% 3.56/2.69 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a633) | c0_1(a633) | c3_1(a633) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604))),
% 3.56/2.69 inference(modus_ponens,[status(thm)],[4723, 4722])).
% 3.56/2.69 tff(4725,plain,
% 3.56/2.69 (hskp1),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[4724, 107, 4655, 4718, 4717, 3981, 3980, 4716, 1555])).
% 3.56/2.69 tff(4726,plain,
% 3.56/2.69 (~c0_1(a585)),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[1250, 4725])).
% 3.56/2.69 tff(4727,plain,
% 3.56/2.69 (c2_1(a585)),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[1261, 4725])).
% 3.56/2.69 tff(4728,plain,
% 3.56/2.69 (c1_1(a585)),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[1272, 4725])).
% 3.56/2.69 tff(4729,plain,
% 3.56/2.69 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)))),
% 3.56/2.69 inference(rewrite,[status(thm)],[])).
% 3.56/2.69 tff(4730,plain,
% 3.56/2.69 ((hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585))) <=> (hskp12 | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)))),
% 3.56/2.69 inference(rewrite,[status(thm)],[])).
% 3.56/2.69 tff(4731,plain,
% 3.56/2.69 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583))))),
% 3.56/2.69 inference(monotonicity,[status(thm)],[4730])).
% 3.56/2.69 tff(4732,plain,
% 3.56/2.69 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)))),
% 3.56/2.69 inference(transitivity,[status(thm)],[4731, 4729])).
% 3.56/2.69 tff(4733,plain,
% 3.56/2.69 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))),
% 3.56/2.69 inference(quant_inst,[status(thm)],[])).
% 3.56/2.69 tff(4734,plain,
% 3.56/2.69 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583))),
% 3.56/2.69 inference(modus_ponens,[status(thm)],[4733, 4732])).
% 3.56/2.69 tff(4735,plain,
% 3.56/2.69 (hskp12),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[4734, 107, 3321, 3322, 3330, 4728, 4727, 4726, 2727])).
% 3.56/2.69 tff(4736,plain,
% 3.56/2.69 (~c3_1(a600)),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[741, 4735])).
% 3.56/2.69 tff(4737,plain,
% 3.56/2.69 (c2_1(a600)),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[752, 4735])).
% 3.56/2.69 tff(4738,plain,
% 3.56/2.69 (c0_1(a600)),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[763, 4735])).
% 3.56/2.69 tff(4739,plain,
% 3.56/2.69 (hskp4),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[4673, 1974])).
% 3.56/2.69 tff(4740,plain,
% 3.56/2.69 (hskp6),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[147, 4739, 4656])).
% 3.56/2.69 tff(4741,plain,
% 3.56/2.69 (~c0_1(a590)),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[666, 4740])).
% 3.56/2.69 tff(4742,plain,
% 3.56/2.69 (c3_1(a590)),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[677, 4740])).
% 3.56/2.69 tff(4743,plain,
% 3.56/2.69 (c2_1(a590)),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[688, 4740])).
% 3.56/2.69 tff(4744,plain,
% 3.56/2.69 (~c1_1(a678)),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[4684, 107, 4669, 4667, 4655, 4743, 4742, 3981, 4741, 65, 4290])).
% 3.56/2.69 tff(4745,assumption,(~c3_1(a600)), introduced(assumption)).
% 3.56/2.69 tff(4746,plain,
% 3.56/2.69 (hskp15),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[4714, 1638, 2987, 4655, 3981, 4290])).
% 3.56/2.69 tff(4747,plain,
% 3.56/2.69 (~c0_1(a604)),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[1591, 4746])).
% 3.56/2.69 tff(4748,plain,
% 3.56/2.69 (c3_1(a604)),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[1602, 4746])).
% 3.56/2.69 tff(4749,plain,
% 3.56/2.69 (c1_1(a604)),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[1613, 4746])).
% 3.56/2.69 tff(4750,plain,
% 3.56/2.69 (hskp16),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[1849, 107, 3321, 3322, 4749, 4748, 4747, 1425, 1974])).
% 3.56/2.69 tff(4751,plain,
% 3.56/2.69 (~c3_1(a606)),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[1075, 4750])).
% 3.56/2.69 tff(4752,assumption,(c2_1(a600)), introduced(assumption)).
% 3.56/2.69 tff(4753,assumption,(c0_1(a600)), introduced(assumption)).
% 3.56/2.69 tff(4754,plain,
% 3.56/2.69 (c1_1(a606)),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[1088, 4750])).
% 3.56/2.69 tff(4755,plain,
% 3.56/2.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a606) | c3_1(a600) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c2_1(a600)) | (~c0_1(a600)) | c0_1(a606) | (~c1_1(a606)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a606) | c3_1(a600) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c2_1(a600)) | (~c0_1(a600)) | c0_1(a606) | (~c1_1(a606)))),
% 3.56/2.69 inference(rewrite,[status(thm)],[])).
% 3.56/2.69 tff(4756,plain,
% 3.56/2.69 (((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a678) | (~c3_1(a678)) | (~c2_1(a678)) | c3_1(a606) | c0_1(a606) | (~c1_1(a606))) <=> (c3_1(a606) | c3_1(a600) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c2_1(a600)) | (~c0_1(a600)) | c0_1(a606) | (~c1_1(a606)))),
% 3.56/2.69 inference(rewrite,[status(thm)],[])).
% 3.56/2.69 tff(4757,plain,
% 3.56/2.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a678) | (~c3_1(a678)) | (~c2_1(a678)) | c3_1(a606) | c0_1(a606) | (~c1_1(a606)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a606) | c3_1(a600) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c2_1(a600)) | (~c0_1(a600)) | c0_1(a606) | (~c1_1(a606))))),
% 3.56/2.69 inference(monotonicity,[status(thm)],[4756])).
% 3.56/2.69 tff(4758,plain,
% 3.56/2.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a678) | (~c3_1(a678)) | (~c2_1(a678)) | c3_1(a606) | c0_1(a606) | (~c1_1(a606)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a606) | c3_1(a600) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c2_1(a600)) | (~c0_1(a600)) | c0_1(a606) | (~c1_1(a606)))),
% 3.56/2.69 inference(transitivity,[status(thm)],[4757, 4755])).
% 3.56/2.69 tff(4759,plain,
% 3.56/2.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a678) | (~c3_1(a678)) | (~c2_1(a678)) | c3_1(a606) | c0_1(a606) | (~c1_1(a606)))),
% 3.56/2.69 inference(quant_inst,[status(thm)],[])).
% 3.56/2.69 tff(4760,plain,
% 3.56/2.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a606) | c3_1(a600) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | c1_1(a678) | (~c2_1(a600)) | (~c0_1(a600)) | c0_1(a606) | (~c1_1(a606))),
% 3.56/2.69 inference(modus_ponens,[status(thm)],[4759, 4758])).
% 3.56/2.69 tff(4761,plain,
% 3.56/2.69 (c0_1(a606)),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[4760, 107, 4668, 4667, 4754, 4753, 4752, 4751, 4745, 258, 4744])).
% 3.56/2.69 tff(4762,plain,
% 3.56/2.69 (~c2_1(a606)),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[1111, 4750])).
% 3.56/2.69 tff(4763,plain,
% 3.56/2.69 (~hskp0),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[3804, 4744, 2987, 4668, 4669])).
% 3.56/2.69 tff(4764,plain,
% 3.56/2.69 ($false),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[2354, 1638, 107, 4763, 4754, 4762, 2347, 4761])).
% 3.56/2.69 tff(4765,plain,(c3_1(a583) | hskp11 | (~c0_1(a600)) | (~c2_1(a600)) | c3_1(a600) | hskp17 | c1_1(a633) | c0_1(a633) | (~c2_1(a633))), inference(lemma,lemma(discharge,[]))).
% 3.56/2.69 tff(4766,plain,
% 3.56/2.69 (c3_1(a583)),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[4765, 1638, 4738, 4737, 4736, 2987, 4655, 3981, 4671])).
% 3.56/2.69 tff(4767,plain,
% 3.56/2.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a633) | c0_1(a633) | c0_1(a604) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a633) | c0_1(a633) | c0_1(a604) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a633)))),
% 3.56/2.69 inference(rewrite,[status(thm)],[])).
% 3.56/2.69 tff(4768,plain,
% 3.56/2.69 (((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a633) | c0_1(a633) | (~c2_1(a633))) <=> (c1_1(a633) | c0_1(a633) | c0_1(a604) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a633)))),
% 3.56/2.69 inference(rewrite,[status(thm)],[])).
% 3.56/2.69 tff(4769,plain,
% 3.56/2.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a633) | c0_1(a633) | (~c2_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a633) | c0_1(a633) | c0_1(a604) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a633))))),
% 3.56/2.69 inference(monotonicity,[status(thm)],[4768])).
% 3.56/2.69 tff(4770,plain,
% 3.56/2.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a633) | c0_1(a633) | (~c2_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a633) | c0_1(a633) | c0_1(a604) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a633)))),
% 3.56/2.69 inference(transitivity,[status(thm)],[4769, 4767])).
% 3.56/2.69 tff(4771,plain,
% 3.56/2.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a633) | c0_1(a633) | (~c2_1(a633)))),
% 3.56/2.69 inference(quant_inst,[status(thm)],[])).
% 3.56/2.69 tff(4772,plain,
% 3.56/2.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a633) | c0_1(a633) | c0_1(a604) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a633))),
% 3.56/2.69 inference(modus_ponens,[status(thm)],[4771, 4770])).
% 3.56/2.69 tff(4773,plain,
% 3.56/2.69 (~c2_1(a604)),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[4772, 107, 3321, 3322, 4655, 4717, 3981, 4716, 65, 4766, 4671])).
% 3.56/2.69 tff(4774,plain,
% 3.56/2.69 (hskp10),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[3497, 4766])).
% 3.56/2.69 tff(4775,plain,
% 3.56/2.69 (~c1_1(a598)),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[911, 4774])).
% 3.56/2.69 tff(4776,plain,
% 3.56/2.69 (c3_1(a598)),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[881, 4774])).
% 3.56/2.69 tff(4777,plain,
% 3.56/2.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a598) | c0_1(a585) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a598)) | c2_1(a598))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a598) | c0_1(a585) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a598)) | c2_1(a598))),
% 3.56/2.69 inference(rewrite,[status(thm)],[])).
% 3.56/2.69 tff(4778,plain,
% 3.56/2.69 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585))) <=> (c1_1(a598) | c0_1(a585) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a598)) | c2_1(a598))),
% 3.56/2.69 inference(rewrite,[status(thm)],[])).
% 3.56/2.69 tff(4779,plain,
% 3.56/2.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a598) | c0_1(a585) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a598)) | c2_1(a598)))),
% 3.56/2.69 inference(monotonicity,[status(thm)],[4778])).
% 3.56/2.69 tff(4780,plain,
% 3.56/2.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a598) | c0_1(a585) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a598)) | c2_1(a598))),
% 3.56/2.69 inference(transitivity,[status(thm)],[4779, 4777])).
% 3.56/2.69 tff(4781,plain,
% 3.56/2.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))),
% 3.56/2.69 inference(quant_inst,[status(thm)],[])).
% 3.56/2.69 tff(4782,plain,
% 3.56/2.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a598) | c0_1(a585) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a598)) | c2_1(a598)),
% 3.56/2.69 inference(modus_ponens,[status(thm)],[4781, 4780])).
% 3.56/2.69 tff(4783,plain,
% 3.56/2.69 (c2_1(a598)),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[4782, 107, 4669, 4668, 4667, 4776, 4728, 4727, 4775, 4726, 11])).
% 3.56/2.69 tff(4784,plain,
% 3.56/2.69 (c0_1(a598)),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[892, 4774])).
% 3.56/2.69 tff(4785,plain,
% 3.56/2.69 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a604) | c1_1(a598) | (~ndr1_0) | (~c2_1(a598)) | (~c0_1(a598)) | c2_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a604) | c1_1(a598) | (~ndr1_0) | (~c2_1(a598)) | (~c0_1(a598)) | c2_1(a604) | (~c1_1(a604)))),
% 3.56/2.69 inference(rewrite,[status(thm)],[])).
% 3.56/2.69 tff(4786,plain,
% 3.56/2.69 ((hskp17 | (~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c0_1(a598)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604))) <=> (hskp17 | c0_1(a604) | c1_1(a598) | (~ndr1_0) | (~c2_1(a598)) | (~c0_1(a598)) | c2_1(a604) | (~c1_1(a604)))),
% 3.56/2.69 inference(rewrite,[status(thm)],[])).
% 3.56/2.69 tff(4787,plain,
% 3.56/2.69 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c0_1(a598)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a604) | c1_1(a598) | (~ndr1_0) | (~c2_1(a598)) | (~c0_1(a598)) | c2_1(a604) | (~c1_1(a604))))),
% 3.56/2.69 inference(monotonicity,[status(thm)],[4786])).
% 3.56/2.69 tff(4788,plain,
% 3.56/2.69 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c0_1(a598)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a604) | c1_1(a598) | (~ndr1_0) | (~c2_1(a598)) | (~c0_1(a598)) | c2_1(a604) | (~c1_1(a604)))),
% 3.56/2.69 inference(transitivity,[status(thm)],[4787, 4785])).
% 3.56/2.69 tff(4789,plain,
% 3.56/2.69 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c0_1(a598)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)))),
% 3.56/2.69 inference(quant_inst,[status(thm)],[])).
% 3.56/2.69 tff(4790,plain,
% 3.56/2.69 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a604) | c1_1(a598) | (~ndr1_0) | (~c2_1(a598)) | (~c0_1(a598)) | c2_1(a604) | (~c1_1(a604))),
% 3.56/2.69 inference(modus_ponens,[status(thm)],[4789, 4788])).
% 3.56/2.69 tff(4791,plain,
% 3.56/2.69 ($false),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[4790, 107, 2987, 4718, 4784, 4716, 4775, 32, 4783, 4773])).
% 3.56/2.69 tff(4792,plain,(hskp11 | hskp17 | c1_1(a633) | c0_1(a633) | c3_1(a633)), inference(lemma,lemma(discharge,[]))).
% 3.56/2.69 tff(4793,plain,
% 3.56/2.69 (hskp11),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[4792, 4655, 4654, 3981, 3980])).
% 3.56/2.69 tff(4794,plain,
% 3.56/2.69 (~c1_1(a599)),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[428, 4793])).
% 3.56/2.69 tff(4795,plain,
% 3.56/2.69 (c1_1(a586)),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[229, 4664])).
% 3.56/2.69 tff(4796,plain,
% 3.56/2.69 (c3_1(a599)),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[422, 4793])).
% 3.56/2.69 tff(4797,plain,
% 3.56/2.69 (c2_1(a599)),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[439, 4793])).
% 3.56/2.69 tff(4798,plain,
% 3.56/2.69 (c2_1(a586)),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[1474, 4664])).
% 3.56/2.69 tff(4799,plain,
% 3.56/2.69 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | c3_1(a607) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c3_1(a607) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0))),
% 3.56/2.69 inference(rewrite,[status(thm)],[])).
% 3.56/2.69 tff(4800,plain,
% 3.56/2.69 ((hskp4 | hskp3 | (~ndr1_0) | c1_1(a607) | c3_1(a607) | (~c2_1(a607))) <=> (hskp4 | hskp3 | c3_1(a607) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0))),
% 3.56/2.69 inference(rewrite,[status(thm)],[])).
% 3.56/2.69 tff(4801,plain,
% 3.56/2.69 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a607) | c3_1(a607) | (~c2_1(a607)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | c3_1(a607) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0)))),
% 3.56/2.69 inference(monotonicity,[status(thm)],[4800])).
% 3.56/2.69 tff(4802,plain,
% 3.56/2.69 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a607) | c3_1(a607) | (~c2_1(a607)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c3_1(a607) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0))),
% 3.56/2.69 inference(transitivity,[status(thm)],[4801, 4799])).
% 3.56/2.69 tff(4803,plain,
% 3.56/2.69 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a607) | c3_1(a607) | (~c2_1(a607)))),
% 3.56/2.69 inference(quant_inst,[status(thm)],[])).
% 3.56/2.69 tff(4804,plain,
% 3.56/2.69 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c3_1(a607) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0)),
% 3.56/2.69 inference(modus_ponens,[status(thm)],[4803, 4802])).
% 3.56/2.69 tff(4805,plain,
% 3.56/2.69 (hskp4 | hskp3 | c3_1(a607) | (~c2_1(a607))),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[4804, 107, 66, 840])).
% 3.56/2.69 tff(4806,plain,
% 3.56/2.69 (hskp3),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[4805, 830, 4653, 33])).
% 3.56/2.69 tff(4807,plain,
% 3.56/2.69 (~c1_1(a587)),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[939, 4806])).
% 3.56/2.69 tff(4808,assumption,(~c3_1(a586)), introduced(assumption)).
% 3.56/2.69 tff(4809,assumption,(c1_1(a586)), introduced(assumption)).
% 3.56/2.69 tff(4810,plain,
% 3.56/2.69 (hskp4 | (~c0_1(a586))),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[247, 107, 4654, 4809, 4808, 55])).
% 3.56/2.69 tff(4811,plain,
% 3.56/2.69 (~c0_1(a586)),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[4810, 830])).
% 3.56/2.69 tff(4812,plain,
% 3.56/2.69 (c2_1(a587)),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[950, 4806])).
% 3.56/2.69 tff(4813,plain,
% 3.56/2.69 (c0_1(a587)),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[961, 4806])).
% 3.56/2.69 tff(4814,assumption,(~c0_1(a586)), introduced(assumption)).
% 3.56/2.69 tff(4815,plain,
% 3.56/2.69 (~c2_1(a603)),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[2309, 107, 320, 463, 462, 4809, 318, 461, 4808, 258, 4814])).
% 3.56/2.69 tff(4816,plain,
% 3.56/2.69 ($false),
% 3.56/2.69 inference(unit_resolution,[status(thm)],[1006, 726, 107, 1000, 999, 319, 318, 996, 995, 4815])).
% 3.56/2.70 tff(4817,plain,((~hskp14) | hskp26 | (~c0_1(a587)) | (~c2_1(a587)) | c1_1(a587) | (~c2_1(a599)) | (~c3_1(a599)) | (~c1_1(a586)) | c1_1(a599) | c3_1(a586) | c0_1(a586)), inference(lemma,lemma(discharge,[]))).
% 3.56/2.70 tff(4818,plain,
% 3.56/2.70 (~hskp14),
% 3.56/2.70 inference(unit_resolution,[status(thm)],[4817, 4813, 726, 4812, 4807, 463, 462, 4809, 461, 4808, 4811])).
% 3.56/2.70 tff(4819,plain,
% 3.56/2.70 (~hskp12),
% 3.56/2.70 inference(unit_resolution,[status(thm)],[772, 4818, 44])).
% 3.56/2.70 tff(4820,assumption,(c2_1(a586)), introduced(assumption)).
% 3.56/2.70 tff(4821,plain,
% 3.56/2.70 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~ndr1_0) | (~c2_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586))),
% 3.56/2.70 inference(rewrite,[status(thm)],[])).
% 3.56/2.70 tff(4822,plain,
% 3.56/2.70 ((hskp12 | (~ndr1_0) | (~c2_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a586) | (~c1_1(a586)) | (~c2_1(a586))) <=> (hskp12 | (~ndr1_0) | (~c2_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586))),
% 3.56/2.70 inference(rewrite,[status(thm)],[])).
% 3.56/2.70 tff(4823,plain,
% 3.56/2.70 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586)))),
% 3.56/2.70 inference(monotonicity,[status(thm)],[4822])).
% 3.56/2.70 tff(4824,plain,
% 3.56/2.70 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~ndr1_0) | (~c2_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586))),
% 3.56/2.70 inference(transitivity,[status(thm)],[4823, 4821])).
% 3.56/2.70 tff(4825,plain,
% 3.56/2.70 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))),
% 3.56/2.70 inference(quant_inst,[status(thm)],[])).
% 3.56/2.70 tff(4826,plain,
% 3.56/2.70 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~ndr1_0) | (~c2_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586)),
% 3.56/2.70 inference(modus_ponens,[status(thm)],[4825, 4824])).
% 3.56/2.70 tff(4827,plain,
% 3.56/2.70 (hskp12 | (~c1_1(a678))),
% 3.56/2.70 inference(unit_resolution,[status(thm)],[4826, 107, 2292, 2281, 4809, 4820, 2727, 4811])).
% 3.56/2.70 tff(4828,plain,
% 3.56/2.70 (~c1_1(a678)),
% 3.56/2.70 inference(unit_resolution,[status(thm)],[4827, 4819])).
% 3.56/2.70 tff(4829,plain,
% 3.56/2.70 (~hskp0),
% 3.56/2.70 inference(unit_resolution,[status(thm)],[3804, 4828, 4654, 2281, 2292])).
% 3.56/2.70 tff(4830,plain,
% 3.56/2.70 ((hskp21 | hskp14 | hskp0) <=> (hskp21 | hskp14 | hskp0)),
% 3.56/2.70 inference(rewrite,[status(thm)],[])).
% 3.56/2.70 tff(4831,plain,
% 3.56/2.70 (((hskp14 | hskp21) | hskp0) <=> (hskp21 | hskp14 | hskp0)),
% 3.56/2.70 inference(rewrite,[status(thm)],[])).
% 3.56/2.70 tff(4832,axiom,((hskp14 | hskp21) | hskp0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause35')).
% 3.56/2.70 tff(4833,plain,
% 3.56/2.70 (hskp21 | hskp14 | hskp0),
% 3.56/2.70 inference(modus_ponens,[status(thm)],[4832, 4831])).
% 3.56/2.70 tff(4834,plain,
% 3.56/2.70 (hskp21 | hskp14 | hskp0),
% 3.56/2.70 inference(modus_ponens,[status(thm)],[4833, 4830])).
% 3.56/2.70 tff(4835,plain,
% 3.56/2.70 (hskp21 | hskp14 | hskp0),
% 3.56/2.70 inference(modus_ponens,[status(thm)],[4834, 4830])).
% 3.56/2.70 tff(4836,plain,
% 3.56/2.70 (hskp21 | hskp14 | hskp0),
% 3.56/2.70 inference(modus_ponens,[status(thm)],[4835, 4830])).
% 3.56/2.70 tff(4837,plain,
% 3.56/2.70 (hskp21 | hskp14 | hskp0),
% 3.56/2.70 inference(modus_ponens,[status(thm)],[4836, 4830])).
% 3.56/2.70 tff(4838,plain,
% 3.56/2.70 (hskp21 | hskp14 | hskp0),
% 3.56/2.70 inference(modus_ponens,[status(thm)],[4837, 4830])).
% 3.56/2.70 tff(4839,plain,
% 3.56/2.70 (hskp21 | hskp14 | hskp0),
% 3.56/2.70 inference(modus_ponens,[status(thm)],[4838, 4830])).
% 3.56/2.70 tff(4840,plain,
% 3.56/2.70 (hskp21 | hskp14 | hskp0),
% 3.56/2.70 inference(modus_ponens,[status(thm)],[4839, 4830])).
% 3.56/2.70 tff(4841,plain,
% 3.56/2.70 (hskp21),
% 3.56/2.70 inference(unit_resolution,[status(thm)],[4840, 4829, 4818])).
% 3.56/2.70 tff(4842,plain,
% 3.56/2.70 (((~hskp21) | (~c3_1(a629))) <=> ((~hskp21) | (~c3_1(a629)))),
% 3.56/2.70 inference(rewrite,[status(thm)],[])).
% 3.56/2.70 tff(4843,plain,
% 3.56/2.70 (((~c3_1(a629)) | (~hskp21)) <=> ((~hskp21) | (~c3_1(a629)))),
% 3.56/2.70 inference(rewrite,[status(thm)],[])).
% 3.56/2.70 tff(4844,axiom,((~c3_1(a629)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause90')).
% 3.56/2.70 tff(4845,plain,
% 3.56/2.70 ((~hskp21) | (~c3_1(a629))),
% 3.56/2.70 inference(modus_ponens,[status(thm)],[4844, 4843])).
% 3.56/2.70 tff(4846,plain,
% 3.56/2.70 ((~hskp21) | (~c3_1(a629))),
% 3.56/2.70 inference(modus_ponens,[status(thm)],[4845, 4842])).
% 3.56/2.70 tff(4847,plain,
% 3.56/2.70 (~c3_1(a629)),
% 3.56/2.70 inference(unit_resolution,[status(thm)],[4846, 4841])).
% 3.56/2.70 tff(4848,plain,
% 3.56/2.70 (((~hskp21) | (~c2_1(a629))) <=> ((~hskp21) | (~c2_1(a629)))),
% 3.56/2.70 inference(rewrite,[status(thm)],[])).
% 3.56/2.70 tff(4849,plain,
% 3.56/2.70 (((~c2_1(a629)) | (~hskp21)) <=> ((~hskp21) | (~c2_1(a629)))),
% 3.56/2.70 inference(rewrite,[status(thm)],[])).
% 3.56/2.70 tff(4850,axiom,((~c2_1(a629)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause89')).
% 3.56/2.70 tff(4851,plain,
% 3.56/2.70 ((~hskp21) | (~c2_1(a629))),
% 3.56/2.70 inference(modus_ponens,[status(thm)],[4850, 4849])).
% 3.56/2.70 tff(4852,plain,
% 3.56/2.70 ((~hskp21) | (~c2_1(a629))),
% 3.56/2.70 inference(modus_ponens,[status(thm)],[4851, 4848])).
% 3.56/2.70 tff(4853,plain,
% 3.56/2.70 (~c2_1(a629)),
% 3.56/2.70 inference(unit_resolution,[status(thm)],[4852, 4841])).
% 3.56/2.70 tff(4854,plain,
% 3.56/2.70 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c2_1(a629) | c3_1(a629) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c1_1(a629))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c2_1(a629) | c3_1(a629) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c1_1(a629))),
% 3.56/2.70 inference(rewrite,[status(thm)],[])).
% 3.56/2.70 tff(4855,plain,
% 3.56/2.70 ((hskp26 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a629) | c1_1(a629) | c2_1(a629)) <=> (hskp26 | c2_1(a629) | c3_1(a629) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c1_1(a629))),
% 3.56/2.70 inference(rewrite,[status(thm)],[])).
% 3.56/2.70 tff(4856,plain,
% 3.56/2.70 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a629) | c1_1(a629) | c2_1(a629))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c2_1(a629) | c3_1(a629) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c1_1(a629)))),
% 3.56/2.70 inference(monotonicity,[status(thm)],[4855])).
% 3.56/2.70 tff(4857,plain,
% 3.56/2.70 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a629) | c1_1(a629) | c2_1(a629))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c2_1(a629) | c3_1(a629) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c1_1(a629))),
% 3.56/2.70 inference(transitivity,[status(thm)],[4856, 4854])).
% 3.56/2.70 tff(4858,plain,
% 3.56/2.70 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a629) | c1_1(a629) | c2_1(a629))),
% 3.56/2.70 inference(quant_inst,[status(thm)],[])).
% 3.56/2.70 tff(4859,plain,
% 3.56/2.70 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c2_1(a629) | c3_1(a629) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c1_1(a629)),
% 3.56/2.70 inference(modus_ponens,[status(thm)],[4858, 4857])).
% 3.56/2.70 tff(4860,plain,
% 3.56/2.70 (c1_1(a629)),
% 3.56/2.70 inference(unit_resolution,[status(thm)],[4859, 726, 107, 4813, 4812, 4853, 4847, 4807, 995])).
% 3.56/2.70 tff(4861,plain,
% 3.56/2.70 (((~hskp21) | c0_1(a629)) <=> ((~hskp21) | c0_1(a629))),
% 3.56/2.70 inference(rewrite,[status(thm)],[])).
% 3.56/2.70 tff(4862,axiom,((~hskp21) | c0_1(a629)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause53')).
% 3.56/2.70 tff(4863,plain,
% 3.56/2.70 ((~hskp21) | c0_1(a629)),
% 3.56/2.70 inference(modus_ponens,[status(thm)],[4862, 4861])).
% 3.56/2.70 tff(4864,plain,
% 3.56/2.70 ((~hskp21) | c0_1(a629)),
% 3.56/2.70 inference(modus_ponens,[status(thm)],[4863, 4861])).
% 3.56/2.70 tff(4865,plain,
% 3.56/2.70 ((~hskp21) | c0_1(a629)),
% 3.56/2.70 inference(modus_ponens,[status(thm)],[4864, 4861])).
% 3.56/2.70 tff(4866,plain,
% 3.56/2.70 ((~hskp21) | c0_1(a629)),
% 3.56/2.70 inference(modus_ponens,[status(thm)],[4865, 4861])).
% 3.56/2.70 tff(4867,plain,
% 3.56/2.70 ((~hskp21) | c0_1(a629)),
% 3.56/2.70 inference(modus_ponens,[status(thm)],[4866, 4861])).
% 3.56/2.70 tff(4868,plain,
% 3.56/2.70 ((~hskp21) | c0_1(a629)),
% 3.56/2.70 inference(modus_ponens,[status(thm)],[4867, 4861])).
% 3.56/2.70 tff(4869,plain,
% 3.56/2.70 ((~hskp21) | c0_1(a629)),
% 3.56/2.70 inference(modus_ponens,[status(thm)],[4868, 4861])).
% 3.56/2.70 tff(4870,plain,
% 3.56/2.70 ((~hskp21) | c0_1(a629)),
% 3.56/2.70 inference(modus_ponens,[status(thm)],[4869, 4861])).
% 3.56/2.70 tff(4871,plain,
% 3.56/2.70 (c0_1(a629)),
% 3.56/2.70 inference(unit_resolution,[status(thm)],[4870, 4841])).
% 3.56/2.70 tff(4872,plain,
% 3.56/2.70 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | c3_1(a629) | (~ndr1_0) | (~c0_1(a629)) | (~c1_1(a629)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp4 | c3_1(a629) | (~ndr1_0) | (~c0_1(a629)) | (~c1_1(a629)))),
% 3.56/2.70 inference(rewrite,[status(thm)],[])).
% 3.56/2.70 tff(4873,plain,
% 3.56/2.70 ((hskp17 | hskp4 | (~ndr1_0) | c3_1(a629) | (~c1_1(a629)) | (~c0_1(a629))) <=> (hskp17 | hskp4 | c3_1(a629) | (~ndr1_0) | (~c0_1(a629)) | (~c1_1(a629)))),
% 3.56/2.70 inference(rewrite,[status(thm)],[])).
% 3.56/2.70 tff(4874,plain,
% 3.56/2.70 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c3_1(a629) | (~c1_1(a629)) | (~c0_1(a629)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | c3_1(a629) | (~ndr1_0) | (~c0_1(a629)) | (~c1_1(a629))))),
% 3.56/2.70 inference(monotonicity,[status(thm)],[4873])).
% 3.56/2.70 tff(4875,plain,
% 3.56/2.70 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c3_1(a629) | (~c1_1(a629)) | (~c0_1(a629)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp4 | c3_1(a629) | (~ndr1_0) | (~c0_1(a629)) | (~c1_1(a629)))),
% 3.56/2.70 inference(transitivity,[status(thm)],[4874, 4872])).
% 3.56/2.70 tff(4876,plain,
% 3.56/2.70 ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c3_1(a629) | (~c1_1(a629)) | (~c0_1(a629)))),
% 3.56/2.70 inference(quant_inst,[status(thm)],[])).
% 3.56/2.70 tff(4877,plain,
% 3.56/2.70 ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp4 | c3_1(a629) | (~ndr1_0) | (~c0_1(a629)) | (~c1_1(a629))),
% 3.56/2.70 inference(modus_ponens,[status(thm)],[4876, 4875])).
% 3.56/2.70 tff(4878,plain,
% 3.56/2.70 ($false),
% 3.56/2.70 inference(unit_resolution,[status(thm)],[4877, 107, 4654, 830, 4871, 4847, 55, 4860])).
% 3.56/2.70 tff(4879,plain,(hskp4 | hskp26 | (~c1_1(a586)) | (~c2_1(a586)) | hskp22 | (~c2_1(a599)) | (~c3_1(a599)) | c1_1(a599) | c3_1(a586) | c3_1(a607) | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.56/2.70 tff(4880,plain,
% 3.56/2.70 (hskp4),
% 3.56/2.70 inference(unit_resolution,[status(thm)],[4879, 726, 4795, 4798, 4656, 4797, 4796, 4794, 4665, 33, 66])).
% 3.56/2.70 tff(4881,plain,
% 3.56/2.70 (hskp6),
% 3.56/2.70 inference(unit_resolution,[status(thm)],[147, 4880, 4656])).
% 3.56/2.70 tff(4882,plain,
% 3.56/2.70 (~c0_1(a590)),
% 3.56/2.70 inference(unit_resolution,[status(thm)],[666, 4881])).
% 3.56/2.70 tff(4883,plain,
% 3.56/2.70 (c3_1(a590)),
% 3.56/2.70 inference(unit_resolution,[status(thm)],[677, 4881])).
% 3.56/2.70 tff(4884,plain,
% 3.56/2.70 (c2_1(a590)),
% 3.56/2.70 inference(unit_resolution,[status(thm)],[688, 4881])).
% 3.56/2.70 tff(4885,plain,
% 3.56/2.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a633) | c3_1(a633) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c2_1(a633))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a633) | c3_1(a633) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c2_1(a633))),
% 3.56/2.70 inference(rewrite,[status(thm)],[])).
% 3.56/2.70 tff(4886,plain,
% 3.56/2.70 (((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a633) | c0_1(a633) | c2_1(a633)) <=> (c0_1(a633) | c3_1(a633) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c2_1(a633))),
% 3.56/2.70 inference(rewrite,[status(thm)],[])).
% 3.56/2.70 tff(4887,plain,
% 3.56/2.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a633) | c0_1(a633) | c2_1(a633))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a633) | c3_1(a633) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c2_1(a633)))),
% 3.56/2.70 inference(monotonicity,[status(thm)],[4886])).
% 3.56/2.70 tff(4888,plain,
% 3.56/2.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a633) | c0_1(a633) | c2_1(a633))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a633) | c3_1(a633) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c2_1(a633))),
% 3.56/2.70 inference(transitivity,[status(thm)],[4887, 4885])).
% 3.56/2.70 tff(4889,plain,
% 3.56/2.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a633) | c0_1(a633) | c2_1(a633))),
% 3.56/2.70 inference(quant_inst,[status(thm)],[])).
% 3.56/2.70 tff(4890,plain,
% 3.56/2.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a633) | c3_1(a633) | c1_1(a599) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a599)) | (~c2_1(a599)) | c2_1(a633)),
% 3.56/2.70 inference(modus_ponens,[status(thm)],[4889, 4888])).
% 3.56/2.70 tff(4891,plain,
% 3.56/2.70 (c2_1(a633)),
% 3.56/2.70 inference(unit_resolution,[status(thm)],[4890, 107, 4797, 4796, 4884, 4883, 3981, 3980, 4794, 4882, 1730])).
% 3.56/2.70 tff(4892,plain,
% 3.56/2.70 (hskp28),
% 3.56/2.70 inference(unit_resolution,[status(thm)],[3240, 107, 4797, 4796, 4795, 4798, 4794, 4665, 1748])).
% 3.56/2.70 tff(4893,plain,
% 3.56/2.70 (c3_1(a612)),
% 3.56/2.70 inference(unit_resolution,[status(thm)],[1139, 4892])).
% 3.56/2.70 tff(4894,plain,
% 3.56/2.70 (c1_1(a612)),
% 3.56/2.70 inference(unit_resolution,[status(thm)],[1435, 4892])).
% 3.56/2.70 tff(4895,plain,
% 3.56/2.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a633) | c0_1(a633) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a633) | c0_1(a633) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a633)))),
% 3.56/2.70 inference(rewrite,[status(thm)],[])).
% 3.56/2.70 tff(4896,plain,
% 3.56/2.70 (((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a633) | c0_1(a633) | (~c2_1(a633))) <=> (c1_1(a633) | c0_1(a633) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a633)))),
% 3.56/2.70 inference(rewrite,[status(thm)],[])).
% 3.56/2.70 tff(4897,plain,
% 3.56/2.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a633) | c0_1(a633) | (~c2_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a633) | c0_1(a633) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a633))))),
% 3.56/2.70 inference(monotonicity,[status(thm)],[4896])).
% 3.56/2.70 tff(4898,plain,
% 3.56/2.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a633) | c0_1(a633) | (~c2_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a633) | c0_1(a633) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a633)))),
% 3.56/2.70 inference(transitivity,[status(thm)],[4897, 4895])).
% 3.56/2.70 tff(4899,plain,
% 3.56/2.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a633) | c0_1(a633) | (~c2_1(a633)))),
% 3.56/2.70 inference(quant_inst,[status(thm)],[])).
% 3.56/2.70 tff(4900,plain,
% 3.56/2.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a633) | c0_1(a633) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a633))),
% 3.56/2.70 inference(modus_ponens,[status(thm)],[4899, 4898])).
% 3.56/2.70 tff(4901,plain,
% 3.56/2.70 ((~c0_1(a612)) | (~c2_1(a633))),
% 3.56/2.70 inference(unit_resolution,[status(thm)],[4900, 107, 4894, 4893, 4655, 4884, 4883, 3981, 4882, 65])).
% 3.56/2.70 tff(4902,plain,
% 3.56/2.70 (~c0_1(a612)),
% 3.56/2.70 inference(unit_resolution,[status(thm)],[4901, 4891])).
% 3.56/2.70 tff(4903,plain,
% 3.56/2.70 (~c2_1(a588)),
% 3.56/2.70 inference(unit_resolution,[status(thm)],[121, 4880])).
% 3.56/2.70 tff(4904,plain,
% 3.56/2.70 (~c1_1(a588)),
% 3.56/2.70 inference(unit_resolution,[status(thm)],[127, 4880])).
% 3.56/2.70 tff(4905,plain,
% 3.56/2.70 (c2_1(a612)),
% 3.56/2.70 inference(unit_resolution,[status(thm)],[1150, 4892])).
% 3.56/2.70 tff(4906,plain,
% 3.56/2.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a588)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a588)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))),
% 3.56/2.70 inference(rewrite,[status(thm)],[])).
% 3.56/2.70 tff(4907,plain,
% 3.56/2.70 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a588) | c2_1(a588) | (~c3_1(a588)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612))) <=> (c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a588)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))),
% 3.56/2.70 inference(rewrite,[status(thm)],[])).
% 3.56/2.70 tff(4908,plain,
% 3.56/2.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a588) | c2_1(a588) | (~c3_1(a588)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a588)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612))))),
% 3.56/2.70 inference(monotonicity,[status(thm)],[4907])).
% 3.56/2.70 tff(4909,plain,
% 3.56/2.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a588) | c2_1(a588) | (~c3_1(a588)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a588)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))),
% 3.56/2.70 inference(transitivity,[status(thm)],[4908, 4906])).
% 3.56/2.70 tff(4910,plain,
% 3.56/2.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a588) | c2_1(a588) | (~c3_1(a588)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))),
% 3.56/2.70 inference(quant_inst,[status(thm)],[])).
% 3.56/2.70 tff(4911,plain,
% 3.56/2.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a588)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612))),
% 3.56/2.70 inference(modus_ponens,[status(thm)],[4910, 4909])).
% 3.56/2.70 tff(4912,plain,
% 3.56/2.70 (~c3_1(a588)),
% 3.56/2.70 inference(unit_resolution,[status(thm)],[4911, 107, 4669, 4668, 4667, 4894, 4905, 4904, 4903, 11, 4902])).
% 3.56/2.70 tff(4913,plain,
% 3.56/2.70 ((~c1_1(a678)) | (~c2_1(a633))),
% 3.56/2.70 inference(unit_resolution,[status(thm)],[4684, 107, 4669, 4667, 4655, 4884, 4883, 3981, 4882, 65])).
% 3.56/2.70 tff(4914,plain,
% 3.56/2.70 (~c1_1(a678)),
% 3.56/2.70 inference(unit_resolution,[status(thm)],[4913, 4891])).
% 3.56/2.70 tff(4915,plain,
% 3.56/2.70 (c0_1(a588)),
% 3.56/2.70 inference(unit_resolution,[status(thm)],[138, 4880])).
% 3.56/2.70 tff(4916,plain,
% 3.56/2.70 (hskp14),
% 3.56/2.70 inference(unit_resolution,[status(thm)],[4546, 107, 4915, 3981, 3980, 4904, 4903, 305, 4891])).
% 3.56/2.70 tff(4917,plain,
% 3.56/2.70 (~c3_1(a603)),
% 3.56/2.70 inference(unit_resolution,[status(thm)],[205, 4916])).
% 3.56/2.70 tff(4918,plain,
% 3.56/2.70 (~c1_1(a603)),
% 3.56/2.70 inference(unit_resolution,[status(thm)],[171, 4916])).
% 3.56/2.70 tff(4919,plain,
% 3.56/2.70 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c2_1(a603))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c2_1(a603))),
% 3.56/2.70 inference(rewrite,[status(thm)],[])).
% 3.56/2.70 tff(4920,plain,
% 3.56/2.70 ((hskp26 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c3_1(a603) | c1_1(a603) | c2_1(a603)) <=> (hskp26 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c2_1(a603))),
% 3.56/2.70 inference(rewrite,[status(thm)],[])).
% 3.56/2.70 tff(4921,plain,
% 3.56/2.70 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c3_1(a603) | c1_1(a603) | c2_1(a603))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c2_1(a603)))),
% 3.56/2.71 inference(monotonicity,[status(thm)],[4920])).
% 3.56/2.71 tff(4922,plain,
% 3.56/2.71 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c3_1(a603) | c1_1(a603) | c2_1(a603))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c2_1(a603))),
% 3.56/2.71 inference(transitivity,[status(thm)],[4921, 4919])).
% 3.56/2.71 tff(4923,plain,
% 3.56/2.71 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c3_1(a603) | c1_1(a603) | c2_1(a603))),
% 3.56/2.71 inference(quant_inst,[status(thm)],[])).
% 3.56/2.71 tff(4924,plain,
% 3.56/2.71 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c2_1(a603)),
% 3.56/2.71 inference(modus_ponens,[status(thm)],[4923, 4922])).
% 3.56/2.71 tff(4925,plain,
% 3.56/2.71 (c2_1(a603)),
% 3.56/2.71 inference(unit_resolution,[status(thm)],[4924, 726, 107, 4669, 4668, 4918, 4917, 995, 4914])).
% 3.56/2.71 tff(4926,plain,
% 3.56/2.71 (c0_1(a603)),
% 3.56/2.71 inference(unit_resolution,[status(thm)],[182, 4916])).
% 3.56/2.71 tff(4927,plain,
% 3.56/2.71 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a603) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | c3_1(a588) | (~c2_1(a603)) | (~c0_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a603) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | c3_1(a588) | (~c2_1(a603)) | (~c0_1(a603)))),
% 3.56/2.71 inference(rewrite,[status(thm)],[])).
% 3.56/2.71 tff(4928,plain,
% 3.56/2.71 ((hskp26 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c3_1(a588) | c1_1(a588) | c2_1(a588)) <=> (hskp26 | c1_1(a603) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | c3_1(a588) | (~c2_1(a603)) | (~c0_1(a603)))),
% 3.56/2.71 inference(rewrite,[status(thm)],[])).
% 3.56/2.71 tff(4929,plain,
% 3.56/2.71 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c3_1(a588) | c1_1(a588) | c2_1(a588))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a603) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | c3_1(a588) | (~c2_1(a603)) | (~c0_1(a603))))),
% 3.56/2.71 inference(monotonicity,[status(thm)],[4928])).
% 3.56/2.71 tff(4930,plain,
% 3.56/2.71 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c3_1(a588) | c1_1(a588) | c2_1(a588))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a603) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | c3_1(a588) | (~c2_1(a603)) | (~c0_1(a603)))),
% 3.56/2.71 inference(transitivity,[status(thm)],[4929, 4927])).
% 3.56/2.71 tff(4931,plain,
% 3.56/2.71 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c3_1(a588) | c1_1(a588) | c2_1(a588))),
% 3.56/2.71 inference(quant_inst,[status(thm)],[])).
% 3.56/2.71 tff(4932,plain,
% 3.56/2.71 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a603) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | c3_1(a588) | (~c2_1(a603)) | (~c0_1(a603))),
% 3.56/2.71 inference(modus_ponens,[status(thm)],[4931, 4930])).
% 3.56/2.71 tff(4933,plain,
% 3.56/2.71 ($false),
% 3.56/2.71 inference(unit_resolution,[status(thm)],[4932, 726, 107, 4926, 4918, 4904, 4903, 995, 4925, 4912])).
% 3.56/2.71 tff(4934,plain,(hskp26 | c1_1(a633) | c0_1(a633) | c3_1(a633) | c3_1(a607) | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.56/2.71 tff(4935,plain,
% 3.56/2.71 (hskp26),
% 3.56/2.71 inference(unit_resolution,[status(thm)],[4934, 4655, 3981, 3980, 33, 66])).
% 3.56/2.71 tff(4936,plain,
% 3.56/2.71 (c1_1(a583)),
% 3.56/2.71 inference(unit_resolution,[status(thm)],[351, 4935])).
% 3.56/2.71 tff(4937,plain,
% 3.56/2.71 (c0_1(a583)),
% 3.56/2.71 inference(unit_resolution,[status(thm)],[362, 4935])).
% 3.56/2.71 tff(4938,plain,
% 3.56/2.71 (hskp3 | c3_1(a583)),
% 3.56/2.71 inference(unit_resolution,[status(thm)],[4026, 107, 4654, 1651, 1650, 2368])).
% 3.56/2.71 tff(4939,plain,
% 3.56/2.71 (c3_1(a583)),
% 3.56/2.71 inference(unit_resolution,[status(thm)],[4938, 306])).
% 3.56/2.71 tff(4940,plain,
% 3.56/2.71 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp3 | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)))),
% 3.56/2.71 inference(rewrite,[status(thm)],[])).
% 3.56/2.71 tff(4941,plain,
% 3.56/2.71 ((hskp17 | hskp3 | (~ndr1_0) | c3_1(a586) | (~c1_1(a586)) | (~c0_1(a586))) <=> (hskp17 | hskp3 | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)))),
% 3.56/2.71 inference(rewrite,[status(thm)],[])).
% 3.56/2.71 tff(4942,plain,
% 3.56/2.71 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c3_1(a586) | (~c1_1(a586)) | (~c0_1(a586)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586))))),
% 3.56/2.71 inference(monotonicity,[status(thm)],[4941])).
% 3.56/2.71 tff(4943,plain,
% 3.56/2.71 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c3_1(a586) | (~c1_1(a586)) | (~c0_1(a586)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp3 | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)))),
% 3.56/2.71 inference(transitivity,[status(thm)],[4942, 4940])).
% 3.56/2.71 tff(4944,plain,
% 3.56/2.71 ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c3_1(a586) | (~c1_1(a586)) | (~c0_1(a586)))),
% 3.56/2.71 inference(quant_inst,[status(thm)],[])).
% 3.56/2.71 tff(4945,plain,
% 3.56/2.71 ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp3 | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586))),
% 3.56/2.71 inference(modus_ponens,[status(thm)],[4944, 4943])).
% 3.56/2.71 tff(4946,plain,
% 3.56/2.71 (hskp3 | (~c0_1(a586))),
% 3.56/2.71 inference(unit_resolution,[status(thm)],[4945, 107, 4654, 4809, 4808, 2368])).
% 3.56/2.71 tff(4947,plain,
% 3.56/2.71 (~c0_1(a586)),
% 3.56/2.71 inference(unit_resolution,[status(thm)],[4946, 306])).
% 3.56/2.71 tff(4948,plain,
% 3.56/2.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a607) | (~c2_1(a607)) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a607) | (~c2_1(a607)) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a607)))),
% 3.56/2.71 inference(rewrite,[status(thm)],[])).
% 3.56/2.71 tff(4949,plain,
% 3.56/2.71 (((~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586))) <=> (c3_1(a607) | (~c2_1(a607)) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a607)))),
% 3.56/2.71 inference(rewrite,[status(thm)],[])).
% 3.56/2.71 tff(4950,plain,
% 3.56/2.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a607) | (~c2_1(a607)) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a607))))),
% 3.56/2.71 inference(monotonicity,[status(thm)],[4949])).
% 3.56/2.71 tff(4951,plain,
% 3.56/2.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a607) | (~c2_1(a607)) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a607)))),
% 3.56/2.71 inference(transitivity,[status(thm)],[4950, 4948])).
% 3.56/2.71 tff(4952,plain,
% 3.56/2.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))),
% 3.56/2.71 inference(quant_inst,[status(thm)],[])).
% 3.56/2.71 tff(4953,plain,
% 3.56/2.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a607) | (~c2_1(a607)) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a607))),
% 3.56/2.71 inference(modus_ponens,[status(thm)],[4952, 4951])).
% 3.56/2.71 tff(4954,plain,
% 3.56/2.71 (c0_1(a586) | (~c0_1(a607))),
% 3.56/2.71 inference(unit_resolution,[status(thm)],[4953, 107, 33, 463, 462, 4809, 4653, 461, 4808, 258])).
% 3.56/2.71 tff(4955,plain,
% 3.56/2.71 (~c0_1(a607)),
% 3.56/2.71 inference(unit_resolution,[status(thm)],[4954, 4947])).
% 3.56/2.71 tff(4956,plain,
% 3.56/2.71 (hskp4),
% 3.56/2.71 inference(unit_resolution,[status(thm)],[4805, 306, 4653, 33])).
% 3.56/2.71 tff(4957,plain,
% 3.56/2.71 (hskp6),
% 3.56/2.71 inference(unit_resolution,[status(thm)],[147, 4956, 44])).
% 3.56/2.71 tff(4958,plain,
% 3.56/2.71 (~c0_1(a590)),
% 3.56/2.71 inference(unit_resolution,[status(thm)],[666, 4957])).
% 3.56/2.71 tff(4959,plain,
% 3.56/2.71 (c3_1(a590)),
% 3.56/2.71 inference(unit_resolution,[status(thm)],[677, 4957])).
% 3.56/2.71 tff(4960,plain,
% 3.56/2.71 (c2_1(a590)),
% 3.56/2.71 inference(unit_resolution,[status(thm)],[688, 4957])).
% 3.56/2.71 tff(4961,plain,
% 3.56/2.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a607))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a607))),
% 3.56/2.71 inference(rewrite,[status(thm)],[])).
% 3.56/2.71 tff(4962,plain,
% 3.56/2.71 (((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607))) <=> (c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a607))),
% 3.56/2.71 inference(rewrite,[status(thm)],[])).
% 3.56/2.71 tff(4963,plain,
% 3.56/2.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a607)))),
% 3.56/2.71 inference(monotonicity,[status(thm)],[4962])).
% 3.56/2.71 tff(4964,plain,
% 3.56/2.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a607))),
% 3.56/2.71 inference(transitivity,[status(thm)],[4963, 4961])).
% 3.56/2.71 tff(4965,plain,
% 3.56/2.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607)))),
% 3.56/2.71 inference(quant_inst,[status(thm)],[])).
% 3.56/2.71 tff(4966,plain,
% 3.56/2.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a607)),
% 3.56/2.71 inference(modus_ponens,[status(thm)],[4965, 4964])).
% 3.56/2.71 tff(4967,plain,
% 3.56/2.71 ($false),
% 3.56/2.71 inference(unit_resolution,[status(thm)],[4966, 107, 1651, 1650, 4960, 4959, 66, 4653, 4958, 65, 4955, 4939])).
% 3.56/2.71 tff(4968,plain,(hskp3 | (~c0_1(a583)) | (~c1_1(a583)) | c1_1(a607) | c3_1(a607) | (~c2_1(a599)) | (~c3_1(a599)) | (~c1_1(a586)) | c1_1(a599) | c3_1(a586) | hskp22), inference(lemma,lemma(discharge,[]))).
% 3.56/2.71 tff(4969,plain,
% 3.56/2.71 (hskp3),
% 3.56/2.71 inference(unit_resolution,[status(thm)],[4968, 4937, 4936, 66, 33, 4797, 4796, 4795, 4794, 4665, 4656])).
% 3.56/2.71 tff(4970,plain,
% 3.56/2.71 (~c1_1(a587)),
% 3.56/2.71 inference(unit_resolution,[status(thm)],[939, 4969])).
% 3.56/2.71 tff(4971,plain,
% 3.56/2.71 (c2_1(a583)),
% 3.56/2.71 inference(unit_resolution,[status(thm)],[391, 4935])).
% 3.56/2.71 tff(4972,plain,
% 3.56/2.71 (hskp4 | c3_1(a583)),
% 3.56/2.71 inference(unit_resolution,[status(thm)],[3328, 107, 4654, 1651, 1650, 55])).
% 3.56/2.71 tff(4973,plain,
% 3.56/2.71 (c3_1(a583)),
% 3.56/2.71 inference(unit_resolution,[status(thm)],[4972, 830])).
% 3.56/2.71 tff(4974,plain,
% 3.56/2.71 (~c0_1(a607)),
% 3.56/2.71 inference(unit_resolution,[status(thm)],[4954, 4811])).
% 3.56/2.71 tff(4975,plain,
% 3.56/2.71 (hskp15),
% 3.56/2.71 inference(unit_resolution,[status(thm)],[4629, 4973, 1651, 1650, 1649])).
% 3.56/2.71 tff(4976,plain,
% 3.56/2.71 (~c0_1(a604)),
% 3.56/2.71 inference(unit_resolution,[status(thm)],[1591, 4975])).
% 3.56/2.71 tff(4977,plain,
% 3.56/2.71 (c3_1(a604)),
% 3.56/2.71 inference(unit_resolution,[status(thm)],[1602, 4975])).
% 3.56/2.71 tff(4978,plain,
% 3.56/2.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | c0_1(a607))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | c0_1(a607))),
% 3.56/2.71 inference(rewrite,[status(thm)],[])).
% 3.56/2.71 tff(4979,plain,
% 3.56/2.71 (((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607))) <=> (c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | c0_1(a607))),
% 3.56/2.71 inference(rewrite,[status(thm)],[])).
% 3.56/2.71 tff(4980,plain,
% 3.56/2.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | c0_1(a607)))),
% 3.56/2.71 inference(monotonicity,[status(thm)],[4979])).
% 3.56/2.71 tff(4981,plain,
% 3.56/2.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | c0_1(a607))),
% 3.56/2.71 inference(transitivity,[status(thm)],[4980, 4978])).
% 3.56/2.71 tff(4982,plain,
% 3.56/2.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607)))),
% 3.56/2.71 inference(quant_inst,[status(thm)],[])).
% 3.56/2.71 tff(4983,plain,
% 3.56/2.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c3_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | c0_1(a607)),
% 3.56/2.71 inference(modus_ponens,[status(thm)],[4982, 4981])).
% 3.56/2.71 tff(4984,plain,
% 3.56/2.71 (~c2_1(a604)),
% 3.56/2.71 inference(unit_resolution,[status(thm)],[4983, 107, 1651, 1650, 4977, 66, 4653, 4976, 65, 4974, 4973])).
% 3.56/2.71 tff(4985,plain,
% 3.56/2.71 (hskp28),
% 3.56/2.71 inference(unit_resolution,[status(thm)],[3240, 107, 463, 462, 4809, 4820, 461, 4808, 1748])).
% 3.56/2.71 tff(4986,plain,
% 3.56/2.71 (c3_1(a612)),
% 3.56/2.71 inference(unit_resolution,[status(thm)],[1139, 4985])).
% 3.56/2.71 tff(4987,plain,
% 3.56/2.71 (c2_1(a612)),
% 3.56/2.71 inference(unit_resolution,[status(thm)],[1150, 4985])).
% 3.56/2.71 tff(4988,plain,
% 3.56/2.71 (c1_1(a612)),
% 3.56/2.71 inference(unit_resolution,[status(thm)],[1435, 4985])).
% 3.56/2.71 tff(4989,plain,
% 3.56/2.71 (hskp10),
% 3.56/2.71 inference(unit_resolution,[status(thm)],[1535, 107, 4988, 4987, 4986, 1651, 1650, 1649, 21])).
% 3.56/2.71 tff(4990,plain,
% 3.56/2.71 (~c1_1(a598)),
% 3.56/2.71 inference(unit_resolution,[status(thm)],[911, 4989])).
% 3.56/2.71 tff(4991,plain,
% 3.56/2.71 (c3_1(a598)),
% 3.56/2.71 inference(unit_resolution,[status(thm)],[881, 4989])).
% 3.56/2.71 tff(4992,plain,
% 3.56/2.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a598)) | c2_1(a598))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a598)) | c2_1(a598))),
% 3.56/2.71 inference(rewrite,[status(thm)],[])).
% 3.56/2.71 tff(4993,plain,
% 3.56/2.71 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a586) | (~c1_1(a586)) | (~c2_1(a586))) <=> (c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a598)) | c2_1(a598))),
% 3.56/2.71 inference(rewrite,[status(thm)],[])).
% 3.56/2.71 tff(4994,plain,
% 3.56/2.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a598)) | c2_1(a598)))),
% 3.60/2.71 inference(monotonicity,[status(thm)],[4993])).
% 3.60/2.71 tff(4995,plain,
% 3.60/2.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a598)) | c2_1(a598))),
% 3.60/2.71 inference(transitivity,[status(thm)],[4994, 4992])).
% 3.60/2.71 tff(4996,plain,
% 3.60/2.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))),
% 3.60/2.71 inference(quant_inst,[status(thm)],[])).
% 3.60/2.71 tff(4997,plain,
% 3.60/2.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a598)) | c2_1(a598)),
% 3.60/2.71 inference(modus_ponens,[status(thm)],[4996, 4995])).
% 3.60/2.71 tff(4998,plain,
% 3.60/2.71 (c2_1(a598)),
% 3.60/2.71 inference(unit_resolution,[status(thm)],[4997, 107, 2318, 2317, 2316, 4991, 4809, 4820, 4990, 11, 4811])).
% 3.60/2.71 tff(4999,plain,
% 3.60/2.71 (c0_1(a598)),
% 3.60/2.71 inference(unit_resolution,[status(thm)],[892, 4989])).
% 3.60/2.71 tff(5000,plain,
% 3.60/2.71 (c1_1(a604)),
% 3.60/2.71 inference(unit_resolution,[status(thm)],[1613, 4975])).
% 3.60/2.71 tff(5001,plain,
% 3.60/2.71 ($false),
% 3.60/2.71 inference(unit_resolution,[status(thm)],[4790, 107, 4654, 5000, 4999, 4976, 4990, 32, 4998, 4984])).
% 3.60/2.71 tff(5002,plain,(hskp4 | (~c0_1(a678)) | (~c2_1(a678)) | (~c3_1(a678)) | (~c1_1(a586)) | (~c2_1(a586)) | (~c0_1(a583)) | (~c1_1(a583)) | c1_1(a607) | (~c2_1(a583)) | c3_1(a607) | (~c2_1(a599)) | (~c3_1(a599)) | c1_1(a599) | c3_1(a586)), inference(lemma,lemma(discharge,[]))).
% 3.60/2.71 tff(5003,plain,
% 3.60/2.71 (hskp4),
% 3.60/2.71 inference(unit_resolution,[status(thm)],[5002, 4669, 4668, 4667, 4795, 4798, 4937, 4936, 66, 4971, 33, 4797, 4796, 4794, 4665])).
% 3.60/2.71 tff(5004,plain,
% 3.60/2.71 (hskp6),
% 3.60/2.71 inference(unit_resolution,[status(thm)],[147, 5003, 4656])).
% 3.60/2.71 tff(5005,plain,
% 3.60/2.71 (~c0_1(a590)),
% 3.60/2.71 inference(unit_resolution,[status(thm)],[666, 5004])).
% 3.60/2.71 tff(5006,plain,
% 3.60/2.71 (c3_1(a590)),
% 3.60/2.71 inference(unit_resolution,[status(thm)],[677, 5004])).
% 3.60/2.71 tff(5007,plain,
% 3.60/2.71 (c2_1(a590)),
% 3.60/2.71 inference(unit_resolution,[status(thm)],[688, 5004])).
% 3.60/2.71 tff(5008,plain,
% 3.60/2.71 (c2_1(a633)),
% 3.60/2.71 inference(unit_resolution,[status(thm)],[4890, 107, 4797, 4796, 5007, 5006, 3981, 3980, 4794, 5005, 1730])).
% 3.60/2.71 tff(5009,plain,
% 3.60/2.71 ((~c0_1(a612)) | (~c2_1(a633))),
% 3.60/2.71 inference(unit_resolution,[status(thm)],[4900, 107, 4894, 4893, 4655, 5007, 5006, 3981, 5005, 65])).
% 3.60/2.71 tff(5010,plain,
% 3.60/2.71 (~c0_1(a612)),
% 3.60/2.71 inference(unit_resolution,[status(thm)],[5009, 5008])).
% 3.60/2.71 tff(5011,plain,
% 3.60/2.71 (~c2_1(a588)),
% 3.60/2.71 inference(unit_resolution,[status(thm)],[121, 5003])).
% 3.60/2.71 tff(5012,plain,
% 3.60/2.71 (~c1_1(a588)),
% 3.60/2.71 inference(unit_resolution,[status(thm)],[127, 5003])).
% 3.60/2.71 tff(5013,plain,
% 3.60/2.71 (~c3_1(a588)),
% 3.60/2.71 inference(unit_resolution,[status(thm)],[4911, 107, 4669, 4668, 4667, 4894, 4905, 5012, 5011, 11, 5010])).
% 3.60/2.71 tff(5014,plain,
% 3.60/2.71 (c0_1(a588)),
% 3.60/2.71 inference(unit_resolution,[status(thm)],[138, 5003])).
% 3.60/2.71 tff(5015,plain,
% 3.60/2.71 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)))),
% 3.60/2.71 inference(rewrite,[status(thm)],[])).
% 3.60/2.71 tff(5016,plain,
% 3.60/2.71 ((hskp16 | (~ndr1_0) | c2_1(a588) | c3_1(a588) | (~c0_1(a588)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612))) <=> (hskp16 | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)))),
% 3.60/2.71 inference(rewrite,[status(thm)],[])).
% 3.60/2.71 tff(5017,plain,
% 3.60/2.71 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a588) | c3_1(a588) | (~c0_1(a588)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612))))),
% 3.60/2.71 inference(monotonicity,[status(thm)],[5016])).
% 3.60/2.71 tff(5018,plain,
% 3.60/2.71 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a588) | c3_1(a588) | (~c0_1(a588)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)))),
% 3.60/2.71 inference(transitivity,[status(thm)],[5017, 5015])).
% 3.60/2.71 tff(5019,plain,
% 3.60/2.71 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a588) | c3_1(a588) | (~c0_1(a588)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)))),
% 3.60/2.71 inference(quant_inst,[status(thm)],[])).
% 3.60/2.71 tff(5020,plain,
% 3.60/2.71 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612))),
% 3.60/2.71 inference(modus_ponens,[status(thm)],[5019, 5018])).
% 3.60/2.71 tff(5021,plain,
% 3.60/2.71 (hskp16),
% 3.60/2.71 inference(unit_resolution,[status(thm)],[5020, 107, 4905, 4893, 5014, 5011, 2125, 5010, 5013])).
% 3.60/2.71 tff(5022,plain,
% 3.60/2.71 (~c2_1(a606)),
% 3.60/2.71 inference(unit_resolution,[status(thm)],[1111, 5021])).
% 3.60/2.71 tff(5023,plain,
% 3.60/2.71 (c2_1(a587)),
% 3.60/2.71 inference(unit_resolution,[status(thm)],[950, 4969])).
% 3.60/2.71 tff(5024,plain,
% 3.60/2.71 (c0_1(a587)),
% 3.60/2.71 inference(unit_resolution,[status(thm)],[961, 4969])).
% 3.60/2.71 tff(5025,plain,
% 3.60/2.71 (c1_1(a606)),
% 3.60/2.71 inference(unit_resolution,[status(thm)],[1088, 5021])).
% 3.60/2.71 tff(5026,assumption,(~c0_1(a606)), introduced(assumption)).
% 3.60/2.71 tff(5027,plain,
% 3.60/2.71 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c2_1(a606) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a606) | (~c1_1(a606)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c2_1(a606) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a606) | (~c1_1(a606)))),
% 3.60/2.71 inference(rewrite,[status(thm)],[])).
% 3.60/2.71 tff(5028,plain,
% 3.60/2.71 ((hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a606) | c2_1(a606) | (~c1_1(a606))) <=> (hskp17 | c2_1(a606) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a606) | (~c1_1(a606)))),
% 3.60/2.71 inference(rewrite,[status(thm)],[])).
% 3.60/2.71 tff(5029,plain,
% 3.60/2.71 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a606) | c2_1(a606) | (~c1_1(a606)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c2_1(a606) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a606) | (~c1_1(a606))))),
% 3.60/2.71 inference(monotonicity,[status(thm)],[5028])).
% 3.60/2.71 tff(5030,plain,
% 3.60/2.71 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a606) | c2_1(a606) | (~c1_1(a606)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c2_1(a606) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a606) | (~c1_1(a606)))),
% 3.60/2.72 inference(transitivity,[status(thm)],[5029, 5027])).
% 3.60/2.72 tff(5031,plain,
% 3.60/2.72 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a606) | c2_1(a606) | (~c1_1(a606)))),
% 3.60/2.72 inference(quant_inst,[status(thm)],[])).
% 3.60/2.72 tff(5032,plain,
% 3.60/2.72 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c2_1(a606) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a606) | (~c1_1(a606))),
% 3.60/2.72 inference(modus_ponens,[status(thm)],[5031, 5030])).
% 3.60/2.72 tff(5033,plain,
% 3.60/2.72 ($false),
% 3.60/2.72 inference(unit_resolution,[status(thm)],[5032, 107, 2987, 1876, 1000, 999, 1873, 996, 32, 5026])).
% 3.60/2.72 tff(5034,plain,(c0_1(a606) | hskp17 | (~c1_1(a606)) | (~c0_1(a587)) | (~c2_1(a587)) | c2_1(a606) | c1_1(a587)), inference(lemma,lemma(discharge,[]))).
% 3.60/2.72 tff(5035,plain,
% 3.60/2.72 (c0_1(a606)),
% 3.60/2.72 inference(unit_resolution,[status(thm)],[5034, 5025, 4654, 5024, 5023, 5022, 4970])).
% 3.60/2.72 tff(5036,plain,
% 3.60/2.72 (hskp15),
% 3.60/2.72 inference(unit_resolution,[status(thm)],[2707, 107, 4894, 4893, 4795, 4798, 4665, 2690, 5010])).
% 3.60/2.72 tff(5037,plain,
% 3.60/2.72 (~c0_1(a604)),
% 3.60/2.72 inference(unit_resolution,[status(thm)],[1591, 5036])).
% 3.60/2.72 tff(5038,plain,
% 3.60/2.72 (~c3_1(a606)),
% 3.60/2.72 inference(unit_resolution,[status(thm)],[1075, 5021])).
% 3.60/2.72 tff(5039,plain,
% 3.60/2.72 (c1_1(a604)),
% 3.60/2.72 inference(unit_resolution,[status(thm)],[1613, 5036])).
% 3.60/2.72 tff(5040,plain,
% 3.60/2.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a633) | c0_1(a633) | c3_1(a633) | c2_1(a606) | c3_1(a606) | c0_1(a604) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a606)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a633) | c0_1(a633) | c3_1(a633) | c2_1(a606) | c3_1(a606) | c0_1(a604) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a606)))),
% 3.60/2.72 inference(rewrite,[status(thm)],[])).
% 3.60/2.72 tff(5041,plain,
% 3.60/2.72 (((~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c0_1(a606)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)) | c3_1(a633) | c1_1(a633) | c0_1(a633)) <=> (c1_1(a633) | c0_1(a633) | c3_1(a633) | c2_1(a606) | c3_1(a606) | c0_1(a604) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a606)))),
% 3.60/2.72 inference(rewrite,[status(thm)],[])).
% 3.60/2.72 tff(5042,plain,
% 3.60/2.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c0_1(a606)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)) | c3_1(a633) | c1_1(a633) | c0_1(a633))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a633) | c0_1(a633) | c3_1(a633) | c2_1(a606) | c3_1(a606) | c0_1(a604) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a606))))),
% 3.60/2.72 inference(monotonicity,[status(thm)],[5041])).
% 3.60/2.72 tff(5043,plain,
% 3.60/2.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c0_1(a606)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)) | c3_1(a633) | c1_1(a633) | c0_1(a633))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a633) | c0_1(a633) | c3_1(a633) | c2_1(a606) | c3_1(a606) | c0_1(a604) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a606)))),
% 3.60/2.72 inference(transitivity,[status(thm)],[5042, 5040])).
% 3.60/2.72 tff(5044,plain,
% 3.60/2.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c0_1(a606)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)) | c3_1(a633) | c1_1(a633) | c0_1(a633))),
% 3.60/2.72 inference(quant_inst,[status(thm)],[])).
% 3.60/2.72 tff(5045,plain,
% 3.60/2.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a633) | c0_1(a633) | c3_1(a633) | c2_1(a606) | c3_1(a606) | c0_1(a604) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a606))),
% 3.60/2.72 inference(modus_ponens,[status(thm)],[5044, 5043])).
% 3.60/2.72 tff(5046,plain,
% 3.60/2.72 (c2_1(a604)),
% 3.60/2.72 inference(unit_resolution,[status(thm)],[5045, 107, 4655, 5039, 3981, 3980, 5022, 5038, 5037, 1463, 5035])).
% 3.60/2.72 tff(5047,plain,
% 3.60/2.72 (c3_1(a604)),
% 3.60/2.72 inference(unit_resolution,[status(thm)],[1602, 5036])).
% 3.60/2.72 tff(5048,plain,
% 3.60/2.72 (~hskp13),
% 3.60/2.72 inference(unit_resolution,[status(thm)],[2553, 5046, 4797, 4796, 5037, 4794, 5035, 4669, 4668, 4667, 5025, 5022, 5047])).
% 3.60/2.72 tff(5049,plain,
% 3.60/2.72 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp19 | hskp13 | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))),
% 3.60/2.72 inference(rewrite,[status(thm)],[])).
% 3.60/2.72 tff(5050,plain,
% 3.60/2.72 ((hskp19 | hskp13 | (~ndr1_0) | c0_1(a612) | (~c2_1(a612)) | (~c1_1(a612))) <=> (hskp19 | hskp13 | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))),
% 3.60/2.72 inference(rewrite,[status(thm)],[])).
% 3.60/2.72 tff(5051,plain,
% 3.60/2.72 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c0_1(a612) | (~c2_1(a612)) | (~c1_1(a612)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612))))),
% 3.60/2.72 inference(monotonicity,[status(thm)],[5050])).
% 3.60/2.72 tff(5052,plain,
% 3.60/2.72 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c0_1(a612) | (~c2_1(a612)) | (~c1_1(a612)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp19 | hskp13 | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))),
% 3.60/2.72 inference(transitivity,[status(thm)],[5051, 5049])).
% 3.60/2.72 tff(5053,plain,
% 3.60/2.72 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c0_1(a612) | (~c2_1(a612)) | (~c1_1(a612)))),
% 3.60/2.72 inference(quant_inst,[status(thm)],[])).
% 3.60/2.72 tff(5054,plain,
% 3.60/2.72 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp19 | hskp13 | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612))),
% 3.60/2.72 inference(modus_ponens,[status(thm)],[5053, 5052])).
% 3.60/2.72 tff(5055,plain,
% 3.60/2.72 (hskp19 | hskp13 | c0_1(a612)),
% 3.60/2.72 inference(unit_resolution,[status(thm)],[5054, 107, 4894, 4905, 2564])).
% 3.60/2.72 tff(5056,plain,
% 3.60/2.72 (hskp19),
% 3.60/2.72 inference(unit_resolution,[status(thm)],[5055, 5048, 5010])).
% 3.60/2.72 tff(5057,plain,
% 3.60/2.72 (~c1_1(a617)),
% 3.60/2.72 inference(unit_resolution,[status(thm)],[2588, 5056])).
% 3.60/2.72 tff(5058,plain,
% 3.60/2.72 (~c0_1(a617)),
% 3.60/2.72 inference(unit_resolution,[status(thm)],[2594, 5056])).
% 3.60/2.72 tff(5059,plain,
% 3.60/2.72 (hskp12),
% 3.60/2.72 inference(unit_resolution,[status(thm)],[2734, 107, 4894, 4905, 4937, 4936, 4971, 2727, 5010])).
% 3.60/2.72 tff(5060,plain,
% 3.60/2.72 (~c3_1(a600)),
% 3.60/2.72 inference(unit_resolution,[status(thm)],[741, 5059])).
% 3.60/2.72 tff(5061,plain,
% 3.60/2.72 (c2_1(a600)),
% 3.60/2.72 inference(unit_resolution,[status(thm)],[752, 5059])).
% 3.60/2.72 tff(5062,plain,
% 3.60/2.72 (c0_1(a600)),
% 3.60/2.72 inference(unit_resolution,[status(thm)],[763, 5059])).
% 3.60/2.72 tff(5063,plain,
% 3.60/2.72 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | c3_1(a600) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c2_1(a600)) | (~c0_1(a600)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c3_1(a600) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c2_1(a600)) | (~c0_1(a600)))),
% 3.60/2.72 inference(rewrite,[status(thm)],[])).
% 3.60/2.72 tff(5064,plain,
% 3.60/2.72 ((hskp8 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c3_1(a588) | c2_1(a588) | (~c0_1(a588))) <=> (hskp8 | c3_1(a600) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c2_1(a600)) | (~c0_1(a600)))),
% 3.60/2.72 inference(rewrite,[status(thm)],[])).
% 3.60/2.72 tff(5065,plain,
% 3.60/2.72 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c3_1(a588) | c2_1(a588) | (~c0_1(a588)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | c3_1(a600) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c2_1(a600)) | (~c0_1(a600))))),
% 3.60/2.72 inference(monotonicity,[status(thm)],[5064])).
% 3.60/2.72 tff(5066,plain,
% 3.60/2.72 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c3_1(a588) | c2_1(a588) | (~c0_1(a588)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c3_1(a600) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c2_1(a600)) | (~c0_1(a600)))),
% 3.60/2.72 inference(transitivity,[status(thm)],[5065, 5063])).
% 3.60/2.72 tff(5067,plain,
% 3.60/2.72 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c3_1(a588) | c2_1(a588) | (~c0_1(a588)))),
% 3.60/2.72 inference(quant_inst,[status(thm)],[])).
% 3.60/2.72 tff(5068,plain,
% 3.60/2.72 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c3_1(a600) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c2_1(a600)) | (~c0_1(a600))),
% 3.60/2.72 inference(modus_ponens,[status(thm)],[5067, 5066])).
% 3.60/2.72 tff(5069,plain,
% 3.60/2.72 (hskp8),
% 3.60/2.72 inference(unit_resolution,[status(thm)],[5068, 107, 5062, 5061, 5014, 5060, 5011, 4271, 5013])).
% 3.60/2.72 tff(5070,plain,
% 3.60/2.72 (c3_1(a593)),
% 3.60/2.72 inference(unit_resolution,[status(thm)],[511, 5069])).
% 3.60/2.72 tff(5071,plain,
% 3.60/2.72 (c1_1(a593)),
% 3.60/2.72 inference(unit_resolution,[status(thm)],[522, 5069])).
% 3.60/2.72 tff(5072,plain,
% 3.60/2.72 (c2_1(a617)),
% 3.60/2.72 inference(unit_resolution,[status(thm)],[2605, 5056])).
% 3.60/2.72 tff(5073,plain,
% 3.60/2.72 (~c0_1(a593)),
% 3.60/2.72 inference(unit_resolution,[status(thm)],[2619, 107, 5072, 5047, 5071, 5070, 5058, 5057, 5037, 65, 5046])).
% 3.60/2.72 tff(5074,plain,
% 3.60/2.72 (~c2_1(a593)),
% 3.60/2.72 inference(unit_resolution,[status(thm)],[555, 5069])).
% 3.60/2.72 tff(5075,plain,
% 3.60/2.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a633) | c0_1(a633) | c3_1(a633) | c2_1(a606) | c3_1(a606) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a606)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a633) | c0_1(a633) | c3_1(a633) | c2_1(a606) | c3_1(a606) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a606)))),
% 3.60/2.72 inference(rewrite,[status(thm)],[])).
% 3.60/2.72 tff(5076,plain,
% 3.60/2.72 (((~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c0_1(a606)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a633) | c1_1(a633) | c0_1(a633)) <=> (c1_1(a633) | c0_1(a633) | c3_1(a633) | c2_1(a606) | c3_1(a606) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a606)))),
% 3.60/2.72 inference(rewrite,[status(thm)],[])).
% 3.60/2.72 tff(5077,plain,
% 3.60/2.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c0_1(a606)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a633) | c1_1(a633) | c0_1(a633))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a633) | c0_1(a633) | c3_1(a633) | c2_1(a606) | c3_1(a606) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a606))))),
% 3.60/2.72 inference(monotonicity,[status(thm)],[5076])).
% 3.60/2.72 tff(5078,plain,
% 3.60/2.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c0_1(a606)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a633) | c1_1(a633) | c0_1(a633))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a633) | c0_1(a633) | c3_1(a633) | c2_1(a606) | c3_1(a606) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a606)))),
% 3.60/2.72 inference(transitivity,[status(thm)],[5077, 5075])).
% 3.60/2.72 tff(5079,plain,
% 3.60/2.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c0_1(a606)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a633) | c1_1(a633) | c0_1(a633))),
% 3.60/2.72 inference(quant_inst,[status(thm)],[])).
% 3.60/2.72 tff(5080,plain,
% 3.60/2.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a633) | c0_1(a633) | c3_1(a633) | c2_1(a606) | c3_1(a606) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a606))),
% 3.60/2.72 inference(modus_ponens,[status(thm)],[5079, 5078])).
% 3.60/2.72 tff(5081,plain,
% 3.60/2.72 ($false),
% 3.60/2.72 inference(unit_resolution,[status(thm)],[5080, 107, 4655, 5071, 3981, 3980, 5022, 5038, 5074, 1463, 5073, 5035])).
% 3.60/2.72 tff(5082,plain,(c1_1(a633) | c0_1(a633) | c3_1(a633) | c1_1(a607) | c3_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.60/2.72 tff(5083,plain,
% 3.60/2.72 (c1_1(a633)),
% 3.60/2.72 inference(unit_resolution,[status(thm)],[5082, 3981, 3980, 66, 33])).
% 3.60/2.72 tff(5084,plain,
% 3.60/2.72 (~c3_1(a583)),
% 3.60/2.72 inference(unit_resolution,[status(thm)],[4019, 1638, 3981, 3980, 3992])).
% 3.60/2.72 tff(5085,plain,
% 3.60/2.72 (hskp3),
% 3.60/2.72 inference(unit_resolution,[status(thm)],[4026, 107, 2987, 3321, 3322, 2368, 5084])).
% 3.60/2.72 tff(5086,plain,
% 3.60/2.72 (~c1_1(a587)),
% 3.60/2.72 inference(unit_resolution,[status(thm)],[939, 5085])).
