TSTP Solution File: SYN472-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN472-1 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 23:55:43 EDT 2022
% Result : Unsatisfiable 1.92s 1.49s
% Output : Proof 2.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SYN472-1 : TPTP v8.1.0. Released v2.1.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Sep 5 03:56:35 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 1.92/1.49 % SZS status Unsatisfiable
% 1.92/1.49 % SZS output start Proof
% 1.92/1.49 tff(c2_1_type, type, (
% 1.92/1.49 c2_1: $i > $o)).
% 1.92/1.49 tff(a730_type, type, (
% 1.92/1.49 a730: $i)).
% 1.92/1.49 tff(c3_1_type, type, (
% 1.92/1.49 c3_1: $i > $o)).
% 1.92/1.49 tff(c0_1_type, type, (
% 1.92/1.49 c0_1: $i > $o)).
% 1.92/1.49 tff(c1_1_type, type, (
% 1.92/1.49 c1_1: $i > $o)).
% 1.92/1.49 tff(ndr1_0_type, type, (
% 1.92/1.49 ndr1_0: $o)).
% 1.92/1.49 tff(a710_type, type, (
% 1.92/1.49 a710: $i)).
% 1.92/1.49 tff(hskp8_type, type, (
% 1.92/1.49 hskp8: $o)).
% 1.92/1.49 tff(a695_type, type, (
% 1.92/1.49 a695: $i)).
% 1.92/1.49 tff(a760_type, type, (
% 1.92/1.49 a760: $i)).
% 1.92/1.49 tff(a738_type, type, (
% 1.92/1.49 a738: $i)).
% 1.92/1.49 tff(hskp16_type, type, (
% 1.92/1.49 hskp16: $o)).
% 1.92/1.49 tff(hskp5_type, type, (
% 1.92/1.49 hskp5: $o)).
% 1.92/1.49 tff(a701_type, type, (
% 1.92/1.49 a701: $i)).
% 1.92/1.49 tff(hskp28_type, type, (
% 1.92/1.49 hskp28: $o)).
% 1.92/1.49 tff(a726_type, type, (
% 1.92/1.49 a726: $i)).
% 1.92/1.49 tff(a763_type, type, (
% 1.92/1.49 a763: $i)).
% 1.92/1.49 tff(hskp23_type, type, (
% 1.92/1.49 hskp23: $o)).
% 1.92/1.49 tff(hskp24_type, type, (
% 1.92/1.49 hskp24: $o)).
% 1.92/1.49 tff(hskp6_type, type, (
% 1.92/1.49 hskp6: $o)).
% 1.92/1.49 tff(a702_type, type, (
% 1.92/1.49 a702: $i)).
% 1.92/1.49 tff(a733_type, type, (
% 1.92/1.49 a733: $i)).
% 1.92/1.49 tff(hskp30_type, type, (
% 1.92/1.49 hskp30: $o)).
% 1.92/1.49 tff(a698_type, type, (
% 1.92/1.49 a698: $i)).
% 1.92/1.49 tff(hskp4_type, type, (
% 1.92/1.49 hskp4: $o)).
% 1.92/1.49 tff(hskp3_type, type, (
% 1.92/1.49 hskp3: $o)).
% 1.92/1.49 tff(a697_type, type, (
% 1.92/1.49 a697: $i)).
% 1.92/1.49 tff(hskp14_type, type, (
% 1.92/1.49 hskp14: $o)).
% 1.92/1.49 tff(a691_type, type, (
% 1.92/1.49 a691: $i)).
% 1.92/1.49 tff(a754_type, type, (
% 1.92/1.49 a754: $i)).
% 1.92/1.49 tff(hskp20_type, type, (
% 1.92/1.49 hskp20: $o)).
% 1.92/1.49 tff(hskp1_type, type, (
% 1.92/1.49 hskp1: $o)).
% 1.92/1.49 tff(a693_type, type, (
% 1.92/1.49 a693: $i)).
% 1.92/1.49 tff(a725_type, type, (
% 1.92/1.49 a725: $i)).
% 1.92/1.49 tff(hskp12_type, type, (
% 1.92/1.49 hskp12: $o)).
% 1.92/1.49 tff(a761_type, type, (
% 1.92/1.49 a761: $i)).
% 1.92/1.49 tff(hskp22_type, type, (
% 1.92/1.49 hskp22: $o)).
% 1.92/1.49 tff(hskp25_type, type, (
% 1.92/1.49 hskp25: $o)).
% 1.92/1.49 tff(hskp27_type, type, (
% 1.92/1.49 hskp27: $o)).
% 1.92/1.49 tff(a764_type, type, (
% 1.92/1.49 a764: $i)).
% 1.92/1.49 tff(a773_type, type, (
% 1.92/1.49 a773: $i)).
% 1.92/1.49 tff(a692_type, type, (
% 1.92/1.49 a692: $i)).
% 1.92/1.49 tff(hskp0_type, type, (
% 1.92/1.49 hskp0: $o)).
% 1.92/1.49 tff(hskp9_type, type, (
% 1.92/1.49 hskp9: $o)).
% 1.92/1.49 tff(a712_type, type, (
% 1.92/1.49 a712: $i)).
% 1.92/1.49 tff(hskp10_type, type, (
% 1.92/1.49 hskp10: $o)).
% 1.92/1.49 tff(a717_type, type, (
% 1.92/1.49 a717: $i)).
% 1.92/1.49 tff(a696_type, type, (
% 1.92/1.49 a696: $i)).
% 1.92/1.49 tff(hskp2_type, type, (
% 1.92/1.49 hskp2: $o)).
% 1.92/1.49 tff(hskp13_type, type, (
% 1.92/1.49 hskp13: $o)).
% 1.92/1.49 tff(a722_type, type, (
% 1.92/1.49 a722: $i)).
% 1.92/1.49 tff(hskp11_type, type, (
% 1.92/1.49 hskp11: $o)).
% 1.92/1.49 tff(a751_type, type, (
% 1.92/1.49 a751: $i)).
% 1.92/1.49 tff(hskp18_type, type, (
% 1.92/1.49 hskp18: $o)).
% 1.92/1.49 tff(hskp21_type, type, (
% 1.92/1.49 hskp21: $o)).
% 1.92/1.49 tff(hskp7_type, type, (
% 1.92/1.49 hskp7: $o)).
% 1.92/1.49 tff(a708_type, type, (
% 1.92/1.49 a708: $i)).
% 1.92/1.49 tff(a744_type, type, (
% 1.92/1.49 a744: $i)).
% 1.92/1.49 tff(hskp17_type, type, (
% 1.92/1.49 hskp17: $o)).
% 1.92/1.49 tff(a713_type, type, (
% 1.92/1.49 a713: $i)).
% 1.92/1.49 tff(hskp29_type, type, (
% 1.92/1.49 hskp29: $o)).
% 1.92/1.49 tff(a734_type, type, (
% 1.92/1.49 a734: $i)).
% 1.92/1.49 tff(hskp15_type, type, (
% 1.92/1.49 hskp15: $o)).
% 1.92/1.49 tff(1,plain,
% 1.92/1.49 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))))),
% 1.92/1.49 inference(bind,[status(th)],[])).
% 1.92/1.49 tff(2,plain,
% 1.92/1.49 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.92/1.49 inference(quant_intro,[status(thm)],[1])).
% 1.92/1.49 tff(3,plain,
% 1.92/1.49 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.92/1.49 inference(rewrite,[status(thm)],[])).
% 1.92/1.49 tff(4,plain,
% 1.92/1.49 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))))),
% 1.92/1.49 inference(bind,[status(th)],[])).
% 1.92/1.49 tff(5,plain,
% 1.92/1.49 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.92/1.49 inference(quant_intro,[status(thm)],[4])).
% 1.92/1.49 tff(6,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause195')).
% 1.92/1.49 tff(7,plain,
% 1.92/1.49 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[6, 5])).
% 1.92/1.49 tff(8,plain,
% 1.92/1.49 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.92/1.49 tff(9,plain,(
% 1.92/1.49 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.92/1.49 inference(skolemize,[status(sab)],[8])).
% 1.92/1.49 tff(10,plain,
% 1.92/1.49 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[9, 2])).
% 1.92/1.49 tff(11,assumption,(~c3_1(a695)), introduced(assumption)).
% 1.92/1.49 tff(12,assumption,(~hskp16), introduced(assumption)).
% 1.92/1.49 tff(13,plain,
% 1.92/1.49 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 1.92/1.49 inference(bind,[status(th)],[])).
% 1.92/1.49 tff(14,plain,
% 1.92/1.49 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.92/1.49 inference(quant_intro,[status(thm)],[13])).
% 1.92/1.49 tff(15,plain,
% 1.92/1.49 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.92/1.49 inference(rewrite,[status(thm)],[])).
% 1.92/1.49 tff(16,plain,
% 1.92/1.49 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp16) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp16))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 1.92/1.49 inference(bind,[status(th)],[])).
% 1.92/1.49 tff(17,plain,
% 1.92/1.49 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.92/1.49 inference(quant_intro,[status(thm)],[16])).
% 1.92/1.49 tff(18,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause181')).
% 1.92/1.49 tff(19,plain,
% 1.92/1.49 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[18, 17])).
% 1.92/1.49 tff(20,plain,
% 1.92/1.49 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[19, 15])).
% 1.92/1.49 tff(21,plain,(
% 1.92/1.49 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.92/1.49 inference(skolemize,[status(sab)],[20])).
% 1.92/1.49 tff(22,plain,
% 1.92/1.49 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[21, 14])).
% 1.92/1.49 tff(23,assumption,(hskp5), introduced(assumption)).
% 1.92/1.49 tff(24,plain,
% 1.92/1.49 (((~hskp5) | (~c1_1(a701))) <=> ((~hskp5) | (~c1_1(a701)))),
% 1.92/1.49 inference(rewrite,[status(thm)],[])).
% 1.92/1.49 tff(25,plain,
% 1.92/1.49 (((~c1_1(a701)) | (~hskp5)) <=> ((~hskp5) | (~c1_1(a701)))),
% 1.92/1.49 inference(rewrite,[status(thm)],[])).
% 1.92/1.49 tff(26,axiom,((~c1_1(a701)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause123')).
% 1.92/1.49 tff(27,plain,
% 1.92/1.49 ((~hskp5) | (~c1_1(a701))),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[26, 25])).
% 1.92/1.49 tff(28,plain,
% 1.92/1.49 ((~hskp5) | (~c1_1(a701))),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[27, 24])).
% 1.92/1.49 tff(29,plain,
% 1.92/1.49 (~c1_1(a701)),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[28, 23])).
% 1.92/1.49 tff(30,plain,
% 1.92/1.49 (((~hskp5) | c2_1(a701)) <=> ((~hskp5) | c2_1(a701))),
% 1.92/1.49 inference(rewrite,[status(thm)],[])).
% 1.92/1.49 tff(31,axiom,((~hskp5) | c2_1(a701)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause80')).
% 1.92/1.49 tff(32,plain,
% 1.92/1.49 ((~hskp5) | c2_1(a701)),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[31, 30])).
% 1.92/1.49 tff(33,plain,
% 1.92/1.49 ((~hskp5) | c2_1(a701)),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[32, 30])).
% 1.92/1.49 tff(34,plain,
% 1.92/1.49 ((~hskp5) | c2_1(a701)),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[33, 30])).
% 1.92/1.49 tff(35,plain,
% 1.92/1.49 ((~hskp5) | c2_1(a701)),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[34, 30])).
% 1.92/1.49 tff(36,plain,
% 1.92/1.49 ((~hskp5) | c2_1(a701)),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[35, 30])).
% 1.92/1.49 tff(37,plain,
% 1.92/1.49 ((~hskp5) | c2_1(a701)),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[36, 30])).
% 1.92/1.49 tff(38,plain,
% 1.92/1.49 ((~hskp5) | c2_1(a701)),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[37, 30])).
% 1.92/1.49 tff(39,plain,
% 1.92/1.49 ((~hskp5) | c2_1(a701)),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[38, 30])).
% 1.92/1.49 tff(40,plain,
% 1.92/1.49 (c2_1(a701)),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[39, 23])).
% 1.92/1.49 tff(41,plain,
% 1.92/1.49 (((~hskp5) | c0_1(a701)) <=> ((~hskp5) | c0_1(a701))),
% 1.92/1.49 inference(rewrite,[status(thm)],[])).
% 1.92/1.49 tff(42,axiom,((~hskp5) | c0_1(a701)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause79')).
% 1.92/1.49 tff(43,plain,
% 1.92/1.49 ((~hskp5) | c0_1(a701)),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[42, 41])).
% 1.92/1.49 tff(44,plain,
% 1.92/1.49 ((~hskp5) | c0_1(a701)),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[43, 41])).
% 1.92/1.49 tff(45,plain,
% 1.92/1.49 ((~hskp5) | c0_1(a701)),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[44, 41])).
% 1.92/1.49 tff(46,plain,
% 1.92/1.49 ((~hskp5) | c0_1(a701)),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[45, 41])).
% 1.92/1.49 tff(47,plain,
% 1.92/1.49 ((~hskp5) | c0_1(a701)),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[46, 41])).
% 1.92/1.49 tff(48,plain,
% 1.92/1.49 ((~hskp5) | c0_1(a701)),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[47, 41])).
% 1.92/1.49 tff(49,plain,
% 1.92/1.49 ((~hskp5) | c0_1(a701)),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[48, 41])).
% 1.92/1.49 tff(50,plain,
% 1.92/1.49 ((~hskp5) | c0_1(a701)),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[49, 41])).
% 1.92/1.49 tff(51,plain,
% 1.92/1.49 (c0_1(a701)),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[50, 23])).
% 1.92/1.49 tff(52,plain,
% 1.92/1.49 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 1.92/1.49 inference(bind,[status(th)],[])).
% 1.92/1.49 tff(53,plain,
% 1.92/1.49 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.92/1.49 inference(quant_intro,[status(thm)],[52])).
% 1.92/1.49 tff(54,plain,
% 1.92/1.49 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.92/1.49 inference(rewrite,[status(thm)],[])).
% 1.92/1.49 tff(55,plain,
% 1.92/1.49 (^[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))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp28) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp28))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp28) <=> (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 1.92/1.49 inference(bind,[status(th)],[])).
% 1.92/1.49 tff(56,plain,
% 1.92/1.49 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.92/1.49 inference(quant_intro,[status(thm)],[55])).
% 1.92/1.49 tff(57,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause186')).
% 1.92/1.49 tff(58,plain,
% 1.92/1.49 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[57, 56])).
% 1.92/1.49 tff(59,plain,
% 1.92/1.49 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[58, 54])).
% 1.92/1.49 tff(60,plain,(
% 1.92/1.49 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.92/1.49 inference(skolemize,[status(sab)],[59])).
% 1.92/1.49 tff(61,plain,
% 1.92/1.49 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[60, 53])).
% 1.92/1.49 tff(62,assumption,(~hskp28), introduced(assumption)).
% 1.92/1.49 tff(63,assumption,(hskp6), introduced(assumption)).
% 1.92/1.49 tff(64,plain,
% 1.92/1.49 (((~hskp6) | (~c2_1(a702))) <=> ((~hskp6) | (~c2_1(a702)))),
% 1.92/1.49 inference(rewrite,[status(thm)],[])).
% 1.92/1.49 tff(65,plain,
% 1.92/1.49 (((~c2_1(a702)) | (~hskp6)) <=> ((~hskp6) | (~c2_1(a702)))),
% 1.92/1.49 inference(rewrite,[status(thm)],[])).
% 1.92/1.49 tff(66,axiom,((~c2_1(a702)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause122')).
% 1.92/1.49 tff(67,plain,
% 1.92/1.49 ((~hskp6) | (~c2_1(a702))),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[66, 65])).
% 1.92/1.49 tff(68,plain,
% 1.92/1.49 ((~hskp6) | (~c2_1(a702))),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[67, 64])).
% 1.92/1.49 tff(69,plain,
% 1.92/1.49 (~c2_1(a702)),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[68, 63])).
% 1.92/1.49 tff(70,plain,
% 1.92/1.49 (((~hskp6) | c3_1(a702)) <=> ((~hskp6) | c3_1(a702))),
% 1.92/1.49 inference(rewrite,[status(thm)],[])).
% 1.92/1.49 tff(71,axiom,((~hskp6) | c3_1(a702)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause78')).
% 1.92/1.49 tff(72,plain,
% 1.92/1.49 ((~hskp6) | c3_1(a702)),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[71, 70])).
% 1.92/1.49 tff(73,plain,
% 1.92/1.49 ((~hskp6) | c3_1(a702)),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[72, 70])).
% 1.92/1.49 tff(74,plain,
% 1.92/1.49 ((~hskp6) | c3_1(a702)),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[73, 70])).
% 1.92/1.49 tff(75,plain,
% 1.92/1.49 ((~hskp6) | c3_1(a702)),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[74, 70])).
% 1.92/1.49 tff(76,plain,
% 1.92/1.49 ((~hskp6) | c3_1(a702)),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[75, 70])).
% 1.92/1.49 tff(77,plain,
% 1.92/1.49 ((~hskp6) | c3_1(a702)),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[76, 70])).
% 1.92/1.49 tff(78,plain,
% 1.92/1.49 ((~hskp6) | c3_1(a702)),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[77, 70])).
% 1.92/1.49 tff(79,plain,
% 1.92/1.49 ((~hskp6) | c3_1(a702)),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[78, 70])).
% 1.92/1.49 tff(80,plain,
% 1.92/1.49 (c3_1(a702)),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[79, 63])).
% 1.92/1.49 tff(81,plain,
% 1.92/1.49 (((~hskp6) | c0_1(a702)) <=> ((~hskp6) | c0_1(a702))),
% 1.92/1.49 inference(rewrite,[status(thm)],[])).
