TSTP Solution File: SYN506-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN506-1 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 1.19s 1.03s
% Output : Proof 1.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN506-1 : TPTP v8.1.0. Released v2.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Sep 5 04:57:16 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 1.19/1.03 % SZS status Unsatisfiable
% 1.19/1.03 % SZS output start Proof
% 1.19/1.03 tff(c1_1_type, type, (
% 1.19/1.03 c1_1: $i > $o)).
% 1.19/1.03 tff(a359_type, type, (
% 1.19/1.03 a359: $i)).
% 1.19/1.03 tff(c3_1_type, type, (
% 1.19/1.03 c3_1: $i > $o)).
% 1.19/1.03 tff(a353_type, type, (
% 1.19/1.03 a353: $i)).
% 1.19/1.03 tff(c2_1_type, type, (
% 1.19/1.03 c2_1: $i > $o)).
% 1.19/1.03 tff(ndr1_0_type, type, (
% 1.19/1.03 ndr1_0: $o)).
% 1.19/1.03 tff(hskp22_type, type, (
% 1.19/1.03 hskp22: $o)).
% 1.19/1.03 tff(a347_type, type, (
% 1.19/1.03 a347: $i)).
% 1.19/1.03 tff(hskp14_type, type, (
% 1.19/1.03 hskp14: $o)).
% 1.19/1.03 tff(a337_type, type, (
% 1.19/1.03 a337: $i)).
% 1.19/1.03 tff(hskp21_type, type, (
% 1.19/1.03 hskp21: $o)).
% 1.19/1.03 tff(a349_type, type, (
% 1.19/1.03 a349: $i)).
% 1.19/1.03 tff(hskp16_type, type, (
% 1.19/1.03 hskp16: $o)).
% 1.19/1.03 tff(a330_type, type, (
% 1.19/1.03 a330: $i)).
% 1.19/1.03 tff(hskp7_type, type, (
% 1.19/1.03 hskp7: $o)).
% 1.19/1.03 tff(a358_type, type, (
% 1.19/1.03 a358: $i)).
% 1.19/1.03 tff(c0_1_type, type, (
% 1.19/1.03 c0_1: $i > $o)).
% 1.19/1.03 tff(hskp20_type, type, (
% 1.19/1.03 hskp20: $o)).
% 1.19/1.03 tff(a343_type, type, (
% 1.19/1.03 a343: $i)).
% 1.19/1.03 tff(a401_type, type, (
% 1.19/1.03 a401: $i)).
% 1.19/1.03 tff(hskp24_type, type, (
% 1.19/1.03 hskp24: $o)).
% 1.19/1.03 tff(hskp17_type, type, (
% 1.19/1.03 hskp17: $o)).
% 1.19/1.03 tff(hskp28_type, type, (
% 1.19/1.03 hskp28: $o)).
% 1.19/1.03 tff(a419_type, type, (
% 1.19/1.03 a419: $i)).
% 1.19/1.03 tff(a333_type, type, (
% 1.19/1.03 a333: $i)).
% 1.19/1.03 tff(a326_type, type, (
% 1.19/1.03 a326: $i)).
% 1.19/1.03 tff(hskp4_type, type, (
% 1.19/1.03 hskp4: $o)).
% 1.19/1.03 tff(hskp13_type, type, (
% 1.19/1.03 hskp13: $o)).
% 1.19/1.03 tff(a334_type, type, (
% 1.19/1.03 a334: $i)).
% 1.19/1.03 tff(hskp9_type, type, (
% 1.19/1.03 hskp9: $o)).
% 1.19/1.03 tff(hskp25_type, type, (
% 1.19/1.03 hskp25: $o)).
% 1.19/1.03 tff(hskp26_type, type, (
% 1.19/1.03 hskp26: $o)).
% 1.19/1.03 tff(hskp2_type, type, (
% 1.19/1.03 hskp2: $o)).
% 1.19/1.03 tff(a367_type, type, (
% 1.19/1.03 a367: $i)).
% 1.19/1.03 tff(a345_type, type, (
% 1.19/1.03 a345: $i)).
% 1.19/1.03 tff(hskp12_type, type, (
% 1.19/1.03 hskp12: $o)).
% 1.19/1.03 tff(a377_type, type, (
% 1.19/1.03 a377: $i)).
% 1.19/1.03 tff(hskp23_type, type, (
% 1.19/1.03 hskp23: $o)).
% 1.19/1.03 tff(hskp10_type, type, (
% 1.19/1.03 hskp10: $o)).
% 1.19/1.03 tff(a346_type, type, (
% 1.19/1.03 a346: $i)).
% 1.19/1.03 tff(a332_type, type, (
% 1.19/1.03 a332: $i)).
% 1.19/1.03 tff(hskp8_type, type, (
% 1.19/1.03 hskp8: $o)).
% 1.19/1.03 tff(a325_type, type, (
% 1.19/1.03 a325: $i)).
% 1.19/1.03 tff(hskp3_type, type, (
% 1.19/1.03 hskp3: $o)).
% 1.19/1.03 tff(a327_type, type, (
% 1.19/1.03 a327: $i)).
% 1.19/1.03 tff(hskp5_type, type, (
% 1.19/1.03 hskp5: $o)).
% 1.19/1.03 tff(a348_type, type, (
% 1.19/1.03 a348: $i)).
% 1.19/1.03 tff(hskp15_type, type, (
% 1.19/1.03 hskp15: $o)).
% 1.19/1.03 tff(a324_type, type, (
% 1.19/1.03 a324: $i)).
% 1.19/1.03 tff(a323_type, type, (
% 1.19/1.03 a323: $i)).
% 1.19/1.03 tff(hskp1_type, type, (
% 1.19/1.03 hskp1: $o)).
% 1.19/1.03 tff(hskp11_type, type, (
% 1.19/1.03 hskp11: $o)).
% 1.19/1.03 tff(a338_type, type, (
% 1.19/1.03 a338: $i)).
% 1.19/1.03 tff(a341_type, type, (
% 1.19/1.03 a341: $i)).
% 1.19/1.03 tff(hskp27_type, type, (
% 1.19/1.03 hskp27: $o)).
% 1.19/1.03 tff(1,plain,
% 1.19/1.03 (^[V: $i, U: $i] : refl((hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 1.19/1.03 inference(bind,[status(th)],[])).
% 1.19/1.03 tff(2,plain,
% 1.19/1.03 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.19/1.03 inference(quant_intro,[status(thm)],[1])).
% 1.19/1.03 tff(3,plain,
% 1.19/1.03 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.19/1.03 inference(rewrite,[status(thm)],[])).
% 1.19/1.03 tff(4,plain,
% 1.19/1.03 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp22) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp22))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp22) <=> (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp22) <=> (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 1.19/1.03 inference(bind,[status(th)],[])).
% 1.19/1.03 tff(5,plain,
% 1.19/1.03 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp22) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.19/1.03 inference(quant_intro,[status(thm)],[4])).
% 1.19/1.03 tff(6,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause185')).
% 1.19/1.03 tff(7,plain,
% 1.19/1.03 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.19/1.03 inference(modus_ponens,[status(thm)],[6, 5])).
% 1.19/1.03 tff(8,plain,
% 1.19/1.03 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.19/1.03 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.19/1.03 tff(9,plain,(
% 1.19/1.03 ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.19/1.03 inference(skolemize,[status(sab)],[8])).
% 1.19/1.03 tff(10,plain,
% 1.19/1.03 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.19/1.03 inference(modus_ponens,[status(thm)],[9, 2])).
% 1.19/1.03 tff(11,assumption,(~hskp14), introduced(assumption)).
% 1.19/1.03 tff(12,plain,
% 1.19/1.03 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))))),
% 1.19/1.03 inference(bind,[status(th)],[])).
% 1.19/1.03 tff(13,plain,
% 1.19/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.19/1.03 inference(quant_intro,[status(thm)],[12])).
% 1.19/1.03 tff(14,plain,
% 1.19/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.19/1.03 inference(rewrite,[status(thm)],[])).
% 1.19/1.03 tff(15,plain,
% 1.19/1.03 (^[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))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_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)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_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)) | (~c0_1(U)) | (~c1_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))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))))),
% 1.19/1.03 inference(bind,[status(th)],[])).
% 1.19/1.03 tff(16,plain,
% 1.19/1.03 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.19/1.03 inference(quant_intro,[status(thm)],[15])).
% 1.19/1.03 tff(17,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause194')).
% 1.19/1.03 tff(18,plain,
% 1.19/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.19/1.03 inference(modus_ponens,[status(thm)],[17, 16])).
% 1.19/1.03 tff(19,plain,
% 1.19/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.19/1.03 inference(modus_ponens,[status(thm)],[18, 14])).
% 1.19/1.03 tff(20,plain,(
% 1.19/1.03 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.19/1.03 inference(skolemize,[status(sab)],[19])).
% 1.19/1.03 tff(21,plain,
% 1.19/1.03 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.19/1.03 inference(modus_ponens,[status(thm)],[20, 13])).
% 1.19/1.03 tff(22,plain,
% 1.19/1.03 (^[U: $i] : refl((hskp24 | hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) <=> (hskp24 | hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))),
% 1.19/1.03 inference(bind,[status(th)],[])).
% 1.19/1.03 tff(23,plain,
% 1.19/1.03 (![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.19/1.03 inference(quant_intro,[status(thm)],[22])).
% 1.19/1.03 tff(24,plain,
% 1.19/1.03 (![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.19/1.03 inference(rewrite,[status(thm)],[])).
% 1.19/1.03 tff(25,plain,
% 1.19/1.03 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp17) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp17))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp17) <=> (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp17) <=> (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp17) | hskp24) <=> ((hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp24))), rewrite(((hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp24) <=> (hskp24 | hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp17) | hskp24) <=> (hskp24 | hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))))),
% 1.19/1.03 inference(bind,[status(th)],[])).
% 1.19/1.03 tff(26,plain,
% 1.19/1.03 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp17) | hskp24) <=> ![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.19/1.03 inference(quant_intro,[status(thm)],[25])).
% 1.19/1.03 tff(27,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp17) | hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause148')).
% 1.19/1.03 tff(28,plain,
% 1.19/1.03 (![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.19/1.03 inference(modus_ponens,[status(thm)],[27, 26])).
% 1.19/1.03 tff(29,plain,
% 1.19/1.03 (![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.19/1.03 inference(modus_ponens,[status(thm)],[28, 24])).
% 1.19/1.03 tff(30,plain,(
% 1.19/1.03 ![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.19/1.03 inference(skolemize,[status(sab)],[29])).
% 1.19/1.03 tff(31,plain,
% 1.19/1.03 (![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.19/1.03 inference(modus_ponens,[status(thm)],[30, 23])).
% 1.19/1.03 tff(32,plain,
% 1.19/1.03 (^[U: $i] : refl((hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 1.19/1.03 inference(bind,[status(th)],[])).
% 1.19/1.03 tff(33,plain,
% 1.19/1.03 (![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.19/1.03 inference(quant_intro,[status(thm)],[32])).
% 1.19/1.03 tff(34,plain,
% 1.19/1.03 (![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.19/1.03 inference(rewrite,[status(thm)],[])).
% 1.19/1.03 tff(35,plain,
% 1.19/1.03 (^[U: $i] : 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)) | hskp28) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp28))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 1.19/1.03 inference(bind,[status(th)],[])).
% 1.19/1.03 tff(36,plain,
% 1.19/1.03 (![U: $i] : (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp28) <=> ![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.19/1.03 inference(quant_intro,[status(thm)],[35])).
% 1.19/1.03 tff(37,axiom,(![U: $i] : (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp28)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause137')).
% 1.19/1.03 tff(38,plain,
% 1.19/1.03 (![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.19/1.03 inference(modus_ponens,[status(thm)],[37, 36])).
% 1.19/1.03 tff(39,plain,
% 1.19/1.03 (![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.19/1.03 inference(modus_ponens,[status(thm)],[38, 34])).
% 1.19/1.03 tff(40,plain,(
% 1.19/1.03 ![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.19/1.03 inference(skolemize,[status(sab)],[39])).
% 1.19/1.03 tff(41,plain,
% 1.19/1.03 (![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.19/1.03 inference(modus_ponens,[status(thm)],[40, 33])).
% 1.19/1.03 tff(42,assumption,(~hskp24), introduced(assumption)).
% 1.19/1.03 tff(43,plain,
% 1.19/1.03 ((hskp24 | hskp7) <=> (hskp24 | hskp7)),
% 1.19/1.03 inference(rewrite,[status(thm)],[])).
% 1.19/1.03 tff(44,axiom,(hskp24 | hskp7), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause2')).
% 1.19/1.03 tff(45,plain,
% 1.19/1.03 (hskp24 | hskp7),
% 1.19/1.03 inference(modus_ponens,[status(thm)],[44, 43])).
% 1.19/1.03 tff(46,plain,
% 1.19/1.03 (hskp7),
% 1.19/1.03 inference(unit_resolution,[status(thm)],[45, 42])).
% 1.19/1.03 tff(47,plain,
% 1.19/1.03 (((~hskp7) | (~c1_1(a330))) <=> ((~hskp7) | (~c1_1(a330)))),
% 1.19/1.03 inference(rewrite,[status(thm)],[])).
% 1.19/1.03 tff(48,plain,
% 1.19/1.03 (((~c1_1(a330)) | (~hskp7)) <=> ((~hskp7) | (~c1_1(a330)))),
% 1.19/1.03 inference(rewrite,[status(thm)],[])).
% 1.19/1.03 tff(49,axiom,((~c1_1(a330)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause113')).
% 1.19/1.03 tff(50,plain,
% 1.19/1.03 ((~hskp7) | (~c1_1(a330))),
% 1.19/1.03 inference(modus_ponens,[status(thm)],[49, 48])).
% 1.19/1.03 tff(51,plain,
% 1.19/1.03 ((~hskp7) | (~c1_1(a330))),
% 1.19/1.03 inference(modus_ponens,[status(thm)],[50, 47])).
% 1.19/1.03 tff(52,plain,
% 1.19/1.03 (~c1_1(a330)),
% 1.19/1.03 inference(unit_resolution,[status(thm)],[51, 46])).
% 1.19/1.03 tff(53,plain,
% 1.19/1.03 (((~hskp7) | c3_1(a330)) <=> ((~hskp7) | c3_1(a330))),
% 1.19/1.03 inference(rewrite,[status(thm)],[])).
% 1.19/1.03 tff(54,axiom,((~hskp7) | c3_1(a330)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause71')).
% 1.19/1.03 tff(55,plain,
% 1.19/1.03 ((~hskp7) | c3_1(a330)),
% 1.19/1.03 inference(modus_ponens,[status(thm)],[54, 53])).
% 1.19/1.03 tff(56,plain,
% 1.19/1.03 ((~hskp7) | c3_1(a330)),
% 1.19/1.03 inference(modus_ponens,[status(thm)],[55, 53])).
% 1.19/1.03 tff(57,plain,
% 1.19/1.03 ((~hskp7) | c3_1(a330)),
% 1.19/1.03 inference(modus_ponens,[status(thm)],[56, 53])).
% 1.19/1.03 tff(58,plain,
% 1.19/1.03 ((~hskp7) | c3_1(a330)),
% 1.19/1.03 inference(modus_ponens,[status(thm)],[57, 53])).
% 1.19/1.03 tff(59,plain,
% 1.19/1.03 ((~hskp7) | c3_1(a330)),
% 1.19/1.03 inference(modus_ponens,[status(thm)],[58, 53])).
% 1.19/1.03 tff(60,plain,
% 1.19/1.03 ((~hskp7) | c3_1(a330)),
% 1.19/1.03 inference(modus_ponens,[status(thm)],[59, 53])).
% 1.19/1.03 tff(61,plain,
% 1.19/1.03 ((~hskp7) | c3_1(a330)),
% 1.19/1.03 inference(modus_ponens,[status(thm)],[60, 53])).
% 1.19/1.03 tff(62,plain,
% 1.19/1.03 ((~hskp7) | c3_1(a330)),
% 1.19/1.03 inference(modus_ponens,[status(thm)],[61, 53])).
% 1.19/1.03 tff(63,plain,
% 1.19/1.03 (c3_1(a330)),
% 1.19/1.03 inference(unit_resolution,[status(thm)],[62, 46])).
% 1.19/1.03 tff(64,plain,
% 1.19/1.03 (((~hskp7) | (~c0_1(a330))) <=> ((~hskp7) | (~c0_1(a330)))),
% 1.19/1.03 inference(rewrite,[status(thm)],[])).
% 1.19/1.03 tff(65,plain,
% 1.19/1.03 (((~c0_1(a330)) | (~hskp7)) <=> ((~hskp7) | (~c0_1(a330)))),
% 1.19/1.03 inference(rewrite,[status(thm)],[])).
% 1.19/1.03 tff(66,axiom,((~c0_1(a330)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause112')).
% 1.19/1.03 tff(67,plain,
% 1.19/1.03 ((~hskp7) | (~c0_1(a330))),
% 1.19/1.03 inference(modus_ponens,[status(thm)],[66, 65])).
% 1.19/1.03 tff(68,plain,
% 1.19/1.03 ((~hskp7) | (~c0_1(a330))),
% 1.19/1.03 inference(modus_ponens,[status(thm)],[67, 64])).
% 1.19/1.03 tff(69,plain,
% 1.19/1.03 (~c0_1(a330)),
% 1.19/1.03 inference(unit_resolution,[status(thm)],[68, 46])).
% 1.19/1.03 tff(70,assumption,(~hskp16), introduced(assumption)).
% 1.19/1.03 tff(71,plain,
% 1.19/1.03 (^[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))))),
% 1.19/1.03 inference(bind,[status(th)],[])).
% 1.19/1.03 tff(72,plain,
% 1.19/1.03 (![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)))),
% 1.19/1.03 inference(quant_intro,[status(thm)],[71])).
% 1.19/1.03 tff(73,plain,
% 1.19/1.03 (![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)))),
% 1.19/1.03 inference(rewrite,[status(thm)],[])).
% 1.19/1.03 tff(74,plain,
% 1.19/1.03 (^[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)) | 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)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | 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)) | (~ndr1_0)) | (~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) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | 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)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | 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)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | 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)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | 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)))))),
% 1.19/1.03 inference(bind,[status(th)],[])).
% 1.19/1.03 tff(75,plain,
% 1.19/1.03 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | 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)))),
% 1.19/1.03 inference(quant_intro,[status(thm)],[74])).
% 1.19/1.03 tff(76,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause156')).
% 1.19/1.03 tff(77,plain,
% 1.19/1.03 (![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)))),
% 1.19/1.03 inference(modus_ponens,[status(thm)],[76, 75])).
% 1.19/1.03 tff(78,plain,
% 1.19/1.03 (![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)))),
% 1.19/1.03 inference(modus_ponens,[status(thm)],[77, 73])).
% 1.19/1.03 tff(79,plain,(
% 1.19/1.03 ![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)))),
% 1.19/1.03 inference(skolemize,[status(sab)],[78])).
% 1.19/1.03 tff(80,plain,
% 1.19/1.03 (![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)))),
% 1.19/1.03 inference(modus_ponens,[status(thm)],[79, 72])).
% 1.19/1.03 tff(81,assumption,(~c1_1(a330)), introduced(assumption)).
% 1.19/1.03 tff(82,assumption,(~c0_1(a330)), introduced(assumption)).
% 1.19/1.03 tff(83,plain,
% 1.19/1.03 ((hskp25 | hskp16) <=> (hskp25 | hskp16)),
% 1.19/1.03 inference(rewrite,[status(thm)],[])).
% 1.19/1.03 tff(84,axiom,(hskp25 | hskp16), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 1.19/1.03 tff(85,plain,
% 1.19/1.03 (hskp25 | hskp16),
% 1.19/1.03 inference(modus_ponens,[status(thm)],[84, 83])).
% 1.19/1.03 tff(86,plain,
% 1.19/1.03 (hskp25 | hskp16),
% 1.19/1.03 inference(modus_ponens,[status(thm)],[85, 83])).
% 1.19/1.03 tff(87,plain,
% 1.19/1.03 (hskp25 | hskp16),
% 1.19/1.03 inference(modus_ponens,[status(thm)],[86, 83])).
% 1.19/1.03 tff(88,plain,
% 1.19/1.03 (hskp25 | hskp16),
% 1.19/1.03 inference(modus_ponens,[status(thm)],[87, 83])).
% 1.19/1.03 tff(89,plain,
% 1.19/1.03 (hskp25 | hskp16),
% 1.19/1.03 inference(modus_ponens,[status(thm)],[88, 83])).
% 1.19/1.03 tff(90,plain,
% 1.19/1.03 (hskp25 | hskp16),
% 1.19/1.03 inference(modus_ponens,[status(thm)],[89, 83])).
% 1.19/1.03 tff(91,plain,
% 1.19/1.03 (hskp25 | hskp16),
% 1.19/1.03 inference(modus_ponens,[status(thm)],[90, 83])).
% 1.19/1.03 tff(92,plain,
% 1.19/1.03 (hskp25 | hskp16),
% 1.19/1.03 inference(modus_ponens,[status(thm)],[91, 83])).
% 1.19/1.03 tff(93,plain,
% 1.19/1.03 (hskp25),
% 1.19/1.03 inference(unit_resolution,[status(thm)],[92, 70])).
% 1.19/1.03 tff(94,plain,
% 1.19/1.03 (((~hskp25) | (~c2_1(a419))) <=> ((~hskp25) | (~c2_1(a419)))),
% 1.19/1.03 inference(rewrite,[status(thm)],[])).
% 1.19/1.03 tff(95,plain,
% 1.19/1.03 (((~c2_1(a419)) | (~hskp25)) <=> ((~hskp25) | (~c2_1(a419)))),
% 1.19/1.04 inference(rewrite,[status(thm)],[])).
% 1.19/1.04 tff(96,axiom,((~c2_1(a419)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause82')).
% 1.19/1.04 tff(97,plain,
% 1.19/1.04 ((~hskp25) | (~c2_1(a419))),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[96, 95])).
% 1.19/1.04 tff(98,plain,
% 1.19/1.04 ((~hskp25) | (~c2_1(a419))),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[97, 94])).
% 1.19/1.04 tff(99,plain,
% 1.19/1.04 (~c2_1(a419)),
% 1.19/1.04 inference(unit_resolution,[status(thm)],[98, 93])).
% 1.19/1.04 tff(100,plain,
% 1.19/1.04 (((~hskp25) | (~c1_1(a419))) <=> ((~hskp25) | (~c1_1(a419)))),
% 1.19/1.04 inference(rewrite,[status(thm)],[])).
% 1.19/1.04 tff(101,plain,
% 1.19/1.04 (((~c1_1(a419)) | (~hskp25)) <=> ((~hskp25) | (~c1_1(a419)))),
% 1.19/1.04 inference(rewrite,[status(thm)],[])).
% 1.19/1.04 tff(102,axiom,((~c1_1(a419)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause81')).
% 1.19/1.04 tff(103,plain,
% 1.19/1.04 ((~hskp25) | (~c1_1(a419))),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[102, 101])).
% 1.19/1.04 tff(104,plain,
% 1.19/1.04 ((~hskp25) | (~c1_1(a419))),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[103, 100])).
% 1.19/1.04 tff(105,plain,
% 1.19/1.04 (~c1_1(a419)),
% 1.19/1.04 inference(unit_resolution,[status(thm)],[104, 93])).
% 1.19/1.04 tff(106,assumption,(c3_1(a330)), introduced(assumption)).
% 1.19/1.04 tff(107,plain,
% 1.19/1.04 (((~hskp25) | c0_1(a419)) <=> ((~hskp25) | c0_1(a419))),
% 1.19/1.04 inference(rewrite,[status(thm)],[])).
% 1.19/1.04 tff(108,axiom,((~hskp25) | c0_1(a419)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause48')).
% 1.19/1.04 tff(109,plain,
% 1.19/1.04 ((~hskp25) | c0_1(a419)),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[108, 107])).
% 1.19/1.04 tff(110,plain,
% 1.19/1.04 ((~hskp25) | c0_1(a419)),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[109, 107])).
% 1.19/1.04 tff(111,plain,
% 1.19/1.04 ((~hskp25) | c0_1(a419)),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[110, 107])).
% 1.19/1.04 tff(112,plain,
% 1.19/1.04 ((~hskp25) | c0_1(a419)),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[111, 107])).
% 1.19/1.04 tff(113,plain,
% 1.19/1.04 ((~hskp25) | c0_1(a419)),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[112, 107])).
% 1.19/1.04 tff(114,plain,
% 1.19/1.04 ((~hskp25) | c0_1(a419)),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[113, 107])).
% 1.19/1.04 tff(115,plain,
% 1.19/1.04 ((~hskp25) | c0_1(a419)),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[114, 107])).
% 1.19/1.04 tff(116,plain,
% 1.19/1.04 ((~hskp25) | c0_1(a419)),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[115, 107])).
% 1.19/1.04 tff(117,plain,
% 1.19/1.04 (c0_1(a419)),
% 1.19/1.04 inference(unit_resolution,[status(thm)],[116, 93])).
% 1.19/1.04 tff(118,assumption,(~ndr1_0), introduced(assumption)).
% 1.19/1.04 tff(119,plain,
% 1.19/1.04 ((ndr1_0 | (~hskp24)) <=> (ndr1_0 | (~hskp24))),
% 1.19/1.04 inference(rewrite,[status(thm)],[])).
% 1.19/1.04 tff(120,plain,
% 1.19/1.04 (((~hskp24) | ndr1_0) <=> (ndr1_0 | (~hskp24))),
% 1.19/1.04 inference(rewrite,[status(thm)],[])).
% 1.19/1.04 tff(121,axiom,((~hskp24) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause7')).
% 1.19/1.04 tff(122,plain,
% 1.19/1.04 (ndr1_0 | (~hskp24)),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[121, 120])).
% 1.19/1.04 tff(123,plain,
% 1.19/1.04 (ndr1_0 | (~hskp24)),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[122, 119])).
% 1.19/1.04 tff(124,plain,
% 1.19/1.04 (~hskp24),
% 1.19/1.04 inference(unit_resolution,[status(thm)],[123, 118])).
% 1.19/1.04 tff(125,plain,
% 1.19/1.04 ((ndr1_0 | (~hskp26)) <=> (ndr1_0 | (~hskp26))),
% 1.19/1.04 inference(rewrite,[status(thm)],[])).
% 1.19/1.04 tff(126,plain,
% 1.19/1.04 (((~hskp26) | ndr1_0) <=> (ndr1_0 | (~hskp26))),
% 1.19/1.04 inference(rewrite,[status(thm)],[])).
% 1.19/1.04 tff(127,axiom,((~hskp26) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause5')).
% 1.19/1.04 tff(128,plain,
% 1.19/1.04 (ndr1_0 | (~hskp26)),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[127, 126])).
% 1.19/1.04 tff(129,plain,
% 1.19/1.04 (ndr1_0 | (~hskp26)),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[128, 125])).
% 1.19/1.04 tff(130,plain,
% 1.19/1.04 (~hskp26),
% 1.19/1.04 inference(unit_resolution,[status(thm)],[129, 118])).
% 1.19/1.04 tff(131,plain,
% 1.19/1.04 ((ndr1_0 | (~hskp2)) <=> (ndr1_0 | (~hskp2))),
% 1.19/1.04 inference(rewrite,[status(thm)],[])).
% 1.19/1.04 tff(132,plain,
% 1.19/1.04 (((~hskp2) | ndr1_0) <=> (ndr1_0 | (~hskp2))),
% 1.19/1.04 inference(rewrite,[status(thm)],[])).
% 1.19/1.04 tff(133,axiom,((~hskp2) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause29')).
% 1.19/1.04 tff(134,plain,
% 1.19/1.04 (ndr1_0 | (~hskp2)),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[133, 132])).
% 1.19/1.04 tff(135,plain,
% 1.19/1.04 (ndr1_0 | (~hskp2)),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[134, 131])).
% 1.19/1.04 tff(136,plain,
% 1.19/1.04 (~hskp2),
% 1.19/1.04 inference(unit_resolution,[status(thm)],[135, 118])).
% 1.19/1.04 tff(137,plain,
% 1.19/1.04 ((hskp24 | hskp26 | hskp2) <=> (hskp24 | hskp26 | hskp2)),
% 1.19/1.04 inference(rewrite,[status(thm)],[])).
% 1.19/1.04 tff(138,plain,
% 1.19/1.04 (((hskp24 | hskp26) | hskp2) <=> (hskp24 | hskp26 | hskp2)),
% 1.19/1.04 inference(rewrite,[status(thm)],[])).
% 1.19/1.04 tff(139,plain,
% 1.19/1.04 ((hskp26 | hskp24) <=> (hskp24 | hskp26)),
% 1.19/1.04 inference(rewrite,[status(thm)],[])).
% 1.19/1.04 tff(140,plain,
% 1.19/1.04 (((hskp26 | hskp24) | hskp2) <=> ((hskp24 | hskp26) | hskp2)),
% 1.19/1.04 inference(monotonicity,[status(thm)],[139])).
% 1.19/1.04 tff(141,plain,
% 1.19/1.04 (((hskp26 | hskp24) | hskp2) <=> (hskp24 | hskp26 | hskp2)),
% 1.19/1.04 inference(transitivity,[status(thm)],[140, 138])).
% 1.19/1.04 tff(142,axiom,((hskp26 | hskp24) | hskp2), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause32')).
% 1.19/1.04 tff(143,plain,
% 1.19/1.04 (hskp24 | hskp26 | hskp2),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[142, 141])).
% 1.19/1.04 tff(144,plain,
% 1.19/1.04 (hskp24 | hskp26 | hskp2),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[143, 137])).
% 1.19/1.04 tff(145,plain,
% 1.19/1.04 (hskp24 | hskp26 | hskp2),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[144, 137])).
% 1.19/1.04 tff(146,plain,
% 1.19/1.04 (hskp24 | hskp26 | hskp2),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[145, 137])).
% 1.19/1.04 tff(147,plain,
% 1.19/1.04 (hskp24 | hskp26 | hskp2),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[146, 137])).
% 1.19/1.04 tff(148,plain,
% 1.19/1.04 (hskp24 | hskp26 | hskp2),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[147, 137])).
% 1.19/1.04 tff(149,plain,
% 1.19/1.04 (hskp24 | hskp26 | hskp2),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[148, 137])).
% 1.19/1.04 tff(150,plain,
% 1.19/1.04 (hskp24 | hskp26 | hskp2),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[149, 137])).
% 1.19/1.04 tff(151,plain,
% 1.19/1.04 ($false),
% 1.19/1.04 inference(unit_resolution,[status(thm)],[150, 136, 130, 124])).
% 1.19/1.04 tff(152,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 1.19/1.04 tff(153,plain,
% 1.19/1.04 (((~![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(a419) | c2_1(a419) | c0_1(a330) | c1_1(a330) | (~ndr1_0) | (~c3_1(a330)) | (~c0_1(a419)))) <=> ((~![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(a419) | c2_1(a419) | c0_1(a330) | c1_1(a330) | (~ndr1_0) | (~c3_1(a330)) | (~c0_1(a419)))),
% 1.19/1.04 inference(rewrite,[status(thm)],[])).
% 1.19/1.04 tff(154,plain,
% 1.19/1.04 ((hskp9 | (~ndr1_0) | c2_1(a419) | c1_1(a419) | (~c0_1(a419)) | c1_1(a330) | c0_1(a330) | (~c3_1(a330))) <=> (hskp9 | c1_1(a419) | c2_1(a419) | c0_1(a330) | c1_1(a330) | (~ndr1_0) | (~c3_1(a330)) | (~c0_1(a419)))),
% 1.19/1.04 inference(rewrite,[status(thm)],[])).
% 1.19/1.04 tff(155,plain,
% 1.19/1.04 (((~![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(a419) | c1_1(a419) | (~c0_1(a419)) | c1_1(a330) | c0_1(a330) | (~c3_1(a330)))) <=> ((~![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(a419) | c2_1(a419) | c0_1(a330) | c1_1(a330) | (~ndr1_0) | (~c3_1(a330)) | (~c0_1(a419))))),
% 1.19/1.04 inference(monotonicity,[status(thm)],[154])).
% 1.19/1.04 tff(156,plain,
% 1.19/1.04 (((~![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(a419) | c1_1(a419) | (~c0_1(a419)) | c1_1(a330) | c0_1(a330) | (~c3_1(a330)))) <=> ((~![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(a419) | c2_1(a419) | c0_1(a330) | c1_1(a330) | (~ndr1_0) | (~c3_1(a330)) | (~c0_1(a419)))),
% 1.19/1.04 inference(transitivity,[status(thm)],[155, 153])).
% 1.19/1.04 tff(157,plain,
% 1.19/1.04 ((~![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(a419) | c1_1(a419) | (~c0_1(a419)) | c1_1(a330) | c0_1(a330) | (~c3_1(a330)))),
% 1.19/1.04 inference(quant_inst,[status(thm)],[])).
% 1.19/1.04 tff(158,plain,
% 1.19/1.04 ((~![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(a419) | c2_1(a419) | c0_1(a330) | c1_1(a330) | (~ndr1_0) | (~c3_1(a330)) | (~c0_1(a419))),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[157, 156])).
% 1.19/1.04 tff(159,plain,
% 1.19/1.04 (hskp9),
% 1.19/1.04 inference(unit_resolution,[status(thm)],[158, 152, 117, 106, 105, 99, 82, 81, 80])).
% 1.19/1.04 tff(160,plain,
% 1.19/1.04 (((~hskp9) | (~c0_1(a334))) <=> ((~hskp9) | (~c0_1(a334)))),
% 1.19/1.04 inference(rewrite,[status(thm)],[])).
% 1.19/1.04 tff(161,plain,
% 1.19/1.04 (((~c0_1(a334)) | (~hskp9)) <=> ((~hskp9) | (~c0_1(a334)))),
% 1.19/1.04 inference(rewrite,[status(thm)],[])).
% 1.19/1.04 tff(162,axiom,((~c0_1(a334)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause107')).
% 1.19/1.04 tff(163,plain,
% 1.19/1.04 ((~hskp9) | (~c0_1(a334))),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[162, 161])).
% 1.19/1.04 tff(164,plain,
% 1.19/1.04 ((~hskp9) | (~c0_1(a334))),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[163, 160])).
% 1.19/1.04 tff(165,plain,
% 1.19/1.04 (~c0_1(a334)),
% 1.19/1.04 inference(unit_resolution,[status(thm)],[164, 159])).
% 1.19/1.04 tff(166,plain,
% 1.19/1.04 (((~hskp9) | (~c1_1(a334))) <=> ((~hskp9) | (~c1_1(a334)))),
% 1.19/1.04 inference(rewrite,[status(thm)],[])).
% 1.19/1.04 tff(167,plain,
% 1.19/1.04 (((~c1_1(a334)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a334)))),
% 1.19/1.04 inference(rewrite,[status(thm)],[])).
% 1.19/1.04 tff(168,axiom,((~c1_1(a334)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause108')).
% 1.19/1.04 tff(169,plain,
% 1.19/1.04 ((~hskp9) | (~c1_1(a334))),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[168, 167])).
% 1.19/1.04 tff(170,plain,
% 1.19/1.04 ((~hskp9) | (~c1_1(a334))),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[169, 166])).
% 1.19/1.04 tff(171,plain,
% 1.19/1.04 (~c1_1(a334)),
% 1.19/1.04 inference(unit_resolution,[status(thm)],[170, 159])).
% 1.19/1.04 tff(172,plain,
% 1.19/1.04 (((~hskp9) | c2_1(a334)) <=> ((~hskp9) | c2_1(a334))),
% 1.19/1.04 inference(rewrite,[status(thm)],[])).
% 1.19/1.04 tff(173,axiom,((~hskp9) | c2_1(a334)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause70')).
% 1.19/1.04 tff(174,plain,
% 1.19/1.04 ((~hskp9) | c2_1(a334)),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[173, 172])).
% 1.19/1.04 tff(175,plain,
% 1.19/1.04 ((~hskp9) | c2_1(a334)),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[174, 172])).
% 1.19/1.04 tff(176,plain,
% 1.19/1.04 ((~hskp9) | c2_1(a334)),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[175, 172])).
% 1.19/1.04 tff(177,plain,
% 1.19/1.04 ((~hskp9) | c2_1(a334)),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[176, 172])).
% 1.19/1.04 tff(178,plain,
% 1.19/1.04 ((~hskp9) | c2_1(a334)),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[177, 172])).
% 1.19/1.04 tff(179,plain,
% 1.19/1.04 ((~hskp9) | c2_1(a334)),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[178, 172])).
% 1.19/1.04 tff(180,plain,
% 1.19/1.04 ((~hskp9) | c2_1(a334)),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[179, 172])).
% 1.19/1.04 tff(181,plain,
% 1.19/1.04 ((~hskp9) | c2_1(a334)),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[180, 172])).
% 1.19/1.04 tff(182,plain,
% 1.19/1.04 (c2_1(a334)),
% 1.19/1.04 inference(unit_resolution,[status(thm)],[181, 159])).
% 1.19/1.04 tff(183,plain,
% 1.19/1.04 (^[V: $i, U: $i] : refl((hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.19/1.04 inference(bind,[status(th)],[])).
% 1.19/1.04 tff(184,plain,
% 1.19/1.04 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.19/1.04 inference(quant_intro,[status(thm)],[183])).
% 1.19/1.04 tff(185,plain,
% 1.19/1.04 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.19/1.04 inference(rewrite,[status(thm)],[])).
% 1.19/1.04 tff(186,plain,
% 1.19/1.04 (^[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)) | 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)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | 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)) | (~ndr1_0)) | (~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) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | 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)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | 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)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp26) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp26))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp26) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp26) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.19/1.04 inference(bind,[status(th)],[])).
% 1.19/1.04 tff(187,plain,
% 1.19/1.04 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp26) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.19/1.04 inference(quant_intro,[status(thm)],[186])).
% 1.19/1.04 tff(188,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause155')).
% 1.19/1.04 tff(189,plain,
% 1.19/1.04 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[188, 187])).
% 1.19/1.04 tff(190,plain,
% 1.19/1.04 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[189, 185])).
% 1.19/1.04 tff(191,plain,(
% 1.19/1.04 ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.19/1.04 inference(skolemize,[status(sab)],[190])).
% 1.19/1.04 tff(192,plain,
% 1.19/1.04 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[191, 184])).
% 1.19/1.04 tff(193,plain,
% 1.19/1.04 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c1_1(a419) | c2_1(a419) | c0_1(a330) | c1_1(a330) | (~ndr1_0) | (~c3_1(a330)) | (~c0_1(a419)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c1_1(a419) | c2_1(a419) | c0_1(a330) | c1_1(a330) | (~ndr1_0) | (~c3_1(a330)) | (~c0_1(a419)))),
% 1.19/1.04 inference(rewrite,[status(thm)],[])).
% 1.19/1.04 tff(194,plain,
% 1.19/1.04 ((hskp26 | (~ndr1_0) | c2_1(a419) | c1_1(a419) | (~c0_1(a419)) | c1_1(a330) | c0_1(a330) | (~c3_1(a330))) <=> (hskp26 | c1_1(a419) | c2_1(a419) | c0_1(a330) | c1_1(a330) | (~ndr1_0) | (~c3_1(a330)) | (~c0_1(a419)))),
% 1.19/1.04 inference(rewrite,[status(thm)],[])).
% 1.19/1.04 tff(195,plain,
% 1.19/1.04 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c2_1(a419) | c1_1(a419) | (~c0_1(a419)) | c1_1(a330) | c0_1(a330) | (~c3_1(a330)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | c1_1(a419) | c2_1(a419) | c0_1(a330) | c1_1(a330) | (~ndr1_0) | (~c3_1(a330)) | (~c0_1(a419))))),
% 1.19/1.04 inference(monotonicity,[status(thm)],[194])).
% 1.19/1.04 tff(196,plain,
% 1.19/1.04 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c2_1(a419) | c1_1(a419) | (~c0_1(a419)) | c1_1(a330) | c0_1(a330) | (~c3_1(a330)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c1_1(a419) | c2_1(a419) | c0_1(a330) | c1_1(a330) | (~ndr1_0) | (~c3_1(a330)) | (~c0_1(a419)))),
% 1.19/1.04 inference(transitivity,[status(thm)],[195, 193])).
% 1.19/1.04 tff(197,plain,
% 1.19/1.04 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp26 | (~ndr1_0) | c2_1(a419) | c1_1(a419) | (~c0_1(a419)) | c1_1(a330) | c0_1(a330) | (~c3_1(a330)))),
% 1.19/1.04 inference(quant_inst,[status(thm)],[])).
% 1.19/1.04 tff(198,plain,
% 1.19/1.04 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp26 | c1_1(a419) | c2_1(a419) | c0_1(a330) | c1_1(a330) | (~ndr1_0) | (~c3_1(a330)) | (~c0_1(a419))),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[197, 196])).
% 1.19/1.04 tff(199,plain,
% 1.19/1.04 (hskp26),
% 1.19/1.04 inference(unit_resolution,[status(thm)],[198, 152, 117, 106, 105, 99, 82, 81, 192])).
% 1.19/1.04 tff(200,plain,
% 1.19/1.04 (((~hskp26) | c1_1(a333)) <=> ((~hskp26) | c1_1(a333))),
% 1.19/1.04 inference(rewrite,[status(thm)],[])).
% 1.19/1.04 tff(201,axiom,((~hskp26) | c1_1(a333)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause46')).
% 1.19/1.04 tff(202,plain,
% 1.19/1.04 ((~hskp26) | c1_1(a333)),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[201, 200])).
% 1.19/1.04 tff(203,plain,
% 1.19/1.04 ((~hskp26) | c1_1(a333)),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[202, 200])).
% 1.19/1.04 tff(204,plain,
% 1.19/1.04 ((~hskp26) | c1_1(a333)),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[203, 200])).
% 1.19/1.04 tff(205,plain,
% 1.19/1.04 ((~hskp26) | c1_1(a333)),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[204, 200])).
% 1.19/1.04 tff(206,plain,
% 1.19/1.04 ((~hskp26) | c1_1(a333)),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[205, 200])).
% 1.19/1.04 tff(207,plain,
% 1.19/1.04 ((~hskp26) | c1_1(a333)),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[206, 200])).
% 1.19/1.04 tff(208,plain,
% 1.19/1.04 ((~hskp26) | c1_1(a333)),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[207, 200])).
% 1.19/1.04 tff(209,plain,
% 1.19/1.04 ((~hskp26) | c1_1(a333)),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[208, 200])).
% 1.19/1.04 tff(210,plain,
% 1.19/1.04 (c1_1(a333)),
% 1.19/1.04 inference(unit_resolution,[status(thm)],[209, 199])).
% 1.19/1.04 tff(211,plain,
% 1.19/1.04 (((~hskp26) | c3_1(a333)) <=> ((~hskp26) | c3_1(a333))),
% 1.19/1.04 inference(rewrite,[status(thm)],[])).
% 1.19/1.04 tff(212,axiom,((~hskp26) | c3_1(a333)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause47')).
% 1.19/1.04 tff(213,plain,
% 1.19/1.04 ((~hskp26) | c3_1(a333)),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[212, 211])).
% 1.19/1.04 tff(214,plain,
% 1.19/1.04 ((~hskp26) | c3_1(a333)),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[213, 211])).
% 1.19/1.04 tff(215,plain,
% 1.19/1.04 ((~hskp26) | c3_1(a333)),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[214, 211])).
% 1.19/1.04 tff(216,plain,
% 1.19/1.04 ((~hskp26) | c3_1(a333)),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[215, 211])).
% 1.19/1.04 tff(217,plain,
% 1.19/1.04 ((~hskp26) | c3_1(a333)),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[216, 211])).
% 1.19/1.04 tff(218,plain,
% 1.19/1.04 ((~hskp26) | c3_1(a333)),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[217, 211])).
% 1.19/1.04 tff(219,plain,
% 1.19/1.04 ((~hskp26) | c3_1(a333)),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[218, 211])).
% 1.19/1.04 tff(220,plain,
% 1.19/1.04 ((~hskp26) | c3_1(a333)),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[219, 211])).
% 1.19/1.04 tff(221,plain,
% 1.19/1.04 (c3_1(a333)),
% 1.19/1.04 inference(unit_resolution,[status(thm)],[220, 199])).
% 1.19/1.04 tff(222,plain,
% 1.19/1.04 (((~hskp26) | c0_1(a333)) <=> ((~hskp26) | c0_1(a333))),
% 1.19/1.04 inference(rewrite,[status(thm)],[])).
% 1.19/1.04 tff(223,axiom,((~hskp26) | c0_1(a333)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause45')).
% 1.19/1.04 tff(224,plain,
% 1.19/1.04 ((~hskp26) | c0_1(a333)),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[223, 222])).
% 1.19/1.04 tff(225,plain,
% 1.19/1.04 ((~hskp26) | c0_1(a333)),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[224, 222])).
% 1.19/1.04 tff(226,plain,
% 1.19/1.04 ((~hskp26) | c0_1(a333)),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[225, 222])).
% 1.19/1.04 tff(227,plain,
% 1.19/1.04 ((~hskp26) | c0_1(a333)),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[226, 222])).
% 1.19/1.04 tff(228,plain,
% 1.19/1.04 ((~hskp26) | c0_1(a333)),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[227, 222])).
% 1.19/1.04 tff(229,plain,
% 1.19/1.04 ((~hskp26) | c0_1(a333)),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[228, 222])).
% 1.19/1.04 tff(230,plain,
% 1.19/1.04 ((~hskp26) | c0_1(a333)),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[229, 222])).
% 1.19/1.04 tff(231,plain,
% 1.19/1.04 ((~hskp26) | c0_1(a333)),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[230, 222])).
% 1.19/1.04 tff(232,plain,
% 1.19/1.04 (c0_1(a333)),
% 1.19/1.04 inference(unit_resolution,[status(thm)],[231, 199])).
% 1.19/1.04 tff(233,assumption,(~hskp22), introduced(assumption)).
% 1.19/1.04 tff(234,plain,
% 1.19/1.04 (^[V: $i, U: $i] : refl((hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))),
% 1.19/1.04 inference(bind,[status(th)],[])).
% 1.19/1.04 tff(235,plain,
% 1.19/1.04 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.19/1.04 inference(quant_intro,[status(thm)],[234])).
% 1.19/1.04 tff(236,plain,
% 1.19/1.04 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.19/1.04 inference(rewrite,[status(thm)],[])).
% 1.19/1.04 tff(237,plain,
% 1.19/1.04 (^[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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | 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) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | 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)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_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(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp22) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp22))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))))),
% 1.19/1.04 inference(bind,[status(th)],[])).
% 1.19/1.04 tff(238,plain,
% 1.19/1.04 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp22) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.19/1.04 inference(quant_intro,[status(thm)],[237])).
% 1.19/1.04 tff(239,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause162')).
% 1.19/1.04 tff(240,plain,
% 1.19/1.04 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[239, 238])).
% 1.19/1.04 tff(241,plain,
% 1.19/1.04 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[240, 236])).
% 1.19/1.04 tff(242,plain,(
% 1.19/1.04 ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.19/1.04 inference(skolemize,[status(sab)],[241])).
% 1.19/1.04 tff(243,plain,
% 1.19/1.04 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[242, 235])).
% 1.19/1.04 tff(244,assumption,(~c2_1(a419)), introduced(assumption)).
% 1.19/1.04 tff(245,assumption,(~c1_1(a419)), introduced(assumption)).
% 1.19/1.04 tff(246,assumption,(c0_1(a419)), introduced(assumption)).
% 1.19/1.04 tff(247,plain,
% 1.19/1.04 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a419) | c2_1(a419) | (~ndr1_0) | c3_1(a419) | (~c0_1(a419)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a419) | c2_1(a419) | (~ndr1_0) | c3_1(a419) | (~c0_1(a419)))),
% 1.19/1.04 inference(rewrite,[status(thm)],[])).
% 1.19/1.04 tff(248,plain,
% 1.19/1.04 ((hskp22 | (~ndr1_0) | c2_1(a419) | c3_1(a419) | (~c0_1(a419)) | c1_1(a419) | c3_1(a419) | (~c0_1(a419))) <=> (hskp22 | c1_1(a419) | c2_1(a419) | (~ndr1_0) | c3_1(a419) | (~c0_1(a419)))),
% 1.19/1.04 inference(rewrite,[status(thm)],[])).
% 1.19/1.04 tff(249,plain,
% 1.19/1.04 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a419) | c3_1(a419) | (~c0_1(a419)) | c1_1(a419) | c3_1(a419) | (~c0_1(a419)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a419) | c2_1(a419) | (~ndr1_0) | c3_1(a419) | (~c0_1(a419))))),
% 1.19/1.04 inference(monotonicity,[status(thm)],[248])).
% 1.19/1.04 tff(250,plain,
% 1.19/1.04 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a419) | c3_1(a419) | (~c0_1(a419)) | c1_1(a419) | c3_1(a419) | (~c0_1(a419)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a419) | c2_1(a419) | (~ndr1_0) | c3_1(a419) | (~c0_1(a419)))),
% 1.19/1.04 inference(transitivity,[status(thm)],[249, 247])).
% 1.19/1.04 tff(251,plain,
% 1.19/1.04 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a419) | c3_1(a419) | (~c0_1(a419)) | c1_1(a419) | c3_1(a419) | (~c0_1(a419)))),
% 1.19/1.04 inference(quant_inst,[status(thm)],[])).
% 1.19/1.04 tff(252,plain,
% 1.19/1.04 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a419) | c2_1(a419) | (~ndr1_0) | c3_1(a419) | (~c0_1(a419))),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[251, 250])).
% 1.19/1.04 tff(253,plain,
% 1.19/1.04 (hskp22 | c3_1(a419)),
% 1.19/1.04 inference(unit_resolution,[status(thm)],[252, 152, 246, 245, 244, 243])).
% 1.19/1.04 tff(254,plain,
% 1.19/1.04 (c3_1(a419)),
% 1.19/1.04 inference(unit_resolution,[status(thm)],[253, 233])).
% 1.19/1.04 tff(255,plain,
% 1.19/1.04 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))))),
% 1.19/1.04 inference(bind,[status(th)],[])).
% 1.19/1.04 tff(256,plain,
% 1.19/1.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 1.19/1.04 inference(quant_intro,[status(thm)],[255])).
% 1.19/1.04 tff(257,plain,
% 1.19/1.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 1.19/1.04 inference(rewrite,[status(thm)],[])).
% 1.19/1.04 tff(258,plain,
% 1.19/1.04 (^[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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))))),
% 1.19/1.04 inference(bind,[status(th)],[])).
% 1.19/1.04 tff(259,plain,
% 1.19/1.04 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 1.19/1.04 inference(quant_intro,[status(thm)],[258])).
% 1.19/1.04 tff(260,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause191')).
% 1.19/1.04 tff(261,plain,
% 1.19/1.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[260, 259])).
% 1.19/1.04 tff(262,plain,
% 1.19/1.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[261, 257])).
% 1.19/1.04 tff(263,plain,(
% 1.19/1.04 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 1.19/1.04 inference(skolemize,[status(sab)],[262])).
% 1.19/1.04 tff(264,plain,
% 1.19/1.04 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 1.19/1.04 inference(modus_ponens,[status(thm)],[263, 256])).
% 1.19/1.04 tff(265,assumption,(~c1_1(a334)), introduced(assumption)).
% 1.19/1.04 tff(266,assumption,(~c0_1(a334)), introduced(assumption)).
% 1.19/1.04 tff(267,assumption,(c2_1(a334)), introduced(assumption)).
% 1.19/1.04 tff(268,plain,
% 1.19/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a419) | c0_1(a334) | c1_1(a334) | (~ndr1_0) | (~c2_1(a334)) | (~c3_1(a334)) | (~c3_1(a419)) | (~c0_1(a419)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a419) | c0_1(a334) | c1_1(a334) | (~ndr1_0) | (~c2_1(a334)) | (~c3_1(a334)) | (~c3_1(a419)) | (~c0_1(a419)))),
% 1.19/1.04 inference(rewrite,[status(thm)],[])).
% 1.19/1.04 tff(269,plain,
% 1.19/1.04 (((~ndr1_0) | c1_1(a334) | (~c2_1(a334)) | (~c3_1(a334)) | c1_1(a419) | (~c3_1(a419)) | (~c0_1(a419)) | c0_1(a334) | c1_1(a334) | (~c2_1(a334))) <=> (c1_1(a419) | c0_1(a334) | c1_1(a334) | (~ndr1_0) | (~c2_1(a334)) | (~c3_1(a334)) | (~c3_1(a419)) | (~c0_1(a419)))),
% 1.19/1.04 inference(rewrite,[status(thm)],[])).
% 1.19/1.05 tff(270,plain,
% 1.19/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a334) | (~c2_1(a334)) | (~c3_1(a334)) | c1_1(a419) | (~c3_1(a419)) | (~c0_1(a419)) | c0_1(a334) | c1_1(a334) | (~c2_1(a334)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a419) | c0_1(a334) | c1_1(a334) | (~ndr1_0) | (~c2_1(a334)) | (~c3_1(a334)) | (~c3_1(a419)) | (~c0_1(a419))))),
% 1.19/1.05 inference(monotonicity,[status(thm)],[269])).
% 1.19/1.05 tff(271,plain,
% 1.19/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a334) | (~c2_1(a334)) | (~c3_1(a334)) | c1_1(a419) | (~c3_1(a419)) | (~c0_1(a419)) | c0_1(a334) | c1_1(a334) | (~c2_1(a334)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a419) | c0_1(a334) | c1_1(a334) | (~ndr1_0) | (~c2_1(a334)) | (~c3_1(a334)) | (~c3_1(a419)) | (~c0_1(a419)))),
% 1.19/1.05 inference(transitivity,[status(thm)],[270, 268])).
% 1.19/1.05 tff(272,plain,
% 1.19/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a334) | (~c2_1(a334)) | (~c3_1(a334)) | c1_1(a419) | (~c3_1(a419)) | (~c0_1(a419)) | c0_1(a334) | c1_1(a334) | (~c2_1(a334)))),
% 1.19/1.05 inference(quant_inst,[status(thm)],[])).
% 1.19/1.05 tff(273,plain,
% 1.19/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a419) | c0_1(a334) | c1_1(a334) | (~ndr1_0) | (~c2_1(a334)) | (~c3_1(a334)) | (~c3_1(a419)) | (~c0_1(a419))),
% 1.19/1.05 inference(modus_ponens,[status(thm)],[272, 271])).
% 1.19/1.05 tff(274,plain,
% 1.19/1.05 ((~c3_1(a334)) | (~c3_1(a419))),
% 1.19/1.05 inference(unit_resolution,[status(thm)],[273, 152, 246, 267, 245, 266, 265, 264])).
% 1.19/1.05 tff(275,plain,
% 1.19/1.05 (~c3_1(a334)),
% 1.19/1.05 inference(unit_resolution,[status(thm)],[274, 254])).
% 1.19/1.05 tff(276,plain,
% 1.19/1.05 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> (hskp12 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))))),
% 1.19/1.05 inference(bind,[status(th)],[])).
% 1.19/1.05 tff(277,plain,
% 1.19/1.05 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.19/1.05 inference(quant_intro,[status(thm)],[276])).
% 1.19/1.05 tff(278,plain,
% 1.19/1.05 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.19/1.05 inference(rewrite,[status(thm)],[])).
% 1.19/1.05 tff(279,plain,
% 1.19/1.05 (^[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) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp12) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | hskp12))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))))),
% 1.19/1.05 inference(bind,[status(th)],[])).
% 1.19/1.05 tff(280,plain,
% 1.19/1.05 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.19/1.05 inference(quant_intro,[status(thm)],[279])).
% 1.19/1.05 tff(281,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause170')).
% 1.19/1.05 tff(282,plain,
% 1.19/1.05 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.19/1.05 inference(modus_ponens,[status(thm)],[281, 280])).
% 1.19/1.05 tff(283,plain,
% 1.19/1.05 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.19/1.05 inference(modus_ponens,[status(thm)],[282, 278])).
% 1.19/1.05 tff(284,plain,(
% 1.19/1.05 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.19/1.05 inference(skolemize,[status(sab)],[283])).
% 1.19/1.05 tff(285,plain,
% 1.19/1.05 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.19/1.05 inference(modus_ponens,[status(thm)],[284, 277])).
% 1.19/1.05 tff(286,plain,
% 1.19/1.05 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp12 | c1_1(a419) | c0_1(a334) | (~ndr1_0) | (~c2_1(a334)) | c3_1(a334) | (~c3_1(a419)) | (~c0_1(a419)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp12 | c1_1(a419) | c0_1(a334) | (~ndr1_0) | (~c2_1(a334)) | c3_1(a334) | (~c3_1(a419)) | (~c0_1(a419)))),
% 1.19/1.05 inference(rewrite,[status(thm)],[])).
% 1.19/1.05 tff(287,plain,
% 1.19/1.05 ((hskp12 | (~ndr1_0) | c1_1(a419) | (~c0_1(a419)) | (~c3_1(a419)) | c0_1(a334) | c3_1(a334) | (~c2_1(a334))) <=> (hskp12 | c1_1(a419) | c0_1(a334) | (~ndr1_0) | (~c2_1(a334)) | c3_1(a334) | (~c3_1(a419)) | (~c0_1(a419)))),
% 1.19/1.05 inference(rewrite,[status(thm)],[])).
% 1.19/1.05 tff(288,plain,
% 1.19/1.05 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c1_1(a419) | (~c0_1(a419)) | (~c3_1(a419)) | c0_1(a334) | c3_1(a334) | (~c2_1(a334)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp12 | c1_1(a419) | c0_1(a334) | (~ndr1_0) | (~c2_1(a334)) | c3_1(a334) | (~c3_1(a419)) | (~c0_1(a419))))),
% 1.19/1.05 inference(monotonicity,[status(thm)],[287])).
% 1.19/1.05 tff(289,plain,
% 1.19/1.05 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c1_1(a419) | (~c0_1(a419)) | (~c3_1(a419)) | c0_1(a334) | c3_1(a334) | (~c2_1(a334)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp12 | c1_1(a419) | c0_1(a334) | (~ndr1_0) | (~c2_1(a334)) | c3_1(a334) | (~c3_1(a419)) | (~c0_1(a419)))),
% 1.19/1.05 inference(transitivity,[status(thm)],[288, 286])).
% 1.19/1.05 tff(290,plain,
% 1.19/1.05 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp12 | (~ndr1_0) | c1_1(a419) | (~c0_1(a419)) | (~c3_1(a419)) | c0_1(a334) | c3_1(a334) | (~c2_1(a334)))),
% 1.19/1.05 inference(quant_inst,[status(thm)],[])).
% 1.19/1.05 tff(291,plain,
% 1.19/1.05 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp12 | c1_1(a419) | c0_1(a334) | (~ndr1_0) | (~c2_1(a334)) | c3_1(a334) | (~c3_1(a419)) | (~c0_1(a419))),
% 1.19/1.05 inference(modus_ponens,[status(thm)],[290, 289])).
% 1.19/1.05 tff(292,plain,
% 1.19/1.05 (hskp12 | c3_1(a334) | (~c3_1(a419))),
% 1.19/1.05 inference(unit_resolution,[status(thm)],[291, 152, 246, 267, 245, 266, 285])).
% 1.19/1.05 tff(293,plain,
% 1.19/1.05 (hskp12),
% 1.19/1.05 inference(unit_resolution,[status(thm)],[292, 254, 275])).
% 1.19/1.05 tff(294,plain,
% 1.19/1.05 (((~hskp12) | c3_1(a345)) <=> ((~hskp12) | c3_1(a345))),
% 1.19/1.05 inference(rewrite,[status(thm)],[])).
% 1.19/1.05 tff(295,axiom,((~hskp12) | c3_1(a345)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause68')).
% 1.19/1.05 tff(296,plain,
% 1.19/1.05 ((~hskp12) | c3_1(a345)),
% 1.19/1.05 inference(modus_ponens,[status(thm)],[295, 294])).
% 1.19/1.05 tff(297,plain,
% 1.19/1.05 ((~hskp12) | c3_1(a345)),
% 1.19/1.05 inference(modus_ponens,[status(thm)],[296, 294])).
% 1.19/1.05 tff(298,plain,
% 1.19/1.05 ((~hskp12) | c3_1(a345)),
% 1.19/1.05 inference(modus_ponens,[status(thm)],[297, 294])).
% 1.19/1.05 tff(299,plain,
% 1.19/1.05 ((~hskp12) | c3_1(a345)),
% 1.19/1.05 inference(modus_ponens,[status(thm)],[298, 294])).
% 1.19/1.05 tff(300,plain,
% 1.19/1.05 ((~hskp12) | c3_1(a345)),
% 1.19/1.05 inference(modus_ponens,[status(thm)],[299, 294])).
% 1.19/1.05 tff(301,plain,
% 1.19/1.05 ((~hskp12) | c3_1(a345)),
% 1.19/1.05 inference(modus_ponens,[status(thm)],[300, 294])).
% 1.19/1.05 tff(302,plain,
% 1.19/1.05 ((~hskp12) | c3_1(a345)),
% 1.19/1.05 inference(modus_ponens,[status(thm)],[301, 294])).
% 1.19/1.05 tff(303,plain,
% 1.19/1.05 ((~hskp12) | c3_1(a345)),
% 1.19/1.05 inference(modus_ponens,[status(thm)],[302, 294])).
% 1.19/1.05 tff(304,plain,
% 1.19/1.05 (c3_1(a345)),
% 1.19/1.05 inference(unit_resolution,[status(thm)],[303, 293])).