% 3.60/2.72 tff(5087,plain,
% 3.60/2.72 (c2_1(a587)),
% 3.60/2.72 inference(unit_resolution,[status(thm)],[950, 5085])).
% 3.60/2.72 tff(5088,plain,
% 3.60/2.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a633) | c3_1(a633) | c1_1(a587) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a587)) | (~c2_1(a587)) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a633) | c3_1(a633) | c1_1(a587) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a587)) | (~c2_1(a587)) | (~c1_1(a633)))),
% 3.60/2.72 inference(rewrite,[status(thm)],[])).
% 3.60/2.72 tff(5089,plain,
% 3.60/2.72 (((~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a587) | (~c3_1(a587)) | (~c2_1(a587)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633))) <=> (c0_1(a633) | c3_1(a633) | c1_1(a587) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a587)) | (~c2_1(a587)) | (~c1_1(a633)))),
% 3.60/2.72 inference(rewrite,[status(thm)],[])).
% 3.60/2.72 tff(5090,plain,
% 3.60/2.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a587) | (~c3_1(a587)) | (~c2_1(a587)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a633) | c3_1(a633) | c1_1(a587) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a587)) | (~c2_1(a587)) | (~c1_1(a633))))),
% 3.60/2.72 inference(monotonicity,[status(thm)],[5089])).
% 3.60/2.72 tff(5091,plain,
% 3.60/2.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a587) | (~c3_1(a587)) | (~c2_1(a587)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a633) | c3_1(a633) | c1_1(a587) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a587)) | (~c2_1(a587)) | (~c1_1(a633)))),
% 3.60/2.72 inference(transitivity,[status(thm)],[5090, 5088])).
% 3.60/2.72 tff(5092,plain,
% 3.60/2.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c0_1(a583)) | c1_1(a587) | (~c3_1(a587)) | (~c2_1(a587)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))),
% 3.60/2.72 inference(quant_inst,[status(thm)],[])).
% 3.60/2.72 tff(5093,plain,
% 3.60/2.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a633) | c3_1(a633) | c1_1(a587) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c0_1(a583)) | (~c3_1(a587)) | (~c2_1(a587)) | (~c1_1(a633))),
% 3.60/2.72 inference(modus_ponens,[status(thm)],[5092, 5091])).
% 3.60/2.72 tff(5094,plain,
% 3.60/2.72 (~c3_1(a587)),
% 3.60/2.72 inference(unit_resolution,[status(thm)],[5093, 107, 3321, 3330, 3992, 5087, 3981, 3980, 5086, 258, 5084])).
% 3.60/2.72 tff(5095,plain,
% 3.60/2.72 (^[U: $i] : refl((hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))),
% 3.60/2.72 inference(bind,[status(th)],[])).
% 3.60/2.72 tff(5096,plain,
% 3.60/2.72 (![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 3.60/2.72 inference(quant_intro,[status(thm)],[5095])).
% 3.60/2.72 tff(5097,plain,
% 3.60/2.72 (![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 3.60/2.72 inference(rewrite,[status(thm)],[])).
% 3.60/2.72 tff(5098,plain,
% 3.60/2.72 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp21) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp21))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp21) <=> (hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp21) <=> (hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp21) | hskp11) <=> ((hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp11))), rewrite(((hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp11) <=> (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp21) | hskp11) <=> (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))))),
% 3.60/2.72 inference(bind,[status(th)],[])).
% 3.60/2.72 tff(5099,plain,
% 3.60/2.72 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp21) | hskp11) <=> ![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 3.60/2.72 inference(quant_intro,[status(thm)],[5098])).
% 3.60/2.72 tff(5100,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp21) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause136')).
% 3.60/2.72 tff(5101,plain,
% 3.60/2.72 (![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 3.60/2.72 inference(modus_ponens,[status(thm)],[5100, 5099])).
% 3.60/2.72 tff(5102,plain,
% 3.60/2.72 (![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 3.60/2.72 inference(modus_ponens,[status(thm)],[5101, 5097])).
% 3.60/2.72 tff(5103,plain,(
% 3.60/2.72 ![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 3.60/2.72 inference(skolemize,[status(sab)],[5102])).
% 3.60/2.72 tff(5104,plain,
% 3.60/2.72 (![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 3.60/2.72 inference(modus_ponens,[status(thm)],[5103, 5096])).
% 3.60/2.72 tff(5105,plain,
% 3.60/2.72 (hskp4),
% 3.60/2.72 inference(unit_resolution,[status(thm)],[3328, 107, 2987, 3321, 3322, 55, 5084])).
% 3.60/2.72 tff(5106,plain,
% 3.60/2.72 (~c2_1(a588)),
% 3.60/2.72 inference(unit_resolution,[status(thm)],[121, 5105])).
% 3.60/2.72 tff(5107,plain,
% 3.60/2.72 (~c1_1(a588)),
% 3.60/2.72 inference(unit_resolution,[status(thm)],[127, 5105])).
% 3.60/2.72 tff(5108,plain,
% 3.60/2.72 (c0_1(a588)),
% 3.60/2.72 inference(unit_resolution,[status(thm)],[138, 5105])).
% 3.60/2.72 tff(5109,plain,
% 3.60/2.72 (((~![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp11 | hskp21 | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)))) <=> ((~![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp11 | hskp21 | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)))),
% 3.60/2.72 inference(rewrite,[status(thm)],[])).
% 3.60/2.72 tff(5110,plain,
% 3.60/2.72 ((hskp11 | hskp21 | (~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588))) <=> (hskp11 | hskp21 | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)))),
% 3.60/2.72 inference(rewrite,[status(thm)],[])).
% 3.60/2.72 tff(5111,plain,
% 3.60/2.72 (((~![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp11 | hskp21 | (~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588)))) <=> ((~![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp11 | hskp21 | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588))))),
% 3.60/2.72 inference(monotonicity,[status(thm)],[5110])).
% 3.60/2.72 tff(5112,plain,
% 3.60/2.72 (((~![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp11 | hskp21 | (~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588)))) <=> ((~![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp11 | hskp21 | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)))),
% 3.60/2.72 inference(transitivity,[status(thm)],[5111, 5109])).
% 3.60/2.72 tff(5113,plain,
% 3.60/2.72 ((~![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp11 | hskp21 | (~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588)))),
% 3.60/2.72 inference(quant_inst,[status(thm)],[])).
% 3.60/2.72 tff(5114,plain,
% 3.60/2.72 ((~![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp11 | hskp21 | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588))),
% 3.60/2.72 inference(modus_ponens,[status(thm)],[5113, 5112])).
% 3.60/2.72 tff(5115,plain,
% 3.60/2.72 (hskp21),
% 3.60/2.72 inference(unit_resolution,[status(thm)],[5114, 1638, 107, 5108, 5107, 5106, 5104])).
% 3.60/2.72 tff(5116,plain,
% 3.60/2.72 (~c3_1(a629)),
% 3.60/2.72 inference(unit_resolution,[status(thm)],[4846, 5115])).
% 3.60/2.72 tff(5117,plain,
% 3.60/2.72 (~c2_1(a629)),
% 3.60/2.72 inference(unit_resolution,[status(thm)],[4852, 5115])).
% 3.60/2.72 tff(5118,plain,
% 3.60/2.72 (c0_1(a587)),
% 3.60/2.72 inference(unit_resolution,[status(thm)],[961, 5085])).
% 3.60/2.72 tff(5119,plain,
% 3.60/2.72 (c0_1(a629)),
% 3.60/2.72 inference(unit_resolution,[status(thm)],[4870, 5115])).
% 3.60/2.72 tff(5120,plain,
% 3.60/2.72 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | c2_1(a629) | c3_1(a629) | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | (~c0_1(a629)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c2_1(a629) | c3_1(a629) | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | (~c0_1(a629)))),
% 3.60/2.72 inference(rewrite,[status(thm)],[])).
% 3.60/2.72 tff(5121,plain,
% 3.60/2.72 ((hskp8 | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a629) | c2_1(a629) | (~c0_1(a629))) <=> (hskp8 | c2_1(a629) | c3_1(a629) | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | (~c0_1(a629)))),
% 3.60/2.72 inference(rewrite,[status(thm)],[])).
% 3.60/2.72 tff(5122,plain,
% 3.60/2.72 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a629) | c2_1(a629) | (~c0_1(a629)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | c2_1(a629) | c3_1(a629) | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | (~c0_1(a629))))),
% 3.60/2.73 inference(monotonicity,[status(thm)],[5121])).
% 3.60/2.73 tff(5123,plain,
% 3.60/2.73 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a629) | c2_1(a629) | (~c0_1(a629)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c2_1(a629) | c3_1(a629) | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | (~c0_1(a629)))),
% 3.60/2.73 inference(transitivity,[status(thm)],[5122, 5120])).
% 3.60/2.73 tff(5124,plain,
% 3.60/2.73 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a629) | c2_1(a629) | (~c0_1(a629)))),
% 3.60/2.73 inference(quant_inst,[status(thm)],[])).
% 3.60/2.73 tff(5125,plain,
% 3.60/2.73 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c2_1(a629) | c3_1(a629) | (~ndr1_0) | c3_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | (~c0_1(a629))),
% 3.60/2.73 inference(modus_ponens,[status(thm)],[5124, 5123])).
% 3.60/2.73 tff(5126,plain,
% 3.60/2.73 (hskp8),
% 3.60/2.73 inference(unit_resolution,[status(thm)],[5125, 107, 5119, 5118, 5087, 5117, 5116, 4271, 5094])).
% 3.60/2.73 tff(5127,plain,
% 3.60/2.73 (~c2_1(a593)),
% 3.60/2.73 inference(unit_resolution,[status(thm)],[555, 5126])).
% 3.60/2.73 tff(5128,plain,
% 3.60/2.73 (c3_1(a593)),
% 3.60/2.73 inference(unit_resolution,[status(thm)],[511, 5126])).
% 3.60/2.73 tff(5129,plain,
% 3.60/2.73 (c1_1(a593)),
% 3.60/2.73 inference(unit_resolution,[status(thm)],[522, 5126])).
% 3.60/2.73 tff(5130,plain,
% 3.60/2.73 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a633) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a633) | (~c1_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a633) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a633) | (~c1_1(a633)))),
% 3.60/2.73 inference(rewrite,[status(thm)],[])).
% 3.60/2.73 tff(5131,plain,
% 3.60/2.73 ((hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a633) | c2_1(a633) | (~c1_1(a633))) <=> (hskp17 | c0_1(a633) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a633) | (~c1_1(a633)))),
% 3.60/2.73 inference(rewrite,[status(thm)],[])).
% 3.60/2.73 tff(5132,plain,
% 3.60/2.73 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a633) | c2_1(a633) | (~c1_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a633) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a633) | (~c1_1(a633))))),
% 3.60/2.73 inference(monotonicity,[status(thm)],[5131])).
% 3.60/2.73 tff(5133,plain,
% 3.60/2.73 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a633) | c2_1(a633) | (~c1_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a633) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a633) | (~c1_1(a633)))),
% 3.60/2.73 inference(transitivity,[status(thm)],[5132, 5130])).
% 3.60/2.73 tff(5134,plain,
% 3.60/2.73 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a633) | c2_1(a633) | (~c1_1(a633)))),
% 3.60/2.73 inference(quant_inst,[status(thm)],[])).
% 3.60/2.73 tff(5135,plain,
% 3.60/2.73 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a633) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a633) | (~c1_1(a633))),
% 3.60/2.73 inference(modus_ponens,[status(thm)],[5134, 5133])).
% 3.60/2.73 tff(5136,plain,
% 3.60/2.73 (c2_1(a633)),
% 3.60/2.73 inference(unit_resolution,[status(thm)],[5135, 107, 2987, 3992, 5118, 5087, 3981, 5086, 32])).
% 3.60/2.73 tff(5137,plain,
% 3.60/2.73 (hskp15),
% 3.60/2.73 inference(unit_resolution,[status(thm)],[4316, 5127, 1638, 5128, 3980, 5136, 5129, 3992])).
% 3.60/2.73 tff(5138,plain,
% 3.60/2.73 (~c0_1(a604)),
% 3.60/2.73 inference(unit_resolution,[status(thm)],[1591, 5137])).
% 3.60/2.73 tff(5139,plain,
% 3.60/2.73 (c3_1(a604)),
% 3.60/2.73 inference(unit_resolution,[status(thm)],[1602, 5137])).
% 3.60/2.73 tff(5140,plain,
% 3.60/2.73 (c1_1(a604)),
% 3.60/2.73 inference(unit_resolution,[status(thm)],[1613, 5137])).
% 3.60/2.73 tff(5141,plain,
% 3.60/2.73 (hskp16),
% 3.60/2.73 inference(unit_resolution,[status(thm)],[1849, 107, 3321, 3322, 5140, 5139, 5138, 1425, 5084])).
% 3.60/2.73 tff(5142,plain,
% 3.60/2.73 (~c2_1(a606)),
% 3.60/2.73 inference(unit_resolution,[status(thm)],[1111, 5141])).
% 3.60/2.73 tff(5143,plain,
% 3.60/2.73 (c1_1(a606)),
% 3.60/2.73 inference(unit_resolution,[status(thm)],[1088, 5141])).
% 3.60/2.73 tff(5144,plain,
% 3.60/2.73 (c0_1(a606)),
% 3.60/2.73 inference(unit_resolution,[status(thm)],[5034, 5143, 2987, 5118, 5087, 5142, 5086])).
% 3.60/2.73 tff(5145,plain,
% 3.60/2.73 (hskp0),
% 3.60/2.73 inference(unit_resolution,[status(thm)],[2354, 1638, 107, 5143, 5142, 2347, 5144])).
% 3.60/2.73 tff(5146,plain,
% 3.60/2.73 (~c2_1(a584)),
% 3.60/2.73 inference(unit_resolution,[status(thm)],[1045, 5145])).
% 3.60/2.73 tff(5147,plain,
% 3.60/2.73 (c1_1(a584)),
% 3.60/2.73 inference(unit_resolution,[status(thm)],[1062, 5145])).
% 3.60/2.73 tff(5148,plain,
% 3.60/2.73 (~c0_1(a584)),
% 3.60/2.73 inference(unit_resolution,[status(thm)],[1051, 5145])).
% 3.60/2.73 tff(5149,plain,
% 3.60/2.73 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp3 | c2_1(a593) | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp3 | c2_1(a593) | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)))),
% 3.60/2.73 inference(rewrite,[status(thm)],[])).
% 3.60/2.73 tff(5150,plain,
% 3.60/2.73 ((hskp17 | hskp3 | (~ndr1_0) | c2_1(a593) | (~c3_1(a593)) | (~c1_1(a593))) <=> (hskp17 | hskp3 | c2_1(a593) | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)))),
% 3.60/2.73 inference(rewrite,[status(thm)],[])).
% 3.60/2.73 tff(5151,plain,
% 3.60/2.73 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c2_1(a593) | (~c3_1(a593)) | (~c1_1(a593)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp3 | c2_1(a593) | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593))))),
% 3.60/2.73 inference(monotonicity,[status(thm)],[5150])).
% 3.60/2.73 tff(5152,plain,
% 3.60/2.73 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c2_1(a593) | (~c3_1(a593)) | (~c1_1(a593)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp3 | c2_1(a593) | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)))),
% 3.60/2.73 inference(transitivity,[status(thm)],[5151, 5149])).
% 3.60/2.73 tff(5153,plain,
% 3.60/2.73 ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c2_1(a593) | (~c3_1(a593)) | (~c1_1(a593)))),
% 3.60/2.73 inference(quant_inst,[status(thm)],[])).
% 3.60/2.73 tff(5154,plain,
% 3.60/2.73 ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp3 | c2_1(a593) | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593))),
% 3.60/2.73 inference(modus_ponens,[status(thm)],[5153, 5152])).
% 3.60/2.73 tff(5155,plain,
% 3.60/2.73 (hskp17 | hskp3),
% 3.60/2.73 inference(unit_resolution,[status(thm)],[5154, 107, 1894, 1903, 1893, 3420])).
% 3.60/2.73 tff(5156,plain,
% 3.60/2.73 (hskp3),
% 3.60/2.73 inference(unit_resolution,[status(thm)],[5155, 2987])).
% 3.60/2.73 tff(5157,plain,
% 3.60/2.73 (~c1_1(a587)),
% 3.60/2.73 inference(unit_resolution,[status(thm)],[939, 5156])).
% 3.60/2.73 tff(5158,plain,
% 3.60/2.73 (c2_1(a587)),
% 3.60/2.73 inference(unit_resolution,[status(thm)],[950, 5156])).
% 3.60/2.73 tff(5159,plain,
% 3.60/2.73 (c0_1(a587)),
% 3.60/2.73 inference(unit_resolution,[status(thm)],[961, 5156])).
% 3.60/2.73 tff(5160,plain,
% 3.60/2.73 ($false),
% 3.60/2.73 inference(unit_resolution,[status(thm)],[2386, 107, 2987, 5159, 5158, 4584, 5157, 3642, 3641, 32])).
% 3.60/2.73 tff(5161,plain,(hskp17 | (~c1_1(a584)) | c0_1(a584) | c2_1(a584) | (~c1_1(a593)) | (~c3_1(a593)) | c2_1(a593)), inference(lemma,lemma(discharge,[]))).
% 3.60/2.73 tff(5162,plain,
% 3.60/2.73 ($false),
% 3.60/2.73 inference(unit_resolution,[status(thm)],[5161, 5148, 5147, 2987, 5146, 5129, 5128, 5127])).
% 3.60/2.73 tff(5163,plain,(hskp11 | hskp17 | c3_1(a633) | (~c1_1(a633)) | c0_1(a633)), inference(lemma,lemma(discharge,[]))).
% 3.60/2.73 tff(5164,plain,
% 3.60/2.73 (hskp11),
% 3.60/2.73 inference(unit_resolution,[status(thm)],[5163, 5083, 3980, 4654, 3981])).
% 3.60/2.73 tff(5165,plain,
% 3.60/2.73 (~c1_1(a599)),
% 3.60/2.73 inference(unit_resolution,[status(thm)],[428, 5164])).
% 3.60/2.73 tff(5166,plain,
% 3.60/2.73 (c3_1(a599)),
% 3.60/2.73 inference(unit_resolution,[status(thm)],[422, 5164])).
% 3.60/2.73 tff(5167,plain,
% 3.60/2.73 (c2_1(a599)),
% 3.60/2.73 inference(unit_resolution,[status(thm)],[439, 5164])).
% 3.60/2.73 tff(5168,plain,
% 3.60/2.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a607) | c0_1(a633) | c3_1(a633) | (~c2_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a607)) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a607) | c0_1(a633) | c3_1(a633) | (~c2_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a607)) | (~c1_1(a633)))),
% 3.60/2.73 inference(rewrite,[status(thm)],[])).
% 3.60/2.73 tff(5169,plain,
% 3.60/2.73 (((~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633))) <=> (c3_1(a607) | c0_1(a633) | c3_1(a633) | (~c2_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a607)) | (~c1_1(a633)))),
% 3.60/2.73 inference(rewrite,[status(thm)],[])).
% 3.60/2.73 tff(5170,plain,
% 3.60/2.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a607) | c0_1(a633) | c3_1(a633) | (~c2_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a607)) | (~c1_1(a633))))),
% 3.60/2.73 inference(monotonicity,[status(thm)],[5169])).
% 3.60/2.73 tff(5171,plain,
% 3.60/2.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a607) | c0_1(a633) | c3_1(a633) | (~c2_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a607)) | (~c1_1(a633)))),
% 3.60/2.73 inference(transitivity,[status(thm)],[5170, 5168])).
% 3.60/2.73 tff(5172,plain,
% 3.60/2.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))),
% 3.60/2.73 inference(quant_inst,[status(thm)],[])).
% 3.60/2.73 tff(5173,plain,
% 3.60/2.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a607) | c0_1(a633) | c3_1(a633) | (~c2_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a607)) | (~c1_1(a633))),
% 3.60/2.73 inference(modus_ponens,[status(thm)],[5172, 5171])).
% 3.60/2.73 tff(5174,plain,
% 3.60/2.73 (~c0_1(a607)),
% 3.60/2.73 inference(unit_resolution,[status(thm)],[5173, 107, 5083, 33, 5167, 5166, 3981, 3980, 4653, 5165, 258])).
% 3.60/2.73 tff(5175,plain,
% 3.60/2.73 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c3_1(a607) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c3_1(a607) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607))),
% 3.60/2.73 inference(rewrite,[status(thm)],[])).
% 3.60/2.73 tff(5176,plain,
% 3.60/2.73 ((hskp2 | (~ndr1_0) | c1_1(a607) | c3_1(a607) | (~c2_1(a607)) | c3_1(a607) | c1_1(a607) | c0_1(a607)) <=> (hskp2 | c3_1(a607) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607))),
% 3.60/2.73 inference(rewrite,[status(thm)],[])).
% 3.60/2.73 tff(5177,plain,
% 3.60/2.73 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a607) | c3_1(a607) | (~c2_1(a607)) | c3_1(a607) | c1_1(a607) | c0_1(a607))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c3_1(a607) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607)))),
% 3.60/2.73 inference(monotonicity,[status(thm)],[5176])).
% 3.60/2.73 tff(5178,plain,
% 3.60/2.73 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a607) | c3_1(a607) | (~c2_1(a607)) | c3_1(a607) | c1_1(a607) | c0_1(a607))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c3_1(a607) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607))),
% 3.60/2.73 inference(transitivity,[status(thm)],[5177, 5175])).
% 3.60/2.73 tff(5179,plain,
% 3.60/2.73 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a607) | c3_1(a607) | (~c2_1(a607)) | c3_1(a607) | c1_1(a607) | c0_1(a607))),
% 3.60/2.73 inference(quant_inst,[status(thm)],[])).
% 3.60/2.73 tff(5180,plain,
% 3.60/2.73 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c3_1(a607) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607)),
% 3.60/2.73 inference(modus_ponens,[status(thm)],[5179, 5178])).
% 3.60/2.73 tff(5181,plain,
% 3.60/2.73 (hskp2 | c0_1(a607)),
% 3.60/2.73 inference(unit_resolution,[status(thm)],[5180, 107, 33, 66, 4653, 200])).
% 3.60/2.73 tff(5182,plain,
% 3.60/2.73 (hskp2),
% 3.60/2.73 inference(unit_resolution,[status(thm)],[5181, 5174])).
% 3.60/2.73 tff(5183,plain,
% 3.60/2.73 (~c3_1(a586)),
% 3.60/2.73 inference(unit_resolution,[status(thm)],[218, 5182])).
% 3.60/2.73 tff(5184,plain,
% 3.60/2.73 (c2_1(a586)),
% 3.60/2.73 inference(unit_resolution,[status(thm)],[1474, 5182])).
% 3.60/2.73 tff(5185,plain,
% 3.60/2.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a633) | c3_1(a633) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a633) | c3_1(a633) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a633)))),
% 3.60/2.73 inference(rewrite,[status(thm)],[])).
% 3.60/2.73 tff(5186,plain,
% 3.60/2.73 (((~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633))) <=> (c0_1(a633) | c3_1(a633) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a633)))),
% 3.60/2.73 inference(rewrite,[status(thm)],[])).
% 3.60/2.73 tff(5187,plain,
% 3.60/2.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a633) | c3_1(a633) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a633))))),
% 3.60/2.73 inference(monotonicity,[status(thm)],[5186])).
% 3.60/2.73 tff(5188,plain,
% 3.60/2.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a633) | c3_1(a633) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a633)))),
% 3.60/2.73 inference(transitivity,[status(thm)],[5187, 5185])).
% 3.60/2.73 tff(5189,plain,
% 3.60/2.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a633) | c0_1(a633) | (~c1_1(a633)))),
% 3.60/2.73 inference(quant_inst,[status(thm)],[])).
% 3.60/2.73 tff(5190,plain,
% 3.60/2.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a633) | c3_1(a633) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a633))),
% 3.60/2.73 inference(modus_ponens,[status(thm)],[5189, 5188])).
% 3.60/2.73 tff(5191,plain,
% 3.60/2.73 (~c0_1(a586)),
% 3.60/2.73 inference(unit_resolution,[status(thm)],[5190, 107, 5083, 5167, 5166, 5184, 3981, 3980, 5165, 5183, 258])).
% 3.60/2.73 tff(5192,plain,
% 3.60/2.73 (c1_1(a586)),
% 3.60/2.73 inference(unit_resolution,[status(thm)],[229, 5182])).
% 3.60/2.73 tff(5193,plain,
% 3.60/2.73 (hskp28),
% 3.60/2.73 inference(unit_resolution,[status(thm)],[3240, 107, 5167, 5166, 5192, 5184, 5165, 5183, 1748])).
% 3.60/2.73 tff(5194,plain,
% 3.60/2.73 (c2_1(a612)),
% 3.60/2.73 inference(unit_resolution,[status(thm)],[1150, 5193])).
% 3.60/2.73 tff(5195,plain,
% 3.60/2.73 (c1_1(a612)),
% 3.60/2.73 inference(unit_resolution,[status(thm)],[1435, 5193])).
% 3.60/2.73 tff(5196,plain,
% 3.60/2.73 (~hskp12),
% 3.60/2.73 inference(unit_resolution,[status(thm)],[4342, 5166, 5083, 5167, 3981, 3980, 5165])).
% 3.60/2.73 tff(5197,plain,
% 3.60/2.73 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586) | (~c1_1(a612)) | (~c0_1(a612)) | (~c2_1(a612)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586) | (~c1_1(a612)) | (~c0_1(a612)) | (~c2_1(a612)))),
% 3.60/2.73 inference(rewrite,[status(thm)],[])).
% 3.60/2.73 tff(5198,plain,
% 3.60/2.73 ((hskp12 | (~ndr1_0) | (~c2_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a586) | (~c1_1(a586)) | (~c2_1(a586))) <=> (hskp12 | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586) | (~c1_1(a612)) | (~c0_1(a612)) | (~c2_1(a612)))),
% 3.60/2.73 inference(rewrite,[status(thm)],[])).
% 3.60/2.73 tff(5199,plain,
% 3.60/2.73 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586) | (~c1_1(a612)) | (~c0_1(a612)) | (~c2_1(a612))))),
% 3.60/2.73 inference(monotonicity,[status(thm)],[5198])).
% 3.60/2.73 tff(5200,plain,
% 3.60/2.73 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586) | (~c1_1(a612)) | (~c0_1(a612)) | (~c2_1(a612)))),
% 3.60/2.73 inference(transitivity,[status(thm)],[5199, 5197])).
% 3.60/2.73 tff(5201,plain,
% 3.60/2.73 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a586) | (~c1_1(a586)) | (~c2_1(a586)))),
% 3.60/2.73 inference(quant_inst,[status(thm)],[])).
% 3.60/2.73 tff(5202,plain,
% 3.60/2.73 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586) | (~c1_1(a612)) | (~c0_1(a612)) | (~c2_1(a612))),
% 3.60/2.73 inference(modus_ponens,[status(thm)],[5201, 5200])).
% 3.60/2.73 tff(5203,plain,
% 3.60/2.73 (~c0_1(a612)),
% 3.60/2.73 inference(unit_resolution,[status(thm)],[5202, 107, 5196, 5195, 5194, 5192, 5184, 2727, 5191])).
% 3.60/2.73 tff(5204,plain,
% 3.60/2.73 (c3_1(a612)),
% 3.60/2.73 inference(unit_resolution,[status(thm)],[1139, 5193])).
% 3.60/2.73 tff(5205,plain,
% 3.60/2.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a633) | c3_1(a633) | c1_1(a599) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c3_1(a599)) | (~c2_1(a599)) | c2_1(a633))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a633) | c3_1(a633) | c1_1(a599) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c3_1(a599)) | (~c2_1(a599)) | c2_1(a633))),
% 3.60/2.73 inference(rewrite,[status(thm)],[])).
% 3.60/2.73 tff(5206,plain,
% 3.60/2.73 (((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c3_1(a633) | c0_1(a633) | c2_1(a633)) <=> (c0_1(a633) | c3_1(a633) | c1_1(a599) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c3_1(a599)) | (~c2_1(a599)) | c2_1(a633))),
% 3.60/2.73 inference(rewrite,[status(thm)],[])).
% 3.60/2.73 tff(5207,plain,
% 3.60/2.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c3_1(a633) | c0_1(a633) | c2_1(a633))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a633) | c3_1(a633) | c1_1(a599) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c3_1(a599)) | (~c2_1(a599)) | c2_1(a633)))),
% 3.60/2.73 inference(monotonicity,[status(thm)],[5206])).
% 3.60/2.73 tff(5208,plain,
% 3.60/2.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c3_1(a633) | c0_1(a633) | c2_1(a633))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a633) | c3_1(a633) | c1_1(a599) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c3_1(a599)) | (~c2_1(a599)) | c2_1(a633))),
% 3.60/2.73 inference(transitivity,[status(thm)],[5207, 5205])).
% 3.60/2.73 tff(5209,plain,
% 3.60/2.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c3_1(a633) | c0_1(a633) | c2_1(a633))),
% 3.60/2.73 inference(quant_inst,[status(thm)],[])).
% 3.60/2.73 tff(5210,plain,
% 3.60/2.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c0_1(a633) | c3_1(a633) | c1_1(a599) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c3_1(a599)) | (~c2_1(a599)) | c2_1(a633)),
% 3.60/2.73 inference(modus_ponens,[status(thm)],[5209, 5208])).
% 3.60/2.73 tff(5211,plain,
% 3.60/2.73 (c2_1(a633)),
% 3.60/2.73 inference(unit_resolution,[status(thm)],[5210, 107, 5194, 5204, 5167, 5166, 3981, 3980, 5165, 1730, 5203])).
% 3.60/2.73 tff(5212,assumption,(hskp8), introduced(assumption)).
% 3.60/2.73 tff(5213,plain,
% 3.60/2.73 (c3_1(a593)),
% 3.60/2.73 inference(unit_resolution,[status(thm)],[511, 5212])).
% 3.62/2.73 tff(5214,plain,
% 3.62/2.73 (c1_1(a593)),
% 3.62/2.73 inference(unit_resolution,[status(thm)],[522, 5212])).
% 3.62/2.73 tff(5215,plain,
% 3.62/2.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | c0_1(a607))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | c0_1(a607))),
% 3.62/2.73 inference(rewrite,[status(thm)],[])).
% 3.62/2.73 tff(5216,plain,
% 3.62/2.73 (((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607))) <=> (c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | c0_1(a607))),
% 3.62/2.74 inference(rewrite,[status(thm)],[])).
% 3.62/2.74 tff(5217,plain,
% 3.62/2.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | c0_1(a607)))),
% 3.62/2.74 inference(monotonicity,[status(thm)],[5216])).
% 3.62/2.74 tff(5218,plain,
% 3.62/2.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | c0_1(a607))),
% 3.62/2.74 inference(transitivity,[status(thm)],[5217, 5215])).
% 3.62/2.74 tff(5219,plain,
% 3.62/2.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607)))),
% 3.62/2.74 inference(quant_inst,[status(thm)],[])).
% 3.62/2.74 tff(5220,plain,
% 3.62/2.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | c0_1(a607)),
% 3.62/2.74 inference(modus_ponens,[status(thm)],[5219, 5218])).
% 3.62/2.74 tff(5221,plain,
% 3.62/2.74 (~c0_1(a593)),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[5220, 107, 1884, 1883, 5214, 5213, 66, 4653, 65, 1, 1880])).
% 3.62/2.74 tff(5222,plain,
% 3.62/2.74 (~c2_1(a593)),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[555, 5212])).
% 3.62/2.74 tff(5223,plain,
% 3.62/2.74 (hskp3),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[5154, 107, 4654, 5214, 5213, 5222, 3420])).
% 3.62/2.74 tff(5224,plain,
% 3.62/2.74 (~c1_1(a587)),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[939, 5223])).
% 3.62/2.74 tff(5225,plain,
% 3.62/2.74 (c2_1(a587)),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[950, 5223])).
% 3.62/2.74 tff(5226,plain,
% 3.62/2.74 (c0_1(a587)),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[961, 5223])).
% 3.62/2.74 tff(5227,plain,
% 3.62/2.74 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c2_1(a593) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a593) | (~c1_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c2_1(a593) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a593) | (~c1_1(a593)))),
% 3.62/2.74 inference(rewrite,[status(thm)],[])).
% 3.62/2.74 tff(5228,plain,
% 3.62/2.74 ((hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593))) <=> (hskp17 | c2_1(a593) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a593) | (~c1_1(a593)))),
% 3.62/2.74 inference(rewrite,[status(thm)],[])).
% 3.62/2.74 tff(5229,plain,
% 3.62/2.74 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c2_1(a593) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a593) | (~c1_1(a593))))),
% 3.62/2.74 inference(monotonicity,[status(thm)],[5228])).
% 3.62/2.74 tff(5230,plain,
% 3.62/2.74 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c2_1(a593) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a593) | (~c1_1(a593)))),
% 3.62/2.74 inference(transitivity,[status(thm)],[5229, 5227])).
% 3.62/2.74 tff(5231,plain,
% 3.62/2.74 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)))),
% 3.62/2.74 inference(quant_inst,[status(thm)],[])).
% 3.62/2.74 tff(5232,plain,
% 3.62/2.74 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c2_1(a593) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c0_1(a593) | (~c1_1(a593))),
% 3.62/2.74 inference(modus_ponens,[status(thm)],[5231, 5230])).
% 3.62/2.74 tff(5233,plain,
% 3.62/2.74 ($false),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[5232, 107, 4654, 5214, 5226, 5225, 5222, 5224, 32, 5221])).
% 3.62/2.74 tff(5234,plain,((~hskp8) | (~c2_1(a612)) | (~c3_1(a612)) | c1_1(a607) | c0_1(a607) | c0_1(a612)), inference(lemma,lemma(discharge,[]))).
% 3.62/2.74 tff(5235,plain,
% 3.62/2.74 (~hskp8),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[5234, 5194, 5204, 66, 5174, 5203])).
% 3.62/2.74 tff(5236,plain,
% 3.62/2.74 (hskp26),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[787, 5235, 5196])).
% 3.62/2.74 tff(5237,plain,
% 3.62/2.74 (c2_1(a583)),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[391, 5236])).
% 3.62/2.74 tff(5238,plain,
% 3.62/2.74 (c1_1(a583)),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[351, 5236])).
% 3.62/2.74 tff(5239,plain,
% 3.62/2.74 (c0_1(a583)),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[362, 5236])).
% 3.62/2.74 tff(5240,plain,
% 3.62/2.74 ($false),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[3998, 107, 5196, 5239, 5238, 5237, 5083, 3981, 2727, 5211])).
% 3.62/2.74 tff(5241,plain,(c0_1(a633) | c1_1(a607) | c3_1(a633) | c3_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.62/2.74 tff(5242,plain,
% 3.62/2.74 (c0_1(a633)),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[5241, 3980, 66, 33])).
% 3.62/2.74 tff(5243,plain,
% 3.62/2.74 (~hskp22),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[3968, 5242])).
% 3.62/2.74 tff(5244,plain,
% 3.62/2.74 (hskp2),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[5181, 1])).
% 3.62/2.74 tff(5245,plain,
% 3.62/2.74 (~c3_1(a586)),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[218, 5244])).
% 3.62/2.74 tff(5246,plain,
% 3.62/2.74 (hskp4 | c3_1(a583)),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[3328, 107, 4654, 3321, 3322, 55])).
% 3.62/2.74 tff(5247,plain,
% 3.62/2.74 (c3_1(a583)),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[5246, 830])).
% 3.62/2.74 tff(5248,plain,
% 3.62/2.74 (hskp10),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[3497, 5247])).
% 3.62/2.74 tff(5249,plain,
% 3.62/2.74 (~c1_1(a598)),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[911, 5248])).
% 3.62/2.74 tff(5250,plain,
% 3.62/2.74 (c3_1(a598)),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[881, 5248])).
% 3.62/2.74 tff(5251,plain,
% 3.62/2.74 (c0_1(a598)),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[892, 5248])).
% 3.62/2.74 tff(5252,plain,
% 3.62/2.74 (hskp23),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[1688, 1638, 107, 5251, 5250, 5249, 1648])).
% 3.62/2.74 tff(5253,plain,
% 3.62/2.74 (~c1_1(a636)),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[475, 5252])).
% 3.62/2.74 tff(5254,plain,
% 3.62/2.74 (~c0_1(a636)),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[481, 5252])).
% 3.62/2.74 tff(5255,plain,
% 3.62/2.74 (c3_1(a636)),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[492, 5252])).
% 3.62/2.74 tff(5256,plain,
% 3.62/2.74 (~c2_1(a636)),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[3348, 5255, 3322, 5247, 5254, 5253, 3321])).
% 3.62/2.74 tff(5257,plain,
% 3.62/2.74 (hskp15),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[4629, 5247, 3321, 3322, 3330])).
% 3.62/2.74 tff(5258,plain,
% 3.62/2.74 (~c0_1(a604)),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[1591, 5257])).
% 3.62/2.74 tff(5259,plain,
% 3.62/2.74 (c1_1(a604)),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[1613, 5257])).
% 3.62/2.74 tff(5260,plain,
% 3.62/2.74 (c2_1(a604)),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[3120, 107, 4654, 5259, 4813, 4812, 5258, 4807, 32])).
% 3.62/2.74 tff(5261,plain,
% 3.62/2.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a604) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | (~c2_1(a604)) | (~c1_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a604) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | (~c2_1(a604)) | (~c1_1(a604)))),
% 3.62/2.74 inference(rewrite,[status(thm)],[])).
% 3.62/2.74 tff(5262,plain,
% 3.62/2.74 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604))) <=> (c0_1(a604) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | (~c2_1(a604)) | (~c1_1(a604)))),
% 3.62/2.74 inference(rewrite,[status(thm)],[])).
% 3.62/2.74 tff(5263,plain,
% 3.62/2.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a604) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | (~c2_1(a604)) | (~c1_1(a604))))),
% 3.62/2.74 inference(monotonicity,[status(thm)],[5262])).
% 3.62/2.74 tff(5264,plain,
% 3.62/2.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a604) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | (~c2_1(a604)) | (~c1_1(a604)))),
% 3.62/2.74 inference(transitivity,[status(thm)],[5263, 5261])).
% 3.62/2.74 tff(5265,plain,
% 3.62/2.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))),
% 3.62/2.74 inference(quant_inst,[status(thm)],[])).
% 3.62/2.74 tff(5266,plain,
% 3.62/2.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a604) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | (~c2_1(a604)) | (~c1_1(a604))),
% 3.62/2.74 inference(modus_ponens,[status(thm)],[5265, 5264])).
% 3.62/2.74 tff(5267,plain,
% 3.62/2.74 (c2_1(a598) | (~c2_1(a604))),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[5266, 107, 2318, 2317, 2316, 5259, 5250, 5258, 5249, 11])).
% 3.62/2.74 tff(5268,plain,
% 3.62/2.74 (c2_1(a598)),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[5267, 5260])).
% 3.62/2.74 tff(5269,plain,
% 3.62/2.74 ($false),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[3516, 107, 5255, 5259, 5251, 5250, 5253, 5258, 11, 5268, 5260, 5256])).
% 3.62/2.74 tff(5270,plain,(hskp4 | (~c0_1(a678)) | (~c2_1(a678)) | (~c3_1(a678)) | hskp11 | c3_1(a607) | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.62/2.74 tff(5271,plain,
% 3.62/2.74 (hskp4),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[5270, 1638, 2281, 2270, 2292, 33, 66])).
% 3.62/2.74 tff(5272,plain,
% 3.62/2.74 (hskp6),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[147, 5271, 44])).
% 3.62/2.74 tff(5273,plain,
% 3.62/2.74 (~c0_1(a590)),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[666, 5272])).
% 3.62/2.74 tff(5274,plain,
% 3.62/2.74 (~c2_1(a588)),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[121, 5271])).
% 3.62/2.74 tff(5275,plain,
% 3.62/2.74 (~c1_1(a588)),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[127, 5271])).
% 3.62/2.74 tff(5276,plain,
% 3.62/2.74 (c0_1(a588)),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[138, 5271])).
% 3.62/2.74 tff(5277,plain,
% 3.62/2.74 (hskp21),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[5114, 1638, 107, 5276, 5275, 5274, 5104])).
% 3.62/2.74 tff(5278,plain,
% 3.62/2.74 (~c3_1(a629)),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[4846, 5277])).
% 3.62/2.74 tff(5279,plain,
% 3.62/2.74 (~c2_1(a629)),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[4852, 5277])).
% 3.62/2.74 tff(5280,plain,
% 3.62/2.74 (c3_1(a590)),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[677, 5272])).
% 3.62/2.74 tff(5281,plain,
% 3.62/2.74 (c2_1(a590)),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[688, 5272])).
% 3.62/2.74 tff(5282,plain,
% 3.62/2.74 (c0_1(a629)),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[4870, 5277])).
% 3.62/2.74 tff(5283,plain,
% 3.62/2.74 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | c2_1(a629) | c3_1(a629) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a629)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c2_1(a629) | c3_1(a629) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a629)))),
% 3.62/2.74 inference(rewrite,[status(thm)],[])).
% 3.62/2.74 tff(5284,plain,
% 3.62/2.74 ((hskp16 | (~ndr1_0) | c2_1(a629) | c3_1(a629) | (~c0_1(a629)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590))) <=> (hskp16 | c2_1(a629) | c3_1(a629) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a629)))),
% 3.62/2.74 inference(rewrite,[status(thm)],[])).
% 3.62/2.74 tff(5285,plain,
% 3.62/2.74 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a629) | c3_1(a629) | (~c0_1(a629)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | c2_1(a629) | c3_1(a629) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a629))))),
% 3.62/2.74 inference(monotonicity,[status(thm)],[5284])).
% 3.62/2.74 tff(5286,plain,
% 3.62/2.74 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a629) | c3_1(a629) | (~c0_1(a629)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c2_1(a629) | c3_1(a629) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a629)))),
% 3.62/2.74 inference(transitivity,[status(thm)],[5285, 5283])).
% 3.62/2.74 tff(5287,plain,
% 3.62/2.74 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a629) | c3_1(a629) | (~c0_1(a629)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)))),
% 3.62/2.74 inference(quant_inst,[status(thm)],[])).
% 3.62/2.74 tff(5288,plain,
% 3.62/2.74 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c2_1(a629) | c3_1(a629) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a629))),
% 3.62/2.74 inference(modus_ponens,[status(thm)],[5287, 5286])).
% 3.62/2.74 tff(5289,plain,
% 3.62/2.74 (hskp16),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[5288, 107, 5282, 5281, 5280, 5279, 5278, 5273, 2125])).
% 3.62/2.74 tff(5290,plain,
% 3.62/2.74 (~c3_1(a606)),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[1075, 5289])).
% 3.62/2.74 tff(5291,plain,
% 3.62/2.74 (~c2_1(a606)),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[1111, 5289])).
% 3.62/2.74 tff(5292,plain,
% 3.62/2.74 (c0_1(a606)),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[2336, 1638, 107, 2292, 2281, 2270, 5291, 5290, 268])).
% 3.62/2.74 tff(5293,plain,
% 3.62/2.74 (c1_1(a606)),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[1088, 5289])).
% 3.62/2.74 tff(5294,plain,
% 3.62/2.74 (hskp0 | (~c0_1(a606))),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[2354, 1638, 107, 5293, 5291, 2347])).
% 3.62/2.74 tff(5295,plain,
% 3.62/2.74 (hskp0),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[5294, 5292])).
% 3.62/2.74 tff(5296,plain,
% 3.62/2.74 (c1_1(a678)),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[3804, 5295, 4654, 2281, 2292])).
% 3.62/2.74 tff(5297,plain,
% 3.62/2.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a607))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a607))),
% 3.62/2.74 inference(rewrite,[status(thm)],[])).
% 3.62/2.74 tff(5298,plain,
% 3.62/2.74 (((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607))) <=> (c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a607))),
% 3.62/2.74 inference(rewrite,[status(thm)],[])).
% 3.62/2.74 tff(5299,plain,
% 3.62/2.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a607)))),
% 3.62/2.74 inference(monotonicity,[status(thm)],[5298])).
% 3.62/2.74 tff(5300,plain,
% 3.62/2.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a607))),
% 3.62/2.74 inference(transitivity,[status(thm)],[5299, 5297])).
% 3.62/2.74 tff(5301,plain,
% 3.62/2.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607)))),
% 3.62/2.74 inference(quant_inst,[status(thm)],[])).
% 3.62/2.74 tff(5302,plain,
% 3.62/2.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a607)),
% 3.62/2.74 inference(modus_ponens,[status(thm)],[5301, 5300])).
% 3.62/2.74 tff(5303,plain,
% 3.62/2.74 ((~c1_1(a678)) | c0_1(a607)),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[5302, 107, 2292, 2270, 5281, 5280, 66, 4653, 5273, 65])).
% 3.62/2.74 tff(5304,plain,
% 3.62/2.74 (c0_1(a607)),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[5303, 5296])).
% 3.62/2.74 tff(5305,plain,
% 3.62/2.74 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | c3_1(a607) | c2_1(a629) | c3_1(a629) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c0_1(a629)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c3_1(a607) | c2_1(a629) | c3_1(a629) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c0_1(a629)))),
% 3.62/2.74 inference(rewrite,[status(thm)],[])).
% 3.62/2.74 tff(5306,plain,
% 3.62/2.74 ((hskp8 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a629) | c2_1(a629) | (~c0_1(a629))) <=> (hskp8 | c3_1(a607) | c2_1(a629) | c3_1(a629) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c0_1(a629)))),
% 3.62/2.74 inference(rewrite,[status(thm)],[])).
% 3.62/2.74 tff(5307,plain,
% 3.62/2.74 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a629) | c2_1(a629) | (~c0_1(a629)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | c3_1(a607) | c2_1(a629) | c3_1(a629) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c0_1(a629))))),
% 3.62/2.74 inference(monotonicity,[status(thm)],[5306])).
% 3.62/2.74 tff(5308,plain,
% 3.62/2.74 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a629) | c2_1(a629) | (~c0_1(a629)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c3_1(a607) | c2_1(a629) | c3_1(a629) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c0_1(a629)))),
% 3.62/2.74 inference(transitivity,[status(thm)],[5307, 5305])).
% 3.62/2.74 tff(5309,plain,
% 3.62/2.74 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a629) | c2_1(a629) | (~c0_1(a629)))),
% 3.62/2.74 inference(quant_inst,[status(thm)],[])).
% 3.62/2.74 tff(5310,plain,
% 3.62/2.74 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c3_1(a607) | c2_1(a629) | c3_1(a629) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c0_1(a629))),
% 3.62/2.74 inference(modus_ponens,[status(thm)],[5309, 5308])).
% 3.62/2.74 tff(5311,plain,
% 3.62/2.74 (hskp8 | (~c0_1(a607))),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[5310, 107, 5282, 33, 5279, 5278, 4653, 4271])).
% 3.62/2.74 tff(5312,plain,
% 3.62/2.74 (hskp8),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[5311, 5304])).
% 3.62/2.74 tff(5313,plain,
% 3.62/2.74 (~c2_1(a593)),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[555, 5312])).
% 3.62/2.74 tff(5314,plain,
% 3.62/2.74 (~c0_1(a584)),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[1051, 5295])).
% 3.62/2.74 tff(5315,plain,
% 3.62/2.74 (c1_1(a584)),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[1062, 5295])).
% 3.62/2.74 tff(5316,plain,
% 3.62/2.74 (~c2_1(a584)),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[1045, 5295])).
% 3.62/2.74 tff(5317,plain,
% 3.62/2.74 (c1_1(a593)),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[522, 5312])).
% 3.62/2.74 tff(5318,plain,
% 3.62/2.74 (c3_1(a593)),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[511, 5312])).
% 3.62/2.74 tff(5319,plain,
% 3.62/2.74 ($false),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[5161, 5318, 5317, 4654, 5316, 5315, 5314, 5313])).
% 3.62/2.74 tff(5320,plain,(hskp11 | c3_1(a607) | c1_1(a607) | hskp22), inference(lemma,lemma(discharge,[]))).
% 3.62/2.74 tff(5321,plain,
% 3.62/2.74 (hskp11),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[5320, 5243, 66, 33])).
% 3.62/2.74 tff(5322,plain,
% 3.62/2.74 (~c1_1(a599)),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[428, 5321])).
% 3.62/2.74 tff(5323,plain,
% 3.62/2.74 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | (~c0_1(a633)) | c3_1(a633) | (~ndr1_0) | (~c1_1(a633)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp4 | (~c0_1(a633)) | c3_1(a633) | (~ndr1_0) | (~c1_1(a633)))),
% 3.62/2.74 inference(rewrite,[status(thm)],[])).
% 3.62/2.74 tff(5324,plain,
% 3.62/2.74 ((hskp17 | hskp4 | (~ndr1_0) | c3_1(a633) | (~c1_1(a633)) | (~c0_1(a633))) <=> (hskp17 | hskp4 | (~c0_1(a633)) | c3_1(a633) | (~ndr1_0) | (~c1_1(a633)))),
% 3.62/2.74 inference(rewrite,[status(thm)],[])).
% 3.62/2.74 tff(5325,plain,
% 3.62/2.74 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c3_1(a633) | (~c1_1(a633)) | (~c0_1(a633)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | (~c0_1(a633)) | c3_1(a633) | (~ndr1_0) | (~c1_1(a633))))),
% 3.62/2.74 inference(monotonicity,[status(thm)],[5324])).
% 3.62/2.74 tff(5326,plain,
% 3.62/2.74 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c3_1(a633) | (~c1_1(a633)) | (~c0_1(a633)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp4 | (~c0_1(a633)) | c3_1(a633) | (~ndr1_0) | (~c1_1(a633)))),
% 3.62/2.74 inference(transitivity,[status(thm)],[5325, 5323])).
% 3.62/2.74 tff(5327,plain,
% 3.62/2.74 ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c3_1(a633) | (~c1_1(a633)) | (~c0_1(a633)))),
% 3.62/2.74 inference(quant_inst,[status(thm)],[])).
% 3.62/2.74 tff(5328,plain,
% 3.62/2.74 ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp4 | (~c0_1(a633)) | c3_1(a633) | (~ndr1_0) | (~c1_1(a633))),
% 3.62/2.74 inference(modus_ponens,[status(thm)],[5327, 5326])).
% 3.62/2.74 tff(5329,plain,
% 3.62/2.74 (hskp4 | (~c0_1(a633)) | (~c1_1(a633))),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[5328, 107, 4654, 3980, 55])).
% 3.62/2.74 tff(5330,plain,
% 3.62/2.74 (~c1_1(a633)),
% 3.62/2.74 inference(unit_resolution,[status(thm)],[5329, 830, 5242])).
% 3.62/2.74 tff(5331,plain,
% 3.62/2.74 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a633) | c3_1(a633) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a633))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a633) | c3_1(a633) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a633))),
% 3.62/2.74 inference(rewrite,[status(thm)],[])).
% 3.62/2.74 tff(5332,plain,
% 3.62/2.74 ((hskp26 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a633) | c1_1(a633) | c2_1(a633)) <=> (hskp26 | c1_1(a633) | c3_1(a633) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a633))),
% 3.62/2.74 inference(rewrite,[status(thm)],[])).
% 3.62/2.74 tff(5333,plain,
% 3.62/2.74 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a633) | c1_1(a633) | c2_1(a633))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a633) | c3_1(a633) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a633)))),
% 3.62/2.74 inference(monotonicity,[status(thm)],[5332])).
% 3.62/2.74 tff(5334,plain,
% 3.62/2.74 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a633) | c1_1(a633) | c2_1(a633))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a633) | c3_1(a633) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a633))),
% 3.62/2.74 inference(transitivity,[status(thm)],[5333, 5331])).
% 3.62/2.74 tff(5335,plain,
% 3.62/2.74 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a587) | (~c2_1(a587)) | (~c0_1(a587)) | c3_1(a633) | c1_1(a633) | c2_1(a633))),
% 3.62/2.74 inference(quant_inst,[status(thm)],[])).
% 3.62/2.74 tff(5336,plain,
% 3.62/2.74 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a633) | c3_1(a633) | c1_1(a587) | (~ndr1_0) | (~c2_1(a587)) | (~c0_1(a587)) | c2_1(a633)),
% 3.62/2.75 inference(modus_ponens,[status(thm)],[5335, 5334])).
% 3.62/2.75 tff(5337,plain,
% 3.62/2.75 (c2_1(a633)),
% 3.62/2.75 inference(unit_resolution,[status(thm)],[5336, 726, 107, 5330, 4813, 4812, 3980, 4807, 995])).
% 3.62/2.75 tff(5338,assumption,(hskp2), introduced(assumption)).
% 3.62/2.75 tff(5339,plain,
% 3.62/2.75 (~c3_1(a586)),
% 3.62/2.75 inference(unit_resolution,[status(thm)],[218, 5338])).
% 3.62/2.75 tff(5340,plain,
% 3.62/2.75 (hskp11),
% 3.62/2.75 inference(unit_resolution,[status(thm)],[5320, 44, 66, 33])).
% 3.62/2.75 tff(5341,plain,
% 3.62/2.75 (~c1_1(a599)),
% 3.62/2.75 inference(unit_resolution,[status(thm)],[428, 5340])).
% 3.62/2.75 tff(5342,plain,
% 3.62/2.75 (c3_1(a599)),
% 3.62/2.75 inference(unit_resolution,[status(thm)],[422, 5340])).
% 3.62/2.75 tff(5343,plain,
% 3.62/2.75 (c2_1(a599)),
% 3.62/2.75 inference(unit_resolution,[status(thm)],[439, 5340])).
% 3.62/2.75 tff(5344,plain,
% 3.62/2.75 (c1_1(a586)),
% 3.62/2.75 inference(unit_resolution,[status(thm)],[229, 5338])).
% 3.62/2.75 tff(5345,plain,
% 3.62/2.75 (c2_1(a586)),
% 3.62/2.75 inference(unit_resolution,[status(thm)],[1474, 5338])).
% 3.62/2.75 tff(5346,plain,
% 3.62/2.75 ($false),
% 3.62/2.75 inference(unit_resolution,[status(thm)],[4879, 5345, 5344, 44, 830, 726, 5343, 5342, 5341, 5339, 33, 66])).
% 3.62/2.75 tff(5347,plain,((~hskp2) | hskp22 | hskp4 | hskp26 | c3_1(a607) | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.62/2.75 tff(5348,plain,
% 3.62/2.75 (~hskp2),
% 3.62/2.75 inference(unit_resolution,[status(thm)],[5347, 830, 5243, 726, 33, 66])).
% 3.62/2.75 tff(5349,plain,
% 3.62/2.75 (c0_1(a607)),
% 3.62/2.75 inference(unit_resolution,[status(thm)],[5181, 5348])).
% 3.62/2.75 tff(5350,plain,
% 3.62/2.75 (c3_1(a599)),
% 3.62/2.75 inference(unit_resolution,[status(thm)],[422, 5321])).
% 3.62/2.75 tff(5351,plain,
% 3.62/2.75 (c2_1(a599)),
% 3.62/2.75 inference(unit_resolution,[status(thm)],[439, 5321])).
% 3.62/2.75 tff(5352,assumption,(hskp7), introduced(assumption)).
% 3.62/2.75 tff(5353,plain,
% 3.62/2.75 (~c3_1(a592)),
% 3.62/2.75 inference(unit_resolution,[status(thm)],[811, 5352])).
% 3.62/2.75 tff(5354,plain,
% 3.62/2.75 (~c0_1(a592)),
% 3.62/2.75 inference(unit_resolution,[status(thm)],[817, 5352])).
% 3.62/2.75 tff(5355,assumption,(c2_1(a607)), introduced(assumption)).
% 3.62/2.75 tff(5356,plain,
% 3.62/2.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a607) | (~c2_1(a607)) | c1_1(a599) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a607) | (~c2_1(a607)) | c1_1(a599) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a607)))),
% 3.62/2.75 inference(rewrite,[status(thm)],[])).
% 3.62/2.75 tff(5357,plain,
% 3.62/2.75 (((~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a592) | c0_1(a592) | (~c1_1(a592))) <=> (c3_1(a607) | (~c2_1(a607)) | c1_1(a599) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a607)))),
% 3.62/2.75 inference(rewrite,[status(thm)],[])).
% 3.62/2.75 tff(5358,plain,
% 3.62/2.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a592) | c0_1(a592) | (~c1_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a607) | (~c2_1(a607)) | c1_1(a599) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a607))))),
% 3.62/2.75 inference(monotonicity,[status(thm)],[5357])).
% 3.62/2.75 tff(5359,plain,
% 3.62/2.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a592) | c0_1(a592) | (~c1_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a607) | (~c2_1(a607)) | c1_1(a599) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a607)))),
% 3.62/2.75 inference(transitivity,[status(thm)],[5358, 5356])).
% 3.62/2.75 tff(5360,plain,
% 3.62/2.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a592) | c0_1(a592) | (~c1_1(a592)))),
% 3.62/2.75 inference(quant_inst,[status(thm)],[])).
% 3.62/2.75 tff(5361,plain,
% 3.62/2.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a607) | (~c2_1(a607)) | c1_1(a599) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a607))),
% 3.62/2.75 inference(modus_ponens,[status(thm)],[5360, 5359])).
% 3.62/2.75 tff(5362,plain,
% 3.62/2.75 (~c1_1(a592)),
% 3.62/2.75 inference(unit_resolution,[status(thm)],[5361, 107, 33, 463, 462, 5355, 461, 5354, 5353, 258, 2486])).
% 3.62/2.75 tff(5363,plain,
% 3.62/2.75 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a633) | c3_1(a633) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | (~c2_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a633) | c3_1(a633) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | (~c2_1(a633)))),
% 3.62/2.75 inference(rewrite,[status(thm)],[])).
% 3.62/2.75 tff(5364,plain,
% 3.62/2.75 ((hskp2 | (~ndr1_0) | c1_1(a633) | c3_1(a633) | (~c2_1(a633)) | c3_1(a592) | c1_1(a592) | c0_1(a592)) <=> (hskp2 | c1_1(a633) | c3_1(a633) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | (~c2_1(a633)))),
% 3.62/2.75 inference(rewrite,[status(thm)],[])).
% 3.62/2.75 tff(5365,plain,
% 3.62/2.75 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a633) | c3_1(a633) | (~c2_1(a633)) | c3_1(a592) | c1_1(a592) | c0_1(a592))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a633) | c3_1(a633) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | (~c2_1(a633))))),
% 3.62/2.75 inference(monotonicity,[status(thm)],[5364])).
% 3.62/2.75 tff(5366,plain,
% 3.62/2.75 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a633) | c3_1(a633) | (~c2_1(a633)) | c3_1(a592) | c1_1(a592) | c0_1(a592))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a633) | c3_1(a633) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | (~c2_1(a633)))),
% 3.62/2.75 inference(transitivity,[status(thm)],[5365, 5363])).
% 3.62/2.75 tff(5367,plain,
% 3.62/2.75 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a633) | c3_1(a633) | (~c2_1(a633)) | c3_1(a592) | c1_1(a592) | c0_1(a592))),
% 3.62/2.75 inference(quant_inst,[status(thm)],[])).
% 3.62/2.75 tff(5368,plain,
% 3.62/2.75 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a633) | c3_1(a633) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | (~c2_1(a633))),
% 3.62/2.75 inference(modus_ponens,[status(thm)],[5367, 5366])).
% 3.62/2.75 tff(5369,plain,
% 3.62/2.75 ($false),
% 3.62/2.75 inference(unit_resolution,[status(thm)],[5368, 107, 1797, 4655, 3980, 5354, 5353, 200, 5362, 4290])).
% 3.62/2.75 tff(5370,plain,((~hskp7) | hskp2 | c1_1(a633) | c3_1(a633) | (~c2_1(a633)) | c3_1(a607) | (~c2_1(a599)) | (~c3_1(a599)) | (~c2_1(a607)) | c1_1(a599) | (~c0_1(a607))), inference(lemma,lemma(discharge,[]))).
% 3.62/2.75 tff(5371,plain,
% 3.62/2.75 (~hskp7),
% 3.62/2.75 inference(unit_resolution,[status(thm)],[5370, 5348, 5330, 3980, 5337, 33, 5351, 5350, 4653, 5322, 5349])).
% 3.62/2.75 tff(5372,plain,
% 3.62/2.75 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | c3_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | hskp7 | c3_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)))),
% 3.62/2.75 inference(rewrite,[status(thm)],[])).
% 3.62/2.75 tff(5373,plain,
% 3.62/2.75 ((hskp20 | hskp7 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607))) <=> (hskp20 | hskp7 | c3_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)))),
% 3.62/2.75 inference(rewrite,[status(thm)],[])).
% 3.62/2.75 tff(5374,plain,
% 3.62/2.75 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | c3_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607))))),
% 3.62/2.75 inference(monotonicity,[status(thm)],[5373])).
% 3.62/2.75 tff(5375,plain,
% 3.62/2.75 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | hskp7 | c3_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)))),
% 3.62/2.75 inference(transitivity,[status(thm)],[5374, 5372])).
% 3.62/2.75 tff(5376,plain,
% 3.62/2.75 ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)))),
% 3.62/2.75 inference(quant_inst,[status(thm)],[])).
% 3.62/2.75 tff(5377,plain,
% 3.62/2.75 ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | hskp7 | c3_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607))),
% 3.62/2.75 inference(modus_ponens,[status(thm)],[5376, 5375])).
% 3.62/2.75 tff(5378,plain,
% 3.62/2.75 (hskp20 | hskp7 | c3_1(a607) | (~c0_1(a607))),
% 3.62/2.75 inference(unit_resolution,[status(thm)],[5377, 107, 4653, 1382])).
% 3.62/2.75 tff(5379,plain,
% 3.62/2.75 (hskp20),
% 3.62/2.75 inference(unit_resolution,[status(thm)],[5378, 5371, 33, 5349])).
% 3.62/2.75 tff(5380,plain,
% 3.62/2.75 (~c3_1(a623)),
% 3.62/2.75 inference(unit_resolution,[status(thm)],[709, 5379])).
% 3.62/2.75 tff(5381,plain,
% 3.62/2.75 (~c2_1(a623)),
% 3.62/2.75 inference(unit_resolution,[status(thm)],[715, 5379])).
% 3.62/2.75 tff(5382,plain,
% 3.62/2.75 (~c1_1(a623)),
% 3.62/2.75 inference(unit_resolution,[status(thm)],[721, 5379])).
% 3.62/2.75 tff(5383,plain,
% 3.62/2.75 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a633) | (~c0_1(a633)) | c1_1(a623) | c2_1(a623) | c3_1(a623) | (~ndr1_0) | (~c2_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a633) | (~c0_1(a633)) | c1_1(a623) | c2_1(a623) | c3_1(a623) | (~ndr1_0) | (~c2_1(a633)))),
% 3.62/2.75 inference(rewrite,[status(thm)],[])).
% 3.62/2.75 tff(5384,plain,
% 3.62/2.75 ((hskp26 | (~ndr1_0) | c1_1(a633) | (~c2_1(a633)) | (~c0_1(a633)) | c3_1(a623) | c1_1(a623) | c2_1(a623)) <=> (hskp26 | c1_1(a633) | (~c0_1(a633)) | c1_1(a623) | c2_1(a623) | c3_1(a623) | (~ndr1_0) | (~c2_1(a633)))),
% 3.62/2.75 inference(rewrite,[status(thm)],[])).
% 3.62/2.75 tff(5385,plain,
% 3.62/2.75 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a633) | (~c2_1(a633)) | (~c0_1(a633)) | c3_1(a623) | c1_1(a623) | c2_1(a623))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a633) | (~c0_1(a633)) | c1_1(a623) | c2_1(a623) | c3_1(a623) | (~ndr1_0) | (~c2_1(a633))))),
% 3.62/2.75 inference(monotonicity,[status(thm)],[5384])).
% 3.62/2.75 tff(5386,plain,
% 3.62/2.75 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a633) | (~c2_1(a633)) | (~c0_1(a633)) | c3_1(a623) | c1_1(a623) | c2_1(a623))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a633) | (~c0_1(a633)) | c1_1(a623) | c2_1(a623) | c3_1(a623) | (~ndr1_0) | (~c2_1(a633)))),
% 3.62/2.75 inference(transitivity,[status(thm)],[5385, 5383])).
% 3.62/2.75 tff(5387,plain,
% 3.62/2.75 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a633) | (~c2_1(a633)) | (~c0_1(a633)) | c3_1(a623) | c1_1(a623) | c2_1(a623))),
% 3.62/2.75 inference(quant_inst,[status(thm)],[])).
% 3.62/2.75 tff(5388,plain,
% 3.62/2.75 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a633) | (~c0_1(a633)) | c1_1(a623) | c2_1(a623) | c3_1(a623) | (~ndr1_0) | (~c2_1(a633))),
% 3.62/2.75 inference(modus_ponens,[status(thm)],[5387, 5386])).
% 3.62/2.75 tff(5389,plain,
% 3.62/2.75 ($false),
% 3.62/2.75 inference(unit_resolution,[status(thm)],[5388, 726, 107, 5330, 5242, 5382, 5381, 5380, 995, 5337])).
% 3.62/2.75 tff(5390,plain,(hskp4 | hskp26 | c3_1(a607) | c3_1(a633) | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.62/2.75 tff(5391,plain,
% 3.62/2.75 (hskp4),
% 3.62/2.75 inference(unit_resolution,[status(thm)],[5390, 726, 33, 3980, 66])).
% 3.62/2.75 tff(5392,plain,
% 3.62/2.75 (~c2_1(a588)),
% 3.62/2.75 inference(unit_resolution,[status(thm)],[121, 5391])).
% 3.62/2.75 tff(5393,plain,
% 3.62/2.75 (~c1_1(a588)),
% 3.62/2.75 inference(unit_resolution,[status(thm)],[127, 5391])).
% 3.62/2.75 tff(5394,plain,
% 3.62/2.75 (c0_1(a588)),
% 3.62/2.75 inference(unit_resolution,[status(thm)],[138, 5391])).
% 3.62/2.75 tff(5395,plain,
% 3.62/2.75 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c3_1(a607) | (~c2_1(a607)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c0_1(a607))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a607) | (~c2_1(a607)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c0_1(a607))),
% 3.62/2.75 inference(rewrite,[status(thm)],[])).
% 3.62/2.75 tff(5396,plain,
% 3.62/2.75 ((hskp14 | (~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588)) | c3_1(a607) | c0_1(a607) | (~c2_1(a607))) <=> (hskp14 | c3_1(a607) | (~c2_1(a607)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c0_1(a607))),
% 3.62/2.75 inference(rewrite,[status(thm)],[])).
% 3.62/2.75 tff(5397,plain,
% 3.62/2.75 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588)) | c3_1(a607) | c0_1(a607) | (~c2_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c3_1(a607) | (~c2_1(a607)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c0_1(a607)))),
% 3.62/2.75 inference(monotonicity,[status(thm)],[5396])).
% 3.62/2.75 tff(5398,plain,
% 3.62/2.75 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588)) | c3_1(a607) | c0_1(a607) | (~c2_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a607) | (~c2_1(a607)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c0_1(a607))),
% 3.62/2.75 inference(transitivity,[status(thm)],[5397, 5395])).
% 3.62/2.75 tff(5399,plain,
% 3.62/2.75 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a588) | c1_1(a588) | (~c0_1(a588)) | c3_1(a607) | c0_1(a607) | (~c2_1(a607)))),
% 3.62/2.75 inference(quant_inst,[status(thm)],[])).
% 3.62/2.75 tff(5400,plain,
% 3.62/2.75 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a607) | (~c2_1(a607)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c0_1(a607)),
% 3.62/2.75 inference(modus_ponens,[status(thm)],[5399, 5398])).
% 3.62/2.75 tff(5401,plain,
% 3.62/2.75 (hskp14 | c0_1(a607)),
% 3.62/2.75 inference(unit_resolution,[status(thm)],[5400, 107, 33, 5394, 4653, 5393, 5392, 305])).
% 3.62/2.75 tff(5402,plain,
% 3.62/2.75 (hskp14),
% 3.62/2.75 inference(unit_resolution,[status(thm)],[5401, 1])).
% 3.62/2.75 tff(5403,plain,
% 3.62/2.75 (hskp6),
% 3.62/2.75 inference(unit_resolution,[status(thm)],[147, 5391, 5243])).
% 3.62/2.75 tff(5404,plain,
% 3.62/2.75 (~c0_1(a590)),
% 3.62/2.75 inference(unit_resolution,[status(thm)],[666, 5403])).
% 3.62/2.75 tff(5405,plain,
% 3.62/2.75 (c3_1(a590)),
% 3.62/2.75 inference(unit_resolution,[status(thm)],[677, 5403])).
% 3.62/2.75 tff(5406,plain,
% 3.62/2.75 (c2_1(a590)),
% 3.62/2.75 inference(unit_resolution,[status(thm)],[688, 5403])).
% 3.62/2.75 tff(5407,plain,
% 3.62/2.75 (hskp29),
% 3.62/2.75 inference(unit_resolution,[status(thm)],[2258, 5243])).
% 3.62/2.75 tff(5408,plain,
% 3.62/2.75 (c3_1(a678)),
% 3.62/2.75 inference(unit_resolution,[status(thm)],[2269, 5407])).
% 3.62/2.75 tff(5409,plain,
% 3.62/2.75 (c0_1(a678)),
% 3.62/2.75 inference(unit_resolution,[status(thm)],[2291, 5407])).
% 3.62/2.75 tff(5410,plain,
% 3.62/2.75 ((~c1_1(a678)) | c0_1(a607)),
% 3.62/2.75 inference(unit_resolution,[status(thm)],[5302, 107, 5409, 5408, 5406, 5405, 66, 4653, 5404, 65])).
% 3.62/2.75 tff(5411,plain,
% 3.62/2.75 (~c1_1(a678)),
% 3.62/2.75 inference(unit_resolution,[status(thm)],[5410, 1])).
% 3.62/2.75 tff(5412,plain,
% 3.62/2.75 (c2_1(a678)),
% 3.62/2.75 inference(unit_resolution,[status(thm)],[2280, 5407])).
% 3.62/2.75 tff(5413,plain,
% 3.62/2.75 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c2_1(a633))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c2_1(a633))),
% 3.62/2.75 inference(rewrite,[status(thm)],[])).
% 3.62/2.75 tff(5414,plain,
% 3.62/2.75 ((hskp26 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c3_1(a633) | c1_1(a633) | c2_1(a633)) <=> (hskp26 | c1_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c2_1(a633))),
% 3.62/2.75 inference(rewrite,[status(thm)],[])).
% 3.62/2.75 tff(5415,plain,
% 3.62/2.75 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c3_1(a633) | c1_1(a633) | c2_1(a633))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c2_1(a633)))),
% 3.62/2.75 inference(monotonicity,[status(thm)],[5414])).
% 3.62/2.75 tff(5416,plain,
% 3.62/2.75 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c3_1(a633) | c1_1(a633) | c2_1(a633))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c2_1(a633))),
% 3.62/2.75 inference(transitivity,[status(thm)],[5415, 5413])).
% 3.62/2.75 tff(5417,plain,
% 3.62/2.75 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c3_1(a633) | c1_1(a633) | c2_1(a633))),
% 3.62/2.75 inference(quant_inst,[status(thm)],[])).
% 3.62/2.75 tff(5418,plain,
% 3.62/2.75 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a633) | c3_1(a633) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c2_1(a633)),
% 3.62/2.75 inference(modus_ponens,[status(thm)],[5417, 5416])).
% 3.62/2.75 tff(5419,plain,
% 3.62/2.75 (c2_1(a633)),
% 3.62/2.75 inference(unit_resolution,[status(thm)],[5418, 726, 107, 5409, 5412, 4655, 3980, 995, 5411])).
% 3.62/2.75 tff(5420,plain,
% 3.62/2.75 (c1_1(a586)),
% 3.62/2.75 inference(unit_resolution,[status(thm)],[229, 5244])).
% 3.62/2.75 tff(5421,plain,
% 3.62/2.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~c0_1(a633)) | c3_1(a633) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a633)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (~c0_1(a633)) | c3_1(a633) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a633)))),
% 3.62/2.75 inference(rewrite,[status(thm)],[])).
% 3.62/2.75 tff(5422,plain,
% 3.62/2.75 (((~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c0_1(a633)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586))) <=> ((~c0_1(a633)) | c3_1(a633) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a633)))),
% 3.62/2.75 inference(rewrite,[status(thm)],[])).
% 3.62/2.75 tff(5423,plain,
% 3.62/2.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c0_1(a633)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~c0_1(a633)) | c3_1(a633) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a633))))),
% 3.62/2.75 inference(monotonicity,[status(thm)],[5422])).
% 3.62/2.75 tff(5424,plain,
% 3.62/2.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c0_1(a633)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (~c0_1(a633)) | c3_1(a633) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a633)))),
% 3.62/2.75 inference(transitivity,[status(thm)],[5423, 5421])).
% 3.62/2.75 tff(5425,plain,
% 3.62/2.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c0_1(a633)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))),
% 3.62/2.75 inference(quant_inst,[status(thm)],[])).
% 3.62/2.75 tff(5426,plain,
% 3.62/2.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (~c0_1(a633)) | c3_1(a633) | c1_1(a599) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a633))),
% 3.62/2.75 inference(modus_ponens,[status(thm)],[5425, 5424])).
% 3.62/2.75 tff(5427,plain,
% 3.62/2.75 (c0_1(a586)),
% 3.62/2.75 inference(unit_resolution,[status(thm)],[5426, 107, 5351, 5350, 5420, 5242, 3980, 5322, 5245, 258, 5419])).
% 3.62/2.75 tff(5428,plain,
% 3.62/2.75 (c2_1(a586)),
% 3.62/2.75 inference(unit_resolution,[status(thm)],[1474, 5244])).
% 3.62/2.75 tff(5429,plain,
% 3.62/2.75 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | c1_1(a588) | c2_1(a588) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c0_1(a588)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a588) | c2_1(a588) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c0_1(a588)))),
% 3.62/2.75 inference(rewrite,[status(thm)],[])).
% 3.62/2.75 tff(5430,plain,
% 3.62/2.75 ((hskp1 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c1_1(a588) | c2_1(a588) | (~c0_1(a588))) <=> (hskp1 | c1_1(a588) | c2_1(a588) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c0_1(a588)))),
% 3.62/2.75 inference(rewrite,[status(thm)],[])).
% 3.62/2.75 tff(5431,plain,
% 3.62/2.75 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c1_1(a588) | c2_1(a588) | (~c0_1(a588)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | c1_1(a588) | c2_1(a588) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c0_1(a588))))),
% 3.62/2.75 inference(monotonicity,[status(thm)],[5430])).
% 3.62/2.75 tff(5432,plain,
% 3.62/2.75 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c1_1(a588) | c2_1(a588) | (~c0_1(a588)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a588) | c2_1(a588) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c0_1(a588)))),
% 3.62/2.76 inference(transitivity,[status(thm)],[5431, 5429])).
% 3.62/2.76 tff(5433,plain,
% 3.62/2.76 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c1_1(a588) | c2_1(a588) | (~c0_1(a588)))),
% 3.62/2.76 inference(quant_inst,[status(thm)],[])).
% 3.62/2.76 tff(5434,plain,
% 3.62/2.76 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp1 | c1_1(a588) | c2_1(a588) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c0_1(a588))),
% 3.62/2.76 inference(modus_ponens,[status(thm)],[5433, 5432])).
% 3.62/2.76 tff(5435,plain,
% 3.62/2.76 (hskp1),
% 3.62/2.76 inference(unit_resolution,[status(thm)],[5434, 107, 5394, 5428, 5393, 5392, 5245, 1237, 5427])).
% 3.62/2.76 tff(5436,plain,
% 3.62/2.76 (~c0_1(a585)),
% 3.62/2.76 inference(unit_resolution,[status(thm)],[1250, 5435])).
% 3.62/2.76 tff(5437,plain,
% 3.62/2.76 (c2_1(a585)),
% 3.62/2.76 inference(unit_resolution,[status(thm)],[1261, 5435])).
% 3.62/2.76 tff(5438,plain,
% 3.62/2.76 (c1_1(a585)),
% 3.62/2.76 inference(unit_resolution,[status(thm)],[1272, 5435])).
% 3.62/2.76 tff(5439,plain,
% 3.62/2.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a588) | c2_1(a588) | c0_1(a585) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a588)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a588) | c2_1(a588) | c0_1(a585) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a588)))),
% 3.62/2.76 inference(rewrite,[status(thm)],[])).
% 3.62/2.76 tff(5440,plain,
% 3.62/2.76 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a588) | c2_1(a588) | (~c3_1(a588)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585))) <=> (c1_1(a588) | c2_1(a588) | c0_1(a585) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a588)))),
% 3.62/2.76 inference(rewrite,[status(thm)],[])).
% 3.62/2.76 tff(5441,plain,
% 3.62/2.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a588) | c2_1(a588) | (~c3_1(a588)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a588) | c2_1(a588) | c0_1(a585) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a588))))),
% 3.62/2.76 inference(monotonicity,[status(thm)],[5440])).
% 3.62/2.76 tff(5442,plain,
% 3.62/2.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a588) | c2_1(a588) | (~c3_1(a588)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a588) | c2_1(a588) | c0_1(a585) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a588)))),
% 3.62/2.76 inference(transitivity,[status(thm)],[5441, 5439])).
% 3.62/2.76 tff(5443,plain,
% 3.62/2.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a588) | c2_1(a588) | (~c3_1(a588)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))),
% 3.62/2.76 inference(quant_inst,[status(thm)],[])).
% 3.62/2.76 tff(5444,plain,
% 3.62/2.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a588) | c2_1(a588) | c0_1(a585) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a585)) | (~c1_1(a585)) | (~c3_1(a588))),
% 3.62/2.76 inference(modus_ponens,[status(thm)],[5443, 5442])).
% 3.62/2.76 tff(5445,plain,
% 3.62/2.76 (~c3_1(a588)),
% 3.62/2.76 inference(unit_resolution,[status(thm)],[5444, 107, 5409, 5412, 5408, 5438, 5437, 5393, 5392, 5436, 11])).
% 3.62/2.76 tff(5446,plain,
% 3.62/2.76 (hskp28),
% 3.62/2.76 inference(unit_resolution,[status(thm)],[2820, 107, 5412, 5408, 5420, 5428, 5245, 1748, 5411])).
% 3.62/2.76 tff(5447,plain,
% 3.62/2.76 (c3_1(a612)),
% 3.62/2.76 inference(unit_resolution,[status(thm)],[1139, 5446])).
% 3.62/2.76 tff(5448,plain,
% 3.62/2.76 (c2_1(a612)),
% 3.62/2.76 inference(unit_resolution,[status(thm)],[1150, 5446])).
% 3.62/2.76 tff(5449,plain,
% 3.62/2.76 (c1_1(a612)),
% 3.62/2.76 inference(unit_resolution,[status(thm)],[1435, 5446])).
% 3.62/2.76 tff(5450,plain,
% 3.62/2.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a607))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a607))),
% 3.62/2.76 inference(rewrite,[status(thm)],[])).
% 3.62/2.76 tff(5451,plain,
% 3.62/2.76 (((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607))) <=> (c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a607))),
% 3.62/2.76 inference(rewrite,[status(thm)],[])).