% 1.92/1.49 tff(82,axiom,((~hskp6) | c0_1(a702)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause77')).
% 1.92/1.49 tff(83,plain,
% 1.92/1.49 ((~hskp6) | c0_1(a702)),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[82, 81])).
% 1.92/1.49 tff(84,plain,
% 1.92/1.49 ((~hskp6) | c0_1(a702)),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[83, 81])).
% 1.92/1.49 tff(85,plain,
% 1.92/1.49 ((~hskp6) | c0_1(a702)),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[84, 81])).
% 1.92/1.49 tff(86,plain,
% 1.92/1.49 ((~hskp6) | c0_1(a702)),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[85, 81])).
% 1.92/1.49 tff(87,plain,
% 1.92/1.49 ((~hskp6) | c0_1(a702)),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[86, 81])).
% 1.92/1.49 tff(88,plain,
% 1.92/1.49 ((~hskp6) | c0_1(a702)),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[87, 81])).
% 1.92/1.49 tff(89,plain,
% 1.92/1.49 ((~hskp6) | c0_1(a702)),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[88, 81])).
% 1.92/1.49 tff(90,plain,
% 1.92/1.49 ((~hskp6) | c0_1(a702)),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[89, 81])).
% 1.92/1.49 tff(91,plain,
% 1.92/1.49 (c0_1(a702)),
% 1.92/1.49 inference(unit_resolution,[status(thm)],[90, 63])).
% 1.92/1.49 tff(92,plain,
% 1.92/1.49 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))),
% 1.92/1.49 inference(bind,[status(th)],[])).
% 1.92/1.49 tff(93,plain,
% 1.92/1.49 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.92/1.49 inference(quant_intro,[status(thm)],[92])).
% 1.92/1.49 tff(94,plain,
% 1.92/1.49 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.92/1.49 inference(rewrite,[status(thm)],[])).
% 1.92/1.49 tff(95,plain,
% 1.92/1.49 (^[V: $i, U: $i] : 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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp6) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp6))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))))),
% 1.92/1.49 inference(bind,[status(th)],[])).
% 1.92/1.49 tff(96,plain,
% 1.92/1.49 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.92/1.49 inference(quant_intro,[status(thm)],[95])).
% 1.92/1.49 tff(97,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause165')).
% 1.92/1.49 tff(98,plain,
% 1.92/1.49 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[97, 96])).
% 1.92/1.49 tff(99,plain,
% 1.92/1.49 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[98, 94])).
% 1.92/1.49 tff(100,plain,(
% 1.92/1.49 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.92/1.49 inference(skolemize,[status(sab)],[99])).
% 1.92/1.49 tff(101,plain,
% 1.92/1.49 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[100, 93])).
% 1.92/1.49 tff(102,assumption,(~hskp30), introduced(assumption)).
% 1.92/1.49 tff(103,plain,
% 1.92/1.49 (^[U: $i] : refl((hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))),
% 1.92/1.49 inference(bind,[status(th)],[])).
% 1.92/1.49 tff(104,plain,
% 1.92/1.49 (![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.92/1.49 inference(quant_intro,[status(thm)],[103])).
% 1.92/1.49 tff(105,plain,
% 1.92/1.49 (![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.92/1.49 inference(rewrite,[status(thm)],[])).
% 1.92/1.49 tff(106,plain,
% 1.92/1.49 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp14) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp14))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp14) | hskp30) <=> ((hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp30))), rewrite(((hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp30) <=> (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp14) | hskp30) <=> (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))))),
% 1.92/1.49 inference(bind,[status(th)],[])).
% 1.92/1.49 tff(107,plain,
% 1.92/1.49 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp14) | hskp30) <=> ![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.92/1.49 inference(quant_intro,[status(thm)],[106])).
% 1.92/1.49 tff(108,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp14) | hskp30)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause142')).
% 1.92/1.49 tff(109,plain,
% 1.92/1.49 (![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[108, 107])).
% 1.92/1.49 tff(110,plain,
% 1.92/1.49 (![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[109, 105])).
% 1.92/1.49 tff(111,plain,(
% 1.92/1.49 ![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.92/1.49 inference(skolemize,[status(sab)],[110])).
% 1.92/1.49 tff(112,plain,
% 1.92/1.49 (![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.92/1.49 inference(modus_ponens,[status(thm)],[111, 104])).
% 1.92/1.49 tff(113,plain,
% 1.92/1.49 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W)))),
% 1.92/1.49 inference(bind,[status(th)],[])).
% 1.92/1.49 tff(114,plain,
% 1.92/1.49 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.92/1.49 inference(quant_intro,[status(thm)],[113])).
% 1.92/1.49 tff(115,plain,
% 1.92/1.49 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.92/1.49 inference(rewrite,[status(thm)],[])).
% 1.92/1.49 tff(116,plain,
% 1.92/1.49 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c1_1(V))), (((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c1_1(V) | c2_1(V))), (((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c1_1(V) | c2_1(V)))), ((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), ((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), (((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), (((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), ((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), ((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), (((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | c0_1(W)) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c0_1(W))), (((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c0_1(W)))), ((((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W))), ((((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W)))), (((((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))), (((((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))))),
% 1.92/1.50 inference(bind,[status(th)],[])).
% 1.92/1.50 tff(117,plain,
% 1.92/1.50 (![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.92/1.50 inference(quant_intro,[status(thm)],[116])).
% 1.92/1.50 tff(118,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause184')).
% 1.92/1.50 tff(119,plain,
% 1.92/1.50 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[118, 117])).
% 1.92/1.50 tff(120,plain,
% 1.92/1.50 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[119, 115])).
% 1.92/1.50 tff(121,plain,(
% 1.92/1.50 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.92/1.50 inference(skolemize,[status(sab)],[120])).
% 1.92/1.50 tff(122,plain,
% 1.92/1.50 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[121, 114])).
% 1.92/1.50 tff(123,plain,
% 1.92/1.50 ((hskp30 | hskp28 | hskp12) <=> (hskp30 | hskp28 | hskp12)),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(124,plain,
% 1.92/1.50 (((hskp28 | hskp30) | hskp12) <=> (hskp30 | hskp28 | hskp12)),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(125,axiom,((hskp28 | hskp30) | hskp12), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause32')).
% 1.92/1.50 tff(126,plain,
% 1.92/1.50 (hskp30 | hskp28 | hskp12),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[125, 124])).
% 1.92/1.50 tff(127,plain,
% 1.92/1.50 (hskp30 | hskp28 | hskp12),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[126, 123])).
% 1.92/1.50 tff(128,plain,
% 1.92/1.50 (hskp30 | hskp28 | hskp12),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[127, 123])).
% 1.92/1.50 tff(129,plain,
% 1.92/1.50 (hskp30 | hskp28 | hskp12),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[128, 123])).
% 1.92/1.50 tff(130,plain,
% 1.92/1.50 (hskp30 | hskp28 | hskp12),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[129, 123])).
% 1.92/1.50 tff(131,plain,
% 1.92/1.50 (hskp30 | hskp28 | hskp12),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[130, 123])).
% 1.92/1.50 tff(132,plain,
% 1.92/1.50 (hskp30 | hskp28 | hskp12),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[131, 123])).
% 1.92/1.50 tff(133,plain,
% 1.92/1.50 (hskp30 | hskp28 | hskp12),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[132, 123])).
% 1.92/1.50 tff(134,plain,
% 1.92/1.50 (hskp12),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[133, 102, 62])).
% 1.92/1.50 tff(135,plain,
% 1.92/1.50 (((~hskp12) | (~c3_1(a725))) <=> ((~hskp12) | (~c3_1(a725)))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(136,plain,
% 1.92/1.50 (((~c3_1(a725)) | (~hskp12)) <=> ((~hskp12) | (~c3_1(a725)))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(137,axiom,((~c3_1(a725)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause114')).
% 1.92/1.50 tff(138,plain,
% 1.92/1.50 ((~hskp12) | (~c3_1(a725))),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[137, 136])).
% 1.92/1.50 tff(139,plain,
% 1.92/1.50 ((~hskp12) | (~c3_1(a725))),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[138, 135])).
% 1.92/1.50 tff(140,plain,
% 1.92/1.50 (~c3_1(a725)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[139, 134])).
% 1.92/1.50 tff(141,plain,
% 1.92/1.50 (((~hskp12) | (~c1_1(a725))) <=> ((~hskp12) | (~c1_1(a725)))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(142,plain,
% 1.92/1.50 (((~c1_1(a725)) | (~hskp12)) <=> ((~hskp12) | (~c1_1(a725)))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(143,axiom,((~c1_1(a725)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause113')).
% 1.92/1.50 tff(144,plain,
% 1.92/1.50 ((~hskp12) | (~c1_1(a725))),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[143, 142])).
% 1.92/1.50 tff(145,plain,
% 1.92/1.50 ((~hskp12) | (~c1_1(a725))),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[144, 141])).
% 1.92/1.50 tff(146,plain,
% 1.92/1.50 (~c1_1(a725)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[145, 134])).
% 1.92/1.50 tff(147,plain,
% 1.92/1.50 (((~hskp12) | (~c0_1(a725))) <=> ((~hskp12) | (~c0_1(a725)))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(148,plain,
% 1.92/1.50 (((~c0_1(a725)) | (~hskp12)) <=> ((~hskp12) | (~c0_1(a725)))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(149,axiom,((~c0_1(a725)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause112')).
% 1.92/1.50 tff(150,plain,
% 1.92/1.50 ((~hskp12) | (~c0_1(a725))),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[149, 148])).
% 1.92/1.50 tff(151,plain,
% 1.92/1.50 ((~hskp12) | (~c0_1(a725))),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[150, 147])).
% 1.92/1.50 tff(152,plain,
% 1.92/1.50 (~c0_1(a725)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[151, 134])).
% 1.92/1.50 tff(153,assumption,(~c3_1(a693)), introduced(assumption)).
% 1.92/1.50 tff(154,plain,
% 1.92/1.50 (^[U: $i] : refl((hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) <=> (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))),
% 1.92/1.50 inference(bind,[status(th)],[])).
% 1.92/1.50 tff(155,plain,
% 1.92/1.50 (![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.92/1.50 inference(quant_intro,[status(thm)],[154])).
% 1.92/1.50 tff(156,plain,
% 1.92/1.50 (![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(157,plain,
% 1.92/1.50 (^[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)) | hskp23) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp23))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp23) <=> (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp23) <=> (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp23) | hskp24) <=> ((hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp24))), rewrite(((hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp24) <=> (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp23) | hskp24) <=> (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))))),
% 1.92/1.50 inference(bind,[status(th)],[])).
% 1.92/1.50 tff(158,plain,
% 1.92/1.50 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp23) | hskp24) <=> ![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.92/1.50 inference(quant_intro,[status(thm)],[157])).
% 1.92/1.50 tff(159,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp23) | hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause153')).
% 1.92/1.50 tff(160,plain,
% 1.92/1.50 (![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[159, 158])).
% 1.92/1.50 tff(161,plain,
% 1.92/1.50 (![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[160, 156])).
% 1.92/1.50 tff(162,plain,(
% 1.92/1.50 ![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.92/1.50 inference(skolemize,[status(sab)],[161])).
% 1.92/1.50 tff(163,plain,
% 1.92/1.50 (![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[162, 155])).
% 1.92/1.50 tff(164,assumption,(~c1_1(a693)), introduced(assumption)).
% 1.92/1.50 tff(165,plain,
% 1.92/1.50 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))))),
% 1.92/1.50 inference(bind,[status(th)],[])).
% 1.92/1.50 tff(166,plain,
% 1.92/1.50 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_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)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.92/1.50 inference(quant_intro,[status(thm)],[165])).
% 1.92/1.50 tff(167,plain,
% 1.92/1.50 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_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)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(168,plain,
% 1.92/1.50 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_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)) | c3_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)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_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)) | (~c0_1(U)) | c3_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)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))))),
% 1.92/1.50 inference(bind,[status(th)],[])).
% 1.92/1.50 tff(169,plain,
% 1.92/1.50 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.92/1.50 inference(quant_intro,[status(thm)],[168])).
% 1.92/1.50 tff(170,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause192')).
% 1.92/1.50 tff(171,plain,
% 1.92/1.50 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[170, 169])).
% 1.92/1.50 tff(172,plain,
% 1.92/1.50 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[171, 167])).
% 1.92/1.50 tff(173,plain,(
% 1.92/1.50 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.92/1.50 inference(skolemize,[status(sab)],[172])).
% 1.92/1.50 tff(174,plain,
% 1.92/1.50 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[173, 166])).
% 1.92/1.50 tff(175,assumption,(~c3_1(a697)), introduced(assumption)).
% 1.92/1.50 tff(176,assumption,(~hskp4), introduced(assumption)).
% 1.92/1.50 tff(177,assumption,(~hskp6), introduced(assumption)).
% 1.92/1.50 tff(178,assumption,(~c3_1(a754)), introduced(assumption)).
% 1.92/1.50 tff(179,assumption,(~c0_1(a754)), introduced(assumption)).
% 1.92/1.50 tff(180,assumption,(~c2_1(a754)), introduced(assumption)).
% 1.92/1.50 tff(181,plain,
% 1.92/1.50 (((~hskp20) | c2_1(a754)) <=> ((~hskp20) | c2_1(a754))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(182,axiom,((~hskp20) | c2_1(a754)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause60')).
% 1.92/1.50 tff(183,plain,
% 1.92/1.50 ((~hskp20) | c2_1(a754)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[182, 181])).
% 1.92/1.50 tff(184,plain,
% 1.92/1.50 ((~hskp20) | c2_1(a754)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[183, 181])).
% 1.92/1.50 tff(185,plain,
% 1.92/1.50 ((~hskp20) | c2_1(a754)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[184, 181])).
% 1.92/1.50 tff(186,plain,
% 1.92/1.50 ((~hskp20) | c2_1(a754)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[185, 181])).
% 1.92/1.50 tff(187,plain,
% 1.92/1.50 ((~hskp20) | c2_1(a754)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[186, 181])).
% 1.92/1.50 tff(188,plain,
% 1.92/1.50 ((~hskp20) | c2_1(a754)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[187, 181])).
% 1.92/1.50 tff(189,plain,
% 1.92/1.50 ((~hskp20) | c2_1(a754)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[188, 181])).
% 1.92/1.50 tff(190,plain,
% 1.92/1.50 ((~hskp20) | c2_1(a754)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[189, 181])).
% 1.92/1.50 tff(191,plain,
% 1.92/1.50 (~hskp20),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[190, 180])).
% 1.92/1.50 tff(192,plain,
% 1.92/1.50 (^[U: $i] : refl((hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))),
% 1.92/1.50 inference(bind,[status(th)],[])).
% 1.92/1.50 tff(193,plain,
% 1.92/1.50 (![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> ![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.92/1.50 inference(quant_intro,[status(thm)],[192])).
% 1.92/1.50 tff(194,plain,
% 1.92/1.50 (![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> ![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(195,plain,
% 1.92/1.50 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_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) | c3_1(U) | c0_1(U) | c2_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp27))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) | hskp6) <=> ((hskp27 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp6))), rewrite(((hskp27 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp6) <=> (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) | hskp6) <=> (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))))),
% 1.92/1.50 inference(bind,[status(th)],[])).
% 1.92/1.50 tff(196,plain,
% 1.92/1.50 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) | hskp6) <=> ![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.92/1.50 inference(quant_intro,[status(thm)],[195])).
% 1.92/1.50 tff(197,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause134')).
% 1.92/1.50 tff(198,plain,
% 1.92/1.50 (![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[197, 196])).
% 1.92/1.50 tff(199,plain,
% 1.92/1.50 (![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[198, 194])).
% 1.92/1.50 tff(200,plain,(
% 1.92/1.50 ![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.92/1.50 inference(skolemize,[status(sab)],[199])).
% 1.92/1.50 tff(201,plain,
% 1.92/1.50 (![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[200, 193])).
% 1.92/1.50 tff(202,assumption,(~ndr1_0), introduced(assumption)).
% 1.92/1.50 tff(203,plain,
% 1.92/1.50 ((ndr1_0 | (~hskp12)) <=> (ndr1_0 | (~hskp12))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(204,plain,
% 1.92/1.50 (((~hskp12) | ndr1_0) <=> (ndr1_0 | (~hskp12))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(205,axiom,((~hskp12) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause19')).
% 1.92/1.50 tff(206,plain,
% 1.92/1.50 (ndr1_0 | (~hskp12)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[205, 204])).
% 1.92/1.50 tff(207,plain,
% 1.92/1.50 (ndr1_0 | (~hskp12)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[206, 203])).
% 1.92/1.50 tff(208,plain,
% 1.92/1.50 (~hskp12),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[207, 202])).
% 1.92/1.50 tff(209,plain,
% 1.92/1.50 (((~hskp30) | ndr1_0) <=> ((~hskp30) | ndr1_0)),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(210,axiom,((~hskp30) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause1')).
% 1.92/1.50 tff(211,plain,
% 1.92/1.50 ((~hskp30) | ndr1_0),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[210, 209])).
% 1.92/1.50 tff(212,plain,
% 1.92/1.50 ((~hskp30) | ndr1_0),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[211, 209])).
% 1.92/1.50 tff(213,plain,
% 1.92/1.50 ((~hskp30) | ndr1_0),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[212, 209])).
% 1.92/1.50 tff(214,plain,
% 1.92/1.50 ((~hskp30) | ndr1_0),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[213, 209])).
% 1.92/1.50 tff(215,plain,
% 1.92/1.50 ((~hskp30) | ndr1_0),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[214, 209])).