% 1.19/1.05 tff(305,plain,
% 1.19/1.05 (((~hskp12) | c0_1(a345)) <=> ((~hskp12) | c0_1(a345))),
% 1.19/1.05 inference(rewrite,[status(thm)],[])).
% 1.19/1.05 tff(306,axiom,((~hskp12) | c0_1(a345)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause67')).
% 1.19/1.05 tff(307,plain,
% 1.19/1.05 ((~hskp12) | c0_1(a345)),
% 1.19/1.05 inference(modus_ponens,[status(thm)],[306, 305])).
% 1.19/1.05 tff(308,plain,
% 1.19/1.05 ((~hskp12) | c0_1(a345)),
% 1.19/1.05 inference(modus_ponens,[status(thm)],[307, 305])).
% 1.19/1.05 tff(309,plain,
% 1.19/1.05 ((~hskp12) | c0_1(a345)),
% 1.19/1.05 inference(modus_ponens,[status(thm)],[308, 305])).
% 1.19/1.05 tff(310,plain,
% 1.19/1.05 ((~hskp12) | c0_1(a345)),
% 1.19/1.05 inference(modus_ponens,[status(thm)],[309, 305])).
% 1.19/1.05 tff(311,plain,
% 1.19/1.05 ((~hskp12) | c0_1(a345)),
% 1.19/1.05 inference(modus_ponens,[status(thm)],[310, 305])).
% 1.19/1.05 tff(312,plain,
% 1.19/1.05 ((~hskp12) | c0_1(a345)),
% 1.19/1.05 inference(modus_ponens,[status(thm)],[311, 305])).
% 1.19/1.05 tff(313,plain,
% 1.19/1.05 ((~hskp12) | c0_1(a345)),
% 1.19/1.05 inference(modus_ponens,[status(thm)],[312, 305])).
% 1.19/1.05 tff(314,plain,
% 1.19/1.05 ((~hskp12) | c0_1(a345)),
% 1.19/1.05 inference(modus_ponens,[status(thm)],[313, 305])).
% 1.19/1.05 tff(315,plain,
% 1.19/1.05 (c0_1(a345)),
% 1.19/1.05 inference(unit_resolution,[status(thm)],[314, 293])).
% 1.19/1.05 tff(316,assumption,(c1_1(a333)), introduced(assumption)).
% 1.19/1.05 tff(317,assumption,(c3_1(a333)), introduced(assumption)).
% 1.19/1.05 tff(318,plain,
% 1.19/1.05 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W))))),
% 1.19/1.05 inference(bind,[status(th)],[])).
% 1.19/1.05 tff(319,plain,
% 1.28/1.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_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)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 1.28/1.05 inference(quant_intro,[status(thm)],[318])).
% 1.28/1.05 tff(320,plain,
% 1.28/1.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_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)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 1.28/1.05 inference(rewrite,[status(thm)],[])).
% 1.28/1.05 tff(321,plain,
% 1.28/1.05 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(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(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))))),
% 1.28/1.05 inference(bind,[status(th)],[])).
% 1.28/1.05 tff(322,plain,
% 1.28/1.05 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 1.28/1.05 inference(quant_intro,[status(thm)],[321])).
% 1.28/1.05 tff(323,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause192')).
% 1.28/1.05 tff(324,plain,
% 1.28/1.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 1.28/1.05 inference(modus_ponens,[status(thm)],[323, 322])).
% 1.28/1.05 tff(325,plain,
% 1.28/1.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 1.28/1.05 inference(modus_ponens,[status(thm)],[324, 320])).
% 1.28/1.05 tff(326,plain,(
% 1.28/1.05 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 1.28/1.05 inference(skolemize,[status(sab)],[325])).
% 1.28/1.05 tff(327,plain,
% 1.28/1.05 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 1.28/1.05 inference(modus_ponens,[status(thm)],[326, 319])).
% 1.28/1.05 tff(328,plain,
% 1.28/1.05 (((~hskp12) | (~c2_1(a345))) <=> ((~hskp12) | (~c2_1(a345)))),
% 1.28/1.05 inference(rewrite,[status(thm)],[])).
% 1.28/1.05 tff(329,plain,
% 1.28/1.05 (((~c2_1(a345)) | (~hskp12)) <=> ((~hskp12) | (~c2_1(a345)))),
% 1.28/1.05 inference(rewrite,[status(thm)],[])).
% 1.28/1.05 tff(330,axiom,((~c2_1(a345)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause101')).
% 1.28/1.05 tff(331,plain,
% 1.28/1.05 ((~hskp12) | (~c2_1(a345))),
% 1.28/1.05 inference(modus_ponens,[status(thm)],[330, 329])).
% 1.28/1.05 tff(332,plain,
% 1.28/1.05 ((~hskp12) | (~c2_1(a345))),
% 1.28/1.05 inference(modus_ponens,[status(thm)],[331, 328])).
% 1.28/1.05 tff(333,plain,
% 1.28/1.05 (~c2_1(a345)),
% 1.28/1.05 inference(unit_resolution,[status(thm)],[332, 293])).
% 1.28/1.05 tff(334,plain,
% 1.28/1.05 (^[U: $i] : refl((hskp23 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) <=> (hskp23 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))))),
% 1.28/1.05 inference(bind,[status(th)],[])).
% 1.28/1.05 tff(335,plain,
% 1.28/1.05 (![U: $i] : (hskp23 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp23 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.28/1.05 inference(quant_intro,[status(thm)],[334])).
% 1.28/1.05 tff(336,plain,
% 1.28/1.05 (![U: $i] : (hskp23 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp23 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.28/1.05 inference(rewrite,[status(thm)],[])).
% 1.28/1.05 tff(337,plain,
% 1.28/1.05 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | 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)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp23) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp23))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp23) <=> (hskp23 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp23) <=> (hskp23 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp23) | hskp22) <=> ((hskp23 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp22))), rewrite(((hskp23 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U))) | hskp22) <=> (hskp23 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp23) | hskp22) <=> (hskp23 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))))),
% 1.28/1.05 inference(bind,[status(th)],[])).
% 1.28/1.05 tff(338,plain,
% 1.28/1.05 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp23) | hskp22) <=> ![U: $i] : (hskp23 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.28/1.05 inference(quant_intro,[status(thm)],[337])).
% 1.28/1.05 tff(339,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp23) | hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause142')).
% 1.28/1.05 tff(340,plain,
% 1.28/1.05 (![U: $i] : (hskp23 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.28/1.05 inference(modus_ponens,[status(thm)],[339, 338])).
% 1.28/1.05 tff(341,plain,
% 1.28/1.05 (![U: $i] : (hskp23 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.28/1.05 inference(modus_ponens,[status(thm)],[340, 336])).
% 1.28/1.05 tff(342,plain,(
% 1.28/1.05 ![U: $i] : (hskp23 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.28/1.05 inference(skolemize,[status(sab)],[341])).
% 1.28/1.05 tff(343,plain,
% 1.28/1.05 (![U: $i] : (hskp23 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))),
% 1.28/1.05 inference(modus_ponens,[status(thm)],[342, 335])).
% 1.28/1.05 tff(344,plain,
% 1.28/1.05 (((~![U: $i] : (hskp23 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp23 | hskp22 | c1_1(a419) | (~ndr1_0) | (~c3_1(a419)) | (~c0_1(a419)))) <=> ((~![U: $i] : (hskp23 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp23 | hskp22 | c1_1(a419) | (~ndr1_0) | (~c3_1(a419)) | (~c0_1(a419)))),
% 1.28/1.05 inference(rewrite,[status(thm)],[])).
% 1.28/1.05 tff(345,plain,
% 1.28/1.05 ((hskp23 | hskp22 | (~ndr1_0) | c1_1(a419) | (~c0_1(a419)) | (~c3_1(a419))) <=> (hskp23 | hskp22 | c1_1(a419) | (~ndr1_0) | (~c3_1(a419)) | (~c0_1(a419)))),
% 1.28/1.05 inference(rewrite,[status(thm)],[])).
% 1.28/1.05 tff(346,plain,
% 1.28/1.05 (((~![U: $i] : (hskp23 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp23 | hskp22 | (~ndr1_0) | c1_1(a419) | (~c0_1(a419)) | (~c3_1(a419)))) <=> ((~![U: $i] : (hskp23 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp23 | hskp22 | c1_1(a419) | (~ndr1_0) | (~c3_1(a419)) | (~c0_1(a419))))),
% 1.28/1.05 inference(monotonicity,[status(thm)],[345])).
% 1.28/1.05 tff(347,plain,
% 1.28/1.05 (((~![U: $i] : (hskp23 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp23 | hskp22 | (~ndr1_0) | c1_1(a419) | (~c0_1(a419)) | (~c3_1(a419)))) <=> ((~![U: $i] : (hskp23 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp23 | hskp22 | c1_1(a419) | (~ndr1_0) | (~c3_1(a419)) | (~c0_1(a419)))),
% 1.28/1.05 inference(transitivity,[status(thm)],[346, 344])).
% 1.28/1.05 tff(348,plain,
% 1.28/1.05 ((~![U: $i] : (hskp23 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | (hskp23 | hskp22 | (~ndr1_0) | c1_1(a419) | (~c0_1(a419)) | (~c3_1(a419)))),
% 1.28/1.05 inference(quant_inst,[status(thm)],[])).
% 1.28/1.05 tff(349,plain,
% 1.28/1.05 ((~![U: $i] : (hskp23 | hskp22 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(U)))) | hskp23 | hskp22 | c1_1(a419) | (~ndr1_0) | (~c3_1(a419)) | (~c0_1(a419))),
% 1.28/1.05 inference(modus_ponens,[status(thm)],[348, 347])).
% 1.28/1.05 tff(350,plain,
% 1.28/1.05 (hskp23 | hskp22 | (~c3_1(a419))),
% 1.28/1.05 inference(unit_resolution,[status(thm)],[349, 152, 246, 245, 343])).
% 1.28/1.05 tff(351,plain,
% 1.28/1.05 (hskp23),
% 1.28/1.05 inference(unit_resolution,[status(thm)],[350, 254, 233])).
% 1.28/1.05 tff(352,plain,
% 1.28/1.05 (((~hskp23) | (~c0_1(a377))) <=> ((~hskp23) | (~c0_1(a377)))),
% 1.28/1.05 inference(rewrite,[status(thm)],[])).
% 1.28/1.05 tff(353,plain,
% 1.28/1.05 (((~c0_1(a377)) | (~hskp23)) <=> ((~hskp23) | (~c0_1(a377)))),
% 1.28/1.05 inference(rewrite,[status(thm)],[])).
% 1.28/1.05 tff(354,axiom,((~c0_1(a377)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause85')).
% 1.28/1.05 tff(355,plain,
% 1.28/1.05 ((~hskp23) | (~c0_1(a377))),
% 1.28/1.05 inference(modus_ponens,[status(thm)],[354, 353])).
% 1.28/1.05 tff(356,plain,
% 1.28/1.05 ((~hskp23) | (~c0_1(a377))),
% 1.28/1.05 inference(modus_ponens,[status(thm)],[355, 352])).
% 1.28/1.05 tff(357,plain,
% 1.28/1.05 (~c0_1(a377)),
% 1.28/1.05 inference(unit_resolution,[status(thm)],[356, 351])).
% 1.28/1.05 tff(358,plain,
% 1.28/1.05 (((~hskp23) | c3_1(a377)) <=> ((~hskp23) | c3_1(a377))),
% 1.28/1.05 inference(rewrite,[status(thm)],[])).
% 1.28/1.05 tff(359,axiom,((~hskp23) | c3_1(a377)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause51')).
% 1.28/1.05 tff(360,plain,
% 1.28/1.05 ((~hskp23) | c3_1(a377)),
% 1.28/1.05 inference(modus_ponens,[status(thm)],[359, 358])).
% 1.28/1.05 tff(361,plain,
% 1.28/1.05 ((~hskp23) | c3_1(a377)),
% 1.28/1.05 inference(modus_ponens,[status(thm)],[360, 358])).
% 1.28/1.05 tff(362,plain,
% 1.28/1.05 ((~hskp23) | c3_1(a377)),
% 1.28/1.05 inference(modus_ponens,[status(thm)],[361, 358])).
% 1.28/1.05 tff(363,plain,
% 1.28/1.05 ((~hskp23) | c3_1(a377)),
% 1.28/1.05 inference(modus_ponens,[status(thm)],[362, 358])).
% 1.28/1.05 tff(364,plain,
% 1.28/1.05 ((~hskp23) | c3_1(a377)),
% 1.28/1.05 inference(modus_ponens,[status(thm)],[363, 358])).
% 1.28/1.05 tff(365,plain,
% 1.28/1.05 ((~hskp23) | c3_1(a377)),
% 1.28/1.05 inference(modus_ponens,[status(thm)],[364, 358])).
% 1.28/1.05 tff(366,plain,
% 1.28/1.05 ((~hskp23) | c3_1(a377)),
% 1.28/1.05 inference(modus_ponens,[status(thm)],[365, 358])).
% 1.28/1.05 tff(367,plain,
% 1.28/1.05 ((~hskp23) | c3_1(a377)),
% 1.28/1.05 inference(modus_ponens,[status(thm)],[366, 358])).
% 1.28/1.05 tff(368,plain,
% 1.28/1.05 (c3_1(a377)),
% 1.28/1.05 inference(unit_resolution,[status(thm)],[367, 351])).
% 1.28/1.05 tff(369,plain,
% 1.28/1.05 (((~hskp23) | c1_1(a377)) <=> ((~hskp23) | c1_1(a377))),
% 1.28/1.05 inference(rewrite,[status(thm)],[])).
% 1.28/1.05 tff(370,axiom,((~hskp23) | c1_1(a377)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause50')).
% 1.28/1.05 tff(371,plain,
% 1.28/1.05 ((~hskp23) | c1_1(a377)),
% 1.28/1.05 inference(modus_ponens,[status(thm)],[370, 369])).
% 1.28/1.05 tff(372,plain,
% 1.28/1.05 ((~hskp23) | c1_1(a377)),
% 1.28/1.05 inference(modus_ponens,[status(thm)],[371, 369])).
% 1.28/1.05 tff(373,plain,
% 1.28/1.05 ((~hskp23) | c1_1(a377)),
% 1.28/1.05 inference(modus_ponens,[status(thm)],[372, 369])).
% 1.28/1.05 tff(374,plain,
% 1.28/1.05 ((~hskp23) | c1_1(a377)),
% 1.28/1.05 inference(modus_ponens,[status(thm)],[373, 369])).
% 1.28/1.05 tff(375,plain,
% 1.28/1.05 ((~hskp23) | c1_1(a377)),
% 1.28/1.05 inference(modus_ponens,[status(thm)],[374, 369])).
% 1.28/1.05 tff(376,plain,
% 1.28/1.05 ((~hskp23) | c1_1(a377)),
% 1.28/1.05 inference(modus_ponens,[status(thm)],[375, 369])).
% 1.28/1.05 tff(377,plain,
% 1.28/1.05 ((~hskp23) | c1_1(a377)),
% 1.28/1.05 inference(modus_ponens,[status(thm)],[376, 369])).
% 1.28/1.05 tff(378,plain,
% 1.28/1.05 ((~hskp23) | c1_1(a377)),
% 1.28/1.05 inference(modus_ponens,[status(thm)],[377, 369])).
% 1.28/1.05 tff(379,plain,
% 1.28/1.05 (c1_1(a377)),
% 1.28/1.05 inference(unit_resolution,[status(thm)],[378, 351])).
% 1.28/1.05 tff(380,plain,
% 1.28/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c1_1(a419) | c2_1(a419) | c0_1(a377) | c2_1(a345) | (~ndr1_0) | (~c3_1(a345)) | (~c1_1(a345)) | (~c1_1(a377)) | (~c3_1(a377)) | (~c0_1(a419)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c1_1(a419) | c2_1(a419) | c0_1(a377) | c2_1(a345) | (~ndr1_0) | (~c3_1(a345)) | (~c1_1(a345)) | (~c1_1(a377)) | (~c3_1(a377)) | (~c0_1(a419)))),
% 1.28/1.05 inference(rewrite,[status(thm)],[])).
% 1.28/1.05 tff(381,plain,
% 1.28/1.05 (((~ndr1_0) | c2_1(a345) | (~c3_1(a345)) | (~c1_1(a345)) | c2_1(a419) | c1_1(a419) | (~c0_1(a419)) | c0_1(a377) | (~c1_1(a377)) | (~c3_1(a377))) <=> (c1_1(a419) | c2_1(a419) | c0_1(a377) | c2_1(a345) | (~ndr1_0) | (~c3_1(a345)) | (~c1_1(a345)) | (~c1_1(a377)) | (~c3_1(a377)) | (~c0_1(a419)))),
% 1.28/1.05 inference(rewrite,[status(thm)],[])).
% 1.28/1.05 tff(382,plain,
% 1.28/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a345) | (~c3_1(a345)) | (~c1_1(a345)) | c2_1(a419) | c1_1(a419) | (~c0_1(a419)) | c0_1(a377) | (~c1_1(a377)) | (~c3_1(a377)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c1_1(a419) | c2_1(a419) | c0_1(a377) | c2_1(a345) | (~ndr1_0) | (~c3_1(a345)) | (~c1_1(a345)) | (~c1_1(a377)) | (~c3_1(a377)) | (~c0_1(a419))))),
% 1.28/1.05 inference(monotonicity,[status(thm)],[381])).
% 1.28/1.05 tff(383,plain,
% 1.28/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a345) | (~c3_1(a345)) | (~c1_1(a345)) | c2_1(a419) | c1_1(a419) | (~c0_1(a419)) | c0_1(a377) | (~c1_1(a377)) | (~c3_1(a377)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c1_1(a419) | c2_1(a419) | c0_1(a377) | c2_1(a345) | (~ndr1_0) | (~c3_1(a345)) | (~c1_1(a345)) | (~c1_1(a377)) | (~c3_1(a377)) | (~c0_1(a419)))),
% 1.28/1.05 inference(transitivity,[status(thm)],[382, 380])).
% 1.28/1.05 tff(384,plain,
% 1.28/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a345) | (~c3_1(a345)) | (~c1_1(a345)) | c2_1(a419) | c1_1(a419) | (~c0_1(a419)) | c0_1(a377) | (~c1_1(a377)) | (~c3_1(a377)))),
% 1.28/1.05 inference(quant_inst,[status(thm)],[])).
% 1.28/1.05 tff(385,plain,
% 1.28/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c1_1(a419) | c2_1(a419) | c0_1(a377) | c2_1(a345) | (~ndr1_0) | (~c3_1(a345)) | (~c1_1(a345)) | (~c1_1(a377)) | (~c3_1(a377)) | (~c0_1(a419))),
% 1.28/1.05 inference(modus_ponens,[status(thm)],[384, 383])).
% 1.28/1.05 tff(386,plain,
% 1.28/1.05 (~c1_1(a345)),
% 1.28/1.05 inference(unit_resolution,[status(thm)],[385, 152, 246, 379, 368, 304, 245, 244, 357, 333, 327])).
% 1.28/1.05 tff(387,plain,
% 1.28/1.05 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 1.28/1.05 inference(bind,[status(th)],[])).
% 1.28/1.05 tff(388,plain,
% 1.28/1.05 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.28/1.05 inference(quant_intro,[status(thm)],[387])).
% 1.28/1.05 tff(389,plain,
% 1.28/1.05 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.28/1.05 inference(rewrite,[status(thm)],[])).
% 1.28/1.05 tff(390,plain,
% 1.28/1.05 (^[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(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp14) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp14))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 1.28/1.06 inference(bind,[status(th)],[])).
% 1.28/1.06 tff(391,plain,
% 1.28/1.06 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.28/1.06 inference(quant_intro,[status(thm)],[390])).
% 1.28/1.06 tff(392,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause180')).
% 1.28/1.06 tff(393,plain,
% 1.28/1.06 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.28/1.06 inference(modus_ponens,[status(thm)],[392, 391])).
% 1.28/1.06 tff(394,plain,
% 1.28/1.06 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.28/1.06 inference(modus_ponens,[status(thm)],[393, 389])).
% 1.28/1.06 tff(395,plain,(
% 1.28/1.06 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.28/1.06 inference(skolemize,[status(sab)],[394])).
% 1.28/1.06 tff(396,plain,
% 1.28/1.06 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.28/1.06 inference(modus_ponens,[status(thm)],[395, 388])).
% 1.28/1.06 tff(397,plain,
% 1.28/1.06 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)) | c1_1(a345) | (~c0_1(a345)) | (~c3_1(a345)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp14 | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)) | c1_1(a345) | (~c0_1(a345)) | (~c3_1(a345)))),
% 1.28/1.06 inference(rewrite,[status(thm)],[])).
% 1.28/1.06 tff(398,plain,
% 1.28/1.06 ((hskp14 | (~ndr1_0) | c2_1(a333) | (~c3_1(a333)) | (~c1_1(a333)) | c1_1(a345) | (~c3_1(a345)) | (~c0_1(a345))) <=> (hskp14 | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)) | c1_1(a345) | (~c0_1(a345)) | (~c3_1(a345)))),
% 1.28/1.06 inference(rewrite,[status(thm)],[])).
% 1.28/1.06 tff(399,plain,
% 1.28/1.06 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a333) | (~c3_1(a333)) | (~c1_1(a333)) | c1_1(a345) | (~c3_1(a345)) | (~c0_1(a345)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)) | c1_1(a345) | (~c0_1(a345)) | (~c3_1(a345))))),
% 1.28/1.06 inference(monotonicity,[status(thm)],[398])).
% 1.28/1.06 tff(400,plain,
% 1.28/1.06 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a333) | (~c3_1(a333)) | (~c1_1(a333)) | c1_1(a345) | (~c3_1(a345)) | (~c0_1(a345)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp14 | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)) | c1_1(a345) | (~c0_1(a345)) | (~c3_1(a345)))),
% 1.28/1.06 inference(transitivity,[status(thm)],[399, 397])).
% 1.28/1.06 tff(401,plain,
% 1.28/1.06 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a333) | (~c3_1(a333)) | (~c1_1(a333)) | c1_1(a345) | (~c3_1(a345)) | (~c0_1(a345)))),
% 1.28/1.06 inference(quant_inst,[status(thm)],[])).
% 1.28/1.06 tff(402,plain,
% 1.28/1.06 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp14 | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)) | c1_1(a345) | (~c0_1(a345)) | (~c3_1(a345))),
% 1.28/1.06 inference(modus_ponens,[status(thm)],[401, 400])).
% 1.28/1.06 tff(403,plain,
% 1.28/1.06 (hskp14 | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)) | c1_1(a345) | (~c0_1(a345)) | (~c3_1(a345))),
% 1.28/1.06 inference(unit_resolution,[status(thm)],[402, 396])).
% 1.28/1.06 tff(404,plain,
% 1.28/1.06 (hskp14 | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)) | c1_1(a345) | (~c0_1(a345)) | (~c3_1(a345))),
% 1.28/1.06 inference(unit_resolution,[status(thm)],[403, 152])).
% 1.28/1.06 tff(405,plain,
% 1.28/1.06 (c2_1(a333)),
% 1.28/1.06 inference(unit_resolution,[status(thm)],[404, 386, 11, 317, 316, 315, 304])).
% 1.28/1.06 tff(406,plain,
% 1.28/1.06 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W))))),
% 1.28/1.06 inference(bind,[status(th)],[])).
% 1.28/1.06 tff(407,plain,
% 1.28/1.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.28/1.06 inference(quant_intro,[status(thm)],[406])).
% 1.28/1.06 tff(408,plain,
% 1.28/1.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.28/1.06 inference(rewrite,[status(thm)],[])).
% 1.28/1.06 tff(409,plain,
% 1.28/1.06 (^[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)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c0_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))))),
% 1.28/1.06 inference(bind,[status(th)],[])).
% 1.28/1.06 tff(410,plain,
% 1.28/1.06 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.28/1.06 inference(quant_intro,[status(thm)],[409])).
% 1.28/1.06 tff(411,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause196')).
% 1.28/1.06 tff(412,plain,
% 1.28/1.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.28/1.06 inference(modus_ponens,[status(thm)],[411, 410])).
% 1.28/1.06 tff(413,plain,
% 1.28/1.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.28/1.06 inference(modus_ponens,[status(thm)],[412, 408])).
% 1.28/1.06 tff(414,plain,(
% 1.28/1.06 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.28/1.06 inference(skolemize,[status(sab)],[413])).
% 1.28/1.06 tff(415,plain,
% 1.28/1.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.28/1.06 inference(modus_ponens,[status(thm)],[414, 407])).
% 1.28/1.06 tff(416,plain,
% 1.28/1.06 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))))),
% 1.28/1.06 inference(bind,[status(th)],[])).
% 1.28/1.06 tff(417,plain,
% 1.28/1.06 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))),
% 1.28/1.06 inference(quant_intro,[status(thm)],[416])).
% 1.28/1.06 tff(418,plain,
% 1.28/1.06 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))),
% 1.28/1.06 inference(rewrite,[status(thm)],[])).
% 1.28/1.06 tff(419,plain,
% 1.28/1.06 (^[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))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | hskp10) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))) | hskp10))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))))),
% 1.28/1.06 inference(bind,[status(th)],[])).
% 1.28/1.06 tff(420,plain,
% 1.28/1.06 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))),
% 1.28/1.06 inference(quant_intro,[status(thm)],[419])).
% 1.28/1.06 tff(421,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause187')).
% 1.28/1.06 tff(422,plain,
% 1.28/1.06 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))),
% 1.28/1.06 inference(modus_ponens,[status(thm)],[421, 420])).
% 1.28/1.06 tff(423,plain,
% 1.28/1.06 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))),
% 1.28/1.06 inference(modus_ponens,[status(thm)],[422, 418])).
% 1.28/1.06 tff(424,plain,(
% 1.28/1.06 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))),
% 1.28/1.06 inference(skolemize,[status(sab)],[423])).
% 1.28/1.06 tff(425,plain,
% 1.28/1.06 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))),
% 1.28/1.06 inference(modus_ponens,[status(thm)],[424, 417])).
% 1.28/1.06 tff(426,assumption,(c0_1(a333)), introduced(assumption)).
% 1.28/1.06 tff(427,plain,
% 1.28/1.06 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c1_1(a333)) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c1_1(a333)) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333)))),
% 1.28/1.06 inference(rewrite,[status(thm)],[])).
% 1.28/1.06 tff(428,plain,
% 1.28/1.06 ((hskp10 | (~ndr1_0) | (~c2_1(a333)) | (~c3_1(a333)) | (~c1_1(a333)) | (~c3_1(a333)) | (~c1_1(a333)) | (~c0_1(a333))) <=> (hskp10 | (~ndr1_0) | (~c1_1(a333)) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333)))),
% 1.28/1.06 inference(rewrite,[status(thm)],[])).
% 1.28/1.06 tff(429,plain,
% 1.28/1.06 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a333)) | (~c3_1(a333)) | (~c1_1(a333)) | (~c3_1(a333)) | (~c1_1(a333)) | (~c0_1(a333)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c1_1(a333)) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333))))),
% 1.28/1.06 inference(monotonicity,[status(thm)],[428])).
% 1.28/1.06 tff(430,plain,
% 1.28/1.06 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a333)) | (~c3_1(a333)) | (~c1_1(a333)) | (~c3_1(a333)) | (~c1_1(a333)) | (~c0_1(a333)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c1_1(a333)) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333)))),
% 1.28/1.06 inference(transitivity,[status(thm)],[429, 427])).
% 1.28/1.06 tff(431,plain,
% 1.28/1.06 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a333)) | (~c3_1(a333)) | (~c1_1(a333)) | (~c3_1(a333)) | (~c1_1(a333)) | (~c0_1(a333)))),
% 1.28/1.06 inference(quant_inst,[status(thm)],[])).
% 1.28/1.06 tff(432,plain,
% 1.28/1.06 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c1_1(a333)) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333))),
% 1.28/1.06 inference(modus_ponens,[status(thm)],[431, 430])).
% 1.28/1.06 tff(433,plain,
% 1.28/1.06 (hskp10),
% 1.28/1.06 inference(unit_resolution,[status(thm)],[432, 152, 426, 316, 317, 425, 405])).
% 1.28/1.06 tff(434,plain,
% 1.28/1.06 (((~hskp10) | (~c3_1(a337))) <=> ((~hskp10) | (~c3_1(a337)))),
% 1.28/1.06 inference(rewrite,[status(thm)],[])).
% 1.28/1.06 tff(435,plain,
% 1.28/1.06 (((~c3_1(a337)) | (~hskp10)) <=> ((~hskp10) | (~c3_1(a337)))),
% 1.28/1.06 inference(rewrite,[status(thm)],[])).
% 1.28/1.06 tff(436,axiom,((~c3_1(a337)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause106')).
% 1.28/1.06 tff(437,plain,
% 1.28/1.06 ((~hskp10) | (~c3_1(a337))),
% 1.28/1.06 inference(modus_ponens,[status(thm)],[436, 435])).
% 1.28/1.06 tff(438,plain,
% 1.28/1.06 ((~hskp10) | (~c3_1(a337))),
% 1.28/1.06 inference(modus_ponens,[status(thm)],[437, 434])).
% 1.28/1.06 tff(439,plain,
% 1.28/1.06 (~c3_1(a337)),
% 1.28/1.06 inference(unit_resolution,[status(thm)],[438, 433])).
% 1.28/1.06 tff(440,plain,
% 1.28/1.06 (((~hskp10) | (~c2_1(a337))) <=> ((~hskp10) | (~c2_1(a337)))),
% 1.28/1.06 inference(rewrite,[status(thm)],[])).
% 1.28/1.06 tff(441,plain,
% 1.28/1.06 (((~c2_1(a337)) | (~hskp10)) <=> ((~hskp10) | (~c2_1(a337)))),
% 1.28/1.06 inference(rewrite,[status(thm)],[])).
% 1.28/1.06 tff(442,axiom,((~c2_1(a337)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause105')).
% 1.28/1.06 tff(443,plain,
% 1.28/1.06 ((~hskp10) | (~c2_1(a337))),
% 1.28/1.06 inference(modus_ponens,[status(thm)],[442, 441])).
% 1.28/1.06 tff(444,plain,
% 1.28/1.06 ((~hskp10) | (~c2_1(a337))),
% 1.28/1.06 inference(modus_ponens,[status(thm)],[443, 440])).
% 1.28/1.06 tff(445,plain,
% 1.28/1.06 (~c2_1(a337)),
% 1.28/1.06 inference(unit_resolution,[status(thm)],[444, 433])).
% 1.28/1.06 tff(446,plain,
% 1.28/1.06 (((~hskp10) | c0_1(a337)) <=> ((~hskp10) | c0_1(a337))),
% 1.28/1.06 inference(rewrite,[status(thm)],[])).
% 1.28/1.06 tff(447,axiom,((~hskp10) | c0_1(a337)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause69')).
% 1.28/1.06 tff(448,plain,
% 1.28/1.06 ((~hskp10) | c0_1(a337)),
% 1.28/1.06 inference(modus_ponens,[status(thm)],[447, 446])).
% 1.28/1.06 tff(449,plain,
% 1.28/1.06 ((~hskp10) | c0_1(a337)),
% 1.28/1.06 inference(modus_ponens,[status(thm)],[448, 446])).
% 1.28/1.06 tff(450,plain,
% 1.28/1.06 ((~hskp10) | c0_1(a337)),
% 1.28/1.06 inference(modus_ponens,[status(thm)],[449, 446])).
% 1.28/1.06 tff(451,plain,
% 1.28/1.06 ((~hskp10) | c0_1(a337)),
% 1.28/1.06 inference(modus_ponens,[status(thm)],[450, 446])).
% 1.28/1.06 tff(452,plain,
% 1.28/1.06 ((~hskp10) | c0_1(a337)),
% 1.28/1.06 inference(modus_ponens,[status(thm)],[451, 446])).
% 1.28/1.06 tff(453,plain,
% 1.28/1.06 ((~hskp10) | c0_1(a337)),
% 1.28/1.06 inference(modus_ponens,[status(thm)],[452, 446])).
% 1.28/1.06 tff(454,plain,
% 1.28/1.06 ((~hskp10) | c0_1(a337)),
% 1.28/1.06 inference(modus_ponens,[status(thm)],[453, 446])).
% 1.28/1.06 tff(455,plain,
% 1.28/1.06 ((~hskp10) | c0_1(a337)),
% 1.28/1.06 inference(modus_ponens,[status(thm)],[454, 446])).
% 1.28/1.06 tff(456,plain,
% 1.28/1.06 (c0_1(a337)),
% 1.28/1.06 inference(unit_resolution,[status(thm)],[455, 433])).
% 1.28/1.06 tff(457,plain,
% 1.28/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a419) | c2_1(a337) | c3_1(a337) | (~ndr1_0) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333)) | (~c0_1(a337)) | (~c3_1(a419)) | (~c0_1(a419)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a419) | c2_1(a337) | c3_1(a337) | (~ndr1_0) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333)) | (~c0_1(a337)) | (~c3_1(a419)) | (~c0_1(a419)))),
% 1.28/1.06 inference(rewrite,[status(thm)],[])).
% 1.28/1.06 tff(458,plain,
% 1.28/1.06 (((~ndr1_0) | (~c2_1(a333)) | (~c0_1(a333)) | (~c3_1(a333)) | c2_1(a419) | (~c3_1(a419)) | (~c0_1(a419)) | c2_1(a337) | c3_1(a337) | (~c0_1(a337))) <=> (c2_1(a419) | c2_1(a337) | c3_1(a337) | (~ndr1_0) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333)) | (~c0_1(a337)) | (~c3_1(a419)) | (~c0_1(a419)))),
% 1.28/1.06 inference(rewrite,[status(thm)],[])).
% 1.28/1.06 tff(459,plain,
% 1.28/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a333)) | (~c0_1(a333)) | (~c3_1(a333)) | c2_1(a419) | (~c3_1(a419)) | (~c0_1(a419)) | c2_1(a337) | c3_1(a337) | (~c0_1(a337)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a419) | c2_1(a337) | c3_1(a337) | (~ndr1_0) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333)) | (~c0_1(a337)) | (~c3_1(a419)) | (~c0_1(a419))))),
% 1.28/1.06 inference(monotonicity,[status(thm)],[458])).
% 1.28/1.06 tff(460,plain,
% 1.28/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a333)) | (~c0_1(a333)) | (~c3_1(a333)) | c2_1(a419) | (~c3_1(a419)) | (~c0_1(a419)) | c2_1(a337) | c3_1(a337) | (~c0_1(a337)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a419) | c2_1(a337) | c3_1(a337) | (~ndr1_0) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333)) | (~c0_1(a337)) | (~c3_1(a419)) | (~c0_1(a419)))),
% 1.28/1.06 inference(transitivity,[status(thm)],[459, 457])).
% 1.28/1.06 tff(461,plain,
% 1.28/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a333)) | (~c0_1(a333)) | (~c3_1(a333)) | c2_1(a419) | (~c3_1(a419)) | (~c0_1(a419)) | c2_1(a337) | c3_1(a337) | (~c0_1(a337)))),
% 1.28/1.06 inference(quant_inst,[status(thm)],[])).
% 1.28/1.06 tff(462,plain,
% 1.28/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a419) | c2_1(a337) | c3_1(a337) | (~ndr1_0) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333)) | (~c0_1(a337)) | (~c3_1(a419)) | (~c0_1(a419))),
% 1.28/1.06 inference(modus_ponens,[status(thm)],[461, 460])).
% 1.28/1.06 tff(463,plain,
% 1.28/1.06 ($false),
% 1.28/1.06 inference(unit_resolution,[status(thm)],[462, 152, 426, 317, 246, 456, 244, 445, 439, 415, 405, 254])).
% 1.28/1.06 tff(464,plain,(hskp22 | (~c0_1(a333)) | (~c3_1(a333)) | (~c0_1(a419)) | c2_1(a419) | (~c1_1(a333)) | hskp14 | c1_1(a419) | (~c2_1(a334)) | c0_1(a334) | c1_1(a334)), inference(lemma,lemma(discharge,[]))).
% 1.28/1.06 tff(465,plain,
% 1.28/1.06 (hskp22),
% 1.28/1.06 inference(unit_resolution,[status(thm)],[464, 232, 221, 117, 99, 210, 11, 105, 182, 165, 171])).
% 1.28/1.06 tff(466,plain,
% 1.28/1.06 (((~hskp22) | (~c1_1(a367))) <=> ((~hskp22) | (~c1_1(a367)))),
% 1.28/1.06 inference(rewrite,[status(thm)],[])).
% 1.28/1.06 tff(467,plain,
% 1.28/1.06 (((~c1_1(a367)) | (~hskp22)) <=> ((~hskp22) | (~c1_1(a367)))),
% 1.28/1.06 inference(rewrite,[status(thm)],[])).
% 1.28/1.06 tff(468,axiom,((~c1_1(a367)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause86')).
% 1.28/1.06 tff(469,plain,
% 1.28/1.06 ((~hskp22) | (~c1_1(a367))),
% 1.28/1.06 inference(modus_ponens,[status(thm)],[468, 467])).
% 1.28/1.06 tff(470,plain,
% 1.28/1.06 ((~hskp22) | (~c1_1(a367))),
% 1.28/1.06 inference(modus_ponens,[status(thm)],[469, 466])).
% 1.28/1.06 tff(471,plain,
% 1.28/1.06 (~c1_1(a367)),
% 1.28/1.06 inference(unit_resolution,[status(thm)],[470, 465])).
% 1.28/1.06 tff(472,plain,
% 1.28/1.06 (((~hskp22) | (~c2_1(a367))) <=> ((~hskp22) | (~c2_1(a367)))),
% 1.28/1.06 inference(rewrite,[status(thm)],[])).
% 1.28/1.06 tff(473,plain,
% 1.28/1.06 (((~c2_1(a367)) | (~hskp22)) <=> ((~hskp22) | (~c2_1(a367)))),
% 1.28/1.06 inference(rewrite,[status(thm)],[])).
% 1.28/1.06 tff(474,axiom,((~c2_1(a367)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause87')).
% 1.28/1.06 tff(475,plain,
% 1.28/1.06 ((~hskp22) | (~c2_1(a367))),
% 1.28/1.06 inference(modus_ponens,[status(thm)],[474, 473])).
% 1.28/1.06 tff(476,plain,
% 1.28/1.06 ((~hskp22) | (~c2_1(a367))),
% 1.28/1.06 inference(modus_ponens,[status(thm)],[475, 472])).
% 1.28/1.06 tff(477,plain,
% 1.28/1.06 (~c2_1(a367)),
% 1.28/1.06 inference(unit_resolution,[status(thm)],[476, 465])).
% 1.28/1.06 tff(478,plain,
% 1.28/1.06 (((~hskp22) | c3_1(a367)) <=> ((~hskp22) | c3_1(a367))),
% 1.28/1.06 inference(rewrite,[status(thm)],[])).
% 1.28/1.06 tff(479,axiom,((~hskp22) | c3_1(a367)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause52')).
% 1.28/1.06 tff(480,plain,
% 1.28/1.06 ((~hskp22) | c3_1(a367)),
% 1.28/1.06 inference(modus_ponens,[status(thm)],[479, 478])).
% 1.28/1.06 tff(481,plain,
% 1.28/1.06 ((~hskp22) | c3_1(a367)),
% 1.28/1.06 inference(modus_ponens,[status(thm)],[480, 478])).
% 1.28/1.06 tff(482,plain,
% 1.28/1.06 ((~hskp22) | c3_1(a367)),
% 1.28/1.06 inference(modus_ponens,[status(thm)],[481, 478])).
% 1.28/1.06 tff(483,plain,
% 1.28/1.06 ((~hskp22) | c3_1(a367)),
% 1.28/1.06 inference(modus_ponens,[status(thm)],[482, 478])).
% 1.28/1.06 tff(484,plain,
% 1.28/1.06 ((~hskp22) | c3_1(a367)),
% 1.28/1.06 inference(modus_ponens,[status(thm)],[483, 478])).
% 1.28/1.06 tff(485,plain,
% 1.28/1.06 ((~hskp22) | c3_1(a367)),
% 1.28/1.06 inference(modus_ponens,[status(thm)],[484, 478])).
% 1.28/1.06 tff(486,plain,
% 1.28/1.06 ((~hskp22) | c3_1(a367)),
% 1.28/1.06 inference(modus_ponens,[status(thm)],[485, 478])).
% 1.28/1.06 tff(487,plain,
% 1.28/1.06 ((~hskp22) | c3_1(a367)),
% 1.28/1.06 inference(modus_ponens,[status(thm)],[486, 478])).
% 1.28/1.06 tff(488,plain,
% 1.28/1.06 (c3_1(a367)),
% 1.28/1.06 inference(unit_resolution,[status(thm)],[487, 465])).
% 1.28/1.06 tff(489,assumption,(c3_1(a334)), introduced(assumption)).
% 1.28/1.06 tff(490,assumption,(~c1_1(a367)), introduced(assumption)).
% 1.28/1.06 tff(491,assumption,(c3_1(a367)), introduced(assumption)).
% 1.28/1.06 tff(492,plain,
% 1.28/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a367) | c0_1(a334) | c1_1(a334) | (~ndr1_0) | (~c3_1(a367)) | (~c0_1(a367)) | (~c2_1(a334)) | (~c3_1(a334)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a367) | c0_1(a334) | c1_1(a334) | (~ndr1_0) | (~c3_1(a367)) | (~c0_1(a367)) | (~c2_1(a334)) | (~c3_1(a334)))),
% 1.28/1.06 inference(rewrite,[status(thm)],[])).
% 1.28/1.06 tff(493,plain,
% 1.28/1.06 (((~ndr1_0) | c1_1(a334) | (~c2_1(a334)) | (~c3_1(a334)) | c1_1(a367) | (~c3_1(a367)) | (~c0_1(a367)) | c0_1(a334) | c1_1(a334) | (~c2_1(a334))) <=> (c1_1(a367) | c0_1(a334) | c1_1(a334) | (~ndr1_0) | (~c3_1(a367)) | (~c0_1(a367)) | (~c2_1(a334)) | (~c3_1(a334)))),
% 1.28/1.06 inference(rewrite,[status(thm)],[])).
% 1.28/1.06 tff(494,plain,
% 1.28/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a334) | (~c2_1(a334)) | (~c3_1(a334)) | c1_1(a367) | (~c3_1(a367)) | (~c0_1(a367)) | c0_1(a334) | c1_1(a334) | (~c2_1(a334)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a367) | c0_1(a334) | c1_1(a334) | (~ndr1_0) | (~c3_1(a367)) | (~c0_1(a367)) | (~c2_1(a334)) | (~c3_1(a334))))),
% 1.28/1.06 inference(monotonicity,[status(thm)],[493])).
% 1.28/1.06 tff(495,plain,
% 1.28/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a334) | (~c2_1(a334)) | (~c3_1(a334)) | c1_1(a367) | (~c3_1(a367)) | (~c0_1(a367)) | c0_1(a334) | c1_1(a334) | (~c2_1(a334)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a367) | c0_1(a334) | c1_1(a334) | (~ndr1_0) | (~c3_1(a367)) | (~c0_1(a367)) | (~c2_1(a334)) | (~c3_1(a334)))),
% 1.28/1.06 inference(transitivity,[status(thm)],[494, 492])).
% 1.28/1.06 tff(496,plain,
% 1.28/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a334) | (~c2_1(a334)) | (~c3_1(a334)) | c1_1(a367) | (~c3_1(a367)) | (~c0_1(a367)) | c0_1(a334) | c1_1(a334) | (~c2_1(a334)))),
% 1.28/1.06 inference(quant_inst,[status(thm)],[])).
% 1.28/1.06 tff(497,plain,
% 1.28/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a367) | c0_1(a334) | c1_1(a334) | (~ndr1_0) | (~c3_1(a367)) | (~c0_1(a367)) | (~c2_1(a334)) | (~c3_1(a334))),
% 1.28/1.06 inference(modus_ponens,[status(thm)],[496, 495])).
% 1.28/1.06 tff(498,plain,
% 1.28/1.06 ((~c0_1(a367)) | (~c3_1(a334))),
% 1.28/1.06 inference(unit_resolution,[status(thm)],[497, 152, 491, 267, 490, 266, 265, 264])).
% 1.28/1.06 tff(499,plain,
% 1.28/1.06 (~c0_1(a367)),
% 1.28/1.06 inference(unit_resolution,[status(thm)],[498, 489])).
% 1.28/1.06 tff(500,plain,
% 1.28/1.06 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))))),
% 1.28/1.06 inference(bind,[status(th)],[])).
% 1.28/1.06 tff(501,plain,
% 1.28/1.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.28/1.06 inference(quant_intro,[status(thm)],[500])).
% 1.28/1.06 tff(502,plain,
% 1.28/1.06 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.28/1.07 inference(rewrite,[status(thm)],[])).
% 1.28/1.07 tff(503,plain,
% 1.28/1.07 (^[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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(W)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(W))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(W)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(W))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W))))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))))),
% 1.28/1.07 inference(bind,[status(th)],[])).
% 1.28/1.07 tff(504,plain,
% 1.28/1.07 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.28/1.07 inference(quant_intro,[status(thm)],[503])).
% 1.28/1.07 tff(505,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause189')).
% 1.28/1.07 tff(506,plain,
% 1.28/1.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[505, 504])).
% 1.28/1.07 tff(507,plain,
% 1.28/1.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[506, 502])).
% 1.28/1.07 tff(508,plain,(
% 1.28/1.07 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.28/1.07 inference(skolemize,[status(sab)],[507])).
% 1.28/1.07 tff(509,plain,
% 1.28/1.07 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[508, 501])).
% 1.28/1.07 tff(510,assumption,(~c2_1(a367)), introduced(assumption)).
% 1.28/1.07 tff(511,plain,
% 1.28/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a419) | c2_1(a419) | c2_1(a367) | c1_1(a334) | (~ndr1_0) | (~c3_1(a367)) | c0_1(a367) | (~c2_1(a334)) | (~c3_1(a334)) | (~c0_1(a419)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a419) | c2_1(a419) | c2_1(a367) | c1_1(a334) | (~ndr1_0) | (~c3_1(a367)) | c0_1(a367) | (~c2_1(a334)) | (~c3_1(a334)) | (~c0_1(a419)))),
% 1.28/1.07 inference(rewrite,[status(thm)],[])).
% 1.28/1.07 tff(512,plain,
% 1.28/1.07 (((~ndr1_0) | c1_1(a334) | (~c2_1(a334)) | (~c3_1(a334)) | c2_1(a419) | c1_1(a419) | (~c0_1(a419)) | c2_1(a367) | c0_1(a367) | (~c3_1(a367))) <=> (c1_1(a419) | c2_1(a419) | c2_1(a367) | c1_1(a334) | (~ndr1_0) | (~c3_1(a367)) | c0_1(a367) | (~c2_1(a334)) | (~c3_1(a334)) | (~c0_1(a419)))),
% 1.28/1.07 inference(rewrite,[status(thm)],[])).
% 1.28/1.07 tff(513,plain,
% 1.28/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a334) | (~c2_1(a334)) | (~c3_1(a334)) | c2_1(a419) | c1_1(a419) | (~c0_1(a419)) | c2_1(a367) | c0_1(a367) | (~c3_1(a367)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a419) | c2_1(a419) | c2_1(a367) | c1_1(a334) | (~ndr1_0) | (~c3_1(a367)) | c0_1(a367) | (~c2_1(a334)) | (~c3_1(a334)) | (~c0_1(a419))))),
% 1.28/1.07 inference(monotonicity,[status(thm)],[512])).
% 1.28/1.07 tff(514,plain,
% 1.28/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a334) | (~c2_1(a334)) | (~c3_1(a334)) | c2_1(a419) | c1_1(a419) | (~c0_1(a419)) | c2_1(a367) | c0_1(a367) | (~c3_1(a367)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a419) | c2_1(a419) | c2_1(a367) | c1_1(a334) | (~ndr1_0) | (~c3_1(a367)) | c0_1(a367) | (~c2_1(a334)) | (~c3_1(a334)) | (~c0_1(a419)))),
% 1.28/1.07 inference(transitivity,[status(thm)],[513, 511])).
% 1.28/1.07 tff(515,plain,
% 1.28/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a334) | (~c2_1(a334)) | (~c3_1(a334)) | c2_1(a419) | c1_1(a419) | (~c0_1(a419)) | c2_1(a367) | c0_1(a367) | (~c3_1(a367)))),
% 1.28/1.07 inference(quant_inst,[status(thm)],[])).
% 1.28/1.07 tff(516,plain,
% 1.28/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a419) | c2_1(a419) | c2_1(a367) | c1_1(a334) | (~ndr1_0) | (~c3_1(a367)) | c0_1(a367) | (~c2_1(a334)) | (~c3_1(a334)) | (~c0_1(a419))),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[515, 514])).
% 1.28/1.07 tff(517,plain,
% 1.28/1.07 (c0_1(a367) | (~c3_1(a334))),
% 1.28/1.07 inference(unit_resolution,[status(thm)],[516, 152, 246, 491, 267, 245, 244, 510, 265, 509])).
% 1.28/1.07 tff(518,plain,
% 1.28/1.07 ($false),
% 1.28/1.07 inference(unit_resolution,[status(thm)],[517, 499, 489])).
% 1.28/1.07 tff(519,plain,((~c3_1(a334)) | (~c0_1(a419)) | (~c3_1(a367)) | (~c2_1(a334)) | c1_1(a419) | c2_1(a419) | c2_1(a367) | c1_1(a334) | c1_1(a367) | c0_1(a334)), inference(lemma,lemma(discharge,[]))).
% 1.28/1.07 tff(520,plain,
% 1.28/1.07 (~c3_1(a334)),
% 1.28/1.07 inference(unit_resolution,[status(thm)],[519, 117, 488, 182, 105, 99, 477, 171, 471, 165])).
% 1.28/1.07 tff(521,plain,
% 1.28/1.07 (^[U: $i] : refl((hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))),
% 1.28/1.07 inference(bind,[status(th)],[])).
% 1.28/1.07 tff(522,plain,
% 1.28/1.07 (![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.28/1.07 inference(quant_intro,[status(thm)],[521])).
% 1.28/1.07 tff(523,plain,
% 1.28/1.07 (![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.28/1.07 inference(rewrite,[status(thm)],[])).
% 1.28/1.07 tff(524,plain,
% 1.28/1.07 (^[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)) | hskp13) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp13))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp13) <=> (hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp13) <=> (hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp13) | hskp14) <=> ((hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp14))), rewrite(((hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp14) <=> (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp13) | hskp14) <=> (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))))),
% 1.28/1.07 inference(bind,[status(th)],[])).
% 1.28/1.07 tff(525,plain,
% 1.28/1.07 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp13) | hskp14) <=> ![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.28/1.07 inference(quant_intro,[status(thm)],[524])).
% 1.28/1.07 tff(526,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp13) | hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause131')).
% 1.28/1.07 tff(527,plain,
% 1.28/1.07 (![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[526, 525])).
% 1.28/1.07 tff(528,plain,
% 1.28/1.07 (![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[527, 523])).
% 1.28/1.07 tff(529,plain,(
% 1.28/1.07 ![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.28/1.07 inference(skolemize,[status(sab)],[528])).
% 1.28/1.07 tff(530,plain,
% 1.28/1.07 (![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[529, 522])).
% 1.28/1.07 tff(531,plain,
% 1.28/1.07 (((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | hskp13 | c0_1(a334) | (~ndr1_0) | (~c2_1(a334)) | c3_1(a334))) <=> ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp14 | hskp13 | c0_1(a334) | (~ndr1_0) | (~c2_1(a334)) | c3_1(a334))),
% 1.28/1.07 inference(rewrite,[status(thm)],[])).
% 1.28/1.07 tff(532,plain,
% 1.28/1.07 ((hskp14 | hskp13 | (~ndr1_0) | c0_1(a334) | c3_1(a334) | (~c2_1(a334))) <=> (hskp14 | hskp13 | c0_1(a334) | (~ndr1_0) | (~c2_1(a334)) | c3_1(a334))),
% 1.28/1.07 inference(rewrite,[status(thm)],[])).
% 1.28/1.07 tff(533,plain,
% 1.28/1.07 (((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | c0_1(a334) | c3_1(a334) | (~c2_1(a334)))) <=> ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | hskp13 | c0_1(a334) | (~ndr1_0) | (~c2_1(a334)) | c3_1(a334)))),
% 1.28/1.07 inference(monotonicity,[status(thm)],[532])).
% 1.28/1.07 tff(534,plain,
% 1.28/1.07 (((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | c0_1(a334) | c3_1(a334) | (~c2_1(a334)))) <=> ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp14 | hskp13 | c0_1(a334) | (~ndr1_0) | (~c2_1(a334)) | c3_1(a334))),
% 1.28/1.07 inference(transitivity,[status(thm)],[533, 531])).
% 1.28/1.07 tff(535,plain,
% 1.28/1.07 ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | c0_1(a334) | c3_1(a334) | (~c2_1(a334)))),
% 1.28/1.07 inference(quant_inst,[status(thm)],[])).
% 1.28/1.07 tff(536,plain,
% 1.28/1.07 ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp14 | hskp13 | c0_1(a334) | (~ndr1_0) | (~c2_1(a334)) | c3_1(a334)),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[535, 534])).
% 1.28/1.07 tff(537,plain,
% 1.28/1.07 (hskp13 | c3_1(a334)),
% 1.28/1.07 inference(unit_resolution,[status(thm)],[536, 152, 11, 182, 165, 530])).
% 1.28/1.07 tff(538,plain,
% 1.28/1.07 (hskp13),
% 1.28/1.07 inference(unit_resolution,[status(thm)],[537, 520])).
% 1.28/1.07 tff(539,plain,
% 1.28/1.07 (^[U: $i] : refl((hskp16 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp16 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 1.28/1.07 inference(bind,[status(th)],[])).
% 1.28/1.07 tff(540,plain,
% 1.28/1.07 (![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.28/1.07 inference(quant_intro,[status(thm)],[539])).
% 1.28/1.07 tff(541,plain,
% 1.28/1.07 (![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.28/1.07 inference(rewrite,[status(thm)],[])).
% 1.28/1.07 tff(542,plain,
% 1.28/1.07 (^[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)) | hskp4) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp4))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp4) <=> (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp4) | hskp16) <=> ((hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp16))), rewrite(((hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp16) <=> (hskp16 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp4) | hskp16) <=> (hskp16 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 1.28/1.07 inference(bind,[status(th)],[])).
% 1.28/1.07 tff(543,plain,
% 1.28/1.07 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp4) | hskp16) <=> ![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.28/1.07 inference(quant_intro,[status(thm)],[542])).
% 1.28/1.07 tff(544,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp4) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause145')).
% 1.28/1.07 tff(545,plain,
% 1.28/1.07 (![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[544, 543])).
% 1.28/1.07 tff(546,plain,
% 1.28/1.07 (![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[545, 541])).
% 1.28/1.07 tff(547,plain,(
% 1.28/1.07 ![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.28/1.07 inference(skolemize,[status(sab)],[546])).
% 1.28/1.07 tff(548,plain,
% 1.28/1.07 (![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[547, 540])).
% 1.28/1.07 tff(549,assumption,(hskp13), introduced(assumption)).
% 1.28/1.07 tff(550,plain,
% 1.28/1.07 (((~hskp13) | (~c3_1(a346))) <=> ((~hskp13) | (~c3_1(a346)))),
% 1.28/1.07 inference(rewrite,[status(thm)],[])).
% 1.28/1.07 tff(551,plain,
% 1.28/1.07 (((~c3_1(a346)) | (~hskp13)) <=> ((~hskp13) | (~c3_1(a346)))),
% 1.28/1.07 inference(rewrite,[status(thm)],[])).
% 1.28/1.07 tff(552,axiom,((~c3_1(a346)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause100')).
% 1.28/1.07 tff(553,plain,
% 1.28/1.07 ((~hskp13) | (~c3_1(a346))),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[552, 551])).
% 1.28/1.07 tff(554,plain,
% 1.28/1.07 ((~hskp13) | (~c3_1(a346))),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[553, 550])).
% 1.28/1.07 tff(555,plain,
% 1.28/1.07 (~c3_1(a346)),
% 1.28/1.07 inference(unit_resolution,[status(thm)],[554, 549])).
% 1.28/1.07 tff(556,plain,
% 1.28/1.07 (((~hskp13) | c2_1(a346)) <=> ((~hskp13) | c2_1(a346))),
% 1.28/1.07 inference(rewrite,[status(thm)],[])).
% 1.28/1.07 tff(557,axiom,((~hskp13) | c2_1(a346)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause66')).
% 1.28/1.07 tff(558,plain,
% 1.28/1.07 ((~hskp13) | c2_1(a346)),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[557, 556])).
% 1.28/1.07 tff(559,plain,
% 1.28/1.07 ((~hskp13) | c2_1(a346)),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[558, 556])).
% 1.28/1.07 tff(560,plain,
% 1.28/1.07 ((~hskp13) | c2_1(a346)),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[559, 556])).
% 1.28/1.07 tff(561,plain,
% 1.28/1.07 ((~hskp13) | c2_1(a346)),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[560, 556])).
% 1.28/1.07 tff(562,plain,
% 1.28/1.07 ((~hskp13) | c2_1(a346)),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[561, 556])).
% 1.28/1.07 tff(563,plain,
% 1.28/1.07 ((~hskp13) | c2_1(a346)),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[562, 556])).
% 1.28/1.07 tff(564,plain,
% 1.28/1.07 ((~hskp13) | c2_1(a346)),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[563, 556])).
% 1.28/1.07 tff(565,plain,
% 1.28/1.07 ((~hskp13) | c2_1(a346)),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[564, 556])).
% 1.28/1.07 tff(566,plain,
% 1.28/1.07 (c2_1(a346)),
% 1.28/1.07 inference(unit_resolution,[status(thm)],[565, 549])).
% 1.28/1.07 tff(567,plain,
% 1.28/1.07 (((~hskp13) | c0_1(a346)) <=> ((~hskp13) | c0_1(a346))),
% 1.28/1.07 inference(rewrite,[status(thm)],[])).
% 1.28/1.07 tff(568,axiom,((~hskp13) | c0_1(a346)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause65')).
% 1.28/1.07 tff(569,plain,
% 1.28/1.07 ((~hskp13) | c0_1(a346)),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[568, 567])).
% 1.28/1.07 tff(570,plain,
% 1.28/1.07 ((~hskp13) | c0_1(a346)),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[569, 567])).
% 1.28/1.07 tff(571,plain,
% 1.28/1.07 ((~hskp13) | c0_1(a346)),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[570, 567])).
% 1.28/1.07 tff(572,plain,
% 1.28/1.07 ((~hskp13) | c0_1(a346)),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[571, 567])).
% 1.28/1.07 tff(573,plain,
% 1.28/1.07 ((~hskp13) | c0_1(a346)),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[572, 567])).
% 1.28/1.07 tff(574,plain,
% 1.28/1.07 ((~hskp13) | c0_1(a346)),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[573, 567])).
% 1.28/1.07 tff(575,plain,
% 1.28/1.07 ((~hskp13) | c0_1(a346)),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[574, 567])).
% 1.28/1.07 tff(576,plain,
% 1.28/1.07 ((~hskp13) | c0_1(a346)),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[575, 567])).
% 1.28/1.07 tff(577,plain,
% 1.28/1.07 (c0_1(a346)),
% 1.28/1.07 inference(unit_resolution,[status(thm)],[576, 549])).
% 1.28/1.07 tff(578,assumption,(~hskp4), introduced(assumption)).
% 1.28/1.07 tff(579,plain,
% 1.28/1.07 (((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp4 | c3_1(a346) | (~ndr1_0) | (~c0_1(a346)) | (~c2_1(a346)))) <=> ((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp4 | c3_1(a346) | (~ndr1_0) | (~c0_1(a346)) | (~c2_1(a346)))),
% 1.28/1.07 inference(rewrite,[status(thm)],[])).
% 1.28/1.07 tff(580,plain,
% 1.28/1.07 ((hskp16 | hskp4 | (~ndr1_0) | c3_1(a346) | (~c2_1(a346)) | (~c0_1(a346))) <=> (hskp16 | hskp4 | c3_1(a346) | (~ndr1_0) | (~c0_1(a346)) | (~c2_1(a346)))),
% 1.28/1.07 inference(rewrite,[status(thm)],[])).
% 1.28/1.07 tff(581,plain,
% 1.28/1.07 (((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp4 | (~ndr1_0) | c3_1(a346) | (~c2_1(a346)) | (~c0_1(a346)))) <=> ((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp4 | c3_1(a346) | (~ndr1_0) | (~c0_1(a346)) | (~c2_1(a346))))),
% 1.28/1.07 inference(monotonicity,[status(thm)],[580])).
% 1.28/1.07 tff(582,plain,
% 1.28/1.07 (((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp4 | (~ndr1_0) | c3_1(a346) | (~c2_1(a346)) | (~c0_1(a346)))) <=> ((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp4 | c3_1(a346) | (~ndr1_0) | (~c0_1(a346)) | (~c2_1(a346)))),
% 1.28/1.07 inference(transitivity,[status(thm)],[581, 579])).
% 1.28/1.07 tff(583,plain,
% 1.28/1.07 ((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp4 | (~ndr1_0) | c3_1(a346) | (~c2_1(a346)) | (~c0_1(a346)))),
% 1.28/1.07 inference(quant_inst,[status(thm)],[])).
% 1.28/1.07 tff(584,plain,
% 1.28/1.07 ((~![U: $i] : (hskp16 | hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp4 | c3_1(a346) | (~ndr1_0) | (~c0_1(a346)) | (~c2_1(a346))),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[583, 582])).