% 3.62/2.76 tff(5452,plain,
% 3.62/2.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a607)))),
% 3.62/2.76 inference(monotonicity,[status(thm)],[5451])).
% 3.62/2.76 tff(5453,plain,
% 3.62/2.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a607))),
% 3.62/2.76 inference(transitivity,[status(thm)],[5452, 5450])).
% 3.62/2.76 tff(5454,plain,
% 3.62/2.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607)))),
% 3.62/2.76 inference(quant_inst,[status(thm)],[])).
% 3.62/2.76 tff(5455,plain,
% 3.62/2.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a607)),
% 3.62/2.76 inference(modus_ponens,[status(thm)],[5454, 5453])).
% 3.62/2.76 tff(5456,plain,
% 3.62/2.76 (~c0_1(a612)),
% 3.62/2.76 inference(unit_resolution,[status(thm)],[5455, 107, 5449, 5447, 5406, 5405, 66, 4653, 5404, 65, 1])).
% 3.62/2.76 tff(5457,plain,
% 3.62/2.76 (~hskp8),
% 3.62/2.76 inference(unit_resolution,[status(thm)],[5234, 5456, 1, 66, 5448, 5447])).
% 3.62/2.76 tff(5458,plain,
% 3.62/2.76 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~c0_1(a633)) | c3_1(a633) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c2_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | (~c0_1(a633)) | c3_1(a633) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c2_1(a633)))),
% 3.62/2.76 inference(rewrite,[status(thm)],[])).
% 3.62/2.76 tff(5459,plain,
% 3.62/2.76 ((hskp8 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c0_1(a633)) | c3_1(a588) | c2_1(a588) | (~c0_1(a588))) <=> (hskp8 | (~c0_1(a633)) | c3_1(a633) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c2_1(a633)))),
% 3.62/2.76 inference(rewrite,[status(thm)],[])).
% 3.62/2.76 tff(5460,plain,
% 3.62/2.76 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c0_1(a633)) | c3_1(a588) | c2_1(a588) | (~c0_1(a588)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~c0_1(a633)) | c3_1(a633) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c2_1(a633))))),
% 3.62/2.76 inference(monotonicity,[status(thm)],[5459])).
% 3.62/2.76 tff(5461,plain,
% 3.62/2.76 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c0_1(a633)) | c3_1(a588) | c2_1(a588) | (~c0_1(a588)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | (~c0_1(a633)) | c3_1(a633) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c2_1(a633)))),
% 3.62/2.76 inference(transitivity,[status(thm)],[5460, 5458])).
% 3.62/2.76 tff(5462,plain,
% 3.62/2.76 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c0_1(a633)) | c3_1(a588) | c2_1(a588) | (~c0_1(a588)))),
% 3.62/2.76 inference(quant_inst,[status(thm)],[])).
% 3.62/2.76 tff(5463,plain,
% 3.62/2.76 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | (~c0_1(a633)) | c3_1(a633) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c2_1(a633))),
% 3.62/2.76 inference(modus_ponens,[status(thm)],[5462, 5461])).
% 3.62/2.76 tff(5464,plain,
% 3.62/2.76 ($false),
% 3.62/2.76 inference(unit_resolution,[status(thm)],[5463, 107, 5457, 5394, 5242, 3980, 5392, 4271, 5419, 5445])).
% 3.62/2.76 tff(5465,plain,(c0_1(a607) | c3_1(a633) | c1_1(a607) | hskp26 | c1_1(a633) | c3_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.62/2.76 tff(5466,plain,
% 3.62/2.76 (c0_1(a607)),
% 3.62/2.76 inference(unit_resolution,[status(thm)],[5465, 4655, 66, 726, 3980, 33])).
% 3.62/2.76 tff(5467,plain,
% 3.62/2.76 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | c3_1(a607) | (~c2_1(a607)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp1 | c3_1(a607) | (~c2_1(a607)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c0_1(a607)))),
% 3.62/2.76 inference(rewrite,[status(thm)],[])).
% 3.62/2.76 tff(5468,plain,
% 3.62/2.76 ((hskp1 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a588) | c2_1(a588) | (~c0_1(a588))) <=> (hskp1 | c3_1(a607) | (~c2_1(a607)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c0_1(a607)))),
% 3.62/2.76 inference(rewrite,[status(thm)],[])).
% 3.62/2.76 tff(5469,plain,
% 3.62/2.76 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a588) | c2_1(a588) | (~c0_1(a588)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | c3_1(a607) | (~c2_1(a607)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c0_1(a607))))),
% 3.62/2.76 inference(monotonicity,[status(thm)],[5468])).
% 3.62/2.76 tff(5470,plain,
% 3.62/2.76 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a588) | c2_1(a588) | (~c0_1(a588)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp1 | c3_1(a607) | (~c2_1(a607)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c0_1(a607)))),
% 3.62/2.76 inference(transitivity,[status(thm)],[5469, 5467])).
% 3.62/2.76 tff(5471,plain,
% 3.62/2.76 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a588) | c2_1(a588) | (~c0_1(a588)))),
% 3.62/2.76 inference(quant_inst,[status(thm)],[])).
% 3.62/2.76 tff(5472,plain,
% 3.62/2.76 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp1 | c3_1(a607) | (~c2_1(a607)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | (~c0_1(a607))),
% 3.62/2.76 inference(modus_ponens,[status(thm)],[5471, 5470])).
% 3.62/2.76 tff(5473,plain,
% 3.62/2.76 (hskp1 | (~c0_1(a607))),
% 3.62/2.76 inference(unit_resolution,[status(thm)],[5472, 107, 33, 5394, 4653, 5393, 5392, 1237])).
% 3.62/2.76 tff(5474,plain,
% 3.62/2.76 (hskp1),
% 3.62/2.76 inference(unit_resolution,[status(thm)],[5473, 5466])).
% 3.62/2.76 tff(5475,plain,
% 3.62/2.76 (~c0_1(a585)),
% 3.62/2.76 inference(unit_resolution,[status(thm)],[1250, 5474])).
% 3.62/2.76 tff(5476,plain,
% 3.62/2.76 (c2_1(a585)),
% 3.62/2.76 inference(unit_resolution,[status(thm)],[1261, 5474])).
% 3.62/2.76 tff(5477,plain,
% 3.62/2.76 (c1_1(a585)),
% 3.62/2.76 inference(unit_resolution,[status(thm)],[1272, 5474])).
% 3.62/2.76 tff(5478,plain,
% 3.62/2.76 (~c3_1(a588)),
% 3.62/2.76 inference(unit_resolution,[status(thm)],[5444, 107, 5409, 5412, 5408, 5477, 5476, 5393, 5392, 5475, 11])).
% 3.62/2.76 tff(5479,plain,
% 3.62/2.76 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a633) | c3_1(a633) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | c2_1(a633))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a633) | c3_1(a633) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | c2_1(a633))),
% 3.62/2.76 inference(rewrite,[status(thm)],[])).
% 3.62/2.76 tff(5480,plain,
% 3.62/2.76 ((hskp26 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a633) | c1_1(a633) | c2_1(a633)) <=> (hskp26 | c1_1(a633) | c3_1(a633) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | c2_1(a633))),
% 3.62/2.76 inference(rewrite,[status(thm)],[])).
% 3.62/2.76 tff(5481,plain,
% 3.62/2.76 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a633) | c1_1(a633) | c2_1(a633))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a633) | c3_1(a633) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | c2_1(a633)))),
% 3.62/2.76 inference(monotonicity,[status(thm)],[5480])).
% 3.62/2.76 tff(5482,plain,
% 3.62/2.76 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a633) | c1_1(a633) | c2_1(a633))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a633) | c3_1(a633) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | c2_1(a633))),
% 3.62/2.76 inference(transitivity,[status(thm)],[5481, 5479])).
% 3.62/2.76 tff(5483,plain,
% 3.62/2.76 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a633) | c1_1(a633) | c2_1(a633))),
% 3.62/2.76 inference(quant_inst,[status(thm)],[])).
% 3.62/2.76 tff(5484,plain,
% 3.62/2.76 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a633) | c3_1(a633) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | c2_1(a633)),
% 3.62/2.76 inference(modus_ponens,[status(thm)],[5483, 5482])).
% 3.62/2.76 tff(5485,plain,
% 3.62/2.76 (hskp26 | c1_1(a633) | (~c0_1(a607)) | c2_1(a633)),
% 3.62/2.76 inference(unit_resolution,[status(thm)],[5484, 107, 3980, 66, 4653, 995])).
% 3.62/2.76 tff(5486,plain,
% 3.62/2.76 (c2_1(a633)),
% 3.62/2.76 inference(unit_resolution,[status(thm)],[5485, 5466, 726, 4655])).
% 3.62/2.76 tff(5487,plain,
% 3.62/2.76 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a633) | (~c0_1(a633)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | c3_1(a588) | (~c2_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a633) | (~c0_1(a633)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | c3_1(a588) | (~c2_1(a633)))),
% 3.62/2.76 inference(rewrite,[status(thm)],[])).
% 3.62/2.76 tff(5488,plain,
% 3.62/2.76 ((hskp26 | (~ndr1_0) | c1_1(a633) | (~c2_1(a633)) | (~c0_1(a633)) | c3_1(a588) | c1_1(a588) | c2_1(a588)) <=> (hskp26 | c1_1(a633) | (~c0_1(a633)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | c3_1(a588) | (~c2_1(a633)))),
% 3.62/2.76 inference(rewrite,[status(thm)],[])).
% 3.62/2.76 tff(5489,plain,
% 3.62/2.76 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a633) | (~c2_1(a633)) | (~c0_1(a633)) | c3_1(a588) | c1_1(a588) | c2_1(a588))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a633) | (~c0_1(a633)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | c3_1(a588) | (~c2_1(a633))))),
% 3.62/2.76 inference(monotonicity,[status(thm)],[5488])).
% 3.62/2.76 tff(5490,plain,
% 3.62/2.76 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a633) | (~c2_1(a633)) | (~c0_1(a633)) | c3_1(a588) | c1_1(a588) | c2_1(a588))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a633) | (~c0_1(a633)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | c3_1(a588) | (~c2_1(a633)))),
% 3.62/2.76 inference(transitivity,[status(thm)],[5489, 5487])).
% 3.62/2.76 tff(5491,plain,
% 3.62/2.76 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a633) | (~c2_1(a633)) | (~c0_1(a633)) | c3_1(a588) | c1_1(a588) | c2_1(a588))),
% 3.62/2.76 inference(quant_inst,[status(thm)],[])).
% 3.62/2.76 tff(5492,plain,
% 3.62/2.76 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a633) | (~c0_1(a633)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | c3_1(a588) | (~c2_1(a633))),
% 3.62/2.76 inference(modus_ponens,[status(thm)],[5491, 5490])).
% 3.62/2.76 tff(5493,plain,
% 3.62/2.76 ($false),
% 3.62/2.76 inference(unit_resolution,[status(thm)],[5492, 726, 107, 4655, 5242, 5393, 5392, 995, 5486, 5478])).
% 3.62/2.76 tff(5494,plain,(c1_1(a633) | hskp26 | c3_1(a607) | c3_1(a633) | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.62/2.76 tff(5495,plain,
% 3.62/2.76 (c1_1(a633)),
% 3.62/2.76 inference(unit_resolution,[status(thm)],[5494, 726, 33, 3980, 66])).
% 3.62/2.76 tff(5496,plain,
% 3.62/2.76 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | (~c0_1(a633)) | c3_1(a633) | (~ndr1_0) | (~c1_1(a633)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp3 | (~c0_1(a633)) | c3_1(a633) | (~ndr1_0) | (~c1_1(a633)))),
% 3.62/2.76 inference(rewrite,[status(thm)],[])).
% 3.62/2.76 tff(5497,plain,
% 3.62/2.76 ((hskp17 | hskp3 | (~ndr1_0) | c3_1(a633) | (~c1_1(a633)) | (~c0_1(a633))) <=> (hskp17 | hskp3 | (~c0_1(a633)) | c3_1(a633) | (~ndr1_0) | (~c1_1(a633)))),
% 3.62/2.76 inference(rewrite,[status(thm)],[])).
% 3.62/2.76 tff(5498,plain,
% 3.62/2.76 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c3_1(a633) | (~c1_1(a633)) | (~c0_1(a633)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | (~c0_1(a633)) | c3_1(a633) | (~ndr1_0) | (~c1_1(a633))))),
% 3.62/2.76 inference(monotonicity,[status(thm)],[5497])).
% 3.62/2.76 tff(5499,plain,
% 3.62/2.76 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c3_1(a633) | (~c1_1(a633)) | (~c0_1(a633)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp3 | (~c0_1(a633)) | c3_1(a633) | (~ndr1_0) | (~c1_1(a633)))),
% 3.62/2.76 inference(transitivity,[status(thm)],[5498, 5496])).
% 3.62/2.76 tff(5500,plain,
% 3.62/2.76 ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c3_1(a633) | (~c1_1(a633)) | (~c0_1(a633)))),
% 3.62/2.76 inference(quant_inst,[status(thm)],[])).
% 3.62/2.76 tff(5501,plain,
% 3.62/2.76 ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp3 | (~c0_1(a633)) | c3_1(a633) | (~ndr1_0) | (~c1_1(a633))),
% 3.62/2.76 inference(modus_ponens,[status(thm)],[5500, 5499])).
% 3.62/2.76 tff(5502,plain,
% 3.62/2.76 (hskp3 | (~c0_1(a633)) | (~c1_1(a633))),
% 3.62/2.76 inference(unit_resolution,[status(thm)],[5501, 107, 4654, 3980, 2368])).
% 3.62/2.76 tff(5503,plain,
% 3.62/2.76 (hskp3),
% 3.62/2.76 inference(unit_resolution,[status(thm)],[5502, 5495, 5242])).
% 3.62/2.76 tff(5504,plain,
% 3.62/2.76 (c0_1(a587)),
% 3.62/2.76 inference(unit_resolution,[status(thm)],[961, 5503])).
% 3.62/2.76 tff(5505,plain,
% 3.62/2.76 (~c1_1(a587)),
% 3.62/2.76 inference(unit_resolution,[status(thm)],[939, 5503])).
% 3.62/2.76 tff(5506,plain,
% 3.62/2.76 (c2_1(a587)),
% 3.62/2.76 inference(unit_resolution,[status(thm)],[950, 5503])).
% 3.62/2.76 tff(5507,plain,
% 3.62/2.76 (c0_1(a586)),
% 3.62/2.76 inference(unit_resolution,[status(thm)],[4817, 5420, 5351, 5506, 5505, 5504, 5350, 5402, 5322, 5245, 726])).
% 3.62/2.76 tff(5508,plain,
% 3.62/2.76 (hskp1),
% 3.62/2.76 inference(unit_resolution,[status(thm)],[5434, 107, 5394, 5428, 5393, 5392, 5245, 1237, 5507])).
% 3.62/2.76 tff(5509,plain,
% 3.62/2.76 (~c0_1(a585)),
% 3.62/2.76 inference(unit_resolution,[status(thm)],[1250, 5508])).
% 3.62/2.76 tff(5510,plain,
% 3.62/2.76 (c2_1(a585)),
% 3.62/2.76 inference(unit_resolution,[status(thm)],[1261, 5508])).
% 3.62/2.76 tff(5511,plain,
% 3.62/2.76 (c1_1(a585)),
% 3.62/2.76 inference(unit_resolution,[status(thm)],[1272, 5508])).
% 3.62/2.76 tff(5512,plain,
% 3.62/2.76 (~c3_1(a588)),
% 3.62/2.76 inference(unit_resolution,[status(thm)],[5444, 107, 5409, 5412, 5408, 5511, 5510, 5393, 5392, 5509, 11])).
% 3.62/2.76 tff(5513,plain,
% 3.62/2.76 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~c0_1(a633)) | c3_1(a633) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | c2_1(a633))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | (~c0_1(a633)) | c3_1(a633) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | c2_1(a633))),
% 3.62/2.76 inference(rewrite,[status(thm)],[])).
% 3.62/2.76 tff(5514,plain,
% 3.62/2.76 ((hskp8 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c3_1(a633) | c2_1(a633) | (~c0_1(a633))) <=> (hskp8 | (~c0_1(a633)) | c3_1(a633) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | c2_1(a633))),
% 3.62/2.76 inference(rewrite,[status(thm)],[])).
% 3.62/2.76 tff(5515,plain,
% 3.62/2.76 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c3_1(a633) | c2_1(a633) | (~c0_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~c0_1(a633)) | c3_1(a633) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | c2_1(a633)))),
% 3.62/2.76 inference(monotonicity,[status(thm)],[5514])).
% 3.62/2.76 tff(5516,plain,
% 3.62/2.76 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c3_1(a633) | c2_1(a633) | (~c0_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | (~c0_1(a633)) | c3_1(a633) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | c2_1(a633))),
% 3.62/2.76 inference(transitivity,[status(thm)],[5515, 5513])).
% 3.62/2.76 tff(5517,plain,
% 3.62/2.76 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c3_1(a633) | c2_1(a633) | (~c0_1(a633)))),
% 3.62/2.76 inference(quant_inst,[status(thm)],[])).
% 3.62/2.76 tff(5518,plain,
% 3.62/2.76 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | (~c0_1(a633)) | c3_1(a633) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | c2_1(a633)),
% 3.62/2.76 inference(modus_ponens,[status(thm)],[5517, 5516])).
% 3.62/2.76 tff(5519,plain,
% 3.62/2.76 (hskp8 | c2_1(a633)),
% 3.62/2.76 inference(unit_resolution,[status(thm)],[5518, 107, 5428, 5242, 3980, 5245, 4271, 5507])).
% 3.62/2.76 tff(5520,plain,
% 3.62/2.76 (c2_1(a633)),
% 3.62/2.76 inference(unit_resolution,[status(thm)],[5519, 5457])).
% 3.62/2.76 tff(5521,plain,
% 3.62/2.76 ($false),
% 3.62/2.76 inference(unit_resolution,[status(thm)],[5463, 107, 5457, 5394, 5242, 3980, 5392, 4271, 5520, 5512])).
% 3.62/2.76 tff(5522,plain,(c0_1(a607) | c3_1(a633) | c1_1(a607) | hskp26 | c3_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.62/2.76 tff(5523,plain,
% 3.62/2.76 (c0_1(a607)),
% 3.62/2.76 inference(unit_resolution,[status(thm)],[5522, 726, 66, 3980, 33])).
% 3.62/2.76 tff(5524,plain,
% 3.62/2.76 (hskp1),
% 3.62/2.76 inference(unit_resolution,[status(thm)],[5473, 5523])).
% 3.62/2.76 tff(5525,plain,
% 3.62/2.76 (~c0_1(a585)),
% 3.62/2.76 inference(unit_resolution,[status(thm)],[1250, 5524])).
% 3.62/2.76 tff(5526,plain,
% 3.62/2.76 (c2_1(a585)),
% 3.62/2.76 inference(unit_resolution,[status(thm)],[1261, 5524])).
% 3.62/2.76 tff(5527,plain,
% 3.62/2.76 (c1_1(a585)),
% 3.62/2.76 inference(unit_resolution,[status(thm)],[1272, 5524])).
% 3.62/2.76 tff(5528,plain,
% 3.62/2.76 (~c3_1(a588)),
% 3.62/2.76 inference(unit_resolution,[status(thm)],[5444, 107, 5409, 5412, 5408, 5527, 5526, 5393, 5392, 5525, 11])).
% 3.62/2.76 tff(5529,plain,
% 3.62/2.76 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a607) | (~c2_1(a607)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | c3_1(a588) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a607) | (~c2_1(a607)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | c3_1(a588) | (~c0_1(a607)))),
% 3.62/2.76 inference(rewrite,[status(thm)],[])).
% 3.62/2.76 tff(5530,plain,
% 3.62/2.76 ((hskp26 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a588) | c1_1(a588) | c2_1(a588)) <=> (hskp26 | c1_1(a607) | (~c2_1(a607)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | c3_1(a588) | (~c0_1(a607)))),
% 3.62/2.76 inference(rewrite,[status(thm)],[])).
% 3.62/2.76 tff(5531,plain,
% 3.62/2.76 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a588) | c1_1(a588) | c2_1(a588))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a607) | (~c2_1(a607)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | c3_1(a588) | (~c0_1(a607))))),
% 3.62/2.76 inference(monotonicity,[status(thm)],[5530])).
% 3.62/2.76 tff(5532,plain,
% 3.62/2.76 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a588) | c1_1(a588) | c2_1(a588))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a607) | (~c2_1(a607)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | c3_1(a588) | (~c0_1(a607)))),
% 3.62/2.76 inference(transitivity,[status(thm)],[5531, 5529])).
% 3.62/2.76 tff(5533,plain,
% 3.62/2.76 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a588) | c1_1(a588) | c2_1(a588))),
% 3.62/2.76 inference(quant_inst,[status(thm)],[])).
% 3.62/2.76 tff(5534,plain,
% 3.62/2.76 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a607) | (~c2_1(a607)) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | c3_1(a588) | (~c0_1(a607))),
% 3.62/2.76 inference(modus_ponens,[status(thm)],[5533, 5532])).
% 3.62/2.76 tff(5535,plain,
% 3.62/2.76 ($false),
% 3.62/2.76 inference(unit_resolution,[status(thm)],[5534, 726, 107, 66, 4653, 5393, 5392, 995, 5523, 5528])).
% 3.62/2.76 tff(5536,plain,(hskp26 | c1_1(a607) | c3_1(a607) | c3_1(a633)), inference(lemma,lemma(discharge,[]))).
% 3.62/2.77 tff(5537,plain,
% 3.62/2.77 (hskp26),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[5536, 3980, 33, 66])).
% 3.62/2.77 tff(5538,plain,
% 3.62/2.77 (c2_1(a583)),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[391, 5537])).
% 3.62/2.77 tff(5539,plain,
% 3.62/2.77 (c1_1(a583)),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[351, 5537])).
% 3.62/2.77 tff(5540,plain,
% 3.62/2.77 (c0_1(a583)),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[362, 5537])).
% 3.62/2.77 tff(5541,plain,
% 3.62/2.77 (hskp4),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[5002, 5428, 2292, 2270, 2281, 5420, 1651, 1650, 66, 1649, 33, 5343, 5342, 5341, 5245])).
% 3.62/2.77 tff(5542,plain,
% 3.62/2.77 (hskp6),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[147, 5541, 44])).
% 3.62/2.77 tff(5543,plain,
% 3.62/2.77 (~c0_1(a590)),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[666, 5542])).
% 3.62/2.77 tff(5544,plain,
% 3.62/2.77 (c3_1(a590)),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[677, 5542])).
% 3.62/2.77 tff(5545,plain,
% 3.62/2.77 (c2_1(a590)),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[688, 5542])).
% 3.62/2.77 tff(5546,plain,
% 3.62/2.77 (hskp28),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[3240, 107, 5343, 5342, 5420, 5428, 5341, 5245, 1748])).
% 3.62/2.77 tff(5547,plain,
% 3.62/2.77 (c3_1(a612)),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[1139, 5546])).
% 3.62/2.77 tff(5548,plain,
% 3.62/2.77 (c1_1(a612)),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[1435, 5546])).
% 3.62/2.77 tff(5549,plain,
% 3.62/2.77 (~c0_1(a612)),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[5455, 107, 5548, 5547, 5545, 5544, 66, 4653, 5543, 65, 1])).
% 3.62/2.77 tff(5550,plain,
% 3.62/2.77 (~c2_1(a588)),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[121, 5541])).
% 3.62/2.77 tff(5551,plain,
% 3.62/2.77 (~c1_1(a588)),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[127, 5541])).
% 3.62/2.77 tff(5552,plain,
% 3.62/2.77 (c2_1(a612)),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[1150, 5546])).
% 3.62/2.77 tff(5553,plain,
% 3.62/2.77 (~c3_1(a588)),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[4911, 107, 2292, 2281, 2270, 5548, 5552, 5551, 5550, 11, 5549])).
% 3.62/2.77 tff(5554,plain,
% 3.62/2.77 (~hskp8),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[5234, 5549, 1, 66, 5552, 5547])).
% 3.62/2.77 tff(5555,plain,
% 3.62/2.77 (^[U: $i] : refl((hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))),
% 3.62/2.77 inference(bind,[status(th)],[])).
% 3.62/2.77 tff(5556,plain,
% 3.62/2.77 (![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 3.62/2.77 inference(quant_intro,[status(thm)],[5555])).
% 3.62/2.77 tff(5557,plain,
% 3.62/2.77 (![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 3.62/2.77 inference(rewrite,[status(thm)],[])).
% 3.62/2.77 tff(5558,plain,
% 3.62/2.77 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp8) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp8))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp8) <=> (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp8) | hskp18) <=> ((hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp18))), rewrite(((hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp18) <=> (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp8) | hskp18) <=> (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))))),
% 3.62/2.77 inference(bind,[status(th)],[])).
% 3.62/2.77 tff(5559,plain,
% 3.62/2.77 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp8) | hskp18) <=> ![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 3.62/2.77 inference(quant_intro,[status(thm)],[5558])).
% 3.62/2.77 tff(5560,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp8) | hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause135')).
% 3.62/2.77 tff(5561,plain,
% 3.62/2.77 (![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 3.62/2.77 inference(modus_ponens,[status(thm)],[5560, 5559])).
% 3.62/2.77 tff(5562,plain,
% 3.62/2.77 (![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 3.62/2.77 inference(modus_ponens,[status(thm)],[5561, 5557])).
% 3.62/2.77 tff(5563,plain,(
% 3.62/2.77 ![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 3.62/2.77 inference(skolemize,[status(sab)],[5562])).
% 3.62/2.77 tff(5564,plain,
% 3.62/2.77 (![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 3.62/2.77 inference(modus_ponens,[status(thm)],[5563, 5556])).
% 3.62/2.77 tff(5565,plain,
% 3.62/2.77 (((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | hskp8 | c3_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607))) <=> ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | hskp8 | c3_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607))),
% 3.62/2.77 inference(rewrite,[status(thm)],[])).
% 3.62/2.77 tff(5566,plain,
% 3.62/2.77 ((hskp18 | hskp8 | (~ndr1_0) | c0_1(a607) | c3_1(a607) | (~c2_1(a607))) <=> (hskp18 | hskp8 | c3_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607))),
% 3.62/2.77 inference(rewrite,[status(thm)],[])).
% 3.62/2.77 tff(5567,plain,
% 3.62/2.77 (((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | hskp8 | (~ndr1_0) | c0_1(a607) | c3_1(a607) | (~c2_1(a607)))) <=> ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | hskp8 | c3_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607)))),
% 3.62/2.77 inference(monotonicity,[status(thm)],[5566])).
% 3.62/2.77 tff(5568,plain,
% 3.62/2.77 (((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | hskp8 | (~ndr1_0) | c0_1(a607) | c3_1(a607) | (~c2_1(a607)))) <=> ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | hskp8 | c3_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607))),
% 3.62/2.77 inference(transitivity,[status(thm)],[5567, 5565])).
% 3.62/2.77 tff(5569,plain,
% 3.62/2.77 ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | hskp8 | (~ndr1_0) | c0_1(a607) | c3_1(a607) | (~c2_1(a607)))),
% 3.62/2.77 inference(quant_inst,[status(thm)],[])).
% 3.62/2.77 tff(5570,plain,
% 3.62/2.77 ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | hskp8 | c3_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607)),
% 3.62/2.77 inference(modus_ponens,[status(thm)],[5569, 5568])).
% 3.62/2.77 tff(5571,plain,
% 3.62/2.77 (hskp18 | hskp8 | c3_1(a607) | c0_1(a607)),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[5570, 107, 4653, 5564])).
% 3.62/2.77 tff(5572,plain,
% 3.62/2.77 (hskp18),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[5571, 5554, 33, 1])).
% 3.62/2.77 tff(5573,plain,
% 3.62/2.77 (~c2_1(a610)),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[1189, 5572])).
% 3.62/2.77 tff(5574,plain,
% 3.62/2.77 (~c0_1(a610)),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[1195, 5572])).
% 3.62/2.77 tff(5575,plain,
% 3.62/2.77 (c0_1(a588)),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[138, 5541])).
% 3.62/2.77 tff(5576,plain,
% 3.62/2.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a607) | c0_1(a610) | c2_1(a610) | c1_1(a607) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | c0_1(a607) | (~c1_1(a610)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a607) | c0_1(a610) | c2_1(a610) | c1_1(a607) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | c0_1(a607) | (~c1_1(a610)))),
% 3.62/2.77 inference(rewrite,[status(thm)],[])).
% 3.62/2.77 tff(5577,plain,
% 3.62/2.77 (((~ndr1_0) | c2_1(a588) | c3_1(a588) | (~c0_1(a588)) | c0_1(a610) | c2_1(a610) | (~c1_1(a610)) | c3_1(a607) | c1_1(a607) | c0_1(a607)) <=> (c3_1(a607) | c0_1(a610) | c2_1(a610) | c1_1(a607) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | c0_1(a607) | (~c1_1(a610)))),
% 3.62/2.77 inference(rewrite,[status(thm)],[])).
% 3.62/2.77 tff(5578,plain,
% 3.62/2.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a588) | c3_1(a588) | (~c0_1(a588)) | c0_1(a610) | c2_1(a610) | (~c1_1(a610)) | c3_1(a607) | c1_1(a607) | c0_1(a607))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a607) | c0_1(a610) | c2_1(a610) | c1_1(a607) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | c0_1(a607) | (~c1_1(a610))))),
% 3.62/2.77 inference(monotonicity,[status(thm)],[5577])).
% 3.62/2.77 tff(5579,plain,
% 3.62/2.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a588) | c3_1(a588) | (~c0_1(a588)) | c0_1(a610) | c2_1(a610) | (~c1_1(a610)) | c3_1(a607) | c1_1(a607) | c0_1(a607))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a607) | c0_1(a610) | c2_1(a610) | c1_1(a607) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | c0_1(a607) | (~c1_1(a610)))),
% 3.62/2.77 inference(transitivity,[status(thm)],[5578, 5576])).
% 3.62/2.77 tff(5580,plain,
% 3.62/2.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a588) | c3_1(a588) | (~c0_1(a588)) | c0_1(a610) | c2_1(a610) | (~c1_1(a610)) | c3_1(a607) | c1_1(a607) | c0_1(a607))),
% 3.62/2.77 inference(quant_inst,[status(thm)],[])).
% 3.62/2.77 tff(5581,plain,
% 3.62/2.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a607) | c0_1(a610) | c2_1(a610) | c1_1(a607) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | c0_1(a607) | (~c1_1(a610))),
% 3.62/2.77 inference(modus_ponens,[status(thm)],[5580, 5579])).
% 3.62/2.77 tff(5582,plain,
% 3.62/2.77 (~c1_1(a610)),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[5581, 107, 33, 5575, 5574, 5573, 66, 5550, 1463, 1, 5553])).
% 3.62/2.77 tff(5583,plain,
% 3.62/2.77 (hskp3),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[4968, 5420, 44, 66, 33, 5343, 5342, 1651, 5341, 5245, 1650])).
% 3.62/2.77 tff(5584,plain,
% 3.62/2.77 (~c1_1(a587)),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[939, 5583])).
% 3.62/2.77 tff(5585,plain,
% 3.62/2.77 (hskp16),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[5020, 107, 5552, 5547, 5575, 5550, 2125, 5549, 5553])).
% 3.62/2.77 tff(5586,plain,
% 3.62/2.77 (~c2_1(a606)),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[1111, 5585])).
% 3.62/2.77 tff(5587,plain,
% 3.62/2.77 (c2_1(a587)),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[950, 5583])).
% 3.62/2.77 tff(5588,plain,
% 3.62/2.77 (c0_1(a587)),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[961, 5583])).
% 3.62/2.77 tff(5589,plain,
% 3.62/2.77 (c1_1(a606)),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[1088, 5585])).
% 3.62/2.77 tff(5590,plain,
% 3.62/2.77 (c0_1(a606)),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[5034, 5589, 4654, 5588, 5587, 5586, 5584])).
% 3.62/2.77 tff(5591,plain,
% 3.62/2.77 (hskp10),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[1535, 107, 5548, 5552, 5547, 1651, 1650, 1649, 21])).
% 3.62/2.77 tff(5592,plain,
% 3.62/2.77 (~c1_1(a598)),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[911, 5591])).
% 3.62/2.77 tff(5593,plain,
% 3.62/2.77 (c3_1(a598)),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[881, 5591])).
% 3.62/2.77 tff(5594,plain,
% 3.62/2.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c3_1(a598)) | c2_1(a598))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c3_1(a598)) | c2_1(a598))),
% 3.62/2.77 inference(rewrite,[status(thm)],[])).
% 3.62/2.77 tff(5595,plain,
% 3.62/2.77 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612))) <=> (c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c3_1(a598)) | c2_1(a598))),
% 3.62/2.77 inference(rewrite,[status(thm)],[])).
% 3.62/2.77 tff(5596,plain,
% 3.62/2.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c3_1(a598)) | c2_1(a598)))),
% 3.62/2.77 inference(monotonicity,[status(thm)],[5595])).
% 3.62/2.77 tff(5597,plain,
% 3.62/2.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c3_1(a598)) | c2_1(a598))),
% 3.62/2.77 inference(transitivity,[status(thm)],[5596, 5594])).
% 3.62/2.77 tff(5598,plain,
% 3.62/2.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))),
% 3.62/2.77 inference(quant_inst,[status(thm)],[])).
% 3.62/2.77 tff(5599,plain,
% 3.62/2.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c3_1(a598)) | c2_1(a598)),
% 3.62/2.77 inference(modus_ponens,[status(thm)],[5598, 5597])).
% 3.62/2.77 tff(5600,plain,
% 3.62/2.77 (c2_1(a598)),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[5599, 107, 2292, 2281, 2270, 5548, 5552, 5593, 5592, 11, 5549])).
% 3.62/2.77 tff(5601,plain,
% 3.62/2.77 (c0_1(a598)),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[892, 5591])).
% 3.62/2.77 tff(5602,plain,
% 3.62/2.77 (c3_1(a610)),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[1206, 5572])).
% 3.62/2.77 tff(5603,plain,
% 3.62/2.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a610) | c2_1(a606) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c0_1(a606)) | (~c1_1(a606)) | c1_1(a610) | (~c3_1(a610)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a610) | c2_1(a606) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c0_1(a606)) | (~c1_1(a606)) | c1_1(a610) | (~c3_1(a610)))),
% 3.62/2.77 inference(rewrite,[status(thm)],[])).
% 3.62/2.77 tff(5604,plain,
% 3.62/2.77 (((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610))) <=> (c2_1(a610) | c2_1(a606) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c0_1(a606)) | (~c1_1(a606)) | c1_1(a610) | (~c3_1(a610)))),
% 3.62/2.77 inference(rewrite,[status(thm)],[])).
% 3.62/2.77 tff(5605,plain,
% 3.62/2.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a610) | c2_1(a606) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c0_1(a606)) | (~c1_1(a606)) | c1_1(a610) | (~c3_1(a610))))),
% 3.62/2.77 inference(monotonicity,[status(thm)],[5604])).
% 3.62/2.77 tff(5606,plain,
% 3.62/2.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a610) | c2_1(a606) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c0_1(a606)) | (~c1_1(a606)) | c1_1(a610) | (~c3_1(a610)))),
% 3.62/2.77 inference(transitivity,[status(thm)],[5605, 5603])).
% 3.62/2.77 tff(5607,plain,
% 3.62/2.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a598)) | (~c3_1(a598)) | (~c0_1(a598)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610)))),
% 3.62/2.77 inference(quant_inst,[status(thm)],[])).
% 3.62/2.77 tff(5608,plain,
% 3.62/2.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a610) | c2_1(a606) | (~ndr1_0) | (~c3_1(a598)) | (~c2_1(a598)) | (~c0_1(a598)) | (~c0_1(a606)) | (~c1_1(a606)) | c1_1(a610) | (~c3_1(a610))),
% 3.62/2.77 inference(modus_ponens,[status(thm)],[5607, 5606])).
% 3.62/2.77 tff(5609,plain,
% 3.62/2.77 ($false),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[5608, 107, 5602, 5589, 5601, 5593, 5573, 5586, 1106, 5600, 5590, 5582])).
% 3.62/2.77 tff(5610,plain,(c0_1(a607) | c3_1(a607) | c1_1(a607) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a583)) | hskp22), inference(lemma,lemma(discharge,[]))).
% 3.62/2.77 tff(5611,plain,
% 3.62/2.77 (c0_1(a607)),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[5610, 5540, 66, 33, 5539, 5538, 5243])).
% 3.62/2.77 tff(5612,plain,
% 3.62/2.77 (hskp4 | c3_1(a583)),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[3328, 107, 4654, 5540, 5539, 55])).
% 3.62/2.77 tff(5613,plain,
% 3.62/2.77 (c3_1(a583)),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[5612, 830])).
% 3.62/2.77 tff(5614,plain,
% 3.62/2.77 (hskp15),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[4629, 5613, 5540, 5539, 5538])).
% 3.62/2.77 tff(5615,plain,
% 3.62/2.77 (~c0_1(a604)),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[1591, 5614])).
% 3.62/2.77 tff(5616,plain,
% 3.62/2.77 (c1_1(a604)),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[1613, 5614])).
% 3.62/2.77 tff(5617,plain,
% 3.62/2.77 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a607)))),
% 3.62/2.77 inference(rewrite,[status(thm)],[])).
% 3.62/2.77 tff(5618,plain,
% 3.62/2.77 ((hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604))) <=> (hskp17 | c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a607)))),
% 3.62/2.77 inference(rewrite,[status(thm)],[])).
% 3.62/2.77 tff(5619,plain,
% 3.62/2.77 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a607))))),
% 3.62/2.77 inference(monotonicity,[status(thm)],[5618])).
% 3.62/2.77 tff(5620,plain,
% 3.62/2.77 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a607)))),
% 3.62/2.77 inference(transitivity,[status(thm)],[5619, 5617])).
% 3.62/2.77 tff(5621,plain,
% 3.62/2.77 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)))),
% 3.62/2.77 inference(quant_inst,[status(thm)],[])).
% 3.62/2.77 tff(5622,plain,
% 3.62/2.77 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a607))),
% 3.62/2.77 inference(modus_ponens,[status(thm)],[5621, 5620])).
% 3.62/2.77 tff(5623,plain,
% 3.62/2.77 (c2_1(a604)),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[5622, 107, 4654, 5616, 66, 4653, 5615, 32, 5611])).
% 3.62/2.77 tff(5624,plain,
% 3.62/2.77 (c3_1(a604)),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[1602, 5614])).
% 3.62/2.77 tff(5625,assumption,(hskp16), introduced(assumption)).
% 3.62/2.77 tff(5626,plain,
% 3.62/2.77 (~c2_1(a606)),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[1111, 5625])).
% 3.62/2.77 tff(5627,plain,
% 3.62/2.77 (c1_1(a606)),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[1088, 5625])).
% 3.62/2.77 tff(5628,plain,
% 3.62/2.77 (c0_1(a606)),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[5034, 5627, 2987, 1000, 999, 5626, 996])).
% 3.62/2.77 tff(5629,plain,
% 3.62/2.77 (~c3_1(a606)),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[1075, 5625])).
% 3.62/2.77 tff(5630,plain,
% 3.62/2.77 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | c3_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp4 | c3_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)))),
% 3.62/2.77 inference(rewrite,[status(thm)],[])).
% 3.62/2.77 tff(5631,plain,
% 3.62/2.77 ((hskp17 | hskp4 | (~ndr1_0) | c3_1(a606) | (~c1_1(a606)) | (~c0_1(a606))) <=> (hskp17 | hskp4 | c3_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)))),
% 3.62/2.77 inference(rewrite,[status(thm)],[])).
% 3.62/2.77 tff(5632,plain,
% 3.62/2.77 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c3_1(a606) | (~c1_1(a606)) | (~c0_1(a606)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | c3_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606))))),
% 3.62/2.77 inference(monotonicity,[status(thm)],[5631])).
% 3.62/2.77 tff(5633,plain,
% 3.62/2.77 (((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c3_1(a606) | (~c1_1(a606)) | (~c0_1(a606)))) <=> ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp4 | c3_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)))),
% 3.62/2.77 inference(transitivity,[status(thm)],[5632, 5630])).
% 3.62/2.77 tff(5634,plain,
% 3.62/2.77 ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp4 | (~ndr1_0) | c3_1(a606) | (~c1_1(a606)) | (~c0_1(a606)))),
% 3.62/2.77 inference(quant_inst,[status(thm)],[])).
% 3.62/2.77 tff(5635,plain,
% 3.62/2.77 ((~![U: $i] : (hskp17 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp4 | c3_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606))),
% 3.62/2.77 inference(modus_ponens,[status(thm)],[5634, 5633])).
% 3.62/2.77 tff(5636,plain,
% 3.62/2.77 ($false),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[5635, 107, 2987, 830, 5627, 5629, 55, 5628])).
% 3.62/2.77 tff(5637,plain,((~hskp16) | hskp17 | hskp4 | (~c0_1(a587)) | (~c2_1(a587)) | c1_1(a587)), inference(lemma,lemma(discharge,[]))).
% 3.62/2.77 tff(5638,plain,
% 3.62/2.77 (~hskp16),
% 3.62/2.77 inference(unit_resolution,[status(thm)],[5637, 830, 4654, 4813, 4812, 4807])).
% 3.62/2.77 tff(5639,assumption,(c0_1(a633)), introduced(assumption)).
% 3.62/2.77 tff(5640,assumption,(~hskp16), introduced(assumption)).
% 3.62/2.78 tff(5641,plain,
% 3.62/2.78 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~c0_1(a633)) | c3_1(a633) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | c2_1(a633))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | (~c0_1(a633)) | c3_1(a633) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | c2_1(a633))),
% 3.62/2.78 inference(rewrite,[status(thm)],[])).
% 3.62/2.78 tff(5642,plain,
% 3.62/2.78 ((hskp16 | (~ndr1_0) | c2_1(a633) | c3_1(a633) | (~c0_1(a633)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604))) <=> (hskp16 | (~c0_1(a633)) | c3_1(a633) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | c2_1(a633))),
% 3.62/2.78 inference(rewrite,[status(thm)],[])).
% 3.62/2.78 tff(5643,plain,
% 3.62/2.78 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a633) | c3_1(a633) | (~c0_1(a633)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~c0_1(a633)) | c3_1(a633) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | c2_1(a633)))),
% 3.62/2.78 inference(monotonicity,[status(thm)],[5642])).
% 3.62/2.78 tff(5644,plain,
% 3.62/2.78 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a633) | c3_1(a633) | (~c0_1(a633)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | (~c0_1(a633)) | c3_1(a633) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | c2_1(a633))),
% 3.62/2.78 inference(transitivity,[status(thm)],[5643, 5641])).
% 3.62/2.78 tff(5645,plain,
% 3.62/2.78 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a633) | c3_1(a633) | (~c0_1(a633)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)))),
% 3.62/2.78 inference(quant_inst,[status(thm)],[])).
% 3.62/2.78 tff(5646,plain,
% 3.62/2.78 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | (~c0_1(a633)) | c3_1(a633) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | c2_1(a633)),
% 3.62/2.78 inference(modus_ponens,[status(thm)],[5645, 5644])).
% 3.62/2.78 tff(5647,plain,
% 3.62/2.78 ($false),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[5646, 107, 5640, 2545, 5639, 3980, 2475, 2125, 2538, 4482])).
% 3.62/2.78 tff(5648,plain,(c2_1(a633) | hskp16 | (~c3_1(a604)) | (~c0_1(a633)) | c3_1(a633) | c0_1(a604) | (~c2_1(a604))), inference(lemma,lemma(discharge,[]))).
% 3.62/2.78 tff(5649,plain,
% 3.62/2.78 (c2_1(a633)),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[5648, 5638, 5624, 5242, 3980, 5615, 5623])).
% 3.62/2.78 tff(5650,plain,
% 3.62/2.78 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | c2_1(a623) | c3_1(a623) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c0_1(a623)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c2_1(a623) | c3_1(a623) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c0_1(a623)))),
% 3.62/2.78 inference(rewrite,[status(thm)],[])).
% 3.62/2.78 tff(5651,plain,
% 3.62/2.78 ((hskp16 | (~ndr1_0) | c2_1(a623) | c3_1(a623) | (~c0_1(a623)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604))) <=> (hskp16 | c2_1(a623) | c3_1(a623) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c0_1(a623)))),
% 3.62/2.78 inference(rewrite,[status(thm)],[])).
% 3.62/2.78 tff(5652,plain,
% 3.62/2.78 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a623) | c3_1(a623) | (~c0_1(a623)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | c2_1(a623) | c3_1(a623) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c0_1(a623))))),
% 3.62/2.78 inference(monotonicity,[status(thm)],[5651])).
% 3.62/2.78 tff(5653,plain,
% 3.62/2.78 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a623) | c3_1(a623) | (~c0_1(a623)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c2_1(a623) | c3_1(a623) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c0_1(a623)))),
% 3.62/2.78 inference(transitivity,[status(thm)],[5652, 5650])).
% 3.62/2.78 tff(5654,plain,
% 3.62/2.78 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a623) | c3_1(a623) | (~c0_1(a623)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)))),
% 3.62/2.78 inference(quant_inst,[status(thm)],[])).
% 3.62/2.78 tff(5655,plain,
% 3.62/2.78 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c2_1(a623) | c3_1(a623) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c0_1(a623))),
% 3.62/2.78 inference(modus_ponens,[status(thm)],[5654, 5653])).
% 3.62/2.78 tff(5656,plain,
% 3.62/2.78 (~c0_1(a623)),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[5655, 107, 5640, 2545, 716, 710, 2475, 2125, 2538])).
% 3.62/2.78 tff(5657,plain,
% 3.62/2.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a623) | c3_1(a623) | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c3_1(a604)) | (~c2_1(a604)) | c0_1(a623))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a623) | c3_1(a623) | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c3_1(a604)) | (~c2_1(a604)) | c0_1(a623))),
% 3.62/2.78 inference(rewrite,[status(thm)],[])).
% 3.62/2.78 tff(5658,plain,
% 3.62/2.78 (((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c3_1(a623) | c0_1(a623) | c2_1(a623)) <=> (c2_1(a623) | c3_1(a623) | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c3_1(a604)) | (~c2_1(a604)) | c0_1(a623))),
% 3.62/2.78 inference(rewrite,[status(thm)],[])).
% 3.62/2.78 tff(5659,plain,
% 3.62/2.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c3_1(a623) | c0_1(a623) | c2_1(a623))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a623) | c3_1(a623) | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c3_1(a604)) | (~c2_1(a604)) | c0_1(a623)))),
% 3.62/2.78 inference(monotonicity,[status(thm)],[5658])).
% 3.62/2.78 tff(5660,plain,
% 3.62/2.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c3_1(a623) | c0_1(a623) | c2_1(a623))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a623) | c3_1(a623) | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c3_1(a604)) | (~c2_1(a604)) | c0_1(a623))),
% 3.62/2.78 inference(transitivity,[status(thm)],[5659, 5657])).
% 3.62/2.78 tff(5661,plain,
% 3.62/2.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c3_1(a623) | c0_1(a623) | c2_1(a623))),
% 3.62/2.78 inference(quant_inst,[status(thm)],[])).
% 3.62/2.78 tff(5662,plain,
% 3.62/2.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a623) | c3_1(a623) | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c3_1(a604)) | (~c2_1(a604)) | c0_1(a623)),
% 3.62/2.78 inference(modus_ponens,[status(thm)],[5661, 5660])).
% 3.62/2.78 tff(5663,plain,
% 3.62/2.78 ($false),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[5662, 107, 2545, 463, 462, 716, 710, 2475, 461, 1730, 2538, 5656])).
% 3.62/2.78 tff(5664,plain,((~hskp20) | (~c3_1(a604)) | (~c2_1(a599)) | (~c3_1(a599)) | c0_1(a604) | c1_1(a599) | (~c2_1(a604)) | hskp16), inference(lemma,lemma(discharge,[]))).
% 3.62/2.78 tff(5665,plain,
% 3.62/2.78 (~hskp20),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[5664, 5624, 5351, 5350, 5615, 5322, 5623, 5638])).
% 3.62/2.78 tff(5666,plain,
% 3.62/2.78 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | (~c0_1(a633)) | c3_1(a633) | (~ndr1_0) | (~c2_1(a633)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | hskp7 | (~c0_1(a633)) | c3_1(a633) | (~ndr1_0) | (~c2_1(a633)))),
% 3.62/2.78 inference(rewrite,[status(thm)],[])).
% 3.62/2.78 tff(5667,plain,
% 3.62/2.78 ((hskp20 | hskp7 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c0_1(a633))) <=> (hskp20 | hskp7 | (~c0_1(a633)) | c3_1(a633) | (~ndr1_0) | (~c2_1(a633)))),
% 3.62/2.78 inference(rewrite,[status(thm)],[])).
% 3.62/2.78 tff(5668,plain,
% 3.62/2.78 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c0_1(a633)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | (~c0_1(a633)) | c3_1(a633) | (~ndr1_0) | (~c2_1(a633))))),
% 3.62/2.78 inference(monotonicity,[status(thm)],[5667])).
% 3.62/2.78 tff(5669,plain,
% 3.62/2.78 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c0_1(a633)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | hskp7 | (~c0_1(a633)) | c3_1(a633) | (~ndr1_0) | (~c2_1(a633)))),
% 3.62/2.78 inference(transitivity,[status(thm)],[5668, 5666])).
% 3.62/2.78 tff(5670,plain,
% 3.62/2.78 ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c3_1(a633) | (~c2_1(a633)) | (~c0_1(a633)))),
% 3.62/2.78 inference(quant_inst,[status(thm)],[])).
% 3.62/2.78 tff(5671,plain,
% 3.62/2.78 ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | hskp7 | (~c0_1(a633)) | c3_1(a633) | (~ndr1_0) | (~c2_1(a633))),
% 3.62/2.78 inference(modus_ponens,[status(thm)],[5670, 5669])).
% 3.62/2.78 tff(5672,plain,
% 3.62/2.78 (hskp20 | hskp7 | (~c0_1(a633)) | (~c2_1(a633))),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[5671, 107, 3980, 1382])).
% 3.62/2.78 tff(5673,plain,
% 3.62/2.78 (hskp7),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[5672, 5665, 5242, 5649])).
% 3.62/2.78 tff(5674,plain,
% 3.62/2.78 (hskp2),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[5370, 5673, 5330, 3980, 5649, 33, 5351, 5350, 4653, 5322, 5611])).
% 3.62/2.78 tff(5675,plain,
% 3.62/2.78 (~c3_1(a586)),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[218, 5674])).
% 3.62/2.78 tff(5676,plain,
% 3.62/2.78 (c1_1(a586)),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[229, 5674])).
% 3.62/2.78 tff(5677,plain,
% 3.62/2.78 (c2_1(a586)),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[1474, 5674])).
% 3.62/2.78 tff(5678,plain,
% 3.62/2.78 ($false),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[5002, 5677, 5676, 5409, 5408, 5412, 830, 5540, 5539, 66, 5538, 33, 5351, 5350, 5322, 5675])).
% 3.62/2.78 tff(5679,plain,(hskp4 | c1_1(a607) | c3_1(a607) | c3_1(a633)), inference(lemma,lemma(discharge,[]))).
% 3.62/2.78 tff(5680,plain,
% 3.62/2.78 (hskp4),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[5679, 3980, 33, 66])).
% 3.62/2.78 tff(5681,plain,
% 3.62/2.78 (hskp6),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[147, 5680, 5243])).
% 3.62/2.78 tff(5682,plain,
% 3.62/2.78 (~c0_1(a590)),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[666, 5681])).
% 3.62/2.78 tff(5683,plain,
% 3.62/2.78 (~c2_1(a588)),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[121, 5680])).
% 3.62/2.78 tff(5684,plain,
% 3.62/2.78 (~c1_1(a588)),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[127, 5680])).
% 3.62/2.78 tff(5685,plain,
% 3.62/2.78 (c0_1(a588)),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[138, 5680])).
% 3.62/2.78 tff(5686,plain,
% 3.62/2.78 (hskp1),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[5472, 107, 33, 5685, 4653, 5684, 5683, 1237, 5611])).
% 3.62/2.78 tff(5687,plain,
% 3.62/2.78 (~c0_1(a585)),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[1250, 5686])).
% 3.62/2.78 tff(5688,plain,
% 3.62/2.78 (c1_1(a585)),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[1272, 5686])).
% 3.62/2.78 tff(5689,plain,
% 3.62/2.78 (c3_1(a590)),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[677, 5681])).
% 3.62/2.78 tff(5690,plain,
% 3.62/2.78 (c2_1(a590)),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[688, 5681])).
% 3.62/2.78 tff(5691,plain,
% 3.62/2.78 (~c3_1(a583)),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[4629, 3154, 1651, 1650, 1649])).
% 3.62/2.78 tff(5692,assumption,(~c0_1(a585)), introduced(assumption)).
% 3.62/2.78 tff(5693,assumption,(c1_1(a585)), introduced(assumption)).
% 3.62/2.78 tff(5694,plain,
% 3.62/2.78 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | c0_1(a585) | (~ndr1_0) | (~c3_1(a585)) | (~c1_1(a585)) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a585) | (~ndr1_0) | (~c3_1(a585)) | (~c1_1(a585)) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)))),
% 3.62/2.78 inference(rewrite,[status(thm)],[])).
% 3.62/2.78 tff(5695,plain,
% 3.62/2.78 ((hskp15 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c1_1(a583)) | c0_1(a585) | (~c1_1(a585)) | (~c3_1(a585))) <=> (hskp15 | c0_1(a585) | (~ndr1_0) | (~c3_1(a585)) | (~c1_1(a585)) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)))),
% 3.62/2.78 inference(rewrite,[status(thm)],[])).
% 3.62/2.78 tff(5696,plain,
% 3.62/2.78 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c1_1(a583)) | c0_1(a585) | (~c1_1(a585)) | (~c3_1(a585)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | c0_1(a585) | (~ndr1_0) | (~c3_1(a585)) | (~c1_1(a585)) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583))))),
% 3.62/2.78 inference(monotonicity,[status(thm)],[5695])).
% 3.62/2.78 tff(5697,plain,
% 3.62/2.78 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c1_1(a583)) | c0_1(a585) | (~c1_1(a585)) | (~c3_1(a585)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a585) | (~ndr1_0) | (~c3_1(a585)) | (~c1_1(a585)) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)))),
% 3.62/2.78 inference(transitivity,[status(thm)],[5696, 5694])).
% 3.62/2.78 tff(5698,plain,
% 3.62/2.78 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c1_1(a583)) | c0_1(a585) | (~c1_1(a585)) | (~c3_1(a585)))),
% 3.62/2.78 inference(quant_inst,[status(thm)],[])).
% 3.62/2.78 tff(5699,plain,
% 3.62/2.78 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a585) | (~ndr1_0) | (~c3_1(a585)) | (~c1_1(a585)) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583))),
% 3.62/2.78 inference(modus_ponens,[status(thm)],[5698, 5697])).
% 3.62/2.78 tff(5700,plain,
% 3.62/2.78 (~c3_1(a585)),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[5699, 107, 3154, 1650, 1649, 5693, 5692, 2690, 5691])).
% 3.62/2.78 tff(5701,plain,
% 3.62/2.78 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)) | (~c3_1(a590)) | (~c1_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)) | (~c3_1(a590)) | (~c1_1(a590)))),
% 3.62/2.78 inference(rewrite,[status(thm)],[])).
% 3.62/2.78 tff(5702,plain,
% 3.62/2.78 ((hskp15 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c1_1(a583)) | c0_1(a590) | (~c1_1(a590)) | (~c3_1(a590))) <=> (hskp15 | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)) | (~c3_1(a590)) | (~c1_1(a590)))),
% 3.62/2.78 inference(rewrite,[status(thm)],[])).
% 3.62/2.78 tff(5703,plain,
% 3.62/2.78 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c1_1(a583)) | c0_1(a590) | (~c1_1(a590)) | (~c3_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)) | (~c3_1(a590)) | (~c1_1(a590))))),
% 3.62/2.78 inference(monotonicity,[status(thm)],[5702])).
% 3.62/2.78 tff(5704,plain,
% 3.62/2.78 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c1_1(a583)) | c0_1(a590) | (~c1_1(a590)) | (~c3_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)) | (~c3_1(a590)) | (~c1_1(a590)))),
% 3.62/2.78 inference(transitivity,[status(thm)],[5703, 5701])).
% 3.62/2.78 tff(5705,plain,
% 3.62/2.78 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a583) | (~c2_1(a583)) | (~c1_1(a583)) | c0_1(a590) | (~c1_1(a590)) | (~c3_1(a590)))),
% 3.62/2.78 inference(quant_inst,[status(thm)],[])).
% 3.62/2.78 tff(5706,plain,
% 3.62/2.78 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | c3_1(a583) | (~c1_1(a583)) | (~c3_1(a590)) | (~c1_1(a590))),
% 3.62/2.78 inference(modus_ponens,[status(thm)],[5705, 5704])).
% 3.62/2.78 tff(5707,plain,
% 3.62/2.78 (~c1_1(a590)),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[5706, 107, 3154, 1650, 1649, 862, 45, 2690, 5691])).
% 3.62/2.78 tff(5708,plain,
% 3.62/2.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a607) | (~c2_1(a607)) | c0_1(a585) | (~ndr1_0) | c3_1(a585) | (~c1_1(a585)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | (~c0_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a607) | (~c2_1(a607)) | c0_1(a585) | (~ndr1_0) | c3_1(a585) | (~c1_1(a585)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | (~c0_1(a607)))),
% 3.62/2.78 inference(rewrite,[status(thm)],[])).
% 3.62/2.78 tff(5709,plain,
% 3.62/2.78 (((~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a585) | c0_1(a585) | (~c1_1(a585))) <=> (c3_1(a607) | (~c2_1(a607)) | c0_1(a585) | (~ndr1_0) | c3_1(a585) | (~c1_1(a585)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | (~c0_1(a607)))),
% 3.62/2.78 inference(rewrite,[status(thm)],[])).
% 3.62/2.78 tff(5710,plain,
% 3.62/2.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a585) | c0_1(a585) | (~c1_1(a585)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a607) | (~c2_1(a607)) | c0_1(a585) | (~ndr1_0) | c3_1(a585) | (~c1_1(a585)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | (~c0_1(a607))))),
% 3.62/2.78 inference(monotonicity,[status(thm)],[5709])).
% 3.62/2.78 tff(5711,plain,
% 3.62/2.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a585) | c0_1(a585) | (~c1_1(a585)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a607) | (~c2_1(a607)) | c0_1(a585) | (~ndr1_0) | c3_1(a585) | (~c1_1(a585)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | (~c0_1(a607)))),
% 3.62/2.78 inference(transitivity,[status(thm)],[5710, 5708])).
% 3.62/2.78 tff(5712,plain,
% 3.62/2.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a585) | c0_1(a585) | (~c1_1(a585)))),
% 3.62/2.78 inference(quant_inst,[status(thm)],[])).
% 3.62/2.78 tff(5713,plain,
% 3.62/2.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a607) | (~c2_1(a607)) | c0_1(a585) | (~ndr1_0) | c3_1(a585) | (~c1_1(a585)) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a590) | (~c0_1(a607))),
% 3.62/2.78 inference(modus_ponens,[status(thm)],[5712, 5711])).
% 3.62/2.78 tff(5714,plain,
% 3.62/2.78 ($false),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[5713, 107, 33, 863, 862, 5693, 5355, 5692, 258, 2486, 5707, 5700])).
% 3.62/2.78 tff(5715,plain,(hskp15 | c3_1(a607) | (~c2_1(a590)) | (~c3_1(a590)) | (~c1_1(a585)) | (~c2_1(a607)) | c0_1(a585) | (~c0_1(a607)) | (~c1_1(a583)) | (~c2_1(a583)) | c0_1(a590) | (~c0_1(a583))), inference(lemma,lemma(discharge,[]))).
% 3.62/2.78 tff(5716,plain,
% 3.62/2.78 (hskp15),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[5715, 5690, 33, 5689, 5688, 4653, 5687, 5611, 5539, 5538, 5682, 5540])).
% 3.62/2.78 tff(5717,plain,
% 3.62/2.78 (~c0_1(a604)),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[1591, 5716])).
% 3.62/2.78 tff(5718,plain,
% 3.62/2.78 (c1_1(a604)),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[1613, 5716])).
% 3.62/2.78 tff(5719,plain,
% 3.62/2.78 (c2_1(a604)),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[5622, 107, 4654, 5718, 66, 4653, 5717, 32, 5611])).
% 3.62/2.78 tff(5720,plain,
% 3.62/2.78 (c3_1(a604)),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[1602, 5716])).
% 3.62/2.78 tff(5721,plain,
% 3.62/2.78 (c2_1(a585)),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[1261, 5686])).
% 3.62/2.78 tff(5722,plain,
% 3.62/2.78 (~c3_1(a588)),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[5444, 107, 5409, 5412, 5408, 5688, 5721, 5684, 5683, 5687, 11])).
% 3.62/2.78 tff(5723,plain,
% 3.62/2.78 (hskp16 | c3_1(a588)),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[4700, 107, 5690, 5689, 5685, 5682, 5683, 2125])).
% 3.62/2.78 tff(5724,plain,
% 3.62/2.78 (hskp16),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[5723, 5722])).
% 3.62/2.78 tff(5725,plain,
% 3.62/2.78 (~c2_1(a606)),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[1111, 5724])).
% 3.62/2.78 tff(5726,plain,
% 3.62/2.78 (c1_1(a606)),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[1088, 5724])).
% 3.62/2.78 tff(5727,plain,
% 3.62/2.78 (hskp12),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[4734, 107, 5540, 5539, 5538, 5688, 5721, 5687, 2727])).
% 3.62/2.78 tff(5728,plain,
% 3.62/2.78 (~c3_1(a600)),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[741, 5727])).
% 3.62/2.78 tff(5729,plain,
% 3.62/2.78 (~c3_1(a606)),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[1075, 5724])).
% 3.62/2.78 tff(5730,plain,
% 3.62/2.78 (c2_1(a600)),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[752, 5727])).
% 3.62/2.78 tff(5731,plain,
% 3.62/2.78 (c0_1(a600)),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[763, 5727])).
% 3.62/2.78 tff(5732,plain,
% 3.62/2.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a606) | c3_1(a600) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a600)) | (~c0_1(a600)) | c0_1(a606) | (~c1_1(a606)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a606) | c3_1(a600) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a600)) | (~c0_1(a600)) | c0_1(a606) | (~c1_1(a606)))),
% 3.62/2.78 inference(rewrite,[status(thm)],[])).
% 3.62/2.78 tff(5733,plain,
% 3.62/2.78 (((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a606) | c0_1(a606) | (~c1_1(a606))) <=> (c3_1(a606) | c3_1(a600) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a600)) | (~c0_1(a600)) | c0_1(a606) | (~c1_1(a606)))),
% 3.62/2.78 inference(rewrite,[status(thm)],[])).
% 3.62/2.78 tff(5734,plain,
% 3.62/2.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a606) | c0_1(a606) | (~c1_1(a606)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a606) | c3_1(a600) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a600)) | (~c0_1(a600)) | c0_1(a606) | (~c1_1(a606))))),
% 3.62/2.78 inference(monotonicity,[status(thm)],[5733])).
% 3.62/2.78 tff(5735,plain,
% 3.62/2.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a606) | c0_1(a606) | (~c1_1(a606)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a606) | c3_1(a600) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a600)) | (~c0_1(a600)) | c0_1(a606) | (~c1_1(a606)))),
% 3.62/2.78 inference(transitivity,[status(thm)],[5734, 5732])).
% 3.62/2.78 tff(5736,plain,
% 3.62/2.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a606) | c0_1(a606) | (~c1_1(a606)))),
% 3.62/2.78 inference(quant_inst,[status(thm)],[])).
% 3.62/2.78 tff(5737,plain,
% 3.62/2.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a606) | c3_1(a600) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a600)) | (~c0_1(a600)) | c0_1(a606) | (~c1_1(a606))),
% 3.62/2.78 inference(modus_ponens,[status(thm)],[5736, 5735])).
% 3.62/2.78 tff(5738,plain,
% 3.62/2.78 (c0_1(a606)),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[5737, 107, 5726, 5731, 5730, 5351, 5350, 5729, 5728, 5322, 258])).
% 3.62/2.78 tff(5739,plain,
% 3.62/2.78 (~hskp13),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[2553, 5719, 5351, 5350, 5738, 5322, 5717, 5409, 5412, 5408, 5726, 5725, 5720])).
% 3.62/2.78 tff(5740,plain,
% 3.62/2.78 (hskp19 | hskp13),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[2581, 107, 5688, 5721, 5687, 2564])).
% 3.62/2.78 tff(5741,plain,
% 3.62/2.78 (hskp19),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[5740, 5739])).
% 3.62/2.78 tff(5742,plain,
% 3.62/2.78 (~c1_1(a617)),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[2588, 5741])).
% 3.62/2.78 tff(5743,plain,
% 3.62/2.78 (~c0_1(a617)),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[2594, 5741])).
% 3.62/2.78 tff(5744,plain,
% 3.62/2.78 (c2_1(a617)),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[2605, 5741])).
% 3.62/2.78 tff(5745,plain,
% 3.62/2.78 (~c1_1(a678)),
% 3.62/2.78 inference(unit_resolution,[status(thm)],[2612, 107, 5409, 5408, 5744, 5720, 5743, 5742, 5717, 65, 5719])).
% 3.62/2.78 tff(5746,plain,
% 3.62/2.78 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | c3_1(a607) | (~c2_1(a607)) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c3_1(a607) | (~c2_1(a607)) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c0_1(a607)))),
% 3.62/2.78 inference(rewrite,[status(thm)],[])).
% 3.62/2.78 tff(5747,plain,
% 3.62/2.78 ((hskp8 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a588) | c2_1(a588) | (~c0_1(a588))) <=> (hskp8 | c3_1(a607) | (~c2_1(a607)) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c0_1(a607)))),
% 3.62/2.78 inference(rewrite,[status(thm)],[])).
% 3.62/2.78 tff(5748,plain,
% 3.62/2.78 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a588) | c2_1(a588) | (~c0_1(a588)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | c3_1(a607) | (~c2_1(a607)) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c0_1(a607))))),
% 3.62/2.79 inference(monotonicity,[status(thm)],[5747])).
% 3.62/2.79 tff(5749,plain,
% 3.62/2.79 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a588) | c2_1(a588) | (~c0_1(a588)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c3_1(a607) | (~c2_1(a607)) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c0_1(a607)))),
% 3.62/2.79 inference(transitivity,[status(thm)],[5748, 5746])).
% 3.62/2.79 tff(5750,plain,
% 3.62/2.79 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a588) | c2_1(a588) | (~c0_1(a588)))),
% 3.62/2.79 inference(quant_inst,[status(thm)],[])).
% 3.62/2.79 tff(5751,plain,
% 3.62/2.79 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c3_1(a607) | (~c2_1(a607)) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c0_1(a607))),
% 3.62/2.79 inference(modus_ponens,[status(thm)],[5750, 5749])).
% 3.62/2.79 tff(5752,plain,
% 3.62/2.79 (hskp8),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[5751, 107, 33, 5685, 4653, 5683, 4271, 5611, 5722])).
% 3.62/2.79 tff(5753,plain,
% 3.62/2.79 (c3_1(a593)),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[511, 5752])).
% 3.62/2.79 tff(5754,plain,
% 3.62/2.79 (c1_1(a593)),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[522, 5752])).
% 3.62/2.79 tff(5755,plain,
% 3.62/2.79 (~c0_1(a593)),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[2619, 107, 5744, 5720, 5754, 5753, 5743, 5742, 5717, 65, 5719])).
% 3.62/2.79 tff(5756,plain,
% 3.62/2.79 (~c2_1(a593)),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[555, 5752])).
% 3.62/2.79 tff(5757,plain,
% 3.62/2.79 ($false),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[2626, 107, 4654, 5409, 5412, 5754, 5756, 32, 5755, 5745])).
% 3.62/2.79 tff(5758,plain,(c3_1(a633) | c1_1(a607) | c3_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.62/2.79 tff(5759,plain,
% 3.62/2.79 (c3_1(a633)),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[5758, 33, 66])).
% 3.62/2.79 tff(5760,plain,
% 3.62/2.79 (~hskp22),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[3974, 5759])).
% 3.62/2.79 tff(5761,plain,
% 3.62/2.79 ($false),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[5610, 352, 363, 66, 33, 1, 392, 5760])).
% 3.62/2.79 tff(5762,plain,((~hskp26) | c1_1(a607) | c3_1(a607) | c0_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.62/2.79 tff(5763,plain,
% 3.62/2.79 (~hskp26),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[5762, 1, 33, 66])).
% 3.62/2.79 tff(5764,plain,
% 3.62/2.79 (hskp4),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[5347, 5763, 5760, 5244, 33, 66])).
% 3.62/2.79 tff(5765,plain,
% 3.62/2.79 (hskp6),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[147, 5764, 5760])).
% 3.62/2.79 tff(5766,plain,
% 3.62/2.79 (~c0_1(a590)),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[666, 5765])).
% 3.62/2.79 tff(5767,plain,
% 3.62/2.79 (c3_1(a590)),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[677, 5765])).
% 3.62/2.79 tff(5768,plain,
% 3.62/2.79 (c2_1(a590)),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[688, 5765])).
% 3.62/2.79 tff(5769,plain,
% 3.62/2.79 (hskp29),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[2258, 5760])).
% 3.62/2.79 tff(5770,plain,
% 3.62/2.79 (c3_1(a678)),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[2269, 5769])).
% 3.62/2.79 tff(5771,plain,
% 3.62/2.79 (c0_1(a678)),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[2291, 5769])).
% 3.62/2.79 tff(5772,plain,
% 3.62/2.79 (~c1_1(a678)),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[5302, 107, 5771, 5770, 5768, 5767, 66, 4653, 5766, 65, 1])).
% 3.62/2.79 tff(5773,plain,
% 3.62/2.79 (hskp11),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[5320, 5760, 66, 33])).
% 3.62/2.79 tff(5774,plain,
% 3.62/2.79 (~c1_1(a599)),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[428, 5773])).
% 3.62/2.79 tff(5775,plain,
% 3.62/2.79 (c3_1(a599)),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[422, 5773])).
% 3.62/2.79 tff(5776,plain,
% 3.62/2.79 (c2_1(a599)),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[439, 5773])).
% 3.62/2.79 tff(5777,plain,
% 3.62/2.79 (hskp28),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[3240, 107, 5776, 5775, 5420, 5428, 5774, 5245, 1748])).
% 3.62/2.79 tff(5778,plain,
% 3.62/2.79 (c3_1(a612)),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[1139, 5777])).
% 3.62/2.79 tff(5779,plain,
% 3.62/2.79 (c2_1(a612)),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[1150, 5777])).
% 3.62/2.79 tff(5780,plain,
% 3.62/2.79 (c1_1(a612)),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[1435, 5777])).
% 3.62/2.79 tff(5781,plain,
% 3.62/2.79 (~c0_1(a612)),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[5455, 107, 5780, 5778, 5768, 5767, 66, 4653, 5766, 65, 1])).
% 3.62/2.79 tff(5782,plain,
% 3.62/2.79 (~hskp8),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[5234, 5781, 1, 66, 5779, 5778])).
% 3.62/2.79 tff(5783,plain,
% 3.62/2.79 (hskp18),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[5571, 5782, 33, 1])).
% 3.62/2.79 tff(5784,plain,
% 3.62/2.79 (~c2_1(a610)),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[1189, 5783])).
% 3.62/2.79 tff(5785,plain,
% 3.62/2.79 (~c0_1(a610)),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[1195, 5783])).
% 3.62/2.79 tff(5786,plain,
% 3.62/2.79 (c2_1(a678)),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[2280, 5769])).
% 3.62/2.79 tff(5787,plain,
% 3.62/2.79 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a610) | c2_1(a610) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | (~c1_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a610) | c2_1(a610) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | (~c1_1(a610)))),
% 3.62/2.79 inference(rewrite,[status(thm)],[])).
% 3.62/2.79 tff(5788,plain,
% 3.62/2.79 ((hskp17 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c0_1(a610) | c2_1(a610) | (~c1_1(a610))) <=> (hskp17 | c0_1(a610) | c2_1(a610) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | (~c1_1(a610)))),
% 3.62/2.79 inference(rewrite,[status(thm)],[])).
% 3.62/2.79 tff(5789,plain,
% 3.62/2.79 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c0_1(a610) | c2_1(a610) | (~c1_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a610) | c2_1(a610) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | (~c1_1(a610))))),
% 3.62/2.79 inference(monotonicity,[status(thm)],[5788])).
% 3.62/2.79 tff(5790,plain,
% 3.62/2.79 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c0_1(a610) | c2_1(a610) | (~c1_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a610) | c2_1(a610) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | (~c1_1(a610)))),
% 3.62/2.79 inference(transitivity,[status(thm)],[5789, 5787])).
% 3.62/2.79 tff(5791,plain,
% 3.62/2.79 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c0_1(a610) | c2_1(a610) | (~c1_1(a610)))),
% 3.62/2.79 inference(quant_inst,[status(thm)],[])).
% 3.62/2.79 tff(5792,plain,
% 3.62/2.79 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a610) | c2_1(a610) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | (~c1_1(a610))),
% 3.62/2.79 inference(modus_ponens,[status(thm)],[5791, 5790])).
% 3.62/2.79 tff(5793,plain,
% 3.62/2.79 (~c1_1(a610)),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[5792, 107, 4654, 5771, 5786, 5785, 5784, 32, 5772])).
% 3.62/2.79 tff(5794,plain,
% 3.62/2.79 (~hskp0),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[3804, 5772, 4654, 5786, 5771])).
% 3.62/2.79 tff(5795,plain,
% 3.62/2.79 (((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | c0_1(a610) | c2_1(a610) | (~ndr1_0) | c1_1(a610))) <=> ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp0 | c0_1(a610) | c2_1(a610) | (~ndr1_0) | c1_1(a610))),
% 3.62/2.79 inference(rewrite,[status(thm)],[])).
% 3.62/2.79 tff(5796,plain,
% 3.62/2.79 ((hskp26 | hskp0 | (~ndr1_0) | c2_1(a610) | c1_1(a610) | c0_1(a610)) <=> (hskp26 | hskp0 | c0_1(a610) | c2_1(a610) | (~ndr1_0) | c1_1(a610))),
% 3.62/2.79 inference(rewrite,[status(thm)],[])).
% 3.62/2.79 tff(5797,plain,
% 3.62/2.79 (((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | (~ndr1_0) | c2_1(a610) | c1_1(a610) | c0_1(a610))) <=> ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | c0_1(a610) | c2_1(a610) | (~ndr1_0) | c1_1(a610)))),
% 3.62/2.79 inference(monotonicity,[status(thm)],[5796])).
% 3.62/2.79 tff(5798,plain,
% 3.62/2.79 (((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | (~ndr1_0) | c2_1(a610) | c1_1(a610) | c0_1(a610))) <=> ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp0 | c0_1(a610) | c2_1(a610) | (~ndr1_0) | c1_1(a610))),
% 3.62/2.79 inference(transitivity,[status(thm)],[5797, 5795])).
% 3.62/2.79 tff(5799,plain,
% 3.62/2.79 ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | (~ndr1_0) | c2_1(a610) | c1_1(a610) | c0_1(a610))),
% 3.62/2.79 inference(quant_inst,[status(thm)],[])).
% 3.62/2.79 tff(5800,plain,
% 3.62/2.79 ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp0 | c0_1(a610) | c2_1(a610) | (~ndr1_0) | c1_1(a610)),
% 3.62/2.79 inference(modus_ponens,[status(thm)],[5799, 5798])).
% 3.62/2.79 tff(5801,plain,
% 3.62/2.79 ($false),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[5800, 5763, 107, 5794, 5785, 5784, 1032, 5793])).
% 3.62/2.79 tff(5802,plain,(c0_1(a607) | c3_1(a607) | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.62/2.79 tff(5803,plain,
% 3.62/2.79 (c0_1(a607)),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[5802, 33, 66])).
% 3.62/2.79 tff(5804,plain,
% 3.62/2.79 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a623) | c2_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a623) | c2_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)))),
% 3.62/2.79 inference(rewrite,[status(thm)],[])).
% 3.62/2.79 tff(5805,plain,
% 3.62/2.79 ((hskp26 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a623) | c1_1(a623) | c2_1(a623)) <=> (hskp26 | c1_1(a623) | c2_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)))),
% 3.62/2.79 inference(rewrite,[status(thm)],[])).
% 3.62/2.79 tff(5806,plain,
% 3.62/2.79 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a623) | c1_1(a623) | c2_1(a623))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a623) | c2_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607))))),
% 3.62/2.79 inference(monotonicity,[status(thm)],[5805])).
% 3.62/2.79 tff(5807,plain,
% 3.62/2.79 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a623) | c1_1(a623) | c2_1(a623))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a623) | c2_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)))),
% 3.62/2.79 inference(transitivity,[status(thm)],[5806, 5804])).
% 3.62/2.79 tff(5808,plain,
% 3.62/2.79 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a623) | c1_1(a623) | c2_1(a623))),
% 3.62/2.79 inference(quant_inst,[status(thm)],[])).
% 3.62/2.79 tff(5809,plain,
% 3.62/2.79 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a623) | c2_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607))),
% 3.62/2.79 inference(modus_ponens,[status(thm)],[5808, 5807])).
% 3.62/2.79 tff(5810,plain,
% 3.62/2.79 ($false),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[5809, 726, 107, 722, 716, 710, 66, 4653, 995, 2486])).
% 3.62/2.79 tff(5811,plain,((~hskp20) | hskp26 | c1_1(a607) | (~c0_1(a607))), inference(lemma,lemma(discharge,[]))).
% 3.62/2.79 tff(5812,plain,
% 3.62/2.79 (~hskp20),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[5811, 726, 66, 5803])).
% 3.62/2.79 tff(5813,plain,
% 3.62/2.79 (hskp7),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[5378, 5812, 33, 5803])).
% 3.62/2.79 tff(5814,plain,
% 3.62/2.79 (~c1_1(a592)),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[5361, 107, 33, 5776, 5775, 4653, 5774, 5354, 5353, 258, 5803])).
% 3.62/2.79 tff(5815,plain,
% 3.62/2.79 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c3_1(a607) | c1_1(a607) | (~c2_1(a607)) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c3_1(a607) | c1_1(a607) | (~c2_1(a607)) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592))),
% 3.62/2.79 inference(rewrite,[status(thm)],[])).
% 3.62/2.79 tff(5816,plain,
% 3.62/2.79 ((hskp2 | (~ndr1_0) | c1_1(a607) | c3_1(a607) | (~c2_1(a607)) | c3_1(a592) | c1_1(a592) | c0_1(a592)) <=> (hskp2 | c3_1(a607) | c1_1(a607) | (~c2_1(a607)) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592))),
% 3.62/2.79 inference(rewrite,[status(thm)],[])).