% 1.92/1.50 tff(216,plain,
% 1.92/1.50 ((~hskp30) | ndr1_0),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[215, 209])).
% 1.92/1.50 tff(217,plain,
% 1.92/1.50 ((~hskp30) | ndr1_0),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[216, 209])).
% 1.92/1.50 tff(218,plain,
% 1.92/1.50 ((~hskp30) | ndr1_0),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[217, 209])).
% 1.92/1.50 tff(219,plain,
% 1.92/1.50 (~hskp30),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[218, 202])).
% 1.92/1.50 tff(220,plain,
% 1.92/1.50 ((ndr1_0 | (~hskp28)) <=> (ndr1_0 | (~hskp28))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(221,plain,
% 1.92/1.50 (((~hskp28) | ndr1_0) <=> (ndr1_0 | (~hskp28))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(222,axiom,((~hskp28) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause3')).
% 1.92/1.50 tff(223,plain,
% 1.92/1.50 (ndr1_0 | (~hskp28)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[222, 221])).
% 1.92/1.50 tff(224,plain,
% 1.92/1.50 (ndr1_0 | (~hskp28)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[223, 220])).
% 1.92/1.50 tff(225,plain,
% 1.92/1.50 (~hskp28),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[224, 202])).
% 1.92/1.50 tff(226,plain,
% 1.92/1.50 ($false),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[133, 225, 219, 208])).
% 1.92/1.50 tff(227,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 1.92/1.50 tff(228,plain,
% 1.92/1.50 (((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | c2_1(a754) | c0_1(a754) | c3_1(a754) | (~ndr1_0))) <=> ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp27 | hskp6 | c2_1(a754) | c0_1(a754) | c3_1(a754) | (~ndr1_0))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(229,plain,
% 1.92/1.50 ((hskp27 | hskp6 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | c2_1(a754)) <=> (hskp27 | hskp6 | c2_1(a754) | c0_1(a754) | c3_1(a754) | (~ndr1_0))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(230,plain,
% 1.92/1.50 (((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | c2_1(a754))) <=> ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | c2_1(a754) | c0_1(a754) | c3_1(a754) | (~ndr1_0)))),
% 1.92/1.50 inference(monotonicity,[status(thm)],[229])).
% 1.92/1.50 tff(231,plain,
% 1.92/1.50 (((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | c2_1(a754))) <=> ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp27 | hskp6 | c2_1(a754) | c0_1(a754) | c3_1(a754) | (~ndr1_0))),
% 1.92/1.50 inference(transitivity,[status(thm)],[230, 228])).
% 1.92/1.50 tff(232,plain,
% 1.92/1.50 ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | c2_1(a754))),
% 1.92/1.50 inference(quant_inst,[status(thm)],[])).
% 1.92/1.50 tff(233,plain,
% 1.92/1.50 ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp27 | hskp6 | c2_1(a754) | c0_1(a754) | c3_1(a754) | (~ndr1_0)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[232, 231])).
% 1.92/1.50 tff(234,plain,
% 1.92/1.50 (hskp27 | c2_1(a754) | c3_1(a754)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[233, 227, 177, 179, 201])).
% 1.92/1.50 tff(235,plain,
% 1.92/1.50 (hskp27),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[234, 180, 178])).
% 1.92/1.50 tff(236,plain,
% 1.92/1.50 (^[U: $i] : refl((hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) <=> (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))))),
% 1.92/1.50 inference(bind,[status(th)],[])).
% 1.92/1.50 tff(237,plain,
% 1.92/1.50 (![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.92/1.50 inference(quant_intro,[status(thm)],[236])).
% 1.92/1.50 tff(238,plain,
% 1.92/1.50 (![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(239,plain,
% 1.92/1.50 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp30) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp30))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp30) <=> (hskp30 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp30) <=> (hskp30 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp30) | hskp20) <=> ((hskp30 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp20))), rewrite(((hskp30 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp20) <=> (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp30) | hskp20) <=> (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))))),
% 1.92/1.50 inference(bind,[status(th)],[])).
% 1.92/1.50 tff(240,plain,
% 1.92/1.50 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp30) | hskp20) <=> ![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.92/1.50 inference(quant_intro,[status(thm)],[239])).
% 1.92/1.50 tff(241,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp30) | hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause155')).
% 1.92/1.50 tff(242,plain,
% 1.92/1.50 (![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[241, 240])).
% 1.92/1.50 tff(243,plain,
% 1.92/1.50 (![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[242, 238])).
% 1.92/1.50 tff(244,plain,(
% 1.92/1.50 ![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.92/1.50 inference(skolemize,[status(sab)],[243])).
% 1.92/1.50 tff(245,plain,
% 1.92/1.50 (![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[244, 237])).
% 1.92/1.50 tff(246,assumption,(hskp27), introduced(assumption)).
% 1.92/1.50 tff(247,plain,
% 1.92/1.50 (((~hskp27) | c3_1(a691)) <=> ((~hskp27) | c3_1(a691))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(248,axiom,((~hskp27) | c3_1(a691)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause51')).
% 1.92/1.50 tff(249,plain,
% 1.92/1.50 ((~hskp27) | c3_1(a691)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[248, 247])).
% 1.92/1.50 tff(250,plain,
% 1.92/1.50 ((~hskp27) | c3_1(a691)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[249, 247])).
% 1.92/1.50 tff(251,plain,
% 1.92/1.50 ((~hskp27) | c3_1(a691)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[250, 247])).
% 1.92/1.50 tff(252,plain,
% 1.92/1.50 ((~hskp27) | c3_1(a691)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[251, 247])).
% 1.92/1.50 tff(253,plain,
% 1.92/1.50 ((~hskp27) | c3_1(a691)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[252, 247])).
% 1.92/1.50 tff(254,plain,
% 1.92/1.50 ((~hskp27) | c3_1(a691)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[253, 247])).
% 1.92/1.50 tff(255,plain,
% 1.92/1.50 ((~hskp27) | c3_1(a691)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[254, 247])).
% 1.92/1.50 tff(256,plain,
% 1.92/1.50 ((~hskp27) | c3_1(a691)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[255, 247])).
% 1.92/1.50 tff(257,plain,
% 1.92/1.50 (c3_1(a691)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[256, 246])).
% 1.92/1.50 tff(258,plain,
% 1.92/1.50 (((~hskp27) | c1_1(a691)) <=> ((~hskp27) | c1_1(a691))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(259,axiom,((~hskp27) | c1_1(a691)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause50')).
% 1.92/1.50 tff(260,plain,
% 1.92/1.50 ((~hskp27) | c1_1(a691)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[259, 258])).
% 1.92/1.50 tff(261,plain,
% 1.92/1.50 ((~hskp27) | c1_1(a691)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[260, 258])).
% 1.92/1.50 tff(262,plain,
% 1.92/1.50 ((~hskp27) | c1_1(a691)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[261, 258])).
% 1.92/1.50 tff(263,plain,
% 1.92/1.50 ((~hskp27) | c1_1(a691)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[262, 258])).
% 1.92/1.50 tff(264,plain,
% 1.92/1.50 ((~hskp27) | c1_1(a691)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[263, 258])).
% 1.92/1.50 tff(265,plain,
% 1.92/1.50 ((~hskp27) | c1_1(a691)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[264, 258])).
% 1.92/1.50 tff(266,plain,
% 1.92/1.50 ((~hskp27) | c1_1(a691)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[265, 258])).
% 1.92/1.50 tff(267,plain,
% 1.92/1.50 ((~hskp27) | c1_1(a691)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[266, 258])).
% 1.92/1.50 tff(268,plain,
% 1.92/1.50 (c1_1(a691)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[267, 246])).
% 1.92/1.50 tff(269,plain,
% 1.92/1.50 (((~hskp27) | c0_1(a691)) <=> ((~hskp27) | c0_1(a691))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(270,axiom,((~hskp27) | c0_1(a691)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause49')).
% 1.92/1.50 tff(271,plain,
% 1.92/1.50 ((~hskp27) | c0_1(a691)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[270, 269])).
% 1.92/1.50 tff(272,plain,
% 1.92/1.50 ((~hskp27) | c0_1(a691)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[271, 269])).
% 1.92/1.50 tff(273,plain,
% 1.92/1.50 ((~hskp27) | c0_1(a691)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[272, 269])).
% 1.92/1.50 tff(274,plain,
% 1.92/1.50 ((~hskp27) | c0_1(a691)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[273, 269])).
% 1.92/1.50 tff(275,plain,
% 1.92/1.50 ((~hskp27) | c0_1(a691)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[274, 269])).
% 1.92/1.50 tff(276,plain,
% 1.92/1.50 ((~hskp27) | c0_1(a691)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[275, 269])).
% 1.92/1.50 tff(277,plain,
% 1.92/1.50 ((~hskp27) | c0_1(a691)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[276, 269])).
% 1.92/1.50 tff(278,plain,
% 1.92/1.50 ((~hskp27) | c0_1(a691)),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[277, 269])).
% 1.92/1.50 tff(279,plain,
% 1.92/1.50 (c0_1(a691)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[278, 246])).
% 1.92/1.50 tff(280,assumption,(~hskp20), introduced(assumption)).
% 1.92/1.50 tff(281,plain,
% 1.92/1.50 (((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp30 | hskp20 | (~ndr1_0) | (~c1_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))) <=> ((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp30 | hskp20 | (~ndr1_0) | (~c1_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(282,plain,
% 1.92/1.50 ((hskp30 | hskp20 | (~ndr1_0) | (~c3_1(a691)) | (~c0_1(a691)) | (~c1_1(a691))) <=> (hskp30 | hskp20 | (~ndr1_0) | (~c1_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(283,plain,
% 1.92/1.50 (((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(a691)) | (~c0_1(a691)) | (~c1_1(a691)))) <=> ((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp30 | hskp20 | (~ndr1_0) | (~c1_1(a691)) | (~c3_1(a691)) | (~c0_1(a691))))),
% 1.92/1.50 inference(monotonicity,[status(thm)],[282])).
% 1.92/1.50 tff(284,plain,
% 1.92/1.50 (((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(a691)) | (~c0_1(a691)) | (~c1_1(a691)))) <=> ((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp30 | hskp20 | (~ndr1_0) | (~c1_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 1.92/1.50 inference(transitivity,[status(thm)],[283, 281])).
% 1.92/1.50 tff(285,plain,
% 1.92/1.50 ((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(a691)) | (~c0_1(a691)) | (~c1_1(a691)))),
% 1.92/1.50 inference(quant_inst,[status(thm)],[])).
% 1.92/1.50 tff(286,plain,
% 1.92/1.50 ((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp30 | hskp20 | (~ndr1_0) | (~c1_1(a691)) | (~c3_1(a691)) | (~c0_1(a691))),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[285, 284])).
% 1.92/1.50 tff(287,plain,
% 1.92/1.50 ($false),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[286, 102, 227, 280, 279, 268, 257, 245])).
% 1.92/1.50 tff(288,plain,((~hskp27) | hskp30 | hskp20), inference(lemma,lemma(discharge,[]))).
% 1.92/1.50 tff(289,plain,
% 1.92/1.50 ($false),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[288, 235, 191, 102])).
% 1.92/1.50 tff(290,plain,(c2_1(a754) | hskp30 | c3_1(a754) | hskp6 | c0_1(a754)), inference(lemma,lemma(discharge,[]))).
% 1.92/1.50 tff(291,plain,
% 1.92/1.50 (c2_1(a754)),
% 1.92/1.50 inference(unit_resolution,[status(thm)],[290, 179, 102, 177, 178])).
% 1.92/1.50 tff(292,plain,
% 1.92/1.50 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))),
% 1.92/1.50 inference(bind,[status(th)],[])).
% 1.92/1.50 tff(293,plain,
% 1.92/1.50 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.92/1.50 inference(quant_intro,[status(thm)],[292])).
% 1.92/1.50 tff(294,plain,
% 1.92/1.50 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(295,plain,
% 1.92/1.50 (^[V: $i, U: $i] : 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(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | 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)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), ((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | hskp6))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), (((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))))),
% 1.92/1.50 inference(bind,[status(th)],[])).
% 1.92/1.50 tff(296,plain,
% 1.92/1.50 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.92/1.50 inference(quant_intro,[status(thm)],[295])).
% 1.92/1.50 tff(297,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause157')).
% 1.92/1.50 tff(298,plain,
% 1.92/1.50 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[297, 296])).
% 1.92/1.50 tff(299,plain,
% 1.92/1.50 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[298, 294])).
% 1.92/1.50 tff(300,plain,(
% 1.92/1.50 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.92/1.50 inference(skolemize,[status(sab)],[299])).
% 1.92/1.50 tff(301,plain,
% 1.92/1.50 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 1.92/1.50 inference(modus_ponens,[status(thm)],[300, 293])).
% 1.92/1.50 tff(302,assumption,(hskp24), introduced(assumption)).
% 1.92/1.50 tff(303,plain,
% 1.92/1.50 (((~hskp24) | (~c3_1(a764))) <=> ((~hskp24) | (~c3_1(a764)))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(304,plain,
% 1.92/1.50 (((~c3_1(a764)) | (~hskp24)) <=> ((~hskp24) | (~c3_1(a764)))),
% 1.92/1.50 inference(rewrite,[status(thm)],[])).
% 1.92/1.50 tff(305,axiom,((~c3_1(a764)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause91')).
% 1.96/1.50 tff(306,plain,
% 1.96/1.50 ((~hskp24) | (~c3_1(a764))),
% 1.96/1.50 inference(modus_ponens,[status(thm)],[305, 304])).
% 1.96/1.50 tff(307,plain,
% 1.96/1.50 ((~hskp24) | (~c3_1(a764))),
% 1.96/1.50 inference(modus_ponens,[status(thm)],[306, 303])).
% 1.96/1.50 tff(308,plain,
% 1.96/1.50 (~c3_1(a764)),
% 1.96/1.50 inference(unit_resolution,[status(thm)],[307, 302])).
% 1.96/1.50 tff(309,plain,
% 1.96/1.50 (((~hskp24) | (~c2_1(a764))) <=> ((~hskp24) | (~c2_1(a764)))),
% 1.96/1.50 inference(rewrite,[status(thm)],[])).
% 1.96/1.50 tff(310,plain,
% 1.96/1.50 (((~c2_1(a764)) | (~hskp24)) <=> ((~hskp24) | (~c2_1(a764)))),
% 1.96/1.50 inference(rewrite,[status(thm)],[])).
% 1.96/1.50 tff(311,axiom,((~c2_1(a764)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause90')).
% 1.96/1.50 tff(312,plain,
% 1.96/1.50 ((~hskp24) | (~c2_1(a764))),
% 1.96/1.50 inference(modus_ponens,[status(thm)],[311, 310])).
% 1.96/1.50 tff(313,plain,
% 1.96/1.50 ((~hskp24) | (~c2_1(a764))),
% 1.96/1.50 inference(modus_ponens,[status(thm)],[312, 309])).
% 1.96/1.50 tff(314,plain,
% 1.96/1.50 (~c2_1(a764)),
% 1.96/1.50 inference(unit_resolution,[status(thm)],[313, 302])).
% 1.96/1.50 tff(315,plain,
% 1.96/1.50 (((~hskp24) | c1_1(a764)) <=> ((~hskp24) | c1_1(a764))),
% 1.96/1.50 inference(rewrite,[status(thm)],[])).
% 1.96/1.50 tff(316,axiom,((~hskp24) | c1_1(a764)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause55')).
% 1.96/1.50 tff(317,plain,
% 1.96/1.50 ((~hskp24) | c1_1(a764)),
% 1.96/1.50 inference(modus_ponens,[status(thm)],[316, 315])).
% 1.96/1.50 tff(318,plain,
% 1.96/1.50 ((~hskp24) | c1_1(a764)),
% 1.96/1.50 inference(modus_ponens,[status(thm)],[317, 315])).
% 1.96/1.50 tff(319,plain,
% 1.96/1.50 ((~hskp24) | c1_1(a764)),
% 1.96/1.50 inference(modus_ponens,[status(thm)],[318, 315])).
% 1.96/1.50 tff(320,plain,
% 1.96/1.50 ((~hskp24) | c1_1(a764)),
% 1.96/1.50 inference(modus_ponens,[status(thm)],[319, 315])).
% 1.96/1.50 tff(321,plain,
% 1.96/1.50 ((~hskp24) | c1_1(a764)),
% 1.96/1.50 inference(modus_ponens,[status(thm)],[320, 315])).
% 1.96/1.50 tff(322,plain,
% 1.96/1.50 ((~hskp24) | c1_1(a764)),
% 1.96/1.50 inference(modus_ponens,[status(thm)],[321, 315])).
% 1.96/1.50 tff(323,plain,
% 1.96/1.50 ((~hskp24) | c1_1(a764)),
% 1.96/1.50 inference(modus_ponens,[status(thm)],[322, 315])).
% 1.96/1.50 tff(324,plain,
% 1.96/1.50 ((~hskp24) | c1_1(a764)),
% 1.96/1.50 inference(modus_ponens,[status(thm)],[323, 315])).
% 1.96/1.51 tff(325,plain,
% 1.96/1.51 (c1_1(a764)),
% 1.96/1.51 inference(unit_resolution,[status(thm)],[324, 302])).
% 1.96/1.51 tff(326,plain,
% 1.96/1.51 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | c2_1(a764) | c3_1(a764) | (~ndr1_0) | c0_1(a764) | (~c1_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c2_1(a764) | c3_1(a764) | (~ndr1_0) | c0_1(a764) | (~c1_1(a764)))),
% 1.96/1.51 inference(rewrite,[status(thm)],[])).