% 1.28/1.07 tff(585,plain,
% 1.28/1.07 ($false),
% 1.28/1.07 inference(unit_resolution,[status(thm)],[584, 70, 152, 578, 577, 566, 555, 548])).
% 1.28/1.07 tff(586,plain,((~hskp13) | hskp16 | hskp4), inference(lemma,lemma(discharge,[]))).
% 1.28/1.07 tff(587,plain,
% 1.28/1.07 (hskp4),
% 1.28/1.07 inference(unit_resolution,[status(thm)],[586, 538, 70])).
% 1.28/1.07 tff(588,plain,
% 1.28/1.07 (((~hskp4) | (~c1_1(a326))) <=> ((~hskp4) | (~c1_1(a326)))),
% 1.28/1.07 inference(rewrite,[status(thm)],[])).
% 1.28/1.07 tff(589,plain,
% 1.28/1.07 (((~c1_1(a326)) | (~hskp4)) <=> ((~hskp4) | (~c1_1(a326)))),
% 1.28/1.07 inference(rewrite,[status(thm)],[])).
% 1.28/1.07 tff(590,axiom,((~c1_1(a326)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause117')).
% 1.28/1.07 tff(591,plain,
% 1.28/1.07 ((~hskp4) | (~c1_1(a326))),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[590, 589])).
% 1.28/1.07 tff(592,plain,
% 1.28/1.07 ((~hskp4) | (~c1_1(a326))),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[591, 588])).
% 1.28/1.07 tff(593,plain,
% 1.28/1.07 (~c1_1(a326)),
% 1.28/1.07 inference(unit_resolution,[status(thm)],[592, 587])).
% 1.28/1.07 tff(594,plain,
% 1.28/1.07 (((~hskp4) | c2_1(a326)) <=> ((~hskp4) | c2_1(a326))),
% 1.28/1.07 inference(rewrite,[status(thm)],[])).
% 1.28/1.07 tff(595,axiom,((~hskp4) | c2_1(a326)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause76')).
% 1.28/1.07 tff(596,plain,
% 1.28/1.07 ((~hskp4) | c2_1(a326)),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[595, 594])).
% 1.28/1.07 tff(597,plain,
% 1.28/1.07 ((~hskp4) | c2_1(a326)),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[596, 594])).
% 1.28/1.07 tff(598,plain,
% 1.28/1.07 ((~hskp4) | c2_1(a326)),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[597, 594])).
% 1.28/1.07 tff(599,plain,
% 1.28/1.07 ((~hskp4) | c2_1(a326)),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[598, 594])).
% 1.28/1.07 tff(600,plain,
% 1.28/1.07 ((~hskp4) | c2_1(a326)),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[599, 594])).
% 1.28/1.07 tff(601,plain,
% 1.28/1.07 ((~hskp4) | c2_1(a326)),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[600, 594])).
% 1.28/1.07 tff(602,plain,
% 1.28/1.07 ((~hskp4) | c2_1(a326)),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[601, 594])).
% 1.28/1.07 tff(603,plain,
% 1.28/1.07 ((~hskp4) | c2_1(a326)),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[602, 594])).
% 1.28/1.07 tff(604,plain,
% 1.28/1.07 (c2_1(a326)),
% 1.28/1.07 inference(unit_resolution,[status(thm)],[603, 587])).
% 1.28/1.07 tff(605,plain,
% 1.28/1.07 (((~hskp4) | c0_1(a326)) <=> ((~hskp4) | c0_1(a326))),
% 1.28/1.07 inference(rewrite,[status(thm)],[])).
% 1.28/1.07 tff(606,axiom,((~hskp4) | c0_1(a326)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause75')).
% 1.28/1.07 tff(607,plain,
% 1.28/1.07 ((~hskp4) | c0_1(a326)),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[606, 605])).
% 1.28/1.07 tff(608,plain,
% 1.28/1.07 ((~hskp4) | c0_1(a326)),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[607, 605])).
% 1.28/1.07 tff(609,plain,
% 1.28/1.07 ((~hskp4) | c0_1(a326)),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[608, 605])).
% 1.28/1.07 tff(610,plain,
% 1.28/1.07 ((~hskp4) | c0_1(a326)),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[609, 605])).
% 1.28/1.07 tff(611,plain,
% 1.28/1.07 ((~hskp4) | c0_1(a326)),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[610, 605])).
% 1.28/1.07 tff(612,plain,
% 1.28/1.07 ((~hskp4) | c0_1(a326)),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[611, 605])).
% 1.28/1.07 tff(613,plain,
% 1.28/1.07 ((~hskp4) | c0_1(a326)),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[612, 605])).
% 1.28/1.07 tff(614,plain,
% 1.28/1.07 ((~hskp4) | c0_1(a326)),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[613, 605])).
% 1.28/1.07 tff(615,plain,
% 1.28/1.07 (c0_1(a326)),
% 1.28/1.07 inference(unit_resolution,[status(thm)],[614, 587])).
% 1.28/1.07 tff(616,assumption,(~hskp28), introduced(assumption)).
% 1.28/1.07 tff(617,plain,
% 1.28/1.07 (hskp26),
% 1.28/1.07 inference(unit_resolution,[status(thm)],[198, 152, 246, 106, 245, 244, 82, 81, 192])).
% 1.28/1.07 tff(618,plain,
% 1.28/1.07 (c3_1(a333)),
% 1.28/1.07 inference(unit_resolution,[status(thm)],[220, 617])).
% 1.28/1.07 tff(619,plain,
% 1.28/1.07 (c1_1(a333)),
% 1.28/1.07 inference(unit_resolution,[status(thm)],[209, 617])).
% 1.28/1.07 tff(620,plain,
% 1.28/1.07 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)))),
% 1.28/1.07 inference(rewrite,[status(thm)],[])).
% 1.28/1.07 tff(621,plain,
% 1.28/1.07 ((hskp28 | (~ndr1_0) | c2_1(a333) | (~c3_1(a333)) | (~c1_1(a333))) <=> (hskp28 | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)))),
% 1.28/1.07 inference(rewrite,[status(thm)],[])).
% 1.28/1.07 tff(622,plain,
% 1.28/1.07 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | (~ndr1_0) | c2_1(a333) | (~c3_1(a333)) | (~c1_1(a333)))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333))))),
% 1.28/1.07 inference(monotonicity,[status(thm)],[621])).
% 1.28/1.07 tff(623,plain,
% 1.28/1.07 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | (~ndr1_0) | c2_1(a333) | (~c3_1(a333)) | (~c1_1(a333)))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)))),
% 1.28/1.07 inference(transitivity,[status(thm)],[622, 620])).
% 1.28/1.07 tff(624,plain,
% 1.28/1.07 ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | (~ndr1_0) | c2_1(a333) | (~c3_1(a333)) | (~c1_1(a333)))),
% 1.28/1.07 inference(quant_inst,[status(thm)],[])).
% 1.28/1.07 tff(625,plain,
% 1.28/1.07 ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333))),
% 1.28/1.07 inference(modus_ponens,[status(thm)],[624, 623])).
% 1.28/1.07 tff(626,plain,
% 1.28/1.07 (hskp28 | c2_1(a333)),
% 1.28/1.07 inference(unit_resolution,[status(thm)],[625, 152, 619, 618, 41])).
% 1.28/1.07 tff(627,plain,
% 1.28/1.07 (c2_1(a333)),
% 1.28/1.07 inference(unit_resolution,[status(thm)],[626, 616])).
% 1.28/1.07 tff(628,plain,
% 1.28/1.07 (c0_1(a333)),
% 1.28/1.07 inference(unit_resolution,[status(thm)],[231, 617])).
% 1.28/1.07 tff(629,plain,
% 1.28/1.07 (hskp10),
% 1.28/1.07 inference(unit_resolution,[status(thm)],[432, 152, 628, 619, 618, 425, 627])).
% 1.28/1.07 tff(630,plain,
% 1.28/1.07 (~c3_1(a337)),
% 1.28/1.07 inference(unit_resolution,[status(thm)],[438, 629])).
% 1.28/1.07 tff(631,plain,
% 1.28/1.07 (~c2_1(a337)),
% 1.28/1.07 inference(unit_resolution,[status(thm)],[444, 629])).
% 1.28/1.07 tff(632,plain,
% 1.28/1.07 (c0_1(a337)),
% 1.28/1.07 inference(unit_resolution,[status(thm)],[455, 629])).
% 1.28/1.07 tff(633,plain,
% 1.28/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a367) | c2_1(a337) | c3_1(a337) | (~ndr1_0) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333)) | (~c3_1(a367)) | (~c0_1(a367)) | (~c0_1(a337)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a367) | c2_1(a337) | c3_1(a337) | (~ndr1_0) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333)) | (~c3_1(a367)) | (~c0_1(a367)) | (~c0_1(a337)))),
% 1.28/1.07 inference(rewrite,[status(thm)],[])).
% 1.28/1.07 tff(634,plain,
% 1.28/1.07 (((~ndr1_0) | (~c2_1(a333)) | (~c0_1(a333)) | (~c3_1(a333)) | c2_1(a367) | (~c3_1(a367)) | (~c0_1(a367)) | c2_1(a337) | c3_1(a337) | (~c0_1(a337))) <=> (c2_1(a367) | c2_1(a337) | c3_1(a337) | (~ndr1_0) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333)) | (~c3_1(a367)) | (~c0_1(a367)) | (~c0_1(a337)))),
% 1.28/1.07 inference(rewrite,[status(thm)],[])).
% 1.28/1.07 tff(635,plain,
% 1.28/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a333)) | (~c0_1(a333)) | (~c3_1(a333)) | c2_1(a367) | (~c3_1(a367)) | (~c0_1(a367)) | c2_1(a337) | c3_1(a337) | (~c0_1(a337)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a367) | c2_1(a337) | c3_1(a337) | (~ndr1_0) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333)) | (~c3_1(a367)) | (~c0_1(a367)) | (~c0_1(a337))))),
% 1.28/1.08 inference(monotonicity,[status(thm)],[634])).
% 1.28/1.08 tff(636,plain,
% 1.28/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a333)) | (~c0_1(a333)) | (~c3_1(a333)) | c2_1(a367) | (~c3_1(a367)) | (~c0_1(a367)) | c2_1(a337) | c3_1(a337) | (~c0_1(a337)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a367) | c2_1(a337) | c3_1(a337) | (~ndr1_0) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333)) | (~c3_1(a367)) | (~c0_1(a367)) | (~c0_1(a337)))),
% 1.28/1.08 inference(transitivity,[status(thm)],[635, 633])).
% 1.28/1.08 tff(637,plain,
% 1.28/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a333)) | (~c0_1(a333)) | (~c3_1(a333)) | c2_1(a367) | (~c3_1(a367)) | (~c0_1(a367)) | c2_1(a337) | c3_1(a337) | (~c0_1(a337)))),
% 1.28/1.08 inference(quant_inst,[status(thm)],[])).
% 1.28/1.08 tff(638,plain,
% 1.28/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a367) | c2_1(a337) | c3_1(a337) | (~ndr1_0) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333)) | (~c3_1(a367)) | (~c0_1(a367)) | (~c0_1(a337))),
% 1.28/1.08 inference(modus_ponens,[status(thm)],[637, 636])).
% 1.28/1.08 tff(639,plain,
% 1.28/1.08 (~c0_1(a367)),
% 1.28/1.08 inference(unit_resolution,[status(thm)],[638, 152, 628, 618, 491, 632, 510, 631, 630, 415, 627])).
% 1.28/1.08 tff(640,plain,
% 1.28/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a419) | c2_1(a419) | c2_1(a367) | c1_1(a330) | (~ndr1_0) | (~c3_1(a367)) | c0_1(a367) | (~c2_1(a330)) | (~c3_1(a330)) | (~c0_1(a419)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a419) | c2_1(a419) | c2_1(a367) | c1_1(a330) | (~ndr1_0) | (~c3_1(a367)) | c0_1(a367) | (~c2_1(a330)) | (~c3_1(a330)) | (~c0_1(a419)))),
% 1.28/1.08 inference(rewrite,[status(thm)],[])).
% 1.28/1.08 tff(641,plain,
% 1.28/1.08 (((~ndr1_0) | c1_1(a330) | (~c2_1(a330)) | (~c3_1(a330)) | c2_1(a419) | c1_1(a419) | (~c0_1(a419)) | c2_1(a367) | c0_1(a367) | (~c3_1(a367))) <=> (c1_1(a419) | c2_1(a419) | c2_1(a367) | c1_1(a330) | (~ndr1_0) | (~c3_1(a367)) | c0_1(a367) | (~c2_1(a330)) | (~c3_1(a330)) | (~c0_1(a419)))),
% 1.28/1.08 inference(rewrite,[status(thm)],[])).
% 1.28/1.08 tff(642,plain,
% 1.28/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a330) | (~c2_1(a330)) | (~c3_1(a330)) | c2_1(a419) | c1_1(a419) | (~c0_1(a419)) | c2_1(a367) | c0_1(a367) | (~c3_1(a367)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a419) | c2_1(a419) | c2_1(a367) | c1_1(a330) | (~ndr1_0) | (~c3_1(a367)) | c0_1(a367) | (~c2_1(a330)) | (~c3_1(a330)) | (~c0_1(a419))))),
% 1.28/1.08 inference(monotonicity,[status(thm)],[641])).
% 1.28/1.08 tff(643,plain,
% 1.28/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a330) | (~c2_1(a330)) | (~c3_1(a330)) | c2_1(a419) | c1_1(a419) | (~c0_1(a419)) | c2_1(a367) | c0_1(a367) | (~c3_1(a367)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a419) | c2_1(a419) | c2_1(a367) | c1_1(a330) | (~ndr1_0) | (~c3_1(a367)) | c0_1(a367) | (~c2_1(a330)) | (~c3_1(a330)) | (~c0_1(a419)))),
% 1.28/1.08 inference(transitivity,[status(thm)],[642, 640])).
% 1.28/1.08 tff(644,plain,
% 1.28/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a330) | (~c2_1(a330)) | (~c3_1(a330)) | c2_1(a419) | c1_1(a419) | (~c0_1(a419)) | c2_1(a367) | c0_1(a367) | (~c3_1(a367)))),
% 1.28/1.08 inference(quant_inst,[status(thm)],[])).
% 1.28/1.08 tff(645,plain,
% 1.28/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a419) | c2_1(a419) | c2_1(a367) | c1_1(a330) | (~ndr1_0) | (~c3_1(a367)) | c0_1(a367) | (~c2_1(a330)) | (~c3_1(a330)) | (~c0_1(a419))),
% 1.28/1.08 inference(modus_ponens,[status(thm)],[644, 643])).
% 1.28/1.08 tff(646,plain,
% 1.28/1.08 (c0_1(a367) | (~c2_1(a330))),
% 1.28/1.08 inference(unit_resolution,[status(thm)],[645, 152, 246, 491, 106, 245, 244, 510, 81, 509])).
% 1.28/1.08 tff(647,plain,
% 1.28/1.08 (~c2_1(a330)),
% 1.28/1.08 inference(unit_resolution,[status(thm)],[646, 639])).
% 1.28/1.08 tff(648,plain,
% 1.28/1.08 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.28/1.08 inference(bind,[status(th)],[])).
% 1.28/1.08 tff(649,plain,
% 1.28/1.08 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.28/1.08 inference(quant_intro,[status(thm)],[648])).
% 1.28/1.08 tff(650,plain,
% 1.28/1.08 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.28/1.08 inference(rewrite,[status(thm)],[])).
% 1.28/1.08 tff(651,plain,
% 1.28/1.08 (^[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) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp28) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp28))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.28/1.08 inference(bind,[status(th)],[])).
% 1.28/1.08 tff(652,plain,
% 1.28/1.08 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.28/1.08 inference(quant_intro,[status(thm)],[651])).
% 1.28/1.08 tff(653,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp28)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause168')).
% 1.28/1.08 tff(654,plain,
% 1.28/1.08 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.28/1.08 inference(modus_ponens,[status(thm)],[653, 652])).
% 1.28/1.08 tff(655,plain,
% 1.28/1.08 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.28/1.08 inference(modus_ponens,[status(thm)],[654, 650])).
% 1.28/1.08 tff(656,plain,(
% 1.28/1.08 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.28/1.08 inference(skolemize,[status(sab)],[655])).
% 1.28/1.08 tff(657,plain,
% 1.28/1.08 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.28/1.08 inference(modus_ponens,[status(thm)],[656, 649])).
% 1.28/1.08 tff(658,plain,
% 1.28/1.08 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | c3_1(W)))),
% 1.28/1.08 inference(bind,[status(th)],[])).
% 1.28/1.08 tff(659,plain,
% 1.28/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~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) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | c3_1(W))),
% 1.28/1.08 inference(quant_intro,[status(thm)],[658])).
% 1.28/1.08 tff(660,plain,
% 1.28/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~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) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | c3_1(W))),
% 1.28/1.08 inference(rewrite,[status(thm)],[])).
% 1.28/1.08 tff(661,plain,
% 1.28/1.08 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W))))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | c3_1(W))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | c3_1(W))))),
% 1.31/1.08 inference(bind,[status(th)],[])).
% 1.31/1.08 tff(662,plain,
% 1.31/1.08 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | c3_1(W))),
% 1.31/1.08 inference(quant_intro,[status(thm)],[661])).
% 1.31/1.08 tff(663,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause190')).
% 1.31/1.08 tff(664,plain,
% 1.31/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | c3_1(W))),
% 1.31/1.08 inference(modus_ponens,[status(thm)],[663, 662])).
% 1.31/1.08 tff(665,plain,
% 1.31/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | c3_1(W))),
% 1.31/1.08 inference(modus_ponens,[status(thm)],[664, 660])).
% 1.31/1.08 tff(666,plain,(
% 1.31/1.08 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | c3_1(W))),
% 1.31/1.08 inference(skolemize,[status(sab)],[665])).
% 1.31/1.08 tff(667,plain,
% 1.31/1.08 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | c3_1(W))),
% 1.31/1.08 inference(modus_ponens,[status(thm)],[666, 659])).
% 1.31/1.08 tff(668,assumption,(~c1_1(a326)), introduced(assumption)).
% 1.31/1.08 tff(669,plain,
% 1.31/1.08 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 1.31/1.08 inference(bind,[status(th)],[])).
% 1.31/1.08 tff(670,plain,
% 1.31/1.08 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.31/1.08 inference(quant_intro,[status(thm)],[669])).
% 1.31/1.08 tff(671,plain,
% 1.31/1.08 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.31/1.08 inference(rewrite,[status(thm)],[])).
% 1.31/1.08 tff(672,plain,
% 1.31/1.08 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | hskp8) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp8))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 1.31/1.08 inference(bind,[status(th)],[])).
% 1.31/1.08 tff(673,plain,
% 1.31/1.08 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.31/1.08 inference(quant_intro,[status(thm)],[672])).
% 1.31/1.08 tff(674,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause175')).
% 1.31/1.08 tff(675,plain,
% 1.31/1.08 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.31/1.08 inference(modus_ponens,[status(thm)],[674, 673])).
% 1.31/1.08 tff(676,plain,
% 1.31/1.08 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.31/1.08 inference(modus_ponens,[status(thm)],[675, 671])).
% 1.31/1.08 tff(677,plain,(
% 1.31/1.08 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.31/1.08 inference(skolemize,[status(sab)],[676])).
% 1.31/1.08 tff(678,plain,
% 1.31/1.08 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.31/1.08 inference(modus_ponens,[status(thm)],[677, 670])).
% 1.31/1.08 tff(679,plain,
% 1.31/1.08 (hskp9),
% 1.31/1.08 inference(unit_resolution,[status(thm)],[158, 152, 246, 106, 245, 244, 82, 81, 80])).
% 1.31/1.08 tff(680,plain,
% 1.31/1.08 (~c1_1(a334)),
% 1.31/1.08 inference(unit_resolution,[status(thm)],[170, 679])).
% 1.31/1.08 tff(681,plain,
% 1.31/1.08 (~c0_1(a334)),
% 1.31/1.08 inference(unit_resolution,[status(thm)],[164, 679])).
% 1.31/1.08 tff(682,plain,
% 1.31/1.08 (c2_1(a334)),
% 1.31/1.08 inference(unit_resolution,[status(thm)],[181, 679])).
% 1.31/1.08 tff(683,plain,
% 1.31/1.08 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | c0_1(a334) | c1_1(a334) | (~ndr1_0) | (~c1_1(a333)) | (~c3_1(a333)) | (~c2_1(a333)) | (~c2_1(a334)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c0_1(a334) | c1_1(a334) | (~ndr1_0) | (~c1_1(a333)) | (~c3_1(a333)) | (~c2_1(a333)) | (~c2_1(a334)))),
% 1.31/1.08 inference(rewrite,[status(thm)],[])).
% 1.31/1.08 tff(684,plain,
% 1.31/1.08 ((hskp8 | (~ndr1_0) | (~c2_1(a333)) | (~c3_1(a333)) | (~c1_1(a333)) | c1_1(a334) | c0_1(a334) | (~c2_1(a334))) <=> (hskp8 | c0_1(a334) | c1_1(a334) | (~ndr1_0) | (~c1_1(a333)) | (~c3_1(a333)) | (~c2_1(a333)) | (~c2_1(a334)))),
% 1.31/1.08 inference(rewrite,[status(thm)],[])).
% 1.31/1.08 tff(685,plain,
% 1.31/1.08 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a333)) | (~c3_1(a333)) | (~c1_1(a333)) | c1_1(a334) | c0_1(a334) | (~c2_1(a334)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | c0_1(a334) | c1_1(a334) | (~ndr1_0) | (~c1_1(a333)) | (~c3_1(a333)) | (~c2_1(a333)) | (~c2_1(a334))))),
% 1.31/1.08 inference(monotonicity,[status(thm)],[684])).
% 1.31/1.08 tff(686,plain,
% 1.31/1.08 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a333)) | (~c3_1(a333)) | (~c1_1(a333)) | c1_1(a334) | c0_1(a334) | (~c2_1(a334)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c0_1(a334) | c1_1(a334) | (~ndr1_0) | (~c1_1(a333)) | (~c3_1(a333)) | (~c2_1(a333)) | (~c2_1(a334)))),
% 1.31/1.08 inference(transitivity,[status(thm)],[685, 683])).
% 1.31/1.08 tff(687,plain,
% 1.31/1.08 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a333)) | (~c3_1(a333)) | (~c1_1(a333)) | c1_1(a334) | c0_1(a334) | (~c2_1(a334)))),
% 1.31/1.08 inference(quant_inst,[status(thm)],[])).
% 1.31/1.08 tff(688,plain,
% 1.31/1.08 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c0_1(a334) | c1_1(a334) | (~ndr1_0) | (~c1_1(a333)) | (~c3_1(a333)) | (~c2_1(a333)) | (~c2_1(a334))),
% 1.31/1.08 inference(modus_ponens,[status(thm)],[687, 686])).
% 1.31/1.08 tff(689,plain,
% 1.31/1.08 (hskp8),
% 1.31/1.08 inference(unit_resolution,[status(thm)],[688, 152, 619, 618, 682, 681, 680, 678, 627])).
% 1.31/1.08 tff(690,plain,
% 1.31/1.08 (((~hskp8) | (~c3_1(a332))) <=> ((~hskp8) | (~c3_1(a332)))),
% 1.31/1.08 inference(rewrite,[status(thm)],[])).
% 1.31/1.08 tff(691,plain,
% 1.31/1.08 (((~c3_1(a332)) | (~hskp8)) <=> ((~hskp8) | (~c3_1(a332)))),
% 1.31/1.08 inference(rewrite,[status(thm)],[])).
% 1.31/1.08 tff(692,axiom,((~c3_1(a332)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause111')).
% 1.31/1.08 tff(693,plain,
% 1.31/1.08 ((~hskp8) | (~c3_1(a332))),
% 1.31/1.08 inference(modus_ponens,[status(thm)],[692, 691])).
% 1.31/1.08 tff(694,plain,
% 1.31/1.08 ((~hskp8) | (~c3_1(a332))),
% 1.31/1.08 inference(modus_ponens,[status(thm)],[693, 690])).
% 1.31/1.08 tff(695,plain,
% 1.31/1.08 (~c3_1(a332)),
% 1.31/1.08 inference(unit_resolution,[status(thm)],[694, 689])).
% 1.31/1.08 tff(696,plain,
% 1.31/1.08 (((~hskp8) | (~c2_1(a332))) <=> ((~hskp8) | (~c2_1(a332)))),
% 1.31/1.08 inference(rewrite,[status(thm)],[])).
% 1.31/1.08 tff(697,plain,
% 1.31/1.08 (((~c2_1(a332)) | (~hskp8)) <=> ((~hskp8) | (~c2_1(a332)))),
% 1.31/1.08 inference(rewrite,[status(thm)],[])).
% 1.31/1.08 tff(698,axiom,((~c2_1(a332)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause110')).
% 1.31/1.08 tff(699,plain,
% 1.31/1.08 ((~hskp8) | (~c2_1(a332))),
% 1.31/1.08 inference(modus_ponens,[status(thm)],[698, 697])).
% 1.31/1.08 tff(700,plain,
% 1.31/1.08 ((~hskp8) | (~c2_1(a332))),
% 1.31/1.08 inference(modus_ponens,[status(thm)],[699, 696])).
% 1.31/1.08 tff(701,plain,
% 1.31/1.08 (~c2_1(a332)),
% 1.31/1.08 inference(unit_resolution,[status(thm)],[700, 689])).
% 1.31/1.08 tff(702,plain,
% 1.31/1.08 (((~hskp8) | (~c0_1(a332))) <=> ((~hskp8) | (~c0_1(a332)))),
% 1.31/1.08 inference(rewrite,[status(thm)],[])).
% 1.31/1.08 tff(703,plain,
% 1.31/1.08 (((~c0_1(a332)) | (~hskp8)) <=> ((~hskp8) | (~c0_1(a332)))),
% 1.31/1.08 inference(rewrite,[status(thm)],[])).
% 1.31/1.08 tff(704,axiom,((~c0_1(a332)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause109')).
% 1.31/1.08 tff(705,plain,
% 1.31/1.08 ((~hskp8) | (~c0_1(a332))),
% 1.31/1.08 inference(modus_ponens,[status(thm)],[704, 703])).
% 1.31/1.08 tff(706,plain,
% 1.31/1.08 ((~hskp8) | (~c0_1(a332))),
% 1.31/1.08 inference(modus_ponens,[status(thm)],[705, 702])).
% 1.31/1.08 tff(707,plain,
% 1.31/1.08 (~c0_1(a332)),
% 1.31/1.08 inference(unit_resolution,[status(thm)],[706, 689])).
% 1.31/1.08 tff(708,assumption,(c2_1(a326)), introduced(assumption)).
% 1.31/1.08 tff(709,assumption,(c0_1(a326)), introduced(assumption)).
% 1.31/1.08 tff(710,plain,
% 1.31/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | c3_1(W))) | (c0_1(a332) | c2_1(a332) | c3_1(a332) | c1_1(a326) | (~ndr1_0) | (~c2_1(a326)) | (~c0_1(a326)) | (~c1_1(a332)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | c3_1(W))) | c0_1(a332) | c2_1(a332) | c3_1(a332) | c1_1(a326) | (~ndr1_0) | (~c2_1(a326)) | (~c0_1(a326)) | (~c1_1(a332)))),
% 1.31/1.08 inference(rewrite,[status(thm)],[])).
% 1.31/1.08 tff(711,plain,
% 1.31/1.08 (((~ndr1_0) | c2_1(a332) | c3_1(a332) | (~c1_1(a332)) | c1_1(a326) | (~c0_1(a326)) | (~c2_1(a326)) | c0_1(a332) | (~c1_1(a332)) | c3_1(a332)) <=> (c0_1(a332) | c2_1(a332) | c3_1(a332) | c1_1(a326) | (~ndr1_0) | (~c2_1(a326)) | (~c0_1(a326)) | (~c1_1(a332)))),
% 1.31/1.08 inference(rewrite,[status(thm)],[])).
% 1.31/1.08 tff(712,plain,
% 1.31/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | c3_1(W))) | ((~ndr1_0) | c2_1(a332) | c3_1(a332) | (~c1_1(a332)) | c1_1(a326) | (~c0_1(a326)) | (~c2_1(a326)) | c0_1(a332) | (~c1_1(a332)) | c3_1(a332))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | c3_1(W))) | (c0_1(a332) | c2_1(a332) | c3_1(a332) | c1_1(a326) | (~ndr1_0) | (~c2_1(a326)) | (~c0_1(a326)) | (~c1_1(a332))))),
% 1.31/1.08 inference(monotonicity,[status(thm)],[711])).
% 1.31/1.08 tff(713,plain,
% 1.31/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | c3_1(W))) | ((~ndr1_0) | c2_1(a332) | c3_1(a332) | (~c1_1(a332)) | c1_1(a326) | (~c0_1(a326)) | (~c2_1(a326)) | c0_1(a332) | (~c1_1(a332)) | c3_1(a332))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | c3_1(W))) | c0_1(a332) | c2_1(a332) | c3_1(a332) | c1_1(a326) | (~ndr1_0) | (~c2_1(a326)) | (~c0_1(a326)) | (~c1_1(a332)))),
% 1.31/1.08 inference(transitivity,[status(thm)],[712, 710])).
% 1.31/1.08 tff(714,plain,
% 1.31/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | c3_1(W))) | ((~ndr1_0) | c2_1(a332) | c3_1(a332) | (~c1_1(a332)) | c1_1(a326) | (~c0_1(a326)) | (~c2_1(a326)) | c0_1(a332) | (~c1_1(a332)) | c3_1(a332))),
% 1.31/1.08 inference(quant_inst,[status(thm)],[])).
% 1.31/1.08 tff(715,plain,
% 1.31/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | c3_1(W))) | c0_1(a332) | c2_1(a332) | c3_1(a332) | c1_1(a326) | (~ndr1_0) | (~c2_1(a326)) | (~c0_1(a326)) | (~c1_1(a332))),
% 1.31/1.08 inference(modus_ponens,[status(thm)],[714, 713])).
% 1.31/1.08 tff(716,plain,
% 1.31/1.08 (~c1_1(a332)),
% 1.31/1.08 inference(unit_resolution,[status(thm)],[715, 152, 709, 708, 707, 701, 695, 668, 667])).
% 1.31/1.08 tff(717,plain,
% 1.31/1.08 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))),
% 1.31/1.08 inference(bind,[status(th)],[])).
% 1.31/1.08 tff(718,plain,
% 1.31/1.08 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.31/1.08 inference(quant_intro,[status(thm)],[717])).
% 1.31/1.08 tff(719,plain,
% 1.31/1.08 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.31/1.08 inference(rewrite,[status(thm)],[])).
% 1.31/1.08 tff(720,plain,
% 1.31/1.08 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp12) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp12))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))))),
% 1.31/1.08 inference(bind,[status(th)],[])).
% 1.31/1.08 tff(721,plain,
% 1.31/1.08 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.31/1.08 inference(quant_intro,[status(thm)],[720])).
% 1.31/1.08 tff(722,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause154')).
% 1.31/1.08 tff(723,plain,
% 1.31/1.08 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.31/1.08 inference(modus_ponens,[status(thm)],[722, 721])).
% 1.31/1.08 tff(724,plain,
% 1.31/1.08 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.31/1.08 inference(modus_ponens,[status(thm)],[723, 719])).
% 1.31/1.08 tff(725,plain,(
% 1.31/1.08 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.31/1.08 inference(skolemize,[status(sab)],[724])).
% 1.31/1.08 tff(726,plain,
% 1.31/1.08 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.31/1.08 inference(modus_ponens,[status(thm)],[725, 718])).
% 1.31/1.08 tff(727,plain,
% 1.31/1.08 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp12 | c1_1(a367) | c2_1(a367) | c2_1(a332) | c3_1(a332) | (~ndr1_0) | (~c3_1(a367)) | c1_1(a332))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp12 | c1_1(a367) | c2_1(a367) | c2_1(a332) | c3_1(a332) | (~ndr1_0) | (~c3_1(a367)) | c1_1(a332))),
% 1.31/1.08 inference(rewrite,[status(thm)],[])).
% 1.31/1.08 tff(728,plain,
% 1.31/1.08 ((hskp12 | (~ndr1_0) | c2_1(a367) | c1_1(a367) | (~c3_1(a367)) | c2_1(a332) | c1_1(a332) | c3_1(a332)) <=> (hskp12 | c1_1(a367) | c2_1(a367) | c2_1(a332) | c3_1(a332) | (~ndr1_0) | (~c3_1(a367)) | c1_1(a332))),
% 1.31/1.08 inference(rewrite,[status(thm)],[])).
% 1.31/1.08 tff(729,plain,
% 1.31/1.08 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp12 | (~ndr1_0) | c2_1(a367) | c1_1(a367) | (~c3_1(a367)) | c2_1(a332) | c1_1(a332) | c3_1(a332))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp12 | c1_1(a367) | c2_1(a367) | c2_1(a332) | c3_1(a332) | (~ndr1_0) | (~c3_1(a367)) | c1_1(a332)))),
% 1.31/1.08 inference(monotonicity,[status(thm)],[728])).
% 1.31/1.08 tff(730,plain,
% 1.31/1.08 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp12 | (~ndr1_0) | c2_1(a367) | c1_1(a367) | (~c3_1(a367)) | c2_1(a332) | c1_1(a332) | c3_1(a332))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp12 | c1_1(a367) | c2_1(a367) | c2_1(a332) | c3_1(a332) | (~ndr1_0) | (~c3_1(a367)) | c1_1(a332))),
% 1.31/1.09 inference(transitivity,[status(thm)],[729, 727])).
% 1.31/1.09 tff(731,plain,
% 1.31/1.09 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp12 | (~ndr1_0) | c2_1(a367) | c1_1(a367) | (~c3_1(a367)) | c2_1(a332) | c1_1(a332) | c3_1(a332))),
% 1.31/1.09 inference(quant_inst,[status(thm)],[])).
% 1.31/1.09 tff(732,plain,
% 1.31/1.09 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp12 | c1_1(a367) | c2_1(a367) | c2_1(a332) | c3_1(a332) | (~ndr1_0) | (~c3_1(a367)) | c1_1(a332)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[731, 730])).
% 1.31/1.09 tff(733,plain,
% 1.31/1.09 (hskp12),
% 1.31/1.09 inference(unit_resolution,[status(thm)],[732, 152, 491, 490, 510, 701, 695, 726, 716])).
% 1.31/1.09 tff(734,plain,
% 1.31/1.09 (~c2_1(a345)),
% 1.31/1.09 inference(unit_resolution,[status(thm)],[332, 733])).
% 1.31/1.09 tff(735,plain,
% 1.31/1.09 (c3_1(a345)),
% 1.31/1.09 inference(unit_resolution,[status(thm)],[303, 733])).
% 1.31/1.09 tff(736,plain,
% 1.31/1.09 (c0_1(a345)),
% 1.31/1.09 inference(unit_resolution,[status(thm)],[314, 733])).
% 1.31/1.09 tff(737,plain,
% 1.31/1.09 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | c2_1(a345) | c0_1(a330) | (~ndr1_0) | c2_1(a330) | (~c3_1(a330)) | (~c0_1(a345)) | (~c3_1(a345)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c2_1(a345) | c0_1(a330) | (~ndr1_0) | c2_1(a330) | (~c3_1(a330)) | (~c0_1(a345)) | (~c3_1(a345)))),
% 1.31/1.09 inference(rewrite,[status(thm)],[])).
% 1.31/1.09 tff(738,plain,
% 1.31/1.09 ((hskp28 | (~ndr1_0) | c2_1(a345) | (~c0_1(a345)) | (~c3_1(a345)) | c2_1(a330) | c0_1(a330) | (~c3_1(a330))) <=> (hskp28 | c2_1(a345) | c0_1(a330) | (~ndr1_0) | c2_1(a330) | (~c3_1(a330)) | (~c0_1(a345)) | (~c3_1(a345)))),
% 1.31/1.09 inference(rewrite,[status(thm)],[])).
% 1.31/1.09 tff(739,plain,
% 1.31/1.09 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a345) | (~c0_1(a345)) | (~c3_1(a345)) | c2_1(a330) | c0_1(a330) | (~c3_1(a330)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | c2_1(a345) | c0_1(a330) | (~ndr1_0) | c2_1(a330) | (~c3_1(a330)) | (~c0_1(a345)) | (~c3_1(a345))))),
% 1.31/1.09 inference(monotonicity,[status(thm)],[738])).
% 1.31/1.09 tff(740,plain,
% 1.31/1.09 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a345) | (~c0_1(a345)) | (~c3_1(a345)) | c2_1(a330) | c0_1(a330) | (~c3_1(a330)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c2_1(a345) | c0_1(a330) | (~ndr1_0) | c2_1(a330) | (~c3_1(a330)) | (~c0_1(a345)) | (~c3_1(a345)))),
% 1.31/1.09 inference(transitivity,[status(thm)],[739, 737])).
% 1.31/1.09 tff(741,plain,
% 1.31/1.09 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a345) | (~c0_1(a345)) | (~c3_1(a345)) | c2_1(a330) | c0_1(a330) | (~c3_1(a330)))),
% 1.31/1.09 inference(quant_inst,[status(thm)],[])).
% 1.31/1.09 tff(742,plain,
% 1.31/1.09 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp28 | c2_1(a345) | c0_1(a330) | (~ndr1_0) | c2_1(a330) | (~c3_1(a330)) | (~c0_1(a345)) | (~c3_1(a345))),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[741, 740])).
% 1.31/1.09 tff(743,plain,
% 1.31/1.09 ($false),
% 1.31/1.09 inference(unit_resolution,[status(thm)],[742, 616, 152, 736, 735, 106, 734, 82, 657, 647])).
% 1.31/1.09 tff(744,plain,(hskp28 | (~c3_1(a330)) | c0_1(a330) | (~c0_1(a419)) | (~c3_1(a367)) | c1_1(a419) | c2_1(a419) | c2_1(a367) | c1_1(a330) | c1_1(a367) | (~c0_1(a326)) | (~c2_1(a326)) | c1_1(a326)), inference(lemma,lemma(discharge,[]))).
% 1.31/1.09 tff(745,plain,
% 1.31/1.09 (hskp28),
% 1.31/1.09 inference(unit_resolution,[status(thm)],[744, 117, 82, 106, 488, 105, 99, 477, 81, 471, 615, 604, 593])).
% 1.31/1.09 tff(746,plain,
% 1.31/1.09 (((~hskp28) | c0_1(a343)) <=> ((~hskp28) | c0_1(a343))),
% 1.31/1.09 inference(rewrite,[status(thm)],[])).
% 1.31/1.09 tff(747,axiom,((~hskp28) | c0_1(a343)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause39')).
% 1.31/1.09 tff(748,plain,
% 1.31/1.09 ((~hskp28) | c0_1(a343)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[747, 746])).
% 1.31/1.09 tff(749,plain,
% 1.31/1.09 ((~hskp28) | c0_1(a343)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[748, 746])).
% 1.31/1.09 tff(750,plain,
% 1.31/1.09 ((~hskp28) | c0_1(a343)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[749, 746])).
% 1.31/1.09 tff(751,plain,
% 1.31/1.09 ((~hskp28) | c0_1(a343)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[750, 746])).
% 1.31/1.09 tff(752,plain,
% 1.31/1.09 ((~hskp28) | c0_1(a343)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[751, 746])).
% 1.31/1.09 tff(753,plain,
% 1.31/1.09 ((~hskp28) | c0_1(a343)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[752, 746])).
% 1.31/1.09 tff(754,plain,
% 1.31/1.09 ((~hskp28) | c0_1(a343)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[753, 746])).
% 1.31/1.09 tff(755,plain,
% 1.31/1.09 ((~hskp28) | c0_1(a343)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[754, 746])).
% 1.31/1.09 tff(756,plain,
% 1.31/1.09 (c0_1(a343)),
% 1.31/1.09 inference(unit_resolution,[status(thm)],[755, 745])).
% 1.31/1.09 tff(757,plain,
% 1.31/1.09 (((~hskp28) | c1_1(a343)) <=> ((~hskp28) | c1_1(a343))),
% 1.31/1.09 inference(rewrite,[status(thm)],[])).
% 1.31/1.09 tff(758,axiom,((~hskp28) | c1_1(a343)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause40')).
% 1.31/1.09 tff(759,plain,
% 1.31/1.09 ((~hskp28) | c1_1(a343)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[758, 757])).
% 1.31/1.09 tff(760,plain,
% 1.31/1.09 ((~hskp28) | c1_1(a343)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[759, 757])).
% 1.31/1.09 tff(761,plain,
% 1.31/1.09 ((~hskp28) | c1_1(a343)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[760, 757])).
% 1.31/1.09 tff(762,plain,
% 1.31/1.09 ((~hskp28) | c1_1(a343)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[761, 757])).
% 1.31/1.09 tff(763,plain,
% 1.31/1.09 ((~hskp28) | c1_1(a343)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[762, 757])).
% 1.31/1.09 tff(764,plain,
% 1.31/1.09 ((~hskp28) | c1_1(a343)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[763, 757])).
% 1.31/1.09 tff(765,plain,
% 1.31/1.09 ((~hskp28) | c1_1(a343)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[764, 757])).
% 1.31/1.09 tff(766,plain,
% 1.31/1.09 ((~hskp28) | c1_1(a343)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[765, 757])).
% 1.31/1.09 tff(767,plain,
% 1.31/1.09 (c1_1(a343)),
% 1.31/1.09 inference(unit_resolution,[status(thm)],[766, 745])).
% 1.31/1.09 tff(768,plain,
% 1.31/1.09 (((~hskp28) | c2_1(a343)) <=> ((~hskp28) | c2_1(a343))),
% 1.31/1.09 inference(rewrite,[status(thm)],[])).
% 1.31/1.09 tff(769,axiom,((~hskp28) | c2_1(a343)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause41')).
% 1.31/1.09 tff(770,plain,
% 1.31/1.09 ((~hskp28) | c2_1(a343)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[769, 768])).
% 1.31/1.09 tff(771,plain,
% 1.31/1.09 ((~hskp28) | c2_1(a343)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[770, 768])).
% 1.31/1.09 tff(772,plain,
% 1.31/1.09 ((~hskp28) | c2_1(a343)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[771, 768])).
% 1.31/1.09 tff(773,plain,
% 1.31/1.09 ((~hskp28) | c2_1(a343)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[772, 768])).
% 1.31/1.09 tff(774,plain,
% 1.31/1.09 ((~hskp28) | c2_1(a343)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[773, 768])).
% 1.31/1.09 tff(775,plain,
% 1.31/1.09 ((~hskp28) | c2_1(a343)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[774, 768])).
% 1.31/1.09 tff(776,plain,
% 1.31/1.09 ((~hskp28) | c2_1(a343)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[775, 768])).
% 1.31/1.09 tff(777,plain,
% 1.31/1.09 ((~hskp28) | c2_1(a343)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[776, 768])).
% 1.31/1.09 tff(778,plain,
% 1.31/1.09 (c2_1(a343)),
% 1.31/1.09 inference(unit_resolution,[status(thm)],[777, 745])).
% 1.31/1.09 tff(779,plain,
% 1.31/1.09 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))))),
% 1.31/1.09 inference(bind,[status(th)],[])).
% 1.31/1.09 tff(780,plain,
% 1.31/1.09 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.31/1.09 inference(quant_intro,[status(thm)],[779])).
% 1.31/1.09 tff(781,plain,
% 1.31/1.09 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.31/1.09 inference(rewrite,[status(thm)],[])).
% 1.31/1.09 tff(782,plain,
% 1.31/1.09 (^[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))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))))),
% 1.31/1.09 inference(bind,[status(th)],[])).
% 1.31/1.09 tff(783,plain,
% 1.31/1.09 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_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)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.31/1.09 inference(quant_intro,[status(thm)],[782])).
% 1.31/1.09 tff(784,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause195')).
% 1.31/1.09 tff(785,plain,
% 1.31/1.09 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[784, 783])).
% 1.31/1.09 tff(786,plain,
% 1.31/1.09 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[785, 781])).
% 1.31/1.09 tff(787,plain,(
% 1.31/1.09 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.31/1.09 inference(skolemize,[status(sab)],[786])).
% 1.31/1.09 tff(788,plain,
% 1.31/1.09 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[787, 780])).
% 1.31/1.09 tff(789,plain,
% 1.31/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a367) | c2_1(a367) | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)) | (~c3_1(a367)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a367) | c2_1(a367) | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)) | (~c3_1(a367)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.31/1.09 inference(rewrite,[status(thm)],[])).
% 1.31/1.09 tff(790,plain,
% 1.31/1.09 (((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a333) | (~c3_1(a333)) | (~c1_1(a333)) | c2_1(a367) | c1_1(a367) | (~c3_1(a367))) <=> (c1_1(a367) | c2_1(a367) | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)) | (~c3_1(a367)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.31/1.09 inference(rewrite,[status(thm)],[])).
% 1.31/1.09 tff(791,plain,
% 1.31/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a333) | (~c3_1(a333)) | (~c1_1(a333)) | c2_1(a367) | c1_1(a367) | (~c3_1(a367)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a367) | c2_1(a367) | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)) | (~c3_1(a367)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))))),
% 1.31/1.09 inference(monotonicity,[status(thm)],[790])).
% 1.31/1.09 tff(792,plain,
% 1.31/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a333) | (~c3_1(a333)) | (~c1_1(a333)) | c2_1(a367) | c1_1(a367) | (~c3_1(a367)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a367) | c2_1(a367) | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)) | (~c3_1(a367)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.31/1.09 inference(transitivity,[status(thm)],[791, 789])).
% 1.31/1.09 tff(793,plain,
% 1.31/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a333) | (~c3_1(a333)) | (~c1_1(a333)) | c2_1(a367) | c1_1(a367) | (~c3_1(a367)))),
% 1.31/1.09 inference(quant_inst,[status(thm)],[])).
% 1.31/1.09 tff(794,plain,
% 1.31/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a367) | c2_1(a367) | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)) | (~c3_1(a367)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[793, 792])).
% 1.31/1.09 tff(795,plain,
% 1.31/1.09 (c1_1(a367) | c2_1(a367) | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)) | (~c3_1(a367)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))),
% 1.31/1.09 inference(unit_resolution,[status(thm)],[794, 788])).
% 1.31/1.09 tff(796,plain,
% 1.31/1.09 (c1_1(a367) | c2_1(a367) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)) | (~c3_1(a367)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))),
% 1.31/1.09 inference(unit_resolution,[status(thm)],[795, 152])).
% 1.31/1.09 tff(797,plain,
% 1.31/1.09 (c2_1(a333)),
% 1.31/1.09 inference(unit_resolution,[status(thm)],[796, 778, 488, 471, 221, 210, 767, 477, 756])).
% 1.31/1.09 tff(798,plain,
% 1.31/1.09 (hskp10),
% 1.31/1.09 inference(unit_resolution,[status(thm)],[432, 152, 232, 210, 221, 425, 797])).
% 1.31/1.09 tff(799,plain,
% 1.31/1.09 (~c3_1(a337)),
% 1.31/1.09 inference(unit_resolution,[status(thm)],[438, 798])).
% 1.31/1.09 tff(800,plain,
% 1.31/1.09 (~c2_1(a337)),
% 1.31/1.09 inference(unit_resolution,[status(thm)],[444, 798])).
% 1.31/1.09 tff(801,plain,
% 1.31/1.09 (c0_1(a337)),
% 1.31/1.09 inference(unit_resolution,[status(thm)],[455, 798])).
% 1.31/1.09 tff(802,plain,
% 1.31/1.09 (~c3_1(a419)),
% 1.31/1.09 inference(unit_resolution,[status(thm)],[462, 152, 232, 221, 117, 801, 99, 800, 799, 415, 797])).
% 1.31/1.09 tff(803,plain,
% 1.31/1.09 (hskp8),
% 1.31/1.09 inference(unit_resolution,[status(thm)],[688, 152, 210, 221, 182, 165, 171, 678, 797])).
% 1.31/1.09 tff(804,plain,
% 1.31/1.09 (~c3_1(a332)),
% 1.31/1.09 inference(unit_resolution,[status(thm)],[694, 803])).
% 1.31/1.09 tff(805,plain,
% 1.31/1.09 (~c2_1(a332)),
% 1.31/1.09 inference(unit_resolution,[status(thm)],[700, 803])).
% 1.31/1.09 tff(806,plain,
% 1.31/1.09 (~c0_1(a332)),
% 1.31/1.09 inference(unit_resolution,[status(thm)],[706, 803])).
% 1.31/1.09 tff(807,plain,
% 1.31/1.09 (~c1_1(a332)),
% 1.31/1.09 inference(unit_resolution,[status(thm)],[715, 152, 615, 604, 806, 805, 804, 593, 667])).
% 1.31/1.09 tff(808,plain,
% 1.31/1.09 (hskp12),
% 1.31/1.09 inference(unit_resolution,[status(thm)],[732, 152, 488, 471, 477, 805, 804, 726, 807])).
% 1.31/1.09 tff(809,plain,
% 1.31/1.09 (~c2_1(a345)),
% 1.31/1.09 inference(unit_resolution,[status(thm)],[332, 808])).
% 1.31/1.09 tff(810,plain,
% 1.31/1.09 (c3_1(a345)),
% 1.31/1.09 inference(unit_resolution,[status(thm)],[303, 808])).
% 1.31/1.09 tff(811,plain,
% 1.31/1.09 (c0_1(a345)),
% 1.31/1.09 inference(unit_resolution,[status(thm)],[314, 808])).
% 1.31/1.09 tff(812,plain,
% 1.31/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a419) | c2_1(a345) | (~ndr1_0) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333)) | (~c0_1(a345)) | (~c3_1(a345)) | c3_1(a419) | (~c0_1(a419)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a419) | c2_1(a345) | (~ndr1_0) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333)) | (~c0_1(a345)) | (~c3_1(a345)) | c3_1(a419) | (~c0_1(a419)))),
% 1.31/1.09 inference(rewrite,[status(thm)],[])).
% 1.31/1.09 tff(813,plain,
% 1.31/1.09 (((~ndr1_0) | (~c2_1(a333)) | (~c0_1(a333)) | (~c3_1(a333)) | c2_1(a345) | (~c3_1(a345)) | (~c0_1(a345)) | c2_1(a419) | c3_1(a419) | (~c0_1(a419))) <=> (c2_1(a419) | c2_1(a345) | (~ndr1_0) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333)) | (~c0_1(a345)) | (~c3_1(a345)) | c3_1(a419) | (~c0_1(a419)))),
% 1.31/1.09 inference(rewrite,[status(thm)],[])).
% 1.31/1.09 tff(814,plain,
% 1.31/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a333)) | (~c0_1(a333)) | (~c3_1(a333)) | c2_1(a345) | (~c3_1(a345)) | (~c0_1(a345)) | c2_1(a419) | c3_1(a419) | (~c0_1(a419)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a419) | c2_1(a345) | (~ndr1_0) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333)) | (~c0_1(a345)) | (~c3_1(a345)) | c3_1(a419) | (~c0_1(a419))))),
% 1.31/1.09 inference(monotonicity,[status(thm)],[813])).
% 1.31/1.09 tff(815,plain,
% 1.31/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a333)) | (~c0_1(a333)) | (~c3_1(a333)) | c2_1(a345) | (~c3_1(a345)) | (~c0_1(a345)) | c2_1(a419) | c3_1(a419) | (~c0_1(a419)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a419) | c2_1(a345) | (~ndr1_0) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333)) | (~c0_1(a345)) | (~c3_1(a345)) | c3_1(a419) | (~c0_1(a419)))),
% 1.31/1.09 inference(transitivity,[status(thm)],[814, 812])).
% 1.31/1.09 tff(816,plain,
% 1.31/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a333)) | (~c0_1(a333)) | (~c3_1(a333)) | c2_1(a345) | (~c3_1(a345)) | (~c0_1(a345)) | c2_1(a419) | c3_1(a419) | (~c0_1(a419)))),
% 1.31/1.09 inference(quant_inst,[status(thm)],[])).
% 1.31/1.09 tff(817,plain,
% 1.31/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a419) | c2_1(a345) | (~ndr1_0) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333)) | (~c0_1(a345)) | (~c3_1(a345)) | c3_1(a419) | (~c0_1(a419))),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[816, 815])).
% 1.31/1.09 tff(818,plain,
% 1.31/1.09 ($false),
% 1.31/1.09 inference(unit_resolution,[status(thm)],[817, 152, 232, 221, 117, 811, 810, 99, 809, 415, 797, 802])).
% 1.31/1.09 tff(819,plain,(hskp16 | c0_1(a330) | (~c3_1(a330)) | c1_1(a330) | hskp14), inference(lemma,lemma(discharge,[]))).
% 1.31/1.09 tff(820,plain,
% 1.31/1.09 (hskp16),
% 1.31/1.09 inference(unit_resolution,[status(thm)],[819, 69, 63, 52, 11])).
% 1.31/1.09 tff(821,plain,
% 1.31/1.09 (((~hskp16) | (~c2_1(a349))) <=> ((~hskp16) | (~c2_1(a349)))),
% 1.31/1.09 inference(rewrite,[status(thm)],[])).
% 1.31/1.09 tff(822,plain,
% 1.31/1.09 (((~c2_1(a349)) | (~hskp16)) <=> ((~hskp16) | (~c2_1(a349)))),
% 1.31/1.09 inference(rewrite,[status(thm)],[])).
% 1.31/1.09 tff(823,axiom,((~c2_1(a349)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause96')).
% 1.31/1.09 tff(824,plain,
% 1.31/1.09 ((~hskp16) | (~c2_1(a349))),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[823, 822])).
% 1.31/1.09 tff(825,plain,
% 1.31/1.09 ((~hskp16) | (~c2_1(a349))),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[824, 821])).
% 1.31/1.09 tff(826,plain,
% 1.31/1.09 (~c2_1(a349)),
% 1.31/1.09 inference(unit_resolution,[status(thm)],[825, 820])).
% 1.31/1.09 tff(827,plain,
% 1.31/1.09 (((~hskp16) | c3_1(a349)) <=> ((~hskp16) | c3_1(a349))),
% 1.31/1.09 inference(rewrite,[status(thm)],[])).
% 1.31/1.09 tff(828,axiom,((~hskp16) | c3_1(a349)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause61')).
% 1.31/1.09 tff(829,plain,
% 1.31/1.09 ((~hskp16) | c3_1(a349)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[828, 827])).
% 1.31/1.09 tff(830,plain,
% 1.31/1.09 ((~hskp16) | c3_1(a349)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[829, 827])).
% 1.31/1.09 tff(831,plain,
% 1.31/1.09 ((~hskp16) | c3_1(a349)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[830, 827])).
% 1.31/1.09 tff(832,plain,
% 1.31/1.09 ((~hskp16) | c3_1(a349)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[831, 827])).
% 1.31/1.09 tff(833,plain,
% 1.31/1.09 ((~hskp16) | c3_1(a349)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[832, 827])).
% 1.31/1.09 tff(834,plain,
% 1.31/1.09 ((~hskp16) | c3_1(a349)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[833, 827])).
% 1.31/1.09 tff(835,plain,
% 1.31/1.09 ((~hskp16) | c3_1(a349)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[834, 827])).
% 1.31/1.09 tff(836,plain,
% 1.31/1.09 ((~hskp16) | c3_1(a349)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[835, 827])).
% 1.31/1.09 tff(837,plain,
% 1.31/1.09 (c3_1(a349)),
% 1.31/1.09 inference(unit_resolution,[status(thm)],[836, 820])).
% 1.31/1.09 tff(838,plain,
% 1.31/1.09 (((~hskp16) | c1_1(a349)) <=> ((~hskp16) | c1_1(a349))),
% 1.31/1.09 inference(rewrite,[status(thm)],[])).
% 1.31/1.09 tff(839,axiom,((~hskp16) | c1_1(a349)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause60')).
% 1.31/1.09 tff(840,plain,
% 1.31/1.09 ((~hskp16) | c1_1(a349)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[839, 838])).
% 1.31/1.09 tff(841,plain,
% 1.31/1.09 ((~hskp16) | c1_1(a349)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[840, 838])).
% 1.31/1.09 tff(842,plain,
% 1.31/1.09 ((~hskp16) | c1_1(a349)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[841, 838])).
% 1.31/1.09 tff(843,plain,
% 1.31/1.09 ((~hskp16) | c1_1(a349)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[842, 838])).
% 1.31/1.09 tff(844,plain,
% 1.31/1.09 ((~hskp16) | c1_1(a349)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[843, 838])).
% 1.31/1.09 tff(845,plain,
% 1.31/1.09 ((~hskp16) | c1_1(a349)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[844, 838])).
% 1.31/1.09 tff(846,plain,
% 1.31/1.09 ((~hskp16) | c1_1(a349)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[845, 838])).
% 1.31/1.09 tff(847,plain,
% 1.31/1.09 ((~hskp16) | c1_1(a349)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[846, 838])).
% 1.31/1.09 tff(848,plain,
% 1.31/1.09 (c1_1(a349)),
% 1.31/1.09 inference(unit_resolution,[status(thm)],[847, 820])).
% 1.31/1.09 tff(849,plain,
% 1.31/1.09 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | c2_1(a349) | (~ndr1_0) | (~c3_1(a349)) | (~c1_1(a349)))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | c2_1(a349) | (~ndr1_0) | (~c3_1(a349)) | (~c1_1(a349)))),
% 1.31/1.09 inference(rewrite,[status(thm)],[])).
% 1.31/1.09 tff(850,plain,
% 1.31/1.09 ((hskp28 | (~ndr1_0) | c2_1(a349) | (~c3_1(a349)) | (~c1_1(a349))) <=> (hskp28 | c2_1(a349) | (~ndr1_0) | (~c3_1(a349)) | (~c1_1(a349)))),
% 1.31/1.09 inference(rewrite,[status(thm)],[])).
% 1.31/1.09 tff(851,plain,
% 1.31/1.09 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | (~ndr1_0) | c2_1(a349) | (~c3_1(a349)) | (~c1_1(a349)))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | c2_1(a349) | (~ndr1_0) | (~c3_1(a349)) | (~c1_1(a349))))),
% 1.31/1.09 inference(monotonicity,[status(thm)],[850])).
% 1.31/1.09 tff(852,plain,
% 1.31/1.09 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | (~ndr1_0) | c2_1(a349) | (~c3_1(a349)) | (~c1_1(a349)))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | c2_1(a349) | (~ndr1_0) | (~c3_1(a349)) | (~c1_1(a349)))),
% 1.31/1.09 inference(transitivity,[status(thm)],[851, 849])).
% 1.31/1.09 tff(853,plain,
% 1.31/1.09 ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | (~ndr1_0) | c2_1(a349) | (~c3_1(a349)) | (~c1_1(a349)))),
% 1.31/1.09 inference(quant_inst,[status(thm)],[])).
% 1.31/1.09 tff(854,plain,
% 1.31/1.09 ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | c2_1(a349) | (~ndr1_0) | (~c3_1(a349)) | (~c1_1(a349))),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[853, 852])).
% 1.31/1.09 tff(855,plain,
% 1.31/1.09 (hskp28),
% 1.31/1.09 inference(unit_resolution,[status(thm)],[854, 152, 848, 837, 826, 41])).
% 1.31/1.09 tff(856,plain,
% 1.31/1.09 (c2_1(a343)),
% 1.31/1.09 inference(unit_resolution,[status(thm)],[777, 855])).
% 1.31/1.09 tff(857,plain,
% 1.31/1.09 (c1_1(a343)),
% 1.31/1.09 inference(unit_resolution,[status(thm)],[766, 855])).
% 1.31/1.09 tff(858,plain,
% 1.31/1.09 (c0_1(a343)),
% 1.31/1.09 inference(unit_resolution,[status(thm)],[755, 855])).
% 1.31/1.09 tff(859,plain,
% 1.31/1.09 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp17 | (~ndr1_0) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.31/1.09 inference(rewrite,[status(thm)],[])).
% 1.31/1.09 tff(860,plain,
% 1.31/1.09 ((hskp24 | hskp17 | (~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343))) <=> (hskp24 | hskp17 | (~ndr1_0) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.31/1.09 inference(rewrite,[status(thm)],[])).
% 1.31/1.09 tff(861,plain,
% 1.31/1.09 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))))),
% 1.31/1.09 inference(monotonicity,[status(thm)],[860])).
% 1.31/1.09 tff(862,plain,
% 1.31/1.09 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp17 | (~ndr1_0) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.31/1.09 inference(transitivity,[status(thm)],[861, 859])).
% 1.31/1.09 tff(863,plain,
% 1.31/1.09 ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)))),
% 1.31/1.09 inference(quant_inst,[status(thm)],[])).
% 1.31/1.09 tff(864,plain,
% 1.31/1.09 ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp17 | (~ndr1_0) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[863, 862])).
% 1.31/1.09 tff(865,plain,
% 1.31/1.09 (hskp17),
% 1.31/1.09 inference(unit_resolution,[status(thm)],[864, 42, 152, 858, 857, 856, 31])).
% 1.31/1.09 tff(866,plain,
% 1.31/1.09 (((~hskp17) | (~c0_1(a353))) <=> ((~hskp17) | (~c0_1(a353)))),
% 1.31/1.09 inference(rewrite,[status(thm)],[])).
% 1.31/1.09 tff(867,plain,
% 1.31/1.09 (((~c0_1(a353)) | (~hskp17)) <=> ((~hskp17) | (~c0_1(a353)))),
% 1.31/1.09 inference(rewrite,[status(thm)],[])).
% 1.31/1.09 tff(868,axiom,((~c0_1(a353)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause95')).
% 1.31/1.09 tff(869,plain,
% 1.31/1.09 ((~hskp17) | (~c0_1(a353))),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[868, 867])).