% 3.62/2.79 tff(5817,plain,
% 3.62/2.79 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a607) | c3_1(a607) | (~c2_1(a607)) | c3_1(a592) | c1_1(a592) | c0_1(a592))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c3_1(a607) | c1_1(a607) | (~c2_1(a607)) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592)))),
% 3.62/2.79 inference(monotonicity,[status(thm)],[5816])).
% 3.62/2.79 tff(5818,plain,
% 3.62/2.79 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a607) | c3_1(a607) | (~c2_1(a607)) | c3_1(a592) | c1_1(a592) | c0_1(a592))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c3_1(a607) | c1_1(a607) | (~c2_1(a607)) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592))),
% 3.62/2.79 inference(transitivity,[status(thm)],[5817, 5815])).
% 3.62/2.79 tff(5819,plain,
% 3.62/2.79 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a607) | c3_1(a607) | (~c2_1(a607)) | c3_1(a592) | c1_1(a592) | c0_1(a592))),
% 3.62/2.79 inference(quant_inst,[status(thm)],[])).
% 3.62/2.79 tff(5820,plain,
% 3.62/2.79 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c3_1(a607) | c1_1(a607) | (~c2_1(a607)) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592)),
% 3.62/2.79 inference(modus_ponens,[status(thm)],[5819, 5818])).
% 3.62/2.79 tff(5821,plain,
% 3.62/2.79 ($false),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[5820, 107, 1797, 33, 66, 4653, 5354, 5353, 200, 5814])).
% 3.62/2.79 tff(5822,plain,((~hskp7) | hskp2 | c3_1(a607) | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.62/2.79 tff(5823,plain,
% 3.62/2.79 (hskp2),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[5822, 5813, 33, 66])).
% 3.62/2.79 tff(5824,plain,
% 3.62/2.79 (hskp4),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[5347, 5823, 5760, 726, 33, 66])).
% 3.62/2.79 tff(5825,plain,
% 3.62/2.79 (~c2_1(a588)),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[121, 5824])).
% 3.62/2.79 tff(5826,plain,
% 3.62/2.79 (~c1_1(a588)),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[127, 5824])).
% 3.62/2.79 tff(5827,plain,
% 3.62/2.79 (c0_1(a588)),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[138, 5824])).
% 3.62/2.79 tff(5828,plain,
% 3.62/2.79 (hskp1),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[5472, 107, 33, 5827, 4653, 5826, 5825, 1237, 5803])).
% 3.62/2.79 tff(5829,plain,
% 3.62/2.79 (~c0_1(a585)),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[1250, 5828])).
% 3.62/2.79 tff(5830,plain,
% 3.62/2.79 (c2_1(a585)),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[1261, 5828])).
% 3.62/2.79 tff(5831,plain,
% 3.62/2.79 (c1_1(a585)),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[1272, 5828])).
% 3.62/2.79 tff(5832,plain,
% 3.62/2.79 (~c3_1(a588)),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[5444, 107, 5771, 5786, 5770, 5831, 5830, 5826, 5825, 5829, 11])).
% 3.62/2.79 tff(5833,plain,
% 3.62/2.79 (~c3_1(a592)),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[811, 5813])).
% 3.62/2.79 tff(5834,plain,
% 3.62/2.79 (~c0_1(a592)),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[817, 5813])).
% 3.62/2.79 tff(5835,plain,
% 3.62/2.79 (~c1_1(a592)),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[5361, 107, 33, 5776, 5775, 4653, 5774, 5834, 5833, 258, 5803])).
% 3.62/2.79 tff(5836,plain,
% 3.62/2.79 (hskp6),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[147, 5824, 5760])).
% 3.62/2.79 tff(5837,plain,
% 3.62/2.79 (~c0_1(a590)),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[666, 5836])).
% 3.62/2.79 tff(5838,plain,
% 3.62/2.79 (c3_1(a590)),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[677, 5836])).
% 3.62/2.79 tff(5839,plain,
% 3.62/2.79 (c2_1(a590)),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[688, 5836])).
% 3.62/2.79 tff(5840,plain,
% 3.62/2.79 (c2_1(a592)),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[828, 5813])).
% 3.62/2.79 tff(5841,plain,
% 3.62/2.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a592) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a592)) | c1_1(a592))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a592) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a592)) | c1_1(a592))),
% 3.62/2.79 inference(rewrite,[status(thm)],[])).
% 3.62/2.79 tff(5842,plain,
% 3.62/2.79 (((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a592) | c0_1(a592) | (~c2_1(a592))) <=> (c0_1(a592) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a592)) | c1_1(a592))),
% 3.62/2.79 inference(rewrite,[status(thm)],[])).
% 3.62/2.79 tff(5843,plain,
% 3.62/2.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a592) | c0_1(a592) | (~c2_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a592) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a592)) | c1_1(a592)))),
% 3.62/2.79 inference(monotonicity,[status(thm)],[5842])).
% 3.62/2.79 tff(5844,plain,
% 3.62/2.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a592) | c0_1(a592) | (~c2_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a592) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a592)) | c1_1(a592))),
% 3.62/2.79 inference(transitivity,[status(thm)],[5843, 5841])).
% 3.62/2.79 tff(5845,plain,
% 3.62/2.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a592) | c0_1(a592) | (~c2_1(a592)))),
% 3.62/2.79 inference(quant_inst,[status(thm)],[])).
% 3.62/2.79 tff(5846,plain,
% 3.62/2.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a592) | c0_1(a590) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a592)) | c1_1(a592)),
% 3.62/2.79 inference(modus_ponens,[status(thm)],[5845, 5844])).
% 3.62/2.79 tff(5847,plain,
% 3.62/2.79 (~c1_1(a678)),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[5846, 107, 5771, 5770, 5840, 5839, 5838, 5834, 5837, 65, 5835])).
% 3.62/2.79 tff(5848,plain,
% 3.62/2.79 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c3_1(a588))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c3_1(a588))),
% 3.62/2.79 inference(rewrite,[status(thm)],[])).
% 3.62/2.79 tff(5849,plain,
% 3.62/2.79 ((hskp26 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c3_1(a588) | c1_1(a588) | c2_1(a588)) <=> (hskp26 | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c3_1(a588))),
% 3.62/2.79 inference(rewrite,[status(thm)],[])).
% 3.62/2.79 tff(5850,plain,
% 3.62/2.79 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c3_1(a588) | c1_1(a588) | c2_1(a588))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c3_1(a588)))),
% 3.62/2.79 inference(monotonicity,[status(thm)],[5849])).
% 3.62/2.79 tff(5851,plain,
% 3.62/2.79 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c3_1(a588) | c1_1(a588) | c2_1(a588))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c3_1(a588))),
% 3.62/2.79 inference(transitivity,[status(thm)],[5850, 5848])).
% 3.62/2.79 tff(5852,plain,
% 3.62/2.79 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c3_1(a588) | c1_1(a588) | c2_1(a588))),
% 3.62/2.79 inference(quant_inst,[status(thm)],[])).
% 3.62/2.79 tff(5853,plain,
% 3.62/2.79 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c3_1(a588)),
% 3.62/2.79 inference(modus_ponens,[status(thm)],[5852, 5851])).
% 3.62/2.79 tff(5854,plain,
% 3.62/2.79 ($false),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[5853, 726, 107, 5771, 5786, 5826, 5825, 995, 5847, 5832])).
% 3.62/2.79 tff(5855,plain,(hskp26 | c3_1(a607) | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.62/2.79 tff(5856,plain,
% 3.62/2.79 (hskp26),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[5855, 33, 66])).
% 3.62/2.79 tff(5857,plain,
% 3.62/2.79 (c0_1(a583)),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[362, 5856])).
% 3.62/2.79 tff(5858,plain,
% 3.62/2.79 (~hskp7),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[5822, 1797, 33, 66])).
% 3.62/2.79 tff(5859,plain,
% 3.62/2.79 (hskp20),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[5378, 5858, 33, 5803])).
% 3.62/2.79 tff(5860,plain,
% 3.62/2.79 (~c3_1(a623)),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[709, 5859])).
% 3.62/2.79 tff(5861,plain,
% 3.62/2.79 (~c1_1(a623)),
% 3.62/2.79 inference(unit_resolution,[status(thm)],[721, 5859])).
% 3.62/2.79 tff(5862,plain,
% 3.62/2.79 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c3_1(a607) | c1_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a623))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c3_1(a607) | c1_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a623))),
% 3.62/2.79 inference(rewrite,[status(thm)],[])).
% 3.62/2.79 tff(5863,plain,
% 3.62/2.79 ((hskp2 | (~ndr1_0) | c1_1(a607) | c3_1(a607) | (~c2_1(a607)) | c3_1(a623) | c1_1(a623) | c0_1(a623)) <=> (hskp2 | c3_1(a607) | c1_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a623))),
% 3.62/2.79 inference(rewrite,[status(thm)],[])).
% 3.62/2.79 tff(5864,plain,
% 3.62/2.79 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a607) | c3_1(a607) | (~c2_1(a607)) | c3_1(a623) | c1_1(a623) | c0_1(a623))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c3_1(a607) | c1_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a623)))),
% 3.62/2.79 inference(monotonicity,[status(thm)],[5863])).
% 3.62/2.79 tff(5865,plain,
% 3.62/2.80 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a607) | c3_1(a607) | (~c2_1(a607)) | c3_1(a623) | c1_1(a623) | c0_1(a623))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c3_1(a607) | c1_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a623))),
% 3.62/2.80 inference(transitivity,[status(thm)],[5864, 5862])).
% 3.62/2.80 tff(5866,plain,
% 3.62/2.80 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a607) | c3_1(a607) | (~c2_1(a607)) | c3_1(a623) | c1_1(a623) | c0_1(a623))),
% 3.62/2.80 inference(quant_inst,[status(thm)],[])).
% 3.62/2.80 tff(5867,plain,
% 3.62/2.80 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c3_1(a607) | c1_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a623)),
% 3.62/2.80 inference(modus_ponens,[status(thm)],[5866, 5865])).
% 3.62/2.80 tff(5868,plain,
% 3.62/2.80 (c0_1(a623)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[5867, 107, 1797, 33, 5861, 5860, 66, 4653, 200])).
% 3.62/2.80 tff(5869,plain,
% 3.62/2.80 (~c2_1(a623)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[715, 5859])).
% 3.62/2.80 tff(5870,plain,
% 3.62/2.80 (hskp6 | (~c0_1(a623))),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[3930, 107, 5760, 5861, 5869, 43])).
% 3.62/2.80 tff(5871,plain,
% 3.62/2.80 (hskp6),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[5870, 5868])).
% 3.62/2.80 tff(5872,plain,
% 3.62/2.80 (c2_1(a590)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[688, 5871])).
% 3.62/2.80 tff(5873,plain,
% 3.62/2.80 (~c0_1(a590)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[666, 5871])).
% 3.62/2.80 tff(5874,plain,
% 3.62/2.80 (c3_1(a590)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[677, 5871])).
% 3.62/2.80 tff(5875,plain,
% 3.62/2.80 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | c2_1(a623) | c3_1(a623) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a623)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c2_1(a623) | c3_1(a623) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a623)))),
% 3.62/2.80 inference(rewrite,[status(thm)],[])).
% 3.62/2.80 tff(5876,plain,
% 3.62/2.80 ((hskp16 | (~ndr1_0) | c2_1(a623) | c3_1(a623) | (~c0_1(a623)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590))) <=> (hskp16 | c2_1(a623) | c3_1(a623) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a623)))),
% 3.62/2.80 inference(rewrite,[status(thm)],[])).
% 3.62/2.80 tff(5877,plain,
% 3.62/2.80 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a623) | c3_1(a623) | (~c0_1(a623)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | c2_1(a623) | c3_1(a623) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a623))))),
% 3.62/2.80 inference(monotonicity,[status(thm)],[5876])).
% 3.62/2.80 tff(5878,plain,
% 3.62/2.80 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a623) | c3_1(a623) | (~c0_1(a623)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c2_1(a623) | c3_1(a623) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a623)))),
% 3.62/2.80 inference(transitivity,[status(thm)],[5877, 5875])).
% 3.62/2.80 tff(5879,plain,
% 3.62/2.80 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a623) | c3_1(a623) | (~c0_1(a623)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)))),
% 3.62/2.80 inference(quant_inst,[status(thm)],[])).
% 3.62/2.80 tff(5880,plain,
% 3.62/2.80 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c2_1(a623) | c3_1(a623) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c0_1(a623))),
% 3.62/2.80 inference(modus_ponens,[status(thm)],[5879, 5878])).
% 3.62/2.80 tff(5881,plain,
% 3.62/2.80 (hskp16),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[5880, 107, 5872, 5874, 5869, 5860, 5873, 2125, 5868])).
% 3.62/2.80 tff(5882,plain,
% 3.62/2.80 (~c2_1(a606)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[1111, 5881])).
% 3.62/2.80 tff(5883,plain,
% 3.62/2.80 (c2_1(a583)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[391, 5856])).
% 3.62/2.80 tff(5884,plain,
% 3.62/2.80 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | c3_1(a607) | c1_1(a623) | c2_1(a623) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c0_1(a623)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp1 | c3_1(a607) | c1_1(a623) | c2_1(a623) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c0_1(a623)))),
% 3.62/2.80 inference(rewrite,[status(thm)],[])).
% 3.62/2.80 tff(5885,plain,
% 3.62/2.80 ((hskp1 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a623) | c2_1(a623) | (~c0_1(a623))) <=> (hskp1 | c3_1(a607) | c1_1(a623) | c2_1(a623) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c0_1(a623)))),
% 3.62/2.80 inference(rewrite,[status(thm)],[])).
% 3.62/2.80 tff(5886,plain,
% 3.62/2.80 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a623) | c2_1(a623) | (~c0_1(a623)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | c3_1(a607) | c1_1(a623) | c2_1(a623) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c0_1(a623))))),
% 3.62/2.80 inference(monotonicity,[status(thm)],[5885])).
% 3.62/2.80 tff(5887,plain,
% 3.62/2.80 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a623) | c2_1(a623) | (~c0_1(a623)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp1 | c3_1(a607) | c1_1(a623) | c2_1(a623) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c0_1(a623)))),
% 3.62/2.80 inference(transitivity,[status(thm)],[5886, 5884])).
% 3.62/2.80 tff(5888,plain,
% 3.62/2.80 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a623) | c2_1(a623) | (~c0_1(a623)))),
% 3.62/2.80 inference(quant_inst,[status(thm)],[])).
% 3.62/2.80 tff(5889,plain,
% 3.62/2.80 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp1 | c3_1(a607) | c1_1(a623) | c2_1(a623) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c0_1(a623))),
% 3.62/2.80 inference(modus_ponens,[status(thm)],[5888, 5887])).
% 3.62/2.80 tff(5890,plain,
% 3.62/2.80 (hskp1 | (~c0_1(a623))),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[5889, 107, 33, 5861, 5869, 4653, 1237, 5803])).
% 3.62/2.80 tff(5891,plain,
% 3.62/2.80 (hskp1),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[5890, 5868])).
% 3.62/2.80 tff(5892,plain,
% 3.62/2.80 (~c0_1(a585)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[1250, 5891])).
% 3.62/2.80 tff(5893,plain,
% 3.62/2.80 (c1_1(a585)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[1272, 5891])).
% 3.62/2.80 tff(5894,plain,
% 3.62/2.80 (c1_1(a583)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[351, 5856])).
% 3.62/2.80 tff(5895,plain,
% 3.62/2.80 (hskp15),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[5715, 5874, 33, 5894, 5872, 4653, 5893, 5803, 5892, 5883, 5873, 5857])).
% 3.62/2.80 tff(5896,plain,
% 3.62/2.80 (~c0_1(a604)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[1591, 5895])).
% 3.62/2.80 tff(5897,plain,
% 3.62/2.80 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | c3_1(a607) | c2_1(a623) | c3_1(a623) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c0_1(a623)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c3_1(a607) | c2_1(a623) | c3_1(a623) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c0_1(a623)))),
% 3.62/2.80 inference(rewrite,[status(thm)],[])).
% 3.62/2.80 tff(5898,plain,
% 3.62/2.80 ((hskp8 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a623) | c2_1(a623) | (~c0_1(a623))) <=> (hskp8 | c3_1(a607) | c2_1(a623) | c3_1(a623) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c0_1(a623)))),
% 3.62/2.80 inference(rewrite,[status(thm)],[])).
% 3.62/2.80 tff(5899,plain,
% 3.62/2.80 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a623) | c2_1(a623) | (~c0_1(a623)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | c3_1(a607) | c2_1(a623) | c3_1(a623) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c0_1(a623))))),
% 3.62/2.80 inference(monotonicity,[status(thm)],[5898])).
% 3.62/2.80 tff(5900,plain,
% 3.62/2.80 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a623) | c2_1(a623) | (~c0_1(a623)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c3_1(a607) | c2_1(a623) | c3_1(a623) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c0_1(a623)))),
% 3.62/2.80 inference(transitivity,[status(thm)],[5899, 5897])).
% 3.62/2.80 tff(5901,plain,
% 3.62/2.80 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c3_1(a623) | c2_1(a623) | (~c0_1(a623)))),
% 3.62/2.80 inference(quant_inst,[status(thm)],[])).
% 3.62/2.80 tff(5902,plain,
% 3.62/2.80 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c3_1(a607) | c2_1(a623) | c3_1(a623) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c0_1(a623))),
% 3.62/2.80 inference(modus_ponens,[status(thm)],[5901, 5900])).
% 3.62/2.80 tff(5903,plain,
% 3.62/2.80 (hskp8 | (~c0_1(a623))),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[5902, 107, 33, 5869, 5860, 4653, 4271, 5803])).
% 3.62/2.80 tff(5904,plain,
% 3.62/2.80 (hskp8),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[5903, 5868])).
% 3.62/2.80 tff(5905,plain,
% 3.62/2.80 (~c2_1(a593)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[555, 5904])).
% 3.62/2.80 tff(5906,plain,
% 3.62/2.80 (c2_1(a585)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[1261, 5891])).
% 3.62/2.80 tff(5907,plain,
% 3.62/2.80 (c3_1(a593)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[511, 5904])).
% 3.62/2.80 tff(5908,plain,
% 3.62/2.80 (c1_1(a593)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[522, 5904])).
% 3.62/2.80 tff(5909,plain,
% 3.62/2.80 (c1_1(a606)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[1088, 5881])).
% 3.62/2.80 tff(5910,plain,
% 3.62/2.80 (hskp3),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[5154, 107, 4654, 5908, 5907, 5905, 3420])).
% 3.62/2.80 tff(5911,plain,
% 3.62/2.80 (~c1_1(a587)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[939, 5910])).
% 3.62/2.80 tff(5912,plain,
% 3.62/2.80 (c2_1(a587)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[950, 5910])).
% 3.62/2.80 tff(5913,plain,
% 3.62/2.80 (c0_1(a587)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[961, 5910])).
% 3.62/2.80 tff(5914,plain,
% 3.62/2.80 (c0_1(a606)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[5034, 5909, 4654, 5913, 5912, 5882, 5911])).
% 3.62/2.80 tff(5915,plain,
% 3.62/2.80 (((~![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp15 | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)))) <=> ((~![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp15 | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)))),
% 3.62/2.80 inference(rewrite,[status(thm)],[])).
% 3.62/2.80 tff(5916,plain,
% 3.62/2.80 ((hskp25 | hskp15 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606))) <=> (hskp25 | hskp15 | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)))),
% 3.62/2.80 inference(rewrite,[status(thm)],[])).
% 3.62/2.80 tff(5917,plain,
% 3.62/2.80 (((~![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp15 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)))) <=> ((~![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp15 | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606))))),
% 3.62/2.80 inference(monotonicity,[status(thm)],[5916])).
% 3.62/2.80 tff(5918,plain,
% 3.62/2.80 (((~![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp15 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)))) <=> ((~![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp15 | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606)))),
% 3.62/2.80 inference(transitivity,[status(thm)],[5917, 5915])).
% 3.62/2.80 tff(5919,plain,
% 3.62/2.80 ((~![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp15 | (~ndr1_0) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)))),
% 3.62/2.80 inference(quant_inst,[status(thm)],[])).
% 3.62/2.80 tff(5920,plain,
% 3.62/2.80 ((~![U: $i] : (hskp25 | hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp15 | c2_1(a606) | (~ndr1_0) | (~c0_1(a606)) | (~c1_1(a606))),
% 3.62/2.80 inference(modus_ponens,[status(thm)],[5919, 5918])).
% 3.62/2.80 tff(5921,plain,
% 3.62/2.80 (hskp25 | hskp15),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[5920, 107, 1876, 1873, 3004, 2515])).
% 3.62/2.80 tff(5922,plain,
% 3.62/2.80 (hskp25),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[5921, 2490])).
% 3.62/2.80 tff(5923,plain,
% 3.62/2.80 (~c3_1(a651)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[2464, 5922])).
% 3.62/2.80 tff(5924,plain,
% 3.62/2.80 (~c1_1(a651)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[2470, 5922])).
% 3.62/2.80 tff(5925,plain,
% 3.62/2.80 (c2_1(a651)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[2458, 5922])).
% 3.62/2.80 tff(5926,plain,
% 3.62/2.80 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a604) | c3_1(a604) | c1_1(a651) | c3_1(a651) | c0_1(a604) | (~ndr1_0) | (~c2_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a604) | c3_1(a604) | c1_1(a651) | c3_1(a651) | c0_1(a604) | (~ndr1_0) | (~c2_1(a651)))),
% 3.62/2.80 inference(rewrite,[status(thm)],[])).
% 3.62/2.80 tff(5927,plain,
% 3.62/2.80 ((hskp2 | (~ndr1_0) | c1_1(a651) | c3_1(a651) | (~c2_1(a651)) | c3_1(a604) | c1_1(a604) | c0_1(a604)) <=> (hskp2 | c1_1(a604) | c3_1(a604) | c1_1(a651) | c3_1(a651) | c0_1(a604) | (~ndr1_0) | (~c2_1(a651)))),
% 3.62/2.80 inference(rewrite,[status(thm)],[])).
% 3.62/2.80 tff(5928,plain,
% 3.62/2.80 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a651) | c3_1(a651) | (~c2_1(a651)) | c3_1(a604) | c1_1(a604) | c0_1(a604))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a604) | c3_1(a604) | c1_1(a651) | c3_1(a651) | c0_1(a604) | (~ndr1_0) | (~c2_1(a651))))),
% 3.62/2.80 inference(monotonicity,[status(thm)],[5927])).
% 3.62/2.80 tff(5929,plain,
% 3.62/2.80 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a651) | c3_1(a651) | (~c2_1(a651)) | c3_1(a604) | c1_1(a604) | c0_1(a604))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a604) | c3_1(a604) | c1_1(a651) | c3_1(a651) | c0_1(a604) | (~ndr1_0) | (~c2_1(a651)))),
% 3.62/2.80 inference(transitivity,[status(thm)],[5928, 5926])).
% 3.62/2.80 tff(5930,plain,
% 3.62/2.80 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a651) | c3_1(a651) | (~c2_1(a651)) | c3_1(a604) | c1_1(a604) | c0_1(a604))),
% 3.62/2.80 inference(quant_inst,[status(thm)],[])).
% 3.62/2.80 tff(5931,plain,
% 3.62/2.80 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a604) | c3_1(a604) | c1_1(a651) | c3_1(a651) | c0_1(a604) | (~ndr1_0) | (~c2_1(a651))),
% 3.62/2.80 inference(modus_ponens,[status(thm)],[5930, 5929])).
% 3.62/2.80 tff(5932,plain,
% 3.62/2.80 (c1_1(a604)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[5931, 107, 1797, 5925, 2489, 5924, 5923, 2475, 200])).
% 3.62/2.80 tff(5933,plain,
% 3.62/2.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a607) | c3_1(a604) | (~c2_1(a607)) | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a604)) | (~c0_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a607) | c3_1(a604) | (~c2_1(a607)) | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a604)) | (~c0_1(a607)))),
% 3.62/2.80 inference(rewrite,[status(thm)],[])).
% 3.62/2.80 tff(5934,plain,
% 3.62/2.80 (((~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604))) <=> (c3_1(a607) | c3_1(a604) | (~c2_1(a607)) | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a604)) | (~c0_1(a607)))),
% 3.62/2.80 inference(rewrite,[status(thm)],[])).
% 3.62/2.80 tff(5935,plain,
% 3.62/2.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a607) | c3_1(a604) | (~c2_1(a607)) | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a604)) | (~c0_1(a607))))),
% 3.62/2.80 inference(monotonicity,[status(thm)],[5934])).
% 3.62/2.80 tff(5936,plain,
% 3.62/2.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a607) | c3_1(a604) | (~c2_1(a607)) | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a604)) | (~c0_1(a607)))),
% 3.62/2.80 inference(transitivity,[status(thm)],[5935, 5933])).
% 3.62/2.80 tff(5937,plain,
% 3.62/2.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a604) | c0_1(a604) | (~c1_1(a604)))),
% 3.62/2.80 inference(quant_inst,[status(thm)],[])).
% 3.62/2.80 tff(5938,plain,
% 3.62/2.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a607) | c3_1(a604) | (~c2_1(a607)) | c0_1(a604) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c1_1(a604)) | (~c0_1(a607))),
% 3.62/2.80 inference(modus_ponens,[status(thm)],[5937, 5936])).
% 3.62/2.80 tff(5939,plain,
% 3.62/2.80 ($false),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[5938, 107, 33, 5932, 2489, 463, 462, 5355, 2475, 461, 258, 2486])).
% 3.62/2.80 tff(5940,plain,(c3_1(a604) | c3_1(a607) | (~c2_1(a599)) | (~c3_1(a599)) | (~c2_1(a607)) | c0_1(a604) | c1_1(a599) | (~c0_1(a607)) | hskp2 | (~c1_1(a606)) | c2_1(a606) | (~c0_1(a606))), inference(lemma,lemma(discharge,[]))).
% 3.62/2.80 tff(5941,plain,
% 3.62/2.80 (c3_1(a604)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[5940, 2475, 463, 462, 4653, 33, 461, 2486, 1797, 1876, 1873, 2515])).
% 3.62/2.80 tff(5942,plain,
% 3.62/2.80 (~c2_1(a604)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[3040, 3024, 2318, 2317, 2316, 1894, 1893, 862, 1903, 2475, 45, 863, 2987])).
% 3.62/2.80 tff(5943,plain,
% 3.62/2.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a604) | c2_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a604)) | c2_1(a604) | (~c0_1(a606)) | (~c1_1(a606)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a604) | c2_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a604)) | c2_1(a604) | (~c0_1(a606)) | (~c1_1(a606)))),
% 3.62/2.80 inference(rewrite,[status(thm)],[])).
% 3.62/2.80 tff(5944,plain,
% 3.62/2.80 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a604) | c2_1(a604) | (~c3_1(a604))) <=> (c1_1(a604) | c2_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a604)) | c2_1(a604) | (~c0_1(a606)) | (~c1_1(a606)))),
% 3.62/2.80 inference(rewrite,[status(thm)],[])).
% 3.62/2.80 tff(5945,plain,
% 3.62/2.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a604) | c2_1(a604) | (~c3_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c1_1(a604) | c2_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a604)) | c2_1(a604) | (~c0_1(a606)) | (~c1_1(a606))))),
% 3.62/2.80 inference(monotonicity,[status(thm)],[5944])).
% 3.62/2.80 tff(5946,plain,
% 3.62/2.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a604) | c2_1(a604) | (~c3_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a604) | c2_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a604)) | c2_1(a604) | (~c0_1(a606)) | (~c1_1(a606)))),
% 3.62/2.80 inference(transitivity,[status(thm)],[5945, 5943])).
% 3.62/2.80 tff(5947,plain,
% 3.62/2.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a604) | c2_1(a604) | (~c3_1(a604)))),
% 3.62/2.80 inference(quant_inst,[status(thm)],[])).
% 3.62/2.80 tff(5948,plain,
% 3.62/2.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c1_1(a604) | c2_1(a606) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a604)) | c2_1(a604) | (~c0_1(a606)) | (~c1_1(a606))),
% 3.62/2.80 inference(modus_ponens,[status(thm)],[5947, 5946])).
% 3.62/2.80 tff(5949,plain,
% 3.62/2.80 ($false),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[5948, 107, 2318, 2317, 2316, 1876, 3024, 2545, 1873, 1106, 2515, 5942])).
% 3.62/2.80 tff(5950,plain,(c1_1(a604) | (~c0_1(a678)) | (~c2_1(a678)) | (~c3_1(a678)) | (~c1_1(a606)) | (~c3_1(a604)) | c2_1(a606) | (~c0_1(a606)) | (~c1_1(a593)) | c2_1(a593) | (~c3_1(a590)) | (~c3_1(a593)) | c0_1(a604) | c0_1(a590) | (~c2_1(a590)) | hskp17), inference(lemma,lemma(discharge,[]))).
% 3.62/2.80 tff(5951,plain,
% 3.62/2.80 (c1_1(a604)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[5950, 5941, 2317, 2316, 1876, 2318, 1873, 2515, 1894, 1893, 862, 1903, 2475, 45, 863, 4654])).
% 3.62/2.80 tff(5952,plain,
% 3.62/2.80 (c2_1(a604) | (~c1_1(a604))),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[5622, 107, 4654, 66, 4653, 2475, 32, 2486])).
% 3.62/2.80 tff(5953,plain,
% 3.62/2.80 (c2_1(a604)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[5952, 5951])).
% 3.62/2.80 tff(5954,plain,
% 3.62/2.80 (~hskp13),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[2553, 5953, 463, 462, 2515, 461, 2475, 2318, 2317, 2316, 1876, 1873, 5941])).
% 3.62/2.80 tff(5955,assumption,(c2_1(a585)), introduced(assumption)).
% 3.62/2.80 tff(5956,plain,
% 3.62/2.80 (hskp19 | hskp13),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[2581, 107, 5693, 5955, 5692, 2564])).
% 3.62/2.80 tff(5957,plain,
% 3.62/2.80 (hskp19),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[5956, 5954])).
% 3.62/2.80 tff(5958,plain,
% 3.62/2.80 (~c1_1(a617)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[2588, 5957])).
% 3.62/2.80 tff(5959,plain,
% 3.62/2.80 (~c0_1(a617)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[2594, 5957])).
% 3.62/2.80 tff(5960,plain,
% 3.62/2.80 (c2_1(a617)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[2605, 5957])).
% 3.62/2.80 tff(5961,plain,
% 3.62/2.80 (~c1_1(a678)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[2612, 107, 2318, 2316, 5960, 5941, 5959, 5958, 2475, 65, 5953])).
% 3.62/2.80 tff(5962,plain,
% 3.62/2.80 (~c0_1(a593)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[2619, 107, 5960, 5941, 1894, 1903, 5959, 5958, 2475, 65, 5953])).
% 3.62/2.80 tff(5963,plain,
% 3.62/2.80 ($false),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[2626, 107, 4654, 2318, 2317, 1894, 1893, 32, 5962, 5961])).
% 3.62/2.80 tff(5964,plain,(c0_1(a604) | (~c0_1(a678)) | (~c2_1(a678)) | (~c1_1(a593)) | c2_1(a593) | (~c3_1(a593)) | (~c3_1(a678)) | (~c1_1(a585)) | (~c2_1(a585)) | c0_1(a585) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a606)) | c1_1(a599) | (~c1_1(a606)) | c2_1(a606) | c1_1(a607) | (~c0_1(a607)) | (~c3_1(a590)) | c0_1(a590) | (~c2_1(a590)) | c3_1(a607) | hskp2), inference(lemma,lemma(discharge,[]))).
% 3.62/2.80 tff(5965,plain,
% 3.62/2.80 ($false),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[5964, 5914, 5909, 5786, 1797, 5908, 5907, 5770, 5893, 5906, 5892, 5776, 5775, 5905, 5774, 5896, 5882, 66, 5803, 5874, 5873, 5872, 33, 5771])).
% 3.62/2.80 tff(5966,plain,(hskp2 | c1_1(a607) | c3_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.62/2.80 tff(5967,plain,
% 3.62/2.80 (hskp2),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[5966, 33, 66])).
% 3.62/2.80 tff(5968,plain,
% 3.62/2.80 (~c3_1(a586)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[218, 5967])).
% 3.62/2.80 tff(5969,plain,
% 3.62/2.80 (c1_1(a586)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[229, 5967])).
% 3.62/2.80 tff(5970,plain,
% 3.62/2.80 (c2_1(a586)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[1474, 5967])).
% 3.62/2.80 tff(5971,plain,
% 3.62/2.80 (hskp4),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[5002, 5970, 5771, 5770, 5786, 5857, 5894, 5969, 66, 5883, 33, 5776, 5775, 5774, 5968])).
% 3.62/2.80 tff(5972,plain,
% 3.62/2.80 (hskp6),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[147, 5971, 5760])).
% 3.62/2.80 tff(5973,plain,
% 3.62/2.80 (~c0_1(a590)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[666, 5972])).
% 3.62/2.80 tff(5974,plain,
% 3.62/2.80 (~c2_1(a588)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[121, 5971])).
% 3.62/2.80 tff(5975,plain,
% 3.62/2.80 (~c1_1(a588)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[127, 5971])).
% 3.62/2.80 tff(5976,plain,
% 3.62/2.80 (c0_1(a588)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[138, 5971])).
% 3.62/2.80 tff(5977,plain,
% 3.62/2.80 (hskp1),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[5472, 107, 33, 5976, 4653, 5975, 5974, 1237, 5803])).
% 3.62/2.80 tff(5978,plain,
% 3.62/2.80 (~c0_1(a585)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[1250, 5977])).
% 3.62/2.80 tff(5979,plain,
% 3.62/2.80 (c3_1(a590)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[677, 5972])).
% 3.62/2.80 tff(5980,plain,
% 3.62/2.80 (c2_1(a590)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[688, 5972])).
% 3.62/2.80 tff(5981,plain,
% 3.62/2.80 (c1_1(a585)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[1272, 5977])).
% 3.62/2.80 tff(5982,plain,
% 3.62/2.80 (hskp15),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[5715, 5981, 33, 5894, 5980, 4653, 5979, 5803, 5978, 5883, 5973, 5857])).
% 3.62/2.80 tff(5983,plain,
% 3.62/2.80 (~c0_1(a604)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[1591, 5982])).
% 3.62/2.80 tff(5984,plain,
% 3.62/2.80 (c1_1(a604)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[1613, 5982])).
% 3.62/2.80 tff(5985,plain,
% 3.62/2.80 (c2_1(a604)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[5622, 107, 4654, 5984, 66, 4653, 5983, 32, 5803])).
% 3.62/2.80 tff(5986,plain,
% 3.62/2.80 (c3_1(a604)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[1602, 5982])).
% 3.62/2.80 tff(5987,plain,
% 3.62/2.80 (c0_1(a586)),
% 3.62/2.80 inference(unit_resolution,[status(thm)],[4953, 107, 33, 5776, 5775, 5969, 4653, 5774, 5968, 258, 5803])).
% 3.62/2.80 tff(5988,plain,
% 3.62/2.80 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp16 | c0_1(a604) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)) | (~c3_1(a604)) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp16 | c0_1(a604) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)) | (~c3_1(a604)) | (~c1_1(a604)))),
% 3.62/2.80 inference(rewrite,[status(thm)],[])).
% 3.62/2.80 tff(5989,plain,
% 3.62/2.80 ((hskp16 | (~ndr1_0) | c3_1(a586) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604))) <=> (hskp16 | c0_1(a604) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)) | (~c3_1(a604)) | (~c1_1(a604)))),
% 3.62/2.80 inference(rewrite,[status(thm)],[])).
% 3.62/2.81 tff(5990,plain,
% 3.62/2.81 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a586) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp16 | c0_1(a604) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)) | (~c3_1(a604)) | (~c1_1(a604))))),
% 3.62/2.81 inference(monotonicity,[status(thm)],[5989])).
% 3.62/2.81 tff(5991,plain,
% 3.62/2.81 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a586) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp16 | c0_1(a604) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)) | (~c3_1(a604)) | (~c1_1(a604)))),
% 3.62/2.81 inference(transitivity,[status(thm)],[5990, 5988])).
% 3.62/2.81 tff(5992,plain,
% 3.62/2.81 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a586) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a604) | (~c1_1(a604)) | (~c3_1(a604)))),
% 3.62/2.81 inference(quant_inst,[status(thm)],[])).
% 3.62/2.81 tff(5993,plain,
% 3.62/2.81 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp16 | c0_1(a604) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)) | (~c3_1(a604)) | (~c1_1(a604))),
% 3.62/2.81 inference(modus_ponens,[status(thm)],[5992, 5991])).
% 3.62/2.81 tff(5994,plain,
% 3.62/2.81 (hskp16),
% 3.62/2.81 inference(unit_resolution,[status(thm)],[5993, 107, 5984, 5986, 5969, 5983, 5968, 1425, 5987])).
% 3.62/2.81 tff(5995,plain,
% 3.62/2.81 (~c2_1(a606)),
% 3.62/2.81 inference(unit_resolution,[status(thm)],[1111, 5994])).
% 3.62/2.81 tff(5996,plain,
% 3.62/2.81 (c1_1(a606)),
% 3.62/2.81 inference(unit_resolution,[status(thm)],[1088, 5994])).
% 3.62/2.81 tff(5997,plain,
% 3.62/2.81 (hskp3),
% 3.62/2.81 inference(unit_resolution,[status(thm)],[4968, 5969, 5760, 66, 33, 5776, 5775, 5857, 5774, 5968, 5894])).
% 3.62/2.81 tff(5998,plain,
% 3.62/2.81 (~c1_1(a587)),
% 3.62/2.81 inference(unit_resolution,[status(thm)],[939, 5997])).
% 3.62/2.81 tff(5999,plain,
% 3.62/2.81 (c2_1(a587)),
% 3.62/2.81 inference(unit_resolution,[status(thm)],[950, 5997])).
% 3.62/2.81 tff(6000,plain,
% 3.62/2.81 (c0_1(a587)),
% 3.62/2.81 inference(unit_resolution,[status(thm)],[961, 5997])).
% 3.62/2.81 tff(6001,plain,
% 3.62/2.81 (c0_1(a606)),
% 3.62/2.81 inference(unit_resolution,[status(thm)],[5034, 5996, 4654, 6000, 5999, 5995, 5998])).
% 3.62/2.81 tff(6002,plain,
% 3.62/2.81 (~hskp13),
% 3.62/2.81 inference(unit_resolution,[status(thm)],[2553, 6001, 5776, 5775, 5985, 5774, 5983, 5771, 5786, 5770, 5996, 5995, 5986])).
% 3.62/2.81 tff(6003,plain,
% 3.62/2.81 (c2_1(a585)),
% 3.62/2.81 inference(unit_resolution,[status(thm)],[1261, 5977])).
% 3.62/2.81 tff(6004,plain,
% 3.62/2.81 (hskp19 | hskp13),
% 3.62/2.81 inference(unit_resolution,[status(thm)],[2581, 107, 5981, 6003, 5978, 2564])).
% 3.62/2.81 tff(6005,plain,
% 3.62/2.81 (hskp19),
% 3.62/2.81 inference(unit_resolution,[status(thm)],[6004, 6002])).
% 3.62/2.81 tff(6006,plain,
% 3.62/2.81 (~c1_1(a617)),
% 3.62/2.81 inference(unit_resolution,[status(thm)],[2588, 6005])).
% 3.62/2.81 tff(6007,plain,
% 3.62/2.81 (~c0_1(a617)),
% 3.62/2.81 inference(unit_resolution,[status(thm)],[2594, 6005])).
% 3.62/2.81 tff(6008,plain,
% 3.62/2.81 (c2_1(a617)),
% 3.62/2.81 inference(unit_resolution,[status(thm)],[2605, 6005])).
% 3.62/2.81 tff(6009,plain,
% 3.62/2.81 (hskp28),
% 3.62/2.81 inference(unit_resolution,[status(thm)],[3240, 107, 5776, 5775, 5969, 5970, 5774, 5968, 1748])).
% 3.62/2.81 tff(6010,plain,
% 3.62/2.81 (c3_1(a612)),
% 3.62/2.81 inference(unit_resolution,[status(thm)],[1139, 6009])).
% 3.62/2.81 tff(6011,plain,
% 3.62/2.81 (c1_1(a612)),
% 3.62/2.81 inference(unit_resolution,[status(thm)],[1435, 6009])).
% 3.62/2.81 tff(6012,plain,
% 3.62/2.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617)))),
% 3.62/2.81 inference(rewrite,[status(thm)],[])).
% 3.62/2.81 tff(6013,plain,
% 3.62/2.81 (((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617))) <=> (c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617)))),
% 3.62/2.81 inference(rewrite,[status(thm)],[])).
% 3.62/2.81 tff(6014,plain,
% 3.62/2.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617))))),
% 3.62/2.81 inference(monotonicity,[status(thm)],[6013])).
% 3.62/2.81 tff(6015,plain,
% 3.62/2.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617)))),
% 3.62/2.81 inference(transitivity,[status(thm)],[6014, 6012])).
% 3.62/2.81 tff(6016,plain,
% 3.62/2.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))),
% 3.62/2.81 inference(quant_inst,[status(thm)],[])).
% 3.62/2.81 tff(6017,plain,
% 3.62/2.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a617) | c1_1(a617) | c0_1(a604) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c2_1(a617))),
% 3.62/2.81 inference(modus_ponens,[status(thm)],[6016, 6015])).
% 3.62/2.81 tff(6018,plain,
% 3.62/2.81 (~c0_1(a612)),
% 3.62/2.81 inference(unit_resolution,[status(thm)],[6017, 107, 6011, 6010, 6008, 5986, 6007, 6006, 5983, 65, 5985])).
% 3.62/2.81 tff(6019,plain,
% 3.62/2.81 (~c3_1(a588)),
% 3.62/2.81 inference(unit_resolution,[status(thm)],[5444, 107, 5771, 5786, 5770, 5981, 6003, 5975, 5974, 5978, 11])).
% 3.62/2.81 tff(6020,plain,
% 3.62/2.81 (hskp8),
% 3.62/2.81 inference(unit_resolution,[status(thm)],[5751, 107, 33, 5976, 4653, 5974, 4271, 5803, 6019])).
% 3.62/2.81 tff(6021,plain,
% 3.62/2.81 (c3_1(a593)),
% 3.62/2.81 inference(unit_resolution,[status(thm)],[511, 6020])).
% 3.62/2.81 tff(6022,plain,
% 3.62/2.81 (c1_1(a593)),
% 3.62/2.81 inference(unit_resolution,[status(thm)],[522, 6020])).
% 3.62/2.81 tff(6023,plain,
% 3.62/2.81 (c2_1(a612)),
% 3.62/2.81 inference(unit_resolution,[status(thm)],[1150, 6009])).
% 3.62/2.81 tff(6024,plain,
% 3.62/2.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a617) | c1_1(a617) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a617) | c1_1(a617) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a617)))),
% 3.62/2.81 inference(rewrite,[status(thm)],[])).
% 3.62/2.81 tff(6025,plain,
% 3.62/2.81 (((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617))) <=> (c0_1(a617) | c1_1(a617) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a617)))),
% 3.62/2.81 inference(rewrite,[status(thm)],[])).
% 3.62/2.81 tff(6026,plain,
% 3.62/2.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a617) | c1_1(a617) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a617))))),
% 3.62/2.81 inference(monotonicity,[status(thm)],[6025])).
% 3.62/2.81 tff(6027,plain,
% 3.62/2.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a617) | c1_1(a617) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a617)))),
% 3.62/2.81 inference(transitivity,[status(thm)],[6026, 6024])).
% 3.62/2.81 tff(6028,plain,
% 3.62/2.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))),
% 3.62/2.81 inference(quant_inst,[status(thm)],[])).
% 3.62/2.81 tff(6029,plain,
% 3.62/2.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a617) | c1_1(a617) | (~ndr1_0) | c0_1(a612) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c2_1(a617))),
% 3.62/2.81 inference(modus_ponens,[status(thm)],[6028, 6027])).
% 3.62/2.81 tff(6030,plain,
% 3.62/2.81 (~c0_1(a593)),
% 3.62/2.81 inference(unit_resolution,[status(thm)],[6029, 107, 6023, 6010, 6008, 6022, 6021, 6007, 6006, 65, 6018])).
% 3.62/2.81 tff(6031,plain,
% 3.62/2.81 (~c2_1(a593)),
% 3.62/2.81 inference(unit_resolution,[status(thm)],[555, 6020])).
% 3.62/2.81 tff(6032,plain,
% 3.62/2.81 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c1_1(a607) | (~c2_1(a607)) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c1_1(a607) | (~c2_1(a607)) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607)))),
% 3.62/2.81 inference(rewrite,[status(thm)],[])).
% 3.62/2.81 tff(6033,plain,
% 3.62/2.81 ((hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593))) <=> (hskp17 | c1_1(a607) | (~c2_1(a607)) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607)))),
% 3.62/2.81 inference(rewrite,[status(thm)],[])).
% 3.62/2.81 tff(6034,plain,
% 3.62/2.81 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c1_1(a607) | (~c2_1(a607)) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607))))),
% 3.62/2.81 inference(monotonicity,[status(thm)],[6033])).
% 3.62/2.81 tff(6035,plain,
% 3.62/2.81 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c1_1(a607) | (~c2_1(a607)) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607)))),
% 3.62/2.81 inference(transitivity,[status(thm)],[6034, 6032])).
% 3.62/2.81 tff(6036,plain,
% 3.62/2.81 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)))),
% 3.62/2.81 inference(quant_inst,[status(thm)],[])).
% 3.62/2.81 tff(6037,plain,
% 3.62/2.81 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c1_1(a607) | (~c2_1(a607)) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a607))),
% 3.62/2.81 inference(modus_ponens,[status(thm)],[6036, 6035])).
% 3.62/2.81 tff(6038,plain,
% 3.62/2.81 ($false),
% 3.62/2.81 inference(unit_resolution,[status(thm)],[6037, 107, 4654, 6022, 66, 4653, 6031, 32, 6030, 5803])).
% 3.62/2.81 tff(6039,plain,(c3_1(a607) | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.62/2.81 tff(6040,plain,
% 3.62/2.81 (c3_1(a607)),
% 3.62/2.81 inference(unit_resolution,[status(thm)],[6039, 66])).
% 3.62/2.81 tff(6041,assumption,(hskp28), introduced(assumption)).
% 3.62/2.81 tff(6042,plain,
% 3.62/2.81 (c3_1(a612)),
% 3.62/2.81 inference(unit_resolution,[status(thm)],[1139, 6041])).
% 3.62/2.81 tff(6043,plain,
% 3.62/2.81 (c1_1(a612)),
% 3.62/2.81 inference(unit_resolution,[status(thm)],[1435, 6041])).
% 3.62/2.81 tff(6044,plain,
% 3.62/2.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | c0_1(a607) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | c0_1(a607) | (~c3_1(a607)))),
% 3.62/2.81 inference(rewrite,[status(thm)],[])).
% 3.62/2.81 tff(6045,plain,
% 3.62/2.81 (((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a607) | (~c3_1(a607)) | (~c2_1(a607)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607))) <=> (c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | c0_1(a607) | (~c3_1(a607)))),
% 3.62/2.81 inference(rewrite,[status(thm)],[])).
% 3.62/2.81 tff(6046,plain,
% 3.62/2.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a607) | (~c3_1(a607)) | (~c2_1(a607)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | c0_1(a607) | (~c3_1(a607))))),
% 3.62/2.81 inference(monotonicity,[status(thm)],[6045])).
% 3.62/2.81 tff(6047,plain,
% 3.62/2.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a607) | (~c3_1(a607)) | (~c2_1(a607)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | c0_1(a607) | (~c3_1(a607)))),
% 3.62/2.81 inference(transitivity,[status(thm)],[6046, 6044])).
% 3.62/2.81 tff(6048,plain,
% 3.62/2.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a607) | (~c3_1(a607)) | (~c2_1(a607)) | c1_1(a607) | c0_1(a607) | (~c2_1(a607)))),
% 3.62/2.81 inference(quant_inst,[status(thm)],[])).
% 3.62/2.81 tff(6049,plain,
% 3.62/2.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | c0_1(a607) | (~c3_1(a607))),
% 3.62/2.81 inference(modus_ponens,[status(thm)],[6048, 6047])).
% 3.62/2.81 tff(6050,plain,
% 3.62/2.81 (~c0_1(a612)),
% 3.62/2.81 inference(unit_resolution,[status(thm)],[6049, 107, 6043, 6042, 6040, 66, 4653, 65, 1])).
% 3.62/2.81 tff(6051,plain,
% 3.62/2.81 (c2_1(a612)),
% 3.62/2.81 inference(unit_resolution,[status(thm)],[1150, 6041])).
% 3.62/2.81 tff(6052,plain,
% 3.62/2.81 (~hskp8),
% 3.62/2.81 inference(unit_resolution,[status(thm)],[5234, 6050, 1, 66, 6051, 6042])).
% 3.62/2.81 tff(6053,plain,
% 3.62/2.81 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | c1_1(a607) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | c0_1(a607) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c1_1(a607) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | c0_1(a607) | (~c3_1(a607)))),
% 3.62/2.81 inference(rewrite,[status(thm)],[])).
% 3.62/2.81 tff(6054,plain,
% 3.62/2.81 ((hskp8 | (~ndr1_0) | c0_1(a612) | (~c2_1(a612)) | (~c1_1(a612)) | c1_1(a607) | c0_1(a607) | (~c3_1(a607))) <=> (hskp8 | c1_1(a607) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | c0_1(a607) | (~c3_1(a607)))),
% 3.62/2.81 inference(rewrite,[status(thm)],[])).
% 3.62/2.81 tff(6055,plain,
% 3.62/2.81 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a612) | (~c2_1(a612)) | (~c1_1(a612)) | c1_1(a607) | c0_1(a607) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | c1_1(a607) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | c0_1(a607) | (~c3_1(a607))))),
% 3.62/2.81 inference(monotonicity,[status(thm)],[6054])).
% 3.62/2.81 tff(6056,plain,
% 3.62/2.81 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a612) | (~c2_1(a612)) | (~c1_1(a612)) | c1_1(a607) | c0_1(a607) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c1_1(a607) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | c0_1(a607) | (~c3_1(a607)))),
% 3.62/2.81 inference(transitivity,[status(thm)],[6055, 6053])).
% 3.62/2.81 tff(6057,plain,
% 3.62/2.81 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a612) | (~c2_1(a612)) | (~c1_1(a612)) | c1_1(a607) | c0_1(a607) | (~c3_1(a607)))),
% 3.62/2.81 inference(quant_inst,[status(thm)],[])).
% 3.62/2.81 tff(6058,plain,
% 3.62/2.81 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c1_1(a607) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | c0_1(a607) | (~c3_1(a607))),
% 3.62/2.81 inference(modus_ponens,[status(thm)],[6057, 6056])).
% 3.62/2.81 tff(6059,plain,
% 3.62/2.81 ($false),
% 3.62/2.81 inference(unit_resolution,[status(thm)],[6058, 107, 6052, 6043, 6051, 6040, 66, 1317, 1, 6050])).
% 3.62/2.81 tff(6060,plain,((~hskp28) | c1_1(a607) | c0_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.62/2.81 tff(6061,plain,
% 3.62/2.81 (~hskp28),
% 3.62/2.81 inference(unit_resolution,[status(thm)],[6060, 1, 66])).
% 3.62/2.81 tff(6062,plain,
% 3.62/2.81 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c1_1(a607) | (~c2_1(a607)) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a607) | (~c2_1(a607)) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c3_1(a607)))),
% 3.62/2.81 inference(rewrite,[status(thm)],[])).
% 3.62/2.81 tff(6063,plain,
% 3.62/2.81 ((hskp28 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c1_1(a607) | (~c3_1(a607)) | (~c2_1(a607))) <=> (hskp28 | c1_1(a607) | (~c2_1(a607)) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c3_1(a607)))),
% 3.62/2.81 inference(rewrite,[status(thm)],[])).
% 3.62/2.81 tff(6064,plain,
% 3.62/2.81 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c1_1(a607) | (~c3_1(a607)) | (~c2_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c1_1(a607) | (~c2_1(a607)) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c3_1(a607))))),
% 3.62/2.81 inference(monotonicity,[status(thm)],[6063])).
% 3.62/2.81 tff(6065,plain,
% 3.62/2.81 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c1_1(a607) | (~c3_1(a607)) | (~c2_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a607) | (~c2_1(a607)) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c3_1(a607)))),
% 3.62/2.81 inference(transitivity,[status(thm)],[6064, 6062])).
% 3.62/2.81 tff(6066,plain,
% 3.62/2.81 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c1_1(a607) | (~c3_1(a607)) | (~c2_1(a607)))),
% 3.62/2.81 inference(quant_inst,[status(thm)],[])).
% 3.62/2.81 tff(6067,plain,
% 3.62/2.81 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a607) | (~c2_1(a607)) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c3_1(a607))),
% 3.62/2.81 inference(modus_ponens,[status(thm)],[6066, 6065])).
% 3.62/2.81 tff(6068,plain,
% 3.62/2.81 ($false),
% 3.62/2.81 inference(unit_resolution,[status(thm)],[6067, 107, 1973, 6040, 5344, 5345, 66, 4653, 5339, 1748])).
% 3.62/2.81 tff(6069,plain,((~hskp2) | hskp28 | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.62/2.81 tff(6070,plain,
% 3.62/2.81 (~hskp2),
% 3.62/2.81 inference(unit_resolution,[status(thm)],[6069, 6061, 66])).
% 3.62/2.81 tff(6071,plain,
% 3.62/2.81 (^[U: $i] : refl((hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))),
% 3.62/2.81 inference(bind,[status(th)],[])).
% 3.62/2.81 tff(6072,plain,
% 3.62/2.81 (![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 3.62/2.81 inference(quant_intro,[status(thm)],[6071])).
% 3.62/2.81 tff(6073,plain,
% 3.62/2.81 (![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 3.62/2.81 inference(rewrite,[status(thm)],[])).
% 3.62/2.81 tff(6074,plain,
% 3.62/2.81 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp2) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp2))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp2) | hskp7) <=> ((hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp7))), rewrite(((hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp7) <=> (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp2) | hskp7) <=> (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))))),
% 3.62/2.81 inference(bind,[status(th)],[])).
% 3.62/2.81 tff(6075,plain,
% 3.62/2.81 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp2) | hskp7) <=> ![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 3.62/2.81 inference(quant_intro,[status(thm)],[6074])).
% 3.62/2.81 tff(6076,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp2) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause132')).
% 3.62/2.81 tff(6077,plain,
% 3.62/2.81 (![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 3.62/2.81 inference(modus_ponens,[status(thm)],[6076, 6075])).
% 3.62/2.81 tff(6078,plain,
% 3.62/2.81 (![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 3.62/2.81 inference(modus_ponens,[status(thm)],[6077, 6073])).
% 3.62/2.81 tff(6079,plain,(
% 3.62/2.81 ![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 3.62/2.81 inference(skolemize,[status(sab)],[6078])).
% 3.62/2.81 tff(6080,plain,
% 3.62/2.81 (![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 3.62/2.81 inference(modus_ponens,[status(thm)],[6079, 6072])).
% 3.62/2.81 tff(6081,plain,
% 3.62/2.81 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp7 | hskp2 | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp7 | hskp2 | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607))),
% 3.62/2.81 inference(rewrite,[status(thm)],[])).
% 3.62/2.81 tff(6082,plain,
% 3.62/2.81 ((hskp7 | hskp2 | (~ndr1_0) | c1_1(a607) | c0_1(a607) | (~c2_1(a607))) <=> (hskp7 | hskp2 | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607))),
% 3.62/2.81 inference(rewrite,[status(thm)],[])).
% 3.62/2.81 tff(6083,plain,
% 3.62/2.81 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | c1_1(a607) | c0_1(a607) | (~c2_1(a607)))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp7 | hskp2 | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607)))),
% 3.62/2.81 inference(monotonicity,[status(thm)],[6082])).
% 3.62/2.81 tff(6084,plain,
% 3.62/2.81 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | c1_1(a607) | c0_1(a607) | (~c2_1(a607)))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp7 | hskp2 | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607))),
% 3.62/2.81 inference(transitivity,[status(thm)],[6083, 6081])).
% 3.62/2.81 tff(6085,plain,
% 3.62/2.81 ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | c1_1(a607) | c0_1(a607) | (~c2_1(a607)))),
% 3.62/2.81 inference(quant_inst,[status(thm)],[])).
% 3.62/2.81 tff(6086,plain,
% 3.62/2.81 ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp7 | hskp2 | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607)),
% 3.62/2.81 inference(modus_ponens,[status(thm)],[6085, 6084])).
% 3.62/2.81 tff(6087,plain,
% 3.62/2.81 (hskp7 | hskp2 | (~c2_1(a607)) | c0_1(a607)),
% 3.62/2.81 inference(unit_resolution,[status(thm)],[6086, 107, 66, 6080])).
% 3.62/2.81 tff(6088,plain,
% 3.62/2.81 (hskp7),
% 3.62/2.81 inference(unit_resolution,[status(thm)],[6087, 6070, 4653, 1])).
% 3.62/2.81 tff(6089,plain,
% 3.62/2.81 (~c3_1(a592)),
% 3.62/2.81 inference(unit_resolution,[status(thm)],[811, 6088])).
% 3.62/2.81 tff(6090,plain,
% 3.62/2.81 (c2_1(a592)),
% 3.62/2.81 inference(unit_resolution,[status(thm)],[828, 6088])).
% 3.62/2.81 tff(6091,plain,
% 3.62/2.81 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c1_1(a607) | (~c2_1(a607)) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a607) | (~c2_1(a607)) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592)) | (~c3_1(a607)))),
% 3.62/2.81 inference(rewrite,[status(thm)],[])).
% 3.62/2.81 tff(6092,plain,
% 3.62/2.81 ((hskp28 | (~ndr1_0) | c3_1(a592) | (~c2_1(a592)) | (~c1_1(a592)) | c1_1(a607) | (~c3_1(a607)) | (~c2_1(a607))) <=> (hskp28 | c1_1(a607) | (~c2_1(a607)) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592)) | (~c3_1(a607)))),
% 3.62/2.82 inference(rewrite,[status(thm)],[])).
% 3.62/2.82 tff(6093,plain,
% 3.62/2.82 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a592) | (~c2_1(a592)) | (~c1_1(a592)) | c1_1(a607) | (~c3_1(a607)) | (~c2_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c1_1(a607) | (~c2_1(a607)) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592)) | (~c3_1(a607))))),
% 3.62/2.82 inference(monotonicity,[status(thm)],[6092])).
% 3.62/2.82 tff(6094,plain,
% 3.62/2.82 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a592) | (~c2_1(a592)) | (~c1_1(a592)) | c1_1(a607) | (~c3_1(a607)) | (~c2_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a607) | (~c2_1(a607)) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592)) | (~c3_1(a607)))),
% 3.62/2.82 inference(transitivity,[status(thm)],[6093, 6091])).
% 3.62/2.82 tff(6095,plain,
% 3.62/2.82 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a592) | (~c2_1(a592)) | (~c1_1(a592)) | c1_1(a607) | (~c3_1(a607)) | (~c2_1(a607)))),
% 3.62/2.82 inference(quant_inst,[status(thm)],[])).
% 3.62/2.82 tff(6096,plain,
% 3.62/2.82 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a607) | (~c2_1(a607)) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592)) | (~c3_1(a607))),
% 3.62/2.82 inference(modus_ponens,[status(thm)],[6095, 6094])).
% 3.62/2.82 tff(6097,plain,
% 3.62/2.82 (~c1_1(a592)),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[6096, 107, 6061, 6040, 6090, 66, 4653, 6089, 1748])).
% 3.62/2.82 tff(6098,plain,
% 3.62/2.82 (~c0_1(a592)),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[817, 6088])).
% 3.62/2.82 tff(6099,plain,
% 3.62/2.82 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592))),
% 3.62/2.82 inference(rewrite,[status(thm)],[])).
% 3.62/2.82 tff(6100,plain,
% 3.62/2.82 ((hskp2 | (~ndr1_0) | c1_1(a592) | c3_1(a592) | (~c2_1(a592)) | c3_1(a592) | c1_1(a592) | c0_1(a592)) <=> (hskp2 | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592))),
% 3.62/2.82 inference(rewrite,[status(thm)],[])).
% 3.62/2.82 tff(6101,plain,
% 3.62/2.82 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a592) | c3_1(a592) | (~c2_1(a592)) | c3_1(a592) | c1_1(a592) | c0_1(a592))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592)))),
% 3.62/2.82 inference(monotonicity,[status(thm)],[6100])).
% 3.62/2.82 tff(6102,plain,
% 3.62/2.82 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a592) | c3_1(a592) | (~c2_1(a592)) | c3_1(a592) | c1_1(a592) | c0_1(a592))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592))),
% 3.62/2.82 inference(transitivity,[status(thm)],[6101, 6099])).
% 3.62/2.82 tff(6103,plain,
% 3.62/2.82 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a592) | c3_1(a592) | (~c2_1(a592)) | c3_1(a592) | c1_1(a592) | c0_1(a592))),
% 3.62/2.82 inference(quant_inst,[status(thm)],[])).
% 3.62/2.82 tff(6104,plain,
% 3.62/2.82 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592)),
% 3.62/2.82 inference(modus_ponens,[status(thm)],[6103, 6102])).
% 3.62/2.82 tff(6105,plain,
% 3.62/2.82 ($false),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[6104, 107, 6070, 6090, 6098, 6089, 200, 6097])).
% 3.62/2.82 tff(6106,plain,(c0_1(a607) | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.62/2.82 tff(6107,plain,
% 3.62/2.82 (c0_1(a607)),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[6106, 66])).
% 3.62/2.82 tff(6108,assumption,(~hskp7), introduced(assumption)).
% 3.62/2.82 tff(6109,assumption,(~hskp20), introduced(assumption)).
% 3.62/2.82 tff(6110,plain,
% 3.62/2.82 (^[U: $i] : refl((hskp8 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp8 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))),
% 3.62/2.82 inference(bind,[status(th)],[])).
% 3.62/2.82 tff(6111,plain,
% 3.62/2.82 (![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 3.62/2.82 inference(quant_intro,[status(thm)],[6110])).
% 3.62/2.82 tff(6112,plain,
% 3.62/2.82 (![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 3.62/2.82 inference(rewrite,[status(thm)],[])).
% 3.62/2.82 tff(6113,plain,
% 3.62/2.82 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp8) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp8))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp8) | hskp6) <=> ((hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp6))), rewrite(((hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp6) <=> (hskp8 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp8) | hskp6) <=> (hskp8 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))))),
% 3.62/2.82 inference(bind,[status(th)],[])).
% 3.62/2.82 tff(6114,plain,
% 3.62/2.82 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp8) | hskp6) <=> ![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 3.62/2.82 inference(quant_intro,[status(thm)],[6113])).
% 3.62/2.82 tff(6115,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp8) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause141')).
% 3.62/2.82 tff(6116,plain,
% 3.62/2.82 (![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 3.62/2.82 inference(modus_ponens,[status(thm)],[6115, 6114])).
% 3.62/2.82 tff(6117,plain,
% 3.62/2.82 (![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 3.62/2.82 inference(modus_ponens,[status(thm)],[6116, 6112])).
% 3.62/2.82 tff(6118,plain,(
% 3.62/2.82 ![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 3.62/2.82 inference(skolemize,[status(sab)],[6117])).
% 3.62/2.82 tff(6119,plain,
% 3.62/2.82 (![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 3.62/2.82 inference(modus_ponens,[status(thm)],[6118, 6111])).
% 3.62/2.82 tff(6120,plain,
% 3.62/2.82 (~hskp20),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[5811, 726, 66, 6107])).
% 3.62/2.82 tff(6121,assumption,(hskp18), introduced(assumption)).
% 3.62/2.82 tff(6122,plain,
% 3.62/2.82 (~c2_1(a610)),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[1189, 6121])).
% 3.62/2.82 tff(6123,plain,
% 3.62/2.82 (~c0_1(a610)),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[1195, 6121])).
% 3.62/2.82 tff(6124,plain,
% 3.62/2.82 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c1_1(a607) | (~c2_1(a607)) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c1_1(a607) | (~c2_1(a607)) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c0_1(a607)))),
% 3.62/2.82 inference(rewrite,[status(thm)],[])).
% 3.62/2.82 tff(6125,plain,
% 3.62/2.82 ((hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584))) <=> (hskp17 | c1_1(a607) | (~c2_1(a607)) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c0_1(a607)))),
% 3.62/2.82 inference(rewrite,[status(thm)],[])).
% 3.62/2.82 tff(6126,plain,
% 3.62/2.82 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c1_1(a607) | (~c2_1(a607)) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c0_1(a607))))),
% 3.62/2.82 inference(monotonicity,[status(thm)],[6125])).
% 3.62/2.82 tff(6127,plain,
% 3.62/2.82 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c1_1(a607) | (~c2_1(a607)) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c0_1(a607)))),
% 3.62/2.82 inference(transitivity,[status(thm)],[6126, 6124])).
% 3.62/2.82 tff(6128,plain,
% 3.62/2.82 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a584) | c2_1(a584) | (~c1_1(a584)))),
% 3.62/2.82 inference(quant_inst,[status(thm)],[])).
% 3.62/2.82 tff(6129,plain,
% 3.62/2.82 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c1_1(a607) | (~c2_1(a607)) | c0_1(a584) | c2_1(a584) | (~ndr1_0) | (~c1_1(a584)) | (~c0_1(a607))),
% 3.62/2.82 inference(modus_ponens,[status(thm)],[6128, 6127])).
% 3.62/2.82 tff(6130,plain,
% 3.62/2.82 ($false),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[6129, 107, 4654, 3796, 66, 4653, 3795, 3794, 32, 2486])).
% 3.62/2.82 tff(6131,plain,((~hskp0) | c1_1(a607) | (~c0_1(a607))), inference(lemma,lemma(discharge,[]))).
% 3.62/2.82 tff(6132,plain,
% 3.62/2.82 (~hskp0),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[6131, 6107, 66])).
% 3.62/2.82 tff(6133,plain,
% 3.62/2.82 (c1_1(a610)),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[5800, 726, 107, 6132, 6123, 6122, 1032])).
% 3.62/2.82 tff(6134,plain,
% 3.62/2.82 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a610) | c2_1(a610) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c1_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a610) | c2_1(a610) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c1_1(a610)))),
% 3.62/2.82 inference(rewrite,[status(thm)],[])).
% 3.62/2.82 tff(6135,plain,
% 3.62/2.82 ((hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a610) | c2_1(a610) | (~c1_1(a610))) <=> (hskp17 | c0_1(a610) | c2_1(a610) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c1_1(a610)))),
% 3.62/2.82 inference(rewrite,[status(thm)],[])).
% 3.62/2.82 tff(6136,plain,
% 3.62/2.82 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a610) | c2_1(a610) | (~c1_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a610) | c2_1(a610) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c1_1(a610))))),
% 3.62/2.82 inference(monotonicity,[status(thm)],[6135])).
% 3.62/2.82 tff(6137,plain,
% 3.62/2.82 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a610) | c2_1(a610) | (~c1_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a610) | c2_1(a610) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c1_1(a610)))),
% 3.62/2.82 inference(transitivity,[status(thm)],[6136, 6134])).
% 3.62/2.82 tff(6138,plain,
% 3.62/2.82 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a610) | c2_1(a610) | (~c1_1(a610)))),
% 3.62/2.82 inference(quant_inst,[status(thm)],[])).
% 3.62/2.82 tff(6139,plain,
% 3.62/2.82 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a610) | c2_1(a610) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c1_1(a610))),
% 3.62/2.82 inference(modus_ponens,[status(thm)],[6138, 6137])).
% 3.62/2.82 tff(6140,plain,
% 3.62/2.82 ($false),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[6139, 107, 4654, 6123, 6122, 66, 4653, 32, 6107, 6133])).
% 3.62/2.82 tff(6141,plain,((~hskp18) | c1_1(a607) | hskp26), inference(lemma,lemma(discharge,[]))).
% 3.62/2.82 tff(6142,plain,
% 3.62/2.82 (~hskp18),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[6141, 726, 66])).
% 3.62/2.82 tff(6143,plain,
% 3.62/2.82 (hskp12),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[787, 1709, 726])).
% 3.62/2.82 tff(6144,plain,
% 3.62/2.82 (~c3_1(a600)),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[741, 6143])).
% 3.62/2.82 tff(6145,plain,
% 3.62/2.82 (c2_1(a600)),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[752, 6143])).
% 3.62/2.82 tff(6146,plain,
% 3.62/2.82 (c0_1(a600)),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[763, 6143])).
% 3.62/2.82 tff(6147,plain,
% 3.62/2.82 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | hskp7 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)))),
% 3.62/2.82 inference(rewrite,[status(thm)],[])).
% 3.62/2.82 tff(6148,plain,
% 3.62/2.82 ((hskp20 | hskp7 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600))) <=> (hskp20 | hskp7 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)))),
% 3.62/2.82 inference(rewrite,[status(thm)],[])).
% 3.62/2.82 tff(6149,plain,
% 3.62/2.82 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600))))),
% 3.62/2.82 inference(monotonicity,[status(thm)],[6148])).
% 3.62/2.82 tff(6150,plain,
% 3.62/2.82 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | hskp7 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)))),
% 3.62/2.82 inference(transitivity,[status(thm)],[6149, 6147])).
% 3.62/2.82 tff(6151,plain,
% 3.62/2.82 ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)))),
% 3.62/2.82 inference(quant_inst,[status(thm)],[])).
% 3.62/2.82 tff(6152,plain,
% 3.62/2.82 ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | hskp7 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600))),
% 3.62/2.82 inference(modus_ponens,[status(thm)],[6151, 6150])).
% 3.62/2.82 tff(6153,plain,
% 3.62/2.82 (hskp7),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[6152, 107, 6109, 6146, 6145, 6144, 1382])).
% 3.62/2.82 tff(6154,plain,
% 3.62/2.82 (~c3_1(a592)),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[811, 6153])).
% 3.62/2.82 tff(6155,plain,
% 3.62/2.82 (~c0_1(a592)),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[817, 6153])).
% 3.62/2.82 tff(6156,plain,
% 3.62/2.82 (c2_1(a592)),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[828, 6153])).
% 3.62/2.82 tff(6157,assumption,(~hskp18), introduced(assumption)).
% 3.62/2.82 tff(6158,plain,
% 3.62/2.82 (((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | hskp8 | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)))) <=> ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | hskp8 | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)))),
% 3.62/2.82 inference(rewrite,[status(thm)],[])).
% 3.62/2.82 tff(6159,plain,
% 3.62/2.82 ((hskp18 | hskp8 | (~ndr1_0) | c0_1(a592) | c3_1(a592) | (~c2_1(a592))) <=> (hskp18 | hskp8 | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)))),
% 3.62/2.82 inference(rewrite,[status(thm)],[])).
% 3.62/2.82 tff(6160,plain,
% 3.62/2.82 (((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | hskp8 | (~ndr1_0) | c0_1(a592) | c3_1(a592) | (~c2_1(a592)))) <=> ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | hskp8 | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592))))),
% 3.62/2.82 inference(monotonicity,[status(thm)],[6159])).
% 3.62/2.82 tff(6161,plain,
% 3.62/2.82 (((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | hskp8 | (~ndr1_0) | c0_1(a592) | c3_1(a592) | (~c2_1(a592)))) <=> ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | hskp8 | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)))),
% 3.62/2.82 inference(transitivity,[status(thm)],[6160, 6158])).
% 3.62/2.82 tff(6162,plain,
% 3.62/2.82 ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | hskp8 | (~ndr1_0) | c0_1(a592) | c3_1(a592) | (~c2_1(a592)))),
% 3.62/2.82 inference(quant_inst,[status(thm)],[])).
% 3.62/2.82 tff(6163,plain,
% 3.62/2.82 ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | hskp8 | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592))),
% 3.62/2.82 inference(modus_ponens,[status(thm)],[6162, 6161])).
% 3.62/2.82 tff(6164,plain,
% 3.62/2.82 ($false),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[6163, 107, 6157, 1709, 6156, 6155, 6154, 5564])).
% 3.62/2.82 tff(6165,plain,(hskp8 | hskp18 | hskp20 | hskp26), inference(lemma,lemma(discharge,[]))).
% 3.62/2.82 tff(6166,plain,
% 3.62/2.82 (hskp8),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[6165, 6142, 6120, 726])).
% 3.62/2.82 tff(6167,plain,
% 3.62/2.82 (~c2_1(a593)),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[555, 6166])).
% 3.62/2.82 tff(6168,plain,
% 3.62/2.82 (c3_1(a593)),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[511, 6166])).
% 3.62/2.82 tff(6169,plain,
% 3.62/2.82 (c1_1(a593)),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[522, 6166])).
% 3.62/2.82 tff(6170,plain,
% 3.62/2.82 (hskp3),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[5154, 107, 4654, 6169, 6168, 6167, 3420])).
% 3.62/2.82 tff(6171,plain,
% 3.62/2.82 (~c1_1(a587)),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[939, 6170])).
% 3.62/2.82 tff(6172,plain,
% 3.62/2.82 (hskp22),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[105, 269, 4654])).
% 3.62/2.82 tff(6173,plain,
% 3.62/2.82 (~c3_1(a633)),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[3974, 6172])).
% 3.62/2.82 tff(6174,plain,
% 3.62/2.82 (c1_1(a633)),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[3962, 6172])).
% 3.62/2.82 tff(6175,plain,
% 3.62/2.82 (~c2_1(a633)),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[4564, 269, 107, 6157, 6174, 6173, 1796])).
% 3.62/2.82 tff(6176,plain,
% 3.62/2.82 (~c0_1(a633)),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[3968, 6172])).
% 3.62/2.82 tff(6177,plain,
% 3.62/2.82 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a633) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | c2_1(a633) | (~c1_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a633) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | c2_1(a633) | (~c1_1(a633)))),
% 3.62/2.82 inference(rewrite,[status(thm)],[])).
% 3.62/2.82 tff(6178,plain,
% 3.62/2.82 ((hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a633) | c2_1(a633) | (~c1_1(a633))) <=> (hskp17 | c0_1(a633) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | c2_1(a633) | (~c1_1(a633)))),
% 3.62/2.82 inference(rewrite,[status(thm)],[])).
% 3.62/2.82 tff(6179,plain,
% 3.62/2.82 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a633) | c2_1(a633) | (~c1_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a633) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | c2_1(a633) | (~c1_1(a633))))),
% 3.62/2.82 inference(monotonicity,[status(thm)],[6178])).
% 3.62/2.82 tff(6180,plain,
% 3.62/2.82 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a633) | c2_1(a633) | (~c1_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a633) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | c2_1(a633) | (~c1_1(a633)))),
% 3.62/2.82 inference(transitivity,[status(thm)],[6179, 6177])).
% 3.62/2.82 tff(6181,plain,
% 3.62/2.82 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a633) | c2_1(a633) | (~c1_1(a633)))),
% 3.62/2.82 inference(quant_inst,[status(thm)],[])).
% 3.62/2.82 tff(6182,plain,
% 3.62/2.82 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a633) | c1_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | c2_1(a633) | (~c1_1(a633))),
% 3.62/2.82 inference(modus_ponens,[status(thm)],[6181, 6180])).
% 3.62/2.82 tff(6183,plain,
% 3.62/2.82 ($false),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[6182, 107, 4654, 6174, 6176, 66, 4653, 32, 6107, 6175])).
% 3.62/2.82 tff(6184,plain,(hskp29 | c1_1(a607) | hskp18), inference(lemma,lemma(discharge,[]))).
% 3.62/2.82 tff(6185,plain,
% 3.62/2.82 (hskp29),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[6184, 6142, 66])).
% 3.62/2.82 tff(6186,plain,
% 3.62/2.82 (c3_1(a678)),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[2269, 6185])).
% 3.62/2.82 tff(6187,plain,
% 3.62/2.82 (c2_1(a678)),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[2280, 6185])).
% 3.62/2.82 tff(6188,plain,
% 3.62/2.82 (c0_1(a678)),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[2291, 6185])).
% 3.62/2.82 tff(6189,plain,
% 3.62/2.82 (hskp14),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[3394, 107, 6188, 6187, 6186, 6169, 6168, 6167, 550])).
% 3.62/2.82 tff(6190,plain,
% 3.62/2.82 (~c3_1(a603)),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[205, 6189])).
% 3.62/2.82 tff(6191,plain,
% 3.62/2.82 (~c1_1(a603)),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[171, 6189])).
% 3.62/2.82 tff(6192,plain,
% 3.62/2.82 (c2_1(a587)),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[950, 6170])).
% 3.62/2.82 tff(6193,plain,
% 3.62/2.82 (c0_1(a587)),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[961, 6170])).
% 3.62/2.82 tff(6194,plain,
% 3.62/2.82 (c2_1(a603)),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[1006, 726, 107, 6193, 6192, 6191, 6190, 6171, 995])).
% 3.62/2.82 tff(6195,plain,
% 3.62/2.82 (c0_1(a603)),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[182, 6189])).
% 3.62/2.82 tff(6196,plain,
% 3.62/2.82 (hskp7 | (~c2_1(a603))),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[1388, 107, 6120, 6195, 6190, 1382])).
% 3.62/2.82 tff(6197,plain,
% 3.62/2.82 (hskp7),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[6196, 6194])).
% 3.62/2.82 tff(6198,plain,
% 3.62/2.82 (~c3_1(a592)),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[811, 6197])).
% 3.62/2.82 tff(6199,plain,
% 3.62/2.82 (~c0_1(a592)),
% 3.62/2.82 inference(unit_resolution,[status(thm)],[817, 6197])).
% 3.62/2.82 tff(6200,plain,
% 3.62/2.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a607) | (~c2_1(a607)) | c3_1(a603) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a607) | (~c2_1(a607)) | c3_1(a603) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a607)))),
% 3.62/2.82 inference(rewrite,[status(thm)],[])).
% 3.62/2.82 tff(6201,plain,
% 3.62/2.82 (((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a607) | (~c3_1(a607)) | (~c2_1(a607)) | c3_1(a592) | c0_1(a592) | (~c1_1(a592))) <=> (c1_1(a607) | (~c2_1(a607)) | c3_1(a603) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a607)))),
% 3.62/2.83 inference(rewrite,[status(thm)],[])).
% 3.62/2.83 tff(6202,plain,
% 3.62/2.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a607) | (~c3_1(a607)) | (~c2_1(a607)) | c3_1(a592) | c0_1(a592) | (~c1_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a607) | (~c2_1(a607)) | c3_1(a603) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a607))))),
% 3.62/2.83 inference(monotonicity,[status(thm)],[6201])).
% 3.62/2.83 tff(6203,plain,
% 3.62/2.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a607) | (~c3_1(a607)) | (~c2_1(a607)) | c3_1(a592) | c0_1(a592) | (~c1_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a607) | (~c2_1(a607)) | c3_1(a603) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a607)))),
% 3.62/2.83 inference(transitivity,[status(thm)],[6202, 6200])).
% 3.62/2.83 tff(6204,plain,
% 3.62/2.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a607) | (~c3_1(a607)) | (~c2_1(a607)) | c3_1(a592) | c0_1(a592) | (~c1_1(a592)))),
% 3.62/2.83 inference(quant_inst,[status(thm)],[])).