% 1.96/1.51 tff(327,plain,
% 1.96/1.51 ((hskp6 | (~ndr1_0) | c3_1(a764) | c0_1(a764) | (~c1_1(a764)) | c3_1(a764) | c0_1(a764) | c2_1(a764)) <=> (hskp6 | c2_1(a764) | c3_1(a764) | (~ndr1_0) | c0_1(a764) | (~c1_1(a764)))),
% 1.96/1.51 inference(rewrite,[status(thm)],[])).
% 1.96/1.51 tff(328,plain,
% 1.96/1.51 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a764) | c0_1(a764) | (~c1_1(a764)) | c3_1(a764) | c0_1(a764) | c2_1(a764))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | c2_1(a764) | c3_1(a764) | (~ndr1_0) | c0_1(a764) | (~c1_1(a764))))),
% 1.96/1.51 inference(monotonicity,[status(thm)],[327])).
% 1.96/1.51 tff(329,plain,
% 1.96/1.51 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a764) | c0_1(a764) | (~c1_1(a764)) | c3_1(a764) | c0_1(a764) | c2_1(a764))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c2_1(a764) | c3_1(a764) | (~ndr1_0) | c0_1(a764) | (~c1_1(a764)))),
% 1.96/1.51 inference(transitivity,[status(thm)],[328, 326])).
% 1.96/1.51 tff(330,plain,
% 1.96/1.51 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a764) | c0_1(a764) | (~c1_1(a764)) | c3_1(a764) | c0_1(a764) | c2_1(a764))),
% 1.96/1.51 inference(quant_inst,[status(thm)],[])).
% 1.96/1.51 tff(331,plain,
% 1.96/1.51 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c2_1(a764) | c3_1(a764) | (~ndr1_0) | c0_1(a764) | (~c1_1(a764))),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[330, 329])).
% 1.96/1.51 tff(332,plain,
% 1.96/1.51 (c0_1(a764)),
% 1.96/1.51 inference(unit_resolution,[status(thm)],[331, 227, 177, 325, 314, 308, 301])).
% 1.96/1.51 tff(333,plain,
% 1.96/1.51 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))),
% 1.96/1.51 inference(bind,[status(th)],[])).
% 1.96/1.51 tff(334,plain,
% 1.96/1.51 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.96/1.51 inference(quant_intro,[status(thm)],[333])).
% 1.96/1.51 tff(335,plain,
% 1.96/1.51 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.96/1.51 inference(rewrite,[status(thm)],[])).
% 1.96/1.51 tff(336,plain,
% 1.96/1.51 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp28) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp28))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp28) <=> (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))))),
% 1.96/1.51 inference(bind,[status(th)],[])).
% 1.96/1.51 tff(337,plain,
% 1.96/1.51 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.96/1.51 inference(quant_intro,[status(thm)],[336])).
% 1.96/1.51 tff(338,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause168')).
% 1.96/1.51 tff(339,plain,
% 1.96/1.51 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[338, 337])).
% 1.96/1.51 tff(340,plain,
% 1.96/1.51 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[339, 335])).
% 1.96/1.51 tff(341,plain,(
% 1.96/1.51 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.96/1.51 inference(skolemize,[status(sab)],[340])).
% 1.96/1.51 tff(342,plain,
% 1.96/1.51 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[341, 334])).
% 1.96/1.51 tff(343,plain,
% 1.96/1.51 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a764) | c3_1(a764) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c0_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a764) | c3_1(a764) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c0_1(a764)))),
% 1.96/1.51 inference(rewrite,[status(thm)],[])).
% 1.96/1.51 tff(344,plain,
% 1.96/1.51 ((hskp28 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c0_1(a764)) | c3_1(a693) | c1_1(a693) | (~c2_1(a693))) <=> (hskp28 | c2_1(a764) | c3_1(a764) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c0_1(a764)))),
% 1.96/1.51 inference(rewrite,[status(thm)],[])).
% 1.96/1.51 tff(345,plain,
% 1.96/1.51 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c0_1(a764)) | c3_1(a693) | c1_1(a693) | (~c2_1(a693)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a764) | c3_1(a764) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c0_1(a764))))),
% 1.96/1.51 inference(monotonicity,[status(thm)],[344])).
% 1.96/1.51 tff(346,plain,
% 1.96/1.51 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c0_1(a764)) | c3_1(a693) | c1_1(a693) | (~c2_1(a693)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a764) | c3_1(a764) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c0_1(a764)))),
% 1.96/1.51 inference(transitivity,[status(thm)],[345, 343])).
% 1.96/1.51 tff(347,plain,
% 1.96/1.51 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c0_1(a764)) | c3_1(a693) | c1_1(a693) | (~c2_1(a693)))),
% 1.96/1.51 inference(quant_inst,[status(thm)],[])).
% 1.96/1.51 tff(348,plain,
% 1.96/1.51 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a764) | c3_1(a764) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c0_1(a764))),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[347, 346])).
% 1.96/1.51 tff(349,plain,
% 1.96/1.51 ((~c2_1(a693)) | (~c0_1(a764))),
% 1.96/1.51 inference(unit_resolution,[status(thm)],[348, 227, 62, 314, 308, 164, 153, 342])).
% 1.96/1.51 tff(350,plain,
% 1.96/1.51 (~c2_1(a693)),
% 1.96/1.51 inference(unit_resolution,[status(thm)],[349, 332])).
% 1.96/1.51 tff(351,plain,
% 1.96/1.51 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | c2_1(a764) | c3_1(a764) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c2_1(a754)) | (~c1_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c2_1(a764) | c3_1(a764) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c2_1(a754)) | (~c1_1(a764)))),
% 1.96/1.51 inference(rewrite,[status(thm)],[])).
% 1.96/1.51 tff(352,plain,
% 1.96/1.51 ((hskp6 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754))) <=> (hskp6 | c2_1(a764) | c3_1(a764) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c2_1(a754)) | (~c1_1(a764)))),
% 1.96/1.51 inference(rewrite,[status(thm)],[])).
% 1.96/1.51 tff(353,plain,
% 1.96/1.51 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | c2_1(a764) | c3_1(a764) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c2_1(a754)) | (~c1_1(a764))))),
% 1.96/1.51 inference(monotonicity,[status(thm)],[352])).
% 1.96/1.51 tff(354,plain,
% 1.96/1.51 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c2_1(a764) | c3_1(a764) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c2_1(a754)) | (~c1_1(a764)))),
% 1.96/1.51 inference(transitivity,[status(thm)],[353, 351])).
% 1.96/1.51 tff(355,plain,
% 1.96/1.51 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))),
% 1.96/1.51 inference(quant_inst,[status(thm)],[])).
% 1.96/1.51 tff(356,plain,
% 1.96/1.51 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c2_1(a764) | c3_1(a764) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c2_1(a754)) | (~c1_1(a764))),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[355, 354])).
% 1.96/1.51 tff(357,plain,
% 1.96/1.51 (~c2_1(a754)),
% 1.96/1.51 inference(unit_resolution,[status(thm)],[356, 227, 177, 325, 314, 308, 179, 178, 101])).
% 1.96/1.51 tff(358,plain,
% 1.96/1.51 (~hskp20),
% 1.96/1.51 inference(unit_resolution,[status(thm)],[190, 357])).
% 1.96/1.51 tff(359,plain,
% 1.96/1.51 ((hskp30 | hskp20 | hskp1) <=> (hskp30 | hskp20 | hskp1)),
% 1.96/1.51 inference(rewrite,[status(thm)],[])).
% 1.96/1.51 tff(360,plain,
% 1.96/1.51 (((hskp30 | hskp20) | hskp1) <=> (hskp30 | hskp20 | hskp1)),
% 1.96/1.51 inference(rewrite,[status(thm)],[])).
% 1.96/1.51 tff(361,plain,
% 1.96/1.51 ((hskp30 | hskp20) <=> (hskp30 | hskp20)),
% 1.96/1.51 inference(rewrite,[status(thm)],[])).
% 1.96/1.51 tff(362,plain,
% 1.96/1.51 (((hskp30 | hskp20) | hskp1) <=> ((hskp30 | hskp20) | hskp1)),
% 1.96/1.51 inference(monotonicity,[status(thm)],[361])).
% 1.96/1.51 tff(363,plain,
% 1.96/1.51 (((hskp30 | hskp20) | hskp1) <=> (hskp30 | hskp20 | hskp1)),
% 1.96/1.51 inference(transitivity,[status(thm)],[362, 360])).
% 1.96/1.51 tff(364,axiom,((hskp30 | hskp20) | hskp1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause38')).
% 1.96/1.51 tff(365,plain,
% 1.96/1.51 (hskp30 | hskp20 | hskp1),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[364, 363])).
% 1.96/1.51 tff(366,plain,
% 1.96/1.51 (hskp30 | hskp20 | hskp1),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[365, 359])).
% 1.96/1.51 tff(367,plain,
% 1.96/1.51 (hskp30 | hskp20 | hskp1),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[366, 359])).
% 1.96/1.51 tff(368,plain,
% 1.96/1.51 (hskp30 | hskp20 | hskp1),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[367, 359])).
% 1.96/1.51 tff(369,plain,
% 1.96/1.51 (hskp30 | hskp20 | hskp1),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[368, 359])).
% 1.96/1.51 tff(370,plain,
% 1.96/1.51 (hskp30 | hskp20 | hskp1),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[369, 359])).
% 1.96/1.51 tff(371,plain,
% 1.96/1.51 (hskp30 | hskp20 | hskp1),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[370, 359])).
% 1.96/1.51 tff(372,plain,
% 1.96/1.51 (hskp30 | hskp20 | hskp1),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[371, 359])).
% 1.96/1.51 tff(373,plain,
% 1.96/1.51 (hskp1),
% 1.96/1.51 inference(unit_resolution,[status(thm)],[372, 358, 102])).
% 1.96/1.51 tff(374,plain,
% 1.96/1.51 (((~hskp1) | c2_1(a693)) <=> ((~hskp1) | c2_1(a693))),
% 1.96/1.51 inference(rewrite,[status(thm)],[])).
% 1.96/1.51 tff(375,axiom,((~hskp1) | c2_1(a693)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause85')).
% 1.96/1.51 tff(376,plain,
% 1.96/1.51 ((~hskp1) | c2_1(a693)),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[375, 374])).
% 1.96/1.51 tff(377,plain,
% 1.96/1.51 ((~hskp1) | c2_1(a693)),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[376, 374])).
% 1.96/1.51 tff(378,plain,
% 1.96/1.51 ((~hskp1) | c2_1(a693)),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[377, 374])).
% 1.96/1.51 tff(379,plain,
% 1.96/1.51 ((~hskp1) | c2_1(a693)),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[378, 374])).
% 1.96/1.51 tff(380,plain,
% 1.96/1.51 ((~hskp1) | c2_1(a693)),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[379, 374])).
% 1.96/1.51 tff(381,plain,
% 1.96/1.51 ((~hskp1) | c2_1(a693)),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[380, 374])).
% 1.96/1.51 tff(382,plain,
% 1.96/1.51 ((~hskp1) | c2_1(a693)),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[381, 374])).
% 1.96/1.51 tff(383,plain,
% 1.96/1.51 ((~hskp1) | c2_1(a693)),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[382, 374])).
% 1.96/1.51 tff(384,plain,
% 1.96/1.51 ($false),
% 1.96/1.51 inference(unit_resolution,[status(thm)],[383, 373, 350])).
% 1.96/1.51 tff(385,plain,((~hskp24) | hskp30 | hskp28 | c1_1(a693) | c3_1(a693) | hskp6 | c0_1(a754) | c3_1(a754)), inference(lemma,lemma(discharge,[]))).
% 1.96/1.51 tff(386,plain,
% 1.96/1.51 (~hskp24),
% 1.96/1.51 inference(unit_resolution,[status(thm)],[385, 179, 62, 164, 153, 102, 177, 178])).
% 1.96/1.51 tff(387,assumption,(c2_1(a754)), introduced(assumption)).
% 1.96/1.51 tff(388,assumption,(~c1_1(a754)), introduced(assumption)).
% 1.96/1.51 tff(389,plain,
% 1.96/1.51 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 1.96/1.51 inference(bind,[status(th)],[])).
% 1.96/1.51 tff(390,plain,
% 1.96/1.51 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.96/1.51 inference(quant_intro,[status(thm)],[389])).
% 1.96/1.51 tff(391,plain,
% 1.96/1.51 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.96/1.51 inference(rewrite,[status(thm)],[])).
% 1.96/1.51 tff(392,plain,
% 1.96/1.51 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp28) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp28))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp28) <=> (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 1.96/1.51 inference(bind,[status(th)],[])).
% 1.96/1.51 tff(393,plain,
% 1.96/1.51 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.96/1.51 inference(quant_intro,[status(thm)],[392])).
% 1.96/1.51 tff(394,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause159')).
% 1.96/1.51 tff(395,plain,
% 1.96/1.51 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[394, 393])).
% 1.96/1.51 tff(396,plain,
% 1.96/1.51 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[395, 391])).
% 1.96/1.51 tff(397,plain,(
% 1.96/1.51 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.96/1.51 inference(skolemize,[status(sab)],[396])).
% 1.96/1.51 tff(398,plain,
% 1.96/1.51 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[397, 390])).
% 1.96/1.51 tff(399,assumption,(hskp23), introduced(assumption)).
% 1.96/1.51 tff(400,plain,
% 1.96/1.51 (((~hskp23) | (~c2_1(a763))) <=> ((~hskp23) | (~c2_1(a763)))),
% 1.96/1.51 inference(rewrite,[status(thm)],[])).
% 1.96/1.51 tff(401,plain,
% 1.96/1.51 (((~c2_1(a763)) | (~hskp23)) <=> ((~hskp23) | (~c2_1(a763)))),
% 1.96/1.51 inference(rewrite,[status(thm)],[])).
% 1.96/1.51 tff(402,axiom,((~c2_1(a763)) | (~hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause93')).
% 1.96/1.51 tff(403,plain,
% 1.96/1.51 ((~hskp23) | (~c2_1(a763))),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[402, 401])).
% 1.96/1.51 tff(404,plain,
% 1.96/1.51 ((~hskp23) | (~c2_1(a763))),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[403, 400])).
% 1.96/1.51 tff(405,plain,
% 1.96/1.51 (~c2_1(a763)),
% 1.96/1.51 inference(unit_resolution,[status(thm)],[404, 399])).
% 1.96/1.51 tff(406,plain,
% 1.96/1.51 (((~hskp23) | (~c1_1(a763))) <=> ((~hskp23) | (~c1_1(a763)))),
% 1.96/1.51 inference(rewrite,[status(thm)],[])).
% 1.96/1.51 tff(407,plain,
% 1.96/1.51 (((~c1_1(a763)) | (~hskp23)) <=> ((~hskp23) | (~c1_1(a763)))),
% 1.96/1.51 inference(rewrite,[status(thm)],[])).
% 1.96/1.51 tff(408,axiom,((~c1_1(a763)) | (~hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause92')).
% 1.96/1.51 tff(409,plain,
% 1.96/1.51 ((~hskp23) | (~c1_1(a763))),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[408, 407])).
% 1.96/1.51 tff(410,plain,
% 1.96/1.51 ((~hskp23) | (~c1_1(a763))),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[409, 406])).
% 1.96/1.51 tff(411,plain,
% 1.96/1.51 (~c1_1(a763)),
% 1.96/1.51 inference(unit_resolution,[status(thm)],[410, 399])).
% 1.96/1.51 tff(412,plain,
% 1.96/1.51 (((~hskp23) | c0_1(a763)) <=> ((~hskp23) | c0_1(a763))),
% 1.96/1.51 inference(rewrite,[status(thm)],[])).
% 1.96/1.51 tff(413,axiom,((~hskp23) | c0_1(a763)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause56')).
% 1.96/1.51 tff(414,plain,
% 1.96/1.51 ((~hskp23) | c0_1(a763)),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[413, 412])).
% 1.96/1.51 tff(415,plain,
% 1.96/1.51 ((~hskp23) | c0_1(a763)),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[414, 412])).
% 1.96/1.51 tff(416,plain,
% 1.96/1.51 ((~hskp23) | c0_1(a763)),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[415, 412])).
% 1.96/1.51 tff(417,plain,
% 1.96/1.51 ((~hskp23) | c0_1(a763)),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[416, 412])).
% 1.96/1.51 tff(418,plain,
% 1.96/1.51 ((~hskp23) | c0_1(a763)),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[417, 412])).
% 1.96/1.51 tff(419,plain,
% 1.96/1.51 ((~hskp23) | c0_1(a763)),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[418, 412])).
% 1.96/1.51 tff(420,plain,
% 1.96/1.51 ((~hskp23) | c0_1(a763)),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[419, 412])).
% 1.96/1.51 tff(421,plain,
% 1.96/1.51 ((~hskp23) | c0_1(a763)),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[420, 412])).
% 1.96/1.51 tff(422,plain,
% 1.96/1.51 (c0_1(a763)),
% 1.96/1.51 inference(unit_resolution,[status(thm)],[421, 399])).
% 1.96/1.51 tff(423,plain,
% 1.96/1.51 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | c1_1(a763) | c2_1(a763) | c0_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754)) | (~c0_1(a763)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c1_1(a763) | c2_1(a763) | c0_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754)) | (~c0_1(a763)))),
% 1.96/1.51 inference(rewrite,[status(thm)],[])).
% 1.96/1.51 tff(424,plain,
% 1.96/1.51 ((hskp28 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c1_1(a754) | c0_1(a754) | (~c2_1(a754))) <=> (hskp28 | c1_1(a763) | c2_1(a763) | c0_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754)) | (~c0_1(a763)))),
% 1.96/1.51 inference(rewrite,[status(thm)],[])).