% 1.31/1.09 tff(870,plain,
% 1.31/1.09 ((~hskp17) | (~c0_1(a353))),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[869, 866])).
% 1.31/1.09 tff(871,plain,
% 1.31/1.09 (~c0_1(a353)),
% 1.31/1.09 inference(unit_resolution,[status(thm)],[870, 865])).
% 1.31/1.09 tff(872,plain,
% 1.31/1.09 (((~hskp17) | c2_1(a353)) <=> ((~hskp17) | c2_1(a353))),
% 1.31/1.09 inference(rewrite,[status(thm)],[])).
% 1.31/1.09 tff(873,axiom,((~hskp17) | c2_1(a353)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause59')).
% 1.31/1.09 tff(874,plain,
% 1.31/1.09 ((~hskp17) | c2_1(a353)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[873, 872])).
% 1.31/1.09 tff(875,plain,
% 1.31/1.09 ((~hskp17) | c2_1(a353)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[874, 872])).
% 1.31/1.09 tff(876,plain,
% 1.31/1.09 ((~hskp17) | c2_1(a353)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[875, 872])).
% 1.31/1.09 tff(877,plain,
% 1.31/1.09 ((~hskp17) | c2_1(a353)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[876, 872])).
% 1.31/1.09 tff(878,plain,
% 1.31/1.09 ((~hskp17) | c2_1(a353)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[877, 872])).
% 1.31/1.09 tff(879,plain,
% 1.31/1.09 ((~hskp17) | c2_1(a353)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[878, 872])).
% 1.31/1.09 tff(880,plain,
% 1.31/1.09 ((~hskp17) | c2_1(a353)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[879, 872])).
% 1.31/1.09 tff(881,plain,
% 1.31/1.09 ((~hskp17) | c2_1(a353)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[880, 872])).
% 1.31/1.09 tff(882,plain,
% 1.31/1.09 (c2_1(a353)),
% 1.31/1.09 inference(unit_resolution,[status(thm)],[881, 865])).
% 1.31/1.09 tff(883,plain,
% 1.31/1.09 (((~hskp17) | c1_1(a353)) <=> ((~hskp17) | c1_1(a353))),
% 1.31/1.09 inference(rewrite,[status(thm)],[])).
% 1.31/1.09 tff(884,axiom,((~hskp17) | c1_1(a353)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause58')).
% 1.31/1.09 tff(885,plain,
% 1.31/1.09 ((~hskp17) | c1_1(a353)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[884, 883])).
% 1.31/1.09 tff(886,plain,
% 1.31/1.09 ((~hskp17) | c1_1(a353)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[885, 883])).
% 1.31/1.09 tff(887,plain,
% 1.31/1.09 ((~hskp17) | c1_1(a353)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[886, 883])).
% 1.31/1.09 tff(888,plain,
% 1.31/1.09 ((~hskp17) | c1_1(a353)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[887, 883])).
% 1.31/1.09 tff(889,plain,
% 1.31/1.09 ((~hskp17) | c1_1(a353)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[888, 883])).
% 1.31/1.09 tff(890,plain,
% 1.31/1.09 ((~hskp17) | c1_1(a353)),
% 1.31/1.09 inference(modus_ponens,[status(thm)],[889, 883])).
% 1.31/1.10 tff(891,plain,
% 1.31/1.10 ((~hskp17) | c1_1(a353)),
% 1.31/1.10 inference(modus_ponens,[status(thm)],[890, 883])).
% 1.31/1.10 tff(892,plain,
% 1.31/1.10 ((~hskp17) | c1_1(a353)),
% 1.31/1.10 inference(modus_ponens,[status(thm)],[891, 883])).
% 1.31/1.10 tff(893,plain,
% 1.31/1.10 (c1_1(a353)),
% 1.31/1.10 inference(unit_resolution,[status(thm)],[892, 865])).
% 1.31/1.10 tff(894,assumption,(~c2_1(a349)), introduced(assumption)).
% 1.31/1.10 tff(895,plain,
% 1.31/1.10 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))))),
% 1.31/1.10 inference(bind,[status(th)],[])).
% 1.31/1.10 tff(896,plain,
% 1.31/1.10 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.31/1.10 inference(quant_intro,[status(thm)],[895])).
% 1.31/1.10 tff(897,plain,
% 1.31/1.10 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.31/1.10 inference(rewrite,[status(thm)],[])).
% 1.31/1.10 tff(898,plain,
% 1.31/1.10 (^[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)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp10) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) | hskp10))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))))),
% 1.31/1.10 inference(bind,[status(th)],[])).
% 1.31/1.10 tff(899,plain,
% 1.31/1.10 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.31/1.10 inference(quant_intro,[status(thm)],[898])).
% 1.31/1.10 tff(900,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause182')).
% 1.31/1.10 tff(901,plain,
% 1.31/1.10 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.31/1.10 inference(modus_ponens,[status(thm)],[900, 899])).
% 1.31/1.10 tff(902,plain,
% 1.31/1.10 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.31/1.10 inference(modus_ponens,[status(thm)],[901, 897])).
% 1.31/1.10 tff(903,plain,(
% 1.31/1.10 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.31/1.10 inference(skolemize,[status(sab)],[902])).
% 1.31/1.10 tff(904,plain,
% 1.31/1.10 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.31/1.10 inference(modus_ponens,[status(thm)],[903, 896])).
% 1.31/1.10 tff(905,plain,
% 1.31/1.10 (^[U: $i] : refl((hskp10 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp10 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 1.31/1.10 inference(bind,[status(th)],[])).
% 1.31/1.10 tff(906,plain,
% 1.31/1.10 (![U: $i] : (hskp10 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp10 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.31/1.10 inference(quant_intro,[status(thm)],[905])).
% 1.31/1.10 tff(907,plain,
% 1.31/1.10 (![U: $i] : (hskp10 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp10 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.31/1.10 inference(rewrite,[status(thm)],[])).
% 1.31/1.10 tff(908,plain,
% 1.31/1.10 (^[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)) | hskp3) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp3))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp3) | hskp10) <=> ((hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp10))), rewrite(((hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp10) <=> (hskp10 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp3) | hskp10) <=> (hskp10 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 1.31/1.10 inference(bind,[status(th)],[])).
% 1.31/1.10 tff(909,plain,
% 1.31/1.10 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp3) | hskp10) <=> ![U: $i] : (hskp10 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.31/1.10 inference(quant_intro,[status(thm)],[908])).
% 1.31/1.10 tff(910,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp3) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause144')).
% 1.31/1.10 tff(911,plain,
% 1.31/1.10 (![U: $i] : (hskp10 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.31/1.10 inference(modus_ponens,[status(thm)],[910, 909])).
% 1.31/1.10 tff(912,plain,
% 1.31/1.10 (![U: $i] : (hskp10 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.31/1.10 inference(modus_ponens,[status(thm)],[911, 907])).
% 1.31/1.10 tff(913,plain,(
% 1.31/1.10 ![U: $i] : (hskp10 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.31/1.10 inference(skolemize,[status(sab)],[912])).
% 1.31/1.10 tff(914,plain,
% 1.31/1.10 (![U: $i] : (hskp10 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.31/1.10 inference(modus_ponens,[status(thm)],[913, 906])).
% 1.31/1.10 tff(915,assumption,(~c0_1(a353)), introduced(assumption)).
% 1.31/1.10 tff(916,assumption,(c2_1(a353)), introduced(assumption)).
% 1.31/1.10 tff(917,assumption,(c1_1(a353)), introduced(assumption)).
% 1.31/1.10 tff(918,assumption,(c1_1(a349)), introduced(assumption)).
% 1.31/1.10 tff(919,assumption,(c3_1(a349)), introduced(assumption)).
% 1.31/1.10 tff(920,assumption,(~hskp10), introduced(assumption)).
% 1.31/1.10 tff(921,assumption,(~hskp13), introduced(assumption)).
% 1.31/1.10 tff(922,plain,
% 1.31/1.10 (((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | hskp13 | c0_1(a353) | (~ndr1_0) | c3_1(a353) | (~c2_1(a353)))) <=> ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp14 | hskp13 | c0_1(a353) | (~ndr1_0) | c3_1(a353) | (~c2_1(a353)))),
% 1.31/1.10 inference(rewrite,[status(thm)],[])).
% 1.31/1.10 tff(923,plain,
% 1.31/1.10 ((hskp14 | hskp13 | (~ndr1_0) | c0_1(a353) | c3_1(a353) | (~c2_1(a353))) <=> (hskp14 | hskp13 | c0_1(a353) | (~ndr1_0) | c3_1(a353) | (~c2_1(a353)))),
% 1.31/1.10 inference(rewrite,[status(thm)],[])).
% 1.31/1.10 tff(924,plain,
% 1.31/1.10 (((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | c0_1(a353) | c3_1(a353) | (~c2_1(a353)))) <=> ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | hskp13 | c0_1(a353) | (~ndr1_0) | c3_1(a353) | (~c2_1(a353))))),
% 1.31/1.10 inference(monotonicity,[status(thm)],[923])).
% 1.31/1.10 tff(925,plain,
% 1.31/1.10 (((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | c0_1(a353) | c3_1(a353) | (~c2_1(a353)))) <=> ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp14 | hskp13 | c0_1(a353) | (~ndr1_0) | c3_1(a353) | (~c2_1(a353)))),
% 1.31/1.10 inference(transitivity,[status(thm)],[924, 922])).
% 1.31/1.10 tff(926,plain,
% 1.31/1.10 ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | c0_1(a353) | c3_1(a353) | (~c2_1(a353)))),
% 1.31/1.10 inference(quant_inst,[status(thm)],[])).
% 1.31/1.10 tff(927,plain,
% 1.31/1.10 ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp14 | hskp13 | c0_1(a353) | (~ndr1_0) | c3_1(a353) | (~c2_1(a353))),
% 1.31/1.10 inference(modus_ponens,[status(thm)],[926, 925])).
% 1.31/1.10 tff(928,plain,
% 1.31/1.10 (hskp13 | c3_1(a353)),
% 1.31/1.10 inference(unit_resolution,[status(thm)],[927, 152, 11, 916, 915, 530])).
% 1.31/1.10 tff(929,plain,
% 1.31/1.10 (c3_1(a353)),
% 1.31/1.10 inference(unit_resolution,[status(thm)],[928, 921])).
% 1.31/1.10 tff(930,plain,
% 1.31/1.10 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c0_1(a349)) | (~c3_1(a349)) | (~c1_1(a349)) | (~c1_1(a353)) | (~c3_1(a353)) | (~c2_1(a353)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c0_1(a349)) | (~c3_1(a349)) | (~c1_1(a349)) | (~c1_1(a353)) | (~c3_1(a353)) | (~c2_1(a353)))),
% 1.31/1.10 inference(rewrite,[status(thm)],[])).
% 1.31/1.10 tff(931,plain,
% 1.31/1.10 ((hskp10 | (~ndr1_0) | (~c2_1(a353)) | (~c3_1(a353)) | (~c1_1(a353)) | (~c3_1(a349)) | (~c1_1(a349)) | (~c0_1(a349))) <=> (hskp10 | (~ndr1_0) | (~c0_1(a349)) | (~c3_1(a349)) | (~c1_1(a349)) | (~c1_1(a353)) | (~c3_1(a353)) | (~c2_1(a353)))),
% 1.31/1.10 inference(rewrite,[status(thm)],[])).
% 1.31/1.10 tff(932,plain,
% 1.31/1.10 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a353)) | (~c3_1(a353)) | (~c1_1(a353)) | (~c3_1(a349)) | (~c1_1(a349)) | (~c0_1(a349)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c0_1(a349)) | (~c3_1(a349)) | (~c1_1(a349)) | (~c1_1(a353)) | (~c3_1(a353)) | (~c2_1(a353))))),
% 1.31/1.10 inference(monotonicity,[status(thm)],[931])).
% 1.31/1.10 tff(933,plain,
% 1.31/1.10 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a353)) | (~c3_1(a353)) | (~c1_1(a353)) | (~c3_1(a349)) | (~c1_1(a349)) | (~c0_1(a349)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c0_1(a349)) | (~c3_1(a349)) | (~c1_1(a349)) | (~c1_1(a353)) | (~c3_1(a353)) | (~c2_1(a353)))),
% 1.31/1.10 inference(transitivity,[status(thm)],[932, 930])).
% 1.31/1.10 tff(934,plain,
% 1.31/1.10 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a353)) | (~c3_1(a353)) | (~c1_1(a353)) | (~c3_1(a349)) | (~c1_1(a349)) | (~c0_1(a349)))),
% 1.31/1.10 inference(quant_inst,[status(thm)],[])).
% 1.31/1.10 tff(935,plain,
% 1.31/1.10 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c0_1(a349)) | (~c3_1(a349)) | (~c1_1(a349)) | (~c1_1(a353)) | (~c3_1(a353)) | (~c2_1(a353))),
% 1.31/1.10 inference(modus_ponens,[status(thm)],[934, 933])).
% 1.31/1.10 tff(936,plain,
% 1.31/1.10 (hskp10 | (~c0_1(a349)) | (~c3_1(a353))),
% 1.31/1.10 inference(unit_resolution,[status(thm)],[935, 152, 917, 916, 918, 919, 425])).
% 1.31/1.10 tff(937,plain,
% 1.31/1.10 (~c0_1(a349)),
% 1.31/1.10 inference(unit_resolution,[status(thm)],[936, 929, 920])).
% 1.31/1.10 tff(938,plain,
% 1.31/1.10 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))))),
% 1.31/1.10 inference(bind,[status(th)],[])).
% 1.31/1.10 tff(939,plain,
% 1.31/1.10 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.31/1.10 inference(quant_intro,[status(thm)],[938])).
% 1.31/1.10 tff(940,plain,
% 1.31/1.10 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.31/1.10 inference(rewrite,[status(thm)],[])).
% 1.31/1.10 tff(941,plain,
% 1.31/1.10 (^[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)) | (~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))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_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)) | (~c2_1(V))) | c1_1(U)) | c1_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)) | (~c2_1(V))) | c1_1(U)) | c1_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)) | c1_1(V) | c3_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp5) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | hskp5))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))))),
% 1.31/1.10 inference(bind,[status(th)],[])).
% 1.31/1.10 tff(942,plain,
% 1.31/1.10 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.31/1.10 inference(quant_intro,[status(thm)],[941])).
% 1.31/1.10 tff(943,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause173')).
% 1.31/1.10 tff(944,plain,
% 1.31/1.10 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.31/1.10 inference(modus_ponens,[status(thm)],[943, 942])).
% 1.31/1.10 tff(945,plain,
% 1.31/1.10 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.31/1.10 inference(modus_ponens,[status(thm)],[944, 940])).
% 1.31/1.10 tff(946,plain,(
% 1.31/1.10 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.31/1.10 inference(skolemize,[status(sab)],[945])).
% 1.31/1.10 tff(947,plain,
% 1.31/1.10 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.31/1.10 inference(modus_ponens,[status(thm)],[946, 939])).
% 1.31/1.10 tff(948,plain,
% 1.31/1.10 (^[U: $i] : refl((hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> (hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))),
% 1.31/1.10 inference(bind,[status(th)],[])).
% 1.31/1.10 tff(949,plain,
% 1.31/1.10 (![U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.31/1.10 inference(quant_intro,[status(thm)],[948])).
% 1.31/1.10 tff(950,plain,
% 1.31/1.10 (![U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.31/1.10 inference(rewrite,[status(thm)],[])).
% 1.31/1.10 tff(951,plain,
% 1.31/1.10 (^[U: $i] : 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)) | hskp15) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp15))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))))),
% 1.31/1.10 inference(bind,[status(th)],[])).
% 1.31/1.10 tff(952,plain,
% 1.31/1.10 (![U: $i] : (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) <=> ![U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.31/1.10 inference(quant_intro,[status(thm)],[951])).
% 1.31/1.10 tff(953,axiom,(![U: $i] : (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause134')).
% 1.31/1.10 tff(954,plain,
% 1.31/1.10 (![U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.31/1.10 inference(modus_ponens,[status(thm)],[953, 952])).
% 1.31/1.10 tff(955,plain,
% 1.31/1.10 (![U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.31/1.10 inference(modus_ponens,[status(thm)],[954, 950])).
% 1.31/1.10 tff(956,plain,(
% 1.31/1.10 ![U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.31/1.10 inference(skolemize,[status(sab)],[955])).
% 1.31/1.10 tff(957,plain,
% 1.31/1.10 (![U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.31/1.10 inference(modus_ponens,[status(thm)],[956, 949])).
% 1.31/1.10 tff(958,assumption,(~hskp5), introduced(assumption)).
% 1.31/1.10 tff(959,plain,
% 1.31/1.10 (^[U: $i] : refl((hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))),
% 1.31/1.10 inference(bind,[status(th)],[])).
% 1.31/1.10 tff(960,plain,
% 1.31/1.10 (![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> ![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.31/1.10 inference(quant_intro,[status(thm)],[959])).
% 1.31/1.10 tff(961,plain,
% 1.31/1.10 (![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> ![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.31/1.10 inference(rewrite,[status(thm)],[])).
% 1.31/1.10 tff(962,plain,
% 1.31/1.10 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | 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))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U)))), (((((~ndr1_0) | c1_1(U)) | 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) | c1_1(U) | c3_1(U))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp5) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp5))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp5) | hskp14) <=> ((hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp14))), rewrite(((hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp14) <=> (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp5) | hskp14) <=> (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))))),
% 1.31/1.10 inference(bind,[status(th)],[])).
% 1.31/1.10 tff(963,plain,
% 1.31/1.10 (![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp5) | hskp14) <=> ![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.31/1.10 inference(quant_intro,[status(thm)],[962])).
% 1.31/1.10 tff(964,axiom,(![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp5) | hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 1.31/1.10 tff(965,plain,
% 1.31/1.10 (![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.31/1.10 inference(modus_ponens,[status(thm)],[964, 963])).
% 1.31/1.10 tff(966,plain,
% 1.31/1.10 (![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.31/1.10 inference(modus_ponens,[status(thm)],[965, 961])).
% 1.31/1.10 tff(967,plain,(
% 1.31/1.10 ![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.31/1.10 inference(skolemize,[status(sab)],[966])).
% 1.31/1.10 tff(968,plain,
% 1.31/1.10 (![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.31/1.10 inference(modus_ponens,[status(thm)],[967, 960])).
% 1.31/1.10 tff(969,assumption,(~hskp2), introduced(assumption)).
% 1.31/1.10 tff(970,plain,
% 1.31/1.10 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))),
% 1.31/1.10 inference(bind,[status(th)],[])).
% 1.31/1.10 tff(971,plain,
% 1.31/1.10 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.31/1.10 inference(quant_intro,[status(thm)],[970])).
% 1.31/1.10 tff(972,plain,
% 1.31/1.10 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.31/1.10 inference(rewrite,[status(thm)],[])).
% 1.31/1.10 tff(973,plain,
% 1.31/1.10 (^[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) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_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) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_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) | (~c0_1(U)) | (~c3_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) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | 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) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | 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)) | hskp2) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp2))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | 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)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))))),
% 1.31/1.10 inference(bind,[status(th)],[])).
% 1.31/1.10 tff(974,plain,
% 1.31/1.10 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.31/1.10 inference(quant_intro,[status(thm)],[973])).
% 1.31/1.10 tff(975,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)) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause172')).
% 1.31/1.10 tff(976,plain,
% 1.31/1.10 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.31/1.10 inference(modus_ponens,[status(thm)],[975, 974])).
% 1.31/1.10 tff(977,plain,
% 1.31/1.10 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.31/1.10 inference(modus_ponens,[status(thm)],[976, 972])).
% 1.31/1.10 tff(978,plain,(
% 1.31/1.10 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.31/1.10 inference(skolemize,[status(sab)],[977])).
% 1.31/1.10 tff(979,plain,
% 1.31/1.10 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.31/1.10 inference(modus_ponens,[status(thm)],[978, 971])).
% 1.31/1.10 tff(980,assumption,(hskp25), introduced(assumption)).
% 1.31/1.10 tff(981,plain,
% 1.31/1.10 (~c2_1(a419)),
% 1.31/1.10 inference(unit_resolution,[status(thm)],[98, 980])).
% 1.31/1.10 tff(982,plain,
% 1.31/1.10 (~c1_1(a419)),
% 1.31/1.10 inference(unit_resolution,[status(thm)],[104, 980])).
% 1.31/1.10 tff(983,plain,
% 1.31/1.10 (c0_1(a419)),
% 1.31/1.10 inference(unit_resolution,[status(thm)],[116, 980])).
% 1.31/1.10 tff(984,plain,
% 1.31/1.10 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | c1_1(a419) | c2_1(a419) | (~ndr1_0) | (~c3_1(a419)) | (~c0_1(a419)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp2 | c1_1(a419) | c2_1(a419) | (~ndr1_0) | (~c3_1(a419)) | (~c0_1(a419)))),
% 1.31/1.10 inference(rewrite,[status(thm)],[])).
% 1.31/1.10 tff(985,plain,
% 1.31/1.10 ((hskp2 | (~ndr1_0) | c2_1(a419) | (~c0_1(a419)) | (~c3_1(a419)) | c2_1(a419) | c1_1(a419) | (~c3_1(a419))) <=> (hskp2 | c1_1(a419) | c2_1(a419) | (~ndr1_0) | (~c3_1(a419)) | (~c0_1(a419)))),
% 1.31/1.10 inference(rewrite,[status(thm)],[])).
% 1.31/1.10 tff(986,plain,
% 1.31/1.10 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a419) | (~c0_1(a419)) | (~c3_1(a419)) | c2_1(a419) | c1_1(a419) | (~c3_1(a419)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | c1_1(a419) | c2_1(a419) | (~ndr1_0) | (~c3_1(a419)) | (~c0_1(a419))))),
% 1.31/1.10 inference(monotonicity,[status(thm)],[985])).
% 1.31/1.10 tff(987,plain,
% 1.31/1.10 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a419) | (~c0_1(a419)) | (~c3_1(a419)) | c2_1(a419) | c1_1(a419) | (~c3_1(a419)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp2 | c1_1(a419) | c2_1(a419) | (~ndr1_0) | (~c3_1(a419)) | (~c0_1(a419)))),
% 1.31/1.10 inference(transitivity,[status(thm)],[986, 984])).
% 1.31/1.10 tff(988,plain,
% 1.31/1.10 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a419) | (~c0_1(a419)) | (~c3_1(a419)) | c2_1(a419) | c1_1(a419) | (~c3_1(a419)))),
% 1.31/1.10 inference(quant_inst,[status(thm)],[])).
% 1.31/1.10 tff(989,plain,
% 1.31/1.10 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp2 | c1_1(a419) | c2_1(a419) | (~ndr1_0) | (~c3_1(a419)) | (~c0_1(a419))),
% 1.31/1.10 inference(modus_ponens,[status(thm)],[988, 987])).
% 1.31/1.10 tff(990,plain,
% 1.31/1.10 (~c3_1(a419)),
% 1.31/1.10 inference(unit_resolution,[status(thm)],[989, 152, 969, 983, 982, 981, 979])).
% 1.31/1.10 tff(991,plain,
% 1.31/1.10 (((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp14 | hskp5 | c1_1(a419) | c2_1(a419) | (~ndr1_0) | c3_1(a419))) <=> ((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp14 | hskp5 | c1_1(a419) | c2_1(a419) | (~ndr1_0) | c3_1(a419))),
% 1.31/1.10 inference(rewrite,[status(thm)],[])).
% 1.31/1.10 tff(992,plain,
% 1.31/1.10 ((hskp14 | hskp5 | (~ndr1_0) | c2_1(a419) | c1_1(a419) | c3_1(a419)) <=> (hskp14 | hskp5 | c1_1(a419) | c2_1(a419) | (~ndr1_0) | c3_1(a419))),
% 1.31/1.10 inference(rewrite,[status(thm)],[])).
% 1.31/1.10 tff(993,plain,
% 1.31/1.10 (((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp14 | hskp5 | (~ndr1_0) | c2_1(a419) | c1_1(a419) | c3_1(a419))) <=> ((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp14 | hskp5 | c1_1(a419) | c2_1(a419) | (~ndr1_0) | c3_1(a419)))),
% 1.31/1.10 inference(monotonicity,[status(thm)],[992])).
% 1.31/1.10 tff(994,plain,
% 1.31/1.10 (((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp14 | hskp5 | (~ndr1_0) | c2_1(a419) | c1_1(a419) | c3_1(a419))) <=> ((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp14 | hskp5 | c1_1(a419) | c2_1(a419) | (~ndr1_0) | c3_1(a419))),
% 1.31/1.10 inference(transitivity,[status(thm)],[993, 991])).
% 1.31/1.10 tff(995,plain,
% 1.31/1.10 ((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp14 | hskp5 | (~ndr1_0) | c2_1(a419) | c1_1(a419) | c3_1(a419))),
% 1.31/1.10 inference(quant_inst,[status(thm)],[])).
% 1.31/1.10 tff(996,plain,
% 1.31/1.11 ((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp14 | hskp5 | c1_1(a419) | c2_1(a419) | (~ndr1_0) | c3_1(a419)),
% 1.31/1.11 inference(modus_ponens,[status(thm)],[995, 994])).
% 1.31/1.11 tff(997,plain,
% 1.31/1.11 (hskp14 | c3_1(a419)),
% 1.31/1.11 inference(unit_resolution,[status(thm)],[996, 152, 958, 982, 981, 968])).
% 1.31/1.11 tff(998,plain,
% 1.31/1.11 (hskp14),
% 1.31/1.11 inference(unit_resolution,[status(thm)],[997, 990])).
% 1.31/1.11 tff(999,plain,
% 1.31/1.11 (((~hskp14) | (~c1_1(a347))) <=> ((~hskp14) | (~c1_1(a347)))),
% 1.31/1.11 inference(rewrite,[status(thm)],[])).
% 1.31/1.11 tff(1000,plain,
% 1.31/1.11 (((~c1_1(a347)) | (~hskp14)) <=> ((~hskp14) | (~c1_1(a347)))),
% 1.31/1.11 inference(rewrite,[status(thm)],[])).
% 1.31/1.11 tff(1001,axiom,((~c1_1(a347)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause99')).
% 1.31/1.11 tff(1002,plain,
% 1.31/1.11 ((~hskp14) | (~c1_1(a347))),
% 1.31/1.11 inference(modus_ponens,[status(thm)],[1001, 1000])).
% 1.31/1.11 tff(1003,plain,
% 1.31/1.11 ((~hskp14) | (~c1_1(a347))),
% 1.31/1.11 inference(modus_ponens,[status(thm)],[1002, 999])).
% 1.31/1.11 tff(1004,plain,
% 1.31/1.11 (~c1_1(a347)),
% 1.31/1.11 inference(unit_resolution,[status(thm)],[1003, 998])).
% 1.31/1.11 tff(1005,plain,
% 1.31/1.11 (hskp22 | c3_1(a419)),
% 1.31/1.11 inference(unit_resolution,[status(thm)],[252, 152, 983, 982, 981, 243])).
% 1.31/1.11 tff(1006,plain,
% 1.31/1.11 (hskp22),
% 1.31/1.11 inference(unit_resolution,[status(thm)],[1005, 990])).
% 1.31/1.11 tff(1007,plain,
% 1.31/1.11 (~c2_1(a367)),
% 1.31/1.11 inference(unit_resolution,[status(thm)],[476, 1006])).
% 1.31/1.11 tff(1008,plain,
% 1.31/1.11 (((~hskp14) | c3_1(a347)) <=> ((~hskp14) | c3_1(a347))),
% 1.31/1.11 inference(rewrite,[status(thm)],[])).
% 1.31/1.11 tff(1009,axiom,((~hskp14) | c3_1(a347)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause64')).
% 1.31/1.11 tff(1010,plain,
% 1.31/1.11 ((~hskp14) | c3_1(a347)),
% 1.31/1.11 inference(modus_ponens,[status(thm)],[1009, 1008])).
% 1.31/1.11 tff(1011,plain,
% 1.31/1.11 ((~hskp14) | c3_1(a347)),
% 1.31/1.11 inference(modus_ponens,[status(thm)],[1010, 1008])).
% 1.31/1.11 tff(1012,plain,
% 1.31/1.11 ((~hskp14) | c3_1(a347)),
% 1.31/1.11 inference(modus_ponens,[status(thm)],[1011, 1008])).
% 1.31/1.11 tff(1013,plain,
% 1.31/1.11 ((~hskp14) | c3_1(a347)),
% 1.31/1.11 inference(modus_ponens,[status(thm)],[1012, 1008])).
% 1.31/1.11 tff(1014,plain,
% 1.31/1.11 ((~hskp14) | c3_1(a347)),
% 1.31/1.11 inference(modus_ponens,[status(thm)],[1013, 1008])).
% 1.31/1.11 tff(1015,plain,
% 1.31/1.11 ((~hskp14) | c3_1(a347)),
% 1.31/1.11 inference(modus_ponens,[status(thm)],[1014, 1008])).
% 1.31/1.11 tff(1016,plain,
% 1.31/1.11 ((~hskp14) | c3_1(a347)),
% 1.31/1.11 inference(modus_ponens,[status(thm)],[1015, 1008])).
% 1.31/1.11 tff(1017,plain,
% 1.31/1.11 ((~hskp14) | c3_1(a347)),
% 1.31/1.11 inference(modus_ponens,[status(thm)],[1016, 1008])).
% 1.31/1.11 tff(1018,plain,
% 1.31/1.11 (c3_1(a347)),
% 1.31/1.11 inference(unit_resolution,[status(thm)],[1017, 998])).
% 1.31/1.11 tff(1019,plain,
% 1.31/1.11 (((~hskp14) | c2_1(a347)) <=> ((~hskp14) | c2_1(a347))),
% 1.31/1.11 inference(rewrite,[status(thm)],[])).
% 1.31/1.11 tff(1020,axiom,((~hskp14) | c2_1(a347)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause63')).
% 1.31/1.11 tff(1021,plain,
% 1.31/1.11 ((~hskp14) | c2_1(a347)),
% 1.31/1.11 inference(modus_ponens,[status(thm)],[1020, 1019])).
% 1.31/1.11 tff(1022,plain,
% 1.31/1.11 ((~hskp14) | c2_1(a347)),
% 1.31/1.11 inference(modus_ponens,[status(thm)],[1021, 1019])).
% 1.31/1.11 tff(1023,plain,
% 1.31/1.11 ((~hskp14) | c2_1(a347)),
% 1.31/1.11 inference(modus_ponens,[status(thm)],[1022, 1019])).
% 1.31/1.11 tff(1024,plain,
% 1.31/1.11 ((~hskp14) | c2_1(a347)),
% 1.31/1.11 inference(modus_ponens,[status(thm)],[1023, 1019])).
% 1.31/1.11 tff(1025,plain,
% 1.31/1.11 ((~hskp14) | c2_1(a347)),
% 1.31/1.11 inference(modus_ponens,[status(thm)],[1024, 1019])).
% 1.31/1.11 tff(1026,plain,
% 1.31/1.11 ((~hskp14) | c2_1(a347)),
% 1.31/1.11 inference(modus_ponens,[status(thm)],[1025, 1019])).
% 1.31/1.11 tff(1027,plain,
% 1.31/1.11 ((~hskp14) | c2_1(a347)),
% 1.31/1.11 inference(modus_ponens,[status(thm)],[1026, 1019])).
% 1.31/1.11 tff(1028,plain,
% 1.31/1.11 ((~hskp14) | c2_1(a347)),
% 1.31/1.11 inference(modus_ponens,[status(thm)],[1027, 1019])).
% 1.31/1.11 tff(1029,plain,
% 1.31/1.11 (c2_1(a347)),
% 1.31/1.11 inference(unit_resolution,[status(thm)],[1028, 998])).
% 1.31/1.11 tff(1030,plain,
% 1.31/1.11 (c3_1(a367)),
% 1.31/1.11 inference(unit_resolution,[status(thm)],[487, 1006])).
% 1.31/1.11 tff(1031,plain,
% 1.31/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a419) | c2_1(a419) | c2_1(a367) | c1_1(a347) | (~ndr1_0) | (~c3_1(a367)) | c0_1(a367) | (~c2_1(a347)) | (~c3_1(a347)) | (~c0_1(a419)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a419) | c2_1(a419) | c2_1(a367) | c1_1(a347) | (~ndr1_0) | (~c3_1(a367)) | c0_1(a367) | (~c2_1(a347)) | (~c3_1(a347)) | (~c0_1(a419)))),
% 1.31/1.11 inference(rewrite,[status(thm)],[])).
% 1.31/1.11 tff(1032,plain,
% 1.31/1.11 (((~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)) | c2_1(a419) | c1_1(a419) | (~c0_1(a419)) | c2_1(a367) | c0_1(a367) | (~c3_1(a367))) <=> (c1_1(a419) | c2_1(a419) | c2_1(a367) | c1_1(a347) | (~ndr1_0) | (~c3_1(a367)) | c0_1(a367) | (~c2_1(a347)) | (~c3_1(a347)) | (~c0_1(a419)))),
% 1.31/1.11 inference(rewrite,[status(thm)],[])).
% 1.31/1.11 tff(1033,plain,
% 1.31/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)) | c2_1(a419) | c1_1(a419) | (~c0_1(a419)) | c2_1(a367) | c0_1(a367) | (~c3_1(a367)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a419) | c2_1(a419) | c2_1(a367) | c1_1(a347) | (~ndr1_0) | (~c3_1(a367)) | c0_1(a367) | (~c2_1(a347)) | (~c3_1(a347)) | (~c0_1(a419))))),
% 1.31/1.11 inference(monotonicity,[status(thm)],[1032])).
% 1.31/1.11 tff(1034,plain,
% 1.31/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)) | c2_1(a419) | c1_1(a419) | (~c0_1(a419)) | c2_1(a367) | c0_1(a367) | (~c3_1(a367)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a419) | c2_1(a419) | c2_1(a367) | c1_1(a347) | (~ndr1_0) | (~c3_1(a367)) | c0_1(a367) | (~c2_1(a347)) | (~c3_1(a347)) | (~c0_1(a419)))),
% 1.31/1.11 inference(transitivity,[status(thm)],[1033, 1031])).
% 1.31/1.11 tff(1035,plain,
% 1.31/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)) | c2_1(a419) | c1_1(a419) | (~c0_1(a419)) | c2_1(a367) | c0_1(a367) | (~c3_1(a367)))),
% 1.31/1.11 inference(quant_inst,[status(thm)],[])).
% 1.31/1.11 tff(1036,plain,
% 1.31/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a419) | c2_1(a419) | c2_1(a367) | c1_1(a347) | (~ndr1_0) | (~c3_1(a367)) | c0_1(a367) | (~c2_1(a347)) | (~c3_1(a347)) | (~c0_1(a419))),
% 1.31/1.11 inference(modus_ponens,[status(thm)],[1035, 1034])).
% 1.31/1.11 tff(1037,plain,
% 1.31/1.11 (c0_1(a367)),
% 1.31/1.11 inference(unit_resolution,[status(thm)],[1036, 152, 983, 1030, 1029, 1018, 982, 981, 1007, 1004, 509])).
% 1.31/1.11 tff(1038,plain,
% 1.31/1.11 (~c1_1(a367)),
% 1.31/1.11 inference(unit_resolution,[status(thm)],[470, 1006])).
% 1.31/1.11 tff(1039,plain,
% 1.31/1.11 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | c1_1(a367) | c2_1(a367) | (~ndr1_0) | (~c3_1(a367)) | (~c0_1(a367)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp2 | c1_1(a367) | c2_1(a367) | (~ndr1_0) | (~c3_1(a367)) | (~c0_1(a367)))),
% 1.31/1.11 inference(rewrite,[status(thm)],[])).
% 1.31/1.11 tff(1040,plain,
% 1.31/1.11 ((hskp2 | (~ndr1_0) | c2_1(a367) | (~c0_1(a367)) | (~c3_1(a367)) | c2_1(a367) | c1_1(a367) | (~c3_1(a367))) <=> (hskp2 | c1_1(a367) | c2_1(a367) | (~ndr1_0) | (~c3_1(a367)) | (~c0_1(a367)))),
% 1.31/1.11 inference(rewrite,[status(thm)],[])).
% 1.31/1.11 tff(1041,plain,
% 1.31/1.11 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a367) | (~c0_1(a367)) | (~c3_1(a367)) | c2_1(a367) | c1_1(a367) | (~c3_1(a367)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | c1_1(a367) | c2_1(a367) | (~ndr1_0) | (~c3_1(a367)) | (~c0_1(a367))))),
% 1.31/1.11 inference(monotonicity,[status(thm)],[1040])).
% 1.31/1.11 tff(1042,plain,
% 1.31/1.11 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a367) | (~c0_1(a367)) | (~c3_1(a367)) | c2_1(a367) | c1_1(a367) | (~c3_1(a367)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp2 | c1_1(a367) | c2_1(a367) | (~ndr1_0) | (~c3_1(a367)) | (~c0_1(a367)))),
% 1.31/1.11 inference(transitivity,[status(thm)],[1041, 1039])).
% 1.31/1.11 tff(1043,plain,
% 1.31/1.11 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a367) | (~c0_1(a367)) | (~c3_1(a367)) | c2_1(a367) | c1_1(a367) | (~c3_1(a367)))),
% 1.31/1.11 inference(quant_inst,[status(thm)],[])).
% 1.31/1.11 tff(1044,plain,
% 1.31/1.11 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp2 | c1_1(a367) | c2_1(a367) | (~ndr1_0) | (~c3_1(a367)) | (~c0_1(a367))),
% 1.31/1.11 inference(modus_ponens,[status(thm)],[1043, 1042])).
% 1.31/1.11 tff(1045,plain,
% 1.31/1.11 ($false),
% 1.31/1.11 inference(unit_resolution,[status(thm)],[1044, 152, 969, 1030, 1038, 1007, 979, 1037])).
% 1.31/1.11 tff(1046,plain,((~hskp25) | hskp2 | hskp5), inference(lemma,lemma(discharge,[]))).
% 1.31/1.11 tff(1047,plain,
% 1.31/1.11 (~hskp25),
% 1.31/1.11 inference(unit_resolution,[status(thm)],[1046, 969, 958])).
% 1.31/1.11 tff(1048,plain,
% 1.31/1.11 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 1.31/1.11 inference(bind,[status(th)],[])).
% 1.31/1.11 tff(1049,plain,
% 1.31/1.11 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.31/1.11 inference(quant_intro,[status(thm)],[1048])).
% 1.31/1.11 tff(1050,plain,
% 1.31/1.11 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.31/1.11 inference(rewrite,[status(thm)],[])).
% 1.31/1.11 tff(1051,plain,
% 1.31/1.11 (^[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))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_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) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_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) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp5))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 1.31/1.11 inference(bind,[status(th)],[])).
% 1.31/1.11 tff(1052,plain,
% 1.31/1.11 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.31/1.11 inference(quant_intro,[status(thm)],[1051])).
% 1.31/1.11 tff(1053,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause165')).
% 1.31/1.11 tff(1054,plain,
% 1.31/1.11 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.31/1.11 inference(modus_ponens,[status(thm)],[1053, 1052])).
% 1.31/1.11 tff(1055,plain,
% 1.31/1.11 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.31/1.11 inference(modus_ponens,[status(thm)],[1054, 1050])).
% 1.31/1.11 tff(1056,plain,(
% 1.31/1.11 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.31/1.11 inference(skolemize,[status(sab)],[1055])).
% 1.31/1.11 tff(1057,plain,
% 1.31/1.11 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.31/1.11 inference(modus_ponens,[status(thm)],[1056, 1049])).
% 1.31/1.11 tff(1058,assumption,(hskp16), introduced(assumption)).
% 1.31/1.11 tff(1059,plain,
% 1.31/1.11 (~c2_1(a349)),
% 1.31/1.11 inference(unit_resolution,[status(thm)],[825, 1058])).
% 1.31/1.11 tff(1060,plain,
% 1.31/1.11 (c3_1(a349)),
% 1.31/1.11 inference(unit_resolution,[status(thm)],[836, 1058])).
% 1.31/1.11 tff(1061,plain,
% 1.31/1.11 (c1_1(a349)),
% 1.31/1.11 inference(unit_resolution,[status(thm)],[847, 1058])).
% 1.31/1.11 tff(1062,plain,
% 1.31/1.11 (hskp28),
% 1.31/1.11 inference(unit_resolution,[status(thm)],[854, 152, 1061, 1060, 1059, 41])).
% 1.31/1.11 tff(1063,plain,
% 1.31/1.11 (c2_1(a343)),
% 1.31/1.11 inference(unit_resolution,[status(thm)],[777, 1062])).
% 1.31/1.11 tff(1064,plain,
% 1.31/1.11 (c1_1(a343)),
% 1.31/1.11 inference(unit_resolution,[status(thm)],[766, 1062])).
% 1.31/1.11 tff(1065,plain,
% 1.31/1.11 (c0_1(a343)),
% 1.31/1.11 inference(unit_resolution,[status(thm)],[755, 1062])).
% 1.31/1.11 tff(1066,plain,
% 1.31/1.11 (hskp17),
% 1.31/1.11 inference(unit_resolution,[status(thm)],[864, 42, 152, 1065, 1064, 1063, 31])).
% 1.31/1.11 tff(1067,plain,
% 1.31/1.11 (~c0_1(a353)),
% 1.31/1.11 inference(unit_resolution,[status(thm)],[870, 1066])).
% 1.31/1.11 tff(1068,plain,
% 1.31/1.11 (c2_1(a353)),
% 1.31/1.11 inference(unit_resolution,[status(thm)],[881, 1066])).
% 1.31/1.11 tff(1069,plain,
% 1.31/1.11 (c1_1(a353)),
% 1.31/1.11 inference(unit_resolution,[status(thm)],[892, 1066])).
% 1.31/1.11 tff(1070,plain,
% 1.31/1.11 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a353) | c0_1(a330) | c1_1(a330) | (~ndr1_0) | (~c2_1(a330)) | (~c1_1(a353)) | (~c2_1(a353)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a353) | c0_1(a330) | c1_1(a330) | (~ndr1_0) | (~c2_1(a330)) | (~c1_1(a353)) | (~c2_1(a353)))),
% 1.31/1.11 inference(rewrite,[status(thm)],[])).
% 1.31/1.11 tff(1071,plain,
% 1.31/1.11 ((hskp5 | (~ndr1_0) | c0_1(a353) | (~c2_1(a353)) | (~c1_1(a353)) | c1_1(a330) | c0_1(a330) | (~c2_1(a330))) <=> (hskp5 | c0_1(a353) | c0_1(a330) | c1_1(a330) | (~ndr1_0) | (~c2_1(a330)) | (~c1_1(a353)) | (~c2_1(a353)))),
% 1.31/1.11 inference(rewrite,[status(thm)],[])).
% 1.31/1.11 tff(1072,plain,
% 1.31/1.11 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a353) | (~c2_1(a353)) | (~c1_1(a353)) | c1_1(a330) | c0_1(a330) | (~c2_1(a330)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a353) | c0_1(a330) | c1_1(a330) | (~ndr1_0) | (~c2_1(a330)) | (~c1_1(a353)) | (~c2_1(a353))))),
% 1.31/1.11 inference(monotonicity,[status(thm)],[1071])).
% 1.31/1.11 tff(1073,plain,
% 1.31/1.11 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a353) | (~c2_1(a353)) | (~c1_1(a353)) | c1_1(a330) | c0_1(a330) | (~c2_1(a330)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a353) | c0_1(a330) | c1_1(a330) | (~ndr1_0) | (~c2_1(a330)) | (~c1_1(a353)) | (~c2_1(a353)))),
% 1.31/1.11 inference(transitivity,[status(thm)],[1072, 1070])).
% 1.31/1.11 tff(1074,plain,
% 1.31/1.11 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a353) | (~c2_1(a353)) | (~c1_1(a353)) | c1_1(a330) | c0_1(a330) | (~c2_1(a330)))),
% 1.31/1.11 inference(quant_inst,[status(thm)],[])).
% 1.31/1.11 tff(1075,plain,
% 1.31/1.11 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a353) | c0_1(a330) | c1_1(a330) | (~ndr1_0) | (~c2_1(a330)) | (~c1_1(a353)) | (~c2_1(a353))),
% 1.31/1.11 inference(modus_ponens,[status(thm)],[1074, 1073])).
% 1.31/1.11 tff(1076,plain,
% 1.31/1.11 (~c2_1(a330)),
% 1.31/1.11 inference(unit_resolution,[status(thm)],[1075, 152, 958, 1069, 1068, 1067, 69, 52, 1057])).
% 1.31/1.11 tff(1077,plain,
% 1.31/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a349) | c1_1(a330) | (~ndr1_0) | c2_1(a330) | (~c3_1(a330)) | (~c3_1(a349)) | (~c1_1(a349)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a349) | c1_1(a330) | (~ndr1_0) | c2_1(a330) | (~c3_1(a330)) | (~c3_1(a349)) | (~c1_1(a349)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.31/1.11 inference(rewrite,[status(thm)],[])).
% 1.31/1.11 tff(1078,plain,
% 1.31/1.11 (((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a349) | (~c3_1(a349)) | (~c1_1(a349)) | c2_1(a330) | c1_1(a330) | (~c3_1(a330))) <=> (c2_1(a349) | c1_1(a330) | (~ndr1_0) | c2_1(a330) | (~c3_1(a330)) | (~c3_1(a349)) | (~c1_1(a349)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.31/1.11 inference(rewrite,[status(thm)],[])).
% 1.31/1.11 tff(1079,plain,
% 1.31/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a349) | (~c3_1(a349)) | (~c1_1(a349)) | c2_1(a330) | c1_1(a330) | (~c3_1(a330)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a349) | c1_1(a330) | (~ndr1_0) | c2_1(a330) | (~c3_1(a330)) | (~c3_1(a349)) | (~c1_1(a349)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))))),
% 1.31/1.11 inference(monotonicity,[status(thm)],[1078])).
% 1.31/1.11 tff(1080,plain,
% 1.31/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a349) | (~c3_1(a349)) | (~c1_1(a349)) | c2_1(a330) | c1_1(a330) | (~c3_1(a330)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a349) | c1_1(a330) | (~ndr1_0) | c2_1(a330) | (~c3_1(a330)) | (~c3_1(a349)) | (~c1_1(a349)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.31/1.11 inference(transitivity,[status(thm)],[1079, 1077])).
% 1.31/1.11 tff(1081,plain,
% 1.31/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a349) | (~c3_1(a349)) | (~c1_1(a349)) | c2_1(a330) | c1_1(a330) | (~c3_1(a330)))),
% 1.31/1.11 inference(quant_inst,[status(thm)],[])).
% 1.31/1.11 tff(1082,plain,
% 1.31/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a349) | c1_1(a330) | (~ndr1_0) | c2_1(a330) | (~c3_1(a330)) | (~c3_1(a349)) | (~c1_1(a349)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))),
% 1.31/1.11 inference(modus_ponens,[status(thm)],[1081, 1080])).
% 1.31/1.11 tff(1083,plain,
% 1.31/1.11 ($false),
% 1.31/1.11 inference(unit_resolution,[status(thm)],[1082, 152, 1065, 1064, 1063, 1061, 1060, 63, 1059, 52, 788, 1076])).
% 1.31/1.11 tff(1084,plain,((~hskp16) | hskp5 | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.31/1.11 tff(1085,plain,
% 1.31/1.11 (~hskp16),
% 1.31/1.11 inference(unit_resolution,[status(thm)],[1084, 42, 958])).
% 1.31/1.11 tff(1086,plain,
% 1.31/1.11 (^[U: $i] : refl((hskp16 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) <=> (hskp16 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))))),
% 1.31/1.11 inference(bind,[status(th)],[])).
% 1.31/1.11 tff(1087,plain,
% 1.31/1.11 (![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))),
% 1.31/1.11 inference(quant_intro,[status(thm)],[1086])).
% 1.31/1.11 tff(1088,plain,
% 1.31/1.11 (![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))),
% 1.31/1.11 inference(rewrite,[status(thm)],[])).
% 1.31/1.11 tff(1089,plain,
% 1.31/1.11 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp5) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | hskp5))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp5) | hskp16) <=> ((hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | hskp16))), rewrite(((hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | hskp16) <=> (hskp16 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp5) | hskp16) <=> (hskp16 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))))),
% 1.31/1.11 inference(bind,[status(th)],[])).
% 1.31/1.11 tff(1090,plain,
% 1.31/1.11 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp5) | hskp16) <=> ![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))),
% 1.31/1.11 inference(quant_intro,[status(thm)],[1089])).
% 1.31/1.11 tff(1091,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp5) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause149')).
% 1.31/1.11 tff(1092,plain,
% 1.31/1.11 (![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))),
% 1.31/1.11 inference(modus_ponens,[status(thm)],[1091, 1090])).
% 1.31/1.11 tff(1093,plain,
% 1.31/1.11 (![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))),
% 1.31/1.11 inference(modus_ponens,[status(thm)],[1092, 1088])).
% 1.31/1.11 tff(1094,plain,(
% 1.31/1.11 ![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))),
% 1.31/1.11 inference(skolemize,[status(sab)],[1093])).
% 1.31/1.11 tff(1095,plain,
% 1.31/1.11 (![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))),
% 1.31/1.11 inference(modus_ponens,[status(thm)],[1094, 1087])).
% 1.31/1.11 tff(1096,plain,
% 1.31/1.11 (hskp26),
% 1.31/1.11 inference(unit_resolution,[status(thm)],[150, 42, 969])).
% 1.31/1.11 tff(1097,plain,
% 1.31/1.11 (c3_1(a333)),
% 1.31/1.11 inference(unit_resolution,[status(thm)],[220, 1096])).
% 1.31/1.11 tff(1098,plain,
% 1.31/1.11 (c0_1(a333)),
% 1.31/1.11 inference(unit_resolution,[status(thm)],[231, 1096])).
% 1.31/1.11 tff(1099,plain,
% 1.31/1.11 (((~![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp5 | (~ndr1_0) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333)))) <=> ((~![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))) | hskp16 | hskp5 | (~ndr1_0) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333)))),
% 1.31/1.11 inference(rewrite,[status(thm)],[])).
% 1.31/1.11 tff(1100,plain,
% 1.31/1.11 ((hskp16 | hskp5 | (~ndr1_0) | (~c2_1(a333)) | (~c0_1(a333)) | (~c3_1(a333))) <=> (hskp16 | hskp5 | (~ndr1_0) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333)))),
% 1.31/1.11 inference(rewrite,[status(thm)],[])).
% 1.31/1.11 tff(1101,plain,
% 1.31/1.11 (((~![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp5 | (~ndr1_0) | (~c2_1(a333)) | (~c0_1(a333)) | (~c3_1(a333)))) <=> ((~![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp5 | (~ndr1_0) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333))))),
% 1.31/1.11 inference(monotonicity,[status(thm)],[1100])).
% 1.31/1.11 tff(1102,plain,
% 1.31/1.11 (((~![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp5 | (~ndr1_0) | (~c2_1(a333)) | (~c0_1(a333)) | (~c3_1(a333)))) <=> ((~![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))) | hskp16 | hskp5 | (~ndr1_0) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333)))),
% 1.31/1.11 inference(transitivity,[status(thm)],[1101, 1099])).
% 1.31/1.11 tff(1103,plain,
% 1.31/1.11 ((~![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))) | (hskp16 | hskp5 | (~ndr1_0) | (~c2_1(a333)) | (~c0_1(a333)) | (~c3_1(a333)))),
% 1.31/1.11 inference(quant_inst,[status(thm)],[])).
% 1.31/1.11 tff(1104,plain,
% 1.31/1.11 ((~![U: $i] : (hskp16 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))) | hskp16 | hskp5 | (~ndr1_0) | (~c3_1(a333)) | (~c2_1(a333)) | (~c0_1(a333))),
% 1.31/1.11 inference(modus_ponens,[status(thm)],[1103, 1102])).
% 1.31/1.11 tff(1105,plain,
% 1.31/1.11 (hskp16 | (~c2_1(a333))),
% 1.31/1.11 inference(unit_resolution,[status(thm)],[1104, 152, 958, 1098, 1097, 1095])).
% 1.31/1.11 tff(1106,plain,
% 1.31/1.11 (~c2_1(a333)),
% 1.31/1.11 inference(unit_resolution,[status(thm)],[1105, 1085])).
% 1.31/1.11 tff(1107,plain,
% 1.31/1.11 (hskp25),
% 1.31/1.11 inference(unit_resolution,[status(thm)],[92, 1085])).
% 1.31/1.11 tff(1108,plain,
% 1.31/1.11 (~c2_1(a419)),
% 1.31/1.11 inference(unit_resolution,[status(thm)],[98, 1107])).
% 1.31/1.11 tff(1109,plain,
% 1.31/1.11 (~c1_1(a419)),
% 1.31/1.11 inference(unit_resolution,[status(thm)],[104, 1107])).
% 1.31/1.11 tff(1110,plain,
% 1.31/1.11 (c1_1(a333)),
% 1.31/1.11 inference(unit_resolution,[status(thm)],[209, 1096])).
% 1.31/1.11 tff(1111,plain,
% 1.31/1.11 (hskp28 | c2_1(a333)),
% 1.31/1.11 inference(unit_resolution,[status(thm)],[625, 152, 1110, 1097, 41])).
% 1.31/1.11 tff(1112,plain,
% 1.31/1.11 (hskp28),
% 1.31/1.11 inference(unit_resolution,[status(thm)],[1111, 1106])).
% 1.31/1.11 tff(1113,plain,
% 1.31/1.11 (c2_1(a343)),
% 1.31/1.11 inference(unit_resolution,[status(thm)],[777, 1112])).
% 1.31/1.11 tff(1114,plain,
% 1.31/1.11 (c1_1(a343)),
% 1.31/1.11 inference(unit_resolution,[status(thm)],[766, 1112])).
% 1.31/1.11 tff(1115,plain,
% 1.31/1.11 (c0_1(a343)),
% 1.31/1.11 inference(unit_resolution,[status(thm)],[755, 1112])).
% 1.31/1.11 tff(1116,plain,
% 1.31/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a419) | c2_1(a419) | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)) | (~c3_1(a419)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a419) | c2_1(a419) | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)) | (~c3_1(a419)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.31/1.11 inference(rewrite,[status(thm)],[])).
% 1.31/1.11 tff(1117,plain,
% 1.31/1.11 (((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a333) | (~c3_1(a333)) | (~c1_1(a333)) | c2_1(a419) | c1_1(a419) | (~c3_1(a419))) <=> (c1_1(a419) | c2_1(a419) | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)) | (~c3_1(a419)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.31/1.11 inference(rewrite,[status(thm)],[])).
% 1.31/1.11 tff(1118,plain,
% 1.31/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a333) | (~c3_1(a333)) | (~c1_1(a333)) | c2_1(a419) | c1_1(a419) | (~c3_1(a419)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a419) | c2_1(a419) | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)) | (~c3_1(a419)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))))),
% 1.31/1.11 inference(monotonicity,[status(thm)],[1117])).
% 1.31/1.11 tff(1119,plain,
% 1.31/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a333) | (~c3_1(a333)) | (~c1_1(a333)) | c2_1(a419) | c1_1(a419) | (~c3_1(a419)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a419) | c2_1(a419) | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)) | (~c3_1(a419)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.31/1.12 inference(transitivity,[status(thm)],[1118, 1116])).
% 1.31/1.12 tff(1120,plain,
% 1.31/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a333) | (~c3_1(a333)) | (~c1_1(a333)) | c2_1(a419) | c1_1(a419) | (~c3_1(a419)))),
% 1.31/1.12 inference(quant_inst,[status(thm)],[])).
% 1.31/1.12 tff(1121,plain,
% 1.31/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a419) | c2_1(a419) | (~ndr1_0) | (~c1_1(a333)) | c2_1(a333) | (~c3_1(a333)) | (~c3_1(a419)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[1120, 1119])).
% 1.31/1.12 tff(1122,plain,
% 1.31/1.12 (~c3_1(a419)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[1121, 152, 1115, 1114, 1113, 1110, 1097, 1109, 1108, 788, 1106])).
% 1.31/1.12 tff(1123,plain,
% 1.31/1.12 (c0_1(a419)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[116, 1107])).
% 1.31/1.12 tff(1124,plain,
% 1.31/1.12 (hskp22 | c3_1(a419)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[252, 152, 1123, 1109, 1108, 243])).
% 1.31/1.12 tff(1125,plain,
% 1.31/1.12 (hskp22),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[1124, 1122])).
% 1.31/1.12 tff(1126,plain,
% 1.31/1.12 (~c2_1(a367)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[476, 1125])).
% 1.31/1.12 tff(1127,plain,
% 1.31/1.12 (c3_1(a367)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[487, 1125])).
% 1.31/1.12 tff(1128,plain,
% 1.31/1.12 (~c1_1(a367)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[470, 1125])).
% 1.31/1.12 tff(1129,plain,
% 1.31/1.12 ($false),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[795, 1128, 1127, 152, 1113, 1110, 1097, 1115, 1114, 1126, 1106])).
% 1.31/1.12 tff(1130,plain,(hskp24 | hskp5 | hskp2), inference(lemma,lemma(discharge,[]))).
% 1.31/1.12 tff(1131,plain,
% 1.31/1.12 (hskp24),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[1130, 969, 958])).
% 1.31/1.12 tff(1132,plain,
% 1.31/1.12 (((~hskp24) | (~c2_1(a401))) <=> ((~hskp24) | (~c2_1(a401)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(1133,plain,
% 1.31/1.12 (((~c2_1(a401)) | (~hskp24)) <=> ((~hskp24) | (~c2_1(a401)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(1134,axiom,((~c2_1(a401)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause84')).
% 1.31/1.12 tff(1135,plain,
% 1.31/1.12 ((~hskp24) | (~c2_1(a401))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[1134, 1133])).
% 1.31/1.12 tff(1136,plain,
% 1.31/1.12 ((~hskp24) | (~c2_1(a401))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[1135, 1132])).
% 1.31/1.12 tff(1137,plain,
% 1.31/1.12 (~c2_1(a401)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[1136, 1131])).
% 1.31/1.12 tff(1138,plain,
% 1.31/1.12 (((~hskp24) | (~c0_1(a401))) <=> ((~hskp24) | (~c0_1(a401)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(1139,plain,
% 1.31/1.12 (((~c0_1(a401)) | (~hskp24)) <=> ((~hskp24) | (~c0_1(a401)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(1140,axiom,((~c0_1(a401)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 1.31/1.12 tff(1141,plain,
% 1.31/1.12 ((~hskp24) | (~c0_1(a401))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[1140, 1139])).
% 1.31/1.12 tff(1142,plain,
% 1.31/1.12 ((~hskp24) | (~c0_1(a401))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[1141, 1138])).
% 1.31/1.12 tff(1143,plain,
% 1.31/1.12 (~c0_1(a401)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[1142, 1131])).
% 1.31/1.12 tff(1144,plain,
% 1.31/1.12 (((~hskp24) | c1_1(a401)) <=> ((~hskp24) | c1_1(a401))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(1145,axiom,((~hskp24) | c1_1(a401)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause49')).
% 1.31/1.12 tff(1146,plain,
% 1.31/1.12 ((~hskp24) | c1_1(a401)),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[1145, 1144])).
% 1.31/1.12 tff(1147,plain,
% 1.31/1.12 ((~hskp24) | c1_1(a401)),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[1146, 1144])).
% 1.31/1.12 tff(1148,plain,
% 1.31/1.12 ((~hskp24) | c1_1(a401)),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[1147, 1144])).
% 1.31/1.12 tff(1149,plain,
% 1.31/1.12 ((~hskp24) | c1_1(a401)),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[1148, 1144])).
% 1.31/1.12 tff(1150,plain,
% 1.31/1.12 ((~hskp24) | c1_1(a401)),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[1149, 1144])).
% 1.31/1.12 tff(1151,plain,
% 1.31/1.12 ((~hskp24) | c1_1(a401)),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[1150, 1144])).
% 1.31/1.12 tff(1152,plain,
% 1.31/1.12 ((~hskp24) | c1_1(a401)),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[1151, 1144])).
% 1.31/1.12 tff(1153,plain,
% 1.31/1.12 ((~hskp24) | c1_1(a401)),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[1152, 1144])).
% 1.31/1.12 tff(1154,plain,
% 1.31/1.12 (c1_1(a401)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[1153, 1131])).
% 1.31/1.12 tff(1155,plain,
% 1.31/1.12 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 1.31/1.12 inference(bind,[status(th)],[])).
% 1.31/1.12 tff(1156,plain,
% 1.31/1.12 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.31/1.12 inference(quant_intro,[status(thm)],[1155])).
% 1.31/1.12 tff(1157,plain,
% 1.31/1.12 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(1158,plain,
% 1.31/1.12 (^[V: $i, U: $i] : 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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp5) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp5))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 1.31/1.12 inference(bind,[status(th)],[])).
% 1.31/1.12 tff(1159,plain,
% 1.31/1.12 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.31/1.12 inference(quant_intro,[status(thm)],[1158])).
% 1.31/1.12 tff(1160,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause166')).
% 1.31/1.12 tff(1161,plain,
% 1.31/1.12 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[1160, 1159])).
% 1.31/1.12 tff(1162,plain,
% 1.31/1.12 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[1161, 1157])).
% 1.31/1.12 tff(1163,plain,(
% 1.31/1.12 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.31/1.12 inference(skolemize,[status(sab)],[1162])).
% 1.31/1.12 tff(1164,plain,
% 1.31/1.12 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[1163, 1156])).
% 1.31/1.12 tff(1165,assumption,(hskp14), introduced(assumption)).
% 1.31/1.12 tff(1166,plain,
% 1.31/1.12 (~c1_1(a347)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[1003, 1165])).