% 3.62/2.83 tff(6205,plain,
% 3.62/2.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a607) | (~c2_1(a607)) | c3_1(a603) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a607))),
% 3.62/2.83 inference(modus_ponens,[status(thm)],[6204, 6203])).
% 3.62/2.83 tff(6206,plain,
% 3.62/2.83 (~c1_1(a592)),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[6205, 107, 6040, 6195, 66, 4653, 6190, 6199, 6198, 258, 6194])).
% 3.62/2.83 tff(6207,plain,
% 3.62/2.83 ($false),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[1405, 107, 1797, 6191, 6190, 6199, 6198, 200, 6206, 6194])).
% 3.62/2.83 tff(6208,plain,(hskp26 | hskp2 | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.62/2.83 tff(6209,plain,
% 3.62/2.83 (hskp26),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[6208, 1797, 66])).
% 3.62/2.83 tff(6210,plain,
% 3.62/2.83 (c2_1(a583)),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[391, 6209])).
% 3.62/2.83 tff(6211,plain,
% 3.62/2.83 (c1_1(a583)),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[351, 6209])).
% 3.62/2.83 tff(6212,plain,
% 3.62/2.83 (c0_1(a583)),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[362, 6209])).
% 3.62/2.83 tff(6213,plain,
% 3.62/2.83 (hskp11 | hskp23 | (~c0_1(a607)) | (~c3_1(a607))),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[1666, 107, 66, 1648])).
% 3.62/2.83 tff(6214,plain,
% 3.62/2.83 (hskp23),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[6213, 1638, 6040, 6107])).
% 3.62/2.83 tff(6215,plain,
% 3.62/2.83 (~c1_1(a636)),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[475, 6214])).
% 3.62/2.83 tff(6216,plain,
% 3.62/2.83 (~c0_1(a636)),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[481, 6214])).
% 3.62/2.83 tff(6217,plain,
% 3.62/2.83 (c3_1(a636)),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[492, 6214])).
% 3.62/2.83 tff(6218,plain,
% 3.62/2.83 (hskp9),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[1700, 107, 3321, 3322, 3330, 6217, 6216, 6215, 294])).
% 3.62/2.83 tff(6219,plain,
% 3.62/2.83 (~c3_1(a595)),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[1487, 6218])).
% 3.62/2.83 tff(6220,plain,
% 3.62/2.83 (~c1_1(a595)),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[1493, 6218])).
% 3.62/2.83 tff(6221,plain,
% 3.62/2.83 (~c0_1(a595)),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[1499, 6218])).
% 3.62/2.83 tff(6222,plain,
% 3.62/2.83 (~c2_1(a595)),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[1754, 107, 1797, 6221, 6220, 6219, 200])).
% 3.62/2.83 tff(6223,plain,
% 3.62/2.83 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~c2_1(a607)) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a595) | (~c0_1(a607)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | (~c2_1(a607)) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a595) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.62/2.83 inference(rewrite,[status(thm)],[])).
% 3.62/2.83 tff(6224,plain,
% 3.62/2.83 ((hskp11 | (~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c0_1(a607)) | c3_1(a595) | c0_1(a595) | c2_1(a595)) <=> (hskp11 | (~c2_1(a607)) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a595) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.62/2.83 inference(rewrite,[status(thm)],[])).
% 3.62/2.83 tff(6225,plain,
% 3.62/2.83 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c0_1(a607)) | c3_1(a595) | c0_1(a595) | c2_1(a595))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~c2_1(a607)) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a595) | (~c0_1(a607)) | (~c3_1(a607))))),
% 3.62/2.83 inference(monotonicity,[status(thm)],[6224])).
% 3.62/2.83 tff(6226,plain,
% 3.62/2.83 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c0_1(a607)) | c3_1(a595) | c0_1(a595) | c2_1(a595))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | (~c2_1(a607)) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a595) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.62/2.83 inference(transitivity,[status(thm)],[6225, 6223])).
% 3.62/2.83 tff(6227,plain,
% 3.62/2.83 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp11 | (~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c0_1(a607)) | c3_1(a595) | c0_1(a595) | c2_1(a595))),
% 3.62/2.83 inference(quant_inst,[status(thm)],[])).
% 3.62/2.83 tff(6228,plain,
% 3.62/2.83 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp11 | (~c2_1(a607)) | c0_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a595) | (~c0_1(a607)) | (~c3_1(a607))),
% 3.62/2.83 inference(modus_ponens,[status(thm)],[6227, 6226])).
% 3.62/2.83 tff(6229,plain,
% 3.62/2.83 ($false),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[6228, 1638, 107, 6040, 4653, 6221, 6219, 268, 6107, 6222])).
% 3.62/2.83 tff(6230,plain,(hskp11 | hskp2 | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.62/2.83 tff(6231,plain,
% 3.62/2.83 (hskp11),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[6230, 1797, 66])).
% 3.62/2.83 tff(6232,plain,
% 3.62/2.83 (~c1_1(a599)),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[428, 6231])).
% 3.62/2.83 tff(6233,plain,
% 3.62/2.83 (c2_1(a599)),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[439, 6231])).
% 3.62/2.83 tff(6234,plain,
% 3.62/2.83 (c3_1(a599)),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[422, 6231])).
% 3.62/2.83 tff(6235,assumption,(hskp22), introduced(assumption)).
% 3.62/2.83 tff(6236,plain,
% 3.62/2.83 (~c0_1(a633)),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[3968, 6235])).
% 3.62/2.83 tff(6237,plain,
% 3.62/2.83 (c1_1(a633)),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[3962, 6235])).
% 3.62/2.83 tff(6238,plain,
% 3.62/2.83 (~c3_1(a633)),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[3974, 6235])).
% 3.62/2.83 tff(6239,plain,
% 3.62/2.83 (~hskp12),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[4342, 6236, 462, 463, 6237, 6238, 461])).
% 3.62/2.83 tff(6240,plain,
% 3.62/2.83 (~c2_1(a633)),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[3998, 107, 6239, 1651, 1650, 1649, 6237, 6236, 2727])).
% 3.62/2.83 tff(6241,plain,
% 3.62/2.83 ($false),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[6182, 107, 4654, 6237, 6236, 66, 4653, 32, 6107, 6240])).
% 3.62/2.83 tff(6242,plain,((~hskp22) | c1_1(a607) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c3_1(a599)) | (~c2_1(a599)) | c1_1(a599)), inference(lemma,lemma(discharge,[]))).
% 3.62/2.83 tff(6243,plain,
% 3.62/2.83 (~hskp22),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[6242, 6212, 66, 6211, 6210, 6234, 6233, 6232])).
% 3.62/2.83 tff(6244,plain,
% 3.62/2.83 (hskp29),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[2258, 6243])).
% 3.62/2.83 tff(6245,plain,
% 3.62/2.83 (c3_1(a678)),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[2269, 6244])).
% 3.62/2.83 tff(6246,plain,
% 3.62/2.83 (c2_1(a678)),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[2280, 6244])).
% 3.62/2.83 tff(6247,plain,
% 3.62/2.83 (c0_1(a678)),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[2291, 6244])).
% 3.62/2.83 tff(6248,plain,
% 3.62/2.83 (c2_1(a592)),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[828, 5352])).
% 3.62/2.83 tff(6249,plain,
% 3.62/2.83 ($false),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[6163, 107, 6157, 1709, 6248, 5354, 5353, 5564])).
% 3.62/2.83 tff(6250,plain,((~hskp7) | hskp18 | hskp8), inference(lemma,lemma(discharge,[]))).
% 3.62/2.83 tff(6251,plain,
% 3.62/2.83 (hskp18),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[6250, 5352, 1709])).
% 3.62/2.83 tff(6252,plain,
% 3.62/2.83 (~c2_1(a610)),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[1189, 6251])).
% 3.62/2.83 tff(6253,plain,
% 3.62/2.83 (~c0_1(a610)),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[1195, 6251])).
% 3.62/2.83 tff(6254,plain,
% 3.62/2.83 (~c1_1(a610)),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[6139, 107, 4654, 6253, 6252, 66, 4653, 32, 6107])).
% 3.62/2.83 tff(6255,plain,
% 3.62/2.83 (c3_1(a610)),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[1206, 6251])).
% 3.62/2.83 tff(6256,plain,
% 3.62/2.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c2_1(a610) | c0_1(a592) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a592)) | (~c1_1(a592)) | c1_1(a610) | (~c3_1(a610)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a610) | c0_1(a592) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a592)) | (~c1_1(a592)) | c1_1(a610) | (~c3_1(a610)))),
% 3.62/2.83 inference(rewrite,[status(thm)],[])).
% 3.62/2.83 tff(6257,plain,
% 3.62/2.83 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610)) | c0_1(a592) | (~c1_1(a592)) | (~c2_1(a592))) <=> (c2_1(a610) | c0_1(a592) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a592)) | (~c1_1(a592)) | c1_1(a610) | (~c3_1(a610)))),
% 3.62/2.83 inference(rewrite,[status(thm)],[])).
% 3.62/2.83 tff(6258,plain,
% 3.62/2.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610)) | c0_1(a592) | (~c1_1(a592)) | (~c2_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c2_1(a610) | c0_1(a592) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a592)) | (~c1_1(a592)) | c1_1(a610) | (~c3_1(a610))))),
% 3.62/2.83 inference(monotonicity,[status(thm)],[6257])).
% 3.62/2.83 tff(6259,plain,
% 3.62/2.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610)) | c0_1(a592) | (~c1_1(a592)) | (~c2_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a610) | c0_1(a592) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a592)) | (~c1_1(a592)) | c1_1(a610) | (~c3_1(a610)))),
% 3.62/2.83 inference(transitivity,[status(thm)],[6258, 6256])).
% 3.62/2.83 tff(6260,plain,
% 3.62/2.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610)) | c0_1(a592) | (~c1_1(a592)) | (~c2_1(a592)))),
% 3.62/2.83 inference(quant_inst,[status(thm)],[])).
% 3.62/2.83 tff(6261,plain,
% 3.62/2.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a610) | c0_1(a592) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a592)) | (~c1_1(a592)) | c1_1(a610) | (~c3_1(a610))),
% 3.62/2.83 inference(modus_ponens,[status(thm)],[6260, 6259])).
% 3.62/2.83 tff(6262,plain,
% 3.62/2.83 (~c1_1(a592)),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[6261, 107, 6247, 6246, 6245, 6255, 6248, 6252, 5354, 11, 6254])).
% 3.62/2.83 tff(6263,plain,
% 3.62/2.83 (hskp9),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[4110, 107, 6212, 6211, 6210, 6255, 6253, 294, 6254])).
% 3.62/2.83 tff(6264,plain,
% 3.62/2.83 (~c3_1(a595)),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[1487, 6263])).
% 3.62/2.83 tff(6265,plain,
% 3.62/2.83 (~c1_1(a595)),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[1493, 6263])).
% 3.62/2.83 tff(6266,plain,
% 3.62/2.83 (~c0_1(a595)),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[1499, 6263])).
% 3.62/2.83 tff(6267,plain,
% 3.62/2.83 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a595) | c1_1(a595) | c3_1(a595) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a595) | c1_1(a595) | c3_1(a595) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592))),
% 3.62/2.83 inference(rewrite,[status(thm)],[])).
% 3.62/2.83 tff(6268,plain,
% 3.62/2.83 ((hskp2 | (~ndr1_0) | c1_1(a592) | c3_1(a592) | (~c2_1(a592)) | c3_1(a595) | c1_1(a595) | c0_1(a595)) <=> (hskp2 | c0_1(a595) | c1_1(a595) | c3_1(a595) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592))),
% 3.62/2.83 inference(rewrite,[status(thm)],[])).
% 3.62/2.83 tff(6269,plain,
% 3.62/2.83 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a592) | c3_1(a592) | (~c2_1(a592)) | c3_1(a595) | c1_1(a595) | c0_1(a595))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a595) | c1_1(a595) | c3_1(a595) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592)))),
% 3.62/2.83 inference(monotonicity,[status(thm)],[6268])).
% 3.62/2.83 tff(6270,plain,
% 3.62/2.83 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a592) | c3_1(a592) | (~c2_1(a592)) | c3_1(a595) | c1_1(a595) | c0_1(a595))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a595) | c1_1(a595) | c3_1(a595) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592))),
% 3.62/2.83 inference(transitivity,[status(thm)],[6269, 6267])).
% 3.62/2.83 tff(6271,plain,
% 3.62/2.83 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a592) | c3_1(a592) | (~c2_1(a592)) | c3_1(a595) | c1_1(a595) | c0_1(a595))),
% 3.62/2.83 inference(quant_inst,[status(thm)],[])).
% 3.62/2.83 tff(6272,plain,
% 3.62/2.83 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a595) | c1_1(a595) | c3_1(a595) | c3_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592)),
% 3.62/2.83 inference(modus_ponens,[status(thm)],[6271, 6270])).
% 3.62/2.83 tff(6273,plain,
% 3.62/2.83 ($false),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[6272, 107, 1797, 6248, 6266, 6265, 6264, 5353, 200, 6262])).
% 3.62/2.83 tff(6274,plain,((~hskp7) | hskp2 | c1_1(a607) | hskp8), inference(lemma,lemma(discharge,[]))).
% 3.62/2.83 tff(6275,plain,
% 3.62/2.83 (~hskp7),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[6274, 1709, 66, 1797])).
% 3.62/2.83 tff(6276,plain,
% 3.62/2.83 (c3_1(a583)),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[4972, 3571])).
% 3.62/2.83 tff(6277,plain,
% 3.62/2.83 (hskp15),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[4629, 6276, 1651, 1650, 1649])).
% 3.62/2.83 tff(6278,plain,
% 3.62/2.83 (~c0_1(a604)),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[1591, 6277])).
% 3.62/2.83 tff(6279,plain,
% 3.62/2.83 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c2_1(a590) | c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c1_1(a590)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c2_1(a590) | c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c1_1(a590)) | (~c0_1(a607)))),
% 3.62/2.83 inference(rewrite,[status(thm)],[])).
% 3.62/2.83 tff(6280,plain,
% 3.62/2.83 ((hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a590) | c2_1(a590) | (~c1_1(a590))) <=> (hskp17 | c2_1(a590) | c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c1_1(a590)) | (~c0_1(a607)))),
% 3.62/2.83 inference(rewrite,[status(thm)],[])).
% 3.62/2.83 tff(6281,plain,
% 3.62/2.83 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a590) | c2_1(a590) | (~c1_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c2_1(a590) | c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c1_1(a590)) | (~c0_1(a607))))),
% 3.62/2.83 inference(monotonicity,[status(thm)],[6280])).
% 3.62/2.83 tff(6282,plain,
% 3.62/2.83 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a590) | c2_1(a590) | (~c1_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c2_1(a590) | c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c1_1(a590)) | (~c0_1(a607)))),
% 3.62/2.83 inference(transitivity,[status(thm)],[6281, 6279])).
% 3.62/2.83 tff(6283,plain,
% 3.62/2.83 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c0_1(a607)) | c0_1(a590) | c2_1(a590) | (~c1_1(a590)))),
% 3.62/2.83 inference(quant_inst,[status(thm)],[])).
% 3.62/2.83 tff(6284,plain,
% 3.62/2.83 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c2_1(a590) | c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c1_1(a590)) | (~c0_1(a607))),
% 3.62/2.83 inference(modus_ponens,[status(thm)],[6283, 6282])).
% 3.62/2.83 tff(6285,plain,
% 3.62/2.83 (c2_1(a590) | (~c1_1(a590))),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[6284, 107, 4654, 66, 4653, 45, 32, 6107])).
% 3.62/2.83 tff(6286,plain,
% 3.62/2.83 (~c1_1(a590)),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[6285, 3184])).
% 3.62/2.83 tff(6287,plain,
% 3.62/2.83 (((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp6 | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | c1_1(a590))) <=> ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp8 | hskp6 | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | c1_1(a590))),
% 3.62/2.83 inference(rewrite,[status(thm)],[])).
% 3.62/2.83 tff(6288,plain,
% 3.62/2.83 ((hskp8 | hskp6 | (~ndr1_0) | c1_1(a590) | c0_1(a590) | (~c3_1(a590))) <=> (hskp8 | hskp6 | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | c1_1(a590))),
% 3.62/2.83 inference(rewrite,[status(thm)],[])).
% 3.62/2.83 tff(6289,plain,
% 3.62/2.83 (((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp6 | (~ndr1_0) | c1_1(a590) | c0_1(a590) | (~c3_1(a590)))) <=> ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp6 | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | c1_1(a590)))),
% 3.62/2.83 inference(monotonicity,[status(thm)],[6288])).
% 3.62/2.83 tff(6290,plain,
% 3.62/2.83 (((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp6 | (~ndr1_0) | c1_1(a590) | c0_1(a590) | (~c3_1(a590)))) <=> ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp8 | hskp6 | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | c1_1(a590))),
% 3.62/2.83 inference(transitivity,[status(thm)],[6289, 6287])).
% 3.62/2.83 tff(6291,plain,
% 3.62/2.83 ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp6 | (~ndr1_0) | c1_1(a590) | c0_1(a590) | (~c3_1(a590)))),
% 3.62/2.83 inference(quant_inst,[status(thm)],[])).
% 3.62/2.83 tff(6292,plain,
% 3.62/2.83 ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp8 | hskp6 | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | c1_1(a590)),
% 3.62/2.83 inference(modus_ponens,[status(thm)],[6291, 6290])).
% 3.62/2.83 tff(6293,plain,
% 3.62/2.83 (hskp6 | (~c3_1(a590)) | c1_1(a590)),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[6292, 107, 1709, 45, 450])).
% 3.62/2.83 tff(6294,plain,
% 3.62/2.83 (~c3_1(a590)),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[6293, 3383, 6286])).
% 3.62/2.83 tff(6295,plain,
% 3.62/2.83 (c3_1(a604)),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[1602, 6277])).
% 3.62/2.83 tff(6296,plain,
% 3.62/2.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a590) | c3_1(a590) | c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a590) | c3_1(a590) | c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c3_1(a607)))),
% 3.62/2.83 inference(rewrite,[status(thm)],[])).
% 3.62/2.83 tff(6297,plain,
% 3.62/2.83 (((~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c3_1(a607)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c3_1(a590) | c0_1(a590) | c2_1(a590)) <=> (c2_1(a590) | c3_1(a590) | c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c3_1(a607)))),
% 3.62/2.83 inference(rewrite,[status(thm)],[])).
% 3.62/2.83 tff(6298,plain,
% 3.62/2.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c3_1(a607)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c3_1(a590) | c0_1(a590) | c2_1(a590))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a590) | c3_1(a590) | c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c3_1(a607))))),
% 3.62/2.83 inference(monotonicity,[status(thm)],[6297])).
% 3.62/2.83 tff(6299,plain,
% 3.62/2.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c3_1(a607)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c3_1(a590) | c0_1(a590) | c2_1(a590))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a590) | c3_1(a590) | c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c3_1(a607)))),
% 3.62/2.83 inference(transitivity,[status(thm)],[6298, 6296])).
% 3.62/2.83 tff(6300,plain,
% 3.62/2.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c3_1(a607)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c3_1(a590) | c0_1(a590) | c2_1(a590))),
% 3.62/2.83 inference(quant_inst,[status(thm)],[])).
% 3.62/2.83 tff(6301,plain,
% 3.62/2.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a590) | c3_1(a590) | c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | c0_1(a590) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c3_1(a607))),
% 3.62/2.83 inference(modus_ponens,[status(thm)],[6300, 6299])).
% 3.62/2.83 tff(6302,plain,
% 3.62/2.83 (~c2_1(a604)),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[6301, 107, 6040, 6295, 3184, 6294, 66, 4653, 6278, 45, 1730])).
% 3.62/2.83 tff(6303,plain,
% 3.62/2.83 (c1_1(a604)),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[1613, 6277])).
% 3.62/2.83 tff(6304,plain,
% 3.62/2.83 ($false),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[5622, 107, 4654, 6303, 66, 4653, 6278, 32, 6107, 6302])).
% 3.62/2.83 tff(6305,plain,(c2_1(a590) | c1_1(a607) | c0_1(a590) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a583)) | hskp8 | hskp22), inference(lemma,lemma(discharge,[]))).
% 3.62/2.83 tff(6306,plain,
% 3.62/2.83 (c2_1(a590)),
% 3.62/2.83 inference(unit_resolution,[status(thm)],[6305, 45, 66, 6212, 6211, 6210, 1709, 6243])).
% 3.62/2.83 tff(6307,plain,
% 3.62/2.83 (((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | hskp8 | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)))) <=> ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | hskp8 | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)))),
% 3.72/2.83 inference(rewrite,[status(thm)],[])).
% 3.72/2.83 tff(6308,plain,
% 3.72/2.83 ((hskp18 | hskp8 | (~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590))) <=> (hskp18 | hskp8 | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)))),
% 3.72/2.83 inference(rewrite,[status(thm)],[])).
% 3.72/2.83 tff(6309,plain,
% 3.72/2.83 (((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | hskp8 | (~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590)))) <=> ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | hskp8 | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590))))),
% 3.72/2.83 inference(monotonicity,[status(thm)],[6308])).
% 3.72/2.83 tff(6310,plain,
% 3.72/2.83 (((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | hskp8 | (~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590)))) <=> ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | hskp8 | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)))),
% 3.72/2.83 inference(transitivity,[status(thm)],[6309, 6307])).
% 3.72/2.83 tff(6311,plain,
% 3.72/2.83 ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | hskp8 | (~ndr1_0) | c0_1(a590) | c3_1(a590) | (~c2_1(a590)))),
% 3.72/2.83 inference(quant_inst,[status(thm)],[])).
% 3.72/2.83 tff(6312,plain,
% 3.72/2.83 ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | hskp8 | c3_1(a590) | c0_1(a590) | (~ndr1_0) | (~c2_1(a590))),
% 3.72/2.83 inference(modus_ponens,[status(thm)],[6311, 6310])).
% 3.72/2.83 tff(6313,plain,
% 3.72/2.83 (hskp18 | c3_1(a590) | (~c2_1(a590))),
% 3.72/2.83 inference(unit_resolution,[status(thm)],[6312, 107, 1709, 45, 5564])).
% 3.72/2.83 tff(6314,plain,
% 3.72/2.83 (hskp18),
% 3.72/2.83 inference(unit_resolution,[status(thm)],[6313, 3181, 863])).
% 3.72/2.83 tff(6315,plain,
% 3.72/2.83 (~c2_1(a610)),
% 3.72/2.83 inference(unit_resolution,[status(thm)],[1189, 6314])).
% 3.72/2.83 tff(6316,plain,
% 3.72/2.83 (~c0_1(a610)),
% 3.72/2.83 inference(unit_resolution,[status(thm)],[1195, 6314])).
% 3.72/2.83 tff(6317,plain,
% 3.72/2.83 (~c1_1(a610)),
% 3.72/2.83 inference(unit_resolution,[status(thm)],[6139, 107, 4654, 6316, 6315, 66, 4653, 32, 6107])).
% 3.72/2.83 tff(6318,plain,
% 3.72/2.83 (c3_1(a610)),
% 3.72/2.83 inference(unit_resolution,[status(thm)],[1206, 6314])).
% 3.72/2.83 tff(6319,plain,
% 3.72/2.83 (((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp6 | c0_1(a610) | (~ndr1_0) | c1_1(a610) | (~c3_1(a610)))) <=> ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp8 | hskp6 | c0_1(a610) | (~ndr1_0) | c1_1(a610) | (~c3_1(a610)))),
% 3.72/2.83 inference(rewrite,[status(thm)],[])).
% 3.72/2.83 tff(6320,plain,
% 3.72/2.83 ((hskp8 | hskp6 | (~ndr1_0) | c1_1(a610) | c0_1(a610) | (~c3_1(a610))) <=> (hskp8 | hskp6 | c0_1(a610) | (~ndr1_0) | c1_1(a610) | (~c3_1(a610)))),
% 3.72/2.83 inference(rewrite,[status(thm)],[])).
% 3.72/2.83 tff(6321,plain,
% 3.72/2.83 (((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp6 | (~ndr1_0) | c1_1(a610) | c0_1(a610) | (~c3_1(a610)))) <=> ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp6 | c0_1(a610) | (~ndr1_0) | c1_1(a610) | (~c3_1(a610))))),
% 3.72/2.83 inference(monotonicity,[status(thm)],[6320])).
% 3.72/2.83 tff(6322,plain,
% 3.72/2.83 (((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp6 | (~ndr1_0) | c1_1(a610) | c0_1(a610) | (~c3_1(a610)))) <=> ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp8 | hskp6 | c0_1(a610) | (~ndr1_0) | c1_1(a610) | (~c3_1(a610)))),
% 3.72/2.83 inference(transitivity,[status(thm)],[6321, 6319])).
% 3.72/2.83 tff(6323,plain,
% 3.72/2.83 ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp6 | (~ndr1_0) | c1_1(a610) | c0_1(a610) | (~c3_1(a610)))),
% 3.72/2.83 inference(quant_inst,[status(thm)],[])).
% 3.72/2.83 tff(6324,plain,
% 3.72/2.83 ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp8 | hskp6 | c0_1(a610) | (~ndr1_0) | c1_1(a610) | (~c3_1(a610))),
% 3.72/2.83 inference(modus_ponens,[status(thm)],[6323, 6322])).
% 3.72/2.83 tff(6325,plain,
% 3.72/2.83 ($false),
% 3.72/2.83 inference(unit_resolution,[status(thm)],[6324, 107, 1709, 3182, 6318, 6316, 450, 6317])).
% 3.72/2.83 tff(6326,plain,(c3_1(a590) | hskp8 | c1_1(a607) | (~c2_1(a590)) | c0_1(a590)), inference(lemma,lemma(discharge,[]))).
% 3.72/2.84 tff(6327,plain,
% 3.72/2.84 (c3_1(a590)),
% 3.72/2.84 inference(unit_resolution,[status(thm)],[6326, 6306, 66, 1709, 45])).
% 3.72/2.84 tff(6328,plain,
% 3.72/2.84 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp7 | hskp2 | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | c1_1(a590))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp7 | hskp2 | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | c1_1(a590))),
% 3.72/2.84 inference(rewrite,[status(thm)],[])).
% 3.72/2.84 tff(6329,plain,
% 3.72/2.84 ((hskp7 | hskp2 | (~ndr1_0) | c1_1(a590) | c0_1(a590) | (~c2_1(a590))) <=> (hskp7 | hskp2 | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | c1_1(a590))),
% 3.72/2.84 inference(rewrite,[status(thm)],[])).
% 3.72/2.84 tff(6330,plain,
% 3.72/2.84 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | c1_1(a590) | c0_1(a590) | (~c2_1(a590)))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp7 | hskp2 | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | c1_1(a590)))),
% 3.72/2.84 inference(monotonicity,[status(thm)],[6329])).
% 3.72/2.84 tff(6331,plain,
% 3.72/2.84 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | c1_1(a590) | c0_1(a590) | (~c2_1(a590)))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp7 | hskp2 | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | c1_1(a590))),
% 3.72/2.84 inference(transitivity,[status(thm)],[6330, 6328])).
% 3.72/2.84 tff(6332,plain,
% 3.72/2.84 ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | c1_1(a590) | c0_1(a590) | (~c2_1(a590)))),
% 3.72/2.84 inference(quant_inst,[status(thm)],[])).
% 3.72/2.84 tff(6333,plain,
% 3.72/2.84 ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp7 | hskp2 | c0_1(a590) | (~ndr1_0) | (~c2_1(a590)) | c1_1(a590)),
% 3.72/2.84 inference(modus_ponens,[status(thm)],[6332, 6331])).
% 3.72/2.84 tff(6334,plain,
% 3.72/2.84 (hskp7 | (~c2_1(a590)) | c1_1(a590)),
% 3.72/2.84 inference(unit_resolution,[status(thm)],[6333, 107, 1797, 45, 6080])).
% 3.72/2.84 tff(6335,plain,
% 3.72/2.84 (c1_1(a590)),
% 3.72/2.84 inference(unit_resolution,[status(thm)],[6334, 6108, 863])).
% 3.72/2.84 tff(6336,plain,
% 3.72/2.84 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c1_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c1_1(a590)))),
% 3.72/2.84 inference(rewrite,[status(thm)],[])).
% 3.72/2.84 tff(6337,plain,
% 3.72/2.84 ((hskp10 | (~ndr1_0) | (~c2_1(a590)) | (~c3_1(a590)) | (~c1_1(a590)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583))) <=> (hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c1_1(a590)))),
% 3.72/2.84 inference(rewrite,[status(thm)],[])).
% 3.72/2.84 tff(6338,plain,
% 3.72/2.84 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a590)) | (~c3_1(a590)) | (~c1_1(a590)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c1_1(a590))))),
% 3.72/2.84 inference(monotonicity,[status(thm)],[6337])).
% 3.72/2.84 tff(6339,plain,
% 3.72/2.84 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a590)) | (~c3_1(a590)) | (~c1_1(a590)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c1_1(a590)))),
% 3.72/2.84 inference(transitivity,[status(thm)],[6338, 6336])).
% 3.72/2.84 tff(6340,plain,
% 3.72/2.84 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a590)) | (~c3_1(a590)) | (~c1_1(a590)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583)))),
% 3.72/2.84 inference(quant_inst,[status(thm)],[])).
% 3.72/2.84 tff(6341,plain,
% 3.72/2.84 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c1_1(a590))),
% 3.72/2.84 inference(modus_ponens,[status(thm)],[6340, 6339])).
% 3.72/2.84 tff(6342,plain,
% 3.72/2.84 (hskp10 | (~c3_1(a590)) | (~c1_1(a590))),
% 3.72/2.84 inference(unit_resolution,[status(thm)],[6341, 107, 1651, 1650, 1649, 863, 21])).
% 3.72/2.84 tff(6343,plain,
% 3.72/2.84 (hskp10),
% 3.72/2.84 inference(unit_resolution,[status(thm)],[6342, 6335, 862])).
% 3.72/2.84 tff(6344,plain,
% 3.72/2.84 (~c1_1(a598)),
% 3.72/2.84 inference(unit_resolution,[status(thm)],[911, 6343])).
% 3.72/2.84 tff(6345,plain,
% 3.72/2.84 (c3_1(a598)),
% 3.72/2.84 inference(unit_resolution,[status(thm)],[881, 6343])).
% 3.72/2.84 tff(6346,plain,
% 3.72/2.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a598) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a598)) | c2_1(a598))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a598) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a598)) | c2_1(a598))),
% 3.72/2.84 inference(rewrite,[status(thm)],[])).
% 3.72/2.84 tff(6347,plain,
% 3.72/2.84 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a590) | (~c1_1(a590)) | (~c2_1(a590))) <=> (c1_1(a598) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a598)) | c2_1(a598))),
% 3.72/2.84 inference(rewrite,[status(thm)],[])).
% 3.72/2.84 tff(6348,plain,
% 3.72/2.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a590) | (~c1_1(a590)) | (~c2_1(a590)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a598) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a598)) | c2_1(a598)))),
% 3.72/2.84 inference(monotonicity,[status(thm)],[6347])).
% 3.72/2.84 tff(6349,plain,
% 3.72/2.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a590) | (~c1_1(a590)) | (~c2_1(a590)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a598) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a598)) | c2_1(a598))),
% 3.72/2.84 inference(transitivity,[status(thm)],[6348, 6346])).
% 3.72/2.84 tff(6350,plain,
% 3.72/2.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a590) | (~c1_1(a590)) | (~c2_1(a590)))),
% 3.72/2.84 inference(quant_inst,[status(thm)],[])).
% 3.72/2.84 tff(6351,plain,
% 3.72/2.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a598) | c0_1(a590) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a590)) | (~c1_1(a590)) | (~c3_1(a598)) | c2_1(a598)),
% 3.72/2.84 inference(modus_ponens,[status(thm)],[6350, 6349])).
% 3.72/2.84 tff(6352,plain,
% 3.72/2.84 (c2_1(a598)),
% 3.72/2.84 inference(unit_resolution,[status(thm)],[6351, 107, 2318, 2317, 2316, 6345, 863, 6344, 45, 11, 6335])).
% 3.72/2.84 tff(6353,plain,
% 3.72/2.84 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp7 | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c1_1(a590)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp7 | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c1_1(a590)))),
% 3.72/2.84 inference(rewrite,[status(thm)],[])).
% 3.72/2.84 tff(6354,plain,
% 3.72/2.84 ((hskp20 | hskp7 | (~ndr1_0) | c0_1(a590) | (~c3_1(a590)) | (~c1_1(a590))) <=> (hskp20 | hskp7 | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c1_1(a590)))),
% 3.72/2.84 inference(rewrite,[status(thm)],[])).
% 3.72/2.84 tff(6355,plain,
% 3.72/2.84 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c0_1(a590) | (~c3_1(a590)) | (~c1_1(a590)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp7 | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c1_1(a590))))),
% 3.72/2.84 inference(monotonicity,[status(thm)],[6354])).
% 3.72/2.84 tff(6356,plain,
% 3.72/2.84 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c0_1(a590) | (~c3_1(a590)) | (~c1_1(a590)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp7 | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c1_1(a590)))),
% 3.72/2.84 inference(transitivity,[status(thm)],[6355, 6353])).
% 3.72/2.84 tff(6357,plain,
% 3.72/2.84 ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c0_1(a590) | (~c3_1(a590)) | (~c1_1(a590)))),
% 3.72/2.84 inference(quant_inst,[status(thm)],[])).
% 3.72/2.84 tff(6358,plain,
% 3.72/2.84 ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp7 | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c1_1(a590))),
% 3.72/2.84 inference(modus_ponens,[status(thm)],[6357, 6356])).
% 3.72/2.84 tff(6359,plain,
% 3.72/2.84 (hskp20 | hskp7 | (~c3_1(a590)) | (~c1_1(a590))),
% 3.72/2.84 inference(unit_resolution,[status(thm)],[6358, 107, 45, 801])).
% 3.72/2.84 tff(6360,plain,
% 3.72/2.84 (hskp20),
% 3.72/2.84 inference(unit_resolution,[status(thm)],[6359, 6335, 862, 6108])).
% 3.72/2.84 tff(6361,plain,
% 3.72/2.84 (~c3_1(a623)),
% 3.72/2.84 inference(unit_resolution,[status(thm)],[709, 6360])).
% 3.72/2.84 tff(6362,plain,
% 3.72/2.84 (~c2_1(a623)),
% 3.72/2.84 inference(unit_resolution,[status(thm)],[715, 6360])).
% 3.72/2.84 tff(6363,plain,
% 3.72/2.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a623) | c3_1(a623) | c1_1(a598) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a598)) | (~c2_1(a598)) | c0_1(a623))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a623) | c3_1(a623) | c1_1(a598) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a598)) | (~c2_1(a598)) | c0_1(a623))),
% 3.72/2.84 inference(rewrite,[status(thm)],[])).
% 3.72/2.84 tff(6364,plain,
% 3.72/2.84 (((~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c3_1(a598)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a623) | c0_1(a623) | c2_1(a623)) <=> (c2_1(a623) | c3_1(a623) | c1_1(a598) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a598)) | (~c2_1(a598)) | c0_1(a623))),
% 3.72/2.84 inference(rewrite,[status(thm)],[])).
% 3.72/2.84 tff(6365,plain,
% 3.72/2.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c3_1(a598)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a623) | c0_1(a623) | c2_1(a623))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a623) | c3_1(a623) | c1_1(a598) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a598)) | (~c2_1(a598)) | c0_1(a623)))),
% 3.72/2.84 inference(monotonicity,[status(thm)],[6364])).
% 3.72/2.84 tff(6366,plain,
% 3.72/2.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c3_1(a598)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a623) | c0_1(a623) | c2_1(a623))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a623) | c3_1(a623) | c1_1(a598) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a598)) | (~c2_1(a598)) | c0_1(a623))),
% 3.72/2.84 inference(transitivity,[status(thm)],[6365, 6363])).
% 3.72/2.84 tff(6367,plain,
% 3.72/2.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c3_1(a598)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a623) | c0_1(a623) | c2_1(a623))),
% 3.72/2.84 inference(quant_inst,[status(thm)],[])).
% 3.72/2.84 tff(6368,plain,
% 3.72/2.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a623) | c3_1(a623) | c1_1(a598) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a598)) | (~c2_1(a598)) | c0_1(a623)),
% 3.72/2.84 inference(modus_ponens,[status(thm)],[6367, 6366])).
% 3.72/2.84 tff(6369,plain,
% 3.72/2.84 (c0_1(a623)),
% 3.72/2.84 inference(unit_resolution,[status(thm)],[6368, 107, 6345, 863, 862, 6362, 6361, 6344, 45, 1730, 6352])).
% 3.72/2.84 tff(6370,plain,
% 3.72/2.84 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a590)) | (~c1_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a590)) | (~c1_1(a590)))),
% 3.72/2.84 inference(rewrite,[status(thm)],[])).
% 3.72/2.84 tff(6371,plain,
% 3.72/2.84 ((hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a590) | (~c1_1(a590)) | (~c2_1(a590))) <=> (hskp12 | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a590)) | (~c1_1(a590)))),
% 3.72/2.84 inference(rewrite,[status(thm)],[])).
% 3.72/2.84 tff(6372,plain,
% 3.72/2.84 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a590) | (~c1_1(a590)) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a590)) | (~c1_1(a590))))),
% 3.72/2.84 inference(monotonicity,[status(thm)],[6371])).
% 3.72/2.84 tff(6373,plain,
% 3.72/2.84 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a590) | (~c1_1(a590)) | (~c2_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a590)) | (~c1_1(a590)))),
% 3.72/2.84 inference(transitivity,[status(thm)],[6372, 6370])).
% 3.72/2.84 tff(6374,plain,
% 3.72/2.84 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a590) | (~c1_1(a590)) | (~c2_1(a590)))),
% 3.72/2.84 inference(quant_inst,[status(thm)],[])).
% 3.72/2.84 tff(6375,plain,
% 3.72/2.84 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | c0_1(a590) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a590)) | (~c1_1(a590))),
% 3.72/2.84 inference(modus_ponens,[status(thm)],[6374, 6373])).
% 3.72/2.84 tff(6376,plain,
% 3.72/2.84 (hskp12 | (~c2_1(a590)) | (~c1_1(a590))),
% 3.72/2.84 inference(unit_resolution,[status(thm)],[6375, 107, 1651, 1650, 1649, 45, 2727])).
% 3.72/2.84 tff(6377,plain,
% 3.72/2.84 (hskp12),
% 3.72/2.84 inference(unit_resolution,[status(thm)],[6376, 6335, 863])).
% 3.72/2.84 tff(6378,plain,
% 3.72/2.84 (~c3_1(a600)),
% 3.72/2.84 inference(unit_resolution,[status(thm)],[741, 6377])).
% 3.72/2.84 tff(6379,plain,
% 3.72/2.84 (c2_1(a600)),
% 3.72/2.84 inference(unit_resolution,[status(thm)],[752, 6377])).
% 3.72/2.84 tff(6380,plain,
% 3.72/2.84 (c0_1(a600)),
% 3.72/2.84 inference(unit_resolution,[status(thm)],[763, 6377])).
% 3.72/2.84 tff(6381,plain,
% 3.72/2.84 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | c2_1(a623) | c3_1(a623) | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)) | (~c0_1(a623)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c2_1(a623) | c3_1(a623) | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)) | (~c0_1(a623)))),
% 3.72/2.84 inference(rewrite,[status(thm)],[])).
% 3.72/2.84 tff(6382,plain,
% 3.72/2.84 ((hskp8 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c3_1(a623) | c2_1(a623) | (~c0_1(a623))) <=> (hskp8 | c2_1(a623) | c3_1(a623) | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)) | (~c0_1(a623)))),
% 3.72/2.84 inference(rewrite,[status(thm)],[])).
% 3.72/2.84 tff(6383,plain,
% 3.72/2.84 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c3_1(a623) | c2_1(a623) | (~c0_1(a623)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | c2_1(a623) | c3_1(a623) | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)) | (~c0_1(a623))))),
% 3.72/2.84 inference(monotonicity,[status(thm)],[6382])).
% 3.72/2.84 tff(6384,plain,
% 3.72/2.84 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c3_1(a623) | c2_1(a623) | (~c0_1(a623)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c2_1(a623) | c3_1(a623) | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)) | (~c0_1(a623)))),
% 3.72/2.84 inference(transitivity,[status(thm)],[6383, 6381])).
% 3.72/2.84 tff(6385,plain,
% 3.72/2.84 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c3_1(a623) | c2_1(a623) | (~c0_1(a623)))),
% 3.72/2.84 inference(quant_inst,[status(thm)],[])).
% 3.72/2.84 tff(6386,plain,
% 3.72/2.84 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c2_1(a623) | c3_1(a623) | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)) | (~c0_1(a623))),
% 3.72/2.84 inference(modus_ponens,[status(thm)],[6385, 6384])).
% 3.72/2.84 tff(6387,plain,
% 3.72/2.84 ($false),
% 3.72/2.84 inference(unit_resolution,[status(thm)],[6386, 107, 1709, 6380, 6379, 6362, 6361, 6378, 4271, 6369])).
% 3.72/2.84 tff(6388,plain,(hskp7 | hskp8 | (~c2_1(a590)) | (~c3_1(a590)) | c0_1(a590) | (~c0_1(a678)) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a583)) | hskp2), inference(lemma,lemma(discharge,[]))).
% 3.72/2.84 tff(6389,plain,
% 3.72/2.84 ($false),
% 3.72/2.84 inference(unit_resolution,[status(thm)],[6388, 6327, 6306, 1709, 6275, 45, 6247, 6246, 6245, 6212, 6211, 6210, 1797])).
% 3.72/2.84 tff(6390,plain,(c0_1(a590) | hskp8 | hskp2 | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.72/2.84 tff(6391,plain,
% 3.72/2.84 (c0_1(a590)),
% 3.72/2.84 inference(unit_resolution,[status(thm)],[6390, 1709, 1797, 66])).
% 3.72/2.84 tff(6392,plain,
% 3.72/2.84 (~hskp6),
% 3.72/2.84 inference(unit_resolution,[status(thm)],[666, 6391])).
% 3.72/2.84 tff(6393,plain,
% 3.72/2.84 (~hskp4),
% 3.72/2.84 inference(unit_resolution,[status(thm)],[147, 6392, 6243])).
% 3.72/2.84 tff(6394,plain,
% 3.72/2.84 (hskp4 | c3_1(a583)),
% 3.72/2.84 inference(unit_resolution,[status(thm)],[3328, 107, 4654, 6212, 6211, 55])).
% 3.72/2.84 tff(6395,plain,
% 3.72/2.84 (c3_1(a583)),
% 3.72/2.84 inference(unit_resolution,[status(thm)],[6394, 6393])).
% 3.72/2.84 tff(6396,plain,
% 3.72/2.84 (hskp15),
% 3.72/2.84 inference(unit_resolution,[status(thm)],[4629, 6395, 6212, 6211, 6210])).
% 3.72/2.84 tff(6397,plain,
% 3.72/2.84 (c3_1(a604)),
% 3.72/2.84 inference(unit_resolution,[status(thm)],[1602, 6396])).
% 3.72/2.84 tff(6398,plain,
% 3.72/2.84 (~c0_1(a604)),
% 3.72/2.84 inference(unit_resolution,[status(thm)],[1591, 6396])).
% 3.72/2.84 tff(6399,plain,
% 3.72/2.84 (c1_1(a604)),
% 3.72/2.84 inference(unit_resolution,[status(thm)],[1613, 6396])).
% 3.72/2.84 tff(6400,plain,
% 3.72/2.84 (c2_1(a604)),
% 3.72/2.84 inference(unit_resolution,[status(thm)],[5622, 107, 4654, 6399, 66, 4653, 6398, 32, 6107])).
% 3.72/2.84 tff(6401,plain,
% 3.72/2.84 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp7 | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp7 | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)))),
% 3.72/2.84 inference(rewrite,[status(thm)],[])).
% 3.72/2.84 tff(6402,plain,
% 3.72/2.84 ((hskp20 | hskp7 | (~ndr1_0) | c0_1(a604) | (~c3_1(a604)) | (~c1_1(a604))) <=> (hskp20 | hskp7 | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)))),
% 3.72/2.84 inference(rewrite,[status(thm)],[])).
% 3.72/2.84 tff(6403,plain,
% 3.72/2.84 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c0_1(a604) | (~c3_1(a604)) | (~c1_1(a604)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp7 | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604))))),
% 3.72/2.84 inference(monotonicity,[status(thm)],[6402])).
% 3.72/2.84 tff(6404,plain,
% 3.72/2.84 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c0_1(a604) | (~c3_1(a604)) | (~c1_1(a604)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp7 | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604)))),
% 3.72/2.84 inference(transitivity,[status(thm)],[6403, 6401])).
% 3.72/2.84 tff(6405,plain,
% 3.72/2.84 ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c0_1(a604) | (~c3_1(a604)) | (~c1_1(a604)))),
% 3.72/2.84 inference(quant_inst,[status(thm)],[])).
% 3.72/2.84 tff(6406,plain,
% 3.72/2.84 ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp7 | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c1_1(a604))),
% 3.72/2.84 inference(modus_ponens,[status(thm)],[6405, 6404])).
% 3.72/2.84 tff(6407,plain,
% 3.72/2.84 (hskp20),
% 3.72/2.84 inference(unit_resolution,[status(thm)],[6406, 107, 6275, 6399, 6397, 6398, 801])).
% 3.72/2.84 tff(6408,plain,
% 3.72/2.84 (hskp16),
% 3.72/2.84 inference(unit_resolution,[status(thm)],[5664, 6407, 6233, 6234, 6398, 6232, 6400, 6397])).
% 3.72/2.84 tff(6409,plain,
% 3.72/2.84 (~c3_1(a606)),
% 3.72/2.84 inference(unit_resolution,[status(thm)],[1075, 6408])).
% 3.72/2.84 tff(6410,plain,
% 3.72/2.84 (~c2_1(a606)),
% 3.72/2.84 inference(unit_resolution,[status(thm)],[1111, 6408])).
% 3.72/2.84 tff(6411,plain,
% 3.72/2.84 (c1_1(a606)),
% 3.72/2.84 inference(unit_resolution,[status(thm)],[1088, 6408])).
% 3.72/2.84 tff(6412,plain,
% 3.72/2.84 (((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp8 | hskp6 | c2_1(a606) | c3_1(a606) | (~ndr1_0) | (~c1_1(a606)))) <=> ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp8 | hskp6 | c2_1(a606) | c3_1(a606) | (~ndr1_0) | (~c1_1(a606)))),
% 3.72/2.84 inference(rewrite,[status(thm)],[])).
% 3.72/2.84 tff(6413,plain,
% 3.72/2.84 ((hskp8 | hskp6 | (~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c1_1(a606))) <=> (hskp8 | hskp6 | c2_1(a606) | c3_1(a606) | (~ndr1_0) | (~c1_1(a606)))),
% 3.72/2.84 inference(rewrite,[status(thm)],[])).
% 3.72/2.84 tff(6414,plain,
% 3.72/2.84 (((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp8 | hskp6 | (~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c1_1(a606)))) <=> ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp8 | hskp6 | c2_1(a606) | c3_1(a606) | (~ndr1_0) | (~c1_1(a606))))),
% 3.72/2.84 inference(monotonicity,[status(thm)],[6413])).
% 3.72/2.84 tff(6415,plain,
% 3.72/2.84 (((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp8 | hskp6 | (~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c1_1(a606)))) <=> ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp8 | hskp6 | c2_1(a606) | c3_1(a606) | (~ndr1_0) | (~c1_1(a606)))),
% 3.72/2.85 inference(transitivity,[status(thm)],[6414, 6412])).
% 3.72/2.85 tff(6416,plain,
% 3.72/2.85 ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp8 | hskp6 | (~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c1_1(a606)))),
% 3.72/2.85 inference(quant_inst,[status(thm)],[])).
% 3.72/2.85 tff(6417,plain,
% 3.72/2.85 ((~![U: $i] : (hskp8 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp8 | hskp6 | c2_1(a606) | c3_1(a606) | (~ndr1_0) | (~c1_1(a606))),
% 3.72/2.85 inference(modus_ponens,[status(thm)],[6416, 6415])).
% 3.72/2.85 tff(6418,plain,
% 3.72/2.85 ($false),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[6417, 107, 1709, 6392, 6411, 6410, 6409, 6119])).
% 3.72/2.85 tff(6419,plain,(hskp8 | c1_1(a607) | hskp2), inference(lemma,lemma(discharge,[]))).
% 3.72/2.85 tff(6420,plain,
% 3.72/2.85 (hskp8),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[6419, 1797, 66])).
% 3.72/2.85 tff(6421,plain,
% 3.72/2.85 (~c2_1(a593)),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[555, 6420])).
% 3.72/2.85 tff(6422,plain,
% 3.72/2.85 (c3_1(a593)),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[511, 6420])).
% 3.72/2.85 tff(6423,plain,
% 3.72/2.85 (c1_1(a593)),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[522, 6420])).
% 3.72/2.85 tff(6424,plain,
% 3.72/2.85 (hskp14),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[3394, 107, 6247, 6246, 6245, 6423, 6422, 6421, 550])).
% 3.72/2.85 tff(6425,plain,
% 3.72/2.85 (c0_1(a603)),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[182, 6424])).
% 3.72/2.85 tff(6426,plain,
% 3.72/2.85 (~c3_1(a603)),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[205, 6424])).
% 3.72/2.85 tff(6427,plain,
% 3.72/2.85 (~c1_1(a603)),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[171, 6424])).
% 3.72/2.85 tff(6428,plain,
% 3.72/2.85 (c2_1(a603)),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[2029, 67])).
% 3.72/2.85 tff(6429,plain,
% 3.72/2.85 (hskp20),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[1389, 6428, 6108])).
% 3.72/2.85 tff(6430,plain,
% 3.72/2.85 (~c2_1(a623)),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[715, 6429])).
% 3.72/2.85 tff(6431,plain,
% 3.72/2.85 (~c1_1(a623)),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[721, 6429])).
% 3.72/2.85 tff(6432,plain,
% 3.72/2.85 (~c0_1(a623)),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[3930, 107, 44, 67, 6431, 6430, 43])).
% 3.72/2.85 tff(6433,plain,
% 3.72/2.85 (~c3_1(a623)),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[709, 6429])).
% 3.72/2.85 tff(6434,plain,
% 3.72/2.85 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a623) | c3_1(a623) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a623))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a623) | c3_1(a623) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a623))),
% 3.72/2.85 inference(rewrite,[status(thm)],[])).
% 3.72/2.85 tff(6435,plain,
% 3.72/2.85 ((hskp2 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c3_1(a623) | c1_1(a623) | c0_1(a623)) <=> (hskp2 | c1_1(a623) | c3_1(a623) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a623))),
% 3.72/2.85 inference(rewrite,[status(thm)],[])).
% 3.72/2.85 tff(6436,plain,
% 3.72/2.85 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c3_1(a623) | c1_1(a623) | c0_1(a623))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a623) | c3_1(a623) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a623)))),
% 3.72/2.85 inference(monotonicity,[status(thm)],[6435])).
% 3.72/2.85 tff(6437,plain,
% 3.72/2.85 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c3_1(a623) | c1_1(a623) | c0_1(a623))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a623) | c3_1(a623) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a623))),
% 3.72/2.85 inference(transitivity,[status(thm)],[6436, 6434])).
% 3.72/2.85 tff(6438,plain,
% 3.72/2.85 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c3_1(a623) | c1_1(a623) | c0_1(a623))),
% 3.72/2.85 inference(quant_inst,[status(thm)],[])).
% 3.72/2.85 tff(6439,plain,
% 3.72/2.85 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a623) | c3_1(a623) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a623)),
% 3.72/2.85 inference(modus_ponens,[status(thm)],[6438, 6437])).
% 3.72/2.85 tff(6440,plain,
% 3.72/2.85 ($false),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[6439, 107, 1797, 6431, 6433, 998, 997, 200, 6428, 6432])).
% 3.72/2.85 tff(6441,plain,(hskp6 | hskp2 | c1_1(a603) | c3_1(a603) | hskp22 | hskp7 | (~c0_1(a603))), inference(lemma,lemma(discharge,[]))).
% 3.72/2.85 tff(6442,plain,
% 3.72/2.85 (hskp6),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[6441, 6108, 6427, 6426, 6243, 1797, 6425])).
% 3.72/2.85 tff(6443,plain,
% 3.72/2.85 (hskp3),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[5154, 107, 4654, 6423, 6422, 6421, 3420])).
% 3.72/2.85 tff(6444,plain,
% 3.72/2.85 (~c1_1(a587)),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[939, 6443])).
% 3.72/2.85 tff(6445,plain,
% 3.72/2.85 (c2_1(a590)),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[688, 6442])).
% 3.72/2.85 tff(6446,plain,
% 3.72/2.85 (c1_1(a590)),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[6334, 6445, 6108])).
% 3.72/2.85 tff(6447,plain,
% 3.72/2.85 (c3_1(a590)),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[677, 6442])).
% 3.72/2.85 tff(6448,plain,
% 3.72/2.85 (hskp20),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[6359, 6447, 6108, 6446])).
% 3.72/2.85 tff(6449,plain,
% 3.72/2.85 (~c3_1(a623)),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[709, 6448])).
% 3.72/2.85 tff(6450,plain,
% 3.72/2.85 (~c2_1(a623)),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[715, 6448])).
% 3.72/2.85 tff(6451,plain,
% 3.72/2.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a607)) | c0_1(a623))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a607)) | c0_1(a623))),
% 3.72/2.85 inference(rewrite,[status(thm)],[])).
% 3.72/2.85 tff(6452,plain,
% 3.72/2.85 (((~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c3_1(a607)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a623) | c0_1(a623) | c2_1(a623)) <=> (c2_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a607)) | c0_1(a623))),
% 3.72/2.85 inference(rewrite,[status(thm)],[])).
% 3.72/2.85 tff(6453,plain,
% 3.72/2.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c3_1(a607)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a623) | c0_1(a623) | c2_1(a623))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a607)) | c0_1(a623)))),
% 3.72/2.85 inference(monotonicity,[status(thm)],[6452])).
% 3.72/2.85 tff(6454,plain,
% 3.72/2.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c3_1(a607)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a623) | c0_1(a623) | c2_1(a623))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a607)) | c0_1(a623))),
% 3.72/2.85 inference(transitivity,[status(thm)],[6453, 6451])).
% 3.72/2.85 tff(6455,plain,
% 3.72/2.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c3_1(a607)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a623) | c0_1(a623) | c2_1(a623))),
% 3.72/2.85 inference(quant_inst,[status(thm)],[])).
% 3.72/2.85 tff(6456,plain,
% 3.72/2.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | (~c3_1(a607)) | c0_1(a623)),
% 3.72/2.85 inference(modus_ponens,[status(thm)],[6455, 6454])).
% 3.72/2.85 tff(6457,plain,
% 3.72/2.85 (c0_1(a623)),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[6456, 107, 6040, 6445, 6447, 6450, 6449, 66, 4653, 45, 1730])).
% 3.72/2.85 tff(6458,plain,
% 3.72/2.85 (hskp16 | (~c0_1(a623))),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[5880, 107, 6445, 6447, 6450, 6449, 45, 2125])).
% 3.72/2.85 tff(6459,plain,
% 3.72/2.85 (hskp16),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[6458, 6457])).
% 3.72/2.85 tff(6460,plain,
% 3.72/2.85 (~c2_1(a606)),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[1111, 6459])).
% 3.72/2.85 tff(6461,plain,
% 3.72/2.85 (c2_1(a587)),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[950, 6443])).
% 3.72/2.85 tff(6462,plain,
% 3.72/2.85 (c0_1(a587)),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[961, 6443])).
% 3.72/2.85 tff(6463,plain,
% 3.72/2.85 (c1_1(a606)),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[1088, 6459])).
% 3.72/2.85 tff(6464,plain,
% 3.72/2.85 (c0_1(a606)),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[5034, 6463, 4654, 6462, 6461, 6460, 6444])).
% 3.72/2.85 tff(6465,plain,
% 3.72/2.85 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp7 | hskp2 | c0_1(a617) | c1_1(a617) | (~ndr1_0) | (~c2_1(a617)))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp7 | hskp2 | c0_1(a617) | c1_1(a617) | (~ndr1_0) | (~c2_1(a617)))),
% 3.72/2.85 inference(rewrite,[status(thm)],[])).
% 3.72/2.85 tff(6466,plain,
% 3.72/2.85 ((hskp7 | hskp2 | (~ndr1_0) | c1_1(a617) | c0_1(a617) | (~c2_1(a617))) <=> (hskp7 | hskp2 | c0_1(a617) | c1_1(a617) | (~ndr1_0) | (~c2_1(a617)))),
% 3.72/2.85 inference(rewrite,[status(thm)],[])).
% 3.72/2.85 tff(6467,plain,
% 3.72/2.85 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp7 | hskp2 | c0_1(a617) | c1_1(a617) | (~ndr1_0) | (~c2_1(a617))))),
% 3.72/2.85 inference(monotonicity,[status(thm)],[6466])).
% 3.72/2.85 tff(6468,plain,
% 3.72/2.85 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp7 | hskp2 | c0_1(a617) | c1_1(a617) | (~ndr1_0) | (~c2_1(a617)))),
% 3.72/2.85 inference(transitivity,[status(thm)],[6467, 6465])).
% 3.72/2.85 tff(6469,plain,
% 3.72/2.85 ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp7 | hskp2 | (~ndr1_0) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)))),
% 3.72/2.85 inference(quant_inst,[status(thm)],[])).
% 3.72/2.85 tff(6470,plain,
% 3.72/2.85 ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp7 | hskp2 | c0_1(a617) | c1_1(a617) | (~ndr1_0) | (~c2_1(a617))),
% 3.72/2.85 inference(modus_ponens,[status(thm)],[6469, 6468])).
% 3.72/2.85 tff(6471,plain,
% 3.72/2.85 ($false),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[6470, 107, 6108, 1797, 3749, 3748, 3747, 6080])).
% 3.72/2.85 tff(6472,plain,((~hskp19) | hskp7 | hskp2), inference(lemma,lemma(discharge,[]))).
% 3.72/2.85 tff(6473,plain,
% 3.72/2.85 (~hskp19),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[6472, 6108, 1797])).
% 3.72/2.85 tff(6474,plain,
% 3.72/2.85 (hskp13),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[3867, 6473, 6445, 6446])).
% 3.72/2.85 tff(6475,plain,
% 3.72/2.85 (~c2_1(a601)),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[2523, 6474])).
% 3.72/2.85 tff(6476,plain,
% 3.72/2.85 (~c1_1(a601)),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[2529, 6474])).
% 3.72/2.85 tff(6477,plain,
% 3.72/2.85 (~c3_1(a601)),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[2536, 107, 6247, 6246, 6245, 6463, 6460, 6476, 6475, 1106, 6464])).
% 3.72/2.85 tff(6478,plain,
% 3.72/2.85 (~c0_1(a601)),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[2543, 6474])).
% 3.72/2.85 tff(6479,plain,
% 3.72/2.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a607) | (~c2_1(a607)) | c0_1(a601) | c2_1(a601) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a601) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a607) | (~c2_1(a607)) | c0_1(a601) | c2_1(a601) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a601) | (~c3_1(a607)))),
% 3.72/2.85 inference(rewrite,[status(thm)],[])).
% 3.72/2.85 tff(6480,plain,
% 3.72/2.85 (((~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c3_1(a607)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a601) | c0_1(a601) | c2_1(a601)) <=> (c1_1(a607) | (~c2_1(a607)) | c0_1(a601) | c2_1(a601) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a601) | (~c3_1(a607)))),
% 3.72/2.85 inference(rewrite,[status(thm)],[])).
% 3.72/2.85 tff(6481,plain,
% 3.72/2.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c3_1(a607)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a601) | c0_1(a601) | c2_1(a601))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a607) | (~c2_1(a607)) | c0_1(a601) | c2_1(a601) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a601) | (~c3_1(a607))))),
% 3.72/2.85 inference(monotonicity,[status(thm)],[6480])).
% 3.72/2.85 tff(6482,plain,
% 3.72/2.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c3_1(a607)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a601) | c0_1(a601) | c2_1(a601))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a607) | (~c2_1(a607)) | c0_1(a601) | c2_1(a601) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a601) | (~c3_1(a607)))),
% 3.72/2.85 inference(transitivity,[status(thm)],[6481, 6479])).
% 3.72/2.85 tff(6483,plain,
% 3.72/2.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c3_1(a607)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a601) | c0_1(a601) | c2_1(a601))),
% 3.72/2.85 inference(quant_inst,[status(thm)],[])).
% 3.72/2.85 tff(6484,plain,
% 3.72/2.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a607) | (~c2_1(a607)) | c0_1(a601) | c2_1(a601) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a601) | (~c3_1(a607))),
% 3.72/2.85 inference(modus_ponens,[status(thm)],[6483, 6482])).
% 3.72/2.85 tff(6485,plain,
% 3.72/2.85 ($false),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[6484, 107, 6040, 6445, 6447, 66, 4653, 6478, 6475, 45, 1730, 6477])).
% 3.72/2.85 tff(6486,plain,(hskp7 | c1_1(a607) | c0_1(a590) | hskp2), inference(lemma,lemma(discharge,[]))).
% 3.72/2.85 tff(6487,plain,
% 3.72/2.85 (c0_1(a590)),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[6486, 6108, 66, 1797])).
% 3.72/2.85 tff(6488,plain,
% 3.72/2.85 ($false),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[666, 6487, 6442])).
% 3.72/2.85 tff(6489,plain,(hskp7 | c1_1(a607) | hskp2), inference(lemma,lemma(discharge,[]))).
% 3.72/2.85 tff(6490,plain,
% 3.72/2.85 (hskp7),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[6489, 1797, 66])).
% 3.72/2.85 tff(6491,plain,
% 3.72/2.85 (~c3_1(a592)),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[811, 6490])).
% 3.72/2.85 tff(6492,plain,
% 3.72/2.85 (~c0_1(a592)),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[817, 6490])).
% 3.72/2.85 tff(6493,plain,
% 3.72/2.85 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | c1_1(a607) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c0_1(a607)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a607) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.72/2.85 inference(rewrite,[status(thm)],[])).
% 3.72/2.85 tff(6494,plain,
% 3.72/2.85 ((hskp15 | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c1_1(a607) | (~c3_1(a607)) | (~c0_1(a607))) <=> (hskp15 | c1_1(a607) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.72/2.85 inference(rewrite,[status(thm)],[])).
% 3.72/2.85 tff(6495,plain,
% 3.72/2.85 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c1_1(a607) | (~c3_1(a607)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | c1_1(a607) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c0_1(a607)) | (~c3_1(a607))))),
% 3.72/2.85 inference(monotonicity,[status(thm)],[6494])).
% 3.72/2.85 tff(6496,plain,
% 3.72/2.85 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c1_1(a607) | (~c3_1(a607)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a607) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.72/2.85 inference(transitivity,[status(thm)],[6495, 6493])).
% 3.72/2.85 tff(6497,plain,
% 3.72/2.85 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c1_1(a607) | (~c3_1(a607)) | (~c0_1(a607)))),
% 3.72/2.85 inference(quant_inst,[status(thm)],[])).
% 3.72/2.85 tff(6498,plain,
% 3.72/2.85 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a607) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c0_1(a607)) | (~c3_1(a607))),
% 3.72/2.85 inference(modus_ponens,[status(thm)],[6497, 6496])).
% 3.72/2.85 tff(6499,plain,
% 3.72/2.85 (hskp15 | (~c1_1(a678))),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[6498, 107, 2318, 2316, 6040, 66, 1993, 6107])).
% 3.72/2.85 tff(6500,plain,
% 3.72/2.85 (~c1_1(a678)),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[6499, 3154])).
% 3.72/2.85 tff(6501,plain,
% 3.72/2.85 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | c1_1(a607) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a607)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a607) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.72/2.85 inference(rewrite,[status(thm)],[])).
% 3.72/2.85 tff(6502,plain,
% 3.72/2.85 ((hskp15 | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c1_1(a607) | (~c3_1(a607)) | (~c0_1(a607))) <=> (hskp15 | c1_1(a607) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.72/2.85 inference(rewrite,[status(thm)],[])).
% 3.72/2.85 tff(6503,plain,
% 3.72/2.85 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c1_1(a607) | (~c3_1(a607)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | c1_1(a607) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a607)) | (~c3_1(a607))))),
% 3.72/2.85 inference(monotonicity,[status(thm)],[6502])).
% 3.72/2.85 tff(6504,plain,
% 3.72/2.85 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c1_1(a607) | (~c3_1(a607)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a607) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.72/2.85 inference(transitivity,[status(thm)],[6503, 6501])).
% 3.72/2.85 tff(6505,plain,
% 3.72/2.85 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c1_1(a607) | (~c3_1(a607)) | (~c0_1(a607)))),
% 3.72/2.85 inference(quant_inst,[status(thm)],[])).
% 3.72/2.85 tff(6506,plain,
% 3.72/2.85 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a607) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a607)) | (~c3_1(a607))),
% 3.72/2.85 inference(modus_ponens,[status(thm)],[6505, 6504])).
% 3.72/2.85 tff(6507,plain,
% 3.72/2.85 (hskp15 | (~c0_1(a593))),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[6506, 107, 6040, 1894, 1903, 66, 1993, 6107])).
% 3.72/2.85 tff(6508,plain,
% 3.72/2.85 (~c0_1(a593)),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[6507, 3154])).
% 3.72/2.85 tff(6509,plain,
% 3.72/2.85 ($false),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[2626, 107, 4654, 2318, 2317, 1894, 1893, 32, 6508, 6500])).
% 3.72/2.85 tff(6510,plain,(hskp15 | (~c0_1(a678)) | (~c2_1(a678)) | (~c1_1(a593)) | c2_1(a593) | (~c3_1(a593)) | c1_1(a607) | (~c3_1(a678))), inference(lemma,lemma(discharge,[]))).
% 3.72/2.85 tff(6511,plain,
% 3.72/2.85 (hskp15),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[6510, 6247, 6246, 6423, 6421, 6422, 66, 6245])).
% 3.72/2.85 tff(6512,plain,
% 3.72/2.85 (~c0_1(a604)),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[1591, 6511])).
% 3.72/2.85 tff(6513,plain,
% 3.72/2.85 (c1_1(a604)),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[1613, 6511])).
% 3.72/2.85 tff(6514,plain,
% 3.72/2.85 (c2_1(a604)),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[5622, 107, 4654, 6513, 66, 4653, 6512, 32, 6107])).
% 3.72/2.85 tff(6515,plain,
% 3.72/2.85 (hskp12 | (~c2_1(a604))),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[3055, 107, 6212, 6211, 6210, 6513, 6512, 2727])).
% 3.72/2.85 tff(6516,plain,
% 3.72/2.85 (hskp12),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[6515, 6514])).
% 3.72/2.85 tff(6517,plain,
% 3.72/2.85 (~c3_1(a600)),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[741, 6516])).
% 3.72/2.85 tff(6518,plain,
% 3.72/2.85 (c2_1(a600)),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[752, 6516])).
% 3.72/2.85 tff(6519,plain,
% 3.72/2.85 (c0_1(a600)),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[763, 6516])).
% 3.72/2.85 tff(6520,plain,
% 3.72/2.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a607) | (~c2_1(a607)) | c3_1(a600) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c2_1(a600)) | (~c0_1(a600)) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a607) | (~c2_1(a607)) | c3_1(a600) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c2_1(a600)) | (~c0_1(a600)) | (~c3_1(a607)))),
% 3.72/2.85 inference(rewrite,[status(thm)],[])).
% 3.72/2.85 tff(6521,plain,
% 3.72/2.85 (((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a607) | (~c3_1(a607)) | (~c2_1(a607)) | c3_1(a592) | c0_1(a592) | (~c1_1(a592))) <=> (c1_1(a607) | (~c2_1(a607)) | c3_1(a600) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c2_1(a600)) | (~c0_1(a600)) | (~c3_1(a607)))),
% 3.72/2.85 inference(rewrite,[status(thm)],[])).
% 3.72/2.85 tff(6522,plain,
% 3.72/2.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a607) | (~c3_1(a607)) | (~c2_1(a607)) | c3_1(a592) | c0_1(a592) | (~c1_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a607) | (~c2_1(a607)) | c3_1(a600) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c2_1(a600)) | (~c0_1(a600)) | (~c3_1(a607))))),
% 3.72/2.85 inference(monotonicity,[status(thm)],[6521])).
% 3.72/2.85 tff(6523,plain,
% 3.72/2.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a607) | (~c3_1(a607)) | (~c2_1(a607)) | c3_1(a592) | c0_1(a592) | (~c1_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a607) | (~c2_1(a607)) | c3_1(a600) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c2_1(a600)) | (~c0_1(a600)) | (~c3_1(a607)))),
% 3.72/2.85 inference(transitivity,[status(thm)],[6522, 6520])).
% 3.72/2.85 tff(6524,plain,
% 3.72/2.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a607) | (~c3_1(a607)) | (~c2_1(a607)) | c3_1(a592) | c0_1(a592) | (~c1_1(a592)))),
% 3.72/2.85 inference(quant_inst,[status(thm)],[])).
% 3.72/2.85 tff(6525,plain,
% 3.72/2.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a607) | (~c2_1(a607)) | c3_1(a600) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c2_1(a600)) | (~c0_1(a600)) | (~c3_1(a607))),
% 3.72/2.85 inference(modus_ponens,[status(thm)],[6524, 6523])).
% 3.72/2.85 tff(6526,plain,
% 3.72/2.85 (~c1_1(a592)),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[6525, 107, 6040, 6519, 6518, 66, 4653, 6517, 6492, 6491, 258])).
% 3.72/2.85 tff(6527,plain,
% 3.72/2.85 (c2_1(a592)),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[828, 6490])).
% 3.72/2.85 tff(6528,plain,
% 3.72/2.85 ($false),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[6104, 107, 1797, 6527, 6492, 6491, 200, 6526])).
% 3.72/2.85 tff(6529,plain,(hskp2 | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.72/2.85 tff(6530,plain,
% 3.72/2.85 (hskp2),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[6529, 66])).
% 3.72/2.85 tff(6531,plain,
% 3.72/2.85 (hskp28),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[6069, 6530, 66])).
% 3.72/2.85 tff(6532,plain,
% 3.72/2.85 (c3_1(a612)),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[1139, 6531])).
% 3.72/2.85 tff(6533,plain,
% 3.72/2.85 (c1_1(a612)),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[1435, 6531])).
% 3.72/2.85 tff(6534,plain,
% 3.72/2.85 (hskp20 | hskp7 | c0_1(a612)),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[4520, 107, 6533, 6532, 801])).
% 3.72/2.85 tff(6535,plain,
% 3.72/2.85 (c0_1(a612)),
% 3.72/2.85 inference(unit_resolution,[status(thm)],[6534, 6109, 6108])).
% 3.72/2.85 tff(6536,plain,
% 3.72/2.85 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | c1_1(a607) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c0_1(a607)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a607) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.72/2.85 inference(rewrite,[status(thm)],[])).
% 3.72/2.85 tff(6537,plain,
% 3.72/2.85 ((hskp15 | (~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c1_1(a607) | (~c3_1(a607)) | (~c0_1(a607))) <=> (hskp15 | c1_1(a607) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.72/2.85 inference(rewrite,[status(thm)],[])).
% 3.72/2.85 tff(6538,plain,
% 3.72/2.85 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c1_1(a607) | (~c3_1(a607)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | c1_1(a607) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c0_1(a607)) | (~c3_1(a607))))),
% 3.72/2.85 inference(monotonicity,[status(thm)],[6537])).
% 3.72/2.85 tff(6539,plain,
% 3.72/2.85 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c1_1(a607) | (~c3_1(a607)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a607) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.72/2.86 inference(transitivity,[status(thm)],[6538, 6536])).
% 3.72/2.86 tff(6540,plain,
% 3.72/2.86 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c1_1(a607) | (~c3_1(a607)) | (~c0_1(a607)))),
% 3.72/2.86 inference(quant_inst,[status(thm)],[])).
% 3.72/2.86 tff(6541,plain,
% 3.72/2.86 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a607) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c0_1(a607)) | (~c3_1(a607))),
% 3.72/2.86 inference(modus_ponens,[status(thm)],[6540, 6539])).
% 3.72/2.86 tff(6542,plain,
% 3.72/2.86 (hskp15 | (~c0_1(a612))),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[6541, 107, 6533, 6532, 6040, 66, 1993, 6107])).
% 3.72/2.86 tff(6543,plain,
% 3.72/2.86 (hskp15),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[6542, 6535])).
% 3.72/2.86 tff(6544,plain,
% 3.72/2.86 (~c0_1(a604)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[1591, 6543])).
% 3.72/2.86 tff(6545,plain,
% 3.72/2.86 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp20 | hskp19 | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)))),
% 3.72/2.86 inference(rewrite,[status(thm)],[])).
% 3.72/2.86 tff(6546,plain,
% 3.72/2.86 ((hskp20 | hskp19 | (~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612))) <=> (hskp20 | hskp19 | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)))),
% 3.72/2.86 inference(rewrite,[status(thm)],[])).
% 3.72/2.86 tff(6547,plain,
% 3.72/2.86 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612))))),
% 3.72/2.86 inference(monotonicity,[status(thm)],[6546])).
% 3.72/2.86 tff(6548,plain,
% 3.72/2.86 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp20 | hskp19 | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)))),
% 3.72/2.86 inference(transitivity,[status(thm)],[6547, 6545])).
% 3.72/2.86 tff(6549,plain,
% 3.72/2.86 ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)))),
% 3.72/2.86 inference(quant_inst,[status(thm)],[])).
% 3.72/2.86 tff(6550,plain,
% 3.72/2.86 ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp20 | hskp19 | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612))),
% 3.72/2.86 inference(modus_ponens,[status(thm)],[6549, 6548])).
% 3.72/2.86 tff(6551,plain,
% 3.72/2.86 (hskp20 | hskp19 | (~c0_1(a612))),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[6550, 107, 6533, 6532, 3768])).
% 3.72/2.86 tff(6552,plain,
% 3.72/2.86 (hskp19),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[6551, 6535, 6109])).
% 3.72/2.86 tff(6553,plain,
% 3.72/2.86 (~c1_1(a617)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[2588, 6552])).
% 3.72/2.86 tff(6554,plain,
% 3.72/2.86 (~c0_1(a617)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[2594, 6552])).
% 3.72/2.86 tff(6555,plain,
% 3.72/2.86 (c3_1(a604)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[1602, 6543])).
% 3.72/2.86 tff(6556,plain,
% 3.72/2.86 (c2_1(a617)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[2605, 6552])).
% 3.72/2.86 tff(6557,plain,
% 3.72/2.86 (~c2_1(a604)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[6017, 107, 6533, 6532, 6556, 6555, 6554, 6553, 6544, 65, 6535])).
% 3.72/2.86 tff(6558,plain,
% 3.72/2.86 (c1_1(a604)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[1613, 6543])).
% 3.72/2.86 tff(6559,plain,
% 3.72/2.86 ($false),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[5622, 107, 4654, 6558, 66, 4653, 6544, 32, 6107, 6557])).
% 3.72/2.86 tff(6560,plain,(hskp20 | c1_1(a607) | hskp7), inference(lemma,lemma(discharge,[]))).
% 3.72/2.86 tff(6561,plain,
% 3.72/2.86 (hskp20),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[6560, 6108, 66])).
% 3.72/2.86 tff(6562,plain,
% 3.72/2.86 (~c1_1(a623)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[721, 6561])).
% 3.72/2.86 tff(6563,plain,
% 3.72/2.86 (~c3_1(a623)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[709, 6561])).
% 3.72/2.86 tff(6564,plain,
% 3.72/2.86 (~c2_1(a623)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[715, 6561])).
% 3.72/2.86 tff(6565,plain,
% 3.72/2.86 (hskp29),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[4147, 6108, 4654])).
% 3.72/2.86 tff(6566,plain,
% 3.72/2.86 (c3_1(a678)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[2269, 6565])).
% 3.72/2.86 tff(6567,plain,
% 3.72/2.86 (c0_1(a678)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[2291, 6565])).
% 3.72/2.86 tff(6568,plain,
% 3.72/2.86 (c2_1(a678)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[2280, 6565])).
% 3.72/2.86 tff(6569,plain,
% 3.72/2.86 (hskp15),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[6510, 5214, 6568, 6567, 5222, 5213, 66, 6566])).
% 3.72/2.86 tff(6570,plain,
% 3.72/2.86 (~c0_1(a604)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[1591, 6569])).
% 3.72/2.86 tff(6571,plain,
% 3.72/2.86 (c1_1(a604)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[1613, 6569])).
% 3.72/2.86 tff(6572,plain,
% 3.72/2.86 (c2_1(a604)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[5622, 107, 4654, 6571, 66, 4653, 6570, 32, 6107])).
% 3.72/2.86 tff(6573,plain,
% 3.72/2.86 (c3_1(a604)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[1602, 6569])).
% 3.72/2.86 tff(6574,plain,
% 3.72/2.86 (hskp20),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[6406, 107, 6108, 6571, 6573, 6570, 801])).
% 3.72/2.86 tff(6575,plain,
% 3.72/2.86 (~c3_1(a623)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[709, 6574])).
% 3.72/2.86 tff(6576,plain,
% 3.72/2.86 (~c2_1(a623)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[715, 6574])).
% 3.72/2.86 tff(6577,plain,
% 3.72/2.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c3_1(a607)) | c0_1(a623))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c3_1(a607)) | c0_1(a623))),
% 3.72/2.86 inference(rewrite,[status(thm)],[])).
% 3.72/2.86 tff(6578,plain,
% 3.72/2.86 (((~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c3_1(a607)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c3_1(a623) | c0_1(a623) | c2_1(a623)) <=> (c2_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c3_1(a607)) | c0_1(a623))),
% 3.72/2.86 inference(rewrite,[status(thm)],[])).
% 3.72/2.86 tff(6579,plain,
% 3.72/2.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c3_1(a607)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c3_1(a623) | c0_1(a623) | c2_1(a623))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c3_1(a607)) | c0_1(a623)))),
% 3.72/2.86 inference(monotonicity,[status(thm)],[6578])).
% 3.72/2.86 tff(6580,plain,
% 3.72/2.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c3_1(a607)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c3_1(a623) | c0_1(a623) | c2_1(a623))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c3_1(a607)) | c0_1(a623))),
% 3.72/2.86 inference(transitivity,[status(thm)],[6579, 6577])).
% 3.72/2.86 tff(6581,plain,
% 3.72/2.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c3_1(a607)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c3_1(a623) | c0_1(a623) | c2_1(a623))),
% 3.72/2.86 inference(quant_inst,[status(thm)],[])).
% 3.72/2.86 tff(6582,plain,
% 3.72/2.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a623) | c3_1(a623) | c1_1(a607) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c3_1(a604)) | (~c2_1(a604)) | (~c3_1(a607)) | c0_1(a623)),
% 3.72/2.86 inference(modus_ponens,[status(thm)],[6581, 6580])).