% 1.96/1.51 tff(425,plain,
% 1.96/1.51 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c1_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | c1_1(a763) | c2_1(a763) | c0_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754)) | (~c0_1(a763))))),
% 1.96/1.51 inference(monotonicity,[status(thm)],[424])).
% 1.96/1.51 tff(426,plain,
% 1.96/1.51 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c1_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c1_1(a763) | c2_1(a763) | c0_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754)) | (~c0_1(a763)))),
% 1.96/1.51 inference(transitivity,[status(thm)],[425, 423])).
% 1.96/1.51 tff(427,plain,
% 1.96/1.51 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c1_1(a754) | c0_1(a754) | (~c2_1(a754)))),
% 1.96/1.51 inference(quant_inst,[status(thm)],[])).
% 1.96/1.51 tff(428,plain,
% 1.96/1.51 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c1_1(a763) | c2_1(a763) | c0_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754)) | (~c0_1(a763))),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[427, 426])).
% 1.96/1.51 tff(429,plain,
% 1.96/1.51 ($false),
% 1.96/1.51 inference(unit_resolution,[status(thm)],[428, 227, 62, 422, 387, 411, 405, 179, 398, 388])).
% 1.96/1.51 tff(430,plain,((~hskp23) | hskp28 | (~c2_1(a754)) | c0_1(a754) | c1_1(a754)), inference(lemma,lemma(discharge,[]))).
% 1.96/1.51 tff(431,plain,
% 1.96/1.51 (~hskp23),
% 1.96/1.51 inference(unit_resolution,[status(thm)],[430, 388, 387, 179, 62])).
% 1.96/1.51 tff(432,assumption,(~hskp24), introduced(assumption)).
% 1.96/1.51 tff(433,plain,
% 1.96/1.51 (^[U: $i] : refl((hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))),
% 1.96/1.51 inference(bind,[status(th)],[])).
% 1.96/1.51 tff(434,plain,
% 1.96/1.51 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.96/1.51 inference(quant_intro,[status(thm)],[433])).
% 1.96/1.51 tff(435,plain,
% 1.96/1.51 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.96/1.51 inference(rewrite,[status(thm)],[])).
% 1.96/1.51 tff(436,plain,
% 1.96/1.51 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp3) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp3))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp3) | hskp4) <=> ((hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp4))), rewrite(((hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp4) <=> (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp3) | hskp4) <=> (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))))),
% 1.96/1.51 inference(bind,[status(th)],[])).
% 1.96/1.51 tff(437,plain,
% 1.96/1.51 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp3) | hskp4) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.96/1.51 inference(quant_intro,[status(thm)],[436])).
% 1.96/1.51 tff(438,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp3) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause138')).
% 1.96/1.51 tff(439,plain,
% 1.96/1.51 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[438, 437])).
% 1.96/1.51 tff(440,plain,
% 1.96/1.51 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[439, 435])).
% 1.96/1.51 tff(441,plain,(
% 1.96/1.51 ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.96/1.51 inference(skolemize,[status(sab)],[440])).
% 1.96/1.51 tff(442,plain,
% 1.96/1.51 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[441, 434])).
% 1.96/1.51 tff(443,plain,
% 1.96/1.51 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | c0_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c0_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754)))),
% 1.96/1.51 inference(rewrite,[status(thm)],[])).
% 1.96/1.51 tff(444,plain,
% 1.96/1.51 ((hskp4 | hskp3 | (~ndr1_0) | c1_1(a754) | c0_1(a754) | (~c2_1(a754))) <=> (hskp4 | hskp3 | c0_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754)))),
% 1.96/1.51 inference(rewrite,[status(thm)],[])).
% 1.96/1.51 tff(445,plain,
% 1.96/1.51 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | c0_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754))))),
% 1.96/1.51 inference(monotonicity,[status(thm)],[444])).
% 1.96/1.51 tff(446,plain,
% 1.96/1.51 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c0_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754)))),
% 1.96/1.51 inference(transitivity,[status(thm)],[445, 443])).
% 1.96/1.51 tff(447,plain,
% 1.96/1.51 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a754) | c0_1(a754) | (~c2_1(a754)))),
% 1.96/1.51 inference(quant_inst,[status(thm)],[])).
% 1.96/1.51 tff(448,plain,
% 1.96/1.51 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c0_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754))),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[447, 446])).
% 1.96/1.51 tff(449,plain,
% 1.96/1.51 (hskp3 | c1_1(a754)),
% 1.96/1.51 inference(unit_resolution,[status(thm)],[448, 227, 176, 387, 179, 442])).
% 1.96/1.51 tff(450,plain,
% 1.96/1.51 (hskp3),
% 1.96/1.51 inference(unit_resolution,[status(thm)],[449, 388])).
% 1.96/1.51 tff(451,assumption,(hskp14), introduced(assumption)).
% 1.96/1.51 tff(452,plain,
% 1.96/1.51 (((~hskp14) | c1_1(a730)) <=> ((~hskp14) | c1_1(a730))),
% 1.96/1.51 inference(rewrite,[status(thm)],[])).
% 1.96/1.51 tff(453,axiom,((~hskp14) | c1_1(a730)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause67')).
% 1.96/1.51 tff(454,plain,
% 1.96/1.51 ((~hskp14) | c1_1(a730)),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[453, 452])).
% 1.96/1.51 tff(455,plain,
% 1.96/1.51 ((~hskp14) | c1_1(a730)),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[454, 452])).
% 1.96/1.51 tff(456,plain,
% 1.96/1.51 ((~hskp14) | c1_1(a730)),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[455, 452])).
% 1.96/1.51 tff(457,plain,
% 1.96/1.51 ((~hskp14) | c1_1(a730)),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[456, 452])).
% 1.96/1.51 tff(458,plain,
% 1.96/1.51 ((~hskp14) | c1_1(a730)),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[457, 452])).
% 1.96/1.51 tff(459,plain,
% 1.96/1.51 ((~hskp14) | c1_1(a730)),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[458, 452])).
% 1.96/1.51 tff(460,plain,
% 1.96/1.51 ((~hskp14) | c1_1(a730)),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[459, 452])).
% 1.96/1.51 tff(461,plain,
% 1.96/1.51 ((~hskp14) | c1_1(a730)),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[460, 452])).
% 1.96/1.51 tff(462,plain,
% 1.96/1.51 (c1_1(a730)),
% 1.96/1.51 inference(unit_resolution,[status(thm)],[461, 451])).
% 1.96/1.51 tff(463,plain,
% 1.96/1.51 (((~hskp14) | c0_1(a730)) <=> ((~hskp14) | c0_1(a730))),
% 1.96/1.51 inference(rewrite,[status(thm)],[])).
% 1.96/1.51 tff(464,axiom,((~hskp14) | c0_1(a730)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause66')).
% 1.96/1.51 tff(465,plain,
% 1.96/1.51 ((~hskp14) | c0_1(a730)),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[464, 463])).
% 1.96/1.51 tff(466,plain,
% 1.96/1.51 ((~hskp14) | c0_1(a730)),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[465, 463])).
% 1.96/1.51 tff(467,plain,
% 1.96/1.51 ((~hskp14) | c0_1(a730)),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[466, 463])).
% 1.96/1.51 tff(468,plain,
% 1.96/1.51 ((~hskp14) | c0_1(a730)),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[467, 463])).
% 1.96/1.51 tff(469,plain,
% 1.96/1.51 ((~hskp14) | c0_1(a730)),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[468, 463])).
% 1.96/1.51 tff(470,plain,
% 1.96/1.51 ((~hskp14) | c0_1(a730)),
% 1.96/1.51 inference(modus_ponens,[status(thm)],[469, 463])).
% 1.96/1.52 tff(471,plain,
% 1.96/1.52 ((~hskp14) | c0_1(a730)),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[470, 463])).
% 1.96/1.52 tff(472,plain,
% 1.96/1.52 ((~hskp14) | c0_1(a730)),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[471, 463])).
% 1.96/1.52 tff(473,plain,
% 1.96/1.52 (c0_1(a730)),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[472, 451])).
% 1.96/1.52 tff(474,assumption,(~hskp23), introduced(assumption)).
% 1.96/1.52 tff(475,plain,
% 1.96/1.52 (((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | (~c2_1(a730)))) <=> ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | (~c2_1(a730)))),
% 1.96/1.52 inference(rewrite,[status(thm)],[])).
% 1.96/1.52 tff(476,plain,
% 1.96/1.52 ((hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a730)) | (~c0_1(a730)) | (~c1_1(a730))) <=> (hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | (~c2_1(a730)))),
% 1.96/1.52 inference(rewrite,[status(thm)],[])).
% 1.96/1.52 tff(477,plain,
% 1.96/1.52 (((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a730)) | (~c0_1(a730)) | (~c1_1(a730)))) <=> ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | (~c2_1(a730))))),
% 1.96/1.52 inference(monotonicity,[status(thm)],[476])).
% 1.96/1.52 tff(478,plain,
% 1.96/1.52 (((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a730)) | (~c0_1(a730)) | (~c1_1(a730)))) <=> ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | (~c2_1(a730)))),
% 1.96/1.52 inference(transitivity,[status(thm)],[477, 475])).
% 1.96/1.52 tff(479,plain,
% 1.96/1.52 ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a730)) | (~c0_1(a730)) | (~c1_1(a730)))),
% 1.96/1.52 inference(quant_inst,[status(thm)],[])).
% 1.96/1.52 tff(480,plain,
% 1.96/1.52 ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | (~c2_1(a730))),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[479, 478])).
% 1.96/1.52 tff(481,plain,
% 1.96/1.52 (~c2_1(a730)),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[480, 227, 432, 474, 473, 462, 163])).
% 1.96/1.52 tff(482,plain,
% 1.96/1.52 (((~hskp14) | (~c3_1(a730))) <=> ((~hskp14) | (~c3_1(a730)))),
% 1.96/1.52 inference(rewrite,[status(thm)],[])).
% 1.96/1.52 tff(483,plain,
% 1.96/1.52 (((~c3_1(a730)) | (~hskp14)) <=> ((~hskp14) | (~c3_1(a730)))),
% 1.96/1.52 inference(rewrite,[status(thm)],[])).
% 1.96/1.52 tff(484,axiom,((~c3_1(a730)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause109')).
% 1.96/1.52 tff(485,plain,
% 1.96/1.52 ((~hskp14) | (~c3_1(a730))),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[484, 483])).
% 1.96/1.52 tff(486,plain,
% 1.96/1.52 ((~hskp14) | (~c3_1(a730))),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[485, 482])).
% 1.96/1.52 tff(487,plain,
% 1.96/1.52 (~c3_1(a730)),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[486, 451])).
% 1.96/1.52 tff(488,plain,
% 1.96/1.52 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | c3_1(a754) | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | c2_1(a730) | c1_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c3_1(a754) | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | c2_1(a730) | c1_1(a754) | (~c2_1(a754)))),
% 1.96/1.52 inference(rewrite,[status(thm)],[])).
% 1.96/1.52 tff(489,plain,
% 1.96/1.52 ((hskp28 | (~ndr1_0) | c3_1(a730) | c2_1(a730) | (~c0_1(a730)) | c3_1(a754) | c1_1(a754) | (~c2_1(a754))) <=> (hskp28 | c3_1(a754) | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | c2_1(a730) | c1_1(a754) | (~c2_1(a754)))),
% 1.96/1.52 inference(rewrite,[status(thm)],[])).
% 1.96/1.52 tff(490,plain,
% 1.96/1.52 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a730) | c2_1(a730) | (~c0_1(a730)) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | c3_1(a754) | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | c2_1(a730) | c1_1(a754) | (~c2_1(a754))))),
% 1.96/1.52 inference(monotonicity,[status(thm)],[489])).
% 1.96/1.52 tff(491,plain,
% 1.96/1.52 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a730) | c2_1(a730) | (~c0_1(a730)) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c3_1(a754) | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | c2_1(a730) | c1_1(a754) | (~c2_1(a754)))),
% 1.96/1.52 inference(transitivity,[status(thm)],[490, 488])).
% 1.96/1.52 tff(492,plain,
% 1.96/1.52 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a730) | c2_1(a730) | (~c0_1(a730)) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)))),
% 1.96/1.52 inference(quant_inst,[status(thm)],[])).
% 1.96/1.52 tff(493,plain,
% 1.96/1.52 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c3_1(a754) | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | c2_1(a730) | c1_1(a754) | (~c2_1(a754))),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[492, 491])).
% 1.96/1.52 tff(494,plain,
% 1.96/1.52 ($false),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[493, 227, 62, 387, 473, 178, 487, 342, 388, 481])).
% 1.96/1.52 tff(495,plain,((~hskp14) | hskp28 | (~c2_1(a754)) | c3_1(a754) | c1_1(a754) | hskp24 | hskp23), inference(lemma,lemma(discharge,[]))).
% 1.96/1.52 tff(496,plain,
% 1.96/1.52 (~hskp14),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[495, 431, 387, 178, 388, 432, 62])).
% 1.96/1.52 tff(497,assumption,(~hskp14), introduced(assumption)).
% 1.96/1.52 tff(498,assumption,(hskp3), introduced(assumption)).
% 1.96/1.52 tff(499,plain,
% 1.96/1.52 (((~hskp3) | c0_1(a697)) <=> ((~hskp3) | c0_1(a697))),
% 1.96/1.52 inference(rewrite,[status(thm)],[])).
% 1.96/1.52 tff(500,axiom,((~hskp3) | c0_1(a697)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause81')).
% 1.96/1.52 tff(501,plain,
% 1.96/1.52 ((~hskp3) | c0_1(a697)),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[500, 499])).
% 1.96/1.52 tff(502,plain,
% 1.96/1.52 ((~hskp3) | c0_1(a697)),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[501, 499])).
% 1.96/1.52 tff(503,plain,
% 1.96/1.52 ((~hskp3) | c0_1(a697)),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[502, 499])).
% 1.96/1.52 tff(504,plain,
% 1.96/1.52 ((~hskp3) | c0_1(a697)),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[503, 499])).
% 1.96/1.52 tff(505,plain,
% 1.96/1.52 ((~hskp3) | c0_1(a697)),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[504, 499])).
% 1.96/1.52 tff(506,plain,
% 1.96/1.52 ((~hskp3) | c0_1(a697)),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[505, 499])).
% 1.96/1.52 tff(507,plain,
% 1.96/1.52 ((~hskp3) | c0_1(a697)),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[506, 499])).
% 1.96/1.52 tff(508,plain,
% 1.96/1.52 ((~hskp3) | c0_1(a697)),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[507, 499])).
% 1.96/1.52 tff(509,plain,
% 1.96/1.52 (c0_1(a697)),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[508, 498])).
% 1.96/1.52 tff(510,plain,
% 1.96/1.52 (((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp14 | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697))) <=> ((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp30 | hskp14 | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697))),
% 1.96/1.52 inference(rewrite,[status(thm)],[])).
% 1.96/1.52 tff(511,plain,
% 1.96/1.52 ((hskp30 | hskp14 | (~ndr1_0) | c3_1(a697) | c1_1(a697) | (~c0_1(a697))) <=> (hskp30 | hskp14 | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697))),
% 1.96/1.52 inference(rewrite,[status(thm)],[])).
% 1.96/1.52 tff(512,plain,
% 1.96/1.52 (((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp14 | (~ndr1_0) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)))) <=> ((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp14 | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697)))),
% 1.96/1.52 inference(monotonicity,[status(thm)],[511])).
% 1.96/1.52 tff(513,plain,
% 1.96/1.52 (((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp14 | (~ndr1_0) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)))) <=> ((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp30 | hskp14 | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697))),
% 1.96/1.52 inference(transitivity,[status(thm)],[512, 510])).
% 1.96/1.52 tff(514,plain,
% 1.96/1.52 ((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp14 | (~ndr1_0) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)))),
% 1.96/1.52 inference(quant_inst,[status(thm)],[])).
% 1.96/1.52 tff(515,plain,
% 1.96/1.52 ((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp30 | hskp14 | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697)),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[514, 513])).
% 1.96/1.52 tff(516,plain,
% 1.96/1.52 (hskp14 | (~c0_1(a697)) | c1_1(a697)),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[515, 102, 227, 175, 112])).
% 1.96/1.52 tff(517,plain,
% 1.96/1.52 (c1_1(a697)),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[516, 509, 497])).
% 1.96/1.52 tff(518,plain,
% 1.96/1.52 (((~hskp3) | c2_1(a697)) <=> ((~hskp3) | c2_1(a697))),
% 1.96/1.52 inference(rewrite,[status(thm)],[])).
% 1.96/1.52 tff(519,axiom,((~hskp3) | c2_1(a697)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause82')).
% 1.96/1.52 tff(520,plain,
% 1.96/1.52 ((~hskp3) | c2_1(a697)),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[519, 518])).
% 1.96/1.52 tff(521,plain,
% 1.96/1.52 ((~hskp3) | c2_1(a697)),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[520, 518])).
% 1.96/1.52 tff(522,plain,
% 1.96/1.52 ((~hskp3) | c2_1(a697)),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[521, 518])).
% 1.96/1.52 tff(523,plain,
% 1.96/1.52 ((~hskp3) | c2_1(a697)),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[522, 518])).
% 1.96/1.52 tff(524,plain,
% 1.96/1.52 ((~hskp3) | c2_1(a697)),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[523, 518])).
% 1.96/1.52 tff(525,plain,
% 1.96/1.52 ((~hskp3) | c2_1(a697)),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[524, 518])).
% 1.96/1.52 tff(526,plain,
% 1.96/1.52 ((~hskp3) | c2_1(a697)),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[525, 518])).
% 1.96/1.52 tff(527,plain,
% 1.96/1.52 ((~hskp3) | c2_1(a697)),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[526, 518])).