% 1.31/1.12 tff(1167,assumption,(~c2_1(a401)), introduced(assumption)).
% 1.31/1.12 tff(1168,assumption,(~c0_1(a401)), introduced(assumption)).
% 1.31/1.12 tff(1169,plain,
% 1.31/1.12 (c3_1(a347)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[1017, 1165])).
% 1.31/1.12 tff(1170,plain,
% 1.31/1.12 (c2_1(a347)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[1028, 1165])).
% 1.31/1.12 tff(1171,assumption,(c1_1(a401)), introduced(assumption)).
% 1.31/1.12 tff(1172,plain,
% 1.31/1.12 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | c0_1(a401) | c2_1(a401) | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)) | (~c1_1(a401)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a401) | c2_1(a401) | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)) | (~c1_1(a401)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(1173,plain,
% 1.31/1.12 ((hskp5 | (~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)) | c2_1(a401) | c0_1(a401) | (~c1_1(a401))) <=> (hskp5 | c0_1(a401) | c2_1(a401) | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)) | (~c1_1(a401)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(1174,plain,
% 1.31/1.12 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)) | c2_1(a401) | c0_1(a401) | (~c1_1(a401)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | c0_1(a401) | c2_1(a401) | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)) | (~c1_1(a401))))),
% 1.31/1.12 inference(monotonicity,[status(thm)],[1173])).
% 1.31/1.12 tff(1175,plain,
% 1.31/1.12 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)) | c2_1(a401) | c0_1(a401) | (~c1_1(a401)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a401) | c2_1(a401) | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)) | (~c1_1(a401)))),
% 1.31/1.12 inference(transitivity,[status(thm)],[1174, 1172])).
% 1.31/1.12 tff(1176,plain,
% 1.31/1.12 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)) | c2_1(a401) | c0_1(a401) | (~c1_1(a401)))),
% 1.31/1.12 inference(quant_inst,[status(thm)],[])).
% 1.31/1.12 tff(1177,plain,
% 1.31/1.12 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp5 | c0_1(a401) | c2_1(a401) | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)) | (~c1_1(a401))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[1176, 1175])).
% 1.31/1.12 tff(1178,plain,
% 1.31/1.12 ($false),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[1177, 152, 958, 1171, 1170, 1169, 1168, 1167, 1166, 1164])).
% 1.31/1.12 tff(1179,plain,((~hskp14) | hskp5 | (~c1_1(a401)) | c0_1(a401) | c2_1(a401)), inference(lemma,lemma(discharge,[]))).
% 1.31/1.12 tff(1180,plain,
% 1.31/1.12 (~hskp14),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[1179, 1154, 958, 1143, 1137])).
% 1.31/1.12 tff(1181,plain,
% 1.31/1.12 (hskp16),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[92, 1047])).
% 1.31/1.12 tff(1182,plain,
% 1.31/1.12 (~c2_1(a349)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[825, 1181])).
% 1.31/1.12 tff(1183,plain,
% 1.31/1.12 (c3_1(a349)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[836, 1181])).
% 1.31/1.12 tff(1184,plain,
% 1.31/1.12 (c1_1(a349)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[847, 1181])).
% 1.31/1.12 tff(1185,assumption,(hskp11), introduced(assumption)).
% 1.31/1.12 tff(1186,plain,
% 1.31/1.12 (((~hskp11) | (~c2_1(a338))) <=> ((~hskp11) | (~c2_1(a338)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(1187,plain,
% 1.31/1.12 (((~c2_1(a338)) | (~hskp11)) <=> ((~hskp11) | (~c2_1(a338)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(1188,axiom,((~c2_1(a338)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause104')).
% 1.31/1.12 tff(1189,plain,
% 1.31/1.12 ((~hskp11) | (~c2_1(a338))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[1188, 1187])).
% 1.31/1.12 tff(1190,plain,
% 1.31/1.12 ((~hskp11) | (~c2_1(a338))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[1189, 1186])).
% 1.31/1.12 tff(1191,plain,
% 1.31/1.12 (~c2_1(a338)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[1190, 1185])).
% 1.31/1.12 tff(1192,plain,
% 1.31/1.12 (((~hskp11) | (~c1_1(a338))) <=> ((~hskp11) | (~c1_1(a338)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(1193,plain,
% 1.31/1.12 (((~c1_1(a338)) | (~hskp11)) <=> ((~hskp11) | (~c1_1(a338)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(1194,axiom,((~c1_1(a338)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause103')).
% 1.31/1.12 tff(1195,plain,
% 1.31/1.12 ((~hskp11) | (~c1_1(a338))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[1194, 1193])).
% 1.31/1.12 tff(1196,plain,
% 1.31/1.12 ((~hskp11) | (~c1_1(a338))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[1195, 1192])).
% 1.31/1.12 tff(1197,plain,
% 1.31/1.12 (~c1_1(a338)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[1196, 1185])).
% 1.31/1.12 tff(1198,plain,
% 1.31/1.12 (((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp14 | hskp5 | c1_1(a338) | c2_1(a338) | (~ndr1_0) | c3_1(a338))) <=> ((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp14 | hskp5 | c1_1(a338) | c2_1(a338) | (~ndr1_0) | c3_1(a338))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(1199,plain,
% 1.31/1.12 ((hskp14 | hskp5 | (~ndr1_0) | c2_1(a338) | c1_1(a338) | c3_1(a338)) <=> (hskp14 | hskp5 | c1_1(a338) | c2_1(a338) | (~ndr1_0) | c3_1(a338))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(1200,plain,
% 1.31/1.12 (((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp14 | hskp5 | (~ndr1_0) | c2_1(a338) | c1_1(a338) | c3_1(a338))) <=> ((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp14 | hskp5 | c1_1(a338) | c2_1(a338) | (~ndr1_0) | c3_1(a338)))),
% 1.31/1.12 inference(monotonicity,[status(thm)],[1199])).
% 1.31/1.12 tff(1201,plain,
% 1.31/1.12 (((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp14 | hskp5 | (~ndr1_0) | c2_1(a338) | c1_1(a338) | c3_1(a338))) <=> ((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp14 | hskp5 | c1_1(a338) | c2_1(a338) | (~ndr1_0) | c3_1(a338))),
% 1.31/1.12 inference(transitivity,[status(thm)],[1200, 1198])).
% 1.31/1.12 tff(1202,plain,
% 1.31/1.12 ((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp14 | hskp5 | (~ndr1_0) | c2_1(a338) | c1_1(a338) | c3_1(a338))),
% 1.31/1.12 inference(quant_inst,[status(thm)],[])).
% 1.31/1.12 tff(1203,plain,
% 1.31/1.12 ((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp14 | hskp5 | c1_1(a338) | c2_1(a338) | (~ndr1_0) | c3_1(a338)),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[1202, 1201])).
% 1.31/1.12 tff(1204,plain,
% 1.31/1.12 (c3_1(a338)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[1203, 152, 11, 958, 1197, 1191, 968])).
% 1.31/1.12 tff(1205,plain,
% 1.31/1.12 (hskp28),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[854, 152, 918, 919, 894, 41])).
% 1.31/1.12 tff(1206,plain,
% 1.31/1.12 (c2_1(a343)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[777, 1205])).
% 1.31/1.12 tff(1207,plain,
% 1.31/1.12 (c1_1(a343)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[766, 1205])).
% 1.31/1.12 tff(1208,plain,
% 1.31/1.12 (c0_1(a343)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[755, 1205])).
% 1.31/1.12 tff(1209,plain,
% 1.31/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a349) | c1_1(a338) | c2_1(a338) | (~ndr1_0) | (~c3_1(a338)) | (~c3_1(a349)) | (~c1_1(a349)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a349) | c1_1(a338) | c2_1(a338) | (~ndr1_0) | (~c3_1(a338)) | (~c3_1(a349)) | (~c1_1(a349)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(1210,plain,
% 1.31/1.12 (((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a349) | (~c3_1(a349)) | (~c1_1(a349)) | c2_1(a338) | c1_1(a338) | (~c3_1(a338))) <=> (c2_1(a349) | c1_1(a338) | c2_1(a338) | (~ndr1_0) | (~c3_1(a338)) | (~c3_1(a349)) | (~c1_1(a349)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(1211,plain,
% 1.31/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a349) | (~c3_1(a349)) | (~c1_1(a349)) | c2_1(a338) | c1_1(a338) | (~c3_1(a338)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a349) | c1_1(a338) | c2_1(a338) | (~ndr1_0) | (~c3_1(a338)) | (~c3_1(a349)) | (~c1_1(a349)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))))),
% 1.31/1.12 inference(monotonicity,[status(thm)],[1210])).
% 1.31/1.12 tff(1212,plain,
% 1.31/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a349) | (~c3_1(a349)) | (~c1_1(a349)) | c2_1(a338) | c1_1(a338) | (~c3_1(a338)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a349) | c1_1(a338) | c2_1(a338) | (~ndr1_0) | (~c3_1(a338)) | (~c3_1(a349)) | (~c1_1(a349)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.31/1.12 inference(transitivity,[status(thm)],[1211, 1209])).
% 1.31/1.12 tff(1213,plain,
% 1.31/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a349) | (~c3_1(a349)) | (~c1_1(a349)) | c2_1(a338) | c1_1(a338) | (~c3_1(a338)))),
% 1.31/1.12 inference(quant_inst,[status(thm)],[])).
% 1.31/1.12 tff(1214,plain,
% 1.31/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a349) | c1_1(a338) | c2_1(a338) | (~ndr1_0) | (~c3_1(a338)) | (~c3_1(a349)) | (~c1_1(a349)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[1213, 1212])).
% 1.31/1.12 tff(1215,plain,
% 1.31/1.12 ($false),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[1214, 152, 1208, 1207, 1206, 918, 919, 894, 1197, 1191, 788, 1204])).
% 1.31/1.12 tff(1216,plain,((~hskp11) | (~c1_1(a349)) | (~c3_1(a349)) | c2_1(a349) | hskp14 | hskp5), inference(lemma,lemma(discharge,[]))).
% 1.31/1.12 tff(1217,plain,
% 1.31/1.12 (~hskp11),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[1216, 1184, 1183, 1182, 1180, 958])).
% 1.31/1.12 tff(1218,plain,
% 1.31/1.12 ((hskp25 | hskp11 | hskp1) <=> (hskp25 | hskp11 | hskp1)),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(1219,plain,
% 1.31/1.12 (((hskp25 | hskp11) | hskp1) <=> (hskp25 | hskp11 | hskp1)),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(1220,plain,
% 1.31/1.12 ((hskp25 | hskp11) <=> (hskp25 | hskp11)),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(1221,plain,
% 1.31/1.12 (((hskp25 | hskp11) | hskp1) <=> ((hskp25 | hskp11) | hskp1)),
% 1.31/1.12 inference(monotonicity,[status(thm)],[1220])).
% 1.31/1.12 tff(1222,plain,
% 1.31/1.12 (((hskp25 | hskp11) | hskp1) <=> (hskp25 | hskp11 | hskp1)),
% 1.31/1.12 inference(transitivity,[status(thm)],[1221, 1219])).
% 1.31/1.12 tff(1223,axiom,((hskp25 | hskp11) | hskp1), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause36')).
% 1.31/1.12 tff(1224,plain,
% 1.31/1.12 (hskp25 | hskp11 | hskp1),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[1223, 1222])).
% 1.31/1.12 tff(1225,plain,
% 1.31/1.12 (hskp25 | hskp11 | hskp1),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[1224, 1218])).
% 1.31/1.12 tff(1226,plain,
% 1.31/1.12 (hskp25 | hskp11 | hskp1),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[1225, 1218])).
% 1.31/1.12 tff(1227,plain,
% 1.31/1.12 (hskp25 | hskp11 | hskp1),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[1226, 1218])).
% 1.31/1.12 tff(1228,plain,
% 1.31/1.12 (hskp25 | hskp11 | hskp1),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[1227, 1218])).
% 1.31/1.12 tff(1229,plain,
% 1.31/1.12 (hskp25 | hskp11 | hskp1),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[1228, 1218])).
% 1.31/1.12 tff(1230,plain,
% 1.31/1.12 (hskp25 | hskp11 | hskp1),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[1229, 1218])).
% 1.31/1.12 tff(1231,plain,
% 1.31/1.12 (hskp25 | hskp11 | hskp1),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[1230, 1218])).
% 1.31/1.12 tff(1232,plain,
% 1.31/1.12 (hskp1),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[1231, 1217, 1047])).
% 1.31/1.12 tff(1233,plain,
% 1.31/1.12 (((~hskp1) | (~c3_1(a323))) <=> ((~hskp1) | (~c3_1(a323)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(1234,plain,
% 1.31/1.12 (((~c3_1(a323)) | (~hskp1)) <=> ((~hskp1) | (~c3_1(a323)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(1235,axiom,((~c3_1(a323)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause124')).
% 1.31/1.12 tff(1236,plain,
% 1.31/1.12 ((~hskp1) | (~c3_1(a323))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[1235, 1234])).
% 1.31/1.12 tff(1237,plain,
% 1.31/1.12 ((~hskp1) | (~c3_1(a323))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[1236, 1233])).
% 1.31/1.12 tff(1238,plain,
% 1.31/1.12 (~c3_1(a323)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[1237, 1232])).
% 1.31/1.12 tff(1239,plain,
% 1.31/1.12 (((~hskp1) | (~c2_1(a323))) <=> ((~hskp1) | (~c2_1(a323)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(1240,plain,
% 1.31/1.12 (((~c2_1(a323)) | (~hskp1)) <=> ((~hskp1) | (~c2_1(a323)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(1241,axiom,((~c2_1(a323)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause123')).
% 1.31/1.12 tff(1242,plain,
% 1.31/1.12 ((~hskp1) | (~c2_1(a323))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[1241, 1240])).
% 1.31/1.12 tff(1243,plain,
% 1.31/1.12 ((~hskp1) | (~c2_1(a323))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[1242, 1239])).
% 1.31/1.12 tff(1244,plain,
% 1.31/1.12 (~c2_1(a323)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[1243, 1232])).
% 1.31/1.12 tff(1245,plain,
% 1.31/1.12 (((~hskp1) | (~c1_1(a323))) <=> ((~hskp1) | (~c1_1(a323)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(1246,plain,
% 1.31/1.12 (((~c1_1(a323)) | (~hskp1)) <=> ((~hskp1) | (~c1_1(a323)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(1247,axiom,((~c1_1(a323)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause122')).
% 1.31/1.12 tff(1248,plain,
% 1.31/1.12 ((~hskp1) | (~c1_1(a323))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[1247, 1246])).
% 1.31/1.12 tff(1249,plain,
% 1.31/1.12 ((~hskp1) | (~c1_1(a323))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[1248, 1245])).
% 1.31/1.12 tff(1250,plain,
% 1.31/1.12 (~c1_1(a323)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[1249, 1232])).
% 1.31/1.12 tff(1251,plain,
% 1.31/1.12 (((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp14 | hskp5 | c1_1(a323) | c2_1(a323) | c3_1(a323) | (~ndr1_0))) <=> ((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp14 | hskp5 | c1_1(a323) | c2_1(a323) | c3_1(a323) | (~ndr1_0))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(1252,plain,
% 1.31/1.12 ((hskp14 | hskp5 | (~ndr1_0) | c2_1(a323) | c1_1(a323) | c3_1(a323)) <=> (hskp14 | hskp5 | c1_1(a323) | c2_1(a323) | c3_1(a323) | (~ndr1_0))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(1253,plain,
% 1.31/1.12 (((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp14 | hskp5 | (~ndr1_0) | c2_1(a323) | c1_1(a323) | c3_1(a323))) <=> ((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp14 | hskp5 | c1_1(a323) | c2_1(a323) | c3_1(a323) | (~ndr1_0)))),
% 1.31/1.12 inference(monotonicity,[status(thm)],[1252])).
% 1.31/1.12 tff(1254,plain,
% 1.31/1.12 (((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp14 | hskp5 | (~ndr1_0) | c2_1(a323) | c1_1(a323) | c3_1(a323))) <=> ((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp14 | hskp5 | c1_1(a323) | c2_1(a323) | c3_1(a323) | (~ndr1_0))),
% 1.31/1.12 inference(transitivity,[status(thm)],[1253, 1251])).
% 1.31/1.12 tff(1255,plain,
% 1.31/1.12 ((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp14 | hskp5 | (~ndr1_0) | c2_1(a323) | c1_1(a323) | c3_1(a323))),
% 1.31/1.12 inference(quant_inst,[status(thm)],[])).
% 1.31/1.12 tff(1256,plain,
% 1.31/1.12 ((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp14 | hskp5 | c1_1(a323) | c2_1(a323) | c3_1(a323) | (~ndr1_0)),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[1255, 1254])).
% 1.31/1.12 tff(1257,plain,
% 1.31/1.12 ($false),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[1256, 152, 1180, 958, 1250, 1244, 1238, 968])).
% 1.31/1.12 tff(1258,plain,(hskp2 | hskp5), inference(lemma,lemma(discharge,[]))).
% 1.31/1.12 tff(1259,plain,
% 1.31/1.12 (hskp2),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[1258, 958])).
% 1.31/1.12 tff(1260,plain,
% 1.31/1.12 (((~hskp2) | (~c3_1(a324))) <=> ((~hskp2) | (~c3_1(a324)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(1261,plain,
% 1.31/1.12 (((~c3_1(a324)) | (~hskp2)) <=> ((~hskp2) | (~c3_1(a324)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(1262,axiom,((~c3_1(a324)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause121')).
% 1.31/1.12 tff(1263,plain,
% 1.31/1.12 ((~hskp2) | (~c3_1(a324))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[1262, 1261])).
% 1.31/1.12 tff(1264,plain,
% 1.31/1.12 ((~hskp2) | (~c3_1(a324))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[1263, 1260])).
% 1.31/1.12 tff(1265,plain,
% 1.31/1.12 (~c3_1(a324)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[1264, 1259])).
% 1.31/1.12 tff(1266,plain,
% 1.31/1.12 (((~hskp2) | (~c1_1(a324))) <=> ((~hskp2) | (~c1_1(a324)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(1267,plain,
% 1.31/1.12 (((~c1_1(a324)) | (~hskp2)) <=> ((~hskp2) | (~c1_1(a324)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(1268,axiom,((~c1_1(a324)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause120')).
% 1.31/1.12 tff(1269,plain,
% 1.31/1.12 ((~hskp2) | (~c1_1(a324))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[1268, 1267])).
% 1.31/1.12 tff(1270,plain,
% 1.31/1.12 ((~hskp2) | (~c1_1(a324))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[1269, 1266])).
% 1.31/1.12 tff(1271,plain,
% 1.31/1.12 (~c1_1(a324)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[1270, 1259])).
% 1.31/1.12 tff(1272,plain,
% 1.31/1.12 (((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp14 | hskp5 | c1_1(a324) | c3_1(a324) | (~ndr1_0) | c2_1(a324))) <=> ((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp14 | hskp5 | c1_1(a324) | c3_1(a324) | (~ndr1_0) | c2_1(a324))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(1273,plain,
% 1.31/1.12 ((hskp14 | hskp5 | (~ndr1_0) | c2_1(a324) | c1_1(a324) | c3_1(a324)) <=> (hskp14 | hskp5 | c1_1(a324) | c3_1(a324) | (~ndr1_0) | c2_1(a324))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(1274,plain,
% 1.31/1.12 (((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp14 | hskp5 | (~ndr1_0) | c2_1(a324) | c1_1(a324) | c3_1(a324))) <=> ((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp14 | hskp5 | c1_1(a324) | c3_1(a324) | (~ndr1_0) | c2_1(a324)))),
% 1.31/1.12 inference(monotonicity,[status(thm)],[1273])).
% 1.31/1.12 tff(1275,plain,
% 1.31/1.12 (((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp14 | hskp5 | (~ndr1_0) | c2_1(a324) | c1_1(a324) | c3_1(a324))) <=> ((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp14 | hskp5 | c1_1(a324) | c3_1(a324) | (~ndr1_0) | c2_1(a324))),
% 1.31/1.12 inference(transitivity,[status(thm)],[1274, 1272])).
% 1.31/1.12 tff(1276,plain,
% 1.31/1.12 ((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp14 | hskp5 | (~ndr1_0) | c2_1(a324) | c1_1(a324) | c3_1(a324))),
% 1.31/1.12 inference(quant_inst,[status(thm)],[])).
% 1.31/1.12 tff(1277,plain,
% 1.31/1.12 ((~![U: $i] : (hskp14 | hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp14 | hskp5 | c1_1(a324) | c3_1(a324) | (~ndr1_0) | c2_1(a324)),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[1276, 1275])).
% 1.31/1.12 tff(1278,plain,
% 1.31/1.12 (hskp14 | c2_1(a324)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[1277, 152, 958, 1271, 1265, 968])).
% 1.31/1.12 tff(1279,plain,
% 1.31/1.12 (c2_1(a324)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[1278, 11])).
% 1.31/1.12 tff(1280,assumption,(c2_1(a324)), introduced(assumption)).
% 1.31/1.12 tff(1281,plain,
% 1.31/1.12 (((~hskp2) | (~c0_1(a324))) <=> ((~hskp2) | (~c0_1(a324)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(1282,plain,
% 1.31/1.12 (((~c0_1(a324)) | (~hskp2)) <=> ((~hskp2) | (~c0_1(a324)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(1283,axiom,((~c0_1(a324)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause119')).
% 1.31/1.12 tff(1284,plain,
% 1.31/1.12 ((~hskp2) | (~c0_1(a324))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[1283, 1282])).
% 1.31/1.12 tff(1285,plain,
% 1.31/1.12 ((~hskp2) | (~c0_1(a324))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[1284, 1281])).
% 1.31/1.12 tff(1286,plain,
% 1.31/1.12 (~c0_1(a324)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[1285, 1259])).
% 1.31/1.12 tff(1287,assumption,(hskp4), introduced(assumption)).
% 1.31/1.12 tff(1288,plain,
% 1.31/1.12 (~c1_1(a326)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[592, 1287])).
% 1.31/1.12 tff(1289,plain,
% 1.31/1.12 (c2_1(a326)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[603, 1287])).
% 1.31/1.12 tff(1290,plain,
% 1.31/1.12 (c0_1(a326)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[614, 1287])).
% 1.31/1.12 tff(1291,plain,
% 1.31/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a326) | c0_1(a324) | c1_1(a324) | (~ndr1_0) | (~c2_1(a324)) | (~c2_1(a326)) | (~c3_1(a326)) | (~c0_1(a326)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a326) | c0_1(a324) | c1_1(a324) | (~ndr1_0) | (~c2_1(a324)) | (~c2_1(a326)) | (~c3_1(a326)) | (~c0_1(a326)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(1292,plain,
% 1.31/1.12 (((~ndr1_0) | c1_1(a326) | (~c2_1(a326)) | (~c3_1(a326)) | c1_1(a326) | (~c3_1(a326)) | (~c0_1(a326)) | c0_1(a324) | c1_1(a324) | (~c2_1(a324))) <=> (c1_1(a326) | c0_1(a324) | c1_1(a324) | (~ndr1_0) | (~c2_1(a324)) | (~c2_1(a326)) | (~c3_1(a326)) | (~c0_1(a326)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(1293,plain,
% 1.31/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a326) | (~c2_1(a326)) | (~c3_1(a326)) | c1_1(a326) | (~c3_1(a326)) | (~c0_1(a326)) | c0_1(a324) | c1_1(a324) | (~c2_1(a324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a326) | c0_1(a324) | c1_1(a324) | (~ndr1_0) | (~c2_1(a324)) | (~c2_1(a326)) | (~c3_1(a326)) | (~c0_1(a326))))),
% 1.36/1.13 inference(monotonicity,[status(thm)],[1292])).
% 1.36/1.13 tff(1294,plain,
% 1.36/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a326) | (~c2_1(a326)) | (~c3_1(a326)) | c1_1(a326) | (~c3_1(a326)) | (~c0_1(a326)) | c0_1(a324) | c1_1(a324) | (~c2_1(a324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a326) | c0_1(a324) | c1_1(a324) | (~ndr1_0) | (~c2_1(a324)) | (~c2_1(a326)) | (~c3_1(a326)) | (~c0_1(a326)))),
% 1.36/1.13 inference(transitivity,[status(thm)],[1293, 1291])).
% 1.36/1.13 tff(1295,plain,
% 1.36/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a326) | (~c2_1(a326)) | (~c3_1(a326)) | c1_1(a326) | (~c3_1(a326)) | (~c0_1(a326)) | c0_1(a324) | c1_1(a324) | (~c2_1(a324)))),
% 1.36/1.13 inference(quant_inst,[status(thm)],[])).
% 1.36/1.13 tff(1296,plain,
% 1.36/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a326) | c0_1(a324) | c1_1(a324) | (~ndr1_0) | (~c2_1(a324)) | (~c2_1(a326)) | (~c3_1(a326)) | (~c0_1(a326))),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[1295, 1294])).
% 1.36/1.13 tff(1297,plain,
% 1.36/1.13 (~c3_1(a326)),
% 1.36/1.13 inference(unit_resolution,[status(thm)],[1296, 152, 1290, 1289, 1288, 1286, 1271, 264, 1280])).
% 1.36/1.13 tff(1298,plain,
% 1.36/1.13 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp5 | c1_1(a326) | (~ndr1_0) | (~c2_1(a326)) | c3_1(a326) | (~c0_1(a326)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a326) | (~ndr1_0) | (~c2_1(a326)) | c3_1(a326) | (~c0_1(a326)))),
% 1.36/1.13 inference(rewrite,[status(thm)],[])).
% 1.36/1.13 tff(1299,plain,
% 1.36/1.13 ((hskp5 | (~ndr1_0) | c1_1(a326) | (~c2_1(a326)) | (~c0_1(a326)) | c1_1(a326) | c3_1(a326) | (~c2_1(a326))) <=> (hskp5 | c1_1(a326) | (~ndr1_0) | (~c2_1(a326)) | c3_1(a326) | (~c0_1(a326)))),
% 1.36/1.13 inference(rewrite,[status(thm)],[])).
% 1.36/1.13 tff(1300,plain,
% 1.36/1.13 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a326) | (~c2_1(a326)) | (~c0_1(a326)) | c1_1(a326) | c3_1(a326) | (~c2_1(a326)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp5 | c1_1(a326) | (~ndr1_0) | (~c2_1(a326)) | c3_1(a326) | (~c0_1(a326))))),
% 1.36/1.13 inference(monotonicity,[status(thm)],[1299])).
% 1.36/1.13 tff(1301,plain,
% 1.36/1.13 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a326) | (~c2_1(a326)) | (~c0_1(a326)) | c1_1(a326) | c3_1(a326) | (~c2_1(a326)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a326) | (~ndr1_0) | (~c2_1(a326)) | c3_1(a326) | (~c0_1(a326)))),
% 1.36/1.13 inference(transitivity,[status(thm)],[1300, 1298])).
% 1.36/1.13 tff(1302,plain,
% 1.36/1.13 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a326) | (~c2_1(a326)) | (~c0_1(a326)) | c1_1(a326) | c3_1(a326) | (~c2_1(a326)))),
% 1.36/1.13 inference(quant_inst,[status(thm)],[])).
% 1.36/1.13 tff(1303,plain,
% 1.36/1.13 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a326) | (~ndr1_0) | (~c2_1(a326)) | c3_1(a326) | (~c0_1(a326))),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[1302, 1301])).
% 1.36/1.13 tff(1304,plain,
% 1.36/1.13 ($false),
% 1.36/1.13 inference(unit_resolution,[status(thm)],[1303, 152, 958, 1290, 1289, 1288, 947, 1297])).
% 1.36/1.13 tff(1305,plain,((~hskp4) | hskp5 | (~c2_1(a324))), inference(lemma,lemma(discharge,[]))).
% 1.36/1.13 tff(1306,plain,
% 1.36/1.13 (~hskp4),
% 1.36/1.13 inference(unit_resolution,[status(thm)],[1305, 1279, 958])).
% 1.36/1.13 tff(1307,plain,
% 1.36/1.13 (((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | hskp13 | c0_1(a324) | c3_1(a324) | (~ndr1_0) | (~c2_1(a324)))) <=> ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp14 | hskp13 | c0_1(a324) | c3_1(a324) | (~ndr1_0) | (~c2_1(a324)))),
% 1.36/1.13 inference(rewrite,[status(thm)],[])).
% 1.36/1.13 tff(1308,plain,
% 1.36/1.13 ((hskp14 | hskp13 | (~ndr1_0) | c0_1(a324) | c3_1(a324) | (~c2_1(a324))) <=> (hskp14 | hskp13 | c0_1(a324) | c3_1(a324) | (~ndr1_0) | (~c2_1(a324)))),
% 1.36/1.13 inference(rewrite,[status(thm)],[])).
% 1.36/1.13 tff(1309,plain,
% 1.36/1.13 (((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | c0_1(a324) | c3_1(a324) | (~c2_1(a324)))) <=> ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | hskp13 | c0_1(a324) | c3_1(a324) | (~ndr1_0) | (~c2_1(a324))))),
% 1.36/1.13 inference(monotonicity,[status(thm)],[1308])).
% 1.36/1.13 tff(1310,plain,
% 1.36/1.13 (((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | c0_1(a324) | c3_1(a324) | (~c2_1(a324)))) <=> ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp14 | hskp13 | c0_1(a324) | c3_1(a324) | (~ndr1_0) | (~c2_1(a324)))),
% 1.36/1.13 inference(transitivity,[status(thm)],[1309, 1307])).
% 1.36/1.13 tff(1311,plain,
% 1.36/1.13 ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | c0_1(a324) | c3_1(a324) | (~c2_1(a324)))),
% 1.36/1.13 inference(quant_inst,[status(thm)],[])).
% 1.36/1.13 tff(1312,plain,
% 1.36/1.13 ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp14 | hskp13 | c0_1(a324) | c3_1(a324) | (~ndr1_0) | (~c2_1(a324))),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[1311, 1310])).
% 1.36/1.13 tff(1313,plain,
% 1.36/1.13 (hskp14 | hskp13 | (~c2_1(a324))),
% 1.36/1.13 inference(unit_resolution,[status(thm)],[1312, 152, 1286, 1265, 530])).
% 1.36/1.13 tff(1314,plain,
% 1.36/1.13 (hskp13),
% 1.36/1.13 inference(unit_resolution,[status(thm)],[1313, 1279, 11])).
% 1.36/1.13 tff(1315,plain,
% 1.36/1.13 (~c3_1(a346)),
% 1.36/1.13 inference(unit_resolution,[status(thm)],[554, 1314])).
% 1.36/1.13 tff(1316,plain,
% 1.36/1.13 (c2_1(a346)),
% 1.36/1.13 inference(unit_resolution,[status(thm)],[565, 1314])).
% 1.36/1.13 tff(1317,plain,
% 1.36/1.13 (c0_1(a346)),
% 1.36/1.13 inference(unit_resolution,[status(thm)],[576, 1314])).
% 1.36/1.13 tff(1318,plain,
% 1.36/1.13 (hskp16 | hskp4),
% 1.36/1.13 inference(unit_resolution,[status(thm)],[584, 152, 1317, 1316, 1315, 548])).
% 1.36/1.13 tff(1319,plain,
% 1.36/1.13 (hskp16),
% 1.36/1.13 inference(unit_resolution,[status(thm)],[1318, 1306])).
% 1.36/1.13 tff(1320,plain,
% 1.36/1.13 (hskp24),
% 1.36/1.13 inference(unit_resolution,[status(thm)],[1084, 1319, 958])).
% 1.36/1.13 tff(1321,plain,
% 1.36/1.13 (~c2_1(a401)),
% 1.36/1.13 inference(unit_resolution,[status(thm)],[1136, 1320])).
% 1.36/1.13 tff(1322,plain,
% 1.36/1.13 (c1_1(a401)),
% 1.36/1.13 inference(unit_resolution,[status(thm)],[1153, 1320])).
% 1.36/1.13 tff(1323,plain,
% 1.36/1.13 (~c0_1(a401)),
% 1.36/1.13 inference(unit_resolution,[status(thm)],[1142, 1320])).
% 1.36/1.13 tff(1324,plain,
% 1.36/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a401) | c2_1(a401) | c3_1(a346) | (~ndr1_0) | (~c0_1(a346)) | (~c1_1(a346)) | (~c2_1(a346)) | (~c1_1(a401)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a401) | c2_1(a401) | c3_1(a346) | (~ndr1_0) | (~c0_1(a346)) | (~c1_1(a346)) | (~c2_1(a346)) | (~c1_1(a401)))),
% 1.36/1.13 inference(rewrite,[status(thm)],[])).
% 1.36/1.13 tff(1325,plain,
% 1.36/1.13 (((~ndr1_0) | (~c2_1(a346)) | (~c0_1(a346)) | (~c1_1(a346)) | c3_1(a346) | (~c1_1(a346)) | (~c2_1(a346)) | c2_1(a401) | c0_1(a401) | (~c1_1(a401))) <=> (c0_1(a401) | c2_1(a401) | c3_1(a346) | (~ndr1_0) | (~c0_1(a346)) | (~c1_1(a346)) | (~c2_1(a346)) | (~c1_1(a401)))),
% 1.36/1.13 inference(rewrite,[status(thm)],[])).
% 1.36/1.13 tff(1326,plain,
% 1.36/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a346)) | (~c0_1(a346)) | (~c1_1(a346)) | c3_1(a346) | (~c1_1(a346)) | (~c2_1(a346)) | c2_1(a401) | c0_1(a401) | (~c1_1(a401)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a401) | c2_1(a401) | c3_1(a346) | (~ndr1_0) | (~c0_1(a346)) | (~c1_1(a346)) | (~c2_1(a346)) | (~c1_1(a401))))),
% 1.36/1.13 inference(monotonicity,[status(thm)],[1325])).
% 1.36/1.13 tff(1327,plain,
% 1.36/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a346)) | (~c0_1(a346)) | (~c1_1(a346)) | c3_1(a346) | (~c1_1(a346)) | (~c2_1(a346)) | c2_1(a401) | c0_1(a401) | (~c1_1(a401)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a401) | c2_1(a401) | c3_1(a346) | (~ndr1_0) | (~c0_1(a346)) | (~c1_1(a346)) | (~c2_1(a346)) | (~c1_1(a401)))),
% 1.36/1.13 inference(transitivity,[status(thm)],[1326, 1324])).
% 1.36/1.13 tff(1328,plain,
% 1.36/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a346)) | (~c0_1(a346)) | (~c1_1(a346)) | c3_1(a346) | (~c1_1(a346)) | (~c2_1(a346)) | c2_1(a401) | c0_1(a401) | (~c1_1(a401)))),
% 1.36/1.13 inference(quant_inst,[status(thm)],[])).
% 1.36/1.13 tff(1329,plain,
% 1.36/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a401) | c2_1(a401) | c3_1(a346) | (~ndr1_0) | (~c0_1(a346)) | (~c1_1(a346)) | (~c2_1(a346)) | (~c1_1(a401))),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[1328, 1327])).
% 1.36/1.13 tff(1330,plain,
% 1.36/1.13 (~c1_1(a346)),
% 1.36/1.13 inference(unit_resolution,[status(thm)],[1329, 152, 1171, 577, 566, 1168, 1167, 555, 21])).
% 1.36/1.13 tff(1331,plain,
% 1.36/1.13 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp5 | c3_1(a346) | (~ndr1_0) | (~c0_1(a346)) | c1_1(a346) | (~c2_1(a346)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp5 | c3_1(a346) | (~ndr1_0) | (~c0_1(a346)) | c1_1(a346) | (~c2_1(a346)))),
% 1.36/1.13 inference(rewrite,[status(thm)],[])).
% 1.36/1.13 tff(1332,plain,
% 1.36/1.13 ((hskp5 | (~ndr1_0) | c1_1(a346) | (~c2_1(a346)) | (~c0_1(a346)) | c1_1(a346) | c3_1(a346) | (~c2_1(a346))) <=> (hskp5 | c3_1(a346) | (~ndr1_0) | (~c0_1(a346)) | c1_1(a346) | (~c2_1(a346)))),
% 1.36/1.13 inference(rewrite,[status(thm)],[])).
% 1.36/1.13 tff(1333,plain,
% 1.36/1.13 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a346) | (~c2_1(a346)) | (~c0_1(a346)) | c1_1(a346) | c3_1(a346) | (~c2_1(a346)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp5 | c3_1(a346) | (~ndr1_0) | (~c0_1(a346)) | c1_1(a346) | (~c2_1(a346))))),
% 1.36/1.13 inference(monotonicity,[status(thm)],[1332])).
% 1.36/1.13 tff(1334,plain,
% 1.36/1.13 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a346) | (~c2_1(a346)) | (~c0_1(a346)) | c1_1(a346) | c3_1(a346) | (~c2_1(a346)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp5 | c3_1(a346) | (~ndr1_0) | (~c0_1(a346)) | c1_1(a346) | (~c2_1(a346)))),
% 1.36/1.13 inference(transitivity,[status(thm)],[1333, 1331])).
% 1.36/1.13 tff(1335,plain,
% 1.36/1.13 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a346) | (~c2_1(a346)) | (~c0_1(a346)) | c1_1(a346) | c3_1(a346) | (~c2_1(a346)))),
% 1.36/1.13 inference(quant_inst,[status(thm)],[])).
% 1.36/1.13 tff(1336,plain,
% 1.36/1.13 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp5 | c3_1(a346) | (~ndr1_0) | (~c0_1(a346)) | c1_1(a346) | (~c2_1(a346))),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[1335, 1334])).
% 1.36/1.13 tff(1337,plain,
% 1.36/1.13 ($false),
% 1.36/1.13 inference(unit_resolution,[status(thm)],[1336, 152, 958, 577, 566, 555, 947, 1330])).
% 1.36/1.13 tff(1338,plain,((~hskp13) | hskp5 | (~c1_1(a401)) | c0_1(a401) | c2_1(a401)), inference(lemma,lemma(discharge,[]))).
% 1.36/1.13 tff(1339,plain,
% 1.36/1.13 ($false),
% 1.36/1.13 inference(unit_resolution,[status(thm)],[1338, 1323, 1322, 958, 1314, 1321])).
% 1.36/1.13 tff(1340,plain,(hskp14 | hskp5), inference(lemma,lemma(discharge,[]))).
% 1.36/1.13 tff(1341,plain,
% 1.36/1.13 (hskp14),
% 1.36/1.13 inference(unit_resolution,[status(thm)],[1340, 958])).
% 1.36/1.13 tff(1342,plain,
% 1.36/1.13 (~c1_1(a347)),
% 1.36/1.13 inference(unit_resolution,[status(thm)],[1003, 1341])).
% 1.36/1.13 tff(1343,plain,
% 1.36/1.13 (c3_1(a347)),
% 1.36/1.13 inference(unit_resolution,[status(thm)],[1017, 1341])).
% 1.36/1.13 tff(1344,plain,
% 1.36/1.13 (c2_1(a347)),
% 1.36/1.13 inference(unit_resolution,[status(thm)],[1028, 1341])).
% 1.36/1.13 tff(1345,plain,
% 1.36/1.13 (((~![U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp15 | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp15 | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)))),
% 1.36/1.13 inference(rewrite,[status(thm)],[])).
% 1.36/1.13 tff(1346,plain,
% 1.36/1.13 ((hskp15 | (~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347))) <=> (hskp15 | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)))),
% 1.36/1.13 inference(rewrite,[status(thm)],[])).
% 1.36/1.13 tff(1347,plain,
% 1.36/1.13 (((~![U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp15 | (~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp15 | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347))))),
% 1.36/1.13 inference(monotonicity,[status(thm)],[1346])).
% 1.36/1.13 tff(1348,plain,
% 1.36/1.13 (((~![U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp15 | (~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp15 | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)))),
% 1.36/1.13 inference(transitivity,[status(thm)],[1347, 1345])).
% 1.36/1.13 tff(1349,plain,
% 1.36/1.13 ((~![U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp15 | (~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)))),
% 1.36/1.13 inference(quant_inst,[status(thm)],[])).
% 1.36/1.13 tff(1350,plain,
% 1.36/1.13 ((~![U: $i] : (hskp15 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp15 | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347))),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[1349, 1348])).
% 1.36/1.13 tff(1351,plain,
% 1.36/1.13 (hskp15),
% 1.36/1.13 inference(unit_resolution,[status(thm)],[1350, 152, 1344, 1343, 1342, 957])).
% 1.36/1.13 tff(1352,plain,
% 1.36/1.13 (((~hskp15) | (~c3_1(a348))) <=> ((~hskp15) | (~c3_1(a348)))),
% 1.36/1.13 inference(rewrite,[status(thm)],[])).
% 1.36/1.13 tff(1353,plain,
% 1.36/1.13 (((~c3_1(a348)) | (~hskp15)) <=> ((~hskp15) | (~c3_1(a348)))),
% 1.36/1.13 inference(rewrite,[status(thm)],[])).
% 1.36/1.13 tff(1354,axiom,((~c3_1(a348)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause98')).
% 1.36/1.13 tff(1355,plain,
% 1.36/1.13 ((~hskp15) | (~c3_1(a348))),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[1354, 1353])).
% 1.36/1.13 tff(1356,plain,
% 1.36/1.13 ((~hskp15) | (~c3_1(a348))),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[1355, 1352])).
% 1.36/1.13 tff(1357,plain,
% 1.36/1.13 (~c3_1(a348)),
% 1.36/1.13 inference(unit_resolution,[status(thm)],[1356, 1351])).
% 1.36/1.13 tff(1358,plain,
% 1.36/1.13 (((~hskp15) | (~c1_1(a348))) <=> ((~hskp15) | (~c1_1(a348)))),
% 1.36/1.13 inference(rewrite,[status(thm)],[])).
% 1.36/1.13 tff(1359,plain,
% 1.36/1.13 (((~c1_1(a348)) | (~hskp15)) <=> ((~hskp15) | (~c1_1(a348)))),
% 1.36/1.13 inference(rewrite,[status(thm)],[])).
% 1.36/1.13 tff(1360,axiom,((~c1_1(a348)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause97')).
% 1.36/1.13 tff(1361,plain,
% 1.36/1.13 ((~hskp15) | (~c1_1(a348))),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[1360, 1359])).
% 1.36/1.13 tff(1362,plain,
% 1.36/1.13 ((~hskp15) | (~c1_1(a348))),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[1361, 1358])).
% 1.36/1.13 tff(1363,plain,
% 1.36/1.13 (~c1_1(a348)),
% 1.36/1.13 inference(unit_resolution,[status(thm)],[1362, 1351])).
% 1.36/1.13 tff(1364,plain,
% 1.36/1.13 (((~hskp15) | c0_1(a348)) <=> ((~hskp15) | c0_1(a348))),
% 1.36/1.13 inference(rewrite,[status(thm)],[])).
% 1.36/1.13 tff(1365,axiom,((~hskp15) | c0_1(a348)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause62')).
% 1.36/1.13 tff(1366,plain,
% 1.36/1.13 ((~hskp15) | c0_1(a348)),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[1365, 1364])).
% 1.36/1.13 tff(1367,plain,
% 1.36/1.13 ((~hskp15) | c0_1(a348)),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[1366, 1364])).
% 1.36/1.13 tff(1368,plain,
% 1.36/1.13 ((~hskp15) | c0_1(a348)),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[1367, 1364])).
% 1.36/1.13 tff(1369,plain,
% 1.36/1.13 ((~hskp15) | c0_1(a348)),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[1368, 1364])).
% 1.36/1.13 tff(1370,plain,
% 1.36/1.13 ((~hskp15) | c0_1(a348)),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[1369, 1364])).
% 1.36/1.13 tff(1371,plain,
% 1.36/1.13 ((~hskp15) | c0_1(a348)),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[1370, 1364])).
% 1.36/1.13 tff(1372,plain,
% 1.36/1.13 ((~hskp15) | c0_1(a348)),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[1371, 1364])).
% 1.36/1.13 tff(1373,plain,
% 1.36/1.13 ((~hskp15) | c0_1(a348)),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[1372, 1364])).
% 1.36/1.13 tff(1374,plain,
% 1.36/1.13 (c0_1(a348)),
% 1.36/1.13 inference(unit_resolution,[status(thm)],[1373, 1351])).
% 1.36/1.13 tff(1375,plain,
% 1.36/1.13 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp5 | c1_1(a348) | c3_1(a348) | (~ndr1_0) | (~c0_1(a348)) | (~c2_1(a348)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a348) | c3_1(a348) | (~ndr1_0) | (~c0_1(a348)) | (~c2_1(a348)))),
% 1.36/1.13 inference(rewrite,[status(thm)],[])).
% 1.36/1.13 tff(1376,plain,
% 1.36/1.13 ((hskp5 | (~ndr1_0) | c1_1(a348) | (~c2_1(a348)) | (~c0_1(a348)) | c1_1(a348) | c3_1(a348) | (~c2_1(a348))) <=> (hskp5 | c1_1(a348) | c3_1(a348) | (~ndr1_0) | (~c0_1(a348)) | (~c2_1(a348)))),
% 1.36/1.13 inference(rewrite,[status(thm)],[])).
% 1.36/1.13 tff(1377,plain,
% 1.36/1.13 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a348) | (~c2_1(a348)) | (~c0_1(a348)) | c1_1(a348) | c3_1(a348) | (~c2_1(a348)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp5 | c1_1(a348) | c3_1(a348) | (~ndr1_0) | (~c0_1(a348)) | (~c2_1(a348))))),
% 1.36/1.13 inference(monotonicity,[status(thm)],[1376])).
% 1.36/1.13 tff(1378,plain,
% 1.36/1.13 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a348) | (~c2_1(a348)) | (~c0_1(a348)) | c1_1(a348) | c3_1(a348) | (~c2_1(a348)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a348) | c3_1(a348) | (~ndr1_0) | (~c0_1(a348)) | (~c2_1(a348)))),
% 1.36/1.13 inference(transitivity,[status(thm)],[1377, 1375])).
% 1.36/1.13 tff(1379,plain,
% 1.36/1.13 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a348) | (~c2_1(a348)) | (~c0_1(a348)) | c1_1(a348) | c3_1(a348) | (~c2_1(a348)))),
% 1.36/1.13 inference(quant_inst,[status(thm)],[])).
% 1.36/1.13 tff(1380,plain,
% 1.36/1.13 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a348) | c3_1(a348) | (~ndr1_0) | (~c0_1(a348)) | (~c2_1(a348))),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[1379, 1378])).
% 1.36/1.13 tff(1381,plain,
% 1.36/1.13 (~c2_1(a348)),
% 1.36/1.13 inference(unit_resolution,[status(thm)],[1380, 152, 958, 1374, 1363, 1357, 947])).
% 1.36/1.13 tff(1382,plain,
% 1.36/1.13 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a348) | c3_1(a348) | (~ndr1_0) | (~c0_1(a348)) | c2_1(a348))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a348) | c3_1(a348) | (~ndr1_0) | (~c0_1(a348)) | c2_1(a348))),
% 1.36/1.13 inference(rewrite,[status(thm)],[])).
% 1.36/1.13 tff(1383,plain,
% 1.36/1.13 ((hskp22 | (~ndr1_0) | c2_1(a348) | c3_1(a348) | (~c0_1(a348)) | c1_1(a348) | c3_1(a348) | (~c0_1(a348))) <=> (hskp22 | c1_1(a348) | c3_1(a348) | (~ndr1_0) | (~c0_1(a348)) | c2_1(a348))),
% 1.36/1.13 inference(rewrite,[status(thm)],[])).
% 1.36/1.13 tff(1384,plain,
% 1.36/1.13 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a348) | c3_1(a348) | (~c0_1(a348)) | c1_1(a348) | c3_1(a348) | (~c0_1(a348)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a348) | c3_1(a348) | (~ndr1_0) | (~c0_1(a348)) | c2_1(a348)))),
% 1.36/1.13 inference(monotonicity,[status(thm)],[1383])).
% 1.36/1.13 tff(1385,plain,
% 1.36/1.13 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a348) | c3_1(a348) | (~c0_1(a348)) | c1_1(a348) | c3_1(a348) | (~c0_1(a348)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a348) | c3_1(a348) | (~ndr1_0) | (~c0_1(a348)) | c2_1(a348))),
% 1.36/1.13 inference(transitivity,[status(thm)],[1384, 1382])).
% 1.36/1.13 tff(1386,plain,
% 1.36/1.13 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c2_1(a348) | c3_1(a348) | (~c0_1(a348)) | c1_1(a348) | c3_1(a348) | (~c0_1(a348)))),
% 1.36/1.13 inference(quant_inst,[status(thm)],[])).
% 1.36/1.13 tff(1387,plain,
% 1.36/1.13 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a348) | c3_1(a348) | (~ndr1_0) | (~c0_1(a348)) | c2_1(a348)),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[1386, 1385])).
% 1.36/1.13 tff(1388,plain,
% 1.36/1.13 (hskp22),
% 1.36/1.13 inference(unit_resolution,[status(thm)],[1387, 152, 1374, 1363, 1357, 243, 1381])).
% 1.36/1.13 tff(1389,plain,
% 1.36/1.13 (~c2_1(a367)),
% 1.36/1.13 inference(unit_resolution,[status(thm)],[476, 1388])).
% 1.36/1.13 tff(1390,plain,
% 1.36/1.13 (c3_1(a367)),
% 1.36/1.13 inference(unit_resolution,[status(thm)],[487, 1388])).
% 1.36/1.13 tff(1391,plain,
% 1.36/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a367) | c1_1(a348) | c1_1(a347) | (~ndr1_0) | (~c3_1(a367)) | c0_1(a367) | (~c2_1(a347)) | (~c3_1(a347)) | (~c0_1(a348)) | c2_1(a348))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a367) | c1_1(a348) | c1_1(a347) | (~ndr1_0) | (~c3_1(a367)) | c0_1(a367) | (~c2_1(a347)) | (~c3_1(a347)) | (~c0_1(a348)) | c2_1(a348))),
% 1.36/1.13 inference(rewrite,[status(thm)],[])).
% 1.36/1.13 tff(1392,plain,
% 1.36/1.13 (((~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)) | c2_1(a348) | c1_1(a348) | (~c0_1(a348)) | c2_1(a367) | c0_1(a367) | (~c3_1(a367))) <=> (c2_1(a367) | c1_1(a348) | c1_1(a347) | (~ndr1_0) | (~c3_1(a367)) | c0_1(a367) | (~c2_1(a347)) | (~c3_1(a347)) | (~c0_1(a348)) | c2_1(a348))),
% 1.36/1.13 inference(rewrite,[status(thm)],[])).
% 1.36/1.13 tff(1393,plain,
% 1.36/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)) | c2_1(a348) | c1_1(a348) | (~c0_1(a348)) | c2_1(a367) | c0_1(a367) | (~c3_1(a367)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a367) | c1_1(a348) | c1_1(a347) | (~ndr1_0) | (~c3_1(a367)) | c0_1(a367) | (~c2_1(a347)) | (~c3_1(a347)) | (~c0_1(a348)) | c2_1(a348)))),
% 1.36/1.13 inference(monotonicity,[status(thm)],[1392])).
% 1.36/1.13 tff(1394,plain,
% 1.36/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)) | c2_1(a348) | c1_1(a348) | (~c0_1(a348)) | c2_1(a367) | c0_1(a367) | (~c3_1(a367)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a367) | c1_1(a348) | c1_1(a347) | (~ndr1_0) | (~c3_1(a367)) | c0_1(a367) | (~c2_1(a347)) | (~c3_1(a347)) | (~c0_1(a348)) | c2_1(a348))),
% 1.36/1.13 inference(transitivity,[status(thm)],[1393, 1391])).
% 1.36/1.13 tff(1395,plain,
% 1.36/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)) | c2_1(a348) | c1_1(a348) | (~c0_1(a348)) | c2_1(a367) | c0_1(a367) | (~c3_1(a367)))),
% 1.36/1.13 inference(quant_inst,[status(thm)],[])).
% 1.36/1.13 tff(1396,plain,
% 1.36/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a367) | c1_1(a348) | c1_1(a347) | (~ndr1_0) | (~c3_1(a367)) | c0_1(a367) | (~c2_1(a347)) | (~c3_1(a347)) | (~c0_1(a348)) | c2_1(a348)),
% 1.36/1.13 inference(modus_ponens,[status(thm)],[1395, 1394])).
% 1.36/1.13 tff(1397,plain,
% 1.36/1.13 (c0_1(a367)),
% 1.36/1.13 inference(unit_resolution,[status(thm)],[1396, 152, 1390, 1374, 1344, 1343, 1389, 1363, 1342, 509, 1381])).
% 1.36/1.13 tff(1398,plain,
% 1.36/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a367) | c3_1(a348) | (~ndr1_0) | (~c3_1(a367)) | (~c0_1(a367)) | (~c2_1(a347)) | (~c3_1(a347)) | (~c0_1(a347)) | (~c0_1(a348)) | c2_1(a348))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a367) | c3_1(a348) | (~ndr1_0) | (~c3_1(a367)) | (~c0_1(a367)) | (~c2_1(a347)) | (~c3_1(a347)) | (~c0_1(a347)) | (~c0_1(a348)) | c2_1(a348))),
% 1.36/1.14 inference(rewrite,[status(thm)],[])).
% 1.36/1.14 tff(1399,plain,
% 1.36/1.14 (((~ndr1_0) | (~c2_1(a347)) | (~c0_1(a347)) | (~c3_1(a347)) | c2_1(a367) | (~c3_1(a367)) | (~c0_1(a367)) | c2_1(a348) | c3_1(a348) | (~c0_1(a348))) <=> (c2_1(a367) | c3_1(a348) | (~ndr1_0) | (~c3_1(a367)) | (~c0_1(a367)) | (~c2_1(a347)) | (~c3_1(a347)) | (~c0_1(a347)) | (~c0_1(a348)) | c2_1(a348))),
% 1.36/1.14 inference(rewrite,[status(thm)],[])).
% 1.36/1.14 tff(1400,plain,
% 1.36/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a347)) | (~c0_1(a347)) | (~c3_1(a347)) | c2_1(a367) | (~c3_1(a367)) | (~c0_1(a367)) | c2_1(a348) | c3_1(a348) | (~c0_1(a348)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a367) | c3_1(a348) | (~ndr1_0) | (~c3_1(a367)) | (~c0_1(a367)) | (~c2_1(a347)) | (~c3_1(a347)) | (~c0_1(a347)) | (~c0_1(a348)) | c2_1(a348)))),
% 1.36/1.14 inference(monotonicity,[status(thm)],[1399])).
% 1.36/1.14 tff(1401,plain,
% 1.36/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a347)) | (~c0_1(a347)) | (~c3_1(a347)) | c2_1(a367) | (~c3_1(a367)) | (~c0_1(a367)) | c2_1(a348) | c3_1(a348) | (~c0_1(a348)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a367) | c3_1(a348) | (~ndr1_0) | (~c3_1(a367)) | (~c0_1(a367)) | (~c2_1(a347)) | (~c3_1(a347)) | (~c0_1(a347)) | (~c0_1(a348)) | c2_1(a348))),
% 1.36/1.14 inference(transitivity,[status(thm)],[1400, 1398])).
% 1.36/1.14 tff(1402,plain,
% 1.36/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a347)) | (~c0_1(a347)) | (~c3_1(a347)) | c2_1(a367) | (~c3_1(a367)) | (~c0_1(a367)) | c2_1(a348) | c3_1(a348) | (~c0_1(a348)))),
% 1.36/1.14 inference(quant_inst,[status(thm)],[])).
% 1.36/1.14 tff(1403,plain,
% 1.36/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a367) | c3_1(a348) | (~ndr1_0) | (~c3_1(a367)) | (~c0_1(a367)) | (~c2_1(a347)) | (~c3_1(a347)) | (~c0_1(a347)) | (~c0_1(a348)) | c2_1(a348)),
% 1.36/1.14 inference(modus_ponens,[status(thm)],[1402, 1401])).
% 1.36/1.14 tff(1404,plain,
% 1.36/1.14 ((~c0_1(a367)) | (~c0_1(a347))),
% 1.36/1.14 inference(unit_resolution,[status(thm)],[1403, 152, 1390, 1374, 1344, 1343, 1389, 1357, 415, 1381])).
% 1.36/1.14 tff(1405,plain,
% 1.36/1.14 (~c0_1(a347)),
% 1.36/1.14 inference(unit_resolution,[status(thm)],[1404, 1397])).
% 1.36/1.14 tff(1406,plain,
% 1.36/1.14 (~c1_1(a367)),
% 1.36/1.14 inference(unit_resolution,[status(thm)],[470, 1388])).
% 1.36/1.14 tff(1407,plain,
% 1.36/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a367) | c1_1(a347) | (~ndr1_0) | (~c3_1(a367)) | (~c0_1(a367)) | (~c2_1(a347)) | (~c3_1(a347)) | c0_1(a347))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a367) | c1_1(a347) | (~ndr1_0) | (~c3_1(a367)) | (~c0_1(a367)) | (~c2_1(a347)) | (~c3_1(a347)) | c0_1(a347))),
% 1.36/1.14 inference(rewrite,[status(thm)],[])).
% 1.36/1.14 tff(1408,plain,
% 1.36/1.14 (((~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)) | c1_1(a367) | (~c3_1(a367)) | (~c0_1(a367)) | c0_1(a347) | c1_1(a347) | (~c2_1(a347))) <=> (c1_1(a367) | c1_1(a347) | (~ndr1_0) | (~c3_1(a367)) | (~c0_1(a367)) | (~c2_1(a347)) | (~c3_1(a347)) | c0_1(a347))),
% 1.36/1.14 inference(rewrite,[status(thm)],[])).
% 1.36/1.14 tff(1409,plain,
% 1.36/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)) | c1_1(a367) | (~c3_1(a367)) | (~c0_1(a367)) | c0_1(a347) | c1_1(a347) | (~c2_1(a347)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a367) | c1_1(a347) | (~ndr1_0) | (~c3_1(a367)) | (~c0_1(a367)) | (~c2_1(a347)) | (~c3_1(a347)) | c0_1(a347)))),
% 1.36/1.14 inference(monotonicity,[status(thm)],[1408])).
% 1.36/1.14 tff(1410,plain,
% 1.36/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)) | c1_1(a367) | (~c3_1(a367)) | (~c0_1(a367)) | c0_1(a347) | c1_1(a347) | (~c2_1(a347)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a367) | c1_1(a347) | (~ndr1_0) | (~c3_1(a367)) | (~c0_1(a367)) | (~c2_1(a347)) | (~c3_1(a347)) | c0_1(a347))),
% 1.36/1.14 inference(transitivity,[status(thm)],[1409, 1407])).
% 1.36/1.14 tff(1411,plain,
% 1.36/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)) | c1_1(a367) | (~c3_1(a367)) | (~c0_1(a367)) | c0_1(a347) | c1_1(a347) | (~c2_1(a347)))),
% 1.36/1.14 inference(quant_inst,[status(thm)],[])).
% 1.36/1.14 tff(1412,plain,
% 1.36/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a367) | c1_1(a347) | (~ndr1_0) | (~c3_1(a367)) | (~c0_1(a367)) | (~c2_1(a347)) | (~c3_1(a347)) | c0_1(a347)),
% 1.36/1.14 inference(modus_ponens,[status(thm)],[1411, 1410])).
% 1.36/1.14 tff(1413,plain,
% 1.36/1.14 ($false),
% 1.36/1.14 inference(unit_resolution,[status(thm)],[1412, 152, 1390, 1344, 1343, 1406, 1342, 264, 1405, 1397])).
% 1.36/1.14 tff(1414,plain,(hskp5), inference(lemma,lemma(discharge,[]))).
% 1.36/1.14 tff(1415,plain,
% 1.36/1.14 (((~hskp5) | (~c3_1(a327))) <=> ((~hskp5) | (~c3_1(a327)))),
% 1.36/1.14 inference(rewrite,[status(thm)],[])).
% 1.36/1.14 tff(1416,plain,
% 1.36/1.14 (((~c3_1(a327)) | (~hskp5)) <=> ((~hskp5) | (~c3_1(a327)))),
% 1.36/1.14 inference(rewrite,[status(thm)],[])).
% 1.36/1.14 tff(1417,axiom,((~c3_1(a327)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause116')).
% 1.36/1.14 tff(1418,plain,
% 1.36/1.14 ((~hskp5) | (~c3_1(a327))),
% 1.36/1.14 inference(modus_ponens,[status(thm)],[1417, 1416])).
% 1.36/1.14 tff(1419,plain,
% 1.36/1.14 ((~hskp5) | (~c3_1(a327))),
% 1.36/1.14 inference(modus_ponens,[status(thm)],[1418, 1415])).
% 1.36/1.14 tff(1420,plain,
% 1.36/1.14 (~c3_1(a327)),
% 1.36/1.14 inference(unit_resolution,[status(thm)],[1419, 1414])).
% 1.36/1.14 tff(1421,plain,
% 1.36/1.14 (((~hskp5) | c1_1(a327)) <=> ((~hskp5) | c1_1(a327))),
% 1.36/1.14 inference(rewrite,[status(thm)],[])).
% 1.36/1.14 tff(1422,axiom,((~hskp5) | c1_1(a327)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause74')).
% 1.36/1.14 tff(1423,plain,
% 1.36/1.14 ((~hskp5) | c1_1(a327)),
% 1.36/1.14 inference(modus_ponens,[status(thm)],[1422, 1421])).
% 1.36/1.14 tff(1424,plain,
% 1.36/1.14 ((~hskp5) | c1_1(a327)),
% 1.36/1.14 inference(modus_ponens,[status(thm)],[1423, 1421])).