% 3.72/2.86 tff(6583,plain,
% 3.72/2.86 (c0_1(a623)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[6582, 107, 6040, 6573, 6576, 6575, 66, 4653, 6570, 1730, 6572])).
% 3.72/2.86 tff(6584,plain,
% 3.72/2.86 (hskp16 | (~c0_1(a623))),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[5655, 107, 6573, 6576, 6575, 6570, 2125, 6572])).
% 3.72/2.86 tff(6585,plain,
% 3.72/2.86 (hskp16),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[6584, 6583])).
% 3.72/2.86 tff(6586,plain,
% 3.72/2.86 (~c2_1(a606)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[1111, 6585])).
% 3.72/2.86 tff(6587,plain,
% 3.72/2.86 (c1_1(a606)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[1088, 6585])).
% 3.72/2.86 tff(6588,plain,
% 3.72/2.86 (c0_1(a606)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[5034, 6587, 4654, 5226, 5225, 6586, 5224])).
% 3.72/2.86 tff(6589,plain,
% 3.72/2.86 (hskp11),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[2354, 107, 6132, 6587, 6586, 2347, 6588])).
% 3.72/2.86 tff(6590,plain,
% 3.72/2.86 (~c1_1(a599)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[428, 6589])).
% 3.72/2.86 tff(6591,plain,
% 3.72/2.86 (c2_1(a599)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[439, 6589])).
% 3.72/2.86 tff(6592,plain,
% 3.72/2.86 (c3_1(a599)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[422, 6589])).
% 3.72/2.86 tff(6593,plain,
% 3.72/2.86 (~hskp13),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[2553, 6592, 6572, 6588, 6591, 6590, 6570, 6567, 6568, 6566, 6587, 6586, 6573])).
% 3.72/2.86 tff(6594,plain,
% 3.72/2.86 (hskp19 | hskp13 | (~c2_1(a604))),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[2656, 107, 6571, 6570, 2564])).
% 3.72/2.86 tff(6595,plain,
% 3.72/2.86 (hskp19),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[6594, 6593, 6572])).
% 3.72/2.86 tff(6596,plain,
% 3.72/2.86 (~c1_1(a617)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[2588, 6595])).
% 3.72/2.86 tff(6597,plain,
% 3.72/2.86 (~c0_1(a617)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[2594, 6595])).
% 3.72/2.86 tff(6598,plain,
% 3.72/2.86 (c2_1(a617)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[2605, 6595])).
% 3.72/2.86 tff(6599,plain,
% 3.72/2.86 (~c1_1(a678)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[2612, 107, 6567, 6566, 6598, 6573, 6597, 6596, 6570, 65, 6572])).
% 3.72/2.86 tff(6600,plain,
% 3.72/2.86 (~c0_1(a593)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[2619, 107, 6598, 6573, 5214, 5213, 6597, 6596, 6570, 65, 6572])).
% 3.72/2.86 tff(6601,plain,
% 3.72/2.86 ($false),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[2626, 107, 4654, 6567, 6568, 5214, 5222, 32, 6600, 6599])).
% 3.72/2.86 tff(6602,plain,((~hskp8) | c1_1(a607) | hskp7), inference(lemma,lemma(discharge,[]))).
% 3.72/2.86 tff(6603,plain,
% 3.72/2.86 (~hskp8),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[6602, 6108, 66])).
% 3.72/2.86 tff(6604,plain,
% 3.72/2.86 ($false),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[6165, 6120, 726, 1709, 6142])).
% 3.72/2.86 tff(6605,plain,(hskp26 | hskp8 | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.72/2.86 tff(6606,plain,
% 3.72/2.86 (hskp26),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[6605, 1709, 66])).
% 3.72/2.86 tff(6607,plain,
% 3.72/2.86 (c0_1(a583)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[362, 6606])).
% 3.72/2.86 tff(6608,plain,
% 3.72/2.86 (c2_1(a583)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[391, 6606])).
% 3.72/2.86 tff(6609,plain,
% 3.72/2.86 (c1_1(a583)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[351, 6606])).
% 3.72/2.86 tff(6610,plain,
% 3.72/2.86 (~c3_1(a586)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[218, 6530])).
% 3.72/2.86 tff(6611,plain,
% 3.72/2.86 (c2_1(a586)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[1474, 6530])).
% 3.72/2.86 tff(6612,plain,
% 3.72/2.86 (c1_1(a586)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[229, 6530])).
% 3.72/2.86 tff(6613,plain,
% 3.72/2.86 (c3_1(a590)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[6326, 863, 66, 1709, 45])).
% 3.72/2.86 tff(6614,plain,
% 3.72/2.86 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | hskp7 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)))),
% 3.72/2.86 inference(rewrite,[status(thm)],[])).
% 3.72/2.86 tff(6615,plain,
% 3.72/2.86 ((hskp20 | hskp7 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586))) <=> (hskp20 | hskp7 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)))),
% 3.72/2.86 inference(rewrite,[status(thm)],[])).
% 3.72/2.86 tff(6616,plain,
% 3.72/2.86 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586))))),
% 3.72/2.86 inference(monotonicity,[status(thm)],[6615])).
% 3.72/2.86 tff(6617,plain,
% 3.72/2.86 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | hskp7 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)))),
% 3.72/2.86 inference(transitivity,[status(thm)],[6616, 6614])).
% 3.72/2.86 tff(6618,plain,
% 3.72/2.86 ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586)))),
% 3.72/2.86 inference(quant_inst,[status(thm)],[])).
% 3.72/2.86 tff(6619,plain,
% 3.72/2.86 ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | hskp7 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586))),
% 3.72/2.86 inference(modus_ponens,[status(thm)],[6618, 6617])).
% 3.72/2.86 tff(6620,plain,
% 3.72/2.86 (hskp20 | hskp7 | (~c0_1(a586))),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[6619, 107, 4820, 4808, 1382])).
% 3.72/2.86 tff(6621,plain,
% 3.72/2.86 (~c0_1(a586)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[6620, 6109, 6108])).
% 3.72/2.86 tff(6622,plain,
% 3.72/2.86 (hskp20 | (~c3_1(a590)) | (~c1_1(a590))),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[6358, 107, 6108, 45, 801])).
% 3.72/2.86 tff(6623,plain,
% 3.72/2.86 (~c1_1(a590)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[6622, 6109, 862])).
% 3.72/2.86 tff(6624,plain,
% 3.72/2.86 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | c0_1(a590) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a590)) | c1_1(a590))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a590) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a590)) | c1_1(a590))),
% 3.72/2.86 inference(rewrite,[status(thm)],[])).
% 3.72/2.86 tff(6625,plain,
% 3.72/2.86 ((hskp8 | (~ndr1_0) | c0_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c1_1(a590) | c0_1(a590) | (~c3_1(a590))) <=> (hskp8 | c0_1(a590) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a590)) | c1_1(a590))),
% 3.72/2.86 inference(rewrite,[status(thm)],[])).
% 3.72/2.86 tff(6626,plain,
% 3.72/2.86 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c1_1(a590) | c0_1(a590) | (~c3_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | c0_1(a590) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a590)) | c1_1(a590)))),
% 3.72/2.86 inference(monotonicity,[status(thm)],[6625])).
% 3.72/2.86 tff(6627,plain,
% 3.72/2.86 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c1_1(a590) | c0_1(a590) | (~c3_1(a590)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a590) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a590)) | c1_1(a590))),
% 3.72/2.86 inference(transitivity,[status(thm)],[6626, 6624])).
% 3.72/2.86 tff(6628,plain,
% 3.72/2.86 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c1_1(a590) | c0_1(a590) | (~c3_1(a590)))),
% 3.72/2.86 inference(quant_inst,[status(thm)],[])).
% 3.72/2.86 tff(6629,plain,
% 3.72/2.86 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a590) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a586) | (~c3_1(a590)) | c1_1(a590)),
% 3.72/2.86 inference(modus_ponens,[status(thm)],[6628, 6627])).
% 3.72/2.86 tff(6630,plain,
% 3.72/2.86 ($false),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[6629, 107, 1709, 862, 4809, 4820, 45, 1317, 6623, 6621])).
% 3.72/2.86 tff(6631,plain,(hskp20 | hskp8 | (~c3_1(a590)) | (~c1_1(a586)) | (~c2_1(a586)) | c0_1(a590) | hskp7 | c3_1(a586)), inference(lemma,lemma(discharge,[]))).
% 3.72/2.86 tff(6632,plain,
% 3.72/2.86 (hskp20),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[6631, 6613, 1709, 6612, 6611, 45, 6108, 6610])).
% 3.72/2.86 tff(6633,plain,
% 3.72/2.86 (~c3_1(a623)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[709, 6632])).
% 3.72/2.86 tff(6634,plain,
% 3.72/2.86 (~c2_1(a623)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[715, 6632])).
% 3.72/2.86 tff(6635,plain,
% 3.72/2.86 (c0_1(a623)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[6456, 107, 6040, 863, 6613, 6634, 6633, 66, 4653, 45, 1730])).
% 3.72/2.86 tff(6636,plain,
% 3.72/2.86 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | c2_1(a623) | c3_1(a623) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c0_1(a623)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c2_1(a623) | c3_1(a623) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c0_1(a623)))),
% 3.72/2.86 inference(rewrite,[status(thm)],[])).
% 3.72/2.86 tff(6637,plain,
% 3.72/2.86 ((hskp8 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c3_1(a623) | c2_1(a623) | (~c0_1(a623))) <=> (hskp8 | c2_1(a623) | c3_1(a623) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c0_1(a623)))),
% 3.72/2.86 inference(rewrite,[status(thm)],[])).
% 3.72/2.86 tff(6638,plain,
% 3.72/2.86 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c3_1(a623) | c2_1(a623) | (~c0_1(a623)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | c2_1(a623) | c3_1(a623) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c0_1(a623))))),
% 3.72/2.86 inference(monotonicity,[status(thm)],[6637])).
% 3.72/2.86 tff(6639,plain,
% 3.72/2.86 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c3_1(a623) | c2_1(a623) | (~c0_1(a623)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c2_1(a623) | c3_1(a623) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c0_1(a623)))),
% 3.72/2.86 inference(transitivity,[status(thm)],[6638, 6636])).
% 3.72/2.86 tff(6640,plain,
% 3.72/2.86 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c0_1(a586)) | c3_1(a623) | c2_1(a623) | (~c0_1(a623)))),
% 3.72/2.86 inference(quant_inst,[status(thm)],[])).
% 3.72/2.86 tff(6641,plain,
% 3.72/2.86 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c2_1(a623) | c3_1(a623) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c0_1(a586)) | (~c0_1(a623))),
% 3.72/2.86 inference(modus_ponens,[status(thm)],[6640, 6639])).
% 3.72/2.86 tff(6642,plain,
% 3.72/2.86 (~c0_1(a586)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[6641, 107, 1709, 6611, 6634, 6633, 6610, 4271, 6635])).
% 3.72/2.86 tff(6643,plain,
% 3.72/2.86 (((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | hskp8 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | c0_1(a586))) <=> ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | hskp8 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | c0_1(a586))),
% 3.72/2.86 inference(rewrite,[status(thm)],[])).
% 3.72/2.86 tff(6644,plain,
% 3.72/2.86 ((hskp18 | hskp8 | (~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586))) <=> (hskp18 | hskp8 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | c0_1(a586))),
% 3.72/2.86 inference(rewrite,[status(thm)],[])).
% 3.72/2.86 tff(6645,plain,
% 3.72/2.86 (((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | hskp8 | (~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)))) <=> ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | hskp8 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | c0_1(a586)))),
% 3.72/2.86 inference(monotonicity,[status(thm)],[6644])).
% 3.72/2.86 tff(6646,plain,
% 3.72/2.86 (((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | hskp8 | (~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)))) <=> ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | hskp8 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | c0_1(a586))),
% 3.72/2.86 inference(transitivity,[status(thm)],[6645, 6643])).
% 3.72/2.86 tff(6647,plain,
% 3.72/2.86 ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp18 | hskp8 | (~ndr1_0) | c0_1(a586) | c3_1(a586) | (~c2_1(a586)))),
% 3.72/2.86 inference(quant_inst,[status(thm)],[])).
% 3.72/2.86 tff(6648,plain,
% 3.72/2.86 ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp18 | hskp8 | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | c0_1(a586)),
% 3.72/2.86 inference(modus_ponens,[status(thm)],[6647, 6646])).
% 3.72/2.86 tff(6649,plain,
% 3.72/2.86 (hskp18 | hskp8 | c0_1(a586)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[6648, 107, 6611, 6610, 5564])).
% 3.72/2.86 tff(6650,plain,
% 3.72/2.86 (hskp18),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[6649, 6642, 1709])).
% 3.72/2.86 tff(6651,plain,
% 3.72/2.86 (~c2_1(a610)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[1189, 6650])).
% 3.72/2.86 tff(6652,plain,
% 3.72/2.86 (~c0_1(a610)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[1195, 6650])).
% 3.72/2.86 tff(6653,plain,
% 3.72/2.86 (~c1_1(a610)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[6139, 107, 4654, 6652, 6651, 66, 4653, 32, 6107])).
% 3.72/2.86 tff(6654,plain,
% 3.72/2.86 (hskp16 | (~c0_1(a623))),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[5880, 107, 863, 6613, 6634, 6633, 45, 2125])).
% 3.72/2.86 tff(6655,plain,
% 3.72/2.86 (hskp16),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[6654, 6635])).
% 3.72/2.86 tff(6656,plain,
% 3.72/2.86 (~c3_1(a606)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[1075, 6655])).
% 3.72/2.86 tff(6657,plain,
% 3.72/2.86 (~c2_1(a606)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[1111, 6655])).
% 3.72/2.86 tff(6658,plain,
% 3.72/2.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a607) | (~c2_1(a607)) | c2_1(a606) | c3_1(a606) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a606) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a607) | (~c2_1(a607)) | c2_1(a606) | c3_1(a606) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a606) | (~c3_1(a607)))),
% 3.72/2.86 inference(rewrite,[status(thm)],[])).
% 3.72/2.86 tff(6659,plain,
% 3.72/2.86 (((~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c3_1(a607)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a606) | c0_1(a606) | c2_1(a606)) <=> (c1_1(a607) | (~c2_1(a607)) | c2_1(a606) | c3_1(a606) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a606) | (~c3_1(a607)))),
% 3.72/2.86 inference(rewrite,[status(thm)],[])).
% 3.72/2.86 tff(6660,plain,
% 3.72/2.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c3_1(a607)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a606) | c0_1(a606) | c2_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a607) | (~c2_1(a607)) | c2_1(a606) | c3_1(a606) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a606) | (~c3_1(a607))))),
% 3.72/2.86 inference(monotonicity,[status(thm)],[6659])).
% 3.72/2.86 tff(6661,plain,
% 3.72/2.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c3_1(a607)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a606) | c0_1(a606) | c2_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a607) | (~c2_1(a607)) | c2_1(a606) | c3_1(a606) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a606) | (~c3_1(a607)))),
% 3.72/2.86 inference(transitivity,[status(thm)],[6660, 6658])).
% 3.72/2.86 tff(6662,plain,
% 3.72/2.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a607) | (~c2_1(a607)) | (~c3_1(a607)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c3_1(a606) | c0_1(a606) | c2_1(a606))),
% 3.72/2.86 inference(quant_inst,[status(thm)],[])).
% 3.72/2.86 tff(6663,plain,
% 3.72/2.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a607) | (~c2_1(a607)) | c2_1(a606) | c3_1(a606) | c0_1(a590) | (~ndr1_0) | (~c3_1(a590)) | (~c2_1(a590)) | c0_1(a606) | (~c3_1(a607))),
% 3.72/2.86 inference(modus_ponens,[status(thm)],[6662, 6661])).
% 3.72/2.86 tff(6664,plain,
% 3.72/2.86 (c0_1(a606)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[6663, 107, 6040, 863, 6613, 66, 4653, 6657, 6656, 45, 1730])).
% 3.72/2.86 tff(6665,plain,
% 3.72/2.86 (c2_1(a612)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[1150, 6531])).
% 3.72/2.86 tff(6666,plain,
% 3.72/2.86 (hskp10),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[1535, 107, 6533, 6665, 6532, 6607, 6609, 6608, 21])).
% 3.72/2.86 tff(6667,plain,
% 3.72/2.86 (~c1_1(a598)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[911, 6666])).
% 3.72/2.86 tff(6668,plain,
% 3.72/2.86 (c3_1(a598)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[881, 6666])).
% 3.72/2.86 tff(6669,plain,
% 3.72/2.86 (c2_1(a598)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[4997, 107, 6567, 6568, 6566, 6668, 6612, 6611, 6667, 11, 6642])).
% 3.72/2.86 tff(6670,plain,
% 3.72/2.86 (c0_1(a598)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[892, 6666])).
% 3.72/2.86 tff(6671,plain,
% 3.72/2.86 (c1_1(a606)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[1088, 6655])).
% 3.72/2.86 tff(6672,plain,
% 3.72/2.86 (c3_1(a610)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[1206, 6650])).
% 3.72/2.86 tff(6673,plain,
% 3.72/2.86 ($false),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[5608, 107, 6672, 6671, 6670, 6668, 6651, 6657, 1106, 6669, 6664, 6653])).
% 3.72/2.86 tff(6674,plain,((~c2_1(a590)) | c1_1(a607) | c0_1(a590) | hskp8 | hskp7), inference(lemma,lemma(discharge,[]))).
% 3.72/2.86 tff(6675,plain,
% 3.72/2.86 (~c2_1(a590)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[6674, 1709, 45, 66, 6108])).
% 3.72/2.86 tff(6676,plain,
% 3.72/2.86 (hskp22),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[6305, 6675, 66, 1709, 6609, 6608, 45, 6607])).
% 3.72/2.86 tff(6677,plain,
% 3.72/2.86 (c1_1(a633)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[3962, 6676])).
% 3.72/2.86 tff(6678,plain,
% 3.72/2.86 (~c0_1(a633)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[3968, 6676])).
% 3.72/2.86 tff(6679,plain,
% 3.72/2.86 (~c3_1(a633)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[3974, 6676])).
% 3.72/2.86 tff(6680,plain,
% 3.72/2.86 (hskp11),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[5163, 6679, 6678, 4654, 6677])).
% 3.72/2.86 tff(6681,plain,
% 3.72/2.86 (~c1_1(a599)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[428, 6680])).
% 3.72/2.86 tff(6682,plain,
% 3.72/2.86 (c2_1(a599)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[439, 6680])).
% 3.72/2.86 tff(6683,plain,
% 3.72/2.86 (c3_1(a599)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[422, 6680])).
% 3.72/2.86 tff(6684,plain,
% 3.72/2.86 ($false),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[6242, 6683, 6682, 66, 6609, 6608, 6607, 6676, 6681])).
% 3.72/2.86 tff(6685,plain,(hskp8 | c1_1(a607) | c0_1(a590) | hskp7), inference(lemma,lemma(discharge,[]))).
% 3.72/2.86 tff(6686,plain,
% 3.72/2.86 (c0_1(a590)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[6685, 6603, 66, 6108])).
% 3.72/2.86 tff(6687,plain,
% 3.72/2.86 (~hskp6),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[666, 6686])).
% 3.72/2.86 tff(6688,plain,
% 3.72/2.86 (~hskp4),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[147, 44, 67])).
% 3.72/2.86 tff(6689,plain,
% 3.72/2.86 (hskp4 | (~c0_1(a586))),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[247, 107, 4654, 6612, 6610, 55])).
% 3.72/2.86 tff(6690,plain,
% 3.72/2.86 (~c0_1(a586)),
% 3.72/2.86 inference(unit_resolution,[status(thm)],[6689, 6688])).
% 3.72/2.87 tff(6691,assumption,(~c2_1(a623)), introduced(assumption)).
% 3.72/2.87 tff(6692,assumption,(~c1_1(a623)), introduced(assumption)).
% 3.72/2.87 tff(6693,plain,
% 3.72/2.87 (hskp22 | (~c0_1(a623))),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[3930, 107, 67, 6692, 6691, 43])).
% 3.72/2.87 tff(6694,plain,
% 3.72/2.87 (~c0_1(a623)),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[6693, 44])).
% 3.72/2.87 tff(6695,assumption,(~c3_1(a623)), introduced(assumption)).
% 3.72/2.87 tff(6696,plain,
% 3.72/2.87 (((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp14 | hskp4 | c2_1(a623) | c3_1(a623) | (~ndr1_0) | c0_1(a623))) <=> ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp14 | hskp4 | c2_1(a623) | c3_1(a623) | (~ndr1_0) | c0_1(a623))),
% 3.72/2.87 inference(rewrite,[status(thm)],[])).
% 3.72/2.87 tff(6697,plain,
% 3.72/2.87 ((hskp14 | hskp4 | (~ndr1_0) | c2_1(a623) | c0_1(a623) | c3_1(a623)) <=> (hskp14 | hskp4 | c2_1(a623) | c3_1(a623) | (~ndr1_0) | c0_1(a623))),
% 3.72/2.87 inference(rewrite,[status(thm)],[])).
% 3.72/2.87 tff(6698,plain,
% 3.72/2.87 (((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp14 | hskp4 | (~ndr1_0) | c2_1(a623) | c0_1(a623) | c3_1(a623))) <=> ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp14 | hskp4 | c2_1(a623) | c3_1(a623) | (~ndr1_0) | c0_1(a623)))),
% 3.72/2.87 inference(monotonicity,[status(thm)],[6697])).
% 3.72/2.87 tff(6699,plain,
% 3.72/2.87 (((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp14 | hskp4 | (~ndr1_0) | c2_1(a623) | c0_1(a623) | c3_1(a623))) <=> ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp14 | hskp4 | c2_1(a623) | c3_1(a623) | (~ndr1_0) | c0_1(a623))),
% 3.72/2.87 inference(transitivity,[status(thm)],[6698, 6696])).
% 3.72/2.87 tff(6700,plain,
% 3.72/2.87 ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp14 | hskp4 | (~ndr1_0) | c2_1(a623) | c0_1(a623) | c3_1(a623))),
% 3.72/2.87 inference(quant_inst,[status(thm)],[])).
% 3.72/2.87 tff(6701,plain,
% 3.72/2.87 ((~![U: $i] : (hskp14 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp14 | hskp4 | c2_1(a623) | c3_1(a623) | (~ndr1_0) | c0_1(a623)),
% 3.72/2.87 inference(modus_ponens,[status(thm)],[6700, 6699])).
% 3.72/2.87 tff(6702,plain,
% 3.72/2.87 (hskp14 | hskp4 | c0_1(a623)),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[6701, 107, 6691, 6695, 158])).
% 3.72/2.87 tff(6703,plain,
% 3.72/2.87 (hskp14),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[6702, 6688, 6694])).
% 3.72/2.87 tff(6704,plain,
% 3.72/2.87 (~c3_1(a603)),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[205, 6703])).
% 3.72/2.87 tff(6705,plain,
% 3.72/2.87 (c0_1(a603)),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[182, 6703])).
% 3.72/2.87 tff(6706,plain,
% 3.72/2.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a607) | (~c2_1(a607)) | c3_1(a603) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a607) | (~c2_1(a607)) | c3_1(a603) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a607)))),
% 3.72/2.87 inference(rewrite,[status(thm)],[])).
% 3.72/2.87 tff(6707,plain,
% 3.72/2.87 (((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a607) | (~c3_1(a607)) | (~c2_1(a607)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586))) <=> (c1_1(a607) | (~c2_1(a607)) | c3_1(a603) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a607)))),
% 3.72/2.87 inference(rewrite,[status(thm)],[])).
% 3.72/2.87 tff(6708,plain,
% 3.72/2.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a607) | (~c3_1(a607)) | (~c2_1(a607)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a607) | (~c2_1(a607)) | c3_1(a603) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a607))))),
% 3.72/2.87 inference(monotonicity,[status(thm)],[6707])).
% 3.72/2.87 tff(6709,plain,
% 3.72/2.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a607) | (~c3_1(a607)) | (~c2_1(a607)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a607) | (~c2_1(a607)) | c3_1(a603) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a607)))),
% 3.72/2.87 inference(transitivity,[status(thm)],[6708, 6706])).
% 3.72/2.87 tff(6710,plain,
% 3.72/2.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a607) | (~c3_1(a607)) | (~c2_1(a607)) | c3_1(a586) | c0_1(a586) | (~c1_1(a586)))),
% 3.72/2.87 inference(quant_inst,[status(thm)],[])).
% 3.72/2.87 tff(6711,plain,
% 3.72/2.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a607) | (~c2_1(a607)) | c3_1(a603) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | c0_1(a586) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a607))),
% 3.72/2.87 inference(modus_ponens,[status(thm)],[6710, 6709])).
% 3.72/2.87 tff(6712,plain,
% 3.72/2.87 (~c2_1(a603)),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[6711, 107, 6040, 6705, 6612, 66, 4653, 6704, 6610, 258, 6690])).
% 3.72/2.87 tff(6713,plain,
% 3.72/2.87 (~c1_1(a603)),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[171, 6703])).
% 3.72/2.87 tff(6714,plain,
% 3.72/2.87 ($false),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[189, 107, 44, 67, 6705, 6713, 43, 6712])).
% 3.72/2.87 tff(6715,plain,(hskp22 | hskp6 | c1_1(a607) | c2_1(a623) | c3_1(a623) | c1_1(a623)), inference(lemma,lemma(discharge,[]))).
% 3.72/2.87 tff(6716,plain,
% 3.72/2.87 (hskp22),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[6715, 6687, 66, 6564, 6563, 6562])).
% 3.72/2.87 tff(6717,plain,
% 3.72/2.87 (c1_1(a633)),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[3962, 6716])).
% 3.72/2.87 tff(6718,plain,
% 3.72/2.87 (~c0_1(a633)),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[3968, 6716])).
% 3.72/2.87 tff(6719,plain,
% 3.72/2.87 (~c3_1(a633)),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[3974, 6716])).
% 3.72/2.87 tff(6720,plain,
% 3.72/2.87 (hskp11),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[5163, 6719, 6718, 4654, 6717])).
% 3.72/2.87 tff(6721,plain,
% 3.72/2.87 (~c1_1(a599)),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[428, 6720])).
% 3.72/2.87 tff(6722,plain,
% 3.72/2.87 (hskp26),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[6605, 6603, 66])).
% 3.72/2.87 tff(6723,plain,
% 3.72/2.87 (c0_1(a583)),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[362, 6722])).
% 3.72/2.87 tff(6724,plain,
% 3.72/2.87 (c2_1(a583)),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[391, 6722])).
% 3.72/2.87 tff(6725,plain,
% 3.72/2.87 (c1_1(a583)),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[351, 6722])).
% 3.72/2.87 tff(6726,plain,
% 3.72/2.87 (c2_1(a599)),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[439, 6720])).
% 3.72/2.87 tff(6727,plain,
% 3.72/2.87 (c3_1(a599)),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[422, 6720])).
% 3.72/2.87 tff(6728,plain,
% 3.72/2.87 ($false),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[6242, 6727, 6726, 66, 6725, 6724, 6723, 6716, 6721])).
% 3.72/2.87 tff(6729,plain,(hskp7 | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.72/2.87 tff(6730,plain,
% 3.72/2.87 (hskp7),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[6729, 66])).
% 3.72/2.87 tff(6731,plain,
% 3.72/2.87 (hskp18),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[6250, 1709, 6730])).
% 3.72/2.87 tff(6732,plain,
% 3.72/2.87 (~c2_1(a610)),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[1189, 6731])).
% 3.72/2.87 tff(6733,plain,
% 3.72/2.87 (~c0_1(a610)),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[1195, 6731])).
% 3.72/2.87 tff(6734,plain,
% 3.72/2.87 (~c1_1(a610)),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[6139, 107, 4654, 6733, 6732, 66, 4653, 32, 6107])).
% 3.72/2.87 tff(6735,plain,
% 3.72/2.87 (~c0_1(a592)),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[817, 6730])).
% 3.72/2.87 tff(6736,plain,
% 3.72/2.87 (c2_1(a592)),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[828, 6730])).
% 3.72/2.87 tff(6737,plain,
% 3.72/2.87 (c3_1(a610)),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[1206, 6731])).
% 3.72/2.87 tff(6738,plain,
% 3.72/2.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c2_1(a610) | (~c2_1(a607)) | c0_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592)) | (~c0_1(a607)) | (~c3_1(a607)) | c1_1(a610) | (~c3_1(a610)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a610) | (~c2_1(a607)) | c0_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592)) | (~c0_1(a607)) | (~c3_1(a607)) | c1_1(a610) | (~c3_1(a610)))),
% 3.72/2.87 inference(rewrite,[status(thm)],[])).
% 3.72/2.87 tff(6739,plain,
% 3.72/2.87 (((~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c0_1(a607)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610)) | c0_1(a592) | (~c1_1(a592)) | (~c2_1(a592))) <=> (c2_1(a610) | (~c2_1(a607)) | c0_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592)) | (~c0_1(a607)) | (~c3_1(a607)) | c1_1(a610) | (~c3_1(a610)))),
% 3.72/2.87 inference(rewrite,[status(thm)],[])).
% 3.72/2.87 tff(6740,plain,
% 3.72/2.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c0_1(a607)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610)) | c0_1(a592) | (~c1_1(a592)) | (~c2_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c2_1(a610) | (~c2_1(a607)) | c0_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592)) | (~c0_1(a607)) | (~c3_1(a607)) | c1_1(a610) | (~c3_1(a610))))),
% 3.72/2.87 inference(monotonicity,[status(thm)],[6739])).
% 3.72/2.87 tff(6741,plain,
% 3.72/2.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c0_1(a607)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610)) | c0_1(a592) | (~c1_1(a592)) | (~c2_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a610) | (~c2_1(a607)) | c0_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592)) | (~c0_1(a607)) | (~c3_1(a607)) | c1_1(a610) | (~c3_1(a610)))),
% 3.72/2.87 inference(transitivity,[status(thm)],[6740, 6738])).
% 3.72/2.87 tff(6742,plain,
% 3.72/2.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c0_1(a607)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610)) | c0_1(a592) | (~c1_1(a592)) | (~c2_1(a592)))),
% 3.72/2.87 inference(quant_inst,[status(thm)],[])).
% 3.72/2.87 tff(6743,plain,
% 3.72/2.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a610) | (~c2_1(a607)) | c0_1(a592) | (~ndr1_0) | (~c2_1(a592)) | (~c1_1(a592)) | (~c0_1(a607)) | (~c3_1(a607)) | c1_1(a610) | (~c3_1(a610))),
% 3.72/2.87 inference(modus_ponens,[status(thm)],[6742, 6741])).
% 3.72/2.87 tff(6744,plain,
% 3.72/2.87 (~c1_1(a592)),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[6743, 107, 6737, 6040, 6736, 6732, 4653, 6735, 11, 6107, 6734])).
% 3.72/2.87 tff(6745,plain,
% 3.72/2.87 (hskp6),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[6324, 107, 1709, 6737, 6733, 450, 6734])).
% 3.72/2.87 tff(6746,plain,
% 3.72/2.87 (~c0_1(a590)),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[666, 6745])).
% 3.72/2.87 tff(6747,plain,
% 3.72/2.87 (c3_1(a590)),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[677, 6745])).
% 3.72/2.87 tff(6748,plain,
% 3.72/2.87 (c2_1(a590)),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[688, 6745])).
% 3.72/2.87 tff(6749,plain,
% 3.72/2.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a592) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a592)) | c1_1(a592))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a592) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a592)) | c1_1(a592))),
% 3.72/2.87 inference(rewrite,[status(thm)],[])).
% 3.72/2.87 tff(6750,plain,
% 3.72/2.87 (((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a592) | c0_1(a592) | (~c2_1(a592))) <=> (c0_1(a592) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a592)) | c1_1(a592))),
% 3.72/2.87 inference(rewrite,[status(thm)],[])).
% 3.72/2.87 tff(6751,plain,
% 3.72/2.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a592) | c0_1(a592) | (~c2_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a592) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a592)) | c1_1(a592)))),
% 3.72/2.87 inference(monotonicity,[status(thm)],[6750])).
% 3.72/2.87 tff(6752,plain,
% 3.72/2.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a592) | c0_1(a592) | (~c2_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a592) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a592)) | c1_1(a592))),
% 3.72/2.87 inference(transitivity,[status(thm)],[6751, 6749])).
% 3.72/2.87 tff(6753,plain,
% 3.72/2.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a590) | (~c3_1(a590)) | (~c2_1(a590)) | c1_1(a592) | c0_1(a592) | (~c2_1(a592)))),
% 3.72/2.87 inference(quant_inst,[status(thm)],[])).
% 3.72/2.87 tff(6754,plain,
% 3.72/2.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a592) | c0_1(a590) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c3_1(a612)) | (~c3_1(a590)) | (~c2_1(a590)) | (~c2_1(a592)) | c1_1(a592)),
% 3.72/2.87 inference(modus_ponens,[status(thm)],[6753, 6752])).
% 3.72/2.87 tff(6755,plain,
% 3.72/2.87 (~c0_1(a612)),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[6754, 107, 6533, 6532, 6736, 6748, 6747, 6735, 6746, 65, 6744])).
% 3.72/2.87 tff(6756,plain,
% 3.72/2.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c2_1(a610) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c0_1(a607)) | (~c3_1(a607)) | c1_1(a610) | (~c3_1(a610)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a610) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c0_1(a607)) | (~c3_1(a607)) | c1_1(a610) | (~c3_1(a610)))),
% 3.72/2.87 inference(rewrite,[status(thm)],[])).
% 3.72/2.87 tff(6757,plain,
% 3.72/2.87 (((~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c0_1(a607)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612))) <=> (c2_1(a610) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c0_1(a607)) | (~c3_1(a607)) | c1_1(a610) | (~c3_1(a610)))),
% 3.72/2.87 inference(rewrite,[status(thm)],[])).
% 3.72/2.87 tff(6758,plain,
% 3.72/2.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c0_1(a607)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c2_1(a610) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c0_1(a607)) | (~c3_1(a607)) | c1_1(a610) | (~c3_1(a610))))),
% 3.72/2.87 inference(monotonicity,[status(thm)],[6757])).
% 3.72/2.87 tff(6759,plain,
% 3.72/2.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c0_1(a607)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a610) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c0_1(a607)) | (~c3_1(a607)) | c1_1(a610) | (~c3_1(a610)))),
% 3.72/2.87 inference(transitivity,[status(thm)],[6758, 6756])).
% 3.72/2.87 tff(6760,plain,
% 3.72/2.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c0_1(a607)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610)) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)))),
% 3.72/2.87 inference(quant_inst,[status(thm)],[])).
% 3.72/2.87 tff(6761,plain,
% 3.72/2.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a610) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c2_1(a612)) | (~c0_1(a607)) | (~c3_1(a607)) | c1_1(a610) | (~c3_1(a610))),
% 3.72/2.87 inference(modus_ponens,[status(thm)],[6760, 6759])).
% 3.72/2.87 tff(6762,plain,
% 3.72/2.87 ($false),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[6761, 107, 6533, 6665, 6737, 6040, 6732, 4653, 11, 6107, 6755, 6734])).
% 3.72/2.87 tff(6763,plain,(hskp8 | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.72/2.87 tff(6764,plain,
% 3.72/2.87 (hskp8),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[6763, 66])).
% 3.72/2.87 tff(6765,plain,
% 3.72/2.87 (c3_1(a593)),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[511, 6764])).
% 3.72/2.87 tff(6766,plain,
% 3.72/2.87 (~c2_1(a593)),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[555, 6764])).
% 3.72/2.87 tff(6767,plain,
% 3.72/2.87 (c1_1(a593)),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[522, 6764])).
% 3.72/2.87 tff(6768,plain,
% 3.72/2.87 (hskp15),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[6510, 4372, 6767, 4373, 6766, 6765, 66, 4371])).
% 3.72/2.87 tff(6769,plain,
% 3.72/2.87 (~c0_1(a604)),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[1591, 6768])).
% 3.72/2.87 tff(6770,plain,
% 3.72/2.87 (c1_1(a604)),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[1613, 6768])).
% 3.72/2.87 tff(6771,plain,
% 3.72/2.87 (c2_1(a604)),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[5622, 107, 4654, 6770, 66, 4653, 6769, 32, 6107])).
% 3.72/2.87 tff(6772,plain,
% 3.72/2.87 (hskp3),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[5154, 107, 4654, 6767, 6765, 6766, 3420])).
% 3.72/2.87 tff(6773,plain,
% 3.72/2.87 (~c1_1(a587)),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[939, 6772])).
% 3.72/2.87 tff(6774,plain,
% 3.72/2.87 (c3_1(a604)),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[1602, 6768])).
% 3.72/2.87 tff(6775,plain,
% 3.72/2.87 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~c2_1(a607)) | c2_1(a593) | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a607)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp14 | (~c2_1(a607)) | c2_1(a593) | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.72/2.87 inference(rewrite,[status(thm)],[])).
% 3.72/2.87 tff(6776,plain,
% 3.72/2.87 ((hskp14 | (~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c0_1(a607)) | c2_1(a593) | (~c1_1(a593)) | (~c3_1(a593))) <=> (hskp14 | (~c2_1(a607)) | c2_1(a593) | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.72/2.87 inference(rewrite,[status(thm)],[])).
% 3.72/2.87 tff(6777,plain,
% 3.72/2.87 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c0_1(a607)) | c2_1(a593) | (~c1_1(a593)) | (~c3_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~c2_1(a607)) | c2_1(a593) | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a607)) | (~c3_1(a607))))),
% 3.72/2.87 inference(monotonicity,[status(thm)],[6776])).
% 3.72/2.87 tff(6778,plain,
% 3.72/2.87 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c0_1(a607)) | c2_1(a593) | (~c1_1(a593)) | (~c3_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp14 | (~c2_1(a607)) | c2_1(a593) | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.72/2.87 inference(transitivity,[status(thm)],[6777, 6775])).
% 3.72/2.87 tff(6779,plain,
% 3.72/2.87 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c0_1(a607)) | c2_1(a593) | (~c1_1(a593)) | (~c3_1(a593)))),
% 3.72/2.87 inference(quant_inst,[status(thm)],[])).
% 3.72/2.87 tff(6780,plain,
% 3.72/2.87 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp14 | (~c2_1(a607)) | c2_1(a593) | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a607)) | (~c3_1(a607))),
% 3.72/2.87 inference(modus_ponens,[status(thm)],[6779, 6778])).
% 3.72/2.87 tff(6781,plain,
% 3.72/2.87 (hskp14),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[6780, 107, 6040, 6767, 6765, 4653, 6766, 550, 6107])).
% 3.72/2.87 tff(6782,plain,
% 3.72/2.87 (~c3_1(a603)),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[205, 6781])).
% 3.72/2.87 tff(6783,plain,
% 3.72/2.87 (c0_1(a603)),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[182, 6781])).
% 3.72/2.87 tff(6784,plain,
% 3.72/2.87 (c0_1(a586) | (~c2_1(a603))),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[6711, 107, 6040, 6783, 6612, 66, 4653, 6782, 6610, 258])).
% 3.72/2.87 tff(6785,plain,
% 3.72/2.87 (c0_1(a586)),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[6784, 1010])).
% 3.72/2.87 tff(6786,plain,
% 3.72/2.87 (hskp16 | (~c0_1(a586))),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[5993, 107, 4202, 2545, 6612, 2475, 6610, 1425])).
% 3.72/2.87 tff(6787,plain,
% 3.72/2.87 (hskp16),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[6786, 6785])).
% 3.72/2.87 tff(6788,plain,
% 3.72/2.87 (~c2_1(a606)),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[1111, 6787])).
% 3.72/2.87 tff(6789,plain,
% 3.72/2.87 (c2_1(a587)),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[950, 6772])).
% 3.72/2.87 tff(6790,plain,
% 3.72/2.87 (c0_1(a587)),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[961, 6772])).
% 3.72/2.87 tff(6791,plain,
% 3.72/2.87 (c1_1(a606)),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[1088, 6787])).
% 3.72/2.87 tff(6792,plain,
% 3.72/2.87 (c0_1(a606)),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[5034, 6791, 4654, 6790, 6789, 6788, 6773])).
% 3.72/2.87 tff(6793,plain,
% 3.72/2.87 (~c3_1(a592)),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[811, 6730])).
% 3.72/2.87 tff(6794,plain,
% 3.72/2.87 ((~c1_1(a592)) | (~c2_1(a603))),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[6205, 107, 6040, 6783, 66, 4653, 6782, 6735, 6793, 258])).
% 3.72/2.87 tff(6795,plain,
% 3.72/2.87 (~c1_1(a592)),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[6794, 1010])).
% 3.72/2.87 tff(6796,plain,
% 3.72/2.87 (c2_1(a604)),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[5622, 107, 4654, 4202, 66, 4653, 2475, 32, 6107])).
% 3.72/2.87 tff(6797,plain,
% 3.72/2.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a604) | c0_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a604) | c0_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a604)) | (~c2_1(a604)))),
% 3.72/2.87 inference(rewrite,[status(thm)],[])).
% 3.72/2.87 tff(6798,plain,
% 3.72/2.87 (((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a592) | c0_1(a592) | (~c2_1(a592))) <=> (c0_1(a604) | c0_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a604)) | (~c2_1(a604)))),
% 3.72/2.87 inference(rewrite,[status(thm)],[])).
% 3.72/2.87 tff(6799,plain,
% 3.72/2.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a592) | c0_1(a592) | (~c2_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a604) | c0_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a604)) | (~c2_1(a604))))),
% 3.72/2.87 inference(monotonicity,[status(thm)],[6798])).
% 3.72/2.87 tff(6800,plain,
% 3.72/2.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a592) | c0_1(a592) | (~c2_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a604) | c0_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a604)) | (~c2_1(a604)))),
% 3.72/2.87 inference(transitivity,[status(thm)],[6799, 6797])).
% 3.72/2.87 tff(6801,plain,
% 3.72/2.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a592) | c0_1(a592) | (~c2_1(a592)))),
% 3.72/2.87 inference(quant_inst,[status(thm)],[])).
% 3.72/2.87 tff(6802,plain,
% 3.72/2.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a604) | c0_1(a592) | (~ndr1_0) | (~c2_1(a592)) | c1_1(a592) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a604)) | (~c2_1(a604))),
% 3.72/2.87 inference(modus_ponens,[status(thm)],[6801, 6800])).
% 3.72/2.87 tff(6803,plain,
% 3.72/2.87 (~c0_1(a593)),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[6802, 107, 2545, 6767, 6765, 6736, 2475, 6735, 65, 6795, 6796])).
% 3.72/2.87 tff(6804,plain,
% 3.72/2.87 (~c3_1(a606)),
% 3.72/2.87 inference(unit_resolution,[status(thm)],[1075, 6787])).
% 3.72/2.87 tff(6805,plain,
% 3.72/2.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a606) | c3_1(a606) | c2_1(a593) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a606)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a606) | c3_1(a606) | c2_1(a593) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a606)))),
% 3.72/2.87 inference(rewrite,[status(thm)],[])).
% 3.72/2.87 tff(6806,plain,
% 3.72/2.87 (((~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c0_1(a606)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a592) | c1_1(a592) | c0_1(a592)) <=> (c2_1(a606) | c3_1(a606) | c2_1(a593) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a606)))),
% 3.72/2.87 inference(rewrite,[status(thm)],[])).
% 3.72/2.87 tff(6807,plain,
% 3.72/2.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c0_1(a606)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a592) | c1_1(a592) | c0_1(a592))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a606) | c3_1(a606) | c2_1(a593) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a606))))),
% 3.72/2.88 inference(monotonicity,[status(thm)],[6806])).
% 3.72/2.88 tff(6808,plain,
% 3.72/2.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c0_1(a606)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a592) | c1_1(a592) | c0_1(a592))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a606) | c3_1(a606) | c2_1(a593) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a606)))),
% 3.72/2.88 inference(transitivity,[status(thm)],[6807, 6805])).
% 3.72/2.88 tff(6809,plain,
% 3.72/2.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a606) | c3_1(a606) | (~c0_1(a606)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)) | c3_1(a592) | c1_1(a592) | c0_1(a592))),
% 3.72/2.88 inference(quant_inst,[status(thm)],[])).
% 3.72/2.88 tff(6810,plain,
% 3.72/2.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a606) | c3_1(a606) | c2_1(a593) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | c0_1(a593) | (~c1_1(a593)) | (~c0_1(a606))),
% 3.72/2.88 inference(modus_ponens,[status(thm)],[6809, 6808])).
% 3.72/2.88 tff(6811,plain,
% 3.72/2.88 ($false),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[6810, 107, 6767, 6788, 6804, 6766, 6735, 6793, 1463, 6803, 6795, 6792])).
% 3.72/2.88 tff(6812,plain,((~c2_1(a603)) | (~c3_1(a604)) | c0_1(a604) | (~c1_1(a604)) | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.72/2.88 tff(6813,plain,
% 3.72/2.88 (~c2_1(a603)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[6812, 6774, 6769, 6770, 66])).
% 3.72/2.88 tff(6814,plain,
% 3.72/2.88 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | c0_1(a604) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a604)) | (~c2_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c0_1(a604) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a604)) | (~c2_1(a604)))),
% 3.72/2.88 inference(rewrite,[status(thm)],[])).
% 3.72/2.88 tff(6815,plain,
% 3.72/2.88 ((hskp16 | (~ndr1_0) | c2_1(a603) | c3_1(a603) | (~c0_1(a603)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604))) <=> (hskp16 | c0_1(a604) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a604)) | (~c2_1(a604)))),
% 3.72/2.88 inference(rewrite,[status(thm)],[])).
% 3.72/2.88 tff(6816,plain,
% 3.72/2.88 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a603) | c3_1(a603) | (~c0_1(a603)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | c0_1(a604) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a604)) | (~c2_1(a604))))),
% 3.72/2.88 inference(monotonicity,[status(thm)],[6815])).
% 3.72/2.88 tff(6817,plain,
% 3.72/2.88 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a603) | c3_1(a603) | (~c0_1(a603)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c0_1(a604) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a604)) | (~c2_1(a604)))),
% 3.72/2.88 inference(transitivity,[status(thm)],[6816, 6814])).
% 3.72/2.88 tff(6818,plain,
% 3.72/2.88 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a603) | c3_1(a603) | (~c0_1(a603)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)))),
% 3.72/2.88 inference(quant_inst,[status(thm)],[])).
% 3.72/2.88 tff(6819,plain,
% 3.72/2.88 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c0_1(a604) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a604)) | (~c2_1(a604))),
% 3.72/2.88 inference(modus_ponens,[status(thm)],[6818, 6817])).
% 3.72/2.88 tff(6820,plain,
% 3.72/2.88 (hskp16),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[6819, 107, 6774, 6783, 6769, 6782, 2125, 6813, 6771])).
% 3.72/2.88 tff(6821,plain,
% 3.72/2.88 (~c2_1(a606)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[1111, 6820])).
% 3.72/2.88 tff(6822,plain,
% 3.72/2.88 (c1_1(a606)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[1088, 6820])).
% 3.72/2.88 tff(6823,plain,
% 3.72/2.88 (c0_1(a606)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[5034, 6822, 4654, 6790, 6789, 6821, 6773])).
% 3.72/2.88 tff(6824,plain,
% 3.72/2.88 (~c1_1(a603)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[171, 6781])).
% 3.72/2.88 tff(6825,plain,
% 3.72/2.88 (hskp26 | c2_1(a603)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[1006, 107, 6790, 6789, 6824, 6782, 6773, 995])).
% 3.72/2.88 tff(6826,plain,
% 3.72/2.88 (hskp26),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[6825, 6813])).
% 3.72/2.88 tff(6827,plain,
% 3.72/2.88 (c2_1(a583)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[391, 6826])).
% 3.72/2.88 tff(6828,plain,
% 3.72/2.88 (c1_1(a583)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[351, 6826])).
% 3.72/2.88 tff(6829,plain,
% 3.72/2.88 (c0_1(a583)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[362, 6826])).
% 3.72/2.88 tff(6830,plain,
% 3.72/2.88 (hskp10),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[1535, 107, 6533, 6665, 6532, 6829, 6828, 6827, 21])).
% 3.72/2.88 tff(6831,plain,
% 3.72/2.88 (~c1_1(a598)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[911, 6830])).
% 3.72/2.88 tff(6832,plain,
% 3.72/2.88 (c3_1(a598)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[881, 6830])).
% 3.72/2.88 tff(6833,plain,
% 3.72/2.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a606) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | (~c0_1(a606)) | (~c1_1(a606)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a606) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | (~c0_1(a606)) | (~c1_1(a606)))),
% 3.72/2.88 inference(rewrite,[status(thm)],[])).
% 3.72/2.88 tff(6834,plain,
% 3.72/2.88 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598))) <=> (c2_1(a606) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | (~c0_1(a606)) | (~c1_1(a606)))),
% 3.72/2.88 inference(rewrite,[status(thm)],[])).
% 3.72/2.88 tff(6835,plain,
% 3.72/2.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a606) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | (~c0_1(a606)) | (~c1_1(a606))))),
% 3.72/2.88 inference(monotonicity,[status(thm)],[6834])).
% 3.72/2.88 tff(6836,plain,
% 3.72/2.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a606) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | (~c0_1(a606)) | (~c1_1(a606)))),
% 3.72/2.88 inference(transitivity,[status(thm)],[6835, 6833])).
% 3.72/2.88 tff(6837,plain,
% 3.72/2.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c2_1(a606) | (~c1_1(a606)) | (~c0_1(a606)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)))),
% 3.72/2.88 inference(quant_inst,[status(thm)],[])).
% 3.72/2.88 tff(6838,plain,
% 3.72/2.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a606) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | (~c0_1(a606)) | (~c1_1(a606))),
% 3.72/2.88 inference(modus_ponens,[status(thm)],[6837, 6836])).
% 3.72/2.88 tff(6839,plain,
% 3.72/2.88 (c2_1(a598)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[6838, 107, 4373, 4372, 4371, 6822, 6832, 6821, 6831, 1106, 6823])).
% 3.72/2.88 tff(6840,plain,
% 3.72/2.88 (hskp12),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[3055, 107, 6829, 6828, 6827, 6770, 6769, 2727, 6771])).
% 3.72/2.88 tff(6841,plain,
% 3.72/2.88 (~c3_1(a600)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[741, 6840])).
% 3.72/2.88 tff(6842,plain,
% 3.72/2.88 (c2_1(a600)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[752, 6840])).
% 3.72/2.88 tff(6843,plain,
% 3.72/2.88 (c0_1(a600)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[763, 6840])).
% 3.72/2.88 tff(6844,plain,
% 3.72/2.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a600) | c1_1(a598) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c2_1(a600)) | (~c0_1(a600)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a600) | c1_1(a598) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c2_1(a600)) | (~c0_1(a600)))),
% 3.72/2.88 inference(rewrite,[status(thm)],[])).
% 3.72/2.88 tff(6845,plain,
% 3.72/2.88 (((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a598) | (~c3_1(a598)) | (~c2_1(a598)) | c3_1(a592) | c0_1(a592) | (~c1_1(a592))) <=> (c3_1(a600) | c1_1(a598) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c2_1(a600)) | (~c0_1(a600)))),
% 3.72/2.88 inference(rewrite,[status(thm)],[])).
% 3.72/2.88 tff(6846,plain,
% 3.72/2.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a598) | (~c3_1(a598)) | (~c2_1(a598)) | c3_1(a592) | c0_1(a592) | (~c1_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a600) | c1_1(a598) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c2_1(a600)) | (~c0_1(a600))))),
% 3.72/2.88 inference(monotonicity,[status(thm)],[6845])).
% 3.72/2.88 tff(6847,plain,
% 3.72/2.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a598) | (~c3_1(a598)) | (~c2_1(a598)) | c3_1(a592) | c0_1(a592) | (~c1_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a600) | c1_1(a598) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c2_1(a600)) | (~c0_1(a600)))),
% 3.72/2.88 inference(transitivity,[status(thm)],[6846, 6844])).
% 3.72/2.88 tff(6848,plain,
% 3.72/2.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a598) | (~c3_1(a598)) | (~c2_1(a598)) | c3_1(a592) | c0_1(a592) | (~c1_1(a592)))),
% 3.72/2.88 inference(quant_inst,[status(thm)],[])).
% 3.72/2.88 tff(6849,plain,
% 3.72/2.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a600) | c1_1(a598) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | (~c1_1(a592)) | (~c3_1(a598)) | (~c2_1(a598)) | (~c2_1(a600)) | (~c0_1(a600))),
% 3.72/2.88 inference(modus_ponens,[status(thm)],[6848, 6847])).
% 3.72/2.88 tff(6850,plain,
% 3.72/2.88 (~c1_1(a592)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[6849, 107, 6843, 6842, 6832, 6841, 6831, 6735, 6793, 258, 6839])).
% 3.72/2.88 tff(6851,plain,
% 3.72/2.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a604) | c0_1(a592) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c2_1(a592)) | c1_1(a592) | (~c3_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a604) | c0_1(a592) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c2_1(a592)) | c1_1(a592) | (~c3_1(a604)) | (~c2_1(a604)))),
% 3.72/2.88 inference(rewrite,[status(thm)],[])).
% 3.72/2.88 tff(6852,plain,
% 3.72/2.88 (((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a592) | c0_1(a592) | (~c2_1(a592))) <=> (c0_1(a604) | c0_1(a592) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c2_1(a592)) | c1_1(a592) | (~c3_1(a604)) | (~c2_1(a604)))),
% 3.72/2.88 inference(rewrite,[status(thm)],[])).
% 3.72/2.88 tff(6853,plain,
% 3.72/2.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a592) | c0_1(a592) | (~c2_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a604) | c0_1(a592) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c2_1(a592)) | c1_1(a592) | (~c3_1(a604)) | (~c2_1(a604))))),
% 3.72/2.88 inference(monotonicity,[status(thm)],[6852])).
% 3.72/2.88 tff(6854,plain,
% 3.72/2.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a592) | c0_1(a592) | (~c2_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a604) | c0_1(a592) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c2_1(a592)) | c1_1(a592) | (~c3_1(a604)) | (~c2_1(a604)))),
% 3.72/2.88 inference(transitivity,[status(thm)],[6853, 6851])).
% 3.72/2.88 tff(6855,plain,
% 3.72/2.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)) | c1_1(a592) | c0_1(a592) | (~c2_1(a592)))),
% 3.72/2.88 inference(quant_inst,[status(thm)],[])).
% 3.72/2.88 tff(6856,plain,
% 3.72/2.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a604) | c0_1(a592) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c2_1(a592)) | c1_1(a592) | (~c3_1(a604)) | (~c2_1(a604))),
% 3.72/2.88 inference(modus_ponens,[status(thm)],[6855, 6854])).
% 3.72/2.88 tff(6857,plain,
% 3.72/2.88 (~c1_1(a678)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[6856, 107, 4373, 4371, 6774, 6736, 6769, 6735, 65, 6850, 6771])).
% 3.72/2.88 tff(6858,plain,
% 3.72/2.88 (~c0_1(a593)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[6802, 107, 6774, 6767, 6765, 6736, 6769, 6735, 65, 6850, 6771])).
% 3.72/2.88 tff(6859,plain,
% 3.72/2.88 ($false),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[2626, 107, 4654, 4373, 4372, 6767, 6766, 32, 6858, 6857])).
% 3.72/2.88 tff(6860,plain,((~hskp29) | c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.72/2.88 tff(6861,plain,
% 3.72/2.88 (~hskp29),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[6860, 66])).
% 3.72/2.88 tff(6862,plain,
% 3.72/2.88 (hskp22),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[105, 6861, 4654])).
% 3.72/2.88 tff(6863,plain,
% 3.72/2.88 (c1_1(a633)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[3962, 6862])).
% 3.72/2.88 tff(6864,plain,
% 3.72/2.88 (~c0_1(a633)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[3968, 6862])).
% 3.72/2.88 tff(6865,plain,
% 3.72/2.88 (~c3_1(a633)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[3974, 6862])).
% 3.72/2.88 tff(6866,plain,
% 3.72/2.88 (hskp11),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[5163, 6865, 6864, 4654, 6863])).
% 3.72/2.88 tff(6867,plain,
% 3.72/2.88 (~c1_1(a599)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[428, 6866])).
% 3.72/2.88 tff(6868,plain,
% 3.72/2.88 (c2_1(a599)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[439, 6866])).
% 3.72/2.88 tff(6869,plain,
% 3.72/2.88 (hskp18),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[6184, 6861, 66])).
% 3.72/2.88 tff(6870,plain,
% 3.72/2.88 (hskp26),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[6141, 6869, 66])).
% 3.72/2.88 tff(6871,plain,
% 3.72/2.88 (c0_1(a583)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[362, 6870])).
% 3.72/2.88 tff(6872,plain,
% 3.72/2.88 (c2_1(a583)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[391, 6870])).
% 3.72/2.88 tff(6873,plain,
% 3.72/2.88 (c1_1(a583)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[351, 6870])).
% 3.72/2.88 tff(6874,plain,
% 3.72/2.88 (c3_1(a599)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[422, 6866])).
% 3.72/2.88 tff(6875,plain,
% 3.72/2.88 ($false),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[6242, 6874, 6873, 66, 6862, 6872, 6871, 6868, 6867])).
% 3.72/2.88 tff(6876,plain,(c1_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.72/2.88 tff(6877,plain,
% 3.72/2.88 (~hskp17),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[281, 6876])).
% 3.72/2.88 tff(6878,plain,
% 3.72/2.88 (hskp11 | c3_1(a633) | (~c1_1(a633)) | c0_1(a633)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[5163, 6877])).
% 3.72/2.88 tff(6879,plain,
% 3.72/2.88 (hskp11),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[6878, 3975, 3969, 3963])).
% 3.72/2.88 tff(6880,plain,
% 3.72/2.88 (~c1_1(a599)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[428, 6879])).
% 3.72/2.88 tff(6881,plain,
% 3.72/2.88 (c2_1(a599)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[439, 6879])).
% 3.72/2.88 tff(6882,plain,
% 3.72/2.88 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~c1_1(a607)) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c0_1(a607))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | (~c1_1(a607)) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c0_1(a607))),
% 3.72/2.88 inference(rewrite,[status(thm)],[])).
% 3.72/2.88 tff(6883,plain,
% 3.72/2.88 ((hskp17 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c0_1(a599)) | c0_1(a607) | c2_1(a607) | (~c1_1(a607))) <=> (hskp17 | (~c1_1(a607)) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c0_1(a607))),
% 3.72/2.88 inference(rewrite,[status(thm)],[])).
% 3.72/2.88 tff(6884,plain,
% 3.72/2.88 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c0_1(a599)) | c0_1(a607) | c2_1(a607) | (~c1_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~c1_1(a607)) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c0_1(a607)))),
% 3.72/2.88 inference(monotonicity,[status(thm)],[6883])).
% 3.72/2.88 tff(6885,plain,
% 3.72/2.88 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c0_1(a599)) | c0_1(a607) | c2_1(a607) | (~c1_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | (~c1_1(a607)) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c0_1(a607))),
% 3.72/2.88 inference(transitivity,[status(thm)],[6884, 6882])).
% 3.72/2.88 tff(6886,plain,
% 3.72/2.88 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c0_1(a599)) | c0_1(a607) | c2_1(a607) | (~c1_1(a607)))),
% 3.72/2.88 inference(quant_inst,[status(thm)],[])).
% 3.72/2.88 tff(6887,plain,
% 3.72/2.88 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | (~c1_1(a607)) | c2_1(a607) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c0_1(a607)),
% 3.72/2.88 inference(modus_ponens,[status(thm)],[6886, 6885])).
% 3.72/2.88 tff(6888,plain,
% 3.72/2.88 (~c0_1(a599)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[6887, 107, 6877, 6881, 6876, 22, 6880, 32, 1])).
% 3.72/2.88 tff(6889,plain,
% 3.72/2.88 (c3_1(a599)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[422, 6879])).
% 3.72/2.88 tff(6890,plain,
% 3.72/2.88 ($false),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[4183, 107, 33, 6881, 6889, 22, 6880, 1730, 1, 6888])).
% 3.72/2.88 tff(6891,plain,(c0_1(a607) | c3_1(a607) | c2_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.72/2.88 tff(6892,plain,
% 3.72/2.88 (c0_1(a607)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[6891, 33, 22])).
% 3.72/2.88 tff(6893,plain,
% 3.72/2.88 (hskp3 | c3_1(a607) | (~c0_1(a607))),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[2965, 107, 6877, 6876, 2368])).
% 3.72/2.88 tff(6894,plain,
% 3.72/2.88 (hskp3),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[6893, 6892, 33])).
% 3.72/2.88 tff(6895,plain,
% 3.72/2.88 (~c1_1(a587)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[939, 6894])).
% 3.72/2.88 tff(6896,plain,
% 3.72/2.88 (c2_1(a587)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[950, 6894])).
% 3.72/2.88 tff(6897,plain,
% 3.72/2.88 (c0_1(a587)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[961, 6894])).
% 3.72/2.88 tff(6898,plain,
% 3.72/2.88 (c2_1(a633)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[5135, 107, 6877, 3963, 6897, 6896, 3969, 6895, 32])).
% 3.72/2.88 tff(6899,plain,
% 3.72/2.88 (hskp28 | (~c2_1(a633))),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[4497, 107, 3963, 6881, 6889, 3975, 6880, 1748])).
% 3.72/2.88 tff(6900,plain,
% 3.72/2.88 (hskp28),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[6899, 6898])).
% 3.72/2.88 tff(6901,plain,
% 3.72/2.88 (c2_1(a612)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[1150, 6900])).
% 3.72/2.88 tff(6902,plain,
% 3.72/2.88 (c1_1(a612)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[1435, 6900])).
% 3.72/2.88 tff(6903,plain,
% 3.72/2.88 (~hskp12),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[4342, 6889, 3963, 3969, 6881, 3975, 6880])).
% 3.72/2.88 tff(6904,plain,
% 3.72/2.88 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | c0_1(a633) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c2_1(a612)) | (~c2_1(a633)) | (~c1_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | c0_1(a633) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c2_1(a612)) | (~c2_1(a633)) | (~c1_1(a633)))),
% 3.72/2.88 inference(rewrite,[status(thm)],[])).
% 3.72/2.88 tff(6905,plain,
% 3.72/2.88 ((hskp12 | (~ndr1_0) | (~c2_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633))) <=> (hskp12 | c0_1(a633) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c2_1(a612)) | (~c2_1(a633)) | (~c1_1(a633)))),
% 3.72/2.88 inference(rewrite,[status(thm)],[])).
% 3.72/2.88 tff(6906,plain,
% 3.72/2.88 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | c0_1(a633) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c2_1(a612)) | (~c2_1(a633)) | (~c1_1(a633))))),
% 3.72/2.88 inference(monotonicity,[status(thm)],[6905])).
% 3.72/2.88 tff(6907,plain,
% 3.72/2.88 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | c0_1(a633) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c2_1(a612)) | (~c2_1(a633)) | (~c1_1(a633)))),
% 3.72/2.88 inference(transitivity,[status(thm)],[6906, 6904])).
% 3.72/2.88 tff(6908,plain,
% 3.72/2.88 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a633) | (~c1_1(a633)) | (~c2_1(a633)))),
% 3.72/2.88 inference(quant_inst,[status(thm)],[])).
% 3.72/2.88 tff(6909,plain,
% 3.72/2.88 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | c0_1(a633) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c2_1(a612)) | (~c2_1(a633)) | (~c1_1(a633))),
% 3.72/2.88 inference(modus_ponens,[status(thm)],[6908, 6907])).
% 3.72/2.88 tff(6910,plain,
% 3.72/2.88 (~c0_1(a612)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[6909, 107, 6903, 6902, 6901, 3963, 3969, 2727, 6898])).
% 3.72/2.88 tff(6911,plain,
% 3.72/2.88 (hskp4 | c3_1(a607) | (~c0_1(a607))),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[2918, 107, 6877, 6876, 55])).
% 3.72/2.88 tff(6912,plain,
% 3.72/2.88 (hskp4),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[6911, 6892, 33])).
% 3.72/2.88 tff(6913,plain,
% 3.72/2.88 (hskp14),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[4548, 6898, 3969, 3975, 6912])).
% 3.72/2.88 tff(6914,plain,
% 3.72/2.88 (~c3_1(a603)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[205, 6913])).
% 3.72/2.88 tff(6915,plain,
% 3.72/2.88 (c0_1(a603)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[182, 6913])).
% 3.72/2.88 tff(6916,plain,
% 3.72/2.88 (~c2_1(a603)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[4213, 107, 3963, 6915, 6881, 6889, 3969, 3975, 6914, 6880, 258])).
% 3.72/2.88 tff(6917,plain,
% 3.72/2.88 (~c1_1(a603)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[171, 6913])).
% 3.72/2.88 tff(6918,plain,
% 3.72/2.88 (hskp26),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[1006, 107, 6897, 6896, 6917, 6914, 6895, 995, 6916])).
% 3.72/2.88 tff(6919,plain,
% 3.72/2.88 (c2_1(a583)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[391, 6918])).
% 3.72/2.88 tff(6920,plain,
% 3.72/2.88 (c1_1(a583)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[351, 6918])).
% 3.72/2.88 tff(6921,plain,
% 3.72/2.88 (c0_1(a583)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[362, 6918])).
% 3.72/2.88 tff(6922,plain,
% 3.72/2.88 ($false),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[2734, 107, 6903, 6902, 6901, 6921, 6920, 6919, 2727, 6910])).
% 3.72/2.88 tff(6923,plain,(c3_1(a607) | c2_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.72/2.88 tff(6924,plain,
% 3.72/2.88 (c3_1(a607)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[6923, 22])).
% 3.72/2.88 tff(6925,plain,
% 3.72/2.88 (hskp3 | c2_1(a607) | (~c3_1(a607))),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[3426, 107, 6877, 6876, 3420])).
% 3.72/2.88 tff(6926,plain,
% 3.72/2.88 (hskp3),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[6925, 6924, 22])).
% 3.72/2.88 tff(6927,plain,
% 3.72/2.88 (c0_1(a587)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[961, 6926])).
% 3.72/2.88 tff(6928,plain,
% 3.72/2.88 (c2_1(a587)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[950, 6926])).
% 3.72/2.88 tff(6929,plain,
% 3.72/2.88 (~c1_1(a587)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[939, 6926])).
% 3.72/2.88 tff(6930,plain,
% 3.72/2.88 (c0_1(a607) | (~c0_1(a587)) | (~c2_1(a587)) | c2_1(a607) | c1_1(a587)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[3711, 6876])).
% 3.72/2.88 tff(6931,plain,
% 3.72/2.88 (c0_1(a607)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[6930, 6929, 6928, 22, 6927])).
% 3.72/2.88 tff(6932,plain,
% 3.72/2.88 (c0_1(a599) | (~c3_1(a607)) | (~c2_1(a599)) | (~c3_1(a599)) | c1_1(a599) | (~c0_1(a607))),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[3908, 6876])).
% 3.72/2.88 tff(6933,plain,
% 3.72/2.88 (c0_1(a599)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[6932, 6931, 6889, 6881, 6880, 6924])).
% 3.72/2.88 tff(6934,plain,
% 3.72/2.88 ((~c0_1(a599)) | c2_1(a633)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[4159, 107, 6877, 3963, 6881, 3969, 6880, 32])).
% 3.72/2.88 tff(6935,plain,
% 3.72/2.88 (c2_1(a633)),
% 3.72/2.88 inference(unit_resolution,[status(thm)],[6934, 6933])).
% 3.72/2.88 tff(6936,plain,
% 3.72/2.88 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp14 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c3_1(a607)))),
% 3.72/2.88 inference(rewrite,[status(thm)],[])).
% 3.72/2.88 tff(6937,plain,
% 3.72/2.88 ((hskp14 | (~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a607) | (~c1_1(a607)) | (~c3_1(a607))) <=> (hskp14 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c3_1(a607)))),
% 3.72/2.89 inference(rewrite,[status(thm)],[])).
% 3.72/2.89 tff(6938,plain,
% 3.72/2.89 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a607) | (~c1_1(a607)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c3_1(a607))))),
% 3.72/2.89 inference(monotonicity,[status(thm)],[6937])).
% 3.72/2.89 tff(6939,plain,
% 3.72/2.89 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a607) | (~c1_1(a607)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp14 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c3_1(a607)))),
% 3.72/2.89 inference(transitivity,[status(thm)],[6938, 6936])).
% 3.72/2.89 tff(6940,plain,
% 3.72/2.89 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a599)) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a607) | (~c1_1(a607)) | (~c3_1(a607)))),
% 3.72/2.89 inference(quant_inst,[status(thm)],[])).
% 3.72/2.89 tff(6941,plain,
% 3.72/2.89 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp14 | (~c1_1(a607)) | c2_1(a607) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c0_1(a599)) | (~c3_1(a607))),
% 3.72/2.89 inference(modus_ponens,[status(thm)],[6940, 6939])).
% 3.72/2.89 tff(6942,plain,
% 3.72/2.89 (hskp14 | (~c0_1(a599)) | (~c3_1(a607))),
% 3.72/2.89 inference(unit_resolution,[status(thm)],[6941, 107, 6881, 6889, 6876, 22, 550])).
% 3.72/2.89 tff(6943,plain,
% 3.72/2.89 (hskp14),
% 3.72/2.89 inference(unit_resolution,[status(thm)],[6942, 6933, 6924])).
% 3.72/2.89 tff(6944,plain,
% 3.72/2.89 (~c3_1(a603)),
% 3.72/2.89 inference(unit_resolution,[status(thm)],[205, 6943])).
% 3.72/2.89 tff(6945,plain,
% 3.72/2.89 (c0_1(a603)),
% 3.72/2.89 inference(unit_resolution,[status(thm)],[182, 6943])).
% 3.72/2.89 tff(6946,plain,
% 3.72/2.89 (~c2_1(a603)),
% 3.72/2.89 inference(unit_resolution,[status(thm)],[4213, 107, 3963, 6945, 6881, 6889, 3969, 3975, 6944, 6880, 258])).
% 3.72/2.89 tff(6947,plain,
% 3.72/2.89 (~c1_1(a603)),
% 3.72/2.89 inference(unit_resolution,[status(thm)],[171, 6943])).
% 3.72/2.89 tff(6948,plain,
% 3.72/2.89 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a603) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c2_1(a603))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a603) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c2_1(a603))),
% 3.72/2.89 inference(rewrite,[status(thm)],[])).
% 3.72/2.89 tff(6949,plain,
% 3.72/2.89 ((hskp26 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c0_1(a599)) | c3_1(a603) | c1_1(a603) | c2_1(a603)) <=> (hskp26 | c1_1(a603) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c2_1(a603))),
% 3.72/2.89 inference(rewrite,[status(thm)],[])).
% 3.72/2.89 tff(6950,plain,
% 3.72/2.89 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c0_1(a599)) | c3_1(a603) | c1_1(a603) | c2_1(a603))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a603) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c2_1(a603)))),
% 3.72/2.89 inference(monotonicity,[status(thm)],[6949])).
% 3.72/2.89 tff(6951,plain,
% 3.72/2.89 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c0_1(a599)) | c3_1(a603) | c1_1(a603) | c2_1(a603))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a603) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c2_1(a603))),
% 3.72/2.89 inference(transitivity,[status(thm)],[6950, 6948])).
% 3.72/2.89 tff(6952,plain,
% 3.72/2.89 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a599) | (~c2_1(a599)) | (~c0_1(a599)) | c3_1(a603) | c1_1(a603) | c2_1(a603))),
% 3.72/2.89 inference(quant_inst,[status(thm)],[])).
% 3.72/2.89 tff(6953,plain,
% 3.72/2.89 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a603) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c2_1(a599)) | (~c0_1(a599)) | c2_1(a603)),
% 3.72/2.89 inference(modus_ponens,[status(thm)],[6952, 6951])).
% 3.72/2.89 tff(6954,plain,
% 3.72/2.89 (hskp26),
% 3.72/2.89 inference(unit_resolution,[status(thm)],[6953, 107, 6881, 6947, 6944, 6880, 995, 6946, 6933])).
% 3.72/2.89 tff(6955,plain,
% 3.72/2.89 (c2_1(a583)),
% 3.72/2.89 inference(unit_resolution,[status(thm)],[391, 6954])).
% 3.72/2.89 tff(6956,plain,
% 3.72/2.89 (c1_1(a583)),
% 3.72/2.89 inference(unit_resolution,[status(thm)],[351, 6954])).
% 3.72/2.89 tff(6957,plain,
% 3.72/2.89 (c0_1(a583)),
% 3.72/2.89 inference(unit_resolution,[status(thm)],[362, 6954])).
% 3.72/2.89 tff(6958,plain,
% 3.72/2.89 ($false),
% 3.72/2.89 inference(unit_resolution,[status(thm)],[3998, 107, 6903, 6957, 6956, 6955, 3963, 3969, 2727, 6935])).
% 3.72/2.89 tff(6959,plain,(c2_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.72/2.89 tff(6960,plain,
% 3.72/2.89 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c0_1(a607))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c0_1(a607))),
% 3.72/2.89 inference(rewrite,[status(thm)],[])).
% 3.72/2.89 tff(6961,plain,
% 3.72/2.89 ((hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a607) | (~c1_1(a607)) | (~c2_1(a607))) <=> (hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c0_1(a607))),
% 3.72/2.89 inference(rewrite,[status(thm)],[])).
% 3.72/2.89 tff(6962,plain,
% 3.72/2.89 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a607) | (~c1_1(a607)) | (~c2_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c0_1(a607)))),
% 3.72/2.89 inference(monotonicity,[status(thm)],[6961])).
% 3.72/2.89 tff(6963,plain,
% 3.72/2.89 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a607) | (~c1_1(a607)) | (~c2_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c0_1(a607))),
% 3.72/2.89 inference(transitivity,[status(thm)],[6962, 6960])).
% 3.72/2.89 tff(6964,plain,
% 3.72/2.89 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a583)) | (~c1_1(a583)) | (~c0_1(a583)) | c0_1(a607) | (~c1_1(a607)) | (~c2_1(a607)))),
% 3.72/2.89 inference(quant_inst,[status(thm)],[])).
% 3.72/2.89 tff(6965,plain,
% 3.72/2.89 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | c0_1(a607)),
% 3.72/2.89 inference(modus_ponens,[status(thm)],[6964, 6963])).
% 3.72/2.89 tff(6966,plain,
% 3.72/2.89 (hskp12),
% 3.72/2.89 inference(unit_resolution,[status(thm)],[6965, 107, 3321, 3322, 3330, 6876, 6959, 2727, 1])).
% 3.72/2.89 tff(6967,plain,
% 3.72/2.89 (~c3_1(a600)),
% 3.72/2.89 inference(unit_resolution,[status(thm)],[741, 6966])).
% 3.72/2.89 tff(6968,plain,
% 3.72/2.89 (hskp14),
% 3.72/2.89 inference(unit_resolution,[status(thm)],[772, 6966, 44])).
% 3.72/2.89 tff(6969,plain,
% 3.72/2.89 (~c3_1(a603)),
% 3.72/2.89 inference(unit_resolution,[status(thm)],[205, 6968])).
% 3.72/2.89 tff(6970,plain,
% 3.72/2.89 (c2_1(a600)),
% 3.72/2.89 inference(unit_resolution,[status(thm)],[752, 6966])).
% 3.72/2.89 tff(6971,plain,
% 3.72/2.89 (c0_1(a600)),
% 3.72/2.89 inference(unit_resolution,[status(thm)],[763, 6966])).
% 3.72/2.89 tff(6972,plain,
% 3.72/2.89 (~c1_1(a603)),
% 3.72/2.89 inference(unit_resolution,[status(thm)],[171, 6968])).
% 3.72/2.89 tff(6973,plain,
% 3.72/2.89 (c0_1(a603)),
% 3.72/2.89 inference(unit_resolution,[status(thm)],[182, 6968])).
% 3.72/2.89 tff(6974,plain,
% 3.72/2.89 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | c3_1(a603) | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)) | c2_1(a603) | (~c0_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c3_1(a603) | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)) | c2_1(a603) | (~c0_1(a603)))),
% 3.72/2.89 inference(rewrite,[status(thm)],[])).
% 3.72/2.89 tff(6975,plain,
% 3.72/2.89 ((hskp8 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c3_1(a603) | c2_1(a603) | (~c0_1(a603))) <=> (hskp8 | c3_1(a603) | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)) | c2_1(a603) | (~c0_1(a603)))),
% 3.72/2.89 inference(rewrite,[status(thm)],[])).
% 3.72/2.89 tff(6976,plain,
% 3.72/2.89 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c3_1(a603) | c2_1(a603) | (~c0_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | c3_1(a603) | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)) | c2_1(a603) | (~c0_1(a603))))),
% 3.72/2.89 inference(monotonicity,[status(thm)],[6975])).
% 3.72/2.89 tff(6977,plain,
% 3.72/2.89 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c3_1(a603) | c2_1(a603) | (~c0_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c3_1(a603) | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)) | c2_1(a603) | (~c0_1(a603)))),
% 3.72/2.89 inference(transitivity,[status(thm)],[6976, 6974])).
% 3.72/2.89 tff(6978,plain,
% 3.72/2.89 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c3_1(a603) | c2_1(a603) | (~c0_1(a603)))),
% 3.72/2.89 inference(quant_inst,[status(thm)],[])).
% 3.72/2.89 tff(6979,plain,
% 3.72/2.89 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp8 | c3_1(a603) | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)) | c2_1(a603) | (~c0_1(a603))),
% 3.72/2.89 inference(modus_ponens,[status(thm)],[6978, 6977])).
% 3.72/2.89 tff(6980,plain,
% 3.72/2.89 (hskp8 | c2_1(a603)),
% 3.72/2.89 inference(unit_resolution,[status(thm)],[6979, 107, 1009, 4753, 4752, 997, 4745, 4271])).
% 3.72/2.89 tff(6981,plain,
% 3.72/2.89 (c2_1(a603)),
% 3.72/2.89 inference(unit_resolution,[status(thm)],[6980, 1709])).
% 3.72/2.89 tff(6982,plain,
% 3.72/2.89 (hskp18 | hskp8 | c3_1(a607) | c0_1(a607)),
% 3.72/2.89 inference(unit_resolution,[status(thm)],[5570, 107, 6959, 5564])).
% 3.72/2.89 tff(6983,plain,
% 3.72/2.89 (hskp18),
% 3.72/2.89 inference(unit_resolution,[status(thm)],[6982, 1709, 33, 1])).
% 3.72/2.89 tff(6984,plain,
% 3.72/2.89 (~c2_1(a610)),
% 3.72/2.89 inference(unit_resolution,[status(thm)],[1189, 6983])).
% 3.72/2.89 tff(6985,plain,
% 3.72/2.89 (~c0_1(a610)),
% 3.72/2.89 inference(unit_resolution,[status(thm)],[1195, 6983])).
% 3.72/2.89 tff(6986,plain,
% 3.72/2.89 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a610) | c2_1(a610) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c1_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a610) | c2_1(a610) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c1_1(a610)))),
% 3.72/2.89 inference(rewrite,[status(thm)],[])).
% 3.72/2.89 tff(6987,plain,
% 3.72/2.89 ((hskp17 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a610) | c2_1(a610) | (~c1_1(a610))) <=> (hskp17 | c0_1(a610) | c2_1(a610) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c1_1(a610)))),
% 3.72/2.89 inference(rewrite,[status(thm)],[])).