% 1.96/1.52 tff(528,plain,
% 1.96/1.52 (c2_1(a697)),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[527, 498])).
% 1.96/1.52 tff(529,plain,
% 1.96/1.52 (((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a697)))) <=> ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a697)))),
% 1.96/1.52 inference(rewrite,[status(thm)],[])).
% 1.96/1.52 tff(530,plain,
% 1.96/1.52 ((hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a697)) | (~c0_1(a697)) | (~c1_1(a697))) <=> (hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a697)))),
% 1.96/1.52 inference(rewrite,[status(thm)],[])).
% 1.96/1.52 tff(531,plain,
% 1.96/1.52 (((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a697)) | (~c0_1(a697)) | (~c1_1(a697)))) <=> ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a697))))),
% 1.96/1.52 inference(monotonicity,[status(thm)],[530])).
% 1.96/1.52 tff(532,plain,
% 1.96/1.52 (((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a697)) | (~c0_1(a697)) | (~c1_1(a697)))) <=> ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a697)))),
% 1.96/1.52 inference(transitivity,[status(thm)],[531, 529])).
% 1.96/1.52 tff(533,plain,
% 1.96/1.52 ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a697)) | (~c0_1(a697)) | (~c1_1(a697)))),
% 1.96/1.52 inference(quant_inst,[status(thm)],[])).
% 1.96/1.52 tff(534,plain,
% 1.96/1.52 ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a697))),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[533, 532])).
% 1.96/1.52 tff(535,plain,
% 1.96/1.52 ($false),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[534, 227, 432, 474, 509, 528, 163, 517])).
% 1.96/1.52 tff(536,plain,((~hskp3) | hskp24 | hskp23 | hskp14 | hskp30 | c3_1(a697)), inference(lemma,lemma(discharge,[]))).
% 1.96/1.52 tff(537,plain,
% 1.96/1.52 ($false),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[536, 496, 450, 432, 431, 102, 175])).
% 1.96/1.52 tff(538,plain,(c1_1(a754) | hskp24 | hskp30 | c3_1(a697) | (~c2_1(a754)) | c3_1(a754) | hskp28 | hskp4 | c0_1(a754)), inference(lemma,lemma(discharge,[]))).
% 1.96/1.52 tff(539,plain,
% 1.96/1.52 (c1_1(a754)),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[538, 386, 102, 175, 291, 178, 62, 176, 179])).
% 1.96/1.52 tff(540,plain,
% 1.96/1.52 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | c0_1(a754) | c3_1(a754) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c1_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c0_1(a754) | c3_1(a754) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c1_1(a754)))),
% 1.96/1.52 inference(rewrite,[status(thm)],[])).
% 1.96/1.52 tff(541,plain,
% 1.96/1.52 ((hskp6 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)) | c3_1(a725) | c0_1(a725) | c2_1(a725)) <=> (hskp6 | c0_1(a754) | c3_1(a754) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c1_1(a754)))),
% 1.96/1.52 inference(rewrite,[status(thm)],[])).
% 1.96/1.52 tff(542,plain,
% 1.96/1.52 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)) | c3_1(a725) | c0_1(a725) | c2_1(a725))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | c0_1(a754) | c3_1(a754) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c1_1(a754))))),
% 1.96/1.52 inference(monotonicity,[status(thm)],[541])).
% 1.96/1.52 tff(543,plain,
% 1.96/1.52 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)) | c3_1(a725) | c0_1(a725) | c2_1(a725))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c0_1(a754) | c3_1(a754) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c1_1(a754)))),
% 1.96/1.52 inference(transitivity,[status(thm)],[542, 540])).
% 1.96/1.52 tff(544,plain,
% 1.96/1.52 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)) | c3_1(a725) | c0_1(a725) | c2_1(a725))),
% 1.96/1.52 inference(quant_inst,[status(thm)],[])).
% 1.96/1.52 tff(545,plain,
% 1.96/1.52 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c0_1(a754) | c3_1(a754) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c1_1(a754))),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[544, 543])).
% 1.96/1.52 tff(546,plain,
% 1.96/1.52 (c0_1(a754) | c2_1(a725) | (~c1_1(a754))),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[545, 227, 177, 178, 152, 140, 301])).
% 1.96/1.52 tff(547,plain,
% 1.96/1.52 (c2_1(a725)),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[546, 539, 179])).
% 1.96/1.52 tff(548,plain,
% 1.96/1.52 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | c0_1(a725) | c1_1(a725) | (~ndr1_0) | (~c2_1(a725)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c0_1(a725) | c1_1(a725) | (~ndr1_0) | (~c2_1(a725)))),
% 1.96/1.52 inference(rewrite,[status(thm)],[])).
% 1.96/1.52 tff(549,plain,
% 1.96/1.52 ((hskp4 | hskp3 | (~ndr1_0) | c1_1(a725) | c0_1(a725) | (~c2_1(a725))) <=> (hskp4 | hskp3 | c0_1(a725) | c1_1(a725) | (~ndr1_0) | (~c2_1(a725)))),
% 1.96/1.52 inference(rewrite,[status(thm)],[])).
% 1.96/1.52 tff(550,plain,
% 1.96/1.52 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a725) | c0_1(a725) | (~c2_1(a725)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | c0_1(a725) | c1_1(a725) | (~ndr1_0) | (~c2_1(a725))))),
% 1.96/1.52 inference(monotonicity,[status(thm)],[549])).
% 1.96/1.52 tff(551,plain,
% 1.96/1.52 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a725) | c0_1(a725) | (~c2_1(a725)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c0_1(a725) | c1_1(a725) | (~ndr1_0) | (~c2_1(a725)))),
% 1.96/1.52 inference(transitivity,[status(thm)],[550, 548])).
% 1.96/1.52 tff(552,plain,
% 1.96/1.52 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a725) | c0_1(a725) | (~c2_1(a725)))),
% 1.96/1.52 inference(quant_inst,[status(thm)],[])).
% 1.96/1.52 tff(553,plain,
% 1.96/1.52 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c0_1(a725) | c1_1(a725) | (~ndr1_0) | (~c2_1(a725))),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[552, 551])).
% 1.96/1.52 tff(554,plain,
% 1.96/1.52 (hskp4 | hskp3 | (~c2_1(a725))),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[553, 227, 152, 146, 442])).
% 1.96/1.52 tff(555,plain,
% 1.96/1.52 (hskp3),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[554, 547, 176])).
% 1.96/1.52 tff(556,plain,
% 1.96/1.52 (c0_1(a697)),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[508, 555])).
% 1.96/1.52 tff(557,plain,
% 1.96/1.52 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W)))),
% 1.96/1.52 inference(bind,[status(th)],[])).
% 1.96/1.52 tff(558,plain,
% 1.96/1.52 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))),
% 1.96/1.52 inference(quant_intro,[status(thm)],[557])).
% 1.96/1.52 tff(559,plain,
% 1.96/1.52 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))),
% 1.96/1.52 inference(rewrite,[status(thm)],[])).
% 1.96/1.52 tff(560,plain,
% 1.96/1.52 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(W)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(W))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))))),
% 1.96/1.52 inference(bind,[status(th)],[])).
% 1.96/1.52 tff(561,plain,
% 1.96/1.52 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))),
% 1.96/1.52 inference(quant_intro,[status(thm)],[560])).
% 1.96/1.52 tff(562,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause191')).
% 1.96/1.52 tff(563,plain,
% 1.96/1.52 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[562, 561])).
% 1.96/1.52 tff(564,plain,
% 1.96/1.52 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[563, 559])).
% 1.96/1.52 tff(565,plain,(
% 1.96/1.52 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))),
% 1.96/1.52 inference(skolemize,[status(sab)],[564])).
% 1.96/1.52 tff(566,plain,
% 1.96/1.52 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[565, 558])).
% 1.96/1.52 tff(567,plain,
% 1.96/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | (c3_1(a754) | c0_1(a725) | c1_1(a725) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a725)) | (~c1_1(a754)) | (~c2_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c3_1(a754) | c0_1(a725) | c1_1(a725) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a725)) | (~c1_1(a754)) | (~c2_1(a754)))),
% 1.96/1.52 inference(rewrite,[status(thm)],[])).
% 1.96/1.52 tff(568,plain,
% 1.96/1.52 (((~ndr1_0) | c3_1(a754) | (~c2_1(a754)) | (~c1_1(a754)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a725) | (~c2_1(a725)) | c1_1(a725)) <=> (c3_1(a754) | c0_1(a725) | c1_1(a725) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a725)) | (~c1_1(a754)) | (~c2_1(a754)))),
% 1.96/1.52 inference(rewrite,[status(thm)],[])).
% 1.96/1.52 tff(569,plain,
% 1.96/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a754) | (~c2_1(a754)) | (~c1_1(a754)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a725) | (~c2_1(a725)) | c1_1(a725))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | (c3_1(a754) | c0_1(a725) | c1_1(a725) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a725)) | (~c1_1(a754)) | (~c2_1(a754))))),
% 1.96/1.52 inference(monotonicity,[status(thm)],[568])).
% 1.96/1.52 tff(570,plain,
% 1.96/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a754) | (~c2_1(a754)) | (~c1_1(a754)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a725) | (~c2_1(a725)) | c1_1(a725))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c3_1(a754) | c0_1(a725) | c1_1(a725) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a725)) | (~c1_1(a754)) | (~c2_1(a754)))),
% 1.96/1.52 inference(transitivity,[status(thm)],[569, 567])).
% 1.96/1.52 tff(571,plain,
% 1.96/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a754) | (~c2_1(a754)) | (~c1_1(a754)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a725) | (~c2_1(a725)) | c1_1(a725))),
% 1.96/1.52 inference(quant_inst,[status(thm)],[])).
% 1.96/1.52 tff(572,plain,
% 1.96/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c3_1(a754) | c0_1(a725) | c1_1(a725) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a725)) | (~c1_1(a754)) | (~c2_1(a754))),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[571, 570])).
% 1.96/1.52 tff(573,plain,
% 1.96/1.52 ((~c0_1(a697)) | c1_1(a697) | (~c2_1(a725)) | (~c1_1(a754)) | (~c2_1(a754))),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[572, 227, 178, 152, 146, 175, 566])).
% 1.96/1.52 tff(574,plain,
% 1.96/1.52 (c1_1(a697)),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[573, 556, 291, 547, 539])).
% 1.96/1.52 tff(575,plain,
% 1.96/1.52 (c2_1(a697)),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[527, 555])).
% 1.96/1.52 tff(576,assumption,(c2_1(a725)), introduced(assumption)).
% 1.96/1.52 tff(577,assumption,(~c1_1(a725)), introduced(assumption)).
% 1.96/1.52 tff(578,assumption,(~c0_1(a725)), introduced(assumption)).
% 1.96/1.52 tff(579,plain,
% 1.96/1.52 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | c1_1(a763) | c2_1(a763) | c0_1(a725) | c1_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a763)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c1_1(a763) | c2_1(a763) | c0_1(a725) | c1_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a763)))),
% 1.96/1.52 inference(rewrite,[status(thm)],[])).
% 1.96/1.52 tff(580,plain,
% 1.96/1.52 ((hskp28 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c1_1(a725) | c0_1(a725) | (~c2_1(a725))) <=> (hskp28 | c1_1(a763) | c2_1(a763) | c0_1(a725) | c1_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a763)))),
% 1.96/1.52 inference(rewrite,[status(thm)],[])).
% 1.96/1.52 tff(581,plain,
% 1.96/1.52 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c1_1(a725) | c0_1(a725) | (~c2_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | c1_1(a763) | c2_1(a763) | c0_1(a725) | c1_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a763))))),
% 1.96/1.52 inference(monotonicity,[status(thm)],[580])).
% 1.96/1.52 tff(582,plain,
% 1.96/1.52 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c1_1(a725) | c0_1(a725) | (~c2_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c1_1(a763) | c2_1(a763) | c0_1(a725) | c1_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a763)))),
% 1.96/1.52 inference(transitivity,[status(thm)],[581, 579])).
% 1.96/1.52 tff(583,plain,
% 1.96/1.52 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c1_1(a725) | c0_1(a725) | (~c2_1(a725)))),
% 1.96/1.52 inference(quant_inst,[status(thm)],[])).
% 1.96/1.52 tff(584,plain,
% 1.96/1.52 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c1_1(a763) | c2_1(a763) | c0_1(a725) | c1_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a763))),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[583, 582])).
% 1.96/1.52 tff(585,plain,
% 1.96/1.52 ($false),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[584, 227, 62, 422, 411, 405, 578, 577, 398, 576])).
% 1.96/1.52 tff(586,plain,((~hskp23) | hskp28 | c0_1(a725) | c1_1(a725) | (~c2_1(a725))), inference(lemma,lemma(discharge,[]))).
% 1.96/1.52 tff(587,plain,
% 1.96/1.52 (~hskp23),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[586, 547, 152, 146, 62])).
% 1.96/1.52 tff(588,plain,
% 1.96/1.52 ($false),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[534, 227, 386, 587, 556, 575, 163, 574])).
% 1.96/1.52 tff(589,plain,(c0_1(a754) | c3_1(a754) | c3_1(a697) | hskp4 | hskp28 | hskp6 | hskp30 | c1_1(a693) | c3_1(a693)), inference(lemma,lemma(discharge,[]))).
% 1.96/1.52 tff(590,plain,
% 1.96/1.52 (c0_1(a754)),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[589, 178, 175, 176, 62, 177, 102, 164, 153])).
% 1.96/1.52 tff(591,plain,
% 1.96/1.52 (((~hskp20) | (~c0_1(a754))) <=> ((~hskp20) | (~c0_1(a754)))),
% 1.96/1.52 inference(rewrite,[status(thm)],[])).
% 1.96/1.52 tff(592,plain,
% 1.96/1.52 (((~c0_1(a754)) | (~hskp20)) <=> ((~hskp20) | (~c0_1(a754)))),
% 1.96/1.52 inference(rewrite,[status(thm)],[])).
% 1.96/1.52 tff(593,axiom,((~c0_1(a754)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause97')).
% 1.96/1.52 tff(594,plain,
% 1.96/1.52 ((~hskp20) | (~c0_1(a754))),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[593, 592])).
% 1.96/1.52 tff(595,plain,
% 1.96/1.52 ((~hskp20) | (~c0_1(a754))),
% 1.96/1.52 inference(modus_ponens,[status(thm)],[594, 591])).
% 1.96/1.52 tff(596,plain,
% 1.96/1.52 (~hskp20),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[595, 590])).
% 1.96/1.52 tff(597,plain,
% 1.96/1.52 (~hskp27),
% 1.96/1.52 inference(unit_resolution,[status(thm)],[288, 596, 102])).
% 1.96/1.52 tff(598,plain,
% 1.96/1.52 (^[V: $i, U: $i] : refl((hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 1.96/1.52 inference(bind,[status(th)],[])).
% 1.96/1.52 tff(599,plain,
% 1.96/1.52 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.96/1.52 inference(quant_intro,[status(thm)],[598])).
% 1.96/1.52 tff(600,plain,
% 1.96/1.52 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.96/1.52 inference(rewrite,[status(thm)],[])).
% 1.96/1.52 tff(601,plain,
% 1.96/1.52 (^[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)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp27) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp27))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 1.96/1.53 inference(bind,[status(th)],[])).
% 1.96/1.53 tff(602,plain,
% 1.96/1.53 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp27) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.96/1.53 inference(quant_intro,[status(thm)],[601])).
% 1.96/1.53 tff(603,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause156')).
% 1.96/1.53 tff(604,plain,
% 1.96/1.53 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.96/1.53 inference(modus_ponens,[status(thm)],[603, 602])).
% 1.96/1.53 tff(605,plain,
% 1.96/1.53 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.96/1.53 inference(modus_ponens,[status(thm)],[604, 600])).
% 1.96/1.53 tff(606,plain,(
% 1.96/1.53 ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.96/1.53 inference(skolemize,[status(sab)],[605])).
% 1.96/1.53 tff(607,plain,
% 1.96/1.53 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.96/1.53 inference(modus_ponens,[status(thm)],[606, 599])).
% 1.96/1.53 tff(608,plain,
% 1.96/1.53 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~c0_1(a754)) | c3_1(a754) | c0_1(a725) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | c1_1(a754))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp27 | (~c0_1(a754)) | c3_1(a754) | c0_1(a725) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | c1_1(a754))),
% 1.96/1.53 inference(rewrite,[status(thm)],[])).
% 1.96/1.53 tff(609,plain,
% 1.96/1.53 ((hskp27 | (~ndr1_0) | c3_1(a754) | c1_1(a754) | (~c0_1(a754)) | c3_1(a725) | c1_1(a725) | c0_1(a725)) <=> (hskp27 | (~c0_1(a754)) | c3_1(a754) | c0_1(a725) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | c1_1(a754))),
% 1.96/1.53 inference(rewrite,[status(thm)],[])).
% 1.96/1.53 tff(610,plain,
% 1.96/1.53 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c3_1(a754) | c1_1(a754) | (~c0_1(a754)) | c3_1(a725) | c1_1(a725) | c0_1(a725))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~c0_1(a754)) | c3_1(a754) | c0_1(a725) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | c1_1(a754)))),
% 1.96/1.53 inference(monotonicity,[status(thm)],[609])).
% 1.96/1.53 tff(611,plain,
% 1.96/1.53 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c3_1(a754) | c1_1(a754) | (~c0_1(a754)) | c3_1(a725) | c1_1(a725) | c0_1(a725))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp27 | (~c0_1(a754)) | c3_1(a754) | c0_1(a725) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | c1_1(a754))),
% 1.96/1.53 inference(transitivity,[status(thm)],[610, 608])).