% 1.36/1.14 tff(1425,plain,
% 1.36/1.14 ((~hskp5) | c1_1(a327)),
% 1.36/1.14 inference(modus_ponens,[status(thm)],[1424, 1421])).
% 1.36/1.14 tff(1426,plain,
% 1.36/1.14 ((~hskp5) | c1_1(a327)),
% 1.36/1.14 inference(modus_ponens,[status(thm)],[1425, 1421])).
% 1.36/1.14 tff(1427,plain,
% 1.36/1.14 ((~hskp5) | c1_1(a327)),
% 1.36/1.14 inference(modus_ponens,[status(thm)],[1426, 1421])).
% 1.36/1.14 tff(1428,plain,
% 1.36/1.14 ((~hskp5) | c1_1(a327)),
% 1.36/1.14 inference(modus_ponens,[status(thm)],[1427, 1421])).
% 1.36/1.14 tff(1429,plain,
% 1.36/1.14 ((~hskp5) | c1_1(a327)),
% 1.36/1.14 inference(modus_ponens,[status(thm)],[1428, 1421])).
% 1.36/1.14 tff(1430,plain,
% 1.36/1.14 ((~hskp5) | c1_1(a327)),
% 1.36/1.14 inference(modus_ponens,[status(thm)],[1429, 1421])).
% 1.36/1.14 tff(1431,plain,
% 1.36/1.14 (c1_1(a327)),
% 1.36/1.14 inference(unit_resolution,[status(thm)],[1430, 1414])).
% 1.36/1.14 tff(1432,plain,
% 1.36/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a349) | c3_1(a327) | (~ndr1_0) | (~c1_1(a327)) | (~c2_1(a327)) | c0_1(a349) | (~c1_1(a349)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a349) | c3_1(a327) | (~ndr1_0) | (~c1_1(a327)) | (~c2_1(a327)) | c0_1(a349) | (~c1_1(a349)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.36/1.14 inference(rewrite,[status(thm)],[])).
% 1.36/1.14 tff(1433,plain,
% 1.36/1.14 (((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c3_1(a327) | (~c1_1(a327)) | (~c2_1(a327)) | c2_1(a349) | c0_1(a349) | (~c1_1(a349))) <=> (c2_1(a349) | c3_1(a327) | (~ndr1_0) | (~c1_1(a327)) | (~c2_1(a327)) | c0_1(a349) | (~c1_1(a349)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.36/1.14 inference(rewrite,[status(thm)],[])).
% 1.36/1.14 tff(1434,plain,
% 1.36/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c3_1(a327) | (~c1_1(a327)) | (~c2_1(a327)) | c2_1(a349) | c0_1(a349) | (~c1_1(a349)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a349) | c3_1(a327) | (~ndr1_0) | (~c1_1(a327)) | (~c2_1(a327)) | c0_1(a349) | (~c1_1(a349)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))))),
% 1.36/1.14 inference(monotonicity,[status(thm)],[1433])).
% 1.36/1.14 tff(1435,plain,
% 1.36/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c3_1(a327) | (~c1_1(a327)) | (~c2_1(a327)) | c2_1(a349) | c0_1(a349) | (~c1_1(a349)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a349) | c3_1(a327) | (~ndr1_0) | (~c1_1(a327)) | (~c2_1(a327)) | c0_1(a349) | (~c1_1(a349)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.36/1.14 inference(transitivity,[status(thm)],[1434, 1432])).
% 1.36/1.14 tff(1436,plain,
% 1.36/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c3_1(a327) | (~c1_1(a327)) | (~c2_1(a327)) | c2_1(a349) | c0_1(a349) | (~c1_1(a349)))),
% 1.36/1.14 inference(quant_inst,[status(thm)],[])).
% 1.36/1.14 tff(1437,plain,
% 1.36/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a349) | c3_1(a327) | (~ndr1_0) | (~c1_1(a327)) | (~c2_1(a327)) | c0_1(a349) | (~c1_1(a349)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))),
% 1.36/1.14 inference(modus_ponens,[status(thm)],[1436, 1435])).
% 1.36/1.14 tff(1438,plain,
% 1.36/1.14 ((~c2_1(a327)) | c0_1(a349)),
% 1.36/1.14 inference(unit_resolution,[status(thm)],[1437, 152, 1208, 1207, 1206, 918, 1431, 894, 1420, 21])).
% 1.36/1.14 tff(1439,plain,
% 1.36/1.14 (~c2_1(a327)),
% 1.36/1.14 inference(unit_resolution,[status(thm)],[1438, 937])).
% 1.36/1.14 tff(1440,plain,
% 1.36/1.14 (^[U: $i] : refl((hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))))),
% 1.36/1.14 inference(bind,[status(th)],[])).
% 1.36/1.14 tff(1441,plain,
% 1.36/1.14 (![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.36/1.14 inference(quant_intro,[status(thm)],[1440])).
% 1.36/1.14 tff(1442,plain,
% 1.36/1.14 (![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.36/1.14 inference(rewrite,[status(thm)],[])).
% 1.36/1.14 tff(1443,plain,
% 1.36/1.14 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp13) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp13))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp13) <=> (hskp13 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp13) <=> (hskp13 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp13) | hskp12) <=> ((hskp13 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp12))), rewrite(((hskp13 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp12) <=> (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp13) | hskp12) <=> (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))))),
% 1.36/1.14 inference(bind,[status(th)],[])).
% 1.36/1.14 tff(1444,plain,
% 1.36/1.14 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp13) | hskp12) <=> ![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.36/1.14 inference(quant_intro,[status(thm)],[1443])).
% 1.36/1.14 tff(1445,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp13) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause143')).
% 1.36/1.14 tff(1446,plain,
% 1.36/1.14 (![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.36/1.14 inference(modus_ponens,[status(thm)],[1445, 1444])).
% 1.36/1.14 tff(1447,plain,
% 1.36/1.14 (![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.36/1.14 inference(modus_ponens,[status(thm)],[1446, 1442])).
% 1.36/1.14 tff(1448,plain,(
% 1.36/1.14 ![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.36/1.14 inference(skolemize,[status(sab)],[1447])).
% 1.36/1.14 tff(1449,plain,
% 1.36/1.14 (![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.36/1.14 inference(modus_ponens,[status(thm)],[1448, 1441])).
% 1.36/1.14 tff(1450,plain,
% 1.36/1.14 (((~hskp5) | c0_1(a327)) <=> ((~hskp5) | c0_1(a327))),
% 1.36/1.14 inference(rewrite,[status(thm)],[])).
% 1.36/1.14 tff(1451,axiom,((~hskp5) | c0_1(a327)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 1.36/1.14 tff(1452,plain,
% 1.36/1.14 ((~hskp5) | c0_1(a327)),
% 1.36/1.14 inference(modus_ponens,[status(thm)],[1451, 1450])).
% 1.36/1.14 tff(1453,plain,
% 1.36/1.14 ((~hskp5) | c0_1(a327)),
% 1.36/1.14 inference(modus_ponens,[status(thm)],[1452, 1450])).
% 1.36/1.14 tff(1454,plain,
% 1.36/1.14 ((~hskp5) | c0_1(a327)),
% 1.36/1.14 inference(modus_ponens,[status(thm)],[1453, 1450])).
% 1.36/1.14 tff(1455,plain,
% 1.36/1.14 ((~hskp5) | c0_1(a327)),
% 1.36/1.14 inference(modus_ponens,[status(thm)],[1454, 1450])).
% 1.36/1.14 tff(1456,plain,
% 1.36/1.14 ((~hskp5) | c0_1(a327)),
% 1.36/1.14 inference(modus_ponens,[status(thm)],[1455, 1450])).
% 1.36/1.14 tff(1457,plain,
% 1.36/1.14 ((~hskp5) | c0_1(a327)),
% 1.36/1.14 inference(modus_ponens,[status(thm)],[1456, 1450])).
% 1.36/1.14 tff(1458,plain,
% 1.36/1.14 ((~hskp5) | c0_1(a327)),
% 1.36/1.14 inference(modus_ponens,[status(thm)],[1457, 1450])).
% 1.36/1.14 tff(1459,plain,
% 1.36/1.14 ((~hskp5) | c0_1(a327)),
% 1.36/1.14 inference(modus_ponens,[status(thm)],[1458, 1450])).
% 1.36/1.14 tff(1460,plain,
% 1.36/1.14 (c0_1(a327)),
% 1.36/1.14 inference(unit_resolution,[status(thm)],[1459, 1414])).
% 1.36/1.14 tff(1461,plain,
% 1.36/1.14 (((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp13 | hskp12 | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a327))) <=> ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp13 | hskp12 | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a327))),
% 1.36/1.14 inference(rewrite,[status(thm)],[])).
% 1.36/1.14 tff(1462,plain,
% 1.36/1.14 ((hskp13 | hskp12 | (~ndr1_0) | c2_1(a327) | (~c0_1(a327)) | (~c1_1(a327))) <=> (hskp13 | hskp12 | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a327))),
% 1.36/1.14 inference(rewrite,[status(thm)],[])).
% 1.36/1.14 tff(1463,plain,
% 1.36/1.14 (((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp13 | hskp12 | (~ndr1_0) | c2_1(a327) | (~c0_1(a327)) | (~c1_1(a327)))) <=> ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp13 | hskp12 | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a327)))),
% 1.36/1.14 inference(monotonicity,[status(thm)],[1462])).
% 1.36/1.14 tff(1464,plain,
% 1.36/1.14 (((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp13 | hskp12 | (~ndr1_0) | c2_1(a327) | (~c0_1(a327)) | (~c1_1(a327)))) <=> ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp13 | hskp12 | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a327))),
% 1.36/1.14 inference(transitivity,[status(thm)],[1463, 1461])).
% 1.36/1.14 tff(1465,plain,
% 1.36/1.14 ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp13 | hskp12 | (~ndr1_0) | c2_1(a327) | (~c0_1(a327)) | (~c1_1(a327)))),
% 1.36/1.14 inference(quant_inst,[status(thm)],[])).
% 1.36/1.14 tff(1466,plain,
% 1.36/1.14 ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp13 | hskp12 | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a327)),
% 1.36/1.14 inference(modus_ponens,[status(thm)],[1465, 1464])).
% 1.36/1.14 tff(1467,plain,
% 1.36/1.14 (hskp13 | hskp12 | c2_1(a327)),
% 1.36/1.14 inference(unit_resolution,[status(thm)],[1466, 152, 1460, 1431, 1449])).
% 1.36/1.14 tff(1468,plain,
% 1.36/1.14 (hskp12),
% 1.36/1.14 inference(unit_resolution,[status(thm)],[1467, 1439, 921])).
% 1.36/1.14 tff(1469,plain,
% 1.36/1.14 (c3_1(a345)),
% 1.36/1.14 inference(unit_resolution,[status(thm)],[303, 1468])).
% 1.36/1.14 tff(1470,plain,
% 1.36/1.14 (c0_1(a345)),
% 1.36/1.14 inference(unit_resolution,[status(thm)],[314, 1468])).
% 1.36/1.14 tff(1471,plain,
% 1.36/1.14 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c0_1(a345)) | (~c3_1(a345)) | (~c1_1(a345)) | (~c1_1(a353)) | (~c3_1(a353)) | (~c2_1(a353)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c0_1(a345)) | (~c3_1(a345)) | (~c1_1(a345)) | (~c1_1(a353)) | (~c3_1(a353)) | (~c2_1(a353)))),
% 1.36/1.14 inference(rewrite,[status(thm)],[])).
% 1.36/1.14 tff(1472,plain,
% 1.36/1.14 ((hskp10 | (~ndr1_0) | (~c2_1(a353)) | (~c3_1(a353)) | (~c1_1(a353)) | (~c3_1(a345)) | (~c1_1(a345)) | (~c0_1(a345))) <=> (hskp10 | (~ndr1_0) | (~c0_1(a345)) | (~c3_1(a345)) | (~c1_1(a345)) | (~c1_1(a353)) | (~c3_1(a353)) | (~c2_1(a353)))),
% 1.36/1.14 inference(rewrite,[status(thm)],[])).
% 1.36/1.14 tff(1473,plain,
% 1.36/1.14 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a353)) | (~c3_1(a353)) | (~c1_1(a353)) | (~c3_1(a345)) | (~c1_1(a345)) | (~c0_1(a345)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c0_1(a345)) | (~c3_1(a345)) | (~c1_1(a345)) | (~c1_1(a353)) | (~c3_1(a353)) | (~c2_1(a353))))),
% 1.36/1.14 inference(monotonicity,[status(thm)],[1472])).
% 1.36/1.14 tff(1474,plain,
% 1.36/1.14 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a353)) | (~c3_1(a353)) | (~c1_1(a353)) | (~c3_1(a345)) | (~c1_1(a345)) | (~c0_1(a345)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c0_1(a345)) | (~c3_1(a345)) | (~c1_1(a345)) | (~c1_1(a353)) | (~c3_1(a353)) | (~c2_1(a353)))),
% 1.36/1.14 inference(transitivity,[status(thm)],[1473, 1471])).
% 1.36/1.14 tff(1475,plain,
% 1.36/1.14 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a353)) | (~c3_1(a353)) | (~c1_1(a353)) | (~c3_1(a345)) | (~c1_1(a345)) | (~c0_1(a345)))),
% 1.36/1.14 inference(quant_inst,[status(thm)],[])).
% 1.36/1.14 tff(1476,plain,
% 1.36/1.14 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c0_1(a345)) | (~c3_1(a345)) | (~c1_1(a345)) | (~c1_1(a353)) | (~c3_1(a353)) | (~c2_1(a353))),
% 1.36/1.14 inference(modus_ponens,[status(thm)],[1475, 1474])).
% 1.36/1.14 tff(1477,plain,
% 1.36/1.14 (~c1_1(a345)),
% 1.36/1.14 inference(unit_resolution,[status(thm)],[1476, 152, 920, 917, 916, 1470, 1469, 425, 929])).
% 1.36/1.14 tff(1478,plain,
% 1.36/1.14 (~c2_1(a345)),
% 1.36/1.14 inference(unit_resolution,[status(thm)],[332, 1468])).
% 1.36/1.14 tff(1479,plain,
% 1.36/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c2_1(a349) | c2_1(a345) | (~ndr1_0) | c1_1(a345) | (~c0_1(a345)) | c0_1(a349) | (~c3_1(a349)) | (~c1_1(a349)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c2_1(a349) | c2_1(a345) | (~ndr1_0) | c1_1(a345) | (~c0_1(a345)) | c0_1(a349) | (~c3_1(a349)) | (~c1_1(a349)))),
% 1.36/1.14 inference(rewrite,[status(thm)],[])).
% 1.36/1.14 tff(1480,plain,
% 1.36/1.14 (((~ndr1_0) | c2_1(a349) | (~c3_1(a349)) | (~c1_1(a349)) | c2_1(a345) | c1_1(a345) | (~c0_1(a345)) | c0_1(a349) | (~c1_1(a349)) | (~c3_1(a349))) <=> (c2_1(a349) | c2_1(a345) | (~ndr1_0) | c1_1(a345) | (~c0_1(a345)) | c0_1(a349) | (~c3_1(a349)) | (~c1_1(a349)))),
% 1.36/1.14 inference(rewrite,[status(thm)],[])).
% 1.36/1.14 tff(1481,plain,
% 1.36/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a349) | (~c3_1(a349)) | (~c1_1(a349)) | c2_1(a345) | c1_1(a345) | (~c0_1(a345)) | c0_1(a349) | (~c1_1(a349)) | (~c3_1(a349)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c2_1(a349) | c2_1(a345) | (~ndr1_0) | c1_1(a345) | (~c0_1(a345)) | c0_1(a349) | (~c3_1(a349)) | (~c1_1(a349))))),
% 1.36/1.14 inference(monotonicity,[status(thm)],[1480])).
% 1.36/1.14 tff(1482,plain,
% 1.36/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a349) | (~c3_1(a349)) | (~c1_1(a349)) | c2_1(a345) | c1_1(a345) | (~c0_1(a345)) | c0_1(a349) | (~c1_1(a349)) | (~c3_1(a349)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c2_1(a349) | c2_1(a345) | (~ndr1_0) | c1_1(a345) | (~c0_1(a345)) | c0_1(a349) | (~c3_1(a349)) | (~c1_1(a349)))),
% 1.36/1.14 inference(transitivity,[status(thm)],[1481, 1479])).
% 1.36/1.14 tff(1483,plain,
% 1.36/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a349) | (~c3_1(a349)) | (~c1_1(a349)) | c2_1(a345) | c1_1(a345) | (~c0_1(a345)) | c0_1(a349) | (~c1_1(a349)) | (~c3_1(a349)))),
% 1.36/1.14 inference(quant_inst,[status(thm)],[])).
% 1.36/1.14 tff(1484,plain,
% 1.36/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c2_1(a349) | c2_1(a345) | (~ndr1_0) | c1_1(a345) | (~c0_1(a345)) | c0_1(a349) | (~c3_1(a349)) | (~c1_1(a349))),
% 1.36/1.14 inference(modus_ponens,[status(thm)],[1483, 1482])).
% 1.36/1.14 tff(1485,plain,
% 1.36/1.14 ($false),
% 1.36/1.14 inference(unit_resolution,[status(thm)],[1484, 152, 918, 919, 1470, 894, 1478, 327, 1477, 937])).
% 1.36/1.14 tff(1486,plain,(hskp13 | (~c1_1(a349)) | (~c3_1(a349)) | c2_1(a349) | hskp10 | (~c1_1(a353)) | (~c2_1(a353)) | hskp14 | c0_1(a353)), inference(lemma,lemma(discharge,[]))).
% 1.36/1.14 tff(1487,plain,
% 1.36/1.14 (hskp13),
% 1.36/1.14 inference(unit_resolution,[status(thm)],[1486, 920, 919, 894, 918, 917, 916, 11, 915])).
% 1.36/1.14 tff(1488,plain,
% 1.36/1.14 (~c3_1(a346)),
% 1.36/1.14 inference(unit_resolution,[status(thm)],[554, 1487])).
% 1.36/1.14 tff(1489,plain,
% 1.36/1.14 (c2_1(a346)),
% 1.36/1.14 inference(unit_resolution,[status(thm)],[565, 1487])).
% 1.36/1.14 tff(1490,plain,
% 1.36/1.14 (c0_1(a346)),
% 1.36/1.14 inference(unit_resolution,[status(thm)],[576, 1487])).
% 1.36/1.14 tff(1491,plain,
% 1.36/1.14 (((~![U: $i] : (hskp10 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp10 | hskp3 | c3_1(a346) | (~ndr1_0) | (~c0_1(a346)) | (~c2_1(a346)))) <=> ((~![U: $i] : (hskp10 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp10 | hskp3 | c3_1(a346) | (~ndr1_0) | (~c0_1(a346)) | (~c2_1(a346)))),
% 1.36/1.14 inference(rewrite,[status(thm)],[])).
% 1.36/1.14 tff(1492,plain,
% 1.36/1.14 ((hskp10 | hskp3 | (~ndr1_0) | c3_1(a346) | (~c2_1(a346)) | (~c0_1(a346))) <=> (hskp10 | hskp3 | c3_1(a346) | (~ndr1_0) | (~c0_1(a346)) | (~c2_1(a346)))),
% 1.36/1.14 inference(rewrite,[status(thm)],[])).
% 1.36/1.14 tff(1493,plain,
% 1.36/1.14 (((~![U: $i] : (hskp10 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp10 | hskp3 | (~ndr1_0) | c3_1(a346) | (~c2_1(a346)) | (~c0_1(a346)))) <=> ((~![U: $i] : (hskp10 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp10 | hskp3 | c3_1(a346) | (~ndr1_0) | (~c0_1(a346)) | (~c2_1(a346))))),
% 1.36/1.14 inference(monotonicity,[status(thm)],[1492])).
% 1.36/1.14 tff(1494,plain,
% 1.36/1.14 (((~![U: $i] : (hskp10 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp10 | hskp3 | (~ndr1_0) | c3_1(a346) | (~c2_1(a346)) | (~c0_1(a346)))) <=> ((~![U: $i] : (hskp10 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp10 | hskp3 | c3_1(a346) | (~ndr1_0) | (~c0_1(a346)) | (~c2_1(a346)))),
% 1.36/1.14 inference(transitivity,[status(thm)],[1493, 1491])).
% 1.36/1.14 tff(1495,plain,
% 1.36/1.14 ((~![U: $i] : (hskp10 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp10 | hskp3 | (~ndr1_0) | c3_1(a346) | (~c2_1(a346)) | (~c0_1(a346)))),
% 1.36/1.14 inference(quant_inst,[status(thm)],[])).
% 1.36/1.14 tff(1496,plain,
% 1.36/1.14 ((~![U: $i] : (hskp10 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp10 | hskp3 | c3_1(a346) | (~ndr1_0) | (~c0_1(a346)) | (~c2_1(a346))),
% 1.36/1.14 inference(modus_ponens,[status(thm)],[1495, 1494])).
% 1.36/1.14 tff(1497,plain,
% 1.36/1.14 (hskp3),
% 1.36/1.14 inference(unit_resolution,[status(thm)],[1496, 152, 920, 1490, 1489, 1488, 914])).
% 1.36/1.14 tff(1498,plain,
% 1.36/1.14 (((~hskp3) | (~c2_1(a325))) <=> ((~hskp3) | (~c2_1(a325)))),
% 1.36/1.14 inference(rewrite,[status(thm)],[])).
% 1.36/1.14 tff(1499,plain,
% 1.36/1.14 (((~c2_1(a325)) | (~hskp3)) <=> ((~hskp3) | (~c2_1(a325)))),
% 1.36/1.14 inference(rewrite,[status(thm)],[])).
% 1.36/1.14 tff(1500,axiom,((~c2_1(a325)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause118')).
% 1.36/1.14 tff(1501,plain,
% 1.36/1.14 ((~hskp3) | (~c2_1(a325))),
% 1.36/1.14 inference(modus_ponens,[status(thm)],[1500, 1499])).
% 1.36/1.14 tff(1502,plain,
% 1.36/1.14 ((~hskp3) | (~c2_1(a325))),
% 1.36/1.14 inference(modus_ponens,[status(thm)],[1501, 1498])).
% 1.36/1.14 tff(1503,plain,
% 1.36/1.14 (~c2_1(a325)),
% 1.36/1.14 inference(unit_resolution,[status(thm)],[1502, 1497])).
% 1.36/1.14 tff(1504,plain,
% 1.36/1.14 (((~hskp3) | c0_1(a325)) <=> ((~hskp3) | c0_1(a325))),
% 1.36/1.14 inference(rewrite,[status(thm)],[])).
% 1.36/1.14 tff(1505,axiom,((~hskp3) | c0_1(a325)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause77')).
% 1.36/1.14 tff(1506,plain,
% 1.36/1.14 ((~hskp3) | c0_1(a325)),
% 1.36/1.14 inference(modus_ponens,[status(thm)],[1505, 1504])).
% 1.36/1.14 tff(1507,plain,
% 1.36/1.14 ((~hskp3) | c0_1(a325)),
% 1.36/1.14 inference(modus_ponens,[status(thm)],[1506, 1504])).
% 1.36/1.14 tff(1508,plain,
% 1.36/1.15 ((~hskp3) | c0_1(a325)),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[1507, 1504])).
% 1.36/1.15 tff(1509,plain,
% 1.36/1.15 ((~hskp3) | c0_1(a325)),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[1508, 1504])).
% 1.36/1.15 tff(1510,plain,
% 1.36/1.15 ((~hskp3) | c0_1(a325)),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[1509, 1504])).
% 1.36/1.15 tff(1511,plain,
% 1.36/1.15 ((~hskp3) | c0_1(a325)),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[1510, 1504])).
% 1.36/1.15 tff(1512,plain,
% 1.36/1.15 ((~hskp3) | c0_1(a325)),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[1511, 1504])).
% 1.36/1.15 tff(1513,plain,
% 1.36/1.15 ((~hskp3) | c0_1(a325)),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[1512, 1504])).
% 1.36/1.15 tff(1514,plain,
% 1.36/1.15 (c0_1(a325)),
% 1.36/1.15 inference(unit_resolution,[status(thm)],[1513, 1497])).
% 1.36/1.15 tff(1515,plain,
% 1.36/1.15 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp10 | c2_1(a325) | (~ndr1_0) | c3_1(a325) | (~c0_1(a325)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp10 | c2_1(a325) | (~ndr1_0) | c3_1(a325) | (~c0_1(a325)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.36/1.15 inference(rewrite,[status(thm)],[])).
% 1.36/1.15 tff(1516,plain,
% 1.36/1.15 ((hskp10 | (~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a325) | c3_1(a325) | (~c0_1(a325))) <=> (hskp10 | c2_1(a325) | (~ndr1_0) | c3_1(a325) | (~c0_1(a325)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.36/1.15 inference(rewrite,[status(thm)],[])).
% 1.36/1.15 tff(1517,plain,
% 1.36/1.15 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a325) | c3_1(a325) | (~c0_1(a325)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp10 | c2_1(a325) | (~ndr1_0) | c3_1(a325) | (~c0_1(a325)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))))),
% 1.36/1.15 inference(monotonicity,[status(thm)],[1516])).
% 1.36/1.15 tff(1518,plain,
% 1.36/1.15 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a325) | c3_1(a325) | (~c0_1(a325)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp10 | c2_1(a325) | (~ndr1_0) | c3_1(a325) | (~c0_1(a325)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.36/1.15 inference(transitivity,[status(thm)],[1517, 1515])).
% 1.36/1.15 tff(1519,plain,
% 1.36/1.15 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a325) | c3_1(a325) | (~c0_1(a325)))),
% 1.36/1.15 inference(quant_inst,[status(thm)],[])).
% 1.36/1.15 tff(1520,plain,
% 1.36/1.15 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp10 | c2_1(a325) | (~ndr1_0) | c3_1(a325) | (~c0_1(a325)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[1519, 1518])).
% 1.36/1.15 tff(1521,plain,
% 1.36/1.15 (c3_1(a325)),
% 1.36/1.15 inference(unit_resolution,[status(thm)],[1520, 152, 920, 1208, 1207, 1206, 1514, 1503, 904])).
% 1.36/1.15 tff(1522,plain,
% 1.36/1.15 (((~hskp3) | c1_1(a325)) <=> ((~hskp3) | c1_1(a325))),
% 1.36/1.15 inference(rewrite,[status(thm)],[])).
% 1.36/1.15 tff(1523,axiom,((~hskp3) | c1_1(a325)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause78')).
% 1.36/1.15 tff(1524,plain,
% 1.36/1.15 ((~hskp3) | c1_1(a325)),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[1523, 1522])).
% 1.36/1.15 tff(1525,plain,
% 1.36/1.15 ((~hskp3) | c1_1(a325)),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[1524, 1522])).
% 1.36/1.15 tff(1526,plain,
% 1.36/1.15 ((~hskp3) | c1_1(a325)),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[1525, 1522])).
% 1.36/1.15 tff(1527,plain,
% 1.36/1.15 ((~hskp3) | c1_1(a325)),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[1526, 1522])).
% 1.36/1.15 tff(1528,plain,
% 1.36/1.15 ((~hskp3) | c1_1(a325)),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[1527, 1522])).
% 1.36/1.15 tff(1529,plain,
% 1.36/1.15 ((~hskp3) | c1_1(a325)),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[1528, 1522])).
% 1.36/1.15 tff(1530,plain,
% 1.36/1.15 ((~hskp3) | c1_1(a325)),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[1529, 1522])).
% 1.36/1.15 tff(1531,plain,
% 1.36/1.15 ((~hskp3) | c1_1(a325)),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[1530, 1522])).
% 1.36/1.15 tff(1532,plain,
% 1.36/1.15 (c1_1(a325)),
% 1.36/1.15 inference(unit_resolution,[status(thm)],[1531, 1497])).
% 1.36/1.15 tff(1533,plain,
% 1.36/1.15 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a325)) | (~c1_1(a325)) | (~c0_1(a325)) | (~c3_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c3_1(a325)) | (~c1_1(a325)) | (~c0_1(a325)) | (~c3_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.36/1.15 inference(rewrite,[status(thm)],[])).
% 1.36/1.15 tff(1534,plain,
% 1.36/1.15 ((hskp10 | (~ndr1_0) | (~c2_1(a343)) | (~c3_1(a343)) | (~c1_1(a343)) | (~c3_1(a325)) | (~c1_1(a325)) | (~c0_1(a325))) <=> (hskp10 | (~ndr1_0) | (~c3_1(a325)) | (~c1_1(a325)) | (~c0_1(a325)) | (~c3_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.36/1.15 inference(rewrite,[status(thm)],[])).
% 1.36/1.15 tff(1535,plain,
% 1.36/1.15 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a343)) | (~c3_1(a343)) | (~c1_1(a343)) | (~c3_1(a325)) | (~c1_1(a325)) | (~c0_1(a325)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a325)) | (~c1_1(a325)) | (~c0_1(a325)) | (~c3_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))))),
% 1.36/1.15 inference(monotonicity,[status(thm)],[1534])).
% 1.36/1.15 tff(1536,plain,
% 1.36/1.15 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a343)) | (~c3_1(a343)) | (~c1_1(a343)) | (~c3_1(a325)) | (~c1_1(a325)) | (~c0_1(a325)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c3_1(a325)) | (~c1_1(a325)) | (~c0_1(a325)) | (~c3_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.36/1.15 inference(transitivity,[status(thm)],[1535, 1533])).
% 1.36/1.15 tff(1537,plain,
% 1.36/1.15 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a343)) | (~c3_1(a343)) | (~c1_1(a343)) | (~c3_1(a325)) | (~c1_1(a325)) | (~c0_1(a325)))),
% 1.36/1.15 inference(quant_inst,[status(thm)],[])).
% 1.36/1.15 tff(1538,plain,
% 1.36/1.15 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c3_1(a325)) | (~c1_1(a325)) | (~c0_1(a325)) | (~c3_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[1537, 1536])).
% 1.36/1.15 tff(1539,plain,
% 1.36/1.15 (~c3_1(a343)),
% 1.36/1.15 inference(unit_resolution,[status(thm)],[1538, 152, 920, 1207, 1206, 1514, 1532, 425, 1521])).
% 1.36/1.15 tff(1540,plain,
% 1.36/1.15 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 1.36/1.15 inference(bind,[status(th)],[])).
% 1.36/1.15 tff(1541,plain,
% 1.36/1.15 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.36/1.15 inference(quant_intro,[status(thm)],[1540])).
% 1.36/1.15 tff(1542,plain,
% 1.36/1.15 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.36/1.15 inference(rewrite,[status(thm)],[])).
% 1.36/1.15 tff(1543,plain,
% 1.36/1.15 (^[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) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | hskp8) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp8))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 1.36/1.15 inference(bind,[status(th)],[])).
% 1.36/1.15 tff(1544,plain,
% 1.36/1.15 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.36/1.15 inference(quant_intro,[status(thm)],[1543])).
% 1.36/1.15 tff(1545,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause183')).
% 1.36/1.15 tff(1546,plain,
% 1.36/1.15 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[1545, 1544])).
% 1.36/1.15 tff(1547,plain,
% 1.36/1.15 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[1546, 1542])).
% 1.36/1.15 tff(1548,plain,(
% 1.36/1.15 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.36/1.15 inference(skolemize,[status(sab)],[1547])).
% 1.36/1.15 tff(1549,plain,
% 1.36/1.15 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[1548, 1541])).
% 1.36/1.15 tff(1550,plain,
% 1.36/1.15 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | c3_1(a327) | c2_1(a325) | (~ndr1_0) | (~c1_1(a325)) | (~c0_1(a325)) | (~c0_1(a327)) | (~c1_1(a327)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | c3_1(a327) | c2_1(a325) | (~ndr1_0) | (~c1_1(a325)) | (~c0_1(a325)) | (~c0_1(a327)) | (~c1_1(a327)))),
% 1.36/1.15 inference(rewrite,[status(thm)],[])).
% 1.36/1.15 tff(1551,plain,
% 1.36/1.15 ((hskp8 | (~ndr1_0) | c3_1(a327) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a325) | (~c1_1(a325)) | (~c0_1(a325))) <=> (hskp8 | c3_1(a327) | c2_1(a325) | (~ndr1_0) | (~c1_1(a325)) | (~c0_1(a325)) | (~c0_1(a327)) | (~c1_1(a327)))),
% 1.36/1.15 inference(rewrite,[status(thm)],[])).
% 1.36/1.15 tff(1552,plain,
% 1.36/1.15 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a327) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a325) | (~c1_1(a325)) | (~c0_1(a325)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | c3_1(a327) | c2_1(a325) | (~ndr1_0) | (~c1_1(a325)) | (~c0_1(a325)) | (~c0_1(a327)) | (~c1_1(a327))))),
% 1.36/1.15 inference(monotonicity,[status(thm)],[1551])).
% 1.36/1.15 tff(1553,plain,
% 1.36/1.15 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a327) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a325) | (~c1_1(a325)) | (~c0_1(a325)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | c3_1(a327) | c2_1(a325) | (~ndr1_0) | (~c1_1(a325)) | (~c0_1(a325)) | (~c0_1(a327)) | (~c1_1(a327)))),
% 1.36/1.15 inference(transitivity,[status(thm)],[1552, 1550])).
% 1.36/1.15 tff(1554,plain,
% 1.36/1.15 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a327) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a325) | (~c1_1(a325)) | (~c0_1(a325)))),
% 1.36/1.15 inference(quant_inst,[status(thm)],[])).
% 1.36/1.15 tff(1555,plain,
% 1.36/1.15 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | c3_1(a327) | c2_1(a325) | (~ndr1_0) | (~c1_1(a325)) | (~c0_1(a325)) | (~c0_1(a327)) | (~c1_1(a327))),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[1554, 1553])).
% 1.36/1.15 tff(1556,plain,
% 1.36/1.15 (hskp8),
% 1.36/1.15 inference(unit_resolution,[status(thm)],[1555, 152, 1460, 1431, 1514, 1532, 1420, 1503, 1549])).
% 1.36/1.15 tff(1557,plain,
% 1.36/1.15 (~c2_1(a332)),
% 1.36/1.15 inference(unit_resolution,[status(thm)],[700, 1556])).
% 1.36/1.15 tff(1558,plain,
% 1.36/1.15 (~c0_1(a332)),
% 1.36/1.15 inference(unit_resolution,[status(thm)],[706, 1556])).
% 1.36/1.15 tff(1559,plain,
% 1.36/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a332) | c2_1(a332) | (~ndr1_0) | (~c1_1(a332)) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a332) | c2_1(a332) | (~ndr1_0) | (~c1_1(a332)) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.36/1.15 inference(rewrite,[status(thm)],[])).
% 1.36/1.15 tff(1560,plain,
% 1.36/1.15 (((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343)) | c2_1(a332) | c0_1(a332) | (~c1_1(a332))) <=> (c0_1(a332) | c2_1(a332) | (~ndr1_0) | (~c1_1(a332)) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.36/1.15 inference(rewrite,[status(thm)],[])).
% 1.36/1.15 tff(1561,plain,
% 1.36/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343)) | c2_1(a332) | c0_1(a332) | (~c1_1(a332)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a332) | c2_1(a332) | (~ndr1_0) | (~c1_1(a332)) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343))))),
% 1.36/1.15 inference(monotonicity,[status(thm)],[1560])).
% 1.36/1.15 tff(1562,plain,
% 1.36/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343)) | c2_1(a332) | c0_1(a332) | (~c1_1(a332)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a332) | c2_1(a332) | (~ndr1_0) | (~c1_1(a332)) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.36/1.15 inference(transitivity,[status(thm)],[1561, 1559])).
% 1.36/1.15 tff(1563,plain,
% 1.36/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343)) | c2_1(a332) | c0_1(a332) | (~c1_1(a332)))),
% 1.36/1.15 inference(quant_inst,[status(thm)],[])).
% 1.36/1.15 tff(1564,plain,
% 1.36/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a332) | c2_1(a332) | (~ndr1_0) | (~c1_1(a332)) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343))),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[1563, 1562])).
% 1.36/1.15 tff(1565,plain,
% 1.36/1.15 (~c1_1(a332)),
% 1.36/1.15 inference(unit_resolution,[status(thm)],[1564, 152, 1208, 1207, 1206, 1558, 1557, 21, 1539])).
% 1.36/1.15 tff(1566,plain,
% 1.36/1.15 (^[V: $i, U: $i] : refl((hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))),
% 1.36/1.15 inference(bind,[status(th)],[])).
% 1.36/1.15 tff(1567,plain,
% 1.36/1.15 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.36/1.15 inference(quant_intro,[status(thm)],[1566])).
% 1.36/1.15 tff(1568,plain,
% 1.36/1.15 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.36/1.15 inference(rewrite,[status(thm)],[])).
% 1.36/1.15 tff(1569,plain,
% 1.36/1.15 (^[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) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp21) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp21))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))))),
% 1.36/1.15 inference(bind,[status(th)],[])).
% 1.36/1.15 tff(1570,plain,
% 1.36/1.15 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp21) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.36/1.15 inference(quant_intro,[status(thm)],[1569])).
% 1.36/1.15 tff(1571,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause161')).
% 1.36/1.15 tff(1572,plain,
% 1.36/1.15 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[1571, 1570])).
% 1.36/1.15 tff(1573,plain,
% 1.36/1.15 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[1572, 1568])).
% 1.36/1.15 tff(1574,plain,(
% 1.36/1.15 ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.36/1.15 inference(skolemize,[status(sab)],[1573])).
% 1.36/1.15 tff(1575,plain,
% 1.36/1.15 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[1574, 1567])).
% 1.36/1.15 tff(1576,plain,
% 1.36/1.15 (~c3_1(a332)),
% 1.36/1.15 inference(unit_resolution,[status(thm)],[694, 1556])).
% 1.36/1.15 tff(1577,plain,
% 1.36/1.15 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | c2_1(a332) | c3_1(a332) | (~ndr1_0) | c1_1(a332) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp21 | c2_1(a332) | c3_1(a332) | (~ndr1_0) | c1_1(a332) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343)))),
% 1.36/1.15 inference(rewrite,[status(thm)],[])).
% 1.36/1.15 tff(1578,plain,
% 1.36/1.15 ((hskp21 | (~ndr1_0) | c3_1(a343) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a332) | c1_1(a332) | c3_1(a332)) <=> (hskp21 | c2_1(a332) | c3_1(a332) | (~ndr1_0) | c1_1(a332) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343)))),
% 1.36/1.15 inference(rewrite,[status(thm)],[])).
% 1.36/1.15 tff(1579,plain,
% 1.36/1.15 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | (~ndr1_0) | c3_1(a343) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a332) | c1_1(a332) | c3_1(a332))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | c2_1(a332) | c3_1(a332) | (~ndr1_0) | c1_1(a332) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343))))),
% 1.36/1.15 inference(monotonicity,[status(thm)],[1578])).
% 1.36/1.15 tff(1580,plain,
% 1.36/1.15 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | (~ndr1_0) | c3_1(a343) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a332) | c1_1(a332) | c3_1(a332))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp21 | c2_1(a332) | c3_1(a332) | (~ndr1_0) | c1_1(a332) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343)))),
% 1.36/1.15 inference(transitivity,[status(thm)],[1579, 1577])).
% 1.36/1.15 tff(1581,plain,
% 1.36/1.15 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | (~ndr1_0) | c3_1(a343) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a332) | c1_1(a332) | c3_1(a332))),
% 1.36/1.15 inference(quant_inst,[status(thm)],[])).
% 1.36/1.15 tff(1582,plain,
% 1.36/1.15 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp21 | c2_1(a332) | c3_1(a332) | (~ndr1_0) | c1_1(a332) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343))),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[1581, 1580])).
% 1.36/1.15 tff(1583,plain,
% 1.36/1.15 (hskp21),
% 1.36/1.15 inference(unit_resolution,[status(thm)],[1582, 152, 1208, 1207, 1557, 1576, 1575, 1539, 1565])).
% 1.36/1.15 tff(1584,plain,
% 1.36/1.15 (((~hskp21) | (~c2_1(a359))) <=> ((~hskp21) | (~c2_1(a359)))),
% 1.36/1.15 inference(rewrite,[status(thm)],[])).
% 1.36/1.15 tff(1585,plain,
% 1.36/1.15 (((~c2_1(a359)) | (~hskp21)) <=> ((~hskp21) | (~c2_1(a359)))),
% 1.36/1.15 inference(rewrite,[status(thm)],[])).
% 1.36/1.15 tff(1586,axiom,((~c2_1(a359)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause89')).
% 1.36/1.15 tff(1587,plain,
% 1.36/1.15 ((~hskp21) | (~c2_1(a359))),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[1586, 1585])).
% 1.36/1.15 tff(1588,plain,
% 1.36/1.15 ((~hskp21) | (~c2_1(a359))),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[1587, 1584])).
% 1.36/1.15 tff(1589,plain,
% 1.36/1.15 (~c2_1(a359)),
% 1.36/1.15 inference(unit_resolution,[status(thm)],[1588, 1583])).
% 1.36/1.15 tff(1590,plain,
% 1.36/1.15 (((~hskp21) | c3_1(a359)) <=> ((~hskp21) | c3_1(a359))),
% 1.36/1.15 inference(rewrite,[status(thm)],[])).
% 1.36/1.15 tff(1591,axiom,((~hskp21) | c3_1(a359)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause53')).
% 1.36/1.15 tff(1592,plain,
% 1.36/1.15 ((~hskp21) | c3_1(a359)),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[1591, 1590])).
% 1.36/1.15 tff(1593,plain,
% 1.36/1.15 ((~hskp21) | c3_1(a359)),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[1592, 1590])).
% 1.36/1.15 tff(1594,plain,
% 1.36/1.15 ((~hskp21) | c3_1(a359)),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[1593, 1590])).
% 1.36/1.15 tff(1595,plain,
% 1.36/1.15 ((~hskp21) | c3_1(a359)),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[1594, 1590])).
% 1.36/1.15 tff(1596,plain,
% 1.36/1.15 ((~hskp21) | c3_1(a359)),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[1595, 1590])).
% 1.36/1.15 tff(1597,plain,
% 1.36/1.15 ((~hskp21) | c3_1(a359)),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[1596, 1590])).
% 1.36/1.15 tff(1598,plain,
% 1.36/1.15 ((~hskp21) | c3_1(a359)),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[1597, 1590])).
% 1.36/1.15 tff(1599,plain,
% 1.36/1.15 ((~hskp21) | c3_1(a359)),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[1598, 1590])).
% 1.36/1.15 tff(1600,plain,
% 1.36/1.15 (c3_1(a359)),
% 1.36/1.15 inference(unit_resolution,[status(thm)],[1599, 1583])).
% 1.36/1.15 tff(1601,plain,
% 1.36/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a359) | c2_1(a349) | (~ndr1_0) | (~c3_1(a349)) | (~c1_1(a349)) | c1_1(a359) | (~c3_1(a359)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a359) | c2_1(a349) | (~ndr1_0) | (~c3_1(a349)) | (~c1_1(a349)) | c1_1(a359) | (~c3_1(a359)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.36/1.15 inference(rewrite,[status(thm)],[])).
% 1.36/1.15 tff(1602,plain,
% 1.36/1.15 (((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a349) | (~c3_1(a349)) | (~c1_1(a349)) | c2_1(a359) | c1_1(a359) | (~c3_1(a359))) <=> (c2_1(a359) | c2_1(a349) | (~ndr1_0) | (~c3_1(a349)) | (~c1_1(a349)) | c1_1(a359) | (~c3_1(a359)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.36/1.15 inference(rewrite,[status(thm)],[])).
% 1.36/1.15 tff(1603,plain,
% 1.36/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a349) | (~c3_1(a349)) | (~c1_1(a349)) | c2_1(a359) | c1_1(a359) | (~c3_1(a359)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a359) | c2_1(a349) | (~ndr1_0) | (~c3_1(a349)) | (~c1_1(a349)) | c1_1(a359) | (~c3_1(a359)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))))),
% 1.36/1.15 inference(monotonicity,[status(thm)],[1602])).
% 1.36/1.15 tff(1604,plain,
% 1.36/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a349) | (~c3_1(a349)) | (~c1_1(a349)) | c2_1(a359) | c1_1(a359) | (~c3_1(a359)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a359) | c2_1(a349) | (~ndr1_0) | (~c3_1(a349)) | (~c1_1(a349)) | c1_1(a359) | (~c3_1(a359)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.36/1.15 inference(transitivity,[status(thm)],[1603, 1601])).
% 1.36/1.15 tff(1605,plain,
% 1.36/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a349) | (~c3_1(a349)) | (~c1_1(a349)) | c2_1(a359) | c1_1(a359) | (~c3_1(a359)))),
% 1.36/1.15 inference(quant_inst,[status(thm)],[])).
% 1.36/1.15 tff(1606,plain,
% 1.36/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a359) | c2_1(a349) | (~ndr1_0) | (~c3_1(a349)) | (~c1_1(a349)) | c1_1(a359) | (~c3_1(a359)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[1605, 1604])).
% 1.36/1.15 tff(1607,plain,
% 1.36/1.15 (c1_1(a359)),
% 1.36/1.15 inference(unit_resolution,[status(thm)],[1606, 152, 1208, 1207, 1206, 1600, 918, 919, 1589, 894, 788])).
% 1.36/1.15 tff(1608,plain,
% 1.36/1.15 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a325)) | (~c1_1(a325)) | (~c0_1(a325)) | (~c1_1(a353)) | (~c3_1(a353)) | (~c2_1(a353)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c3_1(a325)) | (~c1_1(a325)) | (~c0_1(a325)) | (~c1_1(a353)) | (~c3_1(a353)) | (~c2_1(a353)))),
% 1.36/1.15 inference(rewrite,[status(thm)],[])).
% 1.36/1.15 tff(1609,plain,
% 1.36/1.15 ((hskp10 | (~ndr1_0) | (~c2_1(a353)) | (~c3_1(a353)) | (~c1_1(a353)) | (~c3_1(a325)) | (~c1_1(a325)) | (~c0_1(a325))) <=> (hskp10 | (~ndr1_0) | (~c3_1(a325)) | (~c1_1(a325)) | (~c0_1(a325)) | (~c1_1(a353)) | (~c3_1(a353)) | (~c2_1(a353)))),
% 1.36/1.15 inference(rewrite,[status(thm)],[])).
% 1.36/1.15 tff(1610,plain,
% 1.36/1.15 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a353)) | (~c3_1(a353)) | (~c1_1(a353)) | (~c3_1(a325)) | (~c1_1(a325)) | (~c0_1(a325)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a325)) | (~c1_1(a325)) | (~c0_1(a325)) | (~c1_1(a353)) | (~c3_1(a353)) | (~c2_1(a353))))),
% 1.36/1.15 inference(monotonicity,[status(thm)],[1609])).
% 1.36/1.15 tff(1611,plain,
% 1.36/1.15 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a353)) | (~c3_1(a353)) | (~c1_1(a353)) | (~c3_1(a325)) | (~c1_1(a325)) | (~c0_1(a325)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c3_1(a325)) | (~c1_1(a325)) | (~c0_1(a325)) | (~c1_1(a353)) | (~c3_1(a353)) | (~c2_1(a353)))),
% 1.36/1.15 inference(transitivity,[status(thm)],[1610, 1608])).
% 1.36/1.15 tff(1612,plain,
% 1.36/1.15 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a353)) | (~c3_1(a353)) | (~c1_1(a353)) | (~c3_1(a325)) | (~c1_1(a325)) | (~c0_1(a325)))),
% 1.36/1.15 inference(quant_inst,[status(thm)],[])).
% 1.36/1.15 tff(1613,plain,
% 1.36/1.15 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | (~ndr1_0) | (~c3_1(a325)) | (~c1_1(a325)) | (~c0_1(a325)) | (~c1_1(a353)) | (~c3_1(a353)) | (~c2_1(a353))),
% 1.36/1.15 inference(modus_ponens,[status(thm)],[1612, 1611])).
% 1.36/1.16 tff(1614,plain,
% 1.36/1.16 (~c3_1(a353)),
% 1.36/1.16 inference(unit_resolution,[status(thm)],[1613, 152, 920, 917, 916, 1514, 1532, 425, 1521])).
% 1.36/1.16 tff(1615,plain,
% 1.36/1.16 (((~hskp21) | (~c0_1(a359))) <=> ((~hskp21) | (~c0_1(a359)))),
% 1.36/1.16 inference(rewrite,[status(thm)],[])).
% 1.36/1.16 tff(1616,plain,
% 1.36/1.16 (((~c0_1(a359)) | (~hskp21)) <=> ((~hskp21) | (~c0_1(a359)))),
% 1.36/1.16 inference(rewrite,[status(thm)],[])).
% 1.36/1.16 tff(1617,axiom,((~c0_1(a359)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause88')).
% 1.36/1.16 tff(1618,plain,
% 1.36/1.16 ((~hskp21) | (~c0_1(a359))),
% 1.36/1.16 inference(modus_ponens,[status(thm)],[1617, 1616])).
% 1.36/1.16 tff(1619,plain,
% 1.36/1.16 ((~hskp21) | (~c0_1(a359))),
% 1.36/1.16 inference(modus_ponens,[status(thm)],[1618, 1615])).
% 1.36/1.16 tff(1620,plain,
% 1.36/1.16 (~c0_1(a359)),
% 1.36/1.16 inference(unit_resolution,[status(thm)],[1619, 1583])).
% 1.36/1.16 tff(1621,plain,
% 1.36/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a359) | c2_1(a359) | (~ndr1_0) | (~c1_1(a353)) | c3_1(a353) | (~c2_1(a353)) | (~c1_1(a359)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a359) | c2_1(a359) | (~ndr1_0) | (~c1_1(a353)) | c3_1(a353) | (~c2_1(a353)) | (~c1_1(a359)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.36/1.16 inference(rewrite,[status(thm)],[])).
% 1.36/1.16 tff(1622,plain,
% 1.36/1.16 (((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c3_1(a353) | (~c1_1(a353)) | (~c2_1(a353)) | c2_1(a359) | c0_1(a359) | (~c1_1(a359))) <=> (c0_1(a359) | c2_1(a359) | (~ndr1_0) | (~c1_1(a353)) | c3_1(a353) | (~c2_1(a353)) | (~c1_1(a359)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.36/1.16 inference(rewrite,[status(thm)],[])).
% 1.36/1.16 tff(1623,plain,
% 1.36/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c3_1(a353) | (~c1_1(a353)) | (~c2_1(a353)) | c2_1(a359) | c0_1(a359) | (~c1_1(a359)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a359) | c2_1(a359) | (~ndr1_0) | (~c1_1(a353)) | c3_1(a353) | (~c2_1(a353)) | (~c1_1(a359)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))))),
% 1.36/1.16 inference(monotonicity,[status(thm)],[1622])).
% 1.36/1.16 tff(1624,plain,
% 1.36/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c3_1(a353) | (~c1_1(a353)) | (~c2_1(a353)) | c2_1(a359) | c0_1(a359) | (~c1_1(a359)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a359) | c2_1(a359) | (~ndr1_0) | (~c1_1(a353)) | c3_1(a353) | (~c2_1(a353)) | (~c1_1(a359)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.36/1.16 inference(transitivity,[status(thm)],[1623, 1621])).
% 1.36/1.16 tff(1625,plain,
% 1.36/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c3_1(a353) | (~c1_1(a353)) | (~c2_1(a353)) | c2_1(a359) | c0_1(a359) | (~c1_1(a359)))),
% 1.36/1.16 inference(quant_inst,[status(thm)],[])).
% 1.36/1.16 tff(1626,plain,
% 1.36/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a359) | c2_1(a359) | (~ndr1_0) | (~c1_1(a353)) | c3_1(a353) | (~c2_1(a353)) | (~c1_1(a359)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))),
% 1.36/1.16 inference(modus_ponens,[status(thm)],[1625, 1624])).
% 1.36/1.16 tff(1627,plain,
% 1.36/1.16 ($false),
% 1.36/1.16 inference(unit_resolution,[status(thm)],[1626, 152, 1208, 1207, 1206, 917, 916, 1620, 1589, 21, 1614, 1607])).
% 1.36/1.16 tff(1628,plain,(hskp10 | (~c1_1(a353)) | (~c2_1(a353)) | (~c1_1(a349)) | (~c3_1(a349)) | c2_1(a349) | hskp14 | c0_1(a353)), inference(lemma,lemma(discharge,[]))).
% 1.36/1.16 tff(1629,plain,
% 1.36/1.16 (hskp10),
% 1.36/1.16 inference(unit_resolution,[status(thm)],[1628, 893, 882, 848, 837, 826, 11, 871])).
% 1.36/1.16 tff(1630,plain,
% 1.36/1.16 (~c2_1(a337)),
% 1.36/1.16 inference(unit_resolution,[status(thm)],[444, 1629])).
% 1.36/1.16 tff(1631,plain,
% 1.36/1.16 (~c3_1(a337)),
% 1.36/1.16 inference(unit_resolution,[status(thm)],[438, 1629])).
% 1.36/1.16 tff(1632,assumption,(~c2_1(a337)), introduced(assumption)).
% 1.36/1.16 tff(1633,assumption,(~c3_1(a337)), introduced(assumption)).
% 1.36/1.16 tff(1634,assumption,(~c0_1(a337)), introduced(assumption)).
% 1.36/1.16 tff(1635,plain,
% 1.36/1.16 (~hskp10),
% 1.36/1.16 inference(unit_resolution,[status(thm)],[455, 1634])).
% 1.36/1.16 tff(1636,plain,
% 1.36/1.16 (hskp13),
% 1.36/1.16 inference(unit_resolution,[status(thm)],[1486, 1635, 919, 894, 918, 917, 916, 11, 915])).
% 1.36/1.16 tff(1637,plain,
% 1.36/1.16 (~c3_1(a346)),
% 1.36/1.16 inference(unit_resolution,[status(thm)],[554, 1636])).
% 1.36/1.16 tff(1638,plain,
% 1.36/1.16 (c2_1(a346)),
% 1.36/1.16 inference(unit_resolution,[status(thm)],[565, 1636])).
% 1.36/1.16 tff(1639,plain,
% 1.36/1.16 (c0_1(a346)),
% 1.36/1.16 inference(unit_resolution,[status(thm)],[576, 1636])).
% 1.36/1.16 tff(1640,plain,
% 1.36/1.16 (hskp3),
% 1.36/1.16 inference(unit_resolution,[status(thm)],[1496, 152, 1635, 1639, 1638, 1637, 914])).
% 1.36/1.16 tff(1641,plain,
% 1.36/1.16 (~c2_1(a325)),
% 1.36/1.16 inference(unit_resolution,[status(thm)],[1502, 1640])).
% 1.36/1.16 tff(1642,plain,
% 1.36/1.16 (c0_1(a325)),
% 1.36/1.16 inference(unit_resolution,[status(thm)],[1513, 1640])).
% 1.36/1.16 tff(1643,plain,
% 1.36/1.16 (c3_1(a325)),
% 1.36/1.16 inference(unit_resolution,[status(thm)],[1520, 152, 1635, 1208, 1207, 1206, 1642, 1641, 904])).
% 1.36/1.16 tff(1644,plain,
% 1.36/1.16 (c1_1(a325)),
% 1.36/1.16 inference(unit_resolution,[status(thm)],[1531, 1640])).
% 1.36/1.16 tff(1645,plain,
% 1.36/1.16 (~c3_1(a343)),
% 1.36/1.16 inference(unit_resolution,[status(thm)],[1538, 152, 1635, 1207, 1206, 1642, 1644, 425, 1643])).
% 1.36/1.16 tff(1646,plain,
% 1.36/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a337) | c2_1(a337) | (~ndr1_0) | (~c1_1(a337)) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a337) | c2_1(a337) | (~ndr1_0) | (~c1_1(a337)) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.36/1.16 inference(rewrite,[status(thm)],[])).
% 1.36/1.16 tff(1647,plain,
% 1.36/1.16 (((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343)) | c2_1(a337) | c0_1(a337) | (~c1_1(a337))) <=> (c0_1(a337) | c2_1(a337) | (~ndr1_0) | (~c1_1(a337)) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.36/1.16 inference(rewrite,[status(thm)],[])).
% 1.36/1.16 tff(1648,plain,
% 1.36/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343)) | c2_1(a337) | c0_1(a337) | (~c1_1(a337)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a337) | c2_1(a337) | (~ndr1_0) | (~c1_1(a337)) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343))))),
% 1.36/1.16 inference(monotonicity,[status(thm)],[1647])).
% 1.36/1.16 tff(1649,plain,
% 1.36/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343)) | c2_1(a337) | c0_1(a337) | (~c1_1(a337)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a337) | c2_1(a337) | (~ndr1_0) | (~c1_1(a337)) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.36/1.16 inference(transitivity,[status(thm)],[1648, 1646])).
% 1.36/1.16 tff(1650,plain,
% 1.36/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343)) | c2_1(a337) | c0_1(a337) | (~c1_1(a337)))),
% 1.39/1.16 inference(quant_inst,[status(thm)],[])).
% 1.39/1.16 tff(1651,plain,
% 1.39/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a337) | c2_1(a337) | (~ndr1_0) | (~c1_1(a337)) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343))),
% 1.39/1.16 inference(modus_ponens,[status(thm)],[1650, 1649])).
% 1.39/1.16 tff(1652,plain,
% 1.39/1.16 (~c1_1(a337)),
% 1.39/1.16 inference(unit_resolution,[status(thm)],[1651, 152, 1208, 1207, 1206, 1634, 1632, 21, 1645])).
% 1.39/1.16 tff(1653,plain,
% 1.39/1.16 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | c2_1(a337) | c3_1(a337) | (~ndr1_0) | c1_1(a337) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp21 | c2_1(a337) | c3_1(a337) | (~ndr1_0) | c1_1(a337) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343)))),
% 1.39/1.16 inference(rewrite,[status(thm)],[])).
% 1.39/1.16 tff(1654,plain,
% 1.39/1.16 ((hskp21 | (~ndr1_0) | c3_1(a343) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a337) | c1_1(a337) | c3_1(a337)) <=> (hskp21 | c2_1(a337) | c3_1(a337) | (~ndr1_0) | c1_1(a337) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343)))),
% 1.39/1.16 inference(rewrite,[status(thm)],[])).
% 1.39/1.16 tff(1655,plain,
% 1.39/1.16 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | (~ndr1_0) | c3_1(a343) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a337) | c1_1(a337) | c3_1(a337))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | c2_1(a337) | c3_1(a337) | (~ndr1_0) | c1_1(a337) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343))))),
% 1.39/1.16 inference(monotonicity,[status(thm)],[1654])).
% 1.39/1.16 tff(1656,plain,
% 1.39/1.16 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | (~ndr1_0) | c3_1(a343) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a337) | c1_1(a337) | c3_1(a337))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp21 | c2_1(a337) | c3_1(a337) | (~ndr1_0) | c1_1(a337) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343)))),
% 1.39/1.16 inference(transitivity,[status(thm)],[1655, 1653])).
% 1.39/1.16 tff(1657,plain,
% 1.39/1.16 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | (~ndr1_0) | c3_1(a343) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a337) | c1_1(a337) | c3_1(a337))),
% 1.39/1.16 inference(quant_inst,[status(thm)],[])).
% 1.39/1.16 tff(1658,plain,
% 1.39/1.16 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp21 | c2_1(a337) | c3_1(a337) | (~ndr1_0) | c1_1(a337) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343))),
% 1.39/1.16 inference(modus_ponens,[status(thm)],[1657, 1656])).
% 1.39/1.16 tff(1659,plain,
% 1.39/1.16 (hskp21),
% 1.39/1.16 inference(unit_resolution,[status(thm)],[1658, 152, 1208, 1207, 1632, 1633, 1575, 1645, 1652])).
% 1.39/1.16 tff(1660,plain,
% 1.39/1.16 (~c2_1(a359)),
% 1.39/1.16 inference(unit_resolution,[status(thm)],[1588, 1659])).
% 1.39/1.16 tff(1661,plain,
% 1.39/1.16 (c3_1(a359)),
% 1.39/1.16 inference(unit_resolution,[status(thm)],[1599, 1659])).
% 1.39/1.16 tff(1662,plain,
% 1.39/1.16 (c1_1(a359)),
% 1.39/1.16 inference(unit_resolution,[status(thm)],[1606, 152, 1208, 1207, 1206, 1661, 918, 919, 1660, 894, 788])).
% 1.39/1.16 tff(1663,plain,
% 1.39/1.16 (~c3_1(a353)),
% 1.39/1.16 inference(unit_resolution,[status(thm)],[1613, 152, 1635, 917, 916, 1642, 1644, 425, 1643])).
% 1.39/1.16 tff(1664,plain,
% 1.39/1.16 (~c0_1(a359)),
% 1.39/1.16 inference(unit_resolution,[status(thm)],[1619, 1659])).
% 1.39/1.16 tff(1665,plain,
% 1.39/1.16 ($false),
% 1.39/1.16 inference(unit_resolution,[status(thm)],[1626, 152, 1208, 1207, 1206, 917, 916, 1664, 1660, 21, 1663, 1662])).
% 1.39/1.16 tff(1666,plain,(c0_1(a337) | (~c1_1(a353)) | (~c2_1(a353)) | (~c1_1(a349)) | (~c3_1(a349)) | c2_1(a349) | c2_1(a337) | c3_1(a337) | hskp14 | c0_1(a353)), inference(lemma,lemma(discharge,[]))).
% 1.39/1.16 tff(1667,plain,
% 1.39/1.16 (c0_1(a337)),
% 1.39/1.16 inference(unit_resolution,[status(thm)],[1666, 1632, 916, 918, 919, 894, 917, 1633, 11, 915])).
% 1.39/1.16 tff(1668,assumption,(c0_1(a337)), introduced(assumption)).