% 3.72/2.89 tff(6988,plain,
% 3.72/2.89 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a610) | c2_1(a610) | (~c1_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a610) | c2_1(a610) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c1_1(a610))))),
% 3.72/2.89 inference(monotonicity,[status(thm)],[6987])).
% 3.72/2.89 tff(6989,plain,
% 3.72/2.89 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a610) | c2_1(a610) | (~c1_1(a610)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a610) | c2_1(a610) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c1_1(a610)))),
% 3.72/2.89 inference(transitivity,[status(thm)],[6988, 6986])).
% 3.72/2.89 tff(6990,plain,
% 3.72/2.89 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a610) | c2_1(a610) | (~c1_1(a610)))),
% 3.72/2.89 inference(quant_inst,[status(thm)],[])).
% 3.72/2.89 tff(6991,plain,
% 3.72/2.89 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a610) | c2_1(a610) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c1_1(a610))),
% 3.72/2.89 inference(modus_ponens,[status(thm)],[6990, 6989])).
% 3.72/2.89 tff(6992,plain,
% 3.72/2.89 (~c1_1(a610)),
% 3.72/2.89 inference(unit_resolution,[status(thm)],[6991, 107, 6877, 1009, 6985, 6984, 998, 32, 6981])).
% 3.72/2.89 tff(6993,plain,
% 3.72/2.89 (c3_1(a610)),
% 3.72/2.89 inference(unit_resolution,[status(thm)],[1206, 6983])).
% 3.72/2.89 tff(6994,plain,
% 3.72/2.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c2_1(a610) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a607) | c1_1(a610) | (~c3_1(a610)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a610) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a607) | c1_1(a610) | (~c3_1(a610)))),
% 3.72/2.89 inference(rewrite,[status(thm)],[])).
% 3.72/2.89 tff(6995,plain,
% 3.72/2.89 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610)) | c0_1(a607) | (~c1_1(a607)) | (~c2_1(a607))) <=> (c2_1(a610) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a607) | c1_1(a610) | (~c3_1(a610)))),
% 3.72/2.89 inference(rewrite,[status(thm)],[])).
% 3.72/2.89 tff(6996,plain,
% 3.72/2.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610)) | c0_1(a607) | (~c1_1(a607)) | (~c2_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c2_1(a610) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a607) | c1_1(a610) | (~c3_1(a610))))),
% 3.72/2.89 inference(monotonicity,[status(thm)],[6995])).
% 3.72/2.89 tff(6997,plain,
% 3.72/2.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610)) | c0_1(a607) | (~c1_1(a607)) | (~c2_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a610) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a607) | c1_1(a610) | (~c3_1(a610)))),
% 3.72/2.89 inference(transitivity,[status(thm)],[6996, 6994])).
% 3.72/2.89 tff(6998,plain,
% 3.72/2.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a610) | c2_1(a610) | (~c3_1(a610)) | c0_1(a607) | (~c1_1(a607)) | (~c2_1(a607)))),
% 3.72/2.89 inference(quant_inst,[status(thm)],[])).
% 3.72/2.89 tff(6999,plain,
% 3.72/2.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a610) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c0_1(a607) | c1_1(a610) | (~c3_1(a610))),
% 3.72/2.89 inference(modus_ponens,[status(thm)],[6998, 6997])).
% 3.72/2.89 tff(7000,plain,
% 3.72/2.89 ($false),
% 3.72/2.89 inference(unit_resolution,[status(thm)],[6999, 107, 2318, 2317, 2316, 6993, 6984, 6876, 6959, 11, 1, 6992])).
% 3.72/2.89 tff(7001,plain,(hskp8 | (~c0_1(a678)) | (~c2_1(a678)) | (~c3_1(a678)) | c0_1(a607) | (~c0_1(a603)) | c1_1(a603) | (~c0_1(a600)) | (~c2_1(a600)) | c3_1(a603) | c3_1(a600) | c3_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.72/2.89 tff(7002,plain,
% 3.72/2.89 (hskp8),
% 3.72/2.89 inference(unit_resolution,[status(thm)],[7001, 6973, 2281, 2270, 1, 2292, 6972, 6971, 6970, 6969, 6967, 33])).
% 3.72/2.89 tff(7003,plain,
% 3.72/2.89 (~c2_1(a593)),
% 3.72/2.89 inference(unit_resolution,[status(thm)],[555, 7002])).
% 3.72/2.89 tff(7004,plain,
% 3.72/2.89 (c1_1(a593)),
% 3.72/2.89 inference(unit_resolution,[status(thm)],[522, 7002])).
% 3.72/2.89 tff(7005,plain,
% 3.72/2.89 (c3_1(a593)),
% 3.72/2.89 inference(unit_resolution,[status(thm)],[511, 7002])).
% 3.72/2.89 tff(7006,plain,
% 3.72/2.89 ($false),
% 3.72/2.89 inference(unit_resolution,[status(thm)],[5161, 3794, 3796, 2987, 1894, 1903, 3795, 1893])).
% 3.72/2.89 tff(7007,plain,((~hskp0) | hskp17 | (~c1_1(a593)) | (~c3_1(a593)) | c2_1(a593)), inference(lemma,lemma(discharge,[]))).
% 3.72/2.89 tff(7008,plain,
% 3.72/2.89 ((~hskp0) | (~c1_1(a593)) | (~c3_1(a593)) | c2_1(a593)),
% 3.72/2.89 inference(unit_resolution,[status(thm)],[7007, 6877])).
% 3.72/2.89 tff(7009,plain,
% 3.72/2.89 (~hskp0),
% 3.72/2.89 inference(unit_resolution,[status(thm)],[7008, 7005, 7004, 7003])).
% 3.72/2.89 tff(7010,plain,
% 3.72/2.89 (((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | c2_1(a593) | (~ndr1_0) | (~c0_1(a593)) | (~c1_1(a593)))) <=> ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp11 | hskp0 | c2_1(a593) | (~ndr1_0) | (~c0_1(a593)) | (~c1_1(a593)))),
% 3.72/2.89 inference(rewrite,[status(thm)],[])).
% 3.72/2.89 tff(7011,plain,
% 3.72/2.89 ((hskp11 | hskp0 | (~ndr1_0) | c2_1(a593) | (~c1_1(a593)) | (~c0_1(a593))) <=> (hskp11 | hskp0 | c2_1(a593) | (~ndr1_0) | (~c0_1(a593)) | (~c1_1(a593)))),
% 3.72/2.89 inference(rewrite,[status(thm)],[])).
% 3.72/2.89 tff(7012,plain,
% 3.72/2.89 (((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | (~ndr1_0) | c2_1(a593) | (~c1_1(a593)) | (~c0_1(a593)))) <=> ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | c2_1(a593) | (~ndr1_0) | (~c0_1(a593)) | (~c1_1(a593))))),
% 3.72/2.89 inference(monotonicity,[status(thm)],[7011])).
% 3.72/2.89 tff(7013,plain,
% 3.72/2.89 (((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | (~ndr1_0) | c2_1(a593) | (~c1_1(a593)) | (~c0_1(a593)))) <=> ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp11 | hskp0 | c2_1(a593) | (~ndr1_0) | (~c0_1(a593)) | (~c1_1(a593)))),
% 3.72/2.89 inference(transitivity,[status(thm)],[7012, 7010])).
% 3.72/2.89 tff(7014,plain,
% 3.72/2.89 ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp11 | hskp0 | (~ndr1_0) | c2_1(a593) | (~c1_1(a593)) | (~c0_1(a593)))),
% 3.72/2.89 inference(quant_inst,[status(thm)],[])).
% 3.72/2.89 tff(7015,plain,
% 3.72/2.89 ((~![U: $i] : (hskp11 | hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp11 | hskp0 | c2_1(a593) | (~ndr1_0) | (~c0_1(a593)) | (~c1_1(a593))),
% 3.72/2.89 inference(modus_ponens,[status(thm)],[7014, 7013])).
% 3.72/2.89 tff(7016,plain,
% 3.72/2.89 (~c0_1(a593)),
% 3.72/2.89 inference(unit_resolution,[status(thm)],[7015, 1638, 107, 7009, 7004, 7003, 2347])).
% 3.72/2.89 tff(7017,plain,
% 3.72/2.89 (hskp3),
% 3.72/2.89 inference(unit_resolution,[status(thm)],[5154, 107, 6877, 7004, 7005, 7003, 3420])).
% 3.72/2.89 tff(7018,plain,
% 3.72/2.89 (~c1_1(a587)),
% 3.72/2.89 inference(unit_resolution,[status(thm)],[939, 7017])).
% 3.72/2.89 tff(7019,plain,
% 3.72/2.89 (c2_1(a587)),
% 3.72/2.89 inference(unit_resolution,[status(thm)],[950, 7017])).
% 3.72/2.89 tff(7020,plain,
% 3.72/2.89 (c0_1(a587)),
% 3.72/2.89 inference(unit_resolution,[status(thm)],[961, 7017])).
% 3.72/2.89 tff(7021,plain,
% 3.72/2.89 ($false),
% 3.72/2.89 inference(unit_resolution,[status(thm)],[5232, 107, 6877, 7004, 7020, 7019, 7003, 7018, 32, 7016])).
% 3.72/2.89 tff(7022,plain,(hskp11 | c0_1(a607) | c3_1(a607) | hskp22), inference(lemma,lemma(discharge,[]))).
% 3.72/2.89 tff(7023,plain,
% 3.72/2.89 (hskp11),
% 3.72/2.89 inference(unit_resolution,[status(thm)],[7022, 44, 33, 1])).
% 3.72/2.89 tff(7024,plain,
% 3.72/2.89 (~c1_1(a599)),
% 3.72/2.89 inference(unit_resolution,[status(thm)],[428, 7023])).
% 3.72/2.89 tff(7025,plain,
% 3.72/2.89 (c2_1(a599)),
% 3.72/2.89 inference(unit_resolution,[status(thm)],[439, 7023])).
% 3.72/2.89 tff(7026,plain,
% 3.72/2.89 (c3_1(a599)),
% 3.72/2.89 inference(unit_resolution,[status(thm)],[422, 7023])).
% 3.72/2.89 tff(7027,plain,
% 3.72/2.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a607) | (~c1_1(a607)) | c3_1(a600) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a600)) | (~c0_1(a600)) | c0_1(a607))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a607) | (~c1_1(a607)) | c3_1(a600) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a600)) | (~c0_1(a600)) | c0_1(a607))),
% 3.72/2.89 inference(rewrite,[status(thm)],[])).
% 3.72/2.89 tff(7028,plain,
% 3.72/2.89 (((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a607) | c0_1(a607) | (~c1_1(a607))) <=> (c3_1(a607) | (~c1_1(a607)) | c3_1(a600) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a600)) | (~c0_1(a600)) | c0_1(a607))),
% 3.72/2.89 inference(rewrite,[status(thm)],[])).
% 3.72/2.89 tff(7029,plain,
% 3.72/2.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a607) | c0_1(a607) | (~c1_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a607) | (~c1_1(a607)) | c3_1(a600) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a600)) | (~c0_1(a600)) | c0_1(a607)))),
% 3.72/2.89 inference(monotonicity,[status(thm)],[7028])).
% 3.72/2.89 tff(7030,plain,
% 3.72/2.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a607) | c0_1(a607) | (~c1_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a607) | (~c1_1(a607)) | c3_1(a600) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a600)) | (~c0_1(a600)) | c0_1(a607))),
% 3.72/2.89 inference(transitivity,[status(thm)],[7029, 7027])).
% 3.72/2.89 tff(7031,plain,
% 3.72/2.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a607) | c0_1(a607) | (~c1_1(a607)))),
% 3.72/2.89 inference(quant_inst,[status(thm)],[])).
% 3.72/2.89 tff(7032,plain,
% 3.72/2.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a607) | (~c1_1(a607)) | c3_1(a600) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a600)) | (~c0_1(a600)) | c0_1(a607)),
% 3.72/2.89 inference(modus_ponens,[status(thm)],[7031, 7030])).
% 3.72/2.89 tff(7033,plain,
% 3.72/2.89 ($false),
% 3.72/2.89 inference(unit_resolution,[status(thm)],[7032, 107, 33, 764, 753, 463, 462, 6876, 742, 461, 258, 1])).
% 3.72/2.89 tff(7034,plain,((~hskp12) | c3_1(a607) | (~c2_1(a599)) | (~c3_1(a599)) | c1_1(a599) | c0_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.72/2.89 tff(7035,plain,
% 3.72/2.89 (~hskp12),
% 3.72/2.89 inference(unit_resolution,[status(thm)],[7034, 7026, 33, 7025, 7024, 1])).
% 3.72/2.89 tff(7036,plain,
% 3.72/2.89 (^[U: $i] : refl((hskp12 | hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp12 | hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))),
% 3.72/2.89 inference(bind,[status(th)],[])).
% 3.72/2.89 tff(7037,plain,
% 3.72/2.89 (![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 3.72/2.89 inference(quant_intro,[status(thm)],[7036])).
% 3.72/2.89 tff(7038,plain,
% 3.72/2.89 (![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 3.72/2.89 inference(rewrite,[status(thm)],[])).
% 3.72/2.89 tff(7039,plain,
% 3.72/2.89 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp12) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp12))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp12) <=> (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp12) <=> (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp12) | hskp10) <=> ((hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp10))), rewrite(((hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp10) <=> (hskp12 | hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp12) | hskp10) <=> (hskp12 | hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))))),
% 3.72/2.89 inference(bind,[status(th)],[])).
% 3.72/2.89 tff(7040,plain,
% 3.72/2.89 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp12) | hskp10) <=> ![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 3.72/2.89 inference(quant_intro,[status(thm)],[7039])).
% 3.72/2.89 tff(7041,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp12) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause164')).
% 3.72/2.89 tff(7042,plain,
% 3.72/2.89 (![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 3.72/2.89 inference(modus_ponens,[status(thm)],[7041, 7040])).
% 3.72/2.89 tff(7043,plain,
% 3.72/2.89 (![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 3.72/2.89 inference(modus_ponens,[status(thm)],[7042, 7038])).
% 3.72/2.89 tff(7044,plain,(
% 3.72/2.89 ![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 3.72/2.89 inference(skolemize,[status(sab)],[7043])).
% 3.72/2.89 tff(7045,plain,
% 3.72/2.89 (![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 3.72/2.89 inference(modus_ponens,[status(thm)],[7044, 7037])).
% 3.72/2.89 tff(7046,plain,
% 3.72/2.89 (((~![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp12 | hskp10 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)))) <=> ((~![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp12 | hskp10 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)))),
% 3.78/2.90 inference(rewrite,[status(thm)],[])).
% 3.78/2.90 tff(7047,plain,
% 3.78/2.90 ((~![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp12 | hskp10 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)))),
% 3.78/2.90 inference(quant_inst,[status(thm)],[])).
% 3.78/2.90 tff(7048,plain,
% 3.78/2.90 ((~![U: $i] : (hskp12 | hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp12 | hskp10 | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678))),
% 3.78/2.90 inference(modus_ponens,[status(thm)],[7047, 7046])).
% 3.78/2.90 tff(7049,plain,
% 3.78/2.90 (hskp12 | hskp10),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[7048, 107, 2292, 2281, 2270, 7045])).
% 3.78/2.90 tff(7050,plain,
% 3.78/2.90 (hskp10),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[7049, 7035])).
% 3.78/2.90 tff(7051,plain,
% 3.78/2.90 (~c1_1(a598)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[911, 7050])).
% 3.78/2.90 tff(7052,plain,
% 3.78/2.90 (c3_1(a598)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[881, 7050])).
% 3.78/2.90 tff(7053,plain,
% 3.78/2.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~c1_1(a607)) | (~c2_1(a607)) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | c0_1(a607))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (~c1_1(a607)) | (~c2_1(a607)) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | c0_1(a607))),
% 3.78/2.90 inference(rewrite,[status(thm)],[])).
% 3.78/2.90 tff(7054,plain,
% 3.78/2.90 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a607) | (~c1_1(a607)) | (~c2_1(a607))) <=> ((~c1_1(a607)) | (~c2_1(a607)) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | c0_1(a607))),
% 3.78/2.90 inference(rewrite,[status(thm)],[])).
% 3.78/2.90 tff(7055,plain,
% 3.78/2.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a607) | (~c1_1(a607)) | (~c2_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~c1_1(a607)) | (~c2_1(a607)) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | c0_1(a607)))),
% 3.78/2.90 inference(monotonicity,[status(thm)],[7054])).
% 3.78/2.90 tff(7056,plain,
% 3.78/2.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a607) | (~c1_1(a607)) | (~c2_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (~c1_1(a607)) | (~c2_1(a607)) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | c0_1(a607))),
% 3.78/2.90 inference(transitivity,[status(thm)],[7055, 7053])).
% 3.78/2.90 tff(7057,plain,
% 3.78/2.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a598) | c2_1(a598) | (~c3_1(a598)) | c0_1(a607) | (~c1_1(a607)) | (~c2_1(a607)))),
% 3.78/2.90 inference(quant_inst,[status(thm)],[])).
% 3.78/2.90 tff(7058,plain,
% 3.78/2.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (~c1_1(a607)) | (~c2_1(a607)) | c1_1(a598) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a598)) | c2_1(a598) | c0_1(a607)),
% 3.78/2.90 inference(modus_ponens,[status(thm)],[7057, 7056])).
% 3.78/2.90 tff(7059,plain,
% 3.78/2.90 (c2_1(a598)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[7058, 107, 2292, 2281, 2270, 7052, 6876, 6959, 7051, 11, 1])).
% 3.78/2.90 tff(7060,plain,
% 3.78/2.90 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c3_1(a607) | (~c1_1(a607)) | (~c2_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c3_1(a607) | (~c1_1(a607)) | (~c2_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)))),
% 3.78/2.90 inference(rewrite,[status(thm)],[])).
% 3.78/2.90 tff(7061,plain,
% 3.78/2.90 ((hskp28 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c1_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599))) <=> (hskp28 | c3_1(a607) | (~c1_1(a607)) | (~c2_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)))),
% 3.78/2.90 inference(rewrite,[status(thm)],[])).
% 3.78/2.90 tff(7062,plain,
% 3.78/2.90 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c1_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c3_1(a607) | (~c1_1(a607)) | (~c2_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599))))),
% 3.78/2.90 inference(monotonicity,[status(thm)],[7061])).
% 3.78/2.90 tff(7063,plain,
% 3.78/2.90 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c1_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c3_1(a607) | (~c1_1(a607)) | (~c2_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)))),
% 3.78/2.90 inference(transitivity,[status(thm)],[7062, 7060])).
% 3.78/2.90 tff(7064,plain,
% 3.78/2.90 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c1_1(a607)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)))),
% 3.78/2.90 inference(quant_inst,[status(thm)],[])).
% 3.78/2.90 tff(7065,plain,
% 3.78/2.90 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c3_1(a607) | (~c1_1(a607)) | (~c2_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599))),
% 3.78/2.90 inference(modus_ponens,[status(thm)],[7064, 7063])).
% 3.78/2.90 tff(7066,plain,
% 3.78/2.90 (hskp28),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[7065, 107, 33, 7025, 7026, 6876, 6959, 7024, 1748])).
% 3.78/2.90 tff(7067,plain,
% 3.78/2.90 (c2_1(a612)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[1150, 7066])).
% 3.78/2.90 tff(7068,plain,
% 3.78/2.90 (c1_1(a612)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[1435, 7066])).
% 3.78/2.90 tff(7069,plain,
% 3.78/2.90 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c2_1(a612)) | c0_1(a607))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c2_1(a612)) | c0_1(a607))),
% 3.78/2.90 inference(rewrite,[status(thm)],[])).
% 3.78/2.90 tff(7070,plain,
% 3.78/2.90 ((hskp12 | (~ndr1_0) | (~c2_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a607) | (~c1_1(a607)) | (~c2_1(a607))) <=> (hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c2_1(a612)) | c0_1(a607))),
% 3.78/2.90 inference(rewrite,[status(thm)],[])).
% 3.78/2.90 tff(7071,plain,
% 3.78/2.90 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a607) | (~c1_1(a607)) | (~c2_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c2_1(a612)) | c0_1(a607)))),
% 3.78/2.90 inference(monotonicity,[status(thm)],[7070])).
% 3.78/2.90 tff(7072,plain,
% 3.78/2.90 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a607) | (~c1_1(a607)) | (~c2_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c2_1(a612)) | c0_1(a607))),
% 3.78/2.90 inference(transitivity,[status(thm)],[7071, 7069])).
% 3.78/2.90 tff(7073,plain,
% 3.78/2.90 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a612)) | (~c1_1(a612)) | (~c0_1(a612)) | c0_1(a607) | (~c1_1(a607)) | (~c2_1(a607)))),
% 3.78/2.90 inference(quant_inst,[status(thm)],[])).
% 3.78/2.90 tff(7074,plain,
% 3.78/2.90 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c1_1(a612)) | (~c0_1(a612)) | (~c2_1(a612)) | c0_1(a607)),
% 3.78/2.90 inference(modus_ponens,[status(thm)],[7073, 7072])).
% 3.78/2.90 tff(7075,plain,
% 3.78/2.90 (~c0_1(a612)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[7074, 107, 7035, 7068, 7067, 6876, 6959, 2727, 1])).
% 3.78/2.90 tff(7076,plain,
% 3.78/2.90 (c3_1(a612)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[1139, 7066])).
% 3.78/2.90 tff(7077,plain,
% 3.78/2.90 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | c3_1(a607) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c3_1(a607) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))),
% 3.78/2.90 inference(rewrite,[status(thm)],[])).
% 3.78/2.90 tff(7078,plain,
% 3.78/2.90 ((hskp15 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c1_1(a607)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612))) <=> (hskp15 | c3_1(a607) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))),
% 3.78/2.90 inference(rewrite,[status(thm)],[])).
% 3.78/2.90 tff(7079,plain,
% 3.78/2.90 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c1_1(a607)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | c3_1(a607) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612))))),
% 3.78/2.90 inference(monotonicity,[status(thm)],[7078])).
% 3.78/2.90 tff(7080,plain,
% 3.78/2.90 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c1_1(a607)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c3_1(a607) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))),
% 3.78/2.90 inference(transitivity,[status(thm)],[7079, 7077])).
% 3.78/2.90 tff(7081,plain,
% 3.78/2.90 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c1_1(a607)) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612)))),
% 3.78/2.90 inference(quant_inst,[status(thm)],[])).
% 3.78/2.90 tff(7082,plain,
% 3.78/2.90 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c3_1(a607) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a612) | (~c1_1(a612)) | (~c3_1(a612))),
% 3.78/2.90 inference(modus_ponens,[status(thm)],[7081, 7080])).
% 3.78/2.90 tff(7083,plain,
% 3.78/2.90 (hskp15),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[7082, 107, 7068, 7076, 33, 6876, 6959, 2690, 7075])).
% 3.78/2.90 tff(7084,plain,
% 3.78/2.90 (~c0_1(a604)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[1591, 7083])).
% 3.78/2.90 tff(7085,plain,
% 3.78/2.90 (c0_1(a598)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[892, 7050])).
% 3.78/2.90 tff(7086,plain,
% 3.78/2.90 (c1_1(a604)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[1613, 7083])).
% 3.78/2.90 tff(7087,plain,
% 3.78/2.90 (c2_1(a604)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[4790, 107, 6877, 7086, 7085, 7084, 7051, 32, 7059])).
% 3.78/2.90 tff(7088,plain,
% 3.78/2.90 (~hskp12),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[7034, 462, 33, 463, 461, 1])).
% 3.78/2.90 tff(7089,plain,
% 3.78/2.90 (hskp8),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[787, 726, 7088])).
% 3.78/2.90 tff(7090,plain,
% 3.78/2.90 (~c2_1(a593)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[555, 7089])).
% 3.78/2.90 tff(7091,plain,
% 3.78/2.90 (c3_1(a593)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[511, 7089])).
% 3.78/2.90 tff(7092,plain,
% 3.78/2.90 (c1_1(a593)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[522, 7089])).
% 3.78/2.90 tff(7093,plain,
% 3.78/2.90 (hskp3),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[5154, 107, 6877, 7092, 7091, 7090, 3420])).
% 3.78/2.90 tff(7094,plain,
% 3.78/2.90 (~c1_1(a587)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[939, 7093])).
% 3.78/2.90 tff(7095,plain,
% 3.78/2.90 (hskp14),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[3394, 107, 2318, 2317, 2316, 7092, 7091, 7090, 550])).
% 3.78/2.90 tff(7096,plain,
% 3.78/2.90 (~c3_1(a603)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[205, 7095])).
% 3.78/2.90 tff(7097,plain,
% 3.78/2.90 (~c1_1(a603)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[171, 7095])).
% 3.78/2.90 tff(7098,plain,
% 3.78/2.90 (c2_1(a587)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[950, 7093])).
% 3.78/2.90 tff(7099,plain,
% 3.78/2.90 (c0_1(a587)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[961, 7093])).
% 3.78/2.90 tff(7100,plain,
% 3.78/2.90 (c2_1(a603)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[1006, 726, 107, 7099, 7098, 7097, 7096, 7094, 995])).
% 3.78/2.90 tff(7101,plain,
% 3.78/2.90 (c0_1(a603)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[182, 7095])).
% 3.78/2.90 tff(7102,plain,
% 3.78/2.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a607) | (~c1_1(a607)) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a607) | (~c1_1(a607)) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607))),
% 3.78/2.90 inference(rewrite,[status(thm)],[])).
% 3.78/2.90 tff(7103,plain,
% 3.78/2.90 (((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a607) | c0_1(a607) | (~c1_1(a607))) <=> (c3_1(a607) | (~c1_1(a607)) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607))),
% 3.78/2.90 inference(rewrite,[status(thm)],[])).
% 3.78/2.90 tff(7104,plain,
% 3.78/2.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a607) | c0_1(a607) | (~c1_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a607) | (~c1_1(a607)) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607)))),
% 3.78/2.90 inference(monotonicity,[status(thm)],[7103])).
% 3.78/2.90 tff(7105,plain,
% 3.78/2.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a607) | c0_1(a607) | (~c1_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a607) | (~c1_1(a607)) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607))),
% 3.78/2.90 inference(transitivity,[status(thm)],[7104, 7102])).
% 3.78/2.90 tff(7106,plain,
% 3.78/2.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c1_1(a599) | (~c3_1(a599)) | (~c2_1(a599)) | c3_1(a607) | c0_1(a607) | (~c1_1(a607)))),
% 3.78/2.90 inference(quant_inst,[status(thm)],[])).
% 3.78/2.90 tff(7107,plain,
% 3.78/2.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a607) | (~c1_1(a607)) | c3_1(a603) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | (~c2_1(a599)) | (~c2_1(a603)) | (~c0_1(a603)) | c0_1(a607)),
% 3.78/2.90 inference(modus_ponens,[status(thm)],[7106, 7105])).
% 3.78/2.90 tff(7108,plain,
% 3.78/2.90 ($false),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[7107, 107, 33, 7101, 463, 462, 6876, 7096, 461, 258, 1, 7100])).
% 3.78/2.90 tff(7109,plain,(hskp26 | c3_1(a607) | (~c2_1(a599)) | (~c3_1(a599)) | c1_1(a599) | c0_1(a607) | (~c0_1(a678)) | (~c2_1(a678)) | (~c3_1(a678))), inference(lemma,lemma(discharge,[]))).
% 3.78/2.90 tff(7110,plain,
% 3.78/2.90 (hskp26),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[7109, 7025, 33, 7026, 7024, 1, 2292, 2281, 2270])).
% 3.78/2.90 tff(7111,plain,
% 3.78/2.90 (c2_1(a583)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[391, 7110])).
% 3.78/2.90 tff(7112,plain,
% 3.78/2.90 (c1_1(a583)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[351, 7110])).
% 3.78/2.90 tff(7113,plain,
% 3.78/2.90 (c0_1(a583)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[362, 7110])).
% 3.78/2.90 tff(7114,plain,
% 3.78/2.90 ($false),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[3055, 107, 7035, 7113, 7112, 7111, 7086, 7084, 2727, 7087])).
% 3.78/2.90 tff(7115,plain,(hskp22 | c3_1(a607) | c0_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.78/2.90 tff(7116,plain,
% 3.78/2.90 (hskp22),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[7115, 1, 33])).
% 3.78/2.90 tff(7117,plain,
% 3.78/2.90 (c1_1(a633)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[3962, 7116])).
% 3.78/2.90 tff(7118,plain,
% 3.78/2.90 (~c0_1(a633)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[3968, 7116])).
% 3.78/2.90 tff(7119,plain,
% 3.78/2.90 (~c3_1(a633)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[3974, 7116])).
% 3.78/2.90 tff(7120,plain,
% 3.78/2.90 (hskp11),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[6878, 7119, 7118, 7117])).
% 3.78/2.90 tff(7121,plain,
% 3.78/2.90 (~c1_1(a599)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[428, 7120])).
% 3.78/2.90 tff(7122,plain,
% 3.78/2.90 (c3_1(a599)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[422, 7120])).
% 3.78/2.90 tff(7123,plain,
% 3.78/2.90 (c2_1(a599)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[439, 7120])).
% 3.78/2.90 tff(7124,plain,
% 3.78/2.90 (hskp28),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[7065, 107, 33, 7123, 7122, 6876, 6959, 7121, 1748])).
% 3.78/2.90 tff(7125,plain,
% 3.78/2.90 (c2_1(a612)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[1150, 7124])).
% 3.78/2.90 tff(7126,plain,
% 3.78/2.90 (c1_1(a612)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[1435, 7124])).
% 3.78/2.90 tff(7127,plain,
% 3.78/2.90 (~hskp12),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[7034, 7122, 33, 7123, 7121, 1])).
% 3.78/2.90 tff(7128,plain,
% 3.78/2.90 (~c0_1(a612)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[7074, 107, 7127, 7126, 7125, 6876, 6959, 2727, 1])).
% 3.78/2.90 tff(7129,plain,
% 3.78/2.90 (c3_1(a612)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[1139, 7124])).
% 3.78/2.90 tff(7130,plain,
% 3.78/2.90 (c2_1(a633)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[5210, 107, 7125, 7129, 7123, 7122, 7118, 7119, 7121, 1730, 7128])).
% 3.78/2.90 tff(7131,plain,
% 3.78/2.90 (hskp8),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[787, 726, 7127])).
% 3.78/2.90 tff(7132,plain,
% 3.78/2.90 (~c2_1(a593)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[555, 7131])).
% 3.78/2.90 tff(7133,plain,
% 3.78/2.90 (c3_1(a593)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[511, 7131])).
% 3.78/2.90 tff(7134,plain,
% 3.78/2.90 (c1_1(a593)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[522, 7131])).
% 3.78/2.90 tff(7135,plain,
% 3.78/2.90 (hskp3),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[5154, 107, 6877, 7134, 7133, 7132, 3420])).
% 3.78/2.90 tff(7136,plain,
% 3.78/2.90 (~c1_1(a587)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[939, 7135])).
% 3.78/2.90 tff(7137,plain,
% 3.78/2.90 (c2_1(a587)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[950, 7135])).
% 3.78/2.90 tff(7138,plain,
% 3.78/2.90 (c0_1(a587)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[961, 7135])).
% 3.78/2.90 tff(7139,plain,
% 3.78/2.90 (~hskp0),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[7008, 7133, 7134, 7132])).
% 3.78/2.90 tff(7140,plain,
% 3.78/2.90 (~c1_1(a610)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[4047, 107, 6877, 1000, 999, 6123, 6122, 996, 32])).
% 3.78/2.90 tff(7141,plain,
% 3.78/2.90 ($false),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[5800, 726, 107, 3604, 6123, 6122, 1032, 7140])).
% 3.78/2.90 tff(7142,plain,((~hskp18) | hskp26 | hskp0 | (~c0_1(a587)) | (~c2_1(a587)) | c1_1(a587)), inference(lemma,lemma(discharge,[]))).
% 3.78/2.90 tff(7143,plain,
% 3.78/2.90 (~hskp18),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[7142, 726, 7139, 7138, 7137, 7136])).
% 3.78/2.90 tff(7144,plain,
% 3.78/2.90 (((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp18 | c3_1(a607) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0))) <=> ((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp18 | c3_1(a607) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0))),
% 3.78/2.90 inference(rewrite,[status(thm)],[])).
% 3.78/2.90 tff(7145,plain,
% 3.78/2.90 ((hskp29 | hskp18 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c1_1(a607))) <=> (hskp29 | hskp18 | c3_1(a607) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0))),
% 3.78/2.90 inference(rewrite,[status(thm)],[])).
% 3.78/2.90 tff(7146,plain,
% 3.78/2.90 (((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp18 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c1_1(a607)))) <=> ((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp18 | c3_1(a607) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0)))),
% 3.78/2.90 inference(monotonicity,[status(thm)],[7145])).
% 3.78/2.90 tff(7147,plain,
% 3.78/2.90 (((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp18 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c1_1(a607)))) <=> ((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp18 | c3_1(a607) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0))),
% 3.78/2.90 inference(transitivity,[status(thm)],[7146, 7144])).
% 3.78/2.90 tff(7148,plain,
% 3.78/2.90 ((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp29 | hskp18 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c1_1(a607)))),
% 3.78/2.90 inference(quant_inst,[status(thm)],[])).
% 3.78/2.90 tff(7149,plain,
% 3.78/2.90 ((~![U: $i] : (hskp29 | hskp18 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp29 | hskp18 | c3_1(a607) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0)),
% 3.78/2.90 inference(modus_ponens,[status(thm)],[7148, 7147])).
% 3.78/2.90 tff(7150,plain,
% 3.78/2.90 (hskp29 | hskp18 | c3_1(a607) | (~c2_1(a607))),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[7149, 107, 6876, 1796])).
% 3.78/2.90 tff(7151,plain,
% 3.78/2.90 (hskp29),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[7150, 7143, 33, 6959])).
% 3.78/2.90 tff(7152,plain,
% 3.78/2.90 (c3_1(a678)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[2269, 7151])).
% 3.78/2.90 tff(7153,plain,
% 3.78/2.90 (c0_1(a678)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[2291, 7151])).
% 3.78/2.90 tff(7154,plain,
% 3.78/2.90 (c2_1(a678)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[2280, 7151])).
% 3.78/2.90 tff(7155,plain,
% 3.78/2.90 ($false),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[7109, 7154, 7153, 33, 7122, 7121, 1, 7123, 726, 7152])).
% 3.78/2.90 tff(7156,plain,(hskp26 | c3_1(a607) | c0_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.78/2.90 tff(7157,plain,
% 3.78/2.90 (hskp26),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[7156, 1, 33])).
% 3.78/2.90 tff(7158,plain,
% 3.78/2.90 (c2_1(a583)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[391, 7157])).
% 3.78/2.90 tff(7159,plain,
% 3.78/2.90 (c1_1(a583)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[351, 7157])).
% 3.78/2.90 tff(7160,plain,
% 3.78/2.90 (c0_1(a583)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[362, 7157])).
% 3.78/2.90 tff(7161,plain,
% 3.78/2.90 ($false),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[3998, 107, 7127, 7160, 7159, 7158, 7117, 7118, 2727, 7130])).
% 3.78/2.90 tff(7162,plain,(c0_1(a607) | c3_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.78/2.90 tff(7163,plain,
% 3.78/2.90 (c0_1(a607)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[7162, 33])).
% 3.78/2.90 tff(7164,plain,
% 3.78/2.90 (hskp3),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[6893, 7163, 33])).
% 3.78/2.90 tff(7165,plain,
% 3.78/2.90 (~c1_1(a587)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[939, 7164])).
% 3.78/2.90 tff(7166,plain,
% 3.78/2.90 (hskp4),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[6911, 7163, 33])).
% 3.78/2.90 tff(7167,plain,
% 3.78/2.90 (~c2_1(a588)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[121, 7166])).
% 3.78/2.90 tff(7168,plain,
% 3.78/2.90 (~c1_1(a588)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[127, 7166])).
% 3.78/2.90 tff(7169,plain,
% 3.78/2.90 (c0_1(a588)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[138, 7166])).
% 3.78/2.90 tff(7170,plain,
% 3.78/2.90 (hskp1),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[5472, 107, 33, 7169, 6959, 7168, 7167, 1237, 7163])).
% 3.78/2.90 tff(7171,plain,
% 3.78/2.90 (~c0_1(a585)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[1250, 7170])).
% 3.78/2.90 tff(7172,plain,
% 3.78/2.90 (c2_1(a585)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[1261, 7170])).
% 3.78/2.90 tff(7173,plain,
% 3.78/2.90 (c1_1(a585)),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[1272, 7170])).
% 3.78/2.90 tff(7174,plain,
% 3.78/2.90 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c0_1(a607)))),
% 3.78/2.90 inference(rewrite,[status(thm)],[])).
% 3.78/2.90 tff(7175,plain,
% 3.78/2.90 ((hskp12 | (~ndr1_0) | (~c2_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585))) <=> (hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c0_1(a607)))),
% 3.78/2.90 inference(rewrite,[status(thm)],[])).
% 3.78/2.90 tff(7176,plain,
% 3.78/2.90 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c0_1(a607))))),
% 3.78/2.90 inference(monotonicity,[status(thm)],[7175])).
% 3.78/2.90 tff(7177,plain,
% 3.78/2.90 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c0_1(a607)))),
% 3.78/2.90 inference(transitivity,[status(thm)],[7176, 7174])).
% 3.78/2.90 tff(7178,plain,
% 3.78/2.90 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))),
% 3.78/2.90 inference(quant_inst,[status(thm)],[])).
% 3.78/2.90 tff(7179,plain,
% 3.78/2.90 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c0_1(a607))),
% 3.78/2.90 inference(modus_ponens,[status(thm)],[7178, 7177])).
% 3.78/2.90 tff(7180,plain,
% 3.78/2.90 (hskp12),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[7179, 107, 7173, 7172, 6876, 6959, 7171, 2727, 7163])).
% 3.78/2.90 tff(7181,plain,
% 3.78/2.90 ($false),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[4342, 6236, 6237, 736, 462, 463, 6238, 461])).
% 3.78/2.90 tff(7182,plain,((~hskp22) | (~hskp12) | (~c3_1(a599)) | (~c2_1(a599)) | c1_1(a599)), inference(lemma,lemma(discharge,[]))).
% 3.78/2.90 tff(7183,plain,
% 3.78/2.90 (~hskp22),
% 3.78/2.90 inference(unit_resolution,[status(thm)],[7182, 1077, 7180, 1078, 1012])).
% 3.78/2.91 tff(7184,plain,
% 3.78/2.91 (hskp29),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[2258, 7183])).
% 3.78/2.91 tff(7185,plain,
% 3.78/2.91 (c3_1(a678)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[2269, 7184])).
% 3.78/2.91 tff(7186,plain,
% 3.78/2.91 (c2_1(a678)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[2280, 7184])).
% 3.78/2.91 tff(7187,plain,
% 3.78/2.91 (c0_1(a678)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[2291, 7184])).
% 3.78/2.91 tff(7188,plain,
% 3.78/2.91 (~c3_1(a588)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[5444, 107, 7187, 7186, 7185, 7173, 7172, 7168, 7167, 7171, 11])).
% 3.78/2.91 tff(7189,plain,
% 3.78/2.91 (hskp28),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[7065, 107, 33, 1078, 1077, 6876, 6959, 1012, 1748])).
% 3.78/2.91 tff(7190,plain,
% 3.78/2.91 (c3_1(a612)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[1139, 7189])).
% 3.78/2.91 tff(7191,plain,
% 3.78/2.91 (c2_1(a612)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[1150, 7189])).
% 3.78/2.91 tff(7192,plain,
% 3.78/2.91 (c1_1(a612)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[1435, 7189])).
% 3.78/2.91 tff(7193,plain,
% 3.78/2.91 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c1_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c1_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a607)))),
% 3.78/2.91 inference(rewrite,[status(thm)],[])).
% 3.78/2.91 tff(7194,plain,
% 3.78/2.91 ((hskp10 | (~ndr1_0) | (~c2_1(a612)) | (~c3_1(a612)) | (~c1_1(a612)) | (~c1_1(a607)) | (~c2_1(a607)) | (~c0_1(a607))) <=> (hskp10 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c1_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a607)))),
% 3.78/2.91 inference(rewrite,[status(thm)],[])).
% 3.78/2.91 tff(7195,plain,
% 3.78/2.91 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a612)) | (~c3_1(a612)) | (~c1_1(a612)) | (~c1_1(a607)) | (~c2_1(a607)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c1_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a607))))),
% 3.78/2.91 inference(monotonicity,[status(thm)],[7194])).
% 3.78/2.91 tff(7196,plain,
% 3.78/2.91 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a612)) | (~c3_1(a612)) | (~c1_1(a612)) | (~c1_1(a607)) | (~c2_1(a607)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c1_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a607)))),
% 3.78/2.91 inference(transitivity,[status(thm)],[7195, 7193])).
% 3.78/2.91 tff(7197,plain,
% 3.78/2.91 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a612)) | (~c3_1(a612)) | (~c1_1(a612)) | (~c1_1(a607)) | (~c2_1(a607)) | (~c0_1(a607)))),
% 3.78/2.91 inference(quant_inst,[status(thm)],[])).
% 3.78/2.91 tff(7198,plain,
% 3.78/2.91 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c1_1(a612)) | (~c3_1(a612)) | (~c2_1(a612)) | (~c0_1(a607))),
% 3.78/2.91 inference(modus_ponens,[status(thm)],[7197, 7196])).
% 3.78/2.91 tff(7199,plain,
% 3.78/2.91 (hskp10),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[7198, 107, 7192, 7191, 7190, 6876, 6959, 21, 7163])).
% 3.78/2.91 tff(7200,plain,
% 3.78/2.91 (~c1_1(a598)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[911, 7199])).
% 3.78/2.91 tff(7201,plain,
% 3.78/2.91 (c3_1(a598)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[881, 7199])).
% 3.78/2.91 tff(7202,plain,
% 3.78/2.91 (c2_1(a598)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[4782, 107, 7187, 7186, 7185, 7201, 7173, 7172, 7200, 7171, 11])).
% 3.78/2.91 tff(7203,plain,
% 3.78/2.91 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp14 | c3_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp22 | hskp14 | c3_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)))),
% 3.78/2.91 inference(rewrite,[status(thm)],[])).
% 3.78/2.91 tff(7204,plain,
% 3.78/2.91 ((hskp22 | hskp14 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607))) <=> (hskp22 | hskp14 | c3_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)))),
% 3.78/2.91 inference(rewrite,[status(thm)],[])).
% 3.78/2.91 tff(7205,plain,
% 3.78/2.91 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp14 | c3_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607))))),
% 3.78/2.91 inference(monotonicity,[status(thm)],[7204])).
% 3.78/2.91 tff(7206,plain,
% 3.78/2.91 (((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp22 | hskp14 | c3_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)))),
% 3.78/2.91 inference(transitivity,[status(thm)],[7205, 7203])).
% 3.78/2.91 tff(7207,plain,
% 3.78/2.91 ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp14 | (~ndr1_0) | c3_1(a607) | (~c2_1(a607)) | (~c0_1(a607)))),
% 3.78/2.91 inference(quant_inst,[status(thm)],[])).
% 3.78/2.91 tff(7208,plain,
% 3.78/2.91 ((~![U: $i] : (hskp22 | hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp22 | hskp14 | c3_1(a607) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607))),
% 3.78/2.91 inference(modus_ponens,[status(thm)],[7207, 7206])).
% 3.78/2.91 tff(7209,plain,
% 3.78/2.91 (hskp22 | hskp14 | c3_1(a607) | (~c0_1(a607))),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[7208, 107, 6959, 381])).
% 3.78/2.91 tff(7210,plain,
% 3.78/2.91 (hskp14),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[7209, 7183, 33, 7163])).
% 3.78/2.91 tff(7211,plain,
% 3.78/2.91 (~c3_1(a603)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[205, 7210])).
% 3.78/2.91 tff(7212,plain,
% 3.78/2.91 (~c1_1(a603)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[171, 7210])).
% 3.78/2.91 tff(7213,plain,
% 3.78/2.91 (c0_1(a598)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[892, 7199])).
% 3.78/2.91 tff(7214,plain,
% 3.78/2.91 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a603) | c3_1(a603) | c1_1(a598) | (~ndr1_0) | (~c2_1(a598)) | (~c0_1(a598)) | c2_1(a603))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a603) | c3_1(a603) | c1_1(a598) | (~ndr1_0) | (~c2_1(a598)) | (~c0_1(a598)) | c2_1(a603))),
% 3.78/2.91 inference(rewrite,[status(thm)],[])).
% 3.78/2.91 tff(7215,plain,
% 3.78/2.91 ((hskp26 | (~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c0_1(a598)) | c3_1(a603) | c1_1(a603) | c2_1(a603)) <=> (hskp26 | c1_1(a603) | c3_1(a603) | c1_1(a598) | (~ndr1_0) | (~c2_1(a598)) | (~c0_1(a598)) | c2_1(a603))),
% 3.78/2.91 inference(rewrite,[status(thm)],[])).
% 3.78/2.91 tff(7216,plain,
% 3.78/2.91 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c0_1(a598)) | c3_1(a603) | c1_1(a603) | c2_1(a603))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a603) | c3_1(a603) | c1_1(a598) | (~ndr1_0) | (~c2_1(a598)) | (~c0_1(a598)) | c2_1(a603)))),
% 3.78/2.91 inference(monotonicity,[status(thm)],[7215])).
% 3.78/2.91 tff(7217,plain,
% 3.78/2.91 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c0_1(a598)) | c3_1(a603) | c1_1(a603) | c2_1(a603))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a603) | c3_1(a603) | c1_1(a598) | (~ndr1_0) | (~c2_1(a598)) | (~c0_1(a598)) | c2_1(a603))),
% 3.78/2.91 inference(transitivity,[status(thm)],[7216, 7214])).
% 3.78/2.91 tff(7218,plain,
% 3.78/2.91 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c0_1(a598)) | c3_1(a603) | c1_1(a603) | c2_1(a603))),
% 3.78/2.91 inference(quant_inst,[status(thm)],[])).
% 3.78/2.91 tff(7219,plain,
% 3.78/2.91 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a603) | c3_1(a603) | c1_1(a598) | (~ndr1_0) | (~c2_1(a598)) | (~c0_1(a598)) | c2_1(a603)),
% 3.78/2.91 inference(modus_ponens,[status(thm)],[7218, 7217])).
% 3.78/2.91 tff(7220,plain,
% 3.78/2.91 (c2_1(a603)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[7219, 726, 107, 7213, 7212, 7211, 7200, 995, 7202])).
% 3.78/2.91 tff(7221,plain,
% 3.78/2.91 (c0_1(a603)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[182, 7210])).
% 3.78/2.91 tff(7222,plain,
% 3.78/2.91 ($false),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[4932, 726, 107, 7221, 7212, 7168, 7167, 995, 7220, 7188])).
% 3.78/2.91 tff(7223,plain,(hskp26 | c3_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.78/2.91 tff(7224,plain,
% 3.78/2.91 (hskp26),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[7223, 33])).
% 3.78/2.91 tff(7225,plain,
% 3.78/2.91 (c0_1(a583)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[362, 7224])).
% 3.78/2.91 tff(7226,plain,
% 3.78/2.91 (hskp11 | hskp21),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[5114, 107, 7169, 7168, 7167, 5104])).
% 3.78/2.91 tff(7227,plain,
% 3.78/2.91 (hskp21),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[7226, 1638])).
% 3.78/2.91 tff(7228,plain,
% 3.78/2.91 (~c3_1(a629)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[4846, 7227])).
% 3.78/2.91 tff(7229,plain,
% 3.78/2.91 (~c2_1(a629)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[4852, 7227])).
% 3.78/2.91 tff(7230,plain,
% 3.78/2.91 (c0_1(a629)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[4870, 7227])).
% 3.78/2.91 tff(7231,plain,
% 3.78/2.91 (hskp8),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[5310, 107, 7230, 33, 7229, 7228, 6959, 4271, 7163])).
% 3.78/2.91 tff(7232,plain,
% 3.78/2.91 (~c2_1(a593)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[555, 7231])).
% 3.78/2.91 tff(7233,plain,
% 3.78/2.91 (c1_1(a593)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[522, 7231])).
% 3.78/2.91 tff(7234,plain,
% 3.78/2.91 (c3_1(a593)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[511, 7231])).
% 3.78/2.91 tff(7235,plain,
% 3.78/2.91 (~hskp0),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[7008, 7234, 7233, 7232])).
% 3.78/2.91 tff(7236,plain,
% 3.78/2.91 (~c0_1(a593)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[7015, 1638, 107, 7235, 7233, 7232, 2347])).
% 3.78/2.91 tff(7237,plain,
% 3.78/2.91 (c2_1(a587)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[950, 7164])).
% 3.78/2.91 tff(7238,plain,
% 3.78/2.91 (c0_1(a587)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[961, 7164])).
% 3.78/2.91 tff(7239,plain,
% 3.78/2.91 ($false),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[5232, 107, 6877, 7233, 7238, 7237, 7232, 7165, 32, 7236])).
% 3.78/2.91 tff(7240,plain,(hskp11 | c3_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.78/2.91 tff(7241,plain,
% 3.78/2.91 (hskp11),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[7240, 33])).
% 3.78/2.91 tff(7242,plain,
% 3.78/2.91 (~c1_1(a599)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[428, 7241])).
% 3.78/2.91 tff(7243,plain,
% 3.78/2.91 (c2_1(a599)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[439, 7241])).
% 3.78/2.91 tff(7244,plain,
% 3.78/2.91 (c3_1(a599)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[422, 7241])).
% 3.78/2.91 tff(7245,plain,
% 3.78/2.91 (~hskp22),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[7182, 7244, 7180, 7243, 7242])).
% 3.78/2.91 tff(7246,plain,
% 3.78/2.91 (hskp6),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[147, 7245, 7166])).
% 3.78/2.91 tff(7247,plain,
% 3.78/2.91 (~c0_1(a590)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[666, 7246])).
% 3.78/2.91 tff(7248,plain,
% 3.78/2.91 (c2_1(a583)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[391, 7224])).
% 3.78/2.91 tff(7249,plain,
% 3.78/2.91 (c3_1(a590)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[677, 7246])).
% 3.78/2.91 tff(7250,plain,
% 3.78/2.91 (c1_1(a583)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[351, 7224])).
% 3.78/2.91 tff(7251,plain,
% 3.78/2.91 (c2_1(a590)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[688, 7246])).
% 3.78/2.91 tff(7252,plain,
% 3.78/2.91 (hskp15),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[5715, 7251, 33, 7163, 7250, 6959, 7249, 7173, 7171, 7248, 7247, 7225])).
% 3.78/2.91 tff(7253,plain,
% 3.78/2.91 (~c0_1(a604)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[1591, 7252])).
% 3.78/2.91 tff(7254,plain,
% 3.78/2.91 (c1_1(a604)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[1613, 7252])).
% 3.78/2.91 tff(7255,plain,
% 3.78/2.91 (c2_1(a604)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[3120, 107, 6877, 7254, 7238, 7237, 7253, 7165, 32])).
% 3.78/2.91 tff(7256,plain,
% 3.78/2.91 (c3_1(a604)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[1602, 7252])).
% 3.78/2.91 tff(7257,plain,
% 3.78/2.91 (hskp29),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[2258, 7245])).
% 3.78/2.91 tff(7258,plain,
% 3.78/2.91 (c3_1(a678)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[2269, 7257])).
% 3.78/2.91 tff(7259,plain,
% 3.78/2.91 (c2_1(a678)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[2280, 7257])).
% 3.78/2.91 tff(7260,plain,
% 3.78/2.91 (c0_1(a678)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[2291, 7257])).
% 3.78/2.91 tff(7261,plain,
% 3.78/2.91 (~c3_1(a588)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[5444, 107, 7260, 7259, 7258, 7173, 7172, 7168, 7167, 7171, 11])).
% 3.78/2.91 tff(7262,plain,
% 3.78/2.91 (hskp16),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[4700, 107, 7251, 7249, 7169, 7247, 7167, 2125, 7261])).
% 3.78/2.91 tff(7263,plain,
% 3.78/2.91 (~c2_1(a606)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[1111, 7262])).
% 3.78/2.91 tff(7264,plain,
% 3.78/2.91 (c1_1(a606)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[1088, 7262])).
% 3.78/2.91 tff(7265,plain,
% 3.78/2.91 (c0_1(a606) | (~c1_1(a606)) | (~c0_1(a587)) | (~c2_1(a587)) | c2_1(a606) | c1_1(a587)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[5034, 6877])).
% 3.78/2.91 tff(7266,plain,
% 3.78/2.91 (c0_1(a606)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[7265, 7264, 7238, 7237, 7263, 7165])).
% 3.78/2.91 tff(7267,plain,
% 3.78/2.91 (~hskp13),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[2553, 7266, 7244, 7255, 7243, 7242, 7253, 7260, 7259, 7258, 7264, 7263, 7256])).
% 3.78/2.91 tff(7268,plain,
% 3.78/2.91 (hskp19 | hskp13),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[2581, 107, 7173, 7172, 7171, 2564])).
% 3.78/2.91 tff(7269,plain,
% 3.78/2.91 (hskp19),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[7268, 7267])).
% 3.78/2.91 tff(7270,plain,
% 3.78/2.91 (~c1_1(a617)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[2588, 7269])).
% 3.78/2.91 tff(7271,plain,
% 3.78/2.91 (~c0_1(a617)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[2594, 7269])).
% 3.78/2.91 tff(7272,plain,
% 3.78/2.91 (c2_1(a617)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[2605, 7269])).
% 3.78/2.91 tff(7273,plain,
% 3.78/2.91 (hskp28),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[7065, 107, 33, 7243, 7244, 6876, 6959, 7242, 1748])).
% 3.78/2.91 tff(7274,plain,
% 3.78/2.91 (c3_1(a612)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[1139, 7273])).
% 3.78/2.91 tff(7275,plain,
% 3.78/2.91 (c1_1(a612)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[1435, 7273])).
% 3.78/2.91 tff(7276,plain,
% 3.78/2.91 (~c0_1(a612)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[6017, 107, 7275, 7274, 7272, 7256, 7271, 7270, 7253, 65, 7255])).
% 3.78/2.91 tff(7277,plain,
% 3.78/2.91 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c1_1(a604)))),
% 3.78/2.91 inference(rewrite,[status(thm)],[])).
% 3.78/2.91 tff(7278,plain,
% 3.78/2.91 ((hskp10 | (~ndr1_0) | (~c2_1(a604)) | (~c3_1(a604)) | (~c1_1(a604)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583))) <=> (hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c1_1(a604)))),
% 3.78/2.91 inference(rewrite,[status(thm)],[])).
% 3.78/2.91 tff(7279,plain,
% 3.78/2.91 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a604)) | (~c3_1(a604)) | (~c1_1(a604)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c1_1(a604))))),
% 3.78/2.91 inference(monotonicity,[status(thm)],[7278])).
% 3.78/2.91 tff(7280,plain,
% 3.78/2.91 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a604)) | (~c3_1(a604)) | (~c1_1(a604)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c1_1(a604)))),
% 3.78/2.91 inference(transitivity,[status(thm)],[7279, 7277])).
% 3.78/2.91 tff(7281,plain,
% 3.78/2.91 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a604)) | (~c3_1(a604)) | (~c1_1(a604)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583)))),
% 3.78/2.91 inference(quant_inst,[status(thm)],[])).
% 3.78/2.91 tff(7282,plain,
% 3.78/2.91 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a604)) | (~c2_1(a604)) | (~c1_1(a604))),
% 3.78/2.91 inference(modus_ponens,[status(thm)],[7281, 7280])).
% 3.78/2.91 tff(7283,plain,
% 3.78/2.91 (hskp10),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[7282, 107, 7225, 7250, 7248, 7254, 7256, 21, 7255])).
% 3.78/2.91 tff(7284,plain,
% 3.78/2.91 (~c1_1(a598)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[911, 7283])).
% 3.78/2.91 tff(7285,plain,
% 3.78/2.91 (c3_1(a598)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[881, 7283])).
% 3.78/2.91 tff(7286,plain,
% 3.78/2.91 (c2_1(a612)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[1150, 7273])).
% 3.78/2.91 tff(7287,plain,
% 3.78/2.91 (c2_1(a598)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[5599, 107, 7260, 7259, 7258, 7275, 7286, 7285, 7284, 11, 7276])).
% 3.78/2.91 tff(7288,plain,
% 3.78/2.91 (hskp8),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[5751, 107, 33, 7169, 6959, 7167, 4271, 7163, 7261])).
% 3.78/2.91 tff(7289,plain,
% 3.78/2.91 (c3_1(a593)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[511, 7288])).
% 3.78/2.91 tff(7290,plain,
% 3.78/2.91 (c1_1(a593)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[522, 7288])).
% 3.78/2.91 tff(7291,plain,
% 3.78/2.91 (~c0_1(a593)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[6029, 107, 7286, 7274, 7272, 7290, 7289, 7271, 7270, 65, 7276])).
% 3.78/2.91 tff(7292,plain,
% 3.78/2.91 (~c2_1(a593)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[555, 7288])).
% 3.78/2.91 tff(7293,plain,
% 3.78/2.91 (c0_1(a598)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[892, 7283])).
% 3.78/2.91 tff(7294,plain,
% 3.78/2.91 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c1_1(a598) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a598)) | (~c0_1(a598)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c1_1(a598) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a598)) | (~c0_1(a598)))),
% 3.78/2.91 inference(rewrite,[status(thm)],[])).
% 3.78/2.91 tff(7295,plain,
% 3.78/2.91 ((hskp17 | (~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c0_1(a598)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593))) <=> (hskp17 | c1_1(a598) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a598)) | (~c0_1(a598)))),
% 3.78/2.91 inference(rewrite,[status(thm)],[])).
% 3.78/2.91 tff(7296,plain,
% 3.78/2.91 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c0_1(a598)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c1_1(a598) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a598)) | (~c0_1(a598))))),
% 3.78/2.91 inference(monotonicity,[status(thm)],[7295])).
% 3.78/2.91 tff(7297,plain,
% 3.78/2.91 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c0_1(a598)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c1_1(a598) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a598)) | (~c0_1(a598)))),
% 3.78/2.91 inference(transitivity,[status(thm)],[7296, 7294])).
% 3.78/2.91 tff(7298,plain,
% 3.78/2.91 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a598) | (~c2_1(a598)) | (~c0_1(a598)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)))),
% 3.78/2.91 inference(quant_inst,[status(thm)],[])).
% 3.78/2.91 tff(7299,plain,
% 3.78/2.91 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c1_1(a598) | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a598)) | (~c0_1(a598))),
% 3.78/2.91 inference(modus_ponens,[status(thm)],[7298, 7297])).
% 3.78/2.91 tff(7300,plain,
% 3.78/2.91 ($false),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[7299, 107, 6877, 7293, 7290, 7284, 7292, 32, 7291, 7287])).
% 3.78/2.91 tff(7301,plain,(c3_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.78/2.91 tff(7302,assumption,(~hskp12), introduced(assumption)).
% 3.78/2.91 tff(7303,plain,
% 3.78/2.91 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a607))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a607))),
% 3.78/2.91 inference(rewrite,[status(thm)],[])).
% 3.78/2.91 tff(7304,plain,
% 3.78/2.91 ((hskp12 | (~ndr1_0) | (~c2_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a607) | (~c1_1(a607)) | (~c2_1(a607))) <=> (hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a607))),
% 3.78/2.91 inference(rewrite,[status(thm)],[])).
% 3.78/2.91 tff(7305,plain,
% 3.78/2.91 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a607) | (~c1_1(a607)) | (~c2_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a607)))),
% 3.78/2.91 inference(monotonicity,[status(thm)],[7304])).
% 3.78/2.91 tff(7306,plain,
% 3.78/2.91 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a607) | (~c1_1(a607)) | (~c2_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a607))),
% 3.78/2.91 inference(transitivity,[status(thm)],[7305, 7303])).
% 3.78/2.91 tff(7307,plain,
% 3.78/2.91 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a607) | (~c1_1(a607)) | (~c2_1(a607)))),
% 3.78/2.91 inference(quant_inst,[status(thm)],[])).
% 3.78/2.91 tff(7308,plain,
% 3.78/2.91 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a607)),
% 3.78/2.91 inference(modus_ponens,[status(thm)],[7307, 7306])).
% 3.78/2.91 tff(7309,plain,
% 3.78/2.91 (~c1_1(a678)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[7308, 107, 7302, 4373, 4372, 6876, 6959, 2727, 1])).
% 3.78/2.91 tff(7310,plain,
% 3.78/2.91 (hskp8),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[787, 7302, 726])).
% 3.78/2.91 tff(7311,plain,
% 3.78/2.91 (~c2_1(a593)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[555, 7310])).
% 3.78/2.91 tff(7312,plain,
% 3.78/2.91 (c3_1(a593)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[511, 7310])).
% 3.78/2.91 tff(7313,plain,
% 3.78/2.91 (c1_1(a593)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[522, 7310])).
% 3.78/2.91 tff(7314,plain,
% 3.78/2.91 (hskp14),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[3394, 107, 4373, 4372, 4371, 7313, 7312, 7311, 550])).
% 3.78/2.91 tff(7315,plain,
% 3.78/2.91 (~c3_1(a603)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[205, 7314])).
% 3.78/2.91 tff(7316,plain,
% 3.78/2.91 (~c1_1(a603)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[171, 7314])).
% 3.78/2.91 tff(7317,plain,
% 3.78/2.91 (c2_1(a603)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[4924, 726, 107, 4373, 4372, 7316, 7315, 995, 7309])).
% 3.78/2.91 tff(7318,plain,
% 3.78/2.91 (c0_1(a603)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[182, 7314])).
% 3.78/2.91 tff(7319,plain,
% 3.78/2.91 ($false),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[3785, 726, 107, 1009, 722, 716, 710, 998, 995, 1010])).
% 3.78/2.91 tff(7320,plain,((~hskp20) | hskp26 | (~c0_1(a603)) | c1_1(a603) | (~c2_1(a603))), inference(lemma,lemma(discharge,[]))).
% 3.78/2.91 tff(7321,plain,
% 3.78/2.91 (~hskp20),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[7320, 7318, 726, 7316, 7317])).
% 3.78/2.91 tff(7322,plain,
% 3.78/2.91 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp7 | (~c1_1(a607)) | (~ndr1_0) | c0_1(a607) | (~c3_1(a607)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp7 | (~c1_1(a607)) | (~ndr1_0) | c0_1(a607) | (~c3_1(a607)))),
% 3.78/2.91 inference(rewrite,[status(thm)],[])).
% 3.78/2.91 tff(7323,plain,
% 3.78/2.91 ((hskp20 | hskp7 | (~ndr1_0) | c0_1(a607) | (~c3_1(a607)) | (~c1_1(a607))) <=> (hskp20 | hskp7 | (~c1_1(a607)) | (~ndr1_0) | c0_1(a607) | (~c3_1(a607)))),
% 3.78/2.91 inference(rewrite,[status(thm)],[])).
% 3.78/2.91 tff(7324,plain,
% 3.78/2.91 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c0_1(a607) | (~c3_1(a607)) | (~c1_1(a607)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp7 | (~c1_1(a607)) | (~ndr1_0) | c0_1(a607) | (~c3_1(a607))))),
% 3.78/2.91 inference(monotonicity,[status(thm)],[7323])).
% 3.78/2.91 tff(7325,plain,
% 3.78/2.91 (((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c0_1(a607) | (~c3_1(a607)) | (~c1_1(a607)))) <=> ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp7 | (~c1_1(a607)) | (~ndr1_0) | c0_1(a607) | (~c3_1(a607)))),
% 3.78/2.91 inference(transitivity,[status(thm)],[7324, 7322])).
% 3.78/2.91 tff(7326,plain,
% 3.78/2.91 ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp7 | (~ndr1_0) | c0_1(a607) | (~c3_1(a607)) | (~c1_1(a607)))),
% 3.78/2.91 inference(quant_inst,[status(thm)],[])).
% 3.78/2.91 tff(7327,plain,
% 3.78/2.91 ((~![U: $i] : (hskp20 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp7 | (~c1_1(a607)) | (~ndr1_0) | c0_1(a607) | (~c3_1(a607))),
% 3.78/2.91 inference(modus_ponens,[status(thm)],[7326, 7325])).
% 3.78/2.91 tff(7328,plain,
% 3.78/2.91 (hskp20 | hskp7 | c0_1(a607) | (~c3_1(a607))),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[7327, 107, 6876, 801])).
% 3.78/2.91 tff(7329,plain,
% 3.78/2.91 (hskp7),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[7328, 7321, 7301, 1])).
% 3.78/2.91 tff(7330,plain,
% 3.78/2.91 (~c3_1(a592)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[811, 7329])).
% 3.78/2.91 tff(7331,plain,
% 3.78/2.91 (~c0_1(a592)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[817, 7329])).
% 3.78/2.91 tff(7332,plain,
% 3.78/2.91 (~c1_1(a592)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[1398, 107, 7318, 1078, 1077, 7315, 1012, 7331, 7330, 258, 7317])).
% 3.78/2.91 tff(7333,plain,
% 3.78/2.91 (hskp2),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[1405, 107, 7316, 7315, 7331, 7330, 200, 7332, 7317])).
% 3.78/2.91 tff(7334,plain,
% 3.78/2.91 (~c3_1(a586)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[218, 7333])).
% 3.78/2.91 tff(7335,plain,
% 3.78/2.91 (hskp3),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[5154, 107, 6877, 7313, 7312, 7311, 3420])).
% 3.78/2.91 tff(7336,plain,
% 3.78/2.91 (~c1_1(a587)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[939, 7335])).
% 3.78/2.91 tff(7337,plain,
% 3.78/2.91 (c2_1(a587)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[950, 7335])).
% 3.78/2.91 tff(7338,plain,
% 3.78/2.91 (c0_1(a587)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[961, 7335])).
% 3.78/2.91 tff(7339,plain,
% 3.78/2.91 (c1_1(a586)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[229, 7333])).
% 3.78/2.91 tff(7340,plain,
% 3.78/2.91 (c0_1(a586)),
% 3.78/2.91 inference(unit_resolution,[status(thm)],[4817, 7339, 7338, 7337, 7336, 1078, 1077, 7314, 1012, 7334, 726])).
% 3.78/2.91 tff(7341,plain,
% 3.78/2.91 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~c1_1(a607)) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | c0_1(a607) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | (~c1_1(a607)) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | c0_1(a607) | (~c3_1(a607)))),
% 3.78/2.92 inference(rewrite,[status(thm)],[])).
% 3.78/2.92 tff(7342,plain,
% 3.78/2.92 ((hskp1 | (~ndr1_0) | c0_1(a607) | (~c3_1(a607)) | (~c1_1(a607)) | c3_1(a592) | c1_1(a592) | c0_1(a592)) <=> (hskp1 | (~c1_1(a607)) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | c0_1(a607) | (~c3_1(a607)))),
% 3.78/2.92 inference(rewrite,[status(thm)],[])).
% 3.78/2.92 tff(7343,plain,
% 3.78/2.92 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a607) | (~c3_1(a607)) | (~c1_1(a607)) | c3_1(a592) | c1_1(a592) | c0_1(a592))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~c1_1(a607)) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | c0_1(a607) | (~c3_1(a607))))),
% 3.78/2.92 inference(monotonicity,[status(thm)],[7342])).
% 3.78/2.92 tff(7344,plain,
% 3.78/2.92 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a607) | (~c3_1(a607)) | (~c1_1(a607)) | c3_1(a592) | c1_1(a592) | c0_1(a592))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | (~c1_1(a607)) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | c0_1(a607) | (~c3_1(a607)))),
% 3.78/2.92 inference(transitivity,[status(thm)],[7343, 7341])).
% 3.78/2.92 tff(7345,plain,
% 3.78/2.92 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a607) | (~c3_1(a607)) | (~c1_1(a607)) | c3_1(a592) | c1_1(a592) | c0_1(a592))),
% 3.78/2.92 inference(quant_inst,[status(thm)],[])).
% 3.78/2.92 tff(7346,plain,
% 3.78/2.92 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp1 | (~c1_1(a607)) | c0_1(a592) | c3_1(a592) | (~ndr1_0) | c1_1(a592) | c0_1(a607) | (~c3_1(a607))),
% 3.78/2.92 inference(modus_ponens,[status(thm)],[7345, 7344])).
% 3.78/2.92 tff(7347,plain,
% 3.78/2.92 (hskp1),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[7346, 107, 7301, 6876, 7331, 7330, 1555, 7332, 1])).
% 3.78/2.92 tff(7348,plain,
% 3.78/2.92 (~c0_1(a585)),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[1250, 7347])).
% 3.78/2.92 tff(7349,plain,
% 3.78/2.92 (c2_1(a585)),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[1261, 7347])).
% 3.78/2.92 tff(7350,plain,
% 3.78/2.92 (c1_1(a585)),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[1272, 7347])).
% 3.78/2.92 tff(7351,plain,
% 3.78/2.92 (c2_1(a586)),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[1474, 7333])).
% 3.78/2.92 tff(7352,plain,
% 3.78/2.92 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c2_1(a586)) | (~c1_1(a586)) | (~c0_1(a586)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c2_1(a586)) | (~c1_1(a586)) | (~c0_1(a586)))),
% 3.78/2.92 inference(rewrite,[status(thm)],[])).
% 3.78/2.92 tff(7353,plain,
% 3.78/2.92 ((hskp12 | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585))) <=> (hskp12 | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c2_1(a586)) | (~c1_1(a586)) | (~c0_1(a586)))),
% 3.78/2.92 inference(rewrite,[status(thm)],[])).
% 3.78/2.92 tff(7354,plain,
% 3.78/2.92 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c2_1(a586)) | (~c1_1(a586)) | (~c0_1(a586))))),
% 3.78/2.92 inference(monotonicity,[status(thm)],[7353])).
% 3.78/2.92 tff(7355,plain,
% 3.78/2.92 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c2_1(a586)) | (~c1_1(a586)) | (~c0_1(a586)))),
% 3.78/2.92 inference(transitivity,[status(thm)],[7354, 7352])).
% 3.78/2.92 tff(7356,plain,
% 3.78/2.92 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a585) | (~c1_1(a585)) | (~c2_1(a585)))),
% 3.78/2.92 inference(quant_inst,[status(thm)],[])).
% 3.78/2.92 tff(7357,plain,
% 3.78/2.92 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | c0_1(a585) | (~ndr1_0) | (~c2_1(a585)) | (~c1_1(a585)) | (~c2_1(a586)) | (~c1_1(a586)) | (~c0_1(a586))),
% 3.78/2.92 inference(modus_ponens,[status(thm)],[7356, 7355])).
% 3.78/2.92 tff(7358,plain,
% 3.78/2.92 ($false),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[7357, 107, 7302, 7339, 7351, 7350, 7349, 7348, 2727, 7340])).
% 3.78/2.92 tff(7359,plain,((~hskp29) | hskp12 | hskp26 | c0_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.78/2.92 tff(7360,plain,
% 3.78/2.92 (~hskp29),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[7359, 7302, 726, 1])).
% 3.78/2.92 tff(7361,plain,
% 3.78/2.92 (hskp29 | hskp22),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[105, 6877])).
% 3.78/2.92 tff(7362,plain,
% 3.78/2.92 (hskp22),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[7361, 7360])).
% 3.78/2.92 tff(7363,plain,
% 3.78/2.92 (~c3_1(a633)),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[3974, 7362])).
% 3.78/2.92 tff(7364,plain,
% 3.78/2.92 (c1_1(a633)),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[3962, 7362])).
% 3.78/2.92 tff(7365,plain,
% 3.78/2.92 (~hskp0),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[7008, 7312, 7313, 7311])).
% 3.78/2.92 tff(7366,plain,
% 3.78/2.92 (~hskp18),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[7142, 7338, 726, 7365, 7337, 7336])).
% 3.78/2.92 tff(7367,plain,
% 3.78/2.92 (~c2_1(a633)),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[4564, 7360, 107, 7366, 7364, 7363, 1796])).
% 3.78/2.92 tff(7368,plain,
% 3.78/2.92 (~c0_1(a633)),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[3968, 7362])).
% 3.78/2.92 tff(7369,plain,
% 3.78/2.92 ($false),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[5135, 107, 6877, 7364, 7338, 7337, 7368, 7336, 32, 7367])).
% 3.78/2.92 tff(7370,plain,(hskp12 | hskp26 | c0_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.78/2.92 tff(7371,plain,
% 3.78/2.92 (hskp12),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[7370, 726, 1])).
% 3.78/2.92 tff(7372,plain,
% 3.78/2.92 (~c3_1(a600)),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[741, 7371])).
% 3.78/2.92 tff(7373,plain,
% 3.78/2.92 (~hskp22),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[7182, 7371, 1077, 1078, 1012])).
% 3.78/2.92 tff(7374,plain,
% 3.78/2.92 (hskp14),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[772, 7371, 7373])).
% 3.78/2.92 tff(7375,plain,
% 3.78/2.92 (~c3_1(a603)),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[205, 7374])).
% 3.78/2.92 tff(7376,plain,
% 3.78/2.92 (c2_1(a600)),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[752, 7371])).
% 3.78/2.92 tff(7377,plain,
% 3.78/2.92 (c0_1(a600)),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[763, 7371])).
% 3.78/2.92 tff(7378,plain,
% 3.78/2.92 (~c1_1(a603)),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[171, 7374])).
% 3.78/2.92 tff(7379,plain,
% 3.78/2.92 (c0_1(a603)),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[182, 7374])).
% 3.78/2.92 tff(7380,plain,
% 3.78/2.92 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | c3_1(a600) | (~ndr1_0) | (~c0_1(a600)) | (~c1_1(a600)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp3 | c3_1(a600) | (~ndr1_0) | (~c0_1(a600)) | (~c1_1(a600)))),
% 3.78/2.92 inference(rewrite,[status(thm)],[])).
% 3.78/2.92 tff(7381,plain,
% 3.78/2.92 ((hskp17 | hskp3 | (~ndr1_0) | c3_1(a600) | (~c1_1(a600)) | (~c0_1(a600))) <=> (hskp17 | hskp3 | c3_1(a600) | (~ndr1_0) | (~c0_1(a600)) | (~c1_1(a600)))),
% 3.78/2.92 inference(rewrite,[status(thm)],[])).
% 3.78/2.92 tff(7382,plain,
% 3.78/2.92 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c3_1(a600) | (~c1_1(a600)) | (~c0_1(a600)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | c3_1(a600) | (~ndr1_0) | (~c0_1(a600)) | (~c1_1(a600))))),
% 3.78/2.92 inference(monotonicity,[status(thm)],[7381])).
% 3.78/2.92 tff(7383,plain,
% 3.78/2.92 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c3_1(a600) | (~c1_1(a600)) | (~c0_1(a600)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp3 | c3_1(a600) | (~ndr1_0) | (~c0_1(a600)) | (~c1_1(a600)))),
% 3.78/2.92 inference(transitivity,[status(thm)],[7382, 7380])).
% 3.78/2.92 tff(7384,plain,
% 3.78/2.92 ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c3_1(a600) | (~c1_1(a600)) | (~c0_1(a600)))),
% 3.78/2.92 inference(quant_inst,[status(thm)],[])).
% 3.78/2.92 tff(7385,plain,
% 3.78/2.92 ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp17 | hskp3 | c3_1(a600) | (~ndr1_0) | (~c0_1(a600)) | (~c1_1(a600))),
% 3.78/2.92 inference(modus_ponens,[status(thm)],[7384, 7383])).
% 3.78/2.92 tff(7386,plain,
% 3.78/2.92 (hskp3 | (~c1_1(a600))),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[7385, 107, 6877, 4753, 4745, 2368])).
% 3.78/2.92 tff(7387,plain,
% 3.78/2.92 (~c1_1(a600)),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[7386, 306])).
% 3.78/2.92 tff(7388,plain,
% 3.78/2.92 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | c1_1(a600))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | c1_1(a600))),
% 3.78/2.92 inference(rewrite,[status(thm)],[])).
% 3.78/2.92 tff(7389,plain,
% 3.78/2.92 ((hskp4 | hskp3 | (~ndr1_0) | c1_1(a600) | c3_1(a600) | (~c2_1(a600))) <=> (hskp4 | hskp3 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | c1_1(a600))),
% 3.78/2.92 inference(rewrite,[status(thm)],[])).
% 3.78/2.92 tff(7390,plain,
% 3.78/2.92 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a600) | c3_1(a600) | (~c2_1(a600)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | c1_1(a600)))),
% 3.78/2.92 inference(monotonicity,[status(thm)],[7389])).
% 3.78/2.92 tff(7391,plain,
% 3.78/2.92 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a600) | c3_1(a600) | (~c2_1(a600)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | c1_1(a600))),
% 3.78/2.92 inference(transitivity,[status(thm)],[7390, 7388])).
% 3.78/2.92 tff(7392,plain,
% 3.78/2.92 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a600) | c3_1(a600) | (~c2_1(a600)))),
% 3.78/2.92 inference(quant_inst,[status(thm)],[])).
% 3.78/2.92 tff(7393,plain,
% 3.78/2.92 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | c1_1(a600)),
% 3.78/2.92 inference(modus_ponens,[status(thm)],[7392, 7391])).
% 3.78/2.92 tff(7394,plain,
% 3.78/2.92 (hskp4 | hskp3 | c1_1(a600)),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[7393, 107, 4752, 4745, 840])).
% 3.78/2.92 tff(7395,plain,
% 3.78/2.92 (hskp4),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[7394, 306, 7387])).
% 3.78/2.92 tff(7396,plain,
% 3.78/2.92 (~c2_1(a588)),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[121, 7395])).
% 3.78/2.92 tff(7397,plain,
% 3.78/2.92 (~c1_1(a588)),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[127, 7395])).
% 3.78/2.92 tff(7398,plain,
% 3.78/2.92 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c3_1(a600) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c3_1(a588)) | (~c0_1(a600)) | c1_1(a600))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c3_1(a600) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c3_1(a588)) | (~c0_1(a600)) | c1_1(a600))),
% 3.78/2.92 inference(rewrite,[status(thm)],[])).
% 3.78/2.92 tff(7399,plain,
% 3.78/2.92 ((hskp3 | (~ndr1_0) | c1_1(a600) | c3_1(a600) | (~c0_1(a600)) | c1_1(a588) | c2_1(a588) | (~c3_1(a588))) <=> (hskp3 | c3_1(a600) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c3_1(a588)) | (~c0_1(a600)) | c1_1(a600))),
% 3.78/2.92 inference(rewrite,[status(thm)],[])).
% 3.78/2.92 tff(7400,plain,
% 3.78/2.92 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a600) | c3_1(a600) | (~c0_1(a600)) | c1_1(a588) | c2_1(a588) | (~c3_1(a588)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c3_1(a600) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c3_1(a588)) | (~c0_1(a600)) | c1_1(a600)))),
% 3.78/2.92 inference(monotonicity,[status(thm)],[7399])).