% 1.96/1.53 tff(612,plain,
% 1.96/1.53 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c3_1(a754) | c1_1(a754) | (~c0_1(a754)) | c3_1(a725) | c1_1(a725) | c0_1(a725))),
% 1.96/1.53 inference(quant_inst,[status(thm)],[])).
% 1.96/1.53 tff(613,plain,
% 1.96/1.53 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp27 | (~c0_1(a754)) | c3_1(a754) | c0_1(a725) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | c1_1(a754)),
% 1.96/1.53 inference(modus_ponens,[status(thm)],[612, 611])).
% 1.96/1.53 tff(614,plain,
% 1.96/1.53 (hskp27 | (~c0_1(a754)) | c1_1(a754)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[613, 227, 178, 152, 146, 140, 607])).
% 1.96/1.53 tff(615,plain,
% 1.96/1.53 (c1_1(a754)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[614, 597, 590])).
% 1.96/1.53 tff(616,plain,
% 1.96/1.53 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))))),
% 1.96/1.53 inference(bind,[status(th)],[])).
% 1.96/1.53 tff(617,plain,
% 1.96/1.53 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.96/1.53 inference(quant_intro,[status(thm)],[616])).
% 1.96/1.53 tff(618,plain,
% 1.96/1.53 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.96/1.53 inference(rewrite,[status(thm)],[])).
% 1.96/1.53 tff(619,plain,
% 1.96/1.53 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp28) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) | hskp28))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) | hskp28) <=> (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))))),
% 1.96/1.53 inference(bind,[status(th)],[])).
% 1.96/1.53 tff(620,plain,
% 1.96/1.53 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.96/1.53 inference(quant_intro,[status(thm)],[619])).
% 1.96/1.53 tff(621,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause176')).
% 1.96/1.53 tff(622,plain,
% 1.96/1.53 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.96/1.53 inference(modus_ponens,[status(thm)],[621, 620])).
% 1.96/1.53 tff(623,plain,
% 1.96/1.53 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.96/1.53 inference(modus_ponens,[status(thm)],[622, 618])).
% 1.96/1.53 tff(624,plain,(
% 1.96/1.53 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.96/1.53 inference(skolemize,[status(sab)],[623])).
% 1.96/1.53 tff(625,plain,
% 1.96/1.53 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.96/1.53 inference(modus_ponens,[status(thm)],[624, 617])).
% 1.96/1.53 tff(626,plain,
% 1.96/1.53 (hskp1),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[372, 596, 102])).
% 1.96/1.53 tff(627,plain,
% 1.96/1.53 (c2_1(a693)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[383, 626])).
% 1.96/1.53 tff(628,plain,
% 1.96/1.53 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)))),
% 1.96/1.53 inference(rewrite,[status(thm)],[])).
% 1.96/1.53 tff(629,plain,
% 1.96/1.53 ((hskp28 | (~ndr1_0) | c3_1(a754) | c2_1(a754) | (~c0_1(a754)) | c3_1(a693) | c1_1(a693) | (~c2_1(a693))) <=> (hskp28 | c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)))),
% 1.96/1.53 inference(rewrite,[status(thm)],[])).
% 1.96/1.53 tff(630,plain,
% 1.96/1.53 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a754) | c2_1(a754) | (~c0_1(a754)) | c3_1(a693) | c1_1(a693) | (~c2_1(a693)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693))))),
% 1.96/1.53 inference(monotonicity,[status(thm)],[629])).
% 1.96/1.53 tff(631,plain,
% 1.96/1.53 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a754) | c2_1(a754) | (~c0_1(a754)) | c3_1(a693) | c1_1(a693) | (~c2_1(a693)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)))),
% 1.96/1.53 inference(transitivity,[status(thm)],[630, 628])).
% 1.96/1.53 tff(632,plain,
% 1.96/1.53 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a754) | c2_1(a754) | (~c0_1(a754)) | c3_1(a693) | c1_1(a693) | (~c2_1(a693)))),
% 1.96/1.53 inference(quant_inst,[status(thm)],[])).
% 1.96/1.53 tff(633,plain,
% 1.96/1.53 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693))),
% 1.96/1.53 inference(modus_ponens,[status(thm)],[632, 631])).
% 1.96/1.53 tff(634,plain,
% 1.96/1.53 (c2_1(a754) | (~c0_1(a754)) | (~c2_1(a693))),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[633, 227, 62, 178, 164, 153, 342])).
% 1.96/1.53 tff(635,plain,
% 1.96/1.53 (c2_1(a754)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[634, 627, 590])).
% 1.96/1.53 tff(636,plain,
% 1.96/1.53 (((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725))) <=> ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp27 | hskp6 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725))),
% 1.96/1.53 inference(rewrite,[status(thm)],[])).
% 1.96/1.53 tff(637,plain,
% 1.96/1.53 ((hskp27 | hskp6 | (~ndr1_0) | c3_1(a725) | c0_1(a725) | c2_1(a725)) <=> (hskp27 | hskp6 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725))),
% 1.96/1.53 inference(rewrite,[status(thm)],[])).
% 1.96/1.53 tff(638,plain,
% 1.96/1.53 (((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | (~ndr1_0) | c3_1(a725) | c0_1(a725) | c2_1(a725))) <=> ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725)))),
% 1.96/1.53 inference(monotonicity,[status(thm)],[637])).
% 1.96/1.53 tff(639,plain,
% 1.96/1.53 (((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | (~ndr1_0) | c3_1(a725) | c0_1(a725) | c2_1(a725))) <=> ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp27 | hskp6 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725))),
% 1.96/1.53 inference(transitivity,[status(thm)],[638, 636])).
% 1.96/1.53 tff(640,plain,
% 1.96/1.53 ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | (~ndr1_0) | c3_1(a725) | c0_1(a725) | c2_1(a725))),
% 1.96/1.53 inference(quant_inst,[status(thm)],[])).
% 1.96/1.53 tff(641,plain,
% 1.96/1.53 ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp27 | hskp6 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725)),
% 1.96/1.53 inference(modus_ponens,[status(thm)],[640, 639])).
% 1.96/1.53 tff(642,plain,
% 1.96/1.53 (hskp27 | hskp6 | c2_1(a725)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[641, 227, 152, 140, 201])).
% 1.96/1.53 tff(643,plain,
% 1.96/1.53 (c2_1(a725)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[642, 597, 177])).
% 1.96/1.53 tff(644,plain,
% 1.96/1.53 (~hskp23),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[586, 643, 152, 146, 62])).
% 1.96/1.53 tff(645,plain,
% 1.96/1.53 (((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~c0_1(a754)) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754)))) <=> ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp23 | (~c0_1(a754)) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754)))),
% 1.96/1.53 inference(rewrite,[status(thm)],[])).
% 1.96/1.53 tff(646,plain,
% 1.96/1.53 ((hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a754)) | (~c0_1(a754)) | (~c1_1(a754))) <=> (hskp24 | hskp23 | (~c0_1(a754)) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754)))),
% 1.96/1.53 inference(rewrite,[status(thm)],[])).
% 1.96/1.53 tff(647,plain,
% 1.96/1.53 (((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a754)) | (~c0_1(a754)) | (~c1_1(a754)))) <=> ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~c0_1(a754)) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754))))),
% 1.96/1.53 inference(monotonicity,[status(thm)],[646])).
% 1.96/1.53 tff(648,plain,
% 1.96/1.53 (((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a754)) | (~c0_1(a754)) | (~c1_1(a754)))) <=> ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp23 | (~c0_1(a754)) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754)))),
% 1.96/1.53 inference(transitivity,[status(thm)],[647, 645])).
% 1.96/1.53 tff(649,plain,
% 1.96/1.53 ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a754)) | (~c0_1(a754)) | (~c1_1(a754)))),
% 1.96/1.53 inference(quant_inst,[status(thm)],[])).
% 1.96/1.53 tff(650,plain,
% 1.96/1.53 ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp23 | (~c0_1(a754)) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754))),
% 1.96/1.53 inference(modus_ponens,[status(thm)],[649, 648])).
% 1.96/1.53 tff(651,plain,
% 1.96/1.53 (hskp24),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[650, 227, 644, 635, 590, 163, 615])).
% 1.96/1.53 tff(652,plain,
% 1.96/1.53 (~c3_1(a764)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[307, 651])).
% 1.96/1.53 tff(653,plain,
% 1.96/1.53 (~c2_1(a764)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[313, 651])).
% 1.96/1.53 tff(654,plain,
% 1.96/1.53 (c1_1(a764)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[324, 651])).
% 1.96/1.53 tff(655,plain,
% 1.96/1.53 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754)) | (~c1_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754)) | (~c1_1(a764)))),
% 1.96/1.53 inference(rewrite,[status(thm)],[])).
% 1.96/1.53 tff(656,plain,
% 1.96/1.53 ((hskp28 | (~ndr1_0) | c3_1(a754) | (~c2_1(a754)) | (~c1_1(a754)) | c3_1(a764) | c2_1(a764) | (~c1_1(a764))) <=> (hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754)) | (~c1_1(a764)))),
% 1.96/1.53 inference(rewrite,[status(thm)],[])).
% 1.96/1.53 tff(657,plain,
% 1.96/1.53 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a754) | (~c2_1(a754)) | (~c1_1(a754)) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754)) | (~c1_1(a764))))),
% 1.96/1.53 inference(monotonicity,[status(thm)],[656])).
% 1.96/1.53 tff(658,plain,
% 1.96/1.53 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a754) | (~c2_1(a754)) | (~c1_1(a754)) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754)) | (~c1_1(a764)))),
% 1.96/1.53 inference(transitivity,[status(thm)],[657, 655])).
% 1.96/1.53 tff(659,plain,
% 1.96/1.53 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a754) | (~c2_1(a754)) | (~c1_1(a754)) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)))),
% 1.96/1.53 inference(quant_inst,[status(thm)],[])).
% 1.96/1.53 tff(660,plain,
% 1.96/1.53 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754)) | (~c1_1(a764))),
% 1.96/1.53 inference(modus_ponens,[status(thm)],[659, 658])).
% 1.96/1.53 tff(661,plain,
% 1.96/1.53 ($false),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[660, 227, 62, 654, 635, 653, 652, 178, 625, 615])).
% 1.96/1.53 tff(662,plain,(c3_1(a754) | hskp28 | c1_1(a693) | c3_1(a693) | hskp6 | hskp30 | c3_1(a697) | hskp4), inference(lemma,lemma(discharge,[]))).
% 1.96/1.53 tff(663,plain,
% 1.96/1.53 (c3_1(a754)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[662, 177, 164, 153, 62, 102, 175, 176])).
% 1.96/1.53 tff(664,plain,
% 1.96/1.53 (((~hskp20) | (~c3_1(a754))) <=> ((~hskp20) | (~c3_1(a754)))),
% 1.96/1.53 inference(rewrite,[status(thm)],[])).
% 1.96/1.53 tff(665,plain,
% 1.96/1.53 (((~c3_1(a754)) | (~hskp20)) <=> ((~hskp20) | (~c3_1(a754)))),
% 1.96/1.53 inference(rewrite,[status(thm)],[])).
% 1.96/1.53 tff(666,axiom,((~c3_1(a754)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause98')).
% 1.96/1.53 tff(667,plain,
% 1.96/1.53 ((~hskp20) | (~c3_1(a754))),
% 1.96/1.53 inference(modus_ponens,[status(thm)],[666, 665])).
% 1.96/1.53 tff(668,plain,
% 1.96/1.53 ((~hskp20) | (~c3_1(a754))),
% 1.96/1.53 inference(modus_ponens,[status(thm)],[667, 664])).
% 1.96/1.53 tff(669,plain,
% 1.96/1.53 (~hskp20),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[668, 663])).
% 1.96/1.53 tff(670,plain,
% 1.96/1.53 (~hskp27),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[288, 669, 102])).
% 1.96/1.53 tff(671,plain,
% 1.96/1.53 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | c0_1(a725) | c1_1(a725) | c3_1(a725) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp27 | c0_1(a725) | c1_1(a725) | c3_1(a725) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)))),
% 1.96/1.53 inference(rewrite,[status(thm)],[])).
% 1.96/1.53 tff(672,plain,
% 1.96/1.53 ((hskp27 | (~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c0_1(a693)) | c3_1(a725) | c1_1(a725) | c0_1(a725)) <=> (hskp27 | c0_1(a725) | c1_1(a725) | c3_1(a725) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)))),
% 1.96/1.53 inference(rewrite,[status(thm)],[])).
% 1.96/1.53 tff(673,plain,
% 1.96/1.53 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c0_1(a693)) | c3_1(a725) | c1_1(a725) | c0_1(a725))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | c0_1(a725) | c1_1(a725) | c3_1(a725) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693))))),
% 1.96/1.53 inference(monotonicity,[status(thm)],[672])).
% 1.96/1.53 tff(674,plain,
% 1.96/1.53 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c0_1(a693)) | c3_1(a725) | c1_1(a725) | c0_1(a725))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp27 | c0_1(a725) | c1_1(a725) | c3_1(a725) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)))),
% 1.96/1.53 inference(transitivity,[status(thm)],[673, 671])).
% 1.96/1.53 tff(675,plain,
% 1.96/1.53 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c0_1(a693)) | c3_1(a725) | c1_1(a725) | c0_1(a725))),
% 1.96/1.53 inference(quant_inst,[status(thm)],[])).
% 1.96/1.53 tff(676,plain,
% 1.96/1.53 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp27 | c0_1(a725) | c1_1(a725) | c3_1(a725) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693))),
% 1.96/1.53 inference(modus_ponens,[status(thm)],[675, 674])).
% 1.96/1.53 tff(677,plain,
% 1.96/1.53 (hskp27 | c1_1(a693) | (~c0_1(a693))),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[676, 227, 152, 146, 140, 153, 607])).
% 1.96/1.53 tff(678,plain,
% 1.96/1.53 (~c0_1(a693)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[677, 670, 164])).
% 1.96/1.53 tff(679,plain,
% 1.96/1.53 (hskp1),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[372, 669, 102])).
% 1.96/1.53 tff(680,plain,
% 1.96/1.53 (c2_1(a693)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[383, 679])).
% 1.96/1.53 tff(681,plain,
% 1.96/1.53 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | c1_1(a693) | (~ndr1_0) | c0_1(a693) | (~c2_1(a693)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c1_1(a693) | (~ndr1_0) | c0_1(a693) | (~c2_1(a693)))),
% 1.96/1.53 inference(rewrite,[status(thm)],[])).
% 1.96/1.53 tff(682,plain,
% 1.96/1.53 ((hskp4 | hskp3 | (~ndr1_0) | c1_1(a693) | c0_1(a693) | (~c2_1(a693))) <=> (hskp4 | hskp3 | c1_1(a693) | (~ndr1_0) | c0_1(a693) | (~c2_1(a693)))),
% 1.96/1.53 inference(rewrite,[status(thm)],[])).
% 1.96/1.53 tff(683,plain,
% 1.96/1.53 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a693) | c0_1(a693) | (~c2_1(a693)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | c1_1(a693) | (~ndr1_0) | c0_1(a693) | (~c2_1(a693))))),
% 1.96/1.53 inference(monotonicity,[status(thm)],[682])).
% 1.96/1.53 tff(684,plain,
% 1.96/1.53 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a693) | c0_1(a693) | (~c2_1(a693)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c1_1(a693) | (~ndr1_0) | c0_1(a693) | (~c2_1(a693)))),
% 1.96/1.53 inference(transitivity,[status(thm)],[683, 681])).
% 1.96/1.53 tff(685,plain,
% 1.96/1.53 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a693) | c0_1(a693) | (~c2_1(a693)))),
% 1.96/1.53 inference(quant_inst,[status(thm)],[])).
% 1.96/1.53 tff(686,plain,
% 1.96/1.53 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c1_1(a693) | (~ndr1_0) | c0_1(a693) | (~c2_1(a693))),
% 1.96/1.53 inference(modus_ponens,[status(thm)],[685, 684])).
% 1.96/1.53 tff(687,plain,
% 1.96/1.53 (hskp4 | hskp3 | c0_1(a693) | (~c2_1(a693))),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[686, 227, 164, 442])).
% 1.96/1.53 tff(688,plain,
% 1.96/1.53 (hskp3),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[687, 680, 176, 678])).
% 1.96/1.53 tff(689,plain,
% 1.96/1.53 (c0_1(a697)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[508, 688])).
% 1.96/1.53 tff(690,plain,
% 1.96/1.53 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | c0_1(a725) | c1_1(a725) | c3_1(a725) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp27 | c0_1(a725) | c1_1(a725) | c3_1(a725) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697))),
% 1.96/1.53 inference(rewrite,[status(thm)],[])).
% 1.96/1.53 tff(691,plain,
% 1.96/1.53 ((hskp27 | (~ndr1_0) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c3_1(a725) | c1_1(a725) | c0_1(a725)) <=> (hskp27 | c0_1(a725) | c1_1(a725) | c3_1(a725) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697))),
% 1.96/1.53 inference(rewrite,[status(thm)],[])).
% 1.96/1.53 tff(692,plain,
% 1.96/1.53 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c3_1(a725) | c1_1(a725) | c0_1(a725))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | c0_1(a725) | c1_1(a725) | c3_1(a725) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697)))),
% 1.96/1.53 inference(monotonicity,[status(thm)],[691])).
% 1.96/1.53 tff(693,plain,
% 1.96/1.53 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c3_1(a725) | c1_1(a725) | c0_1(a725))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp27 | c0_1(a725) | c1_1(a725) | c3_1(a725) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697))),
% 1.96/1.53 inference(transitivity,[status(thm)],[692, 690])).
% 1.96/1.53 tff(694,plain,
% 1.96/1.53 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c3_1(a725) | c1_1(a725) | c0_1(a725))),
% 1.96/1.53 inference(quant_inst,[status(thm)],[])).