% 1.39/1.16 tff(1669,plain,
% 1.39/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c0_1(a353) | c2_1(a349) | c2_1(a337) | (~ndr1_0) | (~c0_1(a337)) | c1_1(a337) | (~c3_1(a349)) | (~c1_1(a349)) | (~c1_1(a353)) | (~c3_1(a353)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a353) | c2_1(a349) | c2_1(a337) | (~ndr1_0) | (~c0_1(a337)) | c1_1(a337) | (~c3_1(a349)) | (~c1_1(a349)) | (~c1_1(a353)) | (~c3_1(a353)))),
% 1.39/1.16 inference(rewrite,[status(thm)],[])).
% 1.39/1.16 tff(1670,plain,
% 1.39/1.16 (((~ndr1_0) | c2_1(a349) | (~c3_1(a349)) | (~c1_1(a349)) | c2_1(a337) | c1_1(a337) | (~c0_1(a337)) | c0_1(a353) | (~c1_1(a353)) | (~c3_1(a353))) <=> (c0_1(a353) | c2_1(a349) | c2_1(a337) | (~ndr1_0) | (~c0_1(a337)) | c1_1(a337) | (~c3_1(a349)) | (~c1_1(a349)) | (~c1_1(a353)) | (~c3_1(a353)))),
% 1.39/1.16 inference(rewrite,[status(thm)],[])).
% 1.39/1.16 tff(1671,plain,
% 1.39/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a349) | (~c3_1(a349)) | (~c1_1(a349)) | c2_1(a337) | c1_1(a337) | (~c0_1(a337)) | c0_1(a353) | (~c1_1(a353)) | (~c3_1(a353)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c0_1(a353) | c2_1(a349) | c2_1(a337) | (~ndr1_0) | (~c0_1(a337)) | c1_1(a337) | (~c3_1(a349)) | (~c1_1(a349)) | (~c1_1(a353)) | (~c3_1(a353))))),
% 1.39/1.16 inference(monotonicity,[status(thm)],[1670])).
% 1.39/1.16 tff(1672,plain,
% 1.39/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a349) | (~c3_1(a349)) | (~c1_1(a349)) | c2_1(a337) | c1_1(a337) | (~c0_1(a337)) | c0_1(a353) | (~c1_1(a353)) | (~c3_1(a353)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a353) | c2_1(a349) | c2_1(a337) | (~ndr1_0) | (~c0_1(a337)) | c1_1(a337) | (~c3_1(a349)) | (~c1_1(a349)) | (~c1_1(a353)) | (~c3_1(a353)))),
% 1.39/1.16 inference(transitivity,[status(thm)],[1671, 1669])).
% 1.39/1.16 tff(1673,plain,
% 1.39/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a349) | (~c3_1(a349)) | (~c1_1(a349)) | c2_1(a337) | c1_1(a337) | (~c0_1(a337)) | c0_1(a353) | (~c1_1(a353)) | (~c3_1(a353)))),
% 1.39/1.16 inference(quant_inst,[status(thm)],[])).
% 1.39/1.16 tff(1674,plain,
% 1.39/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a353) | c2_1(a349) | c2_1(a337) | (~ndr1_0) | (~c0_1(a337)) | c1_1(a337) | (~c3_1(a349)) | (~c1_1(a349)) | (~c1_1(a353)) | (~c3_1(a353))),
% 1.39/1.16 inference(modus_ponens,[status(thm)],[1673, 1672])).
% 1.39/1.16 tff(1675,plain,
% 1.39/1.16 ((~c0_1(a337)) | c1_1(a337) | (~c3_1(a353))),
% 1.39/1.16 inference(unit_resolution,[status(thm)],[1674, 152, 917, 918, 919, 915, 894, 1632, 327])).
% 1.39/1.16 tff(1676,plain,
% 1.39/1.16 (c1_1(a337)),
% 1.39/1.16 inference(unit_resolution,[status(thm)],[1675, 929, 1668])).
% 1.39/1.16 tff(1677,plain,
% 1.39/1.16 (^[V: $i, U: $i] : refl((hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 1.39/1.16 inference(bind,[status(th)],[])).
% 1.39/1.16 tff(1678,plain,
% 1.39/1.16 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.39/1.16 inference(quant_intro,[status(thm)],[1677])).
% 1.39/1.16 tff(1679,plain,
% 1.39/1.16 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.39/1.16 inference(rewrite,[status(thm)],[])).
% 1.39/1.16 tff(1680,plain,
% 1.39/1.16 (^[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)) | c2_1(V) | (~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)) | c2_1(V) | (~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)) | hskp20) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp20))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp20) <=> (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~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)) | hskp20) <=> (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 1.39/1.16 inference(bind,[status(th)],[])).
% 1.39/1.16 tff(1681,plain,
% 1.39/1.16 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | hskp20) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.39/1.16 inference(quant_intro,[status(thm)],[1680])).
% 1.39/1.16 tff(1682,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)) | hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause186')).
% 1.39/1.16 tff(1683,plain,
% 1.39/1.16 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.39/1.16 inference(modus_ponens,[status(thm)],[1682, 1681])).
% 1.39/1.16 tff(1684,plain,
% 1.39/1.16 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.39/1.16 inference(modus_ponens,[status(thm)],[1683, 1679])).
% 1.39/1.16 tff(1685,plain,(
% 1.39/1.16 ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.39/1.16 inference(skolemize,[status(sab)],[1684])).
% 1.39/1.16 tff(1686,plain,
% 1.39/1.16 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.39/1.16 inference(modus_ponens,[status(thm)],[1685, 1678])).
% 1.39/1.16 tff(1687,plain,
% 1.39/1.16 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp20 | c2_1(a337) | (~ndr1_0) | (~c0_1(a337)) | (~c1_1(a337)) | (~c1_1(a353)) | (~c3_1(a353)) | (~c2_1(a353)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp20 | c2_1(a337) | (~ndr1_0) | (~c0_1(a337)) | (~c1_1(a337)) | (~c1_1(a353)) | (~c3_1(a353)) | (~c2_1(a353)))),
% 1.39/1.16 inference(rewrite,[status(thm)],[])).
% 1.39/1.16 tff(1688,plain,
% 1.39/1.16 ((hskp20 | (~ndr1_0) | (~c2_1(a353)) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a337) | (~c1_1(a337)) | (~c0_1(a337))) <=> (hskp20 | c2_1(a337) | (~ndr1_0) | (~c0_1(a337)) | (~c1_1(a337)) | (~c1_1(a353)) | (~c3_1(a353)) | (~c2_1(a353)))),
% 1.39/1.16 inference(rewrite,[status(thm)],[])).
% 1.39/1.16 tff(1689,plain,
% 1.39/1.16 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a353)) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a337) | (~c1_1(a337)) | (~c0_1(a337)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp20 | c2_1(a337) | (~ndr1_0) | (~c0_1(a337)) | (~c1_1(a337)) | (~c1_1(a353)) | (~c3_1(a353)) | (~c2_1(a353))))),
% 1.39/1.16 inference(monotonicity,[status(thm)],[1688])).
% 1.39/1.16 tff(1690,plain,
% 1.39/1.16 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a353)) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a337) | (~c1_1(a337)) | (~c0_1(a337)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp20 | c2_1(a337) | (~ndr1_0) | (~c0_1(a337)) | (~c1_1(a337)) | (~c1_1(a353)) | (~c3_1(a353)) | (~c2_1(a353)))),
% 1.39/1.16 inference(transitivity,[status(thm)],[1689, 1687])).
% 1.39/1.16 tff(1691,plain,
% 1.39/1.16 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a353)) | (~c3_1(a353)) | (~c1_1(a353)) | c2_1(a337) | (~c1_1(a337)) | (~c0_1(a337)))),
% 1.39/1.16 inference(quant_inst,[status(thm)],[])).
% 1.39/1.16 tff(1692,plain,
% 1.39/1.16 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp20 | c2_1(a337) | (~ndr1_0) | (~c0_1(a337)) | (~c1_1(a337)) | (~c1_1(a353)) | (~c3_1(a353)) | (~c2_1(a353))),
% 1.39/1.16 inference(modus_ponens,[status(thm)],[1691, 1690])).
% 1.39/1.16 tff(1693,plain,
% 1.39/1.16 (hskp20 | (~c0_1(a337)) | (~c1_1(a337)) | (~c3_1(a353))),
% 1.39/1.16 inference(unit_resolution,[status(thm)],[1692, 152, 917, 916, 1632, 1686])).
% 1.39/1.16 tff(1694,plain,
% 1.39/1.16 (hskp20),
% 1.39/1.16 inference(unit_resolution,[status(thm)],[1693, 929, 1668, 1676])).
% 1.39/1.16 tff(1695,plain,
% 1.39/1.16 (((~hskp20) | (~c3_1(a358))) <=> ((~hskp20) | (~c3_1(a358)))),
% 1.39/1.16 inference(rewrite,[status(thm)],[])).
% 1.39/1.16 tff(1696,plain,
% 1.39/1.16 (((~c3_1(a358)) | (~hskp20)) <=> ((~hskp20) | (~c3_1(a358)))),
% 1.39/1.16 inference(rewrite,[status(thm)],[])).
% 1.39/1.16 tff(1697,axiom,((~c3_1(a358)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause91')).
% 1.39/1.16 tff(1698,plain,
% 1.39/1.16 ((~hskp20) | (~c3_1(a358))),
% 1.39/1.16 inference(modus_ponens,[status(thm)],[1697, 1696])).
% 1.39/1.16 tff(1699,plain,
% 1.39/1.16 ((~hskp20) | (~c3_1(a358))),
% 1.39/1.16 inference(modus_ponens,[status(thm)],[1698, 1695])).
% 1.39/1.16 tff(1700,plain,
% 1.39/1.16 (~c3_1(a358)),
% 1.39/1.16 inference(unit_resolution,[status(thm)],[1699, 1694])).
% 1.39/1.16 tff(1701,plain,
% 1.39/1.16 (((~hskp20) | (~c0_1(a358))) <=> ((~hskp20) | (~c0_1(a358)))),
% 1.39/1.16 inference(rewrite,[status(thm)],[])).
% 1.39/1.16 tff(1702,plain,
% 1.39/1.16 (((~c0_1(a358)) | (~hskp20)) <=> ((~hskp20) | (~c0_1(a358)))),
% 1.39/1.16 inference(rewrite,[status(thm)],[])).
% 1.39/1.16 tff(1703,axiom,((~c0_1(a358)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause90')).
% 1.39/1.16 tff(1704,plain,
% 1.39/1.16 ((~hskp20) | (~c0_1(a358))),
% 1.39/1.16 inference(modus_ponens,[status(thm)],[1703, 1702])).
% 1.39/1.16 tff(1705,plain,
% 1.39/1.16 ((~hskp20) | (~c0_1(a358))),
% 1.39/1.16 inference(modus_ponens,[status(thm)],[1704, 1701])).
% 1.39/1.16 tff(1706,plain,
% 1.39/1.16 (~c0_1(a358)),
% 1.39/1.16 inference(unit_resolution,[status(thm)],[1705, 1694])).
% 1.39/1.16 tff(1707,plain,
% 1.39/1.16 (((~hskp20) | c2_1(a358)) <=> ((~hskp20) | c2_1(a358))),
% 1.39/1.16 inference(rewrite,[status(thm)],[])).
% 1.39/1.16 tff(1708,axiom,((~hskp20) | c2_1(a358)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause54')).
% 1.39/1.16 tff(1709,plain,
% 1.39/1.16 ((~hskp20) | c2_1(a358)),
% 1.39/1.16 inference(modus_ponens,[status(thm)],[1708, 1707])).
% 1.39/1.16 tff(1710,plain,
% 1.39/1.16 ((~hskp20) | c2_1(a358)),
% 1.39/1.16 inference(modus_ponens,[status(thm)],[1709, 1707])).
% 1.39/1.16 tff(1711,plain,
% 1.39/1.16 ((~hskp20) | c2_1(a358)),
% 1.39/1.16 inference(modus_ponens,[status(thm)],[1710, 1707])).
% 1.39/1.16 tff(1712,plain,
% 1.39/1.16 ((~hskp20) | c2_1(a358)),
% 1.39/1.16 inference(modus_ponens,[status(thm)],[1711, 1707])).
% 1.39/1.16 tff(1713,plain,
% 1.39/1.16 ((~hskp20) | c2_1(a358)),
% 1.39/1.16 inference(modus_ponens,[status(thm)],[1712, 1707])).
% 1.39/1.16 tff(1714,plain,
% 1.39/1.16 ((~hskp20) | c2_1(a358)),
% 1.39/1.16 inference(modus_ponens,[status(thm)],[1713, 1707])).
% 1.39/1.16 tff(1715,plain,
% 1.39/1.16 ((~hskp20) | c2_1(a358)),
% 1.39/1.16 inference(modus_ponens,[status(thm)],[1714, 1707])).
% 1.39/1.16 tff(1716,plain,
% 1.39/1.16 ((~hskp20) | c2_1(a358)),
% 1.39/1.16 inference(modus_ponens,[status(thm)],[1715, 1707])).
% 1.39/1.16 tff(1717,plain,
% 1.39/1.16 (c2_1(a358)),
% 1.39/1.16 inference(unit_resolution,[status(thm)],[1716, 1694])).
% 1.39/1.16 tff(1718,plain,
% 1.39/1.16 (((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | hskp13 | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)))) <=> ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp14 | hskp13 | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)))),
% 1.39/1.16 inference(rewrite,[status(thm)],[])).
% 1.39/1.16 tff(1719,plain,
% 1.39/1.16 ((hskp14 | hskp13 | (~ndr1_0) | c0_1(a358) | c3_1(a358) | (~c2_1(a358))) <=> (hskp14 | hskp13 | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)))),
% 1.39/1.16 inference(rewrite,[status(thm)],[])).
% 1.39/1.16 tff(1720,plain,
% 1.39/1.16 (((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | c0_1(a358) | c3_1(a358) | (~c2_1(a358)))) <=> ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | hskp13 | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358))))),
% 1.39/1.16 inference(monotonicity,[status(thm)],[1719])).
% 1.39/1.16 tff(1721,plain,
% 1.39/1.16 (((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | c0_1(a358) | c3_1(a358) | (~c2_1(a358)))) <=> ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp14 | hskp13 | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358)))),
% 1.39/1.16 inference(transitivity,[status(thm)],[1720, 1718])).
% 1.39/1.16 tff(1722,plain,
% 1.39/1.16 ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | c0_1(a358) | c3_1(a358) | (~c2_1(a358)))),
% 1.39/1.16 inference(quant_inst,[status(thm)],[])).
% 1.39/1.16 tff(1723,plain,
% 1.39/1.16 ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp14 | hskp13 | c0_1(a358) | c3_1(a358) | (~ndr1_0) | (~c2_1(a358))),
% 1.39/1.16 inference(modus_ponens,[status(thm)],[1722, 1721])).
% 1.39/1.16 tff(1724,plain,
% 1.39/1.16 ($false),
% 1.39/1.16 inference(unit_resolution,[status(thm)],[1723, 152, 11, 921, 1717, 1706, 1700, 530])).
% 1.39/1.16 tff(1725,plain,(hskp13 | hskp14 | (~c0_1(a337)) | (~c1_1(a353)) | (~c2_1(a353)) | c2_1(a337) | (~c1_1(a349)) | (~c3_1(a349)) | c0_1(a353) | c2_1(a349)), inference(lemma,lemma(discharge,[]))).
% 1.39/1.16 tff(1726,plain,
% 1.39/1.16 (hskp13),
% 1.39/1.16 inference(unit_resolution,[status(thm)],[1725, 1667, 11, 917, 916, 1632, 918, 919, 915, 894])).
% 1.39/1.16 tff(1727,plain,
% 1.39/1.16 (~c3_1(a346)),
% 1.39/1.16 inference(unit_resolution,[status(thm)],[554, 1726])).
% 1.39/1.16 tff(1728,plain,
% 1.39/1.16 (c0_1(a346)),
% 1.39/1.16 inference(unit_resolution,[status(thm)],[576, 1726])).
% 1.39/1.16 tff(1729,plain,
% 1.39/1.16 (c2_1(a346)),
% 1.39/1.16 inference(unit_resolution,[status(thm)],[565, 1726])).
% 1.39/1.17 tff(1730,assumption,(hskp21), introduced(assumption)).
% 1.39/1.17 tff(1731,plain,
% 1.39/1.17 (~c2_1(a359)),
% 1.39/1.17 inference(unit_resolution,[status(thm)],[1588, 1730])).
% 1.39/1.17 tff(1732,plain,
% 1.39/1.17 (c3_1(a359)),
% 1.39/1.17 inference(unit_resolution,[status(thm)],[1599, 1730])).
% 1.39/1.17 tff(1733,plain,
% 1.39/1.17 (c1_1(a359)),
% 1.39/1.17 inference(unit_resolution,[status(thm)],[1606, 152, 1208, 1207, 1206, 1732, 918, 919, 1731, 894, 788])).
% 1.39/1.17 tff(1734,assumption,(~c3_1(a346)), introduced(assumption)).
% 1.39/1.17 tff(1735,plain,
% 1.39/1.17 (~c0_1(a359)),
% 1.39/1.17 inference(unit_resolution,[status(thm)],[1619, 1730])).
% 1.39/1.17 tff(1736,assumption,(c2_1(a346)), introduced(assumption)).
% 1.39/1.17 tff(1737,plain,
% 1.39/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a359) | c2_1(a359) | c3_1(a346) | (~ndr1_0) | (~c1_1(a346)) | (~c2_1(a346)) | (~c1_1(a359)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a359) | c2_1(a359) | c3_1(a346) | (~ndr1_0) | (~c1_1(a346)) | (~c2_1(a346)) | (~c1_1(a359)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.39/1.17 inference(rewrite,[status(thm)],[])).
% 1.39/1.17 tff(1738,plain,
% 1.39/1.17 (((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c3_1(a346) | (~c1_1(a346)) | (~c2_1(a346)) | c2_1(a359) | c0_1(a359) | (~c1_1(a359))) <=> (c0_1(a359) | c2_1(a359) | c3_1(a346) | (~ndr1_0) | (~c1_1(a346)) | (~c2_1(a346)) | (~c1_1(a359)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.39/1.17 inference(rewrite,[status(thm)],[])).
% 1.39/1.17 tff(1739,plain,
% 1.39/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c3_1(a346) | (~c1_1(a346)) | (~c2_1(a346)) | c2_1(a359) | c0_1(a359) | (~c1_1(a359)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a359) | c2_1(a359) | c3_1(a346) | (~ndr1_0) | (~c1_1(a346)) | (~c2_1(a346)) | (~c1_1(a359)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))))),
% 1.39/1.17 inference(monotonicity,[status(thm)],[1738])).
% 1.39/1.17 tff(1740,plain,
% 1.39/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c3_1(a346) | (~c1_1(a346)) | (~c2_1(a346)) | c2_1(a359) | c0_1(a359) | (~c1_1(a359)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a359) | c2_1(a359) | c3_1(a346) | (~ndr1_0) | (~c1_1(a346)) | (~c2_1(a346)) | (~c1_1(a359)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.39/1.17 inference(transitivity,[status(thm)],[1739, 1737])).
% 1.39/1.17 tff(1741,plain,
% 1.39/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c3_1(a346) | (~c1_1(a346)) | (~c2_1(a346)) | c2_1(a359) | c0_1(a359) | (~c1_1(a359)))),
% 1.39/1.17 inference(quant_inst,[status(thm)],[])).
% 1.39/1.17 tff(1742,plain,
% 1.39/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a359) | c2_1(a359) | c3_1(a346) | (~ndr1_0) | (~c1_1(a346)) | (~c2_1(a346)) | (~c1_1(a359)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))),
% 1.39/1.17 inference(modus_ponens,[status(thm)],[1741, 1740])).
% 1.39/1.17 tff(1743,plain,
% 1.39/1.17 (~c1_1(a346)),
% 1.39/1.17 inference(unit_resolution,[status(thm)],[1742, 152, 1208, 1207, 1206, 1736, 1735, 1731, 1734, 21, 1733])).
% 1.39/1.17 tff(1744,plain,
% 1.39/1.17 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))))),
% 1.39/1.17 inference(bind,[status(th)],[])).
% 1.39/1.17 tff(1745,plain,
% 1.39/1.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.39/1.17 inference(quant_intro,[status(thm)],[1744])).
% 1.39/1.17 tff(1746,plain,
% 1.39/1.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.39/1.17 inference(rewrite,[status(thm)],[])).
% 1.39/1.17 tff(1747,plain,
% 1.39/1.17 (^[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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_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) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))))),
% 1.39/1.17 inference(bind,[status(th)],[])).
% 1.39/1.17 tff(1748,plain,
% 1.39/1.17 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_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) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.39/1.17 inference(quant_intro,[status(thm)],[1747])).
% 1.39/1.17 tff(1749,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause188')).
% 1.39/1.17 tff(1750,plain,
% 1.39/1.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.39/1.17 inference(modus_ponens,[status(thm)],[1749, 1748])).
% 1.39/1.17 tff(1751,plain,
% 1.39/1.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.39/1.17 inference(modus_ponens,[status(thm)],[1750, 1746])).
% 1.39/1.17 tff(1752,plain,(
% 1.39/1.17 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.39/1.17 inference(skolemize,[status(sab)],[1751])).
% 1.39/1.17 tff(1753,plain,
% 1.39/1.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.39/1.17 inference(modus_ponens,[status(thm)],[1752, 1745])).
% 1.39/1.17 tff(1754,assumption,(c0_1(a346)), introduced(assumption)).
% 1.39/1.17 tff(1755,plain,
% 1.39/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a359) | c2_1(a359) | c2_1(a337) | c3_1(a337) | (~ndr1_0) | (~c0_1(a337)) | (~c0_1(a346)) | c1_1(a346) | (~c2_1(a346)) | (~c1_1(a359)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a359) | c2_1(a359) | c2_1(a337) | c3_1(a337) | (~ndr1_0) | (~c0_1(a337)) | (~c0_1(a346)) | c1_1(a346) | (~c2_1(a346)) | (~c1_1(a359)))),
% 1.39/1.17 inference(rewrite,[status(thm)],[])).
% 1.39/1.17 tff(1756,plain,
% 1.39/1.17 (((~ndr1_0) | c2_1(a337) | c3_1(a337) | (~c0_1(a337)) | c1_1(a346) | (~c0_1(a346)) | (~c2_1(a346)) | c2_1(a359) | c0_1(a359) | (~c1_1(a359))) <=> (c0_1(a359) | c2_1(a359) | c2_1(a337) | c3_1(a337) | (~ndr1_0) | (~c0_1(a337)) | (~c0_1(a346)) | c1_1(a346) | (~c2_1(a346)) | (~c1_1(a359)))),
% 1.39/1.17 inference(rewrite,[status(thm)],[])).
% 1.39/1.17 tff(1757,plain,
% 1.39/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a337) | c3_1(a337) | (~c0_1(a337)) | c1_1(a346) | (~c0_1(a346)) | (~c2_1(a346)) | c2_1(a359) | c0_1(a359) | (~c1_1(a359)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a359) | c2_1(a359) | c2_1(a337) | c3_1(a337) | (~ndr1_0) | (~c0_1(a337)) | (~c0_1(a346)) | c1_1(a346) | (~c2_1(a346)) | (~c1_1(a359))))),
% 1.39/1.17 inference(monotonicity,[status(thm)],[1756])).
% 1.39/1.17 tff(1758,plain,
% 1.39/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a337) | c3_1(a337) | (~c0_1(a337)) | c1_1(a346) | (~c0_1(a346)) | (~c2_1(a346)) | c2_1(a359) | c0_1(a359) | (~c1_1(a359)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a359) | c2_1(a359) | c2_1(a337) | c3_1(a337) | (~ndr1_0) | (~c0_1(a337)) | (~c0_1(a346)) | c1_1(a346) | (~c2_1(a346)) | (~c1_1(a359)))),
% 1.39/1.17 inference(transitivity,[status(thm)],[1757, 1755])).
% 1.39/1.17 tff(1759,plain,
% 1.39/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a337) | c3_1(a337) | (~c0_1(a337)) | c1_1(a346) | (~c0_1(a346)) | (~c2_1(a346)) | c2_1(a359) | c0_1(a359) | (~c1_1(a359)))),
% 1.39/1.17 inference(quant_inst,[status(thm)],[])).
% 1.39/1.17 tff(1760,plain,
% 1.39/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a359) | c2_1(a359) | c2_1(a337) | c3_1(a337) | (~ndr1_0) | (~c0_1(a337)) | (~c0_1(a346)) | c1_1(a346) | (~c2_1(a346)) | (~c1_1(a359))),
% 1.39/1.17 inference(modus_ponens,[status(thm)],[1759, 1758])).
% 1.39/1.17 tff(1761,plain,
% 1.39/1.17 ($false),
% 1.39/1.17 inference(unit_resolution,[status(thm)],[1760, 152, 1754, 1736, 1668, 1735, 1731, 1632, 1633, 1753, 1743, 1733])).
% 1.39/1.17 tff(1762,plain,((~hskp21) | (~c0_1(a346)) | (~c2_1(a346)) | (~c0_1(a337)) | c2_1(a337) | c3_1(a337) | c3_1(a346) | (~c1_1(a349)) | (~c3_1(a349)) | c2_1(a349)), inference(lemma,lemma(discharge,[]))).
% 1.39/1.17 tff(1763,plain,
% 1.39/1.17 (~hskp21),
% 1.39/1.17 inference(unit_resolution,[status(thm)],[1762, 1729, 1667, 1728, 1632, 1633, 1727, 918, 919, 894])).
% 1.39/1.17 tff(1764,plain,
% 1.39/1.17 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | c2_1(a337) | c3_1(a337) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c1_1(a337))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp21 | c2_1(a337) | c3_1(a337) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c1_1(a337))),
% 1.39/1.17 inference(rewrite,[status(thm)],[])).
% 1.39/1.17 tff(1765,plain,
% 1.39/1.17 ((hskp21 | (~ndr1_0) | c3_1(a327) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a337) | c1_1(a337) | c3_1(a337)) <=> (hskp21 | c2_1(a337) | c3_1(a337) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c1_1(a337))),
% 1.39/1.17 inference(rewrite,[status(thm)],[])).
% 1.39/1.17 tff(1766,plain,
% 1.39/1.17 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | (~ndr1_0) | c3_1(a327) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a337) | c1_1(a337) | c3_1(a337))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | c2_1(a337) | c3_1(a337) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c1_1(a337)))),
% 1.39/1.17 inference(monotonicity,[status(thm)],[1765])).
% 1.39/1.17 tff(1767,plain,
% 1.39/1.17 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | (~ndr1_0) | c3_1(a327) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a337) | c1_1(a337) | c3_1(a337))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp21 | c2_1(a337) | c3_1(a337) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c1_1(a337))),
% 1.39/1.17 inference(transitivity,[status(thm)],[1766, 1764])).
% 1.39/1.17 tff(1768,plain,
% 1.39/1.17 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | (~ndr1_0) | c3_1(a327) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a337) | c1_1(a337) | c3_1(a337))),
% 1.39/1.17 inference(quant_inst,[status(thm)],[])).
% 1.39/1.17 tff(1769,plain,
% 1.39/1.17 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp21 | c2_1(a337) | c3_1(a337) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c1_1(a337)),
% 1.39/1.17 inference(modus_ponens,[status(thm)],[1768, 1767])).
% 1.39/1.17 tff(1770,plain,
% 1.39/1.17 (hskp21 | c1_1(a337)),
% 1.39/1.17 inference(unit_resolution,[status(thm)],[1769, 152, 1460, 1431, 1632, 1633, 1420, 1575])).
% 1.39/1.17 tff(1771,plain,
% 1.39/1.17 (c1_1(a337)),
% 1.39/1.17 inference(unit_resolution,[status(thm)],[1770, 1763])).
% 1.39/1.17 tff(1772,plain,
% 1.39/1.17 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | c2_1(a337) | c3_1(a337) | (~ndr1_0) | (~c0_1(a337)) | (~c1_1(a337)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | c2_1(a337) | c3_1(a337) | (~ndr1_0) | (~c0_1(a337)) | (~c1_1(a337)))),
% 1.39/1.17 inference(rewrite,[status(thm)],[])).
% 1.39/1.17 tff(1773,plain,
% 1.39/1.17 ((hskp8 | (~ndr1_0) | c3_1(a337) | (~c0_1(a337)) | (~c1_1(a337)) | c2_1(a337) | (~c1_1(a337)) | (~c0_1(a337))) <=> (hskp8 | c2_1(a337) | c3_1(a337) | (~ndr1_0) | (~c0_1(a337)) | (~c1_1(a337)))),
% 1.39/1.17 inference(rewrite,[status(thm)],[])).
% 1.39/1.17 tff(1774,plain,
% 1.39/1.17 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a337) | (~c0_1(a337)) | (~c1_1(a337)) | c2_1(a337) | (~c1_1(a337)) | (~c0_1(a337)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | c2_1(a337) | c3_1(a337) | (~ndr1_0) | (~c0_1(a337)) | (~c1_1(a337))))),
% 1.39/1.17 inference(monotonicity,[status(thm)],[1773])).
% 1.39/1.17 tff(1775,plain,
% 1.39/1.17 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a337) | (~c0_1(a337)) | (~c1_1(a337)) | c2_1(a337) | (~c1_1(a337)) | (~c0_1(a337)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | c2_1(a337) | c3_1(a337) | (~ndr1_0) | (~c0_1(a337)) | (~c1_1(a337)))),
% 1.39/1.17 inference(transitivity,[status(thm)],[1774, 1772])).
% 1.39/1.17 tff(1776,plain,
% 1.39/1.17 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a337) | (~c0_1(a337)) | (~c1_1(a337)) | c2_1(a337) | (~c1_1(a337)) | (~c0_1(a337)))),
% 1.39/1.17 inference(quant_inst,[status(thm)],[])).
% 1.39/1.17 tff(1777,plain,
% 1.39/1.17 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | c2_1(a337) | c3_1(a337) | (~ndr1_0) | (~c0_1(a337)) | (~c1_1(a337))),
% 1.39/1.17 inference(modus_ponens,[status(thm)],[1776, 1775])).
% 1.39/1.17 tff(1778,plain,
% 1.39/1.17 (hskp8 | (~c0_1(a337)) | (~c1_1(a337))),
% 1.39/1.17 inference(unit_resolution,[status(thm)],[1777, 152, 1632, 1633, 1549])).
% 1.39/1.17 tff(1779,plain,
% 1.39/1.17 (hskp8),
% 1.39/1.17 inference(unit_resolution,[status(thm)],[1778, 1771, 1667])).
% 1.39/1.17 tff(1780,plain,
% 1.39/1.17 (~c3_1(a332)),
% 1.39/1.17 inference(unit_resolution,[status(thm)],[694, 1779])).
% 1.39/1.17 tff(1781,plain,
% 1.39/1.17 (~c2_1(a332)),
% 1.39/1.17 inference(unit_resolution,[status(thm)],[700, 1779])).
% 1.39/1.17 tff(1782,plain,
% 1.39/1.17 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | c3_1(a337) | c2_1(a332) | c3_1(a332) | (~ndr1_0) | c1_1(a332) | (~c0_1(a337)) | (~c1_1(a337)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp21 | c3_1(a337) | c2_1(a332) | c3_1(a332) | (~ndr1_0) | c1_1(a332) | (~c0_1(a337)) | (~c1_1(a337)))),
% 1.39/1.17 inference(rewrite,[status(thm)],[])).
% 1.39/1.17 tff(1783,plain,
% 1.39/1.17 ((hskp21 | (~ndr1_0) | c3_1(a337) | (~c0_1(a337)) | (~c1_1(a337)) | c2_1(a332) | c1_1(a332) | c3_1(a332)) <=> (hskp21 | c3_1(a337) | c2_1(a332) | c3_1(a332) | (~ndr1_0) | c1_1(a332) | (~c0_1(a337)) | (~c1_1(a337)))),
% 1.39/1.17 inference(rewrite,[status(thm)],[])).
% 1.39/1.17 tff(1784,plain,
% 1.39/1.17 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | (~ndr1_0) | c3_1(a337) | (~c0_1(a337)) | (~c1_1(a337)) | c2_1(a332) | c1_1(a332) | c3_1(a332))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | c3_1(a337) | c2_1(a332) | c3_1(a332) | (~ndr1_0) | c1_1(a332) | (~c0_1(a337)) | (~c1_1(a337))))),
% 1.39/1.17 inference(monotonicity,[status(thm)],[1783])).
% 1.39/1.17 tff(1785,plain,
% 1.39/1.17 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | (~ndr1_0) | c3_1(a337) | (~c0_1(a337)) | (~c1_1(a337)) | c2_1(a332) | c1_1(a332) | c3_1(a332))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp21 | c3_1(a337) | c2_1(a332) | c3_1(a332) | (~ndr1_0) | c1_1(a332) | (~c0_1(a337)) | (~c1_1(a337)))),
% 1.39/1.17 inference(transitivity,[status(thm)],[1784, 1782])).
% 1.39/1.17 tff(1786,plain,
% 1.39/1.17 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | (~ndr1_0) | c3_1(a337) | (~c0_1(a337)) | (~c1_1(a337)) | c2_1(a332) | c1_1(a332) | c3_1(a332))),
% 1.39/1.17 inference(quant_inst,[status(thm)],[])).
% 1.39/1.17 tff(1787,plain,
% 1.39/1.17 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp21 | c3_1(a337) | c2_1(a332) | c3_1(a332) | (~ndr1_0) | c1_1(a332) | (~c0_1(a337)) | (~c1_1(a337))),
% 1.39/1.17 inference(modus_ponens,[status(thm)],[1786, 1785])).
% 1.39/1.17 tff(1788,plain,
% 1.39/1.17 (c1_1(a332)),
% 1.39/1.17 inference(unit_resolution,[status(thm)],[1787, 152, 1763, 1667, 1633, 1781, 1780, 1575, 1771])).
% 1.39/1.17 tff(1789,plain,
% 1.39/1.17 (~c0_1(a332)),
% 1.39/1.17 inference(unit_resolution,[status(thm)],[706, 1779])).
% 1.39/1.17 tff(1790,plain,
% 1.39/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a346) | c0_1(a332) | c2_1(a332) | (~ndr1_0) | (~c1_1(a332)) | (~c0_1(a346)) | (~c1_1(a346)) | (~c2_1(a346)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a346) | c0_1(a332) | c2_1(a332) | (~ndr1_0) | (~c1_1(a332)) | (~c0_1(a346)) | (~c1_1(a346)) | (~c2_1(a346)))),
% 1.39/1.17 inference(rewrite,[status(thm)],[])).
% 1.39/1.17 tff(1791,plain,
% 1.39/1.17 (((~ndr1_0) | (~c2_1(a346)) | (~c0_1(a346)) | (~c1_1(a346)) | c3_1(a346) | (~c1_1(a346)) | (~c2_1(a346)) | c2_1(a332) | c0_1(a332) | (~c1_1(a332))) <=> (c3_1(a346) | c0_1(a332) | c2_1(a332) | (~ndr1_0) | (~c1_1(a332)) | (~c0_1(a346)) | (~c1_1(a346)) | (~c2_1(a346)))),
% 1.39/1.17 inference(rewrite,[status(thm)],[])).
% 1.39/1.17 tff(1792,plain,
% 1.39/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a346)) | (~c0_1(a346)) | (~c1_1(a346)) | c3_1(a346) | (~c1_1(a346)) | (~c2_1(a346)) | c2_1(a332) | c0_1(a332) | (~c1_1(a332)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a346) | c0_1(a332) | c2_1(a332) | (~ndr1_0) | (~c1_1(a332)) | (~c0_1(a346)) | (~c1_1(a346)) | (~c2_1(a346))))),
% 1.39/1.17 inference(monotonicity,[status(thm)],[1791])).
% 1.39/1.17 tff(1793,plain,
% 1.39/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a346)) | (~c0_1(a346)) | (~c1_1(a346)) | c3_1(a346) | (~c1_1(a346)) | (~c2_1(a346)) | c2_1(a332) | c0_1(a332) | (~c1_1(a332)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a346) | c0_1(a332) | c2_1(a332) | (~ndr1_0) | (~c1_1(a332)) | (~c0_1(a346)) | (~c1_1(a346)) | (~c2_1(a346)))),
% 1.39/1.17 inference(transitivity,[status(thm)],[1792, 1790])).
% 1.39/1.17 tff(1794,plain,
% 1.39/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a346)) | (~c0_1(a346)) | (~c1_1(a346)) | c3_1(a346) | (~c1_1(a346)) | (~c2_1(a346)) | c2_1(a332) | c0_1(a332) | (~c1_1(a332)))),
% 1.39/1.17 inference(quant_inst,[status(thm)],[])).
% 1.39/1.17 tff(1795,plain,
% 1.39/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a346) | c0_1(a332) | c2_1(a332) | (~ndr1_0) | (~c1_1(a332)) | (~c0_1(a346)) | (~c1_1(a346)) | (~c2_1(a346))),
% 1.39/1.17 inference(modus_ponens,[status(thm)],[1794, 1793])).
% 1.39/1.17 tff(1796,plain,
% 1.39/1.17 ((~c1_1(a332)) | (~c1_1(a346))),
% 1.39/1.17 inference(unit_resolution,[status(thm)],[1795, 152, 1728, 1729, 1727, 1789, 1781, 21])).
% 1.39/1.17 tff(1797,plain,
% 1.39/1.17 (~c1_1(a346)),
% 1.39/1.17 inference(unit_resolution,[status(thm)],[1796, 1788])).
% 1.39/1.17 tff(1798,plain,
% 1.39/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | c3_1(W))) | (c2_1(a337) | c3_1(a337) | c0_1(a332) | c3_1(a332) | (~ndr1_0) | (~c1_1(a332)) | (~c1_1(a337)) | (~c0_1(a346)) | c1_1(a346) | (~c2_1(a346)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | c3_1(W))) | c2_1(a337) | c3_1(a337) | c0_1(a332) | c3_1(a332) | (~ndr1_0) | (~c1_1(a332)) | (~c1_1(a337)) | (~c0_1(a346)) | c1_1(a346) | (~c2_1(a346)))),
% 1.39/1.18 inference(rewrite,[status(thm)],[])).
% 1.39/1.18 tff(1799,plain,
% 1.39/1.18 (((~ndr1_0) | c2_1(a337) | c3_1(a337) | (~c1_1(a337)) | c1_1(a346) | (~c0_1(a346)) | (~c2_1(a346)) | c0_1(a332) | (~c1_1(a332)) | c3_1(a332)) <=> (c2_1(a337) | c3_1(a337) | c0_1(a332) | c3_1(a332) | (~ndr1_0) | (~c1_1(a332)) | (~c1_1(a337)) | (~c0_1(a346)) | c1_1(a346) | (~c2_1(a346)))),
% 1.39/1.18 inference(rewrite,[status(thm)],[])).
% 1.39/1.18 tff(1800,plain,
% 1.39/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | c3_1(W))) | ((~ndr1_0) | c2_1(a337) | c3_1(a337) | (~c1_1(a337)) | c1_1(a346) | (~c0_1(a346)) | (~c2_1(a346)) | c0_1(a332) | (~c1_1(a332)) | c3_1(a332))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | c3_1(W))) | (c2_1(a337) | c3_1(a337) | c0_1(a332) | c3_1(a332) | (~ndr1_0) | (~c1_1(a332)) | (~c1_1(a337)) | (~c0_1(a346)) | c1_1(a346) | (~c2_1(a346))))),
% 1.39/1.18 inference(monotonicity,[status(thm)],[1799])).
% 1.39/1.18 tff(1801,plain,
% 1.39/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | c3_1(W))) | ((~ndr1_0) | c2_1(a337) | c3_1(a337) | (~c1_1(a337)) | c1_1(a346) | (~c0_1(a346)) | (~c2_1(a346)) | c0_1(a332) | (~c1_1(a332)) | c3_1(a332))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | c3_1(W))) | c2_1(a337) | c3_1(a337) | c0_1(a332) | c3_1(a332) | (~ndr1_0) | (~c1_1(a332)) | (~c1_1(a337)) | (~c0_1(a346)) | c1_1(a346) | (~c2_1(a346)))),
% 1.39/1.18 inference(transitivity,[status(thm)],[1800, 1798])).
% 1.39/1.18 tff(1802,plain,
% 1.39/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | c3_1(W))) | ((~ndr1_0) | c2_1(a337) | c3_1(a337) | (~c1_1(a337)) | c1_1(a346) | (~c0_1(a346)) | (~c2_1(a346)) | c0_1(a332) | (~c1_1(a332)) | c3_1(a332))),
% 1.39/1.18 inference(quant_inst,[status(thm)],[])).
% 1.39/1.18 tff(1803,plain,
% 1.39/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | c3_1(W))) | c2_1(a337) | c3_1(a337) | c0_1(a332) | c3_1(a332) | (~ndr1_0) | (~c1_1(a332)) | (~c1_1(a337)) | (~c0_1(a346)) | c1_1(a346) | (~c2_1(a346))),
% 1.39/1.18 inference(modus_ponens,[status(thm)],[1802, 1801])).
% 1.39/1.18 tff(1804,plain,
% 1.39/1.18 ($false),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[1803, 152, 1728, 1729, 1632, 1633, 1789, 1780, 667, 1797, 1771, 1788])).
% 1.39/1.18 tff(1805,plain,(c2_1(a337) | c3_1(a337) | (~c1_1(a349)) | (~c3_1(a349)) | c2_1(a349) | hskp14 | (~c1_1(a353)) | (~c2_1(a353)) | c0_1(a353)), inference(lemma,lemma(discharge,[]))).
% 1.39/1.18 tff(1806,plain,
% 1.39/1.18 ($false),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[1805, 1631, 1630, 848, 837, 826, 11, 893, 882, 871])).
% 1.39/1.18 tff(1807,plain,(hskp24 | hskp14), inference(lemma,lemma(discharge,[]))).
% 1.39/1.18 tff(1808,plain,
% 1.39/1.18 (hskp24),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[1807, 11])).
% 1.39/1.18 tff(1809,plain,
% 1.39/1.18 (~c2_1(a401)),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[1136, 1808])).
% 1.39/1.18 tff(1810,plain,
% 1.39/1.18 (~c0_1(a401)),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[1142, 1808])).
% 1.39/1.18 tff(1811,plain,
% 1.39/1.18 (c1_1(a401)),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[1153, 1808])).
% 1.39/1.18 tff(1812,plain,
% 1.39/1.18 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | c2_1(a401) | (~ndr1_0) | (~c3_1(a401)) | (~c1_1(a401)))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | c2_1(a401) | (~ndr1_0) | (~c3_1(a401)) | (~c1_1(a401)))),
% 1.39/1.18 inference(rewrite,[status(thm)],[])).
% 1.39/1.18 tff(1813,plain,
% 1.39/1.18 ((hskp28 | (~ndr1_0) | c2_1(a401) | (~c3_1(a401)) | (~c1_1(a401))) <=> (hskp28 | c2_1(a401) | (~ndr1_0) | (~c3_1(a401)) | (~c1_1(a401)))),
% 1.39/1.18 inference(rewrite,[status(thm)],[])).
% 1.39/1.18 tff(1814,plain,
% 1.39/1.18 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | (~ndr1_0) | c2_1(a401) | (~c3_1(a401)) | (~c1_1(a401)))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | c2_1(a401) | (~ndr1_0) | (~c3_1(a401)) | (~c1_1(a401))))),
% 1.39/1.18 inference(monotonicity,[status(thm)],[1813])).
% 1.39/1.18 tff(1815,plain,
% 1.39/1.18 (((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | (~ndr1_0) | c2_1(a401) | (~c3_1(a401)) | (~c1_1(a401)))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | c2_1(a401) | (~ndr1_0) | (~c3_1(a401)) | (~c1_1(a401)))),
% 1.39/1.18 inference(transitivity,[status(thm)],[1814, 1812])).
% 1.39/1.18 tff(1816,plain,
% 1.39/1.18 ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | (~ndr1_0) | c2_1(a401) | (~c3_1(a401)) | (~c1_1(a401)))),
% 1.39/1.18 inference(quant_inst,[status(thm)],[])).
% 1.39/1.18 tff(1817,plain,
% 1.39/1.18 ((~![U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | c2_1(a401) | (~ndr1_0) | (~c3_1(a401)) | (~c1_1(a401))),
% 1.39/1.18 inference(modus_ponens,[status(thm)],[1816, 1815])).
% 1.39/1.18 tff(1818,plain,
% 1.39/1.18 (hskp28 | (~c3_1(a401))),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[1817, 152, 1811, 1809, 41])).
% 1.39/1.18 tff(1819,plain,
% 1.39/1.18 (~c3_1(a401)),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[1818, 616])).
% 1.39/1.18 tff(1820,assumption,(c2_1(a327)), introduced(assumption)).
% 1.39/1.18 tff(1821,plain,
% 1.39/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a401) | c2_1(a401) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | (~c2_1(a327)) | (~c1_1(a401)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a401) | c2_1(a401) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | (~c2_1(a327)) | (~c1_1(a401)))),
% 1.39/1.18 inference(rewrite,[status(thm)],[])).
% 1.39/1.18 tff(1822,plain,
% 1.39/1.18 (((~ndr1_0) | (~c2_1(a327)) | (~c0_1(a327)) | (~c1_1(a327)) | c3_1(a327) | (~c1_1(a327)) | (~c2_1(a327)) | c2_1(a401) | c0_1(a401) | (~c1_1(a401))) <=> (c0_1(a401) | c2_1(a401) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | (~c2_1(a327)) | (~c1_1(a401)))),
% 1.39/1.18 inference(rewrite,[status(thm)],[])).
% 1.39/1.18 tff(1823,plain,
% 1.39/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a327)) | (~c0_1(a327)) | (~c1_1(a327)) | c3_1(a327) | (~c1_1(a327)) | (~c2_1(a327)) | c2_1(a401) | c0_1(a401) | (~c1_1(a401)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a401) | c2_1(a401) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | (~c2_1(a327)) | (~c1_1(a401))))),
% 1.39/1.18 inference(monotonicity,[status(thm)],[1822])).
% 1.39/1.18 tff(1824,plain,
% 1.39/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a327)) | (~c0_1(a327)) | (~c1_1(a327)) | c3_1(a327) | (~c1_1(a327)) | (~c2_1(a327)) | c2_1(a401) | c0_1(a401) | (~c1_1(a401)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a401) | c2_1(a401) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | (~c2_1(a327)) | (~c1_1(a401)))),
% 1.39/1.18 inference(transitivity,[status(thm)],[1823, 1821])).
% 1.39/1.18 tff(1825,plain,
% 1.39/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a327)) | (~c0_1(a327)) | (~c1_1(a327)) | c3_1(a327) | (~c1_1(a327)) | (~c2_1(a327)) | c2_1(a401) | c0_1(a401) | (~c1_1(a401)))),
% 1.39/1.18 inference(quant_inst,[status(thm)],[])).
% 1.39/1.18 tff(1826,plain,
% 1.39/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a401) | c2_1(a401) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | (~c2_1(a327)) | (~c1_1(a401))),
% 1.39/1.18 inference(modus_ponens,[status(thm)],[1825, 1824])).
% 1.39/1.18 tff(1827,plain,
% 1.39/1.18 ($false),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[1826, 152, 1171, 1460, 1431, 1168, 1167, 1420, 21, 1820])).
% 1.39/1.18 tff(1828,plain,((~c2_1(a327)) | (~c1_1(a401)) | c0_1(a401) | c2_1(a401)), inference(lemma,lemma(discharge,[]))).
% 1.39/1.18 tff(1829,plain,
% 1.39/1.18 (~c2_1(a327)),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[1828, 1811, 1810, 1809])).
% 1.39/1.18 tff(1830,plain,
% 1.39/1.18 (^[U: $i] : refl((hskp28 | hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> (hskp28 | hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))),
% 1.39/1.18 inference(bind,[status(th)],[])).
% 1.39/1.18 tff(1831,plain,
% 1.39/1.18 (![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.39/1.18 inference(quant_intro,[status(thm)],[1830])).
% 1.39/1.18 tff(1832,plain,
% 1.39/1.18 (![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.39/1.18 inference(rewrite,[status(thm)],[])).
% 1.39/1.18 tff(1833,plain,
% 1.39/1.18 (^[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)) | 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)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | 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) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp28) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp28))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp28) | hskp27) <=> ((hskp28 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp27))), rewrite(((hskp28 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp27) <=> (hskp28 | hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp28) | hskp27) <=> (hskp28 | hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))))),
% 1.39/1.18 inference(bind,[status(th)],[])).
% 1.39/1.18 tff(1834,plain,
% 1.39/1.18 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp28) | hskp27) <=> ![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.39/1.18 inference(quant_intro,[status(thm)],[1833])).
% 1.39/1.18 tff(1835,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp28) | hskp27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause135')).
% 1.39/1.18 tff(1836,plain,
% 1.39/1.18 (![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.39/1.18 inference(modus_ponens,[status(thm)],[1835, 1834])).
% 1.39/1.18 tff(1837,plain,
% 1.39/1.18 (![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.39/1.18 inference(modus_ponens,[status(thm)],[1836, 1832])).
% 1.39/1.18 tff(1838,plain,(
% 1.39/1.18 ![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.39/1.18 inference(skolemize,[status(sab)],[1837])).
% 1.39/1.18 tff(1839,plain,
% 1.39/1.18 (![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.39/1.18 inference(modus_ponens,[status(thm)],[1838, 1831])).
% 1.39/1.18 tff(1840,plain,
% 1.39/1.18 (((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp28 | hskp27 | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | c2_1(a327))) <=> ((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp28 | hskp27 | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | c2_1(a327))),
% 1.39/1.18 inference(rewrite,[status(thm)],[])).
% 1.39/1.18 tff(1841,plain,
% 1.39/1.18 ((hskp28 | hskp27 | (~ndr1_0) | c2_1(a327) | c3_1(a327) | (~c0_1(a327))) <=> (hskp28 | hskp27 | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | c2_1(a327))),
% 1.39/1.18 inference(rewrite,[status(thm)],[])).
% 1.39/1.18 tff(1842,plain,
% 1.39/1.18 (((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp28 | hskp27 | (~ndr1_0) | c2_1(a327) | c3_1(a327) | (~c0_1(a327)))) <=> ((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp28 | hskp27 | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | c2_1(a327)))),
% 1.39/1.18 inference(monotonicity,[status(thm)],[1841])).
% 1.39/1.18 tff(1843,plain,
% 1.39/1.18 (((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp28 | hskp27 | (~ndr1_0) | c2_1(a327) | c3_1(a327) | (~c0_1(a327)))) <=> ((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp28 | hskp27 | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | c2_1(a327))),
% 1.39/1.18 inference(transitivity,[status(thm)],[1842, 1840])).
% 1.39/1.18 tff(1844,plain,
% 1.39/1.18 ((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp28 | hskp27 | (~ndr1_0) | c2_1(a327) | c3_1(a327) | (~c0_1(a327)))),
% 1.39/1.18 inference(quant_inst,[status(thm)],[])).
% 1.39/1.18 tff(1845,plain,
% 1.39/1.18 ((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp28 | hskp27 | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | c2_1(a327)),
% 1.39/1.18 inference(modus_ponens,[status(thm)],[1844, 1843])).
% 1.39/1.18 tff(1846,plain,
% 1.39/1.18 (hskp28 | hskp27 | c2_1(a327)),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[1845, 152, 1460, 1420, 1839])).
% 1.39/1.18 tff(1847,plain,
% 1.39/1.18 (hskp27),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[1846, 616, 1829])).
% 1.39/1.18 tff(1848,plain,
% 1.39/1.18 (((~hskp27) | c3_1(a341)) <=> ((~hskp27) | c3_1(a341))),
% 1.39/1.18 inference(rewrite,[status(thm)],[])).
% 1.39/1.18 tff(1849,axiom,((~hskp27) | c3_1(a341)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause44')).
% 1.39/1.18 tff(1850,plain,
% 1.39/1.18 ((~hskp27) | c3_1(a341)),
% 1.39/1.18 inference(modus_ponens,[status(thm)],[1849, 1848])).
% 1.39/1.18 tff(1851,plain,
% 1.39/1.18 ((~hskp27) | c3_1(a341)),
% 1.39/1.18 inference(modus_ponens,[status(thm)],[1850, 1848])).
% 1.39/1.18 tff(1852,plain,
% 1.39/1.18 ((~hskp27) | c3_1(a341)),
% 1.39/1.18 inference(modus_ponens,[status(thm)],[1851, 1848])).
% 1.39/1.18 tff(1853,plain,
% 1.39/1.18 ((~hskp27) | c3_1(a341)),
% 1.39/1.18 inference(modus_ponens,[status(thm)],[1852, 1848])).
% 1.39/1.18 tff(1854,plain,
% 1.39/1.18 ((~hskp27) | c3_1(a341)),
% 1.39/1.18 inference(modus_ponens,[status(thm)],[1853, 1848])).
% 1.39/1.18 tff(1855,plain,
% 1.39/1.18 ((~hskp27) | c3_1(a341)),
% 1.39/1.18 inference(modus_ponens,[status(thm)],[1854, 1848])).
% 1.39/1.18 tff(1856,plain,
% 1.39/1.18 ((~hskp27) | c3_1(a341)),
% 1.39/1.18 inference(modus_ponens,[status(thm)],[1855, 1848])).
% 1.39/1.18 tff(1857,plain,
% 1.39/1.18 ((~hskp27) | c3_1(a341)),
% 1.39/1.18 inference(modus_ponens,[status(thm)],[1856, 1848])).
% 1.39/1.18 tff(1858,plain,
% 1.39/1.18 (c3_1(a341)),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[1857, 1847])).
% 1.39/1.18 tff(1859,plain,
% 1.39/1.18 (((~hskp27) | c2_1(a341)) <=> ((~hskp27) | c2_1(a341))),
% 1.39/1.18 inference(rewrite,[status(thm)],[])).
% 1.39/1.18 tff(1860,axiom,((~hskp27) | c2_1(a341)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause43')).
% 1.39/1.18 tff(1861,plain,
% 1.39/1.18 ((~hskp27) | c2_1(a341)),
% 1.39/1.18 inference(modus_ponens,[status(thm)],[1860, 1859])).
% 1.39/1.18 tff(1862,plain,
% 1.39/1.18 ((~hskp27) | c2_1(a341)),
% 1.39/1.18 inference(modus_ponens,[status(thm)],[1861, 1859])).
% 1.39/1.18 tff(1863,plain,
% 1.39/1.18 ((~hskp27) | c2_1(a341)),
% 1.39/1.18 inference(modus_ponens,[status(thm)],[1862, 1859])).
% 1.39/1.18 tff(1864,plain,
% 1.39/1.18 ((~hskp27) | c2_1(a341)),
% 1.39/1.18 inference(modus_ponens,[status(thm)],[1863, 1859])).
% 1.39/1.18 tff(1865,plain,
% 1.39/1.18 ((~hskp27) | c2_1(a341)),
% 1.39/1.18 inference(modus_ponens,[status(thm)],[1864, 1859])).
% 1.39/1.18 tff(1866,plain,
% 1.39/1.18 ((~hskp27) | c2_1(a341)),
% 1.39/1.18 inference(modus_ponens,[status(thm)],[1865, 1859])).
% 1.39/1.18 tff(1867,plain,
% 1.39/1.18 ((~hskp27) | c2_1(a341)),
% 1.39/1.18 inference(modus_ponens,[status(thm)],[1866, 1859])).
% 1.39/1.18 tff(1868,plain,
% 1.39/1.18 ((~hskp27) | c2_1(a341)),
% 1.39/1.18 inference(modus_ponens,[status(thm)],[1867, 1859])).
% 1.39/1.18 tff(1869,plain,
% 1.39/1.18 (c2_1(a341)),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[1868, 1847])).
% 1.39/1.18 tff(1870,plain,
% 1.39/1.18 (((~hskp27) | c1_1(a341)) <=> ((~hskp27) | c1_1(a341))),
% 1.39/1.18 inference(rewrite,[status(thm)],[])).
% 1.39/1.18 tff(1871,axiom,((~hskp27) | c1_1(a341)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause42')).
% 1.39/1.18 tff(1872,plain,
% 1.39/1.18 ((~hskp27) | c1_1(a341)),
% 1.39/1.18 inference(modus_ponens,[status(thm)],[1871, 1870])).
% 1.39/1.18 tff(1873,plain,
% 1.39/1.18 ((~hskp27) | c1_1(a341)),
% 1.39/1.18 inference(modus_ponens,[status(thm)],[1872, 1870])).
% 1.39/1.18 tff(1874,plain,
% 1.39/1.18 ((~hskp27) | c1_1(a341)),
% 1.39/1.18 inference(modus_ponens,[status(thm)],[1873, 1870])).
% 1.39/1.18 tff(1875,plain,
% 1.39/1.18 ((~hskp27) | c1_1(a341)),
% 1.39/1.18 inference(modus_ponens,[status(thm)],[1874, 1870])).
% 1.39/1.18 tff(1876,plain,
% 1.39/1.18 ((~hskp27) | c1_1(a341)),
% 1.39/1.18 inference(modus_ponens,[status(thm)],[1875, 1870])).
% 1.39/1.18 tff(1877,plain,
% 1.39/1.18 ((~hskp27) | c1_1(a341)),
% 1.39/1.18 inference(modus_ponens,[status(thm)],[1876, 1870])).
% 1.39/1.18 tff(1878,plain,
% 1.39/1.18 ((~hskp27) | c1_1(a341)),
% 1.39/1.18 inference(modus_ponens,[status(thm)],[1877, 1870])).
% 1.39/1.18 tff(1879,plain,
% 1.39/1.18 ((~hskp27) | c1_1(a341)),
% 1.39/1.18 inference(modus_ponens,[status(thm)],[1878, 1870])).
% 1.39/1.18 tff(1880,plain,
% 1.39/1.18 (c1_1(a341)),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[1879, 1847])).
% 1.39/1.18 tff(1881,plain,
% 1.39/1.18 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a341)) | (~c3_1(a341)) | (~c1_1(a341)) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a327))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp20 | (~ndr1_0) | (~c2_1(a341)) | (~c3_1(a341)) | (~c1_1(a341)) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a327))),
% 1.39/1.18 inference(rewrite,[status(thm)],[])).
% 1.39/1.18 tff(1882,plain,
% 1.39/1.18 ((hskp20 | (~ndr1_0) | (~c2_1(a341)) | (~c3_1(a341)) | (~c1_1(a341)) | c2_1(a327) | (~c1_1(a327)) | (~c0_1(a327))) <=> (hskp20 | (~ndr1_0) | (~c2_1(a341)) | (~c3_1(a341)) | (~c1_1(a341)) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a327))),
% 1.39/1.18 inference(rewrite,[status(thm)],[])).
% 1.39/1.18 tff(1883,plain,
% 1.39/1.18 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a341)) | (~c3_1(a341)) | (~c1_1(a341)) | c2_1(a327) | (~c1_1(a327)) | (~c0_1(a327)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a341)) | (~c3_1(a341)) | (~c1_1(a341)) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a327)))),
% 1.39/1.18 inference(monotonicity,[status(thm)],[1882])).
% 1.39/1.18 tff(1884,plain,
% 1.39/1.18 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a341)) | (~c3_1(a341)) | (~c1_1(a341)) | c2_1(a327) | (~c1_1(a327)) | (~c0_1(a327)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp20 | (~ndr1_0) | (~c2_1(a341)) | (~c3_1(a341)) | (~c1_1(a341)) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a327))),
% 1.39/1.18 inference(transitivity,[status(thm)],[1883, 1881])).
% 1.39/1.18 tff(1885,plain,
% 1.39/1.18 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a341)) | (~c3_1(a341)) | (~c1_1(a341)) | c2_1(a327) | (~c1_1(a327)) | (~c0_1(a327)))),
% 1.39/1.18 inference(quant_inst,[status(thm)],[])).
% 1.39/1.18 tff(1886,plain,
% 1.39/1.18 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp20 | (~ndr1_0) | (~c2_1(a341)) | (~c3_1(a341)) | (~c1_1(a341)) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a327)),
% 1.39/1.18 inference(modus_ponens,[status(thm)],[1885, 1884])).
% 1.39/1.18 tff(1887,plain,
% 1.39/1.18 (hskp20),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[1886, 152, 1880, 1869, 1858, 1460, 1431, 1686, 1829])).
% 1.39/1.18 tff(1888,plain,
% 1.39/1.18 (~c3_1(a358)),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[1699, 1887])).
% 1.39/1.18 tff(1889,plain,
% 1.39/1.18 (~c0_1(a358)),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[1705, 1887])).
% 1.39/1.18 tff(1890,plain,
% 1.39/1.18 (c2_1(a358)),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[1716, 1887])).
% 1.39/1.18 tff(1891,plain,
% 1.39/1.18 (hskp13),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[1723, 152, 11, 1890, 1889, 1888, 530])).
% 1.39/1.18 tff(1892,plain,
% 1.39/1.18 (~c3_1(a346)),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[554, 1891])).
% 1.39/1.18 tff(1893,plain,
% 1.39/1.18 (c2_1(a346)),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[565, 1891])).
% 1.39/1.18 tff(1894,plain,
% 1.39/1.18 (c0_1(a346)),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[576, 1891])).
% 1.39/1.18 tff(1895,plain,
% 1.39/1.18 (~c1_1(a346)),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[1329, 152, 1811, 1894, 1893, 1810, 1809, 1892, 21])).