% 3.78/2.92 tff(7401,plain,
% 3.78/2.92 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a600) | c3_1(a600) | (~c0_1(a600)) | c1_1(a588) | c2_1(a588) | (~c3_1(a588)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c3_1(a600) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c3_1(a588)) | (~c0_1(a600)) | c1_1(a600))),
% 3.78/2.92 inference(transitivity,[status(thm)],[7400, 7398])).
% 3.78/2.92 tff(7402,plain,
% 3.78/2.92 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a600) | c3_1(a600) | (~c0_1(a600)) | c1_1(a588) | c2_1(a588) | (~c3_1(a588)))),
% 3.78/2.92 inference(quant_inst,[status(thm)],[])).
% 3.78/2.92 tff(7403,plain,
% 3.78/2.92 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c3_1(a600) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c3_1(a588)) | (~c0_1(a600)) | c1_1(a600)),
% 3.78/2.92 inference(modus_ponens,[status(thm)],[7402, 7401])).
% 3.78/2.92 tff(7404,plain,
% 3.78/2.92 (~c3_1(a588)),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[7403, 107, 306, 4753, 4745, 7397, 7396, 316, 7387])).
% 3.78/2.92 tff(7405,plain,
% 3.78/2.92 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a600) | c2_1(a603))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a600) | c2_1(a603))),
% 3.78/2.92 inference(rewrite,[status(thm)],[])).
% 3.78/2.92 tff(7406,plain,
% 3.78/2.92 ((hskp26 | (~ndr1_0) | c1_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c3_1(a603) | c1_1(a603) | c2_1(a603)) <=> (hskp26 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a600) | c2_1(a603))),
% 3.78/2.92 inference(rewrite,[status(thm)],[])).
% 3.78/2.92 tff(7407,plain,
% 3.78/2.92 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c3_1(a603) | c1_1(a603) | c2_1(a603))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a600) | c2_1(a603)))),
% 3.78/2.92 inference(monotonicity,[status(thm)],[7406])).
% 3.78/2.92 tff(7408,plain,
% 3.78/2.92 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c3_1(a603) | c1_1(a603) | c2_1(a603))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a600) | c2_1(a603))),
% 3.78/2.92 inference(transitivity,[status(thm)],[7407, 7405])).
% 3.78/2.92 tff(7409,plain,
% 3.78/2.92 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp26 | (~ndr1_0) | c1_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c3_1(a603) | c1_1(a603) | c2_1(a603))),
% 3.78/2.92 inference(quant_inst,[status(thm)],[])).
% 3.78/2.92 tff(7410,plain,
% 3.78/2.92 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp26 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a600) | c2_1(a603)),
% 3.78/2.92 inference(modus_ponens,[status(thm)],[7409, 7408])).
% 3.78/2.92 tff(7411,plain,
% 3.78/2.92 (c2_1(a603)),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[7410, 726, 107, 4753, 4752, 998, 997, 995, 7387])).
% 3.78/2.92 tff(7412,plain,
% 3.78/2.92 ($false),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[4932, 726, 107, 1009, 998, 7397, 7396, 995, 7411, 7404])).
% 3.78/2.92 tff(7413,plain,(hskp3 | hskp26 | (~c0_1(a603)) | c1_1(a603) | (~c0_1(a600)) | (~c2_1(a600)) | c3_1(a603) | c3_1(a600)), inference(lemma,lemma(discharge,[]))).
% 3.78/2.92 tff(7414,plain,
% 3.78/2.92 (hskp3),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[7413, 726, 7379, 7378, 7377, 7376, 7375, 7372])).
% 3.78/2.92 tff(7415,plain,
% 3.78/2.92 (~c1_1(a587)),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[939, 7414])).
% 3.78/2.92 tff(7416,plain,
% 3.78/2.92 (c2_1(a587)),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[950, 7414])).
% 3.78/2.92 tff(7417,plain,
% 3.78/2.92 (c0_1(a587)),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[961, 7414])).
% 3.78/2.92 tff(7418,plain,
% 3.78/2.92 (c2_1(a603)),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[1006, 726, 107, 7417, 7416, 7378, 7375, 7415, 995])).
% 3.78/2.92 tff(7419,plain,
% 3.78/2.92 (~hskp20),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[7320, 7418, 726, 7378, 7379])).
% 3.78/2.92 tff(7420,plain,
% 3.78/2.92 (hskp7),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[7328, 7419, 7301, 1])).
% 3.78/2.92 tff(7421,plain,
% 3.78/2.92 (~c3_1(a592)),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[811, 7420])).
% 3.78/2.92 tff(7422,plain,
% 3.78/2.92 (~c0_1(a592)),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[817, 7420])).
% 3.78/2.92 tff(7423,plain,
% 3.78/2.92 (~c1_1(a592)),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[1398, 107, 7379, 1078, 1077, 7375, 1012, 7422, 7421, 258, 7418])).
% 3.78/2.92 tff(7424,plain,
% 3.78/2.92 (hskp2),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[1405, 107, 7378, 7375, 7422, 7421, 200, 7423, 7418])).
% 3.78/2.92 tff(7425,plain,
% 3.78/2.92 (~c3_1(a586)),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[218, 7424])).
% 3.78/2.92 tff(7426,plain,
% 3.78/2.92 (c1_1(a586)),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[229, 7424])).
% 3.78/2.92 tff(7427,plain,
% 3.78/2.92 (c0_1(a586)),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[4817, 7426, 7417, 7416, 7415, 1078, 1077, 7374, 1012, 7425, 726])).
% 3.78/2.92 tff(7428,plain,
% 3.78/2.92 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp16 | (~c1_1(a607)) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a607) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp16 | (~c1_1(a607)) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a607) | (~c3_1(a607)))),
% 3.78/2.92 inference(rewrite,[status(thm)],[])).
% 3.78/2.92 tff(7429,plain,
% 3.78/2.92 ((hskp16 | (~ndr1_0) | c3_1(a586) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a607) | (~c1_1(a607)) | (~c3_1(a607))) <=> (hskp16 | (~c1_1(a607)) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a607) | (~c3_1(a607)))),
% 3.78/2.92 inference(rewrite,[status(thm)],[])).
% 3.78/2.92 tff(7430,plain,
% 3.78/2.92 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a586) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a607) | (~c1_1(a607)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp16 | (~c1_1(a607)) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a607) | (~c3_1(a607))))),
% 3.78/2.92 inference(monotonicity,[status(thm)],[7429])).
% 3.78/2.92 tff(7431,plain,
% 3.78/2.92 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a586) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a607) | (~c1_1(a607)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp16 | (~c1_1(a607)) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a607) | (~c3_1(a607)))),
% 3.78/2.92 inference(transitivity,[status(thm)],[7430, 7428])).
% 3.78/2.92 tff(7432,plain,
% 3.78/2.92 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a586) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a607) | (~c1_1(a607)) | (~c3_1(a607)))),
% 3.78/2.92 inference(quant_inst,[status(thm)],[])).
% 3.78/2.92 tff(7433,plain,
% 3.78/2.92 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp16 | (~c1_1(a607)) | c3_1(a586) | (~ndr1_0) | (~c1_1(a586)) | (~c0_1(a586)) | c0_1(a607) | (~c3_1(a607))),
% 3.78/2.92 inference(modus_ponens,[status(thm)],[7432, 7431])).
% 3.78/2.92 tff(7434,plain,
% 3.78/2.92 (hskp16),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[7433, 107, 7301, 7426, 6876, 7425, 1425, 1, 7427])).
% 3.78/2.92 tff(7435,plain,
% 3.78/2.92 (~c2_1(a606)),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[1111, 7434])).
% 3.78/2.92 tff(7436,plain,
% 3.78/2.92 (c1_1(a606)),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[1088, 7434])).
% 3.78/2.92 tff(7437,plain,
% 3.78/2.92 (c0_1(a606)),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[7265, 7436, 7417, 7416, 7435, 7415])).
% 3.78/2.92 tff(7438,plain,
% 3.78/2.92 (c2_1(a592)),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[828, 7420])).
% 3.78/2.92 tff(7439,plain,
% 3.78/2.92 (hskp29),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[2258, 7373])).
% 3.78/2.92 tff(7440,plain,
% 3.78/2.92 (c3_1(a678)),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[2269, 7439])).
% 3.78/2.92 tff(7441,plain,
% 3.78/2.92 (c0_1(a678)),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[2291, 7439])).
% 3.78/2.92 tff(7442,plain,
% 3.78/2.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~c2_1(a607)) | c0_1(a592) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c2_1(a592)) | c1_1(a592) | c0_1(a607) | (~c3_1(a607)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (~c2_1(a607)) | c0_1(a592) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c2_1(a592)) | c1_1(a592) | c0_1(a607) | (~c3_1(a607)))),
% 3.78/2.92 inference(rewrite,[status(thm)],[])).
% 3.78/2.92 tff(7443,plain,
% 3.78/2.92 (((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a607) | (~c3_1(a607)) | (~c2_1(a607)) | c1_1(a592) | c0_1(a592) | (~c2_1(a592))) <=> ((~c2_1(a607)) | c0_1(a592) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c2_1(a592)) | c1_1(a592) | c0_1(a607) | (~c3_1(a607)))),
% 3.78/2.92 inference(rewrite,[status(thm)],[])).
% 3.78/2.92 tff(7444,plain,
% 3.78/2.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a607) | (~c3_1(a607)) | (~c2_1(a607)) | c1_1(a592) | c0_1(a592) | (~c2_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~c2_1(a607)) | c0_1(a592) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c2_1(a592)) | c1_1(a592) | c0_1(a607) | (~c3_1(a607))))),
% 3.78/2.92 inference(monotonicity,[status(thm)],[7443])).
% 3.78/2.92 tff(7445,plain,
% 3.78/2.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a607) | (~c3_1(a607)) | (~c2_1(a607)) | c1_1(a592) | c0_1(a592) | (~c2_1(a592)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (~c2_1(a607)) | c0_1(a592) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c2_1(a592)) | c1_1(a592) | c0_1(a607) | (~c3_1(a607)))),
% 3.78/2.92 inference(transitivity,[status(thm)],[7444, 7442])).
% 3.78/2.92 tff(7446,plain,
% 3.78/2.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a607) | (~c3_1(a607)) | (~c2_1(a607)) | c1_1(a592) | c0_1(a592) | (~c2_1(a592)))),
% 3.78/2.92 inference(quant_inst,[status(thm)],[])).
% 3.78/2.92 tff(7447,plain,
% 3.78/2.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (~c2_1(a607)) | c0_1(a592) | (~ndr1_0) | (~c3_1(a678)) | (~c1_1(a678)) | (~c0_1(a678)) | (~c2_1(a592)) | c1_1(a592) | c0_1(a607) | (~c3_1(a607))),
% 3.78/2.92 inference(modus_ponens,[status(thm)],[7446, 7445])).
% 3.78/2.92 tff(7448,plain,
% 3.78/2.92 (~c1_1(a678)),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[7447, 107, 7441, 7440, 7301, 7438, 6959, 7422, 65, 7423, 1])).
% 3.78/2.92 tff(7449,plain,
% 3.78/2.92 (c2_1(a586)),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[1474, 7424])).
% 3.78/2.92 tff(7450,plain,
% 3.78/2.92 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~c1_1(a607)) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a607) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | (~c1_1(a607)) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a607) | (~c3_1(a607)))),
% 3.78/2.92 inference(rewrite,[status(thm)],[])).
% 3.78/2.92 tff(7451,plain,
% 3.78/2.92 ((hskp15 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a607) | (~c1_1(a607)) | (~c3_1(a607))) <=> (hskp15 | (~c1_1(a607)) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a607) | (~c3_1(a607)))),
% 3.78/2.92 inference(rewrite,[status(thm)],[])).
% 3.78/2.92 tff(7452,plain,
% 3.78/2.92 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a607) | (~c1_1(a607)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~c1_1(a607)) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a607) | (~c3_1(a607))))),
% 3.78/2.92 inference(monotonicity,[status(thm)],[7451])).
% 3.78/2.92 tff(7453,plain,
% 3.78/2.92 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a607) | (~c1_1(a607)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | (~c1_1(a607)) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a607) | (~c3_1(a607)))),
% 3.78/2.92 inference(transitivity,[status(thm)],[7452, 7450])).
% 3.78/2.92 tff(7454,plain,
% 3.78/2.92 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a586) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a607) | (~c1_1(a607)) | (~c3_1(a607)))),
% 3.78/2.92 inference(quant_inst,[status(thm)],[])).
% 3.78/2.92 tff(7455,plain,
% 3.78/2.92 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | (~c1_1(a607)) | c3_1(a586) | (~ndr1_0) | (~c2_1(a586)) | (~c1_1(a586)) | c0_1(a607) | (~c3_1(a607))),
% 3.78/2.92 inference(modus_ponens,[status(thm)],[7454, 7453])).
% 3.78/2.92 tff(7456,plain,
% 3.78/2.92 (hskp15),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[7455, 107, 7301, 7426, 7449, 6876, 7425, 2690, 1])).
% 3.78/2.92 tff(7457,plain,
% 3.78/2.92 (~c0_1(a604)),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[1591, 7456])).
% 3.78/2.92 tff(7458,plain,
% 3.78/2.92 (c1_1(a604)),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[1613, 7456])).
% 3.78/2.92 tff(7459,plain,
% 3.78/2.92 (c2_1(a678)),
% 3.78/2.92 inference(unit_resolution,[status(thm)],[2280, 7439])).
% 3.78/2.92 tff(7460,plain,
% 3.78/2.92 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a604) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c2_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a604) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c2_1(a604) | (~c1_1(a604)))),
% 3.78/2.92 inference(rewrite,[status(thm)],[])).
% 3.78/2.93 tff(7461,plain,
% 3.78/2.93 ((hskp17 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604))) <=> (hskp17 | c0_1(a604) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c2_1(a604) | (~c1_1(a604)))),
% 3.78/2.93 inference(rewrite,[status(thm)],[])).
% 3.78/2.93 tff(7462,plain,
% 3.78/2.93 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a604) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c2_1(a604) | (~c1_1(a604))))),
% 3.78/2.93 inference(monotonicity,[status(thm)],[7461])).
% 3.78/2.93 tff(7463,plain,
% 3.78/2.93 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a604) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c2_1(a604) | (~c1_1(a604)))),
% 3.78/2.93 inference(transitivity,[status(thm)],[7462, 7460])).
% 3.78/2.93 tff(7464,plain,
% 3.78/2.93 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a678) | (~c2_1(a678)) | (~c0_1(a678)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)))),
% 3.78/2.93 inference(quant_inst,[status(thm)],[])).
% 3.78/2.93 tff(7465,plain,
% 3.78/2.93 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a604) | (~ndr1_0) | (~c2_1(a678)) | c1_1(a678) | (~c0_1(a678)) | c2_1(a604) | (~c1_1(a604))),
% 3.78/2.93 inference(modus_ponens,[status(thm)],[7464, 7463])).
% 3.78/2.93 tff(7466,plain,
% 3.78/2.93 (c2_1(a604)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[7465, 107, 6877, 7441, 7459, 7458, 7457, 32, 7448])).
% 3.78/2.93 tff(7467,plain,
% 3.78/2.93 ((~hskp0) | (~c0_1(a678)) | (~c2_1(a678)) | c1_1(a678)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[3804, 6877])).
% 3.78/2.93 tff(7468,plain,
% 3.78/2.93 (~hskp0),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[7467, 7448, 7459, 7441])).
% 3.78/2.93 tff(7469,plain,
% 3.78/2.93 (~hskp18),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[7142, 7468, 726, 7417, 7416, 7415])).
% 3.78/2.93 tff(7470,plain,
% 3.78/2.93 (hskp8),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[6250, 7469, 7420])).
% 3.78/2.93 tff(7471,plain,
% 3.78/2.93 (c3_1(a593)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[511, 7470])).
% 3.78/2.93 tff(7472,plain,
% 3.78/2.93 (c1_1(a593)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[522, 7470])).
% 3.78/2.93 tff(7473,plain,
% 3.78/2.93 (c3_1(a604)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[1602, 7456])).
% 3.78/2.93 tff(7474,plain,
% 3.78/2.93 (~c0_1(a593)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[6802, 107, 7473, 7472, 7471, 7438, 7457, 7422, 65, 7423, 7466])).
% 3.78/2.93 tff(7475,plain,
% 3.78/2.93 (~c2_1(a593)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[555, 7470])).
% 3.78/2.93 tff(7476,plain,
% 3.78/2.93 (~c3_1(a606)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[1075, 7434])).
% 3.78/2.93 tff(7477,plain,
% 3.78/2.93 ($false),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[6810, 107, 7472, 7435, 7476, 7475, 7422, 7421, 1463, 7474, 7423, 7437])).
% 3.78/2.93 tff(7478,plain,(hskp26 | c0_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.78/2.93 tff(7479,plain,
% 3.78/2.93 (hskp26),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[7478, 1])).
% 3.78/2.93 tff(7480,plain,
% 3.78/2.93 (c2_1(a583)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[391, 7479])).
% 3.78/2.93 tff(7481,plain,
% 3.78/2.93 (c1_1(a583)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[351, 7479])).
% 3.78/2.93 tff(7482,plain,
% 3.78/2.93 (c0_1(a583)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[362, 7479])).
% 3.78/2.93 tff(7483,plain,
% 3.78/2.93 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a607)))),
% 3.78/2.93 inference(rewrite,[status(thm)],[])).
% 3.78/2.93 tff(7484,plain,
% 3.78/2.93 ((hskp10 | (~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c1_1(a607)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583))) <=> (hskp10 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a607)))),
% 3.78/2.93 inference(rewrite,[status(thm)],[])).
% 3.78/2.93 tff(7485,plain,
% 3.78/2.93 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c1_1(a607)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a607))))),
% 3.78/2.93 inference(monotonicity,[status(thm)],[7484])).
% 3.78/2.93 tff(7486,plain,
% 3.78/2.93 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c1_1(a607)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a607)))),
% 3.78/2.93 inference(transitivity,[status(thm)],[7485, 7483])).
% 3.78/2.93 tff(7487,plain,
% 3.78/2.93 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c1_1(a607)) | (~c1_1(a583)) | (~c2_1(a583)) | (~c0_1(a583)))),
% 3.78/2.93 inference(quant_inst,[status(thm)],[])).
% 3.78/2.93 tff(7488,plain,
% 3.78/2.93 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c2_1(a583)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c3_1(a607))),
% 3.78/2.93 inference(modus_ponens,[status(thm)],[7487, 7486])).
% 3.78/2.93 tff(7489,plain,
% 3.78/2.93 (hskp10),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[7488, 107, 7482, 7481, 7480, 7301, 6876, 6959, 21])).
% 3.78/2.93 tff(7490,plain,
% 3.78/2.93 (~c1_1(a598)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[911, 7489])).
% 3.78/2.93 tff(7491,plain,
% 3.78/2.93 (c3_1(a598)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[881, 7489])).
% 3.78/2.93 tff(7492,plain,
% 3.78/2.93 (c0_1(a598)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[892, 7489])).
% 3.78/2.93 tff(7493,plain,
% 3.78/2.93 (hskp11 | hskp23),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[1688, 107, 7492, 7491, 7490, 1648])).
% 3.78/2.93 tff(7494,plain,
% 3.78/2.93 (hskp23),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[7493, 1638])).
% 3.78/2.93 tff(7495,plain,
% 3.78/2.93 (~c1_1(a636)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[475, 7494])).
% 3.78/2.93 tff(7496,plain,
% 3.78/2.93 (~c0_1(a636)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[481, 7494])).
% 3.78/2.93 tff(7497,plain,
% 3.78/2.93 (c3_1(a636)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[492, 7494])).
% 3.78/2.93 tff(7498,plain,
% 3.78/2.93 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | c0_1(a636) | c1_1(a636) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607) | (~c3_1(a636)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a636) | c1_1(a636) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607) | (~c3_1(a636)))),
% 3.78/2.93 inference(rewrite,[status(thm)],[])).
% 3.78/2.93 tff(7499,plain,
% 3.78/2.93 ((hskp8 | (~ndr1_0) | c0_1(a607) | (~c2_1(a607)) | (~c1_1(a607)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636))) <=> (hskp8 | c0_1(a636) | c1_1(a636) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607) | (~c3_1(a636)))),
% 3.78/2.93 inference(rewrite,[status(thm)],[])).
% 3.78/2.93 tff(7500,plain,
% 3.78/2.93 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a607) | (~c2_1(a607)) | (~c1_1(a607)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | c0_1(a636) | c1_1(a636) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607) | (~c3_1(a636))))),
% 3.78/2.93 inference(monotonicity,[status(thm)],[7499])).
% 3.78/2.93 tff(7501,plain,
% 3.78/2.93 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a607) | (~c2_1(a607)) | (~c1_1(a607)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a636) | c1_1(a636) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607) | (~c3_1(a636)))),
% 3.78/2.93 inference(transitivity,[status(thm)],[7500, 7498])).
% 3.78/2.93 tff(7502,plain,
% 3.78/2.93 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a607) | (~c2_1(a607)) | (~c1_1(a607)) | c1_1(a636) | c0_1(a636) | (~c3_1(a636)))),
% 3.78/2.93 inference(quant_inst,[status(thm)],[])).
% 3.78/2.93 tff(7503,plain,
% 3.78/2.93 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a636) | c1_1(a636) | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607) | (~c3_1(a636))),
% 3.78/2.93 inference(modus_ponens,[status(thm)],[7502, 7501])).
% 3.78/2.93 tff(7504,plain,
% 3.78/2.93 (hskp8),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[7503, 107, 7497, 7496, 7495, 6876, 6959, 1317, 1])).
% 3.78/2.93 tff(7505,plain,
% 3.78/2.93 (~c2_1(a593)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[555, 7504])).
% 3.78/2.93 tff(7506,plain,
% 3.78/2.93 (c1_1(a593)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[522, 7504])).
% 3.78/2.93 tff(7507,plain,
% 3.78/2.93 (c3_1(a593)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[511, 7504])).
% 3.78/2.93 tff(7508,plain,
% 3.78/2.93 (~hskp0),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[7008, 7507, 7506, 7505])).
% 3.78/2.93 tff(7509,plain,
% 3.78/2.93 (~c0_1(a593)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[7015, 1638, 107, 7508, 7506, 7505, 2347])).
% 3.78/2.93 tff(7510,plain,
% 3.78/2.93 (hskp3),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[5154, 107, 6877, 7506, 7507, 7505, 3420])).
% 3.78/2.93 tff(7511,plain,
% 3.78/2.93 (~c1_1(a587)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[939, 7510])).
% 3.78/2.93 tff(7512,plain,
% 3.78/2.93 (c2_1(a587)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[950, 7510])).
% 3.78/2.93 tff(7513,plain,
% 3.78/2.93 (c0_1(a587)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[961, 7510])).
% 3.78/2.93 tff(7514,plain,
% 3.78/2.93 ($false),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[5232, 107, 6877, 7506, 7513, 7512, 7505, 7511, 32, 7509])).
% 3.78/2.93 tff(7515,plain,(hskp11 | c0_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.78/2.93 tff(7516,plain,
% 3.78/2.93 (hskp11),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[7515, 1])).
% 3.78/2.93 tff(7517,plain,
% 3.78/2.93 (~c1_1(a599)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[428, 7516])).
% 3.78/2.93 tff(7518,plain,
% 3.78/2.93 (c2_1(a599)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[439, 7516])).
% 3.78/2.93 tff(7519,plain,
% 3.78/2.93 (hskp12),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[6965, 107, 7482, 7481, 7480, 6876, 6959, 2727, 1])).
% 3.78/2.93 tff(7520,plain,
% 3.78/2.93 (c3_1(a599)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[422, 7516])).
% 3.78/2.93 tff(7521,plain,
% 3.78/2.93 (~hskp22),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[7182, 7520, 7519, 7518, 7517])).
% 3.78/2.93 tff(7522,plain,
% 3.78/2.93 (hskp29),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[2258, 7521])).
% 3.78/2.93 tff(7523,plain,
% 3.78/2.93 (c3_1(a678)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[2269, 7522])).
% 3.78/2.93 tff(7524,plain,
% 3.78/2.93 (c2_1(a678)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[2280, 7522])).
% 3.78/2.93 tff(7525,plain,
% 3.78/2.93 (c0_1(a678)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[2291, 7522])).
% 3.78/2.93 tff(7526,plain,
% 3.78/2.93 (c2_1(a598)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[7058, 107, 7525, 7524, 7523, 7491, 6876, 6959, 7490, 11, 1])).
% 3.78/2.93 tff(7527,plain,
% 3.78/2.93 (~c3_1(a600)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[741, 7519])).
% 3.78/2.93 tff(7528,plain,
% 3.78/2.93 (c2_1(a600)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[752, 7519])).
% 3.78/2.93 tff(7529,plain,
% 3.78/2.93 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~c1_1(a607)) | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c1_1(a600)) | c0_1(a607) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | (~c1_1(a607)) | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c1_1(a600)) | c0_1(a607) | (~c3_1(a607)))),
% 3.78/2.93 inference(rewrite,[status(thm)],[])).
% 3.78/2.93 tff(7530,plain,
% 3.78/2.93 ((hskp15 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c1_1(a600)) | c0_1(a607) | (~c1_1(a607)) | (~c3_1(a607))) <=> (hskp15 | (~c1_1(a607)) | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c1_1(a600)) | c0_1(a607) | (~c3_1(a607)))),
% 3.78/2.93 inference(rewrite,[status(thm)],[])).
% 3.78/2.93 tff(7531,plain,
% 3.78/2.93 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c1_1(a600)) | c0_1(a607) | (~c1_1(a607)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~c1_1(a607)) | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c1_1(a600)) | c0_1(a607) | (~c3_1(a607))))),
% 3.78/2.93 inference(monotonicity,[status(thm)],[7530])).
% 3.78/2.93 tff(7532,plain,
% 3.78/2.93 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c1_1(a600)) | c0_1(a607) | (~c1_1(a607)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | (~c1_1(a607)) | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c1_1(a600)) | c0_1(a607) | (~c3_1(a607)))),
% 3.78/2.93 inference(transitivity,[status(thm)],[7531, 7529])).
% 3.78/2.93 tff(7533,plain,
% 3.78/2.93 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a600) | (~c2_1(a600)) | (~c1_1(a600)) | c0_1(a607) | (~c1_1(a607)) | (~c3_1(a607)))),
% 3.78/2.93 inference(quant_inst,[status(thm)],[])).
% 3.78/2.93 tff(7534,plain,
% 3.78/2.93 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | (~c1_1(a607)) | c3_1(a600) | (~ndr1_0) | (~c2_1(a600)) | (~c1_1(a600)) | c0_1(a607) | (~c3_1(a607))),
% 3.78/2.93 inference(modus_ponens,[status(thm)],[7533, 7532])).
% 3.78/2.93 tff(7535,plain,
% 3.78/2.93 (hskp15 | (~c1_1(a600))),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[7534, 107, 7301, 7528, 6876, 7527, 2690, 1])).
% 3.78/2.93 tff(7536,plain,
% 3.78/2.93 (~c1_1(a600)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[7535, 3154])).
% 3.78/2.93 tff(7537,plain,
% 3.78/2.93 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~c1_1(a607)) | (~c2_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | c0_1(a599) | c0_1(a607))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | (~c1_1(a607)) | (~c2_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | c0_1(a599) | c0_1(a607))),
% 3.78/2.93 inference(rewrite,[status(thm)],[])).
% 3.78/2.93 tff(7538,plain,
% 3.78/2.93 ((hskp8 | (~ndr1_0) | c0_1(a607) | (~c2_1(a607)) | (~c1_1(a607)) | c1_1(a599) | c0_1(a599) | (~c3_1(a599))) <=> (hskp8 | (~c1_1(a607)) | (~c2_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | c0_1(a599) | c0_1(a607))),
% 3.78/2.93 inference(rewrite,[status(thm)],[])).
% 3.78/2.93 tff(7539,plain,
% 3.78/2.93 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a607) | (~c2_1(a607)) | (~c1_1(a607)) | c1_1(a599) | c0_1(a599) | (~c3_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~c1_1(a607)) | (~c2_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | c0_1(a599) | c0_1(a607)))),
% 3.78/2.93 inference(monotonicity,[status(thm)],[7538])).
% 3.78/2.93 tff(7540,plain,
% 3.78/2.93 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a607) | (~c2_1(a607)) | (~c1_1(a607)) | c1_1(a599) | c0_1(a599) | (~c3_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | (~c1_1(a607)) | (~c2_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | c0_1(a599) | c0_1(a607))),
% 3.78/2.93 inference(transitivity,[status(thm)],[7539, 7537])).
% 3.78/2.93 tff(7541,plain,
% 3.78/2.93 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c0_1(a607) | (~c2_1(a607)) | (~c1_1(a607)) | c1_1(a599) | c0_1(a599) | (~c3_1(a599)))),
% 3.78/2.93 inference(quant_inst,[status(thm)],[])).
% 3.78/2.93 tff(7542,plain,
% 3.78/2.93 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | (~c1_1(a607)) | (~c2_1(a607)) | c1_1(a599) | (~ndr1_0) | (~c3_1(a599)) | c0_1(a599) | c0_1(a607)),
% 3.78/2.93 inference(modus_ponens,[status(thm)],[7541, 7540])).
% 3.78/2.93 tff(7543,plain,
% 3.78/2.93 (hskp8 | c0_1(a599)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[7542, 107, 7520, 6876, 6959, 7517, 1317, 1])).
% 3.78/2.93 tff(7544,plain,
% 3.78/2.93 (c0_1(a599)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[7543, 1709])).
% 3.78/2.93 tff(7545,plain,
% 3.78/2.93 (c0_1(a600)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[763, 7519])).
% 3.78/2.93 tff(7546,plain,
% 3.78/2.93 (hskp27 | hskp8),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[2744, 107, 7545, 7528, 7527, 2080])).
% 3.78/2.93 tff(7547,plain,
% 3.78/2.93 (hskp27),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[7546, 1709])).
% 3.78/2.93 tff(7548,plain,
% 3.78/2.93 (c3_1(a611)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[620, 7547])).
% 3.78/2.93 tff(7549,plain,
% 3.78/2.93 (c1_1(a611)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[631, 7547])).
% 3.78/2.93 tff(7550,plain,
% 3.78/2.93 (c0_1(a611)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[642, 7547])).
% 3.78/2.93 tff(7551,plain,
% 3.78/2.93 (hskp15),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[2879, 107, 7550, 7549, 7548, 7520, 7517, 1993, 7544])).
% 3.78/2.93 tff(7552,plain,
% 3.78/2.93 (c3_1(a604)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[1602, 7551])).
% 3.78/2.93 tff(7553,plain,
% 3.78/2.93 (~c0_1(a604)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[1591, 7551])).
% 3.78/2.93 tff(7554,plain,
% 3.78/2.93 (hskp14),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[772, 7521, 7519])).
% 3.78/2.93 tff(7555,plain,
% 3.78/2.93 (~c3_1(a603)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[205, 7554])).
% 3.78/2.93 tff(7556,plain,
% 3.78/2.93 (c0_1(a603)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[182, 7554])).
% 3.78/2.93 tff(7557,plain,
% 3.78/2.93 (hskp8 | c2_1(a603)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[6979, 107, 7556, 7545, 7528, 7555, 7527, 4271])).
% 3.78/2.93 tff(7558,plain,
% 3.78/2.93 (c2_1(a603)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[7557, 1709])).
% 3.78/2.93 tff(7559,plain,
% 3.78/2.93 (~c1_1(a603)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[171, 7554])).
% 3.78/2.93 tff(7560,plain,
% 3.78/2.93 (c1_1(a604)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[1613, 7551])).
% 3.78/2.93 tff(7561,plain,
% 3.78/2.93 (c2_1(a604)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[3527, 107, 6877, 7560, 7556, 7553, 7559, 32, 7558])).
% 3.78/2.93 tff(7562,assumption,(c3_1(a611)), introduced(assumption)).
% 3.78/2.93 tff(7563,assumption,(c1_1(a611)), introduced(assumption)).
% 3.78/2.93 tff(7564,assumption,(c0_1(a611)), introduced(assumption)).
% 3.78/2.93 tff(7565,plain,
% 3.78/2.93 ($false),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[2909, 107, 7564, 7563, 7562, 3749, 2545, 3748, 3747, 2475, 65, 2538])).
% 3.78/2.93 tff(7566,plain,((~hskp19) | (~c0_1(a611)) | (~c1_1(a611)) | (~c3_1(a611)) | (~c3_1(a604)) | c0_1(a604) | (~c2_1(a604))), inference(lemma,lemma(discharge,[]))).
% 3.78/2.93 tff(7567,plain,
% 3.78/2.93 (~hskp19),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[7566, 7550, 7549, 7548, 7552, 7553, 7561])).
% 3.78/2.93 tff(7568,plain,
% 3.78/2.93 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp20 | hskp19 | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)))),
% 3.78/2.93 inference(rewrite,[status(thm)],[])).
% 3.78/2.93 tff(7569,plain,
% 3.78/2.93 ((hskp20 | hskp19 | (~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611))) <=> (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)))),
% 3.78/2.93 inference(rewrite,[status(thm)],[])).
% 3.78/2.93 tff(7570,plain,
% 3.78/2.93 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611))))),
% 3.78/2.93 inference(monotonicity,[status(thm)],[7569])).
% 3.78/2.93 tff(7571,plain,
% 3.78/2.93 (((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)))) <=> ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp20 | hskp19 | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611)))),
% 3.78/2.93 inference(transitivity,[status(thm)],[7570, 7568])).
% 3.78/2.93 tff(7572,plain,
% 3.78/2.93 ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(a611)) | (~c1_1(a611)) | (~c0_1(a611)))),
% 3.78/2.93 inference(quant_inst,[status(thm)],[])).
% 3.78/2.93 tff(7573,plain,
% 3.78/2.93 ((~![U: $i] : (hskp20 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp20 | hskp19 | (~ndr1_0) | (~c3_1(a611)) | (~c0_1(a611)) | (~c1_1(a611))),
% 3.78/2.93 inference(modus_ponens,[status(thm)],[7572, 7571])).
% 3.78/2.93 tff(7574,plain,
% 3.78/2.93 (hskp20 | hskp19),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[7573, 107, 7550, 7549, 7548, 3768])).
% 3.78/2.93 tff(7575,plain,
% 3.78/2.93 (hskp20),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[7574, 7567])).
% 3.78/2.93 tff(7576,plain,
% 3.78/2.93 (hskp16),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[5664, 7575, 7561, 7520, 7553, 7517, 7518, 7552])).
% 3.78/2.93 tff(7577,plain,
% 3.78/2.93 (~c2_1(a606)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[1111, 7576])).
% 3.78/2.93 tff(7578,plain,
% 3.78/2.93 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp19 | hskp13 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607))),
% 3.78/2.93 inference(rewrite,[status(thm)],[])).
% 3.78/2.93 tff(7579,plain,
% 3.78/2.93 ((hskp19 | hskp13 | (~ndr1_0) | c0_1(a607) | (~c2_1(a607)) | (~c1_1(a607))) <=> (hskp19 | hskp13 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607))),
% 3.78/2.93 inference(rewrite,[status(thm)],[])).
% 3.78/2.93 tff(7580,plain,
% 3.78/2.93 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c0_1(a607) | (~c2_1(a607)) | (~c1_1(a607)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607)))),
% 3.78/2.93 inference(monotonicity,[status(thm)],[7579])).
% 3.78/2.93 tff(7581,plain,
% 3.78/2.93 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c0_1(a607) | (~c2_1(a607)) | (~c1_1(a607)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp19 | hskp13 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607))),
% 3.78/2.93 inference(transitivity,[status(thm)],[7580, 7578])).
% 3.78/2.93 tff(7582,plain,
% 3.78/2.93 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c0_1(a607) | (~c2_1(a607)) | (~c1_1(a607)))),
% 3.78/2.93 inference(quant_inst,[status(thm)],[])).
% 3.78/2.93 tff(7583,plain,
% 3.78/2.93 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp19 | hskp13 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | c0_1(a607)),
% 3.78/2.93 inference(modus_ponens,[status(thm)],[7582, 7581])).
% 3.78/2.93 tff(7584,plain,
% 3.78/2.93 (hskp19 | hskp13 | (~c2_1(a607)) | c0_1(a607)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[7583, 107, 6876, 2564])).
% 3.78/2.93 tff(7585,plain,
% 3.78/2.93 (hskp13),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[7584, 7567, 6959, 1])).
% 3.78/2.93 tff(7586,plain,
% 3.78/2.93 (c1_1(a606)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[1088, 7576])).
% 3.78/2.93 tff(7587,plain,
% 3.78/2.93 (hskp3 | c3_1(a583)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[4026, 107, 6877, 1651, 1650, 2368])).
% 3.78/2.93 tff(7588,plain,
% 3.78/2.93 (c3_1(a583)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[7587, 306])).
% 3.78/2.93 tff(7589,plain,
% 3.78/2.93 (hskp15),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[4629, 7588, 1651, 1650, 1649])).
% 3.78/2.93 tff(7590,plain,
% 3.78/2.93 (c3_1(a604)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[1602, 7589])).
% 3.78/2.93 tff(7591,plain,
% 3.78/2.93 (c1_1(a604)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[1613, 7589])).
% 3.78/2.93 tff(7592,plain,
% 3.78/2.93 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c1_1(a604)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp3 | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c1_1(a604)))),
% 3.78/2.93 inference(rewrite,[status(thm)],[])).
% 3.78/2.93 tff(7593,plain,
% 3.78/2.93 ((hskp17 | hskp3 | (~ndr1_0) | c2_1(a604) | (~c3_1(a604)) | (~c1_1(a604))) <=> (hskp17 | hskp3 | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c1_1(a604)))),
% 3.78/2.93 inference(rewrite,[status(thm)],[])).
% 3.78/2.93 tff(7594,plain,
% 3.78/2.93 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c2_1(a604) | (~c3_1(a604)) | (~c1_1(a604)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c1_1(a604))))),
% 3.78/2.93 inference(monotonicity,[status(thm)],[7593])).
% 3.78/2.93 tff(7595,plain,
% 3.78/2.93 (((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c2_1(a604) | (~c3_1(a604)) | (~c1_1(a604)))) <=> ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp3 | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c1_1(a604)))),
% 3.78/2.93 inference(transitivity,[status(thm)],[7594, 7592])).
% 3.78/2.93 tff(7596,plain,
% 3.78/2.93 ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp3 | (~ndr1_0) | c2_1(a604) | (~c3_1(a604)) | (~c1_1(a604)))),
% 3.78/2.93 inference(quant_inst,[status(thm)],[])).
% 3.78/2.93 tff(7597,plain,
% 3.78/2.93 ((~![U: $i] : (hskp17 | hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp3 | (~ndr1_0) | (~c3_1(a604)) | c2_1(a604) | (~c1_1(a604))),
% 3.78/2.93 inference(modus_ponens,[status(thm)],[7596, 7595])).
% 3.78/2.93 tff(7598,plain,
% 3.78/2.93 (c2_1(a604)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[7597, 107, 6877, 306, 7591, 7590, 3420])).
% 3.78/2.93 tff(7599,plain,
% 3.78/2.93 (~c0_1(a604)),
% 3.78/2.93 inference(unit_resolution,[status(thm)],[1591, 7589])).
% 3.78/2.93 tff(7600,plain,
% 3.78/2.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a604) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a588)) | (~c2_1(a604)) | (~c1_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a604) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a588)) | (~c2_1(a604)) | (~c1_1(a604)))),
% 3.78/2.93 inference(rewrite,[status(thm)],[])).
% 3.78/2.93 tff(7601,plain,
% 3.78/2.93 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a588) | c2_1(a588) | (~c3_1(a588)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604))) <=> (c0_1(a604) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a588)) | (~c2_1(a604)) | (~c1_1(a604)))),
% 3.78/2.93 inference(rewrite,[status(thm)],[])).
% 3.78/2.93 tff(7602,plain,
% 3.78/2.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a588) | c2_1(a588) | (~c3_1(a588)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a604) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a588)) | (~c2_1(a604)) | (~c1_1(a604))))),
% 3.78/2.93 inference(monotonicity,[status(thm)],[7601])).
% 3.78/2.94 tff(7603,plain,
% 3.78/2.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a588) | c2_1(a588) | (~c3_1(a588)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a604) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a588)) | (~c2_1(a604)) | (~c1_1(a604)))),
% 3.78/2.94 inference(transitivity,[status(thm)],[7602, 7600])).
% 3.78/2.94 tff(7604,plain,
% 3.78/2.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a588) | c2_1(a588) | (~c3_1(a588)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))),
% 3.78/2.94 inference(quant_inst,[status(thm)],[])).
% 3.78/2.94 tff(7605,plain,
% 3.78/2.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a604) | c1_1(a588) | c2_1(a588) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a588)) | (~c2_1(a604)) | (~c1_1(a604))),
% 3.78/2.94 inference(modus_ponens,[status(thm)],[7604, 7603])).
% 3.78/2.94 tff(7606,plain,
% 3.78/2.94 (~c3_1(a588)),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[7605, 107, 2318, 2317, 2316, 7591, 7599, 7397, 7396, 11, 7598])).
% 3.78/2.94 tff(7607,plain,
% 3.78/2.94 (c0_1(a588)),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[138, 7395])).
% 3.78/2.94 tff(7608,plain,
% 3.78/2.94 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | c0_1(a604) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c3_1(a604)) | (~c2_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c0_1(a604) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c3_1(a604)) | (~c2_1(a604)))),
% 3.78/2.94 inference(rewrite,[status(thm)],[])).
% 3.78/2.94 tff(7609,plain,
% 3.78/2.94 ((hskp16 | (~ndr1_0) | c2_1(a588) | c3_1(a588) | (~c0_1(a588)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604))) <=> (hskp16 | c0_1(a604) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c3_1(a604)) | (~c2_1(a604)))),
% 3.78/2.94 inference(rewrite,[status(thm)],[])).
% 3.78/2.94 tff(7610,plain,
% 3.78/2.94 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a588) | c3_1(a588) | (~c0_1(a588)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | c0_1(a604) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c3_1(a604)) | (~c2_1(a604))))),
% 3.78/2.94 inference(monotonicity,[status(thm)],[7609])).
% 3.78/2.94 tff(7611,plain,
% 3.78/2.94 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a588) | c3_1(a588) | (~c0_1(a588)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c0_1(a604) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c3_1(a604)) | (~c2_1(a604)))),
% 3.78/2.94 inference(transitivity,[status(thm)],[7610, 7608])).
% 3.78/2.94 tff(7612,plain,
% 3.78/2.94 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a588) | c3_1(a588) | (~c0_1(a588)) | c0_1(a604) | (~c3_1(a604)) | (~c2_1(a604)))),
% 3.78/2.94 inference(quant_inst,[status(thm)],[])).
% 3.78/2.94 tff(7613,plain,
% 3.78/2.94 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c0_1(a604) | c2_1(a588) | (~ndr1_0) | (~c0_1(a588)) | c3_1(a588) | (~c3_1(a604)) | (~c2_1(a604))),
% 3.78/2.94 inference(modus_ponens,[status(thm)],[7612, 7611])).
% 3.78/2.94 tff(7614,plain,
% 3.78/2.94 (hskp16),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[7613, 107, 7590, 7607, 7599, 7396, 2125, 7598, 7606])).
% 3.78/2.94 tff(7615,plain,
% 3.78/2.94 (~c3_1(a606)),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[1075, 7614])).
% 3.78/2.94 tff(7616,plain,
% 3.78/2.94 (c1_1(a606)),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[1088, 7614])).
% 3.78/2.94 tff(7617,plain,
% 3.78/2.94 (c0_1(a606)),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[5737, 107, 7616, 4753, 4752, 463, 462, 7615, 4745, 461, 258])).
% 3.78/2.94 tff(7618,plain,
% 3.78/2.94 ($false),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[2374, 107, 6877, 306, 7616, 7615, 2368, 7617])).
% 3.78/2.94 tff(7619,plain,(hskp3 | (~c0_1(a600)) | (~c2_1(a600)) | (~c2_1(a599)) | (~c3_1(a599)) | c3_1(a600) | c1_1(a599) | (~c0_1(a678)) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a583)) | (~c1_1(a583)) | (~c2_1(a583))), inference(lemma,lemma(discharge,[]))).
% 3.78/2.94 tff(7620,plain,
% 3.78/2.94 (hskp3),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[7619, 7545, 7528, 7518, 7520, 7527, 7517, 7525, 7524, 7523, 7482, 7481, 7480])).
% 3.78/2.94 tff(7621,plain,
% 3.78/2.94 (~c1_1(a587)),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[939, 7620])).
% 3.78/2.94 tff(7622,plain,
% 3.78/2.94 (c2_1(a587)),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[950, 7620])).
% 3.78/2.94 tff(7623,plain,
% 3.78/2.94 (c0_1(a587)),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[961, 7620])).
% 3.78/2.94 tff(7624,plain,
% 3.78/2.94 (c0_1(a606)),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[7265, 7586, 7623, 7622, 7577, 7621])).
% 3.78/2.94 tff(7625,plain,
% 3.78/2.94 ($false),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[2553, 7624, 7586, 7520, 7561, 7518, 7517, 7553, 7525, 7524, 7523, 7585, 7577, 7552])).
% 3.78/2.94 tff(7626,plain,(hskp8 | c0_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.78/2.94 tff(7627,plain,
% 3.78/2.94 (hskp8),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[7626, 1])).
% 3.78/2.94 tff(7628,plain,
% 3.78/2.94 (c3_1(a593)),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[511, 7627])).
% 3.78/2.94 tff(7629,plain,
% 3.78/2.94 (c1_1(a593)),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[522, 7627])).
% 3.78/2.94 tff(7630,plain,
% 3.78/2.94 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | c1_1(a598) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a598)) | (~c0_1(a598)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a598) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a598)) | (~c0_1(a598)))),
% 3.78/2.94 inference(rewrite,[status(thm)],[])).
% 3.78/2.94 tff(7631,plain,
% 3.78/2.94 ((hskp15 | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c1_1(a598) | (~c3_1(a598)) | (~c0_1(a598))) <=> (hskp15 | c1_1(a598) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a598)) | (~c0_1(a598)))),
% 3.78/2.94 inference(rewrite,[status(thm)],[])).
% 3.78/2.94 tff(7632,plain,
% 3.78/2.94 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c1_1(a598) | (~c3_1(a598)) | (~c0_1(a598)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | c1_1(a598) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a598)) | (~c0_1(a598))))),
% 3.78/2.94 inference(monotonicity,[status(thm)],[7631])).
% 3.78/2.94 tff(7633,plain,
% 3.78/2.94 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c1_1(a598) | (~c3_1(a598)) | (~c0_1(a598)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a598) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a598)) | (~c0_1(a598)))),
% 3.78/2.94 inference(transitivity,[status(thm)],[7632, 7630])).
% 3.78/2.94 tff(7634,plain,
% 3.78/2.94 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a593)) | (~c1_1(a593)) | (~c0_1(a593)) | c1_1(a598) | (~c3_1(a598)) | (~c0_1(a598)))),
% 3.78/2.94 inference(quant_inst,[status(thm)],[])).
% 3.78/2.94 tff(7635,plain,
% 3.78/2.94 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | c1_1(a598) | (~ndr1_0) | (~c0_1(a593)) | (~c3_1(a593)) | (~c1_1(a593)) | (~c3_1(a598)) | (~c0_1(a598))),
% 3.78/2.94 inference(modus_ponens,[status(thm)],[7634, 7633])).
% 3.78/2.94 tff(7636,plain,
% 3.78/2.94 (hskp15 | (~c0_1(a593))),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[7635, 107, 7492, 7491, 7629, 7628, 7490, 1993])).
% 3.78/2.94 tff(7637,plain,
% 3.78/2.94 (~c0_1(a593)),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[7636, 3154])).
% 3.78/2.94 tff(7638,plain,
% 3.78/2.94 (~c2_1(a593)),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[555, 7627])).
% 3.78/2.94 tff(7639,plain,
% 3.78/2.94 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a600))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a600))),
% 3.78/2.94 inference(rewrite,[status(thm)],[])).
% 3.78/2.94 tff(7640,plain,
% 3.78/2.94 ((hskp17 | (~ndr1_0) | c1_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593))) <=> (hskp17 | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a600))),
% 3.78/2.94 inference(rewrite,[status(thm)],[])).
% 3.78/2.94 tff(7641,plain,
% 3.78/2.94 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a600)))),
% 3.78/2.94 inference(monotonicity,[status(thm)],[7640])).
% 3.78/2.94 tff(7642,plain,
% 3.78/2.94 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a600))),
% 3.78/2.94 inference(transitivity,[status(thm)],[7641, 7639])).
% 3.78/2.94 tff(7643,plain,
% 3.78/2.94 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a600) | (~c2_1(a600)) | (~c0_1(a600)) | c0_1(a593) | c2_1(a593) | (~c1_1(a593)))),
% 3.78/2.94 inference(quant_inst,[status(thm)],[])).
% 3.78/2.94 tff(7644,plain,
% 3.78/2.94 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp17 | c2_1(a593) | (~ndr1_0) | c0_1(a593) | (~c1_1(a593)) | (~c2_1(a600)) | (~c0_1(a600)) | c1_1(a600)),
% 3.78/2.94 inference(modus_ponens,[status(thm)],[7643, 7642])).
% 3.78/2.94 tff(7645,plain,
% 3.78/2.94 ($false),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[7644, 107, 6877, 7545, 7528, 7629, 7638, 32, 7637, 7536])).
% 3.78/2.94 tff(7646,plain,(hskp15 | c0_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.78/2.94 tff(7647,plain,
% 3.78/2.94 (hskp15),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[7646, 1])).
% 3.78/2.94 tff(7648,plain,
% 3.78/2.94 (~c0_1(a604)),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[1591, 7647])).
% 3.78/2.94 tff(7649,plain,
% 3.78/2.94 (c1_1(a604)),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[1613, 7647])).
% 3.78/2.94 tff(7650,plain,
% 3.78/2.94 (c2_1(a604)),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[4790, 107, 6877, 7649, 7492, 7648, 7490, 32, 7526])).
% 3.78/2.94 tff(7651,plain,
% 3.78/2.94 (c3_1(a604)),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[1602, 7647])).
% 3.78/2.94 tff(7652,plain,
% 3.78/2.94 (~c1_1(a678)),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[2612, 107, 2318, 2316, 3749, 2545, 3748, 3747, 2475, 65, 2538])).
% 3.78/2.94 tff(7653,plain,
% 3.78/2.94 (~c0_1(a593)),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[2619, 107, 3749, 2545, 1894, 1903, 3748, 3747, 2475, 65, 2538])).
% 3.78/2.94 tff(7654,plain,
% 3.78/2.94 ($false),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[2626, 107, 6877, 2318, 2317, 1894, 1893, 32, 7653, 7652])).
% 3.78/2.94 tff(7655,plain,((~hskp19) | (~c0_1(a678)) | (~c2_1(a678)) | (~c1_1(a593)) | c2_1(a593) | (~c3_1(a604)) | (~c3_1(a593)) | c0_1(a604) | (~c2_1(a604)) | (~c3_1(a678))), inference(lemma,lemma(discharge,[]))).
% 3.78/2.94 tff(7656,plain,
% 3.78/2.94 (~hskp19),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[7655, 7525, 7524, 7629, 7638, 7651, 7628, 7648, 7650, 7523])).
% 3.78/2.94 tff(7657,plain,
% 3.78/2.94 (hskp13),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[7584, 7656, 6959, 1])).
% 3.78/2.94 tff(7658,plain,
% 3.78/2.94 (~c2_1(a601)),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[2523, 7657])).
% 3.78/2.94 tff(7659,plain,
% 3.78/2.94 (~c1_1(a601)),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[2529, 7657])).
% 3.78/2.94 tff(7660,plain,
% 3.78/2.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a604) | c1_1(a601) | c2_1(a601) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a601)) | (~c2_1(a604)) | (~c1_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a604) | c1_1(a601) | c2_1(a601) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a601)) | (~c2_1(a604)) | (~c1_1(a604)))),
% 3.78/2.94 inference(rewrite,[status(thm)],[])).
% 3.78/2.94 tff(7661,plain,
% 3.78/2.94 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a601) | c2_1(a601) | (~c3_1(a601)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604))) <=> (c0_1(a604) | c1_1(a601) | c2_1(a601) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a601)) | (~c2_1(a604)) | (~c1_1(a604)))),
% 3.78/2.94 inference(rewrite,[status(thm)],[])).
% 3.78/2.94 tff(7662,plain,
% 3.78/2.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a601) | c2_1(a601) | (~c3_1(a601)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a604) | c1_1(a601) | c2_1(a601) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a601)) | (~c2_1(a604)) | (~c1_1(a604))))),
% 3.78/2.94 inference(monotonicity,[status(thm)],[7661])).
% 3.78/2.94 tff(7663,plain,
% 3.78/2.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a601) | c2_1(a601) | (~c3_1(a601)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a604) | c1_1(a601) | c2_1(a601) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a601)) | (~c2_1(a604)) | (~c1_1(a604)))),
% 3.78/2.94 inference(transitivity,[status(thm)],[7662, 7660])).
% 3.78/2.94 tff(7664,plain,
% 3.78/2.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a601) | c2_1(a601) | (~c3_1(a601)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))),
% 3.78/2.94 inference(quant_inst,[status(thm)],[])).
% 3.78/2.94 tff(7665,plain,
% 3.78/2.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a604) | c1_1(a601) | c2_1(a601) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c3_1(a601)) | (~c2_1(a604)) | (~c1_1(a604))),
% 3.78/2.94 inference(modus_ponens,[status(thm)],[7664, 7663])).
% 3.78/2.94 tff(7666,plain,
% 3.78/2.94 (~c3_1(a601)),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[7665, 107, 7525, 7524, 7523, 7649, 7648, 7659, 7658, 11, 7650])).
% 3.78/2.94 tff(7667,plain,
% 3.78/2.94 (~c0_1(a601)),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[2543, 7657])).
% 3.78/2.94 tff(7668,plain,
% 3.78/2.94 ($false),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[2551, 107, 7651, 7518, 7520, 7648, 7667, 7658, 7517, 1730, 7650, 7666])).
% 3.78/2.94 tff(7669,plain,(c0_1(a607)), inference(lemma,lemma(discharge,[]))).
% 3.78/2.94 tff(7670,plain,
% 3.78/2.94 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.78/2.94 inference(rewrite,[status(thm)],[])).
% 3.78/2.94 tff(7671,plain,
% 3.78/2.94 ((hskp10 | (~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c1_1(a607)) | (~c1_1(a607)) | (~c2_1(a607)) | (~c0_1(a607))) <=> (hskp10 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.78/2.94 inference(rewrite,[status(thm)],[])).
% 3.78/2.94 tff(7672,plain,
% 3.78/2.94 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c1_1(a607)) | (~c1_1(a607)) | (~c2_1(a607)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607))))),
% 3.78/2.94 inference(monotonicity,[status(thm)],[7671])).
% 3.78/2.94 tff(7673,plain,
% 3.78/2.94 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c1_1(a607)) | (~c1_1(a607)) | (~c2_1(a607)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.78/2.94 inference(transitivity,[status(thm)],[7672, 7670])).
% 3.78/2.94 tff(7674,plain,
% 3.78/2.94 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a607)) | (~c3_1(a607)) | (~c1_1(a607)) | (~c1_1(a607)) | (~c2_1(a607)) | (~c0_1(a607)))),
% 3.78/2.94 inference(quant_inst,[status(thm)],[])).
% 3.78/2.94 tff(7675,plain,
% 3.78/2.94 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c0_1(V)))) | hskp10 | (~c1_1(a607)) | (~c2_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607))),
% 3.78/2.94 inference(modus_ponens,[status(thm)],[7674, 7673])).
% 3.78/2.94 tff(7676,plain,
% 3.78/2.94 (hskp10 | (~c0_1(a607)) | (~c3_1(a607))),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[7675, 107, 6876, 6959, 21])).
% 3.78/2.94 tff(7677,plain,
% 3.78/2.94 (hskp10),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[7676, 7669, 7301])).
% 3.78/2.94 tff(7678,plain,
% 3.78/2.94 (~c1_1(a598)),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[911, 7677])).
% 3.78/2.94 tff(7679,plain,
% 3.78/2.94 (c3_1(a598)),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[881, 7677])).
% 3.78/2.94 tff(7680,plain,
% 3.78/2.94 (c0_1(a598)),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[892, 7677])).
% 3.78/2.94 tff(7681,plain,
% 3.78/2.94 (hskp11 | hskp23),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[1688, 107, 7680, 7679, 7678, 1648])).
% 3.78/2.94 tff(7682,plain,
% 3.78/2.94 (hskp23),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[7681, 1638])).
% 3.78/2.94 tff(7683,plain,
% 3.78/2.94 (~c1_1(a636)),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[475, 7682])).
% 3.78/2.94 tff(7684,plain,
% 3.78/2.94 (~c0_1(a636)),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[481, 7682])).
% 3.78/2.94 tff(7685,plain,
% 3.78/2.94 (c3_1(a636)),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[492, 7682])).
% 3.78/2.94 tff(7686,plain,
% 3.78/2.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a636) | c1_1(a636) | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)) | (~c3_1(a636)) | (~c2_1(a636)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a636) | c1_1(a636) | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)) | (~c3_1(a636)) | (~c2_1(a636)))),
% 3.78/2.94 inference(rewrite,[status(thm)],[])).
% 3.78/2.94 tff(7687,plain,
% 3.78/2.94 (((~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a636) | (~c3_1(a636)) | (~c2_1(a636)) | c1_1(a636) | c0_1(a636) | (~c2_1(a636))) <=> (c0_1(a636) | c1_1(a636) | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)) | (~c3_1(a636)) | (~c2_1(a636)))),
% 3.78/2.94 inference(rewrite,[status(thm)],[])).
% 3.78/2.94 tff(7688,plain,
% 3.78/2.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a636) | (~c3_1(a636)) | (~c2_1(a636)) | c1_1(a636) | c0_1(a636) | (~c2_1(a636)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a636) | c1_1(a636) | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)) | (~c3_1(a636)) | (~c2_1(a636))))),
% 3.78/2.94 inference(monotonicity,[status(thm)],[7687])).
% 3.78/2.94 tff(7689,plain,
% 3.78/2.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a636) | (~c3_1(a636)) | (~c2_1(a636)) | c1_1(a636) | c0_1(a636) | (~c2_1(a636)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a636) | c1_1(a636) | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)) | (~c3_1(a636)) | (~c2_1(a636)))),
% 3.78/2.94 inference(transitivity,[status(thm)],[7688, 7686])).
% 3.78/2.94 tff(7690,plain,
% 3.78/2.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a636) | (~c3_1(a636)) | (~c2_1(a636)) | c1_1(a636) | c0_1(a636) | (~c2_1(a636)))),
% 3.78/2.94 inference(quant_inst,[status(thm)],[])).
% 3.78/2.94 tff(7691,plain,
% 3.78/2.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a636) | c1_1(a636) | (~c1_1(a607)) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)) | (~c3_1(a636)) | (~c2_1(a636))),
% 3.78/2.94 inference(modus_ponens,[status(thm)],[7690, 7689])).
% 3.78/2.94 tff(7692,plain,
% 3.78/2.94 (~c2_1(a636)),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[7691, 107, 7685, 7301, 7684, 7683, 6876, 65, 7669])).
% 3.78/2.94 tff(7693,plain,
% 3.78/2.94 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~c1_1(a607)) | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c0_1(a598)) | (~c0_1(a607)) | (~c3_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | (~c1_1(a607)) | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c0_1(a598)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.78/2.94 inference(rewrite,[status(thm)],[])).
% 3.78/2.94 tff(7694,plain,
% 3.78/2.94 ((hskp15 | (~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a598) | (~c3_1(a598)) | (~c0_1(a598))) <=> (hskp15 | (~c1_1(a607)) | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c0_1(a598)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.78/2.94 inference(rewrite,[status(thm)],[])).
% 3.78/2.94 tff(7695,plain,
% 3.78/2.94 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a598) | (~c3_1(a598)) | (~c0_1(a598)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~c1_1(a607)) | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c0_1(a598)) | (~c0_1(a607)) | (~c3_1(a607))))),
% 3.78/2.94 inference(monotonicity,[status(thm)],[7694])).
% 3.78/2.94 tff(7696,plain,
% 3.78/2.94 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a598) | (~c3_1(a598)) | (~c0_1(a598)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | (~c1_1(a607)) | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c0_1(a598)) | (~c0_1(a607)) | (~c3_1(a607)))),
% 3.78/2.94 inference(transitivity,[status(thm)],[7695, 7693])).
% 3.78/2.94 tff(7697,plain,
% 3.78/2.94 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a598) | (~c3_1(a598)) | (~c0_1(a598)))),
% 3.78/2.94 inference(quant_inst,[status(thm)],[])).
% 3.78/2.94 tff(7698,plain,
% 3.78/2.94 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp15 | (~c1_1(a607)) | c1_1(a598) | (~ndr1_0) | (~c3_1(a598)) | (~c0_1(a598)) | (~c0_1(a607)) | (~c3_1(a607))),
% 3.78/2.94 inference(modus_ponens,[status(thm)],[7697, 7696])).
% 3.78/2.94 tff(7699,plain,
% 3.78/2.94 (hskp15),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[7698, 107, 7301, 7680, 7679, 6876, 7678, 1993, 7669])).
% 3.78/2.94 tff(7700,plain,
% 3.78/2.94 (~c0_1(a604)),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[1591, 7699])).
% 3.78/2.94 tff(7701,plain,
% 3.78/2.94 (c1_1(a604)),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[1613, 7699])).
% 3.78/2.94 tff(7702,plain,
% 3.78/2.94 (hskp11),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[6878, 6238, 6236, 6237])).
% 3.78/2.94 tff(7703,plain,
% 3.78/2.94 (~c1_1(a599)),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[428, 7702])).
% 3.78/2.94 tff(7704,plain,
% 3.78/2.94 (c2_1(a599)),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[439, 7702])).
% 3.78/2.94 tff(7705,plain,
% 3.78/2.94 (c3_1(a599)),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[422, 7702])).
% 3.78/2.94 tff(7706,plain,
% 3.78/2.94 (~hskp12),
% 3.78/2.94 inference(unit_resolution,[status(thm)],[7182, 7705, 6235, 7704, 7703])).
% 3.78/2.94 tff(7707,plain,
% 3.78/2.94 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c1_1(a604)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c1_1(a604)) | (~c0_1(a607)))),
% 3.78/2.94 inference(rewrite,[status(thm)],[])).
% 3.78/2.94 tff(7708,plain,
% 3.78/2.94 ((hskp12 | (~ndr1_0) | (~c2_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604))) <=> (hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c1_1(a604)) | (~c0_1(a607)))),
% 3.78/2.94 inference(rewrite,[status(thm)],[])).
% 3.78/2.94 tff(7709,plain,
% 3.78/2.94 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c1_1(a604)) | (~c0_1(a607))))),
% 3.78/2.94 inference(monotonicity,[status(thm)],[7708])).
% 3.78/2.94 tff(7710,plain,
% 3.78/2.94 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c1_1(a604)) | (~c0_1(a607)))),
% 3.78/2.94 inference(transitivity,[status(thm)],[7709, 7707])).
% 3.78/2.94 tff(7711,plain,
% 3.78/2.94 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | (~c2_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))),
% 3.78/2.95 inference(quant_inst,[status(thm)],[])).
% 3.78/2.95 tff(7712,plain,
% 3.78/2.95 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp12 | (~c1_1(a607)) | (~c2_1(a607)) | c0_1(a604) | (~ndr1_0) | (~c2_1(a604)) | (~c1_1(a604)) | (~c0_1(a607))),
% 3.78/2.95 inference(modus_ponens,[status(thm)],[7711, 7710])).
% 3.78/2.95 tff(7713,plain,
% 3.78/2.95 (hskp12 | (~c2_1(a604))),
% 3.78/2.95 inference(unit_resolution,[status(thm)],[7712, 107, 7701, 6876, 6959, 7700, 2727, 7669])).
% 3.78/2.95 tff(7714,plain,
% 3.78/2.95 (~c2_1(a604)),
% 3.78/2.95 inference(unit_resolution,[status(thm)],[7713, 7706])).
% 3.78/2.95 tff(7715,plain,
% 3.78/2.95 (c0_1(a599)),
% 3.78/2.95 inference(unit_resolution,[status(thm)],[6932, 7704, 7301, 7669, 7703, 7705])).
% 3.78/2.95 tff(7716,plain,
% 3.78/2.95 ($false),
% 3.78/2.95 inference(unit_resolution,[status(thm)],[2888, 107, 6877, 7701, 7704, 7700, 7703, 32, 7715, 7714])).
% 3.78/2.95 tff(7717,plain,(~hskp22), inference(lemma,lemma(discharge,[]))).
% 3.78/2.95 tff(7718,plain,
% 3.78/2.95 (hskp29),
% 3.78/2.95 inference(unit_resolution,[status(thm)],[2258, 7717])).
% 3.78/2.95 tff(7719,plain,
% 3.78/2.95 (c3_1(a678)),
% 3.78/2.95 inference(unit_resolution,[status(thm)],[2269, 7718])).
% 3.78/2.95 tff(7720,plain,
% 3.78/2.95 (c2_1(a678)),
% 3.78/2.95 inference(unit_resolution,[status(thm)],[2280, 7718])).
% 3.78/2.95 tff(7721,plain,
% 3.78/2.95 (c0_1(a678)),
% 3.78/2.95 inference(unit_resolution,[status(thm)],[2291, 7718])).
% 3.78/2.95 tff(7722,plain,
% 3.78/2.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a636) | c0_1(a604) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a636)) | c2_1(a636))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a636) | c0_1(a604) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a636)) | c2_1(a636))),
% 3.78/2.95 inference(rewrite,[status(thm)],[])).
% 3.78/2.95 tff(7723,plain,
% 3.78/2.95 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a636) | c2_1(a636) | (~c3_1(a636)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604))) <=> (c1_1(a636) | c0_1(a604) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a636)) | c2_1(a636))),
% 3.78/2.95 inference(rewrite,[status(thm)],[])).
% 3.78/2.95 tff(7724,plain,
% 3.78/2.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a636) | c2_1(a636) | (~c3_1(a636)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a636) | c0_1(a604) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a636)) | c2_1(a636)))),
% 3.78/2.95 inference(monotonicity,[status(thm)],[7723])).
% 3.78/2.95 tff(7725,plain,
% 3.78/2.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a636) | c2_1(a636) | (~c3_1(a636)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a636) | c0_1(a604) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a636)) | c2_1(a636))),
% 3.78/2.95 inference(transitivity,[status(thm)],[7724, 7722])).
% 3.78/2.95 tff(7726,plain,
% 3.78/2.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a636) | c2_1(a636) | (~c3_1(a636)) | c0_1(a604) | (~c1_1(a604)) | (~c2_1(a604)))),
% 3.78/2.95 inference(quant_inst,[status(thm)],[])).
% 3.78/2.95 tff(7727,plain,
% 3.78/2.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a636) | c0_1(a604) | (~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)) | (~c2_1(a604)) | (~c1_1(a604)) | (~c3_1(a636)) | c2_1(a636)),
% 3.78/2.95 inference(modus_ponens,[status(thm)],[7726, 7725])).
% 3.78/2.95 tff(7728,plain,
% 3.78/2.95 (~c2_1(a604)),
% 3.78/2.95 inference(unit_resolution,[status(thm)],[7727, 107, 7721, 7720, 7719, 7685, 7701, 7683, 7700, 11, 7692])).
% 3.78/2.95 tff(7729,plain,
% 3.78/2.95 (hskp9),
% 3.78/2.95 inference(unit_resolution,[status(thm)],[1700, 107, 3321, 3322, 3330, 7685, 7684, 7683, 294])).
% 3.78/2.95 tff(7730,plain,
% 3.78/2.95 (~c3_1(a595)),
% 3.78/2.95 inference(unit_resolution,[status(thm)],[1487, 7729])).
% 3.78/2.95 tff(7731,plain,
% 3.78/2.95 (~c1_1(a595)),
% 3.78/2.95 inference(unit_resolution,[status(thm)],[1493, 7729])).
% 3.78/2.95 tff(7732,plain,
% 3.78/2.95 (~c0_1(a595)),
% 3.78/2.95 inference(unit_resolution,[status(thm)],[1499, 7729])).
% 3.78/2.95 tff(7733,plain,
% 3.78/2.95 ((~c2_1(a598)) | c2_1(a604)),
% 3.78/2.95 inference(unit_resolution,[status(thm)],[4790, 107, 6877, 7701, 7680, 7700, 7678, 32])).
% 3.78/2.95 tff(7734,plain,
% 3.78/2.95 (~c2_1(a598)),
% 3.78/2.95 inference(unit_resolution,[status(thm)],[7733, 7728])).
% 3.78/2.95 tff(7735,plain,
% 3.78/2.95 (((~![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp11 | hskp21 | c1_1(a598) | (~ndr1_0) | c2_1(a598) | (~c0_1(a598)))) <=> ((~![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp11 | hskp21 | c1_1(a598) | (~ndr1_0) | c2_1(a598) | (~c0_1(a598)))),
% 3.78/2.95 inference(rewrite,[status(thm)],[])).
% 3.78/2.95 tff(7736,plain,
% 3.78/2.95 ((hskp11 | hskp21 | (~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598))) <=> (hskp11 | hskp21 | c1_1(a598) | (~ndr1_0) | c2_1(a598) | (~c0_1(a598)))),
% 3.78/2.95 inference(rewrite,[status(thm)],[])).
% 3.78/2.95 tff(7737,plain,
% 3.78/2.95 (((~![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp11 | hskp21 | (~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)))) <=> ((~![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp11 | hskp21 | c1_1(a598) | (~ndr1_0) | c2_1(a598) | (~c0_1(a598))))),
% 3.78/2.95 inference(monotonicity,[status(thm)],[7736])).
% 3.78/2.95 tff(7738,plain,
% 3.78/2.95 (((~![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp11 | hskp21 | (~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)))) <=> ((~![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp11 | hskp21 | c1_1(a598) | (~ndr1_0) | c2_1(a598) | (~c0_1(a598)))),
% 3.78/2.95 inference(transitivity,[status(thm)],[7737, 7735])).
% 3.78/2.95 tff(7739,plain,
% 3.78/2.95 ((~![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp11 | hskp21 | (~ndr1_0) | c2_1(a598) | c1_1(a598) | (~c0_1(a598)))),
% 3.78/2.95 inference(quant_inst,[status(thm)],[])).
% 3.78/2.95 tff(7740,plain,
% 3.78/2.95 ((~![U: $i] : (hskp11 | hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp11 | hskp21 | c1_1(a598) | (~ndr1_0) | c2_1(a598) | (~c0_1(a598))),
% 3.78/2.95 inference(modus_ponens,[status(thm)],[7739, 7738])).
% 3.78/2.95 tff(7741,plain,
% 3.78/2.95 (hskp11 | hskp21 | c2_1(a598)),
% 3.78/2.95 inference(unit_resolution,[status(thm)],[7740, 107, 7680, 7678, 5104])).
% 3.78/2.95 tff(7742,plain,
% 3.78/2.95 (hskp21),
% 3.78/2.95 inference(unit_resolution,[status(thm)],[7741, 7734, 1638])).
% 3.78/2.95 tff(7743,plain,
% 3.78/2.95 (~c3_1(a629)),
% 3.78/2.95 inference(unit_resolution,[status(thm)],[4846, 7742])).
% 3.78/2.95 tff(7744,plain,
% 3.78/2.95 (~c2_1(a629)),
% 3.78/2.95 inference(unit_resolution,[status(thm)],[4852, 7742])).
% 3.78/2.95 tff(7745,plain,
% 3.78/2.95 (c0_1(a629)),
% 3.78/2.95 inference(unit_resolution,[status(thm)],[4870, 7742])).
% 3.78/2.95 tff(7746,plain,
% 3.78/2.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a629) | c3_1(a629) | c0_1(a604) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a629)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a629) | c3_1(a629) | c0_1(a604) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a629)))),
% 3.78/2.95 inference(rewrite,[status(thm)],[])).
% 3.78/2.95 tff(7747,plain,
% 3.78/2.95 (((~ndr1_0) | c2_1(a629) | c3_1(a629) | (~c0_1(a629)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)) | c3_1(a595) | c1_1(a595) | c0_1(a595)) <=> (c2_1(a629) | c3_1(a629) | c0_1(a604) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a629)))),
% 3.78/2.95 inference(rewrite,[status(thm)],[])).
% 3.78/2.95 tff(7748,plain,
% 3.78/2.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a629) | c3_1(a629) | (~c0_1(a629)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)) | c3_1(a595) | c1_1(a595) | c0_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a629) | c3_1(a629) | c0_1(a604) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a629))))),
% 3.78/2.95 inference(monotonicity,[status(thm)],[7747])).
% 3.78/2.95 tff(7749,plain,
% 3.78/2.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a629) | c3_1(a629) | (~c0_1(a629)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)) | c3_1(a595) | c1_1(a595) | c0_1(a595))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a629) | c3_1(a629) | c0_1(a604) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a629)))),
% 3.78/2.95 inference(transitivity,[status(thm)],[7748, 7746])).
% 3.78/2.95 tff(7750,plain,
% 3.78/2.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a629) | c3_1(a629) | (~c0_1(a629)) | c0_1(a604) | c2_1(a604) | (~c1_1(a604)) | c3_1(a595) | c1_1(a595) | c0_1(a595))),
% 3.78/2.95 inference(quant_inst,[status(thm)],[])).
% 3.78/2.95 tff(7751,plain,
% 3.78/2.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a629) | c3_1(a629) | c0_1(a604) | c0_1(a595) | c1_1(a595) | c3_1(a595) | (~ndr1_0) | c2_1(a604) | (~c1_1(a604)) | (~c0_1(a629))),
% 3.78/2.95 inference(modus_ponens,[status(thm)],[7750, 7749])).
% 3.78/2.95 tff(7752,plain,
% 3.78/2.95 ($false),
% 3.78/2.95 inference(unit_resolution,[status(thm)],[7751, 107, 7745, 7701, 7744, 7743, 7700, 7732, 7731, 7730, 1463, 7728])).
% 3.78/2.95 tff(7753,plain,(hskp11), inference(lemma,lemma(discharge,[]))).
% 3.78/2.95 tff(7754,plain,
% 3.78/2.95 (c3_1(a599)),
% 3.78/2.95 inference(unit_resolution,[status(thm)],[422, 7753])).
% 3.78/2.95 tff(7755,plain,
% 3.78/2.95 (~c1_1(a599)),
% 3.78/2.95 inference(unit_resolution,[status(thm)],[428, 7753])).
% 3.78/2.95 tff(7756,plain,
% 3.78/2.95 (c2_1(a599)),
% 3.78/2.95 inference(unit_resolution,[status(thm)],[439, 7753])).
% 3.78/2.95 tff(7757,plain,
% 3.78/2.95 (c0_1(a599)),
% 3.78/2.95 inference(unit_resolution,[status(thm)],[6932, 7756, 7301, 7669, 7755, 7754])).
% 3.78/2.95 tff(7758,plain,
% 3.78/2.95 (c2_1(a604)),
% 3.78/2.95 inference(unit_resolution,[status(thm)],[2888, 107, 6877, 7701, 7756, 7700, 7755, 32, 7757])).
% 3.78/2.95 tff(7759,plain,
% 3.78/2.95 (c3_1(a604)),
% 3.78/2.95 inference(unit_resolution,[status(thm)],[1602, 7699])).
% 3.78/2.95 tff(7760,plain,
% 3.78/2.95 ((~hskp19) | (~c3_1(a607)) | (~c3_1(a604)) | c0_1(a604) | (~c0_1(a607)) | (~c2_1(a604))),
% 3.78/2.95 inference(unit_resolution,[status(thm)],[3757, 6876])).
% 3.78/2.95 tff(7761,plain,
% 3.78/2.95 (~hskp19),
% 3.78/2.95 inference(unit_resolution,[status(thm)],[7760, 7758, 7301, 7669, 7759, 7700])).
% 3.78/2.95 tff(7762,plain,
% 3.78/2.95 (hskp20 | hskp19 | (~c0_1(a607)) | (~c3_1(a607))),
% 3.78/2.95 inference(unit_resolution,[status(thm)],[3774, 107, 6876, 3768])).
% 3.78/2.95 tff(7763,plain,
% 3.78/2.95 (hskp20),
% 3.78/2.95 inference(unit_resolution,[status(thm)],[7762, 7761, 7301, 7669])).
% 3.78/2.95 tff(7764,plain,
% 3.78/2.95 (hskp16),
% 3.78/2.95 inference(unit_resolution,[status(thm)],[5664, 7763, 7758, 7754, 7700, 7755, 7756, 7759])).
% 3.78/2.95 tff(7765,plain,
% 3.78/2.95 (~c2_1(a606)),
% 3.78/2.95 inference(unit_resolution,[status(thm)],[1111, 7764])).
% 3.78/2.95 tff(7766,plain,
% 3.78/2.95 (hskp19 | hskp13 | (~c2_1(a604))),
% 3.78/2.95 inference(unit_resolution,[status(thm)],[2656, 107, 7701, 7700, 2564])).
% 3.78/2.95 tff(7767,plain,
% 3.78/2.95 (hskp13),
% 3.78/2.95 inference(unit_resolution,[status(thm)],[7766, 7761, 7758])).
% 3.84/2.96 tff(7768,plain,
% 3.84/2.96 (c1_1(a606)),
% 3.84/2.96 inference(unit_resolution,[status(thm)],[1088, 7764])).
% 3.84/2.96 tff(7769,plain,
% 3.84/2.96 (~c0_1(a606)),
% 3.84/2.96 inference(unit_resolution,[status(thm)],[2553, 7768, 7754, 7759, 7756, 7755, 7767, 7721, 7720, 7719, 7700, 7765, 7758])).
% 3.84/2.96 tff(7770,plain,
% 3.84/2.96 (hskp12),
% 3.84/2.96 inference(unit_resolution,[status(thm)],[7713, 7758])).
% 3.84/2.96 tff(7771,plain,
% 3.84/2.96 (~c3_1(a600)),
% 3.84/2.96 inference(unit_resolution,[status(thm)],[741, 7770])).
% 3.84/2.96 tff(7772,plain,
% 3.84/2.96 (~c3_1(a606)),
% 3.84/2.96 inference(unit_resolution,[status(thm)],[1075, 7764])).
% 3.84/2.96 tff(7773,plain,
% 3.84/2.96 (c2_1(a600)),
% 3.84/2.96 inference(unit_resolution,[status(thm)],[752, 7770])).
% 3.84/2.96 tff(7774,plain,
% 3.84/2.96 (c0_1(a600)),
% 3.84/2.96 inference(unit_resolution,[status(thm)],[763, 7770])).
% 3.84/2.96 tff(7775,plain,
% 3.84/2.96 ($false),
% 3.84/2.96 inference(unit_resolution,[status(thm)],[5737, 107, 7768, 7774, 7773, 7756, 7754, 7772, 7771, 7755, 258, 7769])).
% 3.84/2.96 % SZS output end Proof
%------------------------------------------------------------------------------