% 1.96/1.53 tff(695,plain,
% 1.96/1.53 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp27 | c0_1(a725) | c1_1(a725) | c3_1(a725) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697)),
% 1.96/1.53 inference(modus_ponens,[status(thm)],[694, 693])).
% 1.96/1.53 tff(696,plain,
% 1.96/1.53 (hskp27 | (~c0_1(a697)) | c1_1(a697)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[695, 227, 152, 146, 140, 175, 607])).
% 1.96/1.53 tff(697,plain,
% 1.96/1.53 (c1_1(a697)),
% 1.96/1.53 inference(unit_resolution,[status(thm)],[696, 689, 670])).
% 1.99/1.53 tff(698,plain,
% 1.99/1.53 (c2_1(a697)),
% 1.99/1.53 inference(unit_resolution,[status(thm)],[527, 688])).
% 1.99/1.53 tff(699,plain,
% 1.99/1.53 (c2_1(a725)),
% 1.99/1.53 inference(unit_resolution,[status(thm)],[642, 670, 177])).
% 1.99/1.53 tff(700,plain,
% 1.99/1.53 (~hskp23),
% 1.99/1.53 inference(unit_resolution,[status(thm)],[586, 699, 152, 146, 62])).
% 1.99/1.53 tff(701,plain,
% 1.99/1.53 (hskp24),
% 1.99/1.53 inference(unit_resolution,[status(thm)],[534, 227, 700, 689, 698, 163, 697])).
% 1.99/1.53 tff(702,plain,
% 1.99/1.53 (~c3_1(a764)),
% 1.99/1.53 inference(unit_resolution,[status(thm)],[307, 701])).
% 1.99/1.53 tff(703,plain,
% 1.99/1.53 (~c2_1(a764)),
% 1.99/1.53 inference(unit_resolution,[status(thm)],[313, 701])).
% 1.99/1.53 tff(704,plain,
% 1.99/1.53 (c1_1(a764)),
% 1.99/1.53 inference(unit_resolution,[status(thm)],[324, 701])).
% 1.99/1.53 tff(705,plain,
% 1.99/1.53 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a697) | (~ndr1_0) | (~c1_1(a697)) | (~c2_1(a697)) | (~c1_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a697) | (~ndr1_0) | (~c1_1(a697)) | (~c2_1(a697)) | (~c1_1(a764)))),
% 1.99/1.53 inference(rewrite,[status(thm)],[])).
% 1.99/1.53 tff(706,plain,
% 1.99/1.53 ((hskp28 | (~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a764) | c2_1(a764) | (~c1_1(a764))) <=> (hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a697) | (~ndr1_0) | (~c1_1(a697)) | (~c2_1(a697)) | (~c1_1(a764)))),
% 1.99/1.53 inference(rewrite,[status(thm)],[])).
% 1.99/1.53 tff(707,plain,
% 1.99/1.53 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a697) | (~ndr1_0) | (~c1_1(a697)) | (~c2_1(a697)) | (~c1_1(a764))))),
% 1.99/1.53 inference(monotonicity,[status(thm)],[706])).
% 1.99/1.53 tff(708,plain,
% 1.99/1.53 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a697) | (~ndr1_0) | (~c1_1(a697)) | (~c2_1(a697)) | (~c1_1(a764)))),
% 1.99/1.53 inference(transitivity,[status(thm)],[707, 705])).
% 1.99/1.53 tff(709,plain,
% 1.99/1.53 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)))),
% 1.99/1.53 inference(quant_inst,[status(thm)],[])).
% 1.99/1.53 tff(710,plain,
% 1.99/1.53 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a697) | (~ndr1_0) | (~c1_1(a697)) | (~c2_1(a697)) | (~c1_1(a764))),
% 1.99/1.53 inference(modus_ponens,[status(thm)],[709, 708])).
% 1.99/1.54 tff(711,plain,
% 1.99/1.54 ($false),
% 1.99/1.54 inference(unit_resolution,[status(thm)],[710, 227, 62, 704, 698, 703, 702, 175, 625, 697])).
% 1.99/1.54 tff(712,plain,(hskp6 | hskp28 | c3_1(a697) | hskp4 | c1_1(a693) | c3_1(a693) | hskp30), inference(lemma,lemma(discharge,[]))).
% 1.99/1.54 tff(713,plain,
% 1.99/1.54 (hskp6),
% 1.99/1.54 inference(unit_resolution,[status(thm)],[712, 176, 175, 62, 164, 153, 102])).
% 1.99/1.54 tff(714,plain,
% 1.99/1.54 (~c2_1(a702)),
% 1.99/1.54 inference(unit_resolution,[status(thm)],[68, 713])).
% 1.99/1.54 tff(715,plain,
% 1.99/1.54 (c0_1(a702)),
% 1.99/1.54 inference(unit_resolution,[status(thm)],[90, 713])).
% 1.99/1.54 tff(716,plain,
% 1.99/1.54 (c3_1(a702)),
% 1.99/1.54 inference(unit_resolution,[status(thm)],[79, 713])).
% 1.99/1.54 tff(717,assumption,(~c2_1(a702)), introduced(assumption)).
% 1.99/1.54 tff(718,assumption,(c3_1(a702)), introduced(assumption)).
% 1.99/1.54 tff(719,assumption,(c0_1(a702)), introduced(assumption)).
% 1.99/1.54 tff(720,assumption,(hskp25), introduced(assumption)).
% 1.99/1.54 tff(721,plain,
% 1.99/1.54 (((~hskp25) | c2_1(a773)) <=> ((~hskp25) | c2_1(a773))),
% 1.99/1.54 inference(rewrite,[status(thm)],[])).
% 1.99/1.54 tff(722,axiom,((~hskp25) | c2_1(a773)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause54')).
% 1.99/1.54 tff(723,plain,
% 1.99/1.54 ((~hskp25) | c2_1(a773)),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[722, 721])).
% 1.99/1.54 tff(724,plain,
% 1.99/1.54 ((~hskp25) | c2_1(a773)),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[723, 721])).
% 1.99/1.54 tff(725,plain,
% 1.99/1.54 ((~hskp25) | c2_1(a773)),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[724, 721])).
% 1.99/1.54 tff(726,plain,
% 1.99/1.54 ((~hskp25) | c2_1(a773)),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[725, 721])).
% 1.99/1.54 tff(727,plain,
% 1.99/1.54 ((~hskp25) | c2_1(a773)),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[726, 721])).
% 1.99/1.54 tff(728,plain,
% 1.99/1.54 ((~hskp25) | c2_1(a773)),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[727, 721])).
% 1.99/1.54 tff(729,plain,
% 1.99/1.54 ((~hskp25) | c2_1(a773)),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[728, 721])).
% 1.99/1.54 tff(730,plain,
% 1.99/1.54 ((~hskp25) | c2_1(a773)),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[729, 721])).
% 1.99/1.54 tff(731,plain,
% 1.99/1.54 (c2_1(a773)),
% 1.99/1.54 inference(unit_resolution,[status(thm)],[730, 720])).
% 1.99/1.54 tff(732,plain,
% 1.99/1.54 (((~hskp25) | c1_1(a773)) <=> ((~hskp25) | c1_1(a773))),
% 1.99/1.54 inference(rewrite,[status(thm)],[])).
% 1.99/1.54 tff(733,axiom,((~hskp25) | c1_1(a773)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause53')).
% 1.99/1.54 tff(734,plain,
% 1.99/1.54 ((~hskp25) | c1_1(a773)),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[733, 732])).
% 1.99/1.54 tff(735,plain,
% 1.99/1.54 ((~hskp25) | c1_1(a773)),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[734, 732])).
% 1.99/1.54 tff(736,plain,
% 1.99/1.54 ((~hskp25) | c1_1(a773)),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[735, 732])).
% 1.99/1.54 tff(737,plain,
% 1.99/1.54 ((~hskp25) | c1_1(a773)),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[736, 732])).
% 1.99/1.54 tff(738,plain,
% 1.99/1.54 ((~hskp25) | c1_1(a773)),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[737, 732])).
% 1.99/1.54 tff(739,plain,
% 1.99/1.54 ((~hskp25) | c1_1(a773)),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[738, 732])).
% 1.99/1.54 tff(740,plain,
% 1.99/1.54 ((~hskp25) | c1_1(a773)),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[739, 732])).
% 1.99/1.54 tff(741,plain,
% 1.99/1.54 ((~hskp25) | c1_1(a773)),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[740, 732])).
% 1.99/1.54 tff(742,plain,
% 1.99/1.54 (c1_1(a773)),
% 1.99/1.54 inference(unit_resolution,[status(thm)],[741, 720])).
% 1.99/1.54 tff(743,plain,
% 1.99/1.54 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c3_1(a773)) | (~c2_1(a773)) | (~c1_1(a773)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c3_1(a773)) | (~c2_1(a773)) | (~c1_1(a773)))),
% 1.99/1.54 inference(rewrite,[status(thm)],[])).
% 1.99/1.54 tff(744,plain,
% 1.99/1.54 ((hskp28 | (~ndr1_0) | (~c2_1(a773)) | (~c3_1(a773)) | (~c1_1(a773)) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702))) <=> (hskp28 | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c3_1(a773)) | (~c2_1(a773)) | (~c1_1(a773)))),
% 1.99/1.54 inference(rewrite,[status(thm)],[])).
% 1.99/1.54 tff(745,plain,
% 1.99/1.54 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a773)) | (~c3_1(a773)) | (~c1_1(a773)) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c3_1(a773)) | (~c2_1(a773)) | (~c1_1(a773))))),
% 1.99/1.54 inference(monotonicity,[status(thm)],[744])).
% 1.99/1.54 tff(746,plain,
% 1.99/1.54 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a773)) | (~c3_1(a773)) | (~c1_1(a773)) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c3_1(a773)) | (~c2_1(a773)) | (~c1_1(a773)))),
% 1.99/1.54 inference(transitivity,[status(thm)],[745, 743])).
% 1.99/1.54 tff(747,plain,
% 1.99/1.54 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a773)) | (~c3_1(a773)) | (~c1_1(a773)) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)))),
% 1.99/1.54 inference(quant_inst,[status(thm)],[])).
% 1.99/1.54 tff(748,plain,
% 1.99/1.54 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c3_1(a773)) | (~c2_1(a773)) | (~c1_1(a773))),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[747, 746])).
% 1.99/1.54 tff(749,plain,
% 1.99/1.54 (~c3_1(a773)),
% 1.99/1.54 inference(unit_resolution,[status(thm)],[748, 227, 62, 742, 731, 719, 718, 717, 61])).
% 1.99/1.54 tff(750,plain,
% 1.99/1.54 (((~hskp25) | (~c0_1(a773))) <=> ((~hskp25) | (~c0_1(a773)))),
% 1.99/1.54 inference(rewrite,[status(thm)],[])).
% 1.99/1.54 tff(751,plain,
% 1.99/1.54 (((~c0_1(a773)) | (~hskp25)) <=> ((~hskp25) | (~c0_1(a773)))),
% 1.99/1.54 inference(rewrite,[status(thm)],[])).
% 1.99/1.54 tff(752,axiom,((~c0_1(a773)) | (~hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause89')).
% 1.99/1.54 tff(753,plain,
% 1.99/1.54 ((~hskp25) | (~c0_1(a773))),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[752, 751])).
% 1.99/1.54 tff(754,plain,
% 1.99/1.54 ((~hskp25) | (~c0_1(a773))),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[753, 750])).
% 1.99/1.54 tff(755,plain,
% 1.99/1.54 (~c0_1(a773)),
% 1.99/1.54 inference(unit_resolution,[status(thm)],[754, 720])).
% 1.99/1.54 tff(756,plain,
% 1.99/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a773) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a773) | (~c2_1(a773)) | (~c1_1(a773)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a773) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a773) | (~c2_1(a773)) | (~c1_1(a773)))),
% 1.99/1.54 inference(rewrite,[status(thm)],[])).
% 1.99/1.54 tff(757,plain,
% 1.99/1.54 (((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a773) | c0_1(a773) | (~c2_1(a773)) | c3_1(a773) | c0_1(a773) | (~c1_1(a773))) <=> (c0_1(a773) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a773) | (~c2_1(a773)) | (~c1_1(a773)))),
% 1.99/1.54 inference(rewrite,[status(thm)],[])).
% 1.99/1.54 tff(758,plain,
% 1.99/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a773) | c0_1(a773) | (~c2_1(a773)) | c3_1(a773) | c0_1(a773) | (~c1_1(a773)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a773) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a773) | (~c2_1(a773)) | (~c1_1(a773))))),
% 1.99/1.54 inference(monotonicity,[status(thm)],[757])).
% 1.99/1.54 tff(759,plain,
% 1.99/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a773) | c0_1(a773) | (~c2_1(a773)) | c3_1(a773) | c0_1(a773) | (~c1_1(a773)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a773) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a773) | (~c2_1(a773)) | (~c1_1(a773)))),
% 1.99/1.54 inference(transitivity,[status(thm)],[758, 756])).
% 1.99/1.54 tff(760,plain,
% 1.99/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a773) | c0_1(a773) | (~c2_1(a773)) | c3_1(a773) | c0_1(a773) | (~c1_1(a773)))),
% 1.99/1.54 inference(quant_inst,[status(thm)],[])).
% 1.99/1.54 tff(761,plain,
% 1.99/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a773) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a773) | (~c2_1(a773)) | (~c1_1(a773))),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[760, 759])).
% 1.99/1.54 tff(762,plain,
% 1.99/1.54 ($false),
% 1.99/1.54 inference(unit_resolution,[status(thm)],[761, 227, 742, 731, 719, 718, 755, 717, 174, 749])).
% 1.99/1.54 tff(763,plain,((~hskp25) | (~c0_1(a702)) | (~c3_1(a702)) | c2_1(a702) | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.99/1.54 tff(764,plain,
% 1.99/1.54 (~hskp25),
% 1.99/1.54 inference(unit_resolution,[status(thm)],[763, 716, 715, 714, 62])).
% 1.99/1.54 tff(765,plain,
% 1.99/1.54 ((hskp28 | hskp25 | hskp22) <=> (hskp28 | hskp25 | hskp22)),
% 1.99/1.54 inference(rewrite,[status(thm)],[])).
% 1.99/1.54 tff(766,plain,
% 1.99/1.54 (((hskp28 | hskp25) | hskp22) <=> (hskp28 | hskp25 | hskp22)),
% 1.99/1.54 inference(rewrite,[status(thm)],[])).
% 1.99/1.54 tff(767,plain,
% 1.99/1.54 ((hskp28 | hskp25) <=> (hskp28 | hskp25)),
% 1.99/1.54 inference(rewrite,[status(thm)],[])).
% 1.99/1.54 tff(768,plain,
% 1.99/1.54 (((hskp28 | hskp25) | hskp22) <=> ((hskp28 | hskp25) | hskp22)),
% 1.99/1.54 inference(monotonicity,[status(thm)],[767])).
% 1.99/1.54 tff(769,plain,
% 1.99/1.54 (((hskp28 | hskp25) | hskp22) <=> (hskp28 | hskp25 | hskp22)),
% 1.99/1.54 inference(transitivity,[status(thm)],[768, 766])).
% 1.99/1.54 tff(770,axiom,((hskp28 | hskp25) | hskp22), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause33')).
% 1.99/1.54 tff(771,plain,
% 1.99/1.54 (hskp28 | hskp25 | hskp22),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[770, 769])).
% 1.99/1.54 tff(772,plain,
% 1.99/1.54 (hskp28 | hskp25 | hskp22),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[771, 765])).
% 1.99/1.54 tff(773,plain,
% 1.99/1.54 (hskp28 | hskp25 | hskp22),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[772, 765])).
% 1.99/1.54 tff(774,plain,
% 1.99/1.54 (hskp28 | hskp25 | hskp22),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[773, 765])).
% 1.99/1.54 tff(775,plain,
% 1.99/1.54 (hskp28 | hskp25 | hskp22),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[774, 765])).
% 1.99/1.54 tff(776,plain,
% 1.99/1.54 (hskp28 | hskp25 | hskp22),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[775, 765])).
% 1.99/1.54 tff(777,plain,
% 1.99/1.54 (hskp28 | hskp25 | hskp22),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[776, 765])).
% 1.99/1.54 tff(778,plain,
% 1.99/1.54 (hskp28 | hskp25 | hskp22),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[777, 765])).
% 1.99/1.54 tff(779,plain,
% 1.99/1.54 (hskp22),
% 1.99/1.54 inference(unit_resolution,[status(thm)],[778, 764, 62])).
% 1.99/1.54 tff(780,plain,
% 1.99/1.54 (((~hskp22) | (~c2_1(a761))) <=> ((~hskp22) | (~c2_1(a761)))),
% 1.99/1.54 inference(rewrite,[status(thm)],[])).
% 1.99/1.54 tff(781,plain,
% 1.99/1.54 (((~c2_1(a761)) | (~hskp22)) <=> ((~hskp22) | (~c2_1(a761)))),
% 1.99/1.54 inference(rewrite,[status(thm)],[])).
% 1.99/1.54 tff(782,axiom,((~c2_1(a761)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause95')).
% 1.99/1.54 tff(783,plain,
% 1.99/1.54 ((~hskp22) | (~c2_1(a761))),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[782, 781])).
% 1.99/1.54 tff(784,plain,
% 1.99/1.54 ((~hskp22) | (~c2_1(a761))),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[783, 780])).
% 1.99/1.54 tff(785,plain,
% 1.99/1.54 (~c2_1(a761)),
% 1.99/1.54 inference(unit_resolution,[status(thm)],[784, 779])).
% 1.99/1.54 tff(786,plain,
% 1.99/1.54 (((~hskp22) | (