% 1.39/1.18 tff(1896,plain,
% 1.39/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | c3_1(W))) | (c0_1(a401) | c2_1(a401) | (~ndr1_0) | (~c0_1(a346)) | c1_1(a346) | (~c2_1(a346)) | c3_1(a401) | (~c1_1(a401)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | c3_1(W))) | c0_1(a401) | c2_1(a401) | (~ndr1_0) | (~c0_1(a346)) | c1_1(a346) | (~c2_1(a346)) | c3_1(a401) | (~c1_1(a401)))),
% 1.39/1.18 inference(rewrite,[status(thm)],[])).
% 1.39/1.18 tff(1897,plain,
% 1.39/1.18 (((~ndr1_0) | c2_1(a401) | c3_1(a401) | (~c1_1(a401)) | c1_1(a346) | (~c0_1(a346)) | (~c2_1(a346)) | c0_1(a401) | (~c1_1(a401)) | c3_1(a401)) <=> (c0_1(a401) | c2_1(a401) | (~ndr1_0) | (~c0_1(a346)) | c1_1(a346) | (~c2_1(a346)) | c3_1(a401) | (~c1_1(a401)))),
% 1.39/1.18 inference(rewrite,[status(thm)],[])).
% 1.39/1.18 tff(1898,plain,
% 1.39/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | c3_1(W))) | ((~ndr1_0) | c2_1(a401) | c3_1(a401) | (~c1_1(a401)) | c1_1(a346) | (~c0_1(a346)) | (~c2_1(a346)) | c0_1(a401) | (~c1_1(a401)) | c3_1(a401))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | c3_1(W))) | (c0_1(a401) | c2_1(a401) | (~ndr1_0) | (~c0_1(a346)) | c1_1(a346) | (~c2_1(a346)) | c3_1(a401) | (~c1_1(a401))))),
% 1.39/1.18 inference(monotonicity,[status(thm)],[1897])).
% 1.39/1.18 tff(1899,plain,
% 1.39/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | c3_1(W))) | ((~ndr1_0) | c2_1(a401) | c3_1(a401) | (~c1_1(a401)) | c1_1(a346) | (~c0_1(a346)) | (~c2_1(a346)) | c0_1(a401) | (~c1_1(a401)) | c3_1(a401))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | c3_1(W))) | c0_1(a401) | c2_1(a401) | (~ndr1_0) | (~c0_1(a346)) | c1_1(a346) | (~c2_1(a346)) | c3_1(a401) | (~c1_1(a401)))),
% 1.39/1.18 inference(transitivity,[status(thm)],[1898, 1896])).
% 1.39/1.18 tff(1900,plain,
% 1.39/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | c3_1(W))) | ((~ndr1_0) | c2_1(a401) | c3_1(a401) | (~c1_1(a401)) | c1_1(a346) | (~c0_1(a346)) | (~c2_1(a346)) | c0_1(a401) | (~c1_1(a401)) | c3_1(a401))),
% 1.39/1.18 inference(quant_inst,[status(thm)],[])).
% 1.39/1.18 tff(1901,plain,
% 1.39/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | c3_1(W))) | c0_1(a401) | c2_1(a401) | (~ndr1_0) | (~c0_1(a346)) | c1_1(a346) | (~c2_1(a346)) | c3_1(a401) | (~c1_1(a401))),
% 1.39/1.18 inference(modus_ponens,[status(thm)],[1900, 1899])).
% 1.39/1.18 tff(1902,plain,
% 1.39/1.18 ($false),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[1901, 152, 1811, 1894, 1893, 1810, 1809, 667, 1895, 1819])).
% 1.39/1.18 tff(1903,plain,(hskp28 | hskp14), inference(lemma,lemma(discharge,[]))).
% 1.39/1.18 tff(1904,plain,
% 1.39/1.18 (hskp28),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[1903, 11])).
% 1.39/1.18 tff(1905,plain,
% 1.39/1.18 (c2_1(a343)),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[777, 1904])).
% 1.39/1.18 tff(1906,plain,
% 1.39/1.18 (c1_1(a343)),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[766, 1904])).
% 1.39/1.18 tff(1907,plain,
% 1.39/1.18 (c0_1(a343)),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[755, 1904])).
% 1.39/1.18 tff(1908,assumption,(~c3_1(a343)), introduced(assumption)).
% 1.39/1.18 tff(1909,assumption,(c2_1(a343)), introduced(assumption)).
% 1.39/1.18 tff(1910,assumption,(c1_1(a343)), introduced(assumption)).
% 1.39/1.18 tff(1911,assumption,(c0_1(a343)), introduced(assumption)).
% 1.39/1.18 tff(1912,plain,
% 1.39/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a401) | c2_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a401) | c2_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.39/1.18 inference(rewrite,[status(thm)],[])).
% 1.39/1.18 tff(1913,plain,
% 1.39/1.18 (((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343)) | c2_1(a401) | c0_1(a401) | (~c1_1(a401))) <=> (c0_1(a401) | c2_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.39/1.18 inference(rewrite,[status(thm)],[])).
% 1.39/1.18 tff(1914,plain,
% 1.39/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343)) | c2_1(a401) | c0_1(a401) | (~c1_1(a401)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a401) | c2_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343))))),
% 1.39/1.18 inference(monotonicity,[status(thm)],[1913])).
% 1.39/1.18 tff(1915,plain,
% 1.39/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343)) | c2_1(a401) | c0_1(a401) | (~c1_1(a401)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a401) | c2_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.39/1.18 inference(transitivity,[status(thm)],[1914, 1912])).
% 1.39/1.18 tff(1916,plain,
% 1.39/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343)) | c2_1(a401) | c0_1(a401) | (~c1_1(a401)))),
% 1.39/1.18 inference(quant_inst,[status(thm)],[])).
% 1.39/1.18 tff(1917,plain,
% 1.39/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a401) | c2_1(a401) | (~ndr1_0) | (~c1_1(a401)) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343))),
% 1.39/1.18 inference(modus_ponens,[status(thm)],[1916, 1915])).
% 1.39/1.18 tff(1918,plain,
% 1.39/1.18 ($false),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[1917, 152, 1911, 1910, 1909, 1171, 1168, 1167, 21, 1908])).
% 1.39/1.18 tff(1919,plain,(c3_1(a343) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)) | (~c1_1(a401)) | c0_1(a401) | c2_1(a401)), inference(lemma,lemma(discharge,[]))).
% 1.39/1.18 tff(1920,plain,
% 1.39/1.18 (c3_1(a343)),
% 1.39/1.18 inference(unit_resolution,[status(thm)],[1919, 1907, 1906, 1905, 1811, 1810, 1809])).
% 1.39/1.18 tff(1921,plain,
% 1.39/1.18 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a327) | (~c3_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp20 | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a327) | (~c3_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.39/1.18 inference(rewrite,[status(thm)],[])).
% 1.39/1.18 tff(1922,plain,
% 1.39/1.18 ((hskp20 | (~ndr1_0) | (~c2_1(a343)) | (~c3_1(a343)) | (~c1_1(a343)) | c2_1(a327) | (~c1_1(a327)) | (~c0_1(a327))) <=> (hskp20 | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a327) | (~c3_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.39/1.18 inference(rewrite,[status(thm)],[])).
% 1.39/1.18 tff(1923,plain,
% 1.39/1.18 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a343)) | (~c3_1(a343)) | (~c1_1(a343)) | c2_1(a327) | (~c1_1(a327)) | (~c0_1(a327)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a327) | (~c3_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))))),
% 1.39/1.18 inference(monotonicity,[status(thm)],[1922])).
% 1.39/1.18 tff(1924,plain,
% 1.39/1.19 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a343)) | (~c3_1(a343)) | (~c1_1(a343)) | c2_1(a327) | (~c1_1(a327)) | (~c0_1(a327)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp20 | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a327) | (~c3_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.39/1.19 inference(transitivity,[status(thm)],[1923, 1921])).
% 1.39/1.19 tff(1925,plain,
% 1.39/1.19 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a343)) | (~c3_1(a343)) | (~c1_1(a343)) | c2_1(a327) | (~c1_1(a327)) | (~c0_1(a327)))),
% 1.39/1.19 inference(quant_inst,[status(thm)],[])).
% 1.39/1.19 tff(1926,plain,
% 1.39/1.19 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp20 | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a327) | (~c3_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))),
% 1.39/1.19 inference(modus_ponens,[status(thm)],[1925, 1924])).
% 1.39/1.19 tff(1927,plain,
% 1.39/1.19 (hskp20 | (~c3_1(a343))),
% 1.39/1.19 inference(unit_resolution,[status(thm)],[1926, 152, 1906, 1905, 1460, 1431, 1686, 1829])).
% 1.39/1.19 tff(1928,plain,
% 1.39/1.19 (hskp20),
% 1.39/1.19 inference(unit_resolution,[status(thm)],[1927, 1920])).
% 1.39/1.19 tff(1929,plain,
% 1.39/1.19 (~c3_1(a358)),
% 1.39/1.19 inference(unit_resolution,[status(thm)],[1699, 1928])).
% 1.39/1.19 tff(1930,plain,
% 1.39/1.19 (c2_1(a358)),
% 1.39/1.19 inference(unit_resolution,[status(thm)],[1716, 1928])).
% 1.39/1.19 tff(1931,plain,
% 1.39/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a401) | c2_1(a401) | c3_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c2_1(a358)) | (~c1_1(a401)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a401) | c2_1(a401) | c3_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c2_1(a358)) | (~c1_1(a401)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.39/1.19 inference(rewrite,[status(thm)],[])).
% 1.39/1.19 tff(1932,plain,
% 1.39/1.19 (((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c3_1(a358) | (~c1_1(a358)) | (~c2_1(a358)) | c2_1(a401) | c0_1(a401) | (~c1_1(a401))) <=> (c0_1(a401) | c2_1(a401) | c3_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c2_1(a358)) | (~c1_1(a401)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.39/1.19 inference(rewrite,[status(thm)],[])).
% 1.39/1.19 tff(1933,plain,
% 1.39/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c3_1(a358) | (~c1_1(a358)) | (~c2_1(a358)) | c2_1(a401) | c0_1(a401) | (~c1_1(a401)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a401) | c2_1(a401) | c3_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c2_1(a358)) | (~c1_1(a401)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))))),
% 1.39/1.19 inference(monotonicity,[status(thm)],[1932])).
% 1.39/1.19 tff(1934,plain,
% 1.39/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c3_1(a358) | (~c1_1(a358)) | (~c2_1(a358)) | c2_1(a401) | c0_1(a401) | (~c1_1(a401)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a401) | c2_1(a401) | c3_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c2_1(a358)) | (~c1_1(a401)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.39/1.19 inference(transitivity,[status(thm)],[1933, 1931])).
% 1.39/1.19 tff(1935,plain,
% 1.39/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c3_1(a358) | (~c1_1(a358)) | (~c2_1(a358)) | c2_1(a401) | c0_1(a401) | (~c1_1(a401)))),
% 1.39/1.19 inference(quant_inst,[status(thm)],[])).
% 1.39/1.19 tff(1936,plain,
% 1.39/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a401) | c2_1(a401) | c3_1(a358) | (~ndr1_0) | (~c1_1(a358)) | (~c2_1(a358)) | (~c1_1(a401)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))),
% 1.39/1.19 inference(modus_ponens,[status(thm)],[1935, 1934])).
% 1.39/1.19 tff(1937,plain,
% 1.39/1.19 (~c1_1(a358)),
% 1.39/1.19 inference(unit_resolution,[status(thm)],[1936, 152, 1907, 1906, 1905, 1811, 1930, 1810, 1809, 1929, 21])).
% 1.39/1.19 tff(1938,plain,
% 1.39/1.19 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))),
% 1.39/1.19 inference(bind,[status(th)],[])).
% 1.39/1.19 tff(1939,plain,
% 1.39/1.19 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.39/1.19 inference(quant_intro,[status(thm)],[1938])).
% 1.39/1.19 tff(1940,plain,
% 1.39/1.19 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.39/1.19 inference(rewrite,[status(thm)],[])).
% 1.39/1.19 tff(1941,plain,
% 1.39/1.19 (^[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)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_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)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_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)) | (~c0_1(U)) | (~c3_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(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp7) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp7))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))))),
% 1.39/1.19 inference(bind,[status(th)],[])).
% 1.39/1.19 tff(1942,plain,
% 1.39/1.19 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.39/1.19 inference(quant_intro,[status(thm)],[1941])).
% 1.39/1.19 tff(1943,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause164')).
% 1.39/1.19 tff(1944,plain,
% 1.39/1.19 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.39/1.19 inference(modus_ponens,[status(thm)],[1943, 1942])).
% 1.39/1.19 tff(1945,plain,
% 1.39/1.19 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.39/1.19 inference(modus_ponens,[status(thm)],[1944, 1940])).
% 1.39/1.19 tff(1946,plain,(
% 1.39/1.19 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.39/1.19 inference(skolemize,[status(sab)],[1945])).
% 1.39/1.19 tff(1947,plain,
% 1.39/1.19 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.39/1.19 inference(modus_ponens,[status(thm)],[1946, 1939])).
% 1.39/1.19 tff(1948,plain,
% 1.39/1.19 (~c0_1(a358)),
% 1.39/1.19 inference(unit_resolution,[status(thm)],[1705, 1928])).
% 1.39/1.19 tff(1949,plain,
% 1.39/1.19 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp7 | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c0_1(a343)) | (~c3_1(a343)) | (~c2_1(a343)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp7 | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c0_1(a343)) | (~c3_1(a343)) | (~c2_1(a343)))),
% 1.39/1.19 inference(rewrite,[status(thm)],[])).
% 1.39/1.19 tff(1950,plain,
% 1.39/1.19 ((hskp7 | (~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c3_1(a343)) | c1_1(a358) | c0_1(a358) | c3_1(a358)) <=> (hskp7 | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c0_1(a343)) | (~c3_1(a343)) | (~c2_1(a343)))),
% 1.39/1.19 inference(rewrite,[status(thm)],[])).
% 1.39/1.19 tff(1951,plain,
% 1.39/1.19 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp7 | (~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c3_1(a343)) | c1_1(a358) | c0_1(a358) | c3_1(a358))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp7 | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c0_1(a343)) | (~c3_1(a343)) | (~c2_1(a343))))),
% 1.39/1.19 inference(monotonicity,[status(thm)],[1950])).
% 1.39/1.19 tff(1952,plain,
% 1.39/1.19 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp7 | (~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c3_1(a343)) | c1_1(a358) | c0_1(a358) | c3_1(a358))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp7 | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c0_1(a343)) | (~c3_1(a343)) | (~c2_1(a343)))),
% 1.39/1.19 inference(transitivity,[status(thm)],[1951, 1949])).
% 1.39/1.19 tff(1953,plain,
% 1.39/1.19 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp7 | (~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c3_1(a343)) | c1_1(a358) | c0_1(a358) | c3_1(a358))),
% 1.39/1.19 inference(quant_inst,[status(thm)],[])).
% 1.39/1.19 tff(1954,plain,
% 1.39/1.19 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp7 | c0_1(a358) | c3_1(a358) | (~ndr1_0) | c1_1(a358) | (~c0_1(a343)) | (~c3_1(a343)) | (~c2_1(a343))),
% 1.39/1.19 inference(modus_ponens,[status(thm)],[1953, 1952])).
% 1.39/1.19 tff(1955,plain,
% 1.39/1.19 (hskp7),
% 1.39/1.19 inference(unit_resolution,[status(thm)],[1954, 152, 1907, 1905, 1948, 1929, 1947, 1920, 1937])).
% 1.39/1.19 tff(1956,plain,
% 1.39/1.19 (~c1_1(a330)),
% 1.39/1.19 inference(unit_resolution,[status(thm)],[51, 1955])).
% 1.39/1.19 tff(1957,plain,
% 1.39/1.19 (c3_1(a330)),
% 1.39/1.19 inference(unit_resolution,[status(thm)],[62, 1955])).
% 1.39/1.19 tff(1958,plain,
% 1.39/1.19 (~c0_1(a330)),
% 1.39/1.19 inference(unit_resolution,[status(thm)],[68, 1955])).
% 1.39/1.19 tff(1959,plain,
% 1.39/1.19 (hskp16),
% 1.39/1.19 inference(unit_resolution,[status(thm)],[819, 1958, 1957, 1956, 11])).
% 1.39/1.19 tff(1960,plain,
% 1.39/1.19 (~c2_1(a349)),
% 1.39/1.19 inference(unit_resolution,[status(thm)],[825, 1959])).
% 1.39/1.19 tff(1961,plain,
% 1.39/1.19 (c3_1(a349)),
% 1.39/1.19 inference(unit_resolution,[status(thm)],[836, 1959])).
% 1.39/1.19 tff(1962,plain,
% 1.39/1.19 (hskp13),
% 1.39/1.19 inference(unit_resolution,[status(thm)],[1723, 152, 11, 1930, 1948, 1929, 530])).
% 1.39/1.19 tff(1963,plain,
% 1.39/1.19 (c2_1(a346)),
% 1.39/1.19 inference(unit_resolution,[status(thm)],[565, 1962])).
% 1.39/1.19 tff(1964,plain,
% 1.39/1.19 (~c3_1(a346)),
% 1.39/1.19 inference(unit_resolution,[status(thm)],[554, 1962])).
% 1.39/1.19 tff(1965,plain,
% 1.39/1.19 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp10 | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | c2_1(a327) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp10 | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | c2_1(a327) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.39/1.19 inference(rewrite,[status(thm)],[])).
% 1.39/1.19 tff(1966,plain,
% 1.39/1.19 ((hskp10 | (~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a327) | c3_1(a327) | (~c0_1(a327))) <=> (hskp10 | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | c2_1(a327) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.39/1.19 inference(rewrite,[status(thm)],[])).
% 1.39/1.19 tff(1967,plain,
% 1.39/1.19 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a327) | c3_1(a327) | (~c0_1(a327)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp10 | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | c2_1(a327) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))))),
% 1.39/1.19 inference(monotonicity,[status(thm)],[1966])).
% 1.39/1.19 tff(1968,plain,
% 1.39/1.19 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a327) | c3_1(a327) | (~c0_1(a327)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp10 | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | c2_1(a327) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.39/1.19 inference(transitivity,[status(thm)],[1967, 1965])).
% 1.39/1.19 tff(1969,plain,
% 1.39/1.19 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a327) | c3_1(a327) | (~c0_1(a327)))),
% 1.39/1.19 inference(quant_inst,[status(thm)],[])).
% 1.39/1.19 tff(1970,plain,
% 1.39/1.19 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp10 | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | c2_1(a327) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))),
% 1.39/1.19 inference(modus_ponens,[status(thm)],[1969, 1968])).
% 1.39/1.19 tff(1971,plain,
% 1.39/1.19 (hskp10),
% 1.39/1.19 inference(unit_resolution,[status(thm)],[1970, 152, 1907, 1906, 1905, 1460, 1420, 904, 1829])).
% 1.39/1.19 tff(1972,plain,
% 1.39/1.19 (~c3_1(a337)),
% 1.39/1.19 inference(unit_resolution,[status(thm)],[438, 1971])).
% 1.39/1.19 tff(1973,plain,
% 1.39/1.19 (c0_1(a346)),
% 1.39/1.19 inference(unit_resolution,[status(thm)],[576, 1962])).
% 1.39/1.19 tff(1974,plain,
% 1.39/1.19 (~c2_1(a337)),
% 1.39/1.19 inference(unit_resolution,[status(thm)],[444, 1971])).
% 1.39/1.19 tff(1975,plain,
% 1.39/1.19 (c0_1(a337)),
% 1.39/1.19 inference(unit_resolution,[status(thm)],[455, 1971])).
% 1.39/1.19 tff(1976,plain,
% 1.39/1.19 (c1_1(a349)),
% 1.39/1.19 inference(unit_resolution,[status(thm)],[847, 1959])).
% 1.39/1.19 tff(1977,plain,
% 1.39/1.19 (~hskp21),
% 1.39/1.19 inference(unit_resolution,[status(thm)],[1762, 1976, 1975, 1974, 1973, 1972, 1964, 1963, 1961, 1960])).
% 1.39/1.19 tff(1978,plain,
% 1.39/1.19 (hskp21 | c1_1(a337)),
% 1.39/1.19 inference(unit_resolution,[status(thm)],[1769, 152, 1460, 1431, 1974, 1972, 1420, 1575])).
% 1.39/1.19 tff(1979,plain,
% 1.39/1.19 (c1_1(a337)),
% 1.39/1.19 inference(unit_resolution,[status(thm)],[1978, 1977])).
% 1.39/1.19 tff(1980,plain,
% 1.39/1.19 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a327))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a327))),
% 1.39/1.19 inference(rewrite,[status(thm)],[])).
% 1.39/1.19 tff(1981,plain,
% 1.39/1.19 ((hskp8 | (~ndr1_0) | c3_1(a327) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a327) | (~c1_1(a327)) | (~c0_1(a327))) <=> (hskp8 | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a327))),
% 1.39/1.19 inference(rewrite,[status(thm)],[])).
% 1.39/1.19 tff(1982,plain,
% 1.39/1.19 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a327) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a327) | (~c1_1(a327)) | (~c0_1(a327)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a327)))),
% 1.39/1.19 inference(monotonicity,[status(thm)],[1981])).
% 1.39/1.19 tff(1983,plain,
% 1.39/1.19 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a327) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a327) | (~c1_1(a327)) | (~c0_1(a327)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a327))),
% 1.39/1.19 inference(transitivity,[status(thm)],[1982, 1980])).
% 1.39/1.19 tff(1984,plain,
% 1.39/1.19 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a327) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a327) | (~c1_1(a327)) | (~c0_1(a327)))),
% 1.39/1.19 inference(quant_inst,[status(thm)],[])).
% 1.39/1.19 tff(1985,plain,
% 1.39/1.19 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a327)),
% 1.39/1.19 inference(modus_ponens,[status(thm)],[1984, 1983])).
% 1.39/1.19 tff(1986,plain,
% 1.39/1.19 (hskp8),
% 1.39/1.19 inference(unit_resolution,[status(thm)],[1985, 152, 1460, 1431, 1420, 1549, 1829])).
% 1.39/1.19 tff(1987,plain,
% 1.39/1.19 (~c3_1(a332)),
% 1.39/1.19 inference(unit_resolution,[status(thm)],[694, 1986])).
% 1.39/1.19 tff(1988,plain,
% 1.39/1.19 (~c2_1(a332)),
% 1.39/1.19 inference(unit_resolution,[status(thm)],[700, 1986])).
% 1.39/1.19 tff(1989,plain,
% 1.39/1.19 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | c2_1(a332) | c3_1(a332) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c1_1(a332))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp21 | c2_1(a332) | c3_1(a332) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c1_1(a332))),
% 1.39/1.19 inference(rewrite,[status(thm)],[])).
% 1.39/1.19 tff(1990,plain,
% 1.39/1.19 ((hskp21 | (~ndr1_0) | c3_1(a327) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a332) | c1_1(a332) | c3_1(a332)) <=> (hskp21 | c2_1(a332) | c3_1(a332) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c1_1(a332))),
% 1.39/1.19 inference(rewrite,[status(thm)],[])).
% 1.39/1.19 tff(1991,plain,
% 1.39/1.19 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | (~ndr1_0) | c3_1(a327) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a332) | c1_1(a332) | c3_1(a332))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | c2_1(a332) | c3_1(a332) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c1_1(a332)))),
% 1.39/1.19 inference(monotonicity,[status(thm)],[1990])).
% 1.39/1.19 tff(1992,plain,
% 1.39/1.19 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | (~ndr1_0) | c3_1(a327) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a332) | c1_1(a332) | c3_1(a332))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp21 | c2_1(a332) | c3_1(a332) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c1_1(a332))),
% 1.39/1.19 inference(transitivity,[status(thm)],[1991, 1989])).
% 1.39/1.19 tff(1993,plain,
% 1.39/1.19 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | (~ndr1_0) | c3_1(a327) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a332) | c1_1(a332) | c3_1(a332))),
% 1.39/1.19 inference(quant_inst,[status(thm)],[])).
% 1.39/1.19 tff(1994,plain,
% 1.39/1.19 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp21 | c2_1(a332) | c3_1(a332) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c1_1(a332)),
% 1.39/1.19 inference(modus_ponens,[status(thm)],[1993, 1992])).
% 1.39/1.19 tff(1995,plain,
% 1.39/1.19 (hskp21 | c1_1(a332)),
% 1.39/1.19 inference(unit_resolution,[status(thm)],[1994, 152, 1460, 1431, 1988, 1987, 1420, 1575])).
% 1.39/1.19 tff(1996,plain,
% 1.39/1.19 (c1_1(a332)),
% 1.39/1.19 inference(unit_resolution,[status(thm)],[1995, 1977])).
% 1.39/1.19 tff(1997,plain,
% 1.39/1.19 (~c1_1(a346)),
% 1.39/1.19 inference(unit_resolution,[status(thm)],[1329, 152, 1811, 1973, 1963, 1810, 1809, 1964, 21])).
% 1.39/1.19 tff(1998,plain,
% 1.39/1.19 (~c0_1(a332)),
% 1.39/1.19 inference(unit_resolution,[status(thm)],[706, 1986])).
% 1.39/1.19 tff(1999,plain,
% 1.39/1.19 ($false),
% 1.39/1.19 inference(unit_resolution,[status(thm)],[1803, 152, 1973, 1963, 1974, 1972, 1998, 1987, 667, 1997, 1996, 1979])).
% 1.39/1.19 tff(2000,plain,(hskp14), inference(lemma,lemma(discharge,[]))).
% 1.39/1.19 tff(2001,plain,
% 1.39/1.19 (~c1_1(a347)),
% 1.39/1.19 inference(unit_resolution,[status(thm)],[1003, 2000])).
% 1.39/1.19 tff(2002,plain,
% 1.39/1.19 (c3_1(a347)),
% 1.39/1.19 inference(unit_resolution,[status(thm)],[1017, 2000])).
% 1.39/1.19 tff(2003,plain,
% 1.39/1.19 (c2_1(a347)),
% 1.39/1.19 inference(unit_resolution,[status(thm)],[1028, 2000])).
% 1.39/1.19 tff(2004,assumption,(c3_1(a359)), introduced(assumption)).
% 1.39/1.19 tff(2005,assumption,(ndr1_0), introduced(assumption)).
% 1.39/1.19 tff(2006,assumption,(~c1_1(a347)), introduced(assumption)).
% 1.39/1.19 tff(2007,assumption,(~c2_1(a359)), introduced(assumption)).
% 1.39/1.19 tff(2008,assumption,(~c0_1(a359)), introduced(assumption)).
% 1.39/1.19 tff(2009,plain,
% 1.39/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a419) | c2_1(a419) | c0_1(a359) | c2_1(a359) | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)) | (~c3_1(a359)) | (~c0_1(a419)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a419) | c2_1(a419) | c0_1(a359) | c2_1(a359) | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)) | (~c3_1(a359)) | (~c0_1(a419)))),
% 1.39/1.19 inference(rewrite,[status(thm)],[])).
% 1.39/1.19 tff(2010,plain,
% 1.39/1.19 (((~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)) | c2_1(a419) | c1_1(a419) | (~c0_1(a419)) | c2_1(a359) | c0_1(a359) | (~c3_1(a359))) <=> (c1_1(a419) | c2_1(a419) | c0_1(a359) | c2_1(a359) | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)) | (~c3_1(a359)) | (~c0_1(a419)))),
% 1.39/1.19 inference(rewrite,[status(thm)],[])).
% 1.39/1.19 tff(2011,plain,
% 1.39/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)) | c2_1(a419) | c1_1(a419) | (~c0_1(a419)) | c2_1(a359) | c0_1(a359) | (~c3_1(a359)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a419) | c2_1(a419) | c0_1(a359) | c2_1(a359) | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)) | (~c3_1(a359)) | (~c0_1(a419))))),
% 1.39/1.19 inference(monotonicity,[status(thm)],[2010])).
% 1.39/1.19 tff(2012,plain,
% 1.39/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)) | c2_1(a419) | c1_1(a419) | (~c0_1(a419)) | c2_1(a359) | c0_1(a359) | (~c3_1(a359)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a419) | c2_1(a419) | c0_1(a359) | c2_1(a359) | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)) | (~c3_1(a359)) | (~c0_1(a419)))),
% 1.39/1.19 inference(transitivity,[status(thm)],[2011, 2009])).
% 1.39/1.19 tff(2013,plain,
% 1.39/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)) | c2_1(a419) | c1_1(a419) | (~c0_1(a419)) | c2_1(a359) | c0_1(a359) | (~c3_1(a359)))),
% 1.39/1.19 inference(quant_inst,[status(thm)],[])).
% 1.39/1.19 tff(2014,plain,
% 1.39/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a419) | c2_1(a419) | c0_1(a359) | c2_1(a359) | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)) | (~c3_1(a359)) | (~c0_1(a419))),
% 1.39/1.19 inference(modus_ponens,[status(thm)],[2013, 2012])).
% 1.39/1.19 tff(2015,plain,
% 1.39/1.19 (c1_1(a419) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)) | (~c3_1(a359)) | (~c0_1(a419))),
% 1.39/1.19 inference(unit_resolution,[status(thm)],[2014, 244, 2008, 2007, 2006, 509])).
% 1.39/1.19 tff(2016,plain,
% 1.39/1.19 ($false),
% 1.39/1.19 inference(unit_resolution,[status(thm)],[2015, 1169, 1170, 2005, 2004, 246, 245])).
% 1.39/1.19 tff(2017,plain,((~hskp14) | (~ndr1_0) | (~c3_1(a359)) | (~c0_1(a419)) | c1_1(a419) | c2_1(a419) | c0_1(a359) | c2_1(a359) | c1_1(a347)), inference(lemma,lemma(discharge,[]))).
% 1.39/1.19 tff(2018,plain,
% 1.39/1.19 ((~hskp14) | (~c3_1(a359)) | (~c0_1(a419)) | c1_1(a419) | c2_1(a419) | c0_1(a359) | c2_1(a359) | c1_1(a347)),
% 1.39/1.19 inference(unit_resolution,[status(thm)],[2017, 152])).
% 1.39/1.19 tff(2019,plain,
% 1.39/1.19 ((~c3_1(a359)) | (~c0_1(a419)) | c1_1(a419) | c2_1(a419) | c0_1(a359) | c2_1(a359)),
% 1.39/1.19 inference(unit_resolution,[status(thm)],[2018, 2000, 2001])).
% 1.39/1.19 tff(2020,plain,
% 1.39/1.19 ($false),
% 1.39/1.19 inference(unit_resolution,[status(thm)],[2019, 1735, 1732, 245, 244, 246, 1731])).
% 1.39/1.19 tff(2021,plain,((~hskp21) | c1_1(a419) | c2_1(a419) | (~c0_1(a419))), inference(lemma,lemma(discharge,[]))).
% 1.39/1.19 tff(2022,plain,
% 1.39/1.19 (~hskp21),
% 1.39/1.19 inference(unit_resolution,[status(thm)],[2021, 982, 981, 983])).
% 1.39/1.19 tff(2023,plain,
% 1.39/1.19 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | c1_1(a419) | c2_1(a419) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c3_1(a419))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp21 | c1_1(a419) | c2_1(a419) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c3_1(a419))),
% 1.39/1.19 inference(rewrite,[status(thm)],[])).
% 1.39/1.19 tff(2024,plain,
% 1.39/1.19 ((hskp21 | (~ndr1_0) | c3_1(a327) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a419) | c1_1(a419) | c3_1(a419)) <=> (hskp21 | c1_1(a419) | c2_1(a419) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c3_1(a419))),
% 1.39/1.19 inference(rewrite,[status(thm)],[])).
% 1.39/1.19 tff(2025,plain,
% 1.39/1.19 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | (~ndr1_0) | c3_1(a327) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a419) | c1_1(a419) | c3_1(a419))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | c1_1(a419) | c2_1(a419) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c3_1(a419)))),
% 1.39/1.19 inference(monotonicity,[status(thm)],[2024])).
% 1.39/1.19 tff(2026,plain,
% 1.39/1.19 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | (~ndr1_0) | c3_1(a327) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a419) | c1_1(a419) | c3_1(a419))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp21 | c1_1(a419) | c2_1(a419) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c3_1(a419))),
% 1.39/1.20 inference(transitivity,[status(thm)],[2025, 2023])).
% 1.39/1.20 tff(2027,plain,
% 1.39/1.20 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | (~ndr1_0) | c3_1(a327) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a419) | c1_1(a419) | c3_1(a419))),
% 1.39/1.20 inference(quant_inst,[status(thm)],[])).
% 1.39/1.20 tff(2028,plain,
% 1.39/1.20 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp21 | c1_1(a419) | c2_1(a419) | c3_1(a327) | (~ndr1_0) | (~c0_1(a327)) | (~c1_1(a327)) | c3_1(a419)),
% 1.39/1.20 inference(modus_ponens,[status(thm)],[2027, 2026])).
% 1.39/1.20 tff(2029,plain,
% 1.39/1.20 (hskp21 | c3_1(a419)),
% 1.39/1.20 inference(unit_resolution,[status(thm)],[2028, 152, 1460, 1431, 982, 981, 1420, 1575])).
% 1.39/1.20 tff(2030,plain,
% 1.39/1.20 (c3_1(a419)),
% 1.39/1.20 inference(unit_resolution,[status(thm)],[2029, 2022])).
% 1.39/1.20 tff(2031,plain,
% 1.39/1.20 (hskp2 | (~c3_1(a419))),
% 1.39/1.20 inference(unit_resolution,[status(thm)],[989, 152, 983, 982, 981, 979])).
% 1.39/1.20 tff(2032,plain,
% 1.39/1.20 (hskp2),
% 1.39/1.20 inference(unit_resolution,[status(thm)],[2031, 2030])).
% 1.39/1.20 tff(2033,plain,
% 1.39/1.20 (~c1_1(a324)),
% 1.39/1.20 inference(unit_resolution,[status(thm)],[1270, 2032])).
% 1.39/1.20 tff(2034,plain,
% 1.39/1.20 (~c0_1(a324)),
% 1.39/1.20 inference(unit_resolution,[status(thm)],[1285, 2032])).
% 1.39/1.20 tff(2035,plain,
% 1.39/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a419) | c1_1(a347) | c0_1(a324) | c1_1(a324) | (~ndr1_0) | (~c2_1(a324)) | (~c2_1(a347)) | (~c3_1(a347)) | (~c3_1(a419)) | (~c0_1(a419)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a419) | c1_1(a347) | c0_1(a324) | c1_1(a324) | (~ndr1_0) | (~c2_1(a324)) | (~c2_1(a347)) | (~c3_1(a347)) | (~c3_1(a419)) | (~c0_1(a419)))),
% 1.39/1.20 inference(rewrite,[status(thm)],[])).
% 1.39/1.20 tff(2036,plain,
% 1.39/1.20 (((~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)) | c1_1(a419) | (~c3_1(a419)) | (~c0_1(a419)) | c0_1(a324) | c1_1(a324) | (~c2_1(a324))) <=> (c1_1(a419) | c1_1(a347) | c0_1(a324) | c1_1(a324) | (~ndr1_0) | (~c2_1(a324)) | (~c2_1(a347)) | (~c3_1(a347)) | (~c3_1(a419)) | (~c0_1(a419)))),
% 1.39/1.20 inference(rewrite,[status(thm)],[])).
% 1.39/1.20 tff(2037,plain,
% 1.39/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)) | c1_1(a419) | (~c3_1(a419)) | (~c0_1(a419)) | c0_1(a324) | c1_1(a324) | (~c2_1(a324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a419) | c1_1(a347) | c0_1(a324) | c1_1(a324) | (~ndr1_0) | (~c2_1(a324)) | (~c2_1(a347)) | (~c3_1(a347)) | (~c3_1(a419)) | (~c0_1(a419))))),
% 1.39/1.20 inference(monotonicity,[status(thm)],[2036])).
% 1.39/1.20 tff(2038,plain,
% 1.39/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)) | c1_1(a419) | (~c3_1(a419)) | (~c0_1(a419)) | c0_1(a324) | c1_1(a324) | (~c2_1(a324)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a419) | c1_1(a347) | c0_1(a324) | c1_1(a324) | (~ndr1_0) | (~c2_1(a324)) | (~c2_1(a347)) | (~c3_1(a347)) | (~c3_1(a419)) | (~c0_1(a419)))),
% 1.39/1.20 inference(transitivity,[status(thm)],[2037, 2035])).
% 1.39/1.20 tff(2039,plain,
% 1.39/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a347) | (~c2_1(a347)) | (~c3_1(a347)) | c1_1(a419) | (~c3_1(a419)) | (~c0_1(a419)) | c0_1(a324) | c1_1(a324) | (~c2_1(a324)))),
% 1.39/1.20 inference(quant_inst,[status(thm)],[])).
% 1.39/1.20 tff(2040,plain,
% 1.39/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a419) | c1_1(a347) | c0_1(a324) | c1_1(a324) | (~ndr1_0) | (~c2_1(a324)) | (~c2_1(a347)) | (~c3_1(a347)) | (~c3_1(a419)) | (~c0_1(a419))),
% 1.39/1.20 inference(modus_ponens,[status(thm)],[2039, 2038])).
% 1.39/1.20 tff(2041,plain,
% 1.39/1.20 (~c2_1(a324)),
% 1.39/1.20 inference(unit_resolution,[status(thm)],[2040, 152, 983, 2003, 2002, 982, 2001, 2034, 2033, 264, 2030])).
% 1.39/1.20 tff(2042,plain,
% 1.39/1.20 (~c3_1(a324)),
% 1.39/1.20 inference(unit_resolution,[status(thm)],[1264, 2032])).
% 1.39/1.20 tff(2043,plain,
% 1.39/1.20 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | c3_1(a327) | c1_1(a324) | c3_1(a324) | (~ndr1_0) | c2_1(a324) | (~c0_1(a327)) | (~c1_1(a327)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp21 | c3_1(a327) | c1_1(a324) | c3_1(a324) | (~ndr1_0) | c2_1(a324) | (~c0_1(a327)) | (~c1_1(a327)))),
% 1.39/1.20 inference(rewrite,[status(thm)],[])).
% 1.39/1.20 tff(2044,plain,
% 1.39/1.20 ((hskp21 | (~ndr1_0) | c3_1(a327) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a324) | c1_1(a324) | c3_1(a324)) <=> (hskp21 | c3_1(a327) | c1_1(a324) | c3_1(a324) | (~ndr1_0) | c2_1(a324) | (~c0_1(a327)) | (~c1_1(a327)))),
% 1.39/1.20 inference(rewrite,[status(thm)],[])).
% 1.39/1.20 tff(2045,plain,
% 1.39/1.20 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | (~ndr1_0) | c3_1(a327) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a324) | c1_1(a324) | c3_1(a324))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | c3_1(a327) | c1_1(a324) | c3_1(a324) | (~ndr1_0) | c2_1(a324) | (~c0_1(a327)) | (~c1_1(a327))))),
% 1.39/1.20 inference(monotonicity,[status(thm)],[2044])).
% 1.39/1.20 tff(2046,plain,
% 1.39/1.20 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | (~ndr1_0) | c3_1(a327) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a324) | c1_1(a324) | c3_1(a324))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp21 | c3_1(a327) | c1_1(a324) | c3_1(a324) | (~ndr1_0) | c2_1(a324) | (~c0_1(a327)) | (~c1_1(a327)))),
% 1.39/1.20 inference(transitivity,[status(thm)],[2045, 2043])).
% 1.39/1.20 tff(2047,plain,
% 1.39/1.20 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp21 | (~ndr1_0) | c3_1(a327) | (~c0_1(a327)) | (~c1_1(a327)) | c2_1(a324) | c1_1(a324) | c3_1(a324))),
% 1.39/1.20 inference(quant_inst,[status(thm)],[])).
% 1.39/1.20 tff(2048,plain,
% 1.39/1.20 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp21 | c3_1(a327) | c1_1(a324) | c3_1(a324) | (~ndr1_0) | c2_1(a324) | (~c0_1(a327)) | (~c1_1(a327))),
% 1.39/1.20 inference(modus_ponens,[status(thm)],[2047, 2046])).
% 1.39/1.20 tff(2049,plain,
% 1.39/1.20 ($false),
% 1.39/1.20 inference(unit_resolution,[status(thm)],[2048, 152, 2022, 1460, 1431, 1420, 2033, 2042, 1575, 2041])).
% 1.39/1.20 tff(2050,plain,(~hskp25), inference(lemma,lemma(discharge,[]))).
% 1.39/1.20 tff(2051,plain,
% 1.39/1.20 (hskp16),
% 1.39/1.20 inference(unit_resolution,[status(thm)],[92, 2050])).
% 1.39/1.20 tff(2052,plain,
% 1.39/1.20 (~c2_1(a349)),
% 1.39/1.20 inference(unit_resolution,[status(thm)],[825, 2051])).
% 1.39/1.20 tff(2053,assumption,(hskp22), introduced(assumption)).
% 1.39/1.20 tff(2054,plain,
% 1.39/1.20 (~c2_1(a367)),
% 1.39/1.20 inference(unit_resolution,[status(thm)],[476, 2053])).
% 1.39/1.20 tff(2055,plain,
% 1.39/1.20 (~c1_1(a367)),
% 1.39/1.20 inference(unit_resolution,[status(thm)],[470, 2053])).
% 1.39/1.20 tff(2056,plain,
% 1.39/1.20 (c3_1(a349)),
% 1.39/1.20 inference(unit_resolution,[status(thm)],[836, 2051])).
% 1.39/1.20 tff(2057,plain,
% 1.39/1.20 (c1_1(a349)),
% 1.39/1.20 inference(unit_resolution,[status(thm)],[847, 2051])).
% 1.39/1.20 tff(2058,plain,
% 1.39/1.20 (c3_1(a367)),
% 1.39/1.20 inference(unit_resolution,[status(thm)],[487, 2053])).
% 1.39/1.20 tff(2059,plain,
% 1.39/1.20 ($false),
% 1.39/1.20 inference(unit_resolution,[status(thm)],[854, 616, 152, 1061, 1060, 1059, 41])).
% 1.39/1.20 tff(2060,plain,((~hskp16) | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.39/1.20 tff(2061,plain,
% 1.39/1.20 (hskp28),
% 1.39/1.20 inference(unit_resolution,[status(thm)],[2060, 2051])).
% 1.39/1.20 tff(2062,plain,
% 1.39/1.20 (c2_1(a343)),
% 1.39/1.20 inference(unit_resolution,[status(thm)],[777, 2061])).
% 1.39/1.20 tff(2063,plain,
% 1.39/1.20 (c1_1(a343)),
% 1.39/1.20 inference(unit_resolution,[status(thm)],[766, 2061])).
% 1.39/1.20 tff(2064,plain,
% 1.39/1.20 (c0_1(a343)),
% 1.39/1.20 inference(unit_resolution,[status(thm)],[755, 2061])).
% 1.39/1.20 tff(2065,plain,
% 1.39/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a367) | c2_1(a367) | c2_1(a349) | (~ndr1_0) | (~c3_1(a367)) | (~c3_1(a349)) | (~c1_1(a349)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a367) | c2_1(a367) | c2_1(a349) | (~ndr1_0) | (~c3_1(a367)) | (~c3_1(a349)) | (~c1_1(a349)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.39/1.20 inference(rewrite,[status(thm)],[])).
% 1.39/1.20 tff(2066,plain,
% 1.39/1.20 (((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a349) | (~c3_1(a349)) | (~c1_1(a349)) | c2_1(a367) | c1_1(a367) | (~c3_1(a367))) <=> (c1_1(a367) | c2_1(a367) | c2_1(a349) | (~ndr1_0) | (~c3_1(a367)) | (~c3_1(a349)) | (~c1_1(a349)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.39/1.20 inference(rewrite,[status(thm)],[])).
% 1.39/1.20 tff(2067,plain,
% 1.39/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a349) | (~c3_1(a349)) | (~c1_1(a349)) | c2_1(a367) | c1_1(a367) | (~c3_1(a367)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a367) | c2_1(a367) | c2_1(a349) | (~ndr1_0) | (~c3_1(a367)) | (~c3_1(a349)) | (~c1_1(a349)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))))),
% 1.39/1.20 inference(monotonicity,[status(thm)],[2066])).
% 1.39/1.20 tff(2068,plain,
% 1.39/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a349) | (~c3_1(a349)) | (~c1_1(a349)) | c2_1(a367) | c1_1(a367) | (~c3_1(a367)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a367) | c2_1(a367) | c2_1(a349) | (~ndr1_0) | (~c3_1(a367)) | (~c3_1(a349)) | (~c1_1(a349)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.39/1.20 inference(transitivity,[status(thm)],[2067, 2065])).
% 1.39/1.20 tff(2069,plain,
% 1.39/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a349) | (~c3_1(a349)) | (~c1_1(a349)) | c2_1(a367) | c1_1(a367) | (~c3_1(a367)))),
% 1.39/1.20 inference(quant_inst,[status(thm)],[])).
% 1.39/1.20 tff(2070,plain,
% 1.39/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a367) | c2_1(a367) | c2_1(a349) | (~ndr1_0) | (~c3_1(a367)) | (~c3_1(a349)) | (~c1_1(a349)) | (~c0_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))),
% 1.39/1.20 inference(modus_ponens,[status(thm)],[2069, 2068])).
% 1.39/1.20 tff(2071,plain,
% 1.39/1.20 ($false),
% 1.39/1.20 inference(unit_resolution,[status(thm)],[2070, 152, 2064, 2063, 2062, 2058, 2057, 2056, 2055, 2054, 2052, 788])).
% 1.39/1.20 tff(2072,plain,(~hskp22), inference(lemma,lemma(discharge,[]))).
% 1.39/1.20 tff(2073,plain,
% 1.39/1.20 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp22 | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)) | (~c3_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp22 | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)) | (~c3_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.39/1.20 inference(rewrite,[status(thm)],[])).
% 1.39/1.20 tff(2074,plain,
% 1.39/1.20 ((hskp22 | (~ndr1_0) | (~c2_1(a343)) | (~c3_1(a343)) | (~c1_1(a343)) | c1_1(a347) | (~c3_1(a347)) | (~c2_1(a347))) <=> (hskp22 | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)) | (~c3_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.39/1.20 inference(rewrite,[status(thm)],[])).
% 1.39/1.20 tff(2075,plain,
% 1.39/1.20 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp22 | (~ndr1_0) | (~c2_1(a343)) | (~c3_1(a343)) | (~c1_1(a343)) | c1_1(a347) | (~c3_1(a347)) | (~c2_1(a347)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp22 | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)) | (~c3_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))))),
% 1.39/1.20 inference(monotonicity,[status(thm)],[2074])).
% 1.39/1.20 tff(2076,plain,
% 1.39/1.20 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp22 | (~ndr1_0) | (~c2_1(a343)) | (~c3_1(a343)) | (~c1_1(a343)) | c1_1(a347) | (~c3_1(a347)) | (~c2_1(a347)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp22 | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)) | (~c3_1(a343)) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.39/1.20 inference(transitivity,[status(thm)],[2075, 2073])).
% 1.39/1.20 tff(2077,plain,
% 1.39/1.20 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp22 | (~ndr1_0) | (~c2_1(a343)) | (~c3_1(a343)) | (~c1_1(a343)) | c1_1(a347) | (~c3_1(a347)) | (~c2_1(a347)))),
% 1.39/1.20 inference(quant_inst,[status(thm)],[])).
% 1.39/1.20 tff(2078,plain,
% 1.39/1.20 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp22 | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)) | (~c3_1(a343)) | (~c1_1(a343)) | (~c2_1(a343))),
% 1.39/1.20 inference(modus_ponens,[status(thm)],[2077, 2076])).
% 1.39/1.20 tff(2079,plain,
% 1.39/1.20 (hskp22 | (~c3_1(a343))),
% 1.39/1.20 inference(unit_resolution,[status(thm)],[2078, 152, 2063, 2062, 2003, 2002, 2001, 10])).
% 1.39/1.20 tff(2080,plain,
% 1.39/1.20 (~c3_1(a343)),
% 1.39/1.20 inference(unit_resolution,[status(thm)],[2079, 2072])).
% 1.39/1.20 tff(2081,plain,
% 1.39/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a349) | (~ndr1_0) | c0_1(a349) | (~c1_1(a349)) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a349) | (~ndr1_0) | c0_1(a349) | (~c1_1(a349)) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.39/1.20 inference(rewrite,[status(thm)],[])).
% 1.39/1.20 tff(2082,plain,
% 1.39/1.20 (((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343)) | c2_1(a349) | c0_1(a349) | (~c1_1(a349))) <=> (c2_1(a349) | (~ndr1_0) | c0_1(a349) | (~c1_1(a349)) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.39/1.20 inference(rewrite,[status(thm)],[])).
% 1.39/1.20 tff(2083,plain,
% 1.39/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343)) | c2_1(a349) | c0_1(a349) | (~c1_1(a349)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a349) | (~ndr1_0) | c0_1(a349) | (~c1_1(a349)) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343))))),
% 1.39/1.20 inference(monotonicity,[status(thm)],[2082])).
% 1.39/1.20 tff(2084,plain,
% 1.39/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343)) | c2_1(a349) | c0_1(a349) | (~c1_1(a349)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a349) | (~ndr1_0) | c0_1(a349) | (~c1_1(a349)) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343)))),
% 1.39/1.20 inference(transitivity,[status(thm)],[2083, 2081])).
% 1.39/1.20 tff(2085,plain,
% 1.39/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a343)) | (~c0_1(a343)) | (~c1_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343)) | c2_1(a349) | c0_1(a349) | (~c1_1(a349)))),
% 1.39/1.20 inference(quant_inst,[status(thm)],[])).
% 1.39/1.20 tff(2086,plain,
% 1.39/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a349) | (~ndr1_0) | c0_1(a349) | (~c1_1(a349)) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343)) | (~c2_1(a343))),
% 1.39/1.20 inference(modus_ponens,[status(thm)],[2085, 2084])).
% 1.39/1.20 tff(2087,plain,
% 1.39/1.20 (c0_1(a349)),
% 1.39/1.20 inference(unit_resolution,[status(thm)],[2086, 152, 2064, 2063, 2062, 2057, 2052, 21, 2080])).
% 1.39/1.20 tff(2088,plain,
% 1.39/1.20 (^[V: $i, U: $i] : refl((hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 1.39/1.20 inference(bind,[status(th)],[])).
% 1.39/1.20 tff(2089,plain,
% 1.39/1.20 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.39/1.20 inference(quant_intro,[status(thm)],[2088])).
% 1.39/1.20 tff(2090,plain,
% 1.39/1.20 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.39/1.20 inference(rewrite,[status(thm)],[])).
% 1.39/1.20 tff(2091,plain,
% 1.39/1.20 (^[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) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp17) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp17))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 1.39/1.20 inference(bind,[status(th)],[])).
% 1.39/1.20 tff(2092,plain,
% 1.39/1.20 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp17) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.39/1.20 inference(quant_intro,[status(thm)],[2091])).
% 1.39/1.20 tff(2093,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause181')).
% 1.39/1.20 tff(2094,plain,
% 1.39/1.20 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.39/1.20 inference(modus_ponens,[status(thm)],[2093, 2092])).
% 1.39/1.20 tff(2095,plain,
% 1.39/1.20 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.39/1.20 inference(modus_ponens,[status(thm)],[2094, 2090])).
% 1.39/1.20 tff(2096,plain,(
% 1.39/1.20 ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.39/1.20 inference(skolemize,[status(sab)],[2095])).
% 1.39/1.20 tff(2097,plain,
% 1.39/1.20 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.39/1.20 inference(modus_ponens,[status(thm)],[2096, 2089])).
% 1.39/1.20 tff(2098,plain,
% 1.39/1.20 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp17 | c2_1(a349) | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)) | (~c0_1(a349)) | (~c1_1(a349)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp17 | c2_1(a349) | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)) | (~c0_1(a349)) | (~c1_1(a349)))),
% 1.39/1.20 inference(rewrite,[status(thm)],[])).
% 1.39/1.20 tff(2099,plain,
% 1.39/1.20 ((hskp17 | (~ndr1_0) | c2_1(a349) | (~c0_1(a349)) | (~c1_1(a349)) | c1_1(a347) | (~c3_1(a347)) | (~c2_1(a347))) <=> (hskp17 | c2_1(a349) | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)) | (~c0_1(a349)) | (~c1_1(a349)))),
% 1.39/1.20 inference(rewrite,[status(thm)],[])).
% 1.39/1.20 tff(2100,plain,
% 1.39/1.20 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a349) | (~c0_1(a349)) | (~c1_1(a349)) | c1_1(a347) | (~c3_1(a347)) | (~c2_1(a347)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp17 | c2_1(a349) | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)) | (~c0_1(a349)) | (~c1_1(a349))))),
% 1.39/1.20 inference(monotonicity,[status(thm)],[2099])).
% 1.39/1.20 tff(2101,plain,
% 1.39/1.20 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a349) | (~c0_1(a349)) | (~c1_1(a349)) | c1_1(a347) | (~c3_1(a347)) | (~c2_1(a347)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp17 | c2_1(a349) | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)) | (~c0_1(a349)) | (~c1_1(a349)))),
% 1.39/1.20 inference(transitivity,[status(thm)],[2100, 2098])).
% 1.39/1.20 tff(2102,plain,
% 1.39/1.20 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a349) | (~c0_1(a349)) | (~c1_1(a349)) | c1_1(a347) | (~c3_1(a347)) | (~c2_1(a347)))),
% 1.39/1.20 inference(quant_inst,[status(thm)],[])).
% 1.39/1.20 tff(2103,plain,
% 1.39/1.20 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp17 | c2_1(a349) | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)) | (~c0_1(a349)) | (~c1_1(a349))),
% 1.39/1.20 inference(modus_ponens,[status(thm)],[2102, 2101])).
% 1.39/1.20 tff(2104,plain,
% 1.39/1.20 (hskp17 | (~c0_1(a349))),
% 1.39/1.20 inference(unit_resolution,[status(thm)],[2103, 152, 2057, 2003, 2002, 2052, 2001, 2097])).
% 1.39/1.20 tff(2105,plain,
% 1.39/1.20 (hskp17),
% 1.39/1.20 inference(unit_resolution,[status(thm)],[2104, 2087])).
% 1.39/1.20 tff(2106,plain,
% 1.39/1.20 (c2_1(a353)),
% 1.39/1.20 inference(unit_resolution,[status(thm)],[881, 2105])).
% 1.39/1.20 tff(2107,plain,
% 1.39/1.20 (c1_1(a353)),
% 1.39/1.20 inference(unit_resolution,[status(thm)],[892, 2105])).
% 1.39/1.20 tff(2108,plain,
% 1.39/1.20 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp22 | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)) | (~c1_1(a353)) | (~c3_1(a353)) | (~c2_1(a353)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp22 | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)) | (~c1_1(a353)) | (~c3_1(a353)) | (~c2_1(a353)))),
% 1.39/1.20 inference(rewrite,[status(thm)],[])).
% 1.39/1.20 tff(2109,plain,
% 1.39/1.20 ((hskp22 | (~ndr1_0) | (~c2_1(a353)) | (~c3_1(a353)) | (~c1_1(a353)) | c1_1(a347) | (~c3_1(a347)) | (~c2_1(a347))) <=> (hskp22 | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)) | (~c1_1(a353)) | (~c3_1(a353)) | (~c2_1(a353)))),
% 1.39/1.20 inference(rewrite,[status(thm)],[])).
% 1.39/1.20 tff(2110,plain,
% 1.39/1.20 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp22 | (~ndr1_0) | (~c2_1(a353)) | (~c3_1(a353)) | (~c1_1(a353)) | c1_1(a347) | (~c3_1(a347)) | (~c2_1(a347)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp22 | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)) | (~c1_1(a353)) | (~c3_1(a353)) | (~c2_1(a353))))),
% 1.39/1.21 inference(monotonicity,[status(thm)],[2109])).
% 1.39/1.21 tff(2111,plain,
% 1.39/1.21 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp22 | (~ndr1_0) | (~c2_1(a353)) | (~c3_1(a353)) | (~c1_1(a353)) | c1_1(a347) | (~c3_1(a347)) | (~c2_1(a347)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp22 | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)) | (~c1_1(a353)) | (~c3_1(a353)) | (~c2_1(a353)))),
% 1.39/1.21 inference(transitivity,[status(thm)],[2110, 2108])).
% 1.39/1.21 tff(2112,plain,
% 1.39/1.21 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp22 | (~ndr1_0) | (~c2_1(a353)) | (~c3_1(a353)) | (~c1_1(a353)) | c1_1(a347) | (~c3_1(a347)) | (~c2_1(a347)))),
% 1.39/1.21 inference(quant_inst,[status(thm)],[])).
% 1.39/1.21 tff(2113,plain,
% 1.39/1.21 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp22 | c1_1(a347) | (~ndr1_0) | (~c2_1(a347)) | (~c3_1(a347)) | (~c1_1(a353)) | (~c3_1(a353)) | (~c2_1(a353))),
% 1.39/1.21 inference(modus_ponens,[status(thm)],[2112, 2111])).
% 1.39/1.21 tff(2114,plain,
% 1.39/1.21 (~c3_1(a353)),
% 1.39/1.21 inference(unit_resolution,[status(thm)],[2113, 152, 2072, 2107, 2106, 2003, 2002, 2001, 10])).
% 1.39/1.21 tff(2115,plain,
% 1.39/1.21 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | c2_1(a349) | (~ndr1_0) | (~c0_1(a349)) | (~c1_1(a349)) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | c2_1(a349) | (~ndr1_0) | (~c0_1(a349)) | (~c1_1(a349)) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343)))),
% 1.39/1.21 inference(rewrite,[status(thm)],[])).
% 1.39/1.21 tff(2116,plain,
% 1.39/1.21 ((hskp8 | (~ndr1_0) | c3_1(a343) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a349) | (~c1_1(a349)) | (~c0_1(a349))) <=> (hskp8 | c2_1(a349) | (~ndr1_0) | (~c0_1(a349)) | (~c1_1(a349)) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343)))),
% 1.39/1.21 inference(rewrite,[status(thm)],[])).
% 1.39/1.21 tff(2117,plain,
% 1.39/1.21 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a343) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a349) | (~c1_1(a349)) | (~c0_1(a349)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | c2_1(a349) | (~ndr1_0) | (~c0_1(a349)) | (~c1_1(a349)) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343))))),
% 1.39/1.21 inference(monotonicity,[status(thm)],[2116])).
% 1.39/1.21 tff(2118,plain,
% 1.39/1.21 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a343) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a349) | (~c1_1(a349)) | (~c0_1(a349)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | c2_1(a349) | (~ndr1_0) | (~c0_1(a349)) | (~c1_1(a349)) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343)))),
% 1.39/1.21 inference(transitivity,[status(thm)],[2117, 2115])).
% 1.39/1.21 tff(2119,plain,
% 1.39/1.21 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a343) | (~c0_1(a343)) | (~c1_1(a343)) | c2_1(a349) | (~c1_1(a349)) | (~c0_1(a349)))),
% 1.39/1.21 inference(quant_inst,[status(thm)],[])).
% 1.39/1.21 tff(2120,plain,
% 1.39/1.21 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | c2_1(a349) | (~ndr1_0) | (~c0_1(a349)) | (~c1_1(a349)) | (~c0_1(a343)) | c3_1(a343) | (~c1_1(a343))),
% 1.39/1.21 inference(modus_ponens,[status(thm)],[2119, 2118])).
% 1.39/1.21 tff(2121,plain,
% 1.39/1.21 (hskp8),
% 1.39/1.21 inference(unit_resolution,[status(thm)],[2120, 152, 2064, 2063, 2057, 2052, 1549, 2080, 2087])).
% 1.39/1.21 tff(2122,plain,
% 1.39/1.21 (~c2_1(a332)),
% 1.39/1.21 inference(unit_resolution,[status(thm)],[700, 2121])).
% 1.39/1.21 tff(2123,plain,
% 1.39/1.21 (~c0_1(a332)),
% 1.39/1.21 inference(unit_resolution,[status(thm)],[706, 2121])).
% 1.39/1.21 tff(2124,plain,
% 1.39/1.21 (~c1_1(a332)),
% 1.39/1.21 inference(unit_resolution,[status(thm)],[1564, 152, 2064, 2063, 2062, 2123, 2122, 21, 2080])).
% 1.39/1.21 tff(2125,plain,
% 1.39/1.21 (~c3_1(a332)),
% 1.39/1.21 inference(unit_resolution,[status(thm)],[694, 2121])).
% 1.39/1.21 tff(2126,plain,
% 1.39/1.21 (hskp21),
% 1.39/1.21 inference(unit_resolution,[status(thm)],[1994, 152, 1460, 1431, 2122, 2125, 1420, 1575, 2124])).
% 1.39/1.21 tff(2127,plain,
% 1.39/1.21 (~c2_1(a359)),
% 1.39/1.21 inference(unit_resolution,[status(thm)],[1588, 2126])).
% 1.39/1.21 tff(2128,plain,
% 1.39/1.21 (~c0_1(a359)),
% 1.39/1.21 inference(unit_resolution,[status(thm)],[1619, 2126])).
% 1.39/1.21 tff(2129,plain,
% 1.39/1.21 (~c1_1(a359)),
% 1.39/1.21 inference(unit_resolution,[status(thm)],[1626, 152, 2064, 2063, 2062, 2107, 2106, 2128, 2127, 21, 2114])).
% 1.39/1.21 tff(2130,plain,
% 1.39/1.21 (c3_1(a359)),
% 1.39/1.21 inference(unit_resolution,[status(thm)],[1599, 2126])).
% 1.39/1.21 tff(2131,plain,
% 1.39/1.21 ($false),
% 1.39/1.21 inference(unit_resolution,[status(thm)],[1606, 152, 2064, 2063, 2062, 2130, 2057, 2056, 2127, 2052, 788, 2129])).
% 1.39/1.21 % SZS output end Proof
%------------------------------------------------------------------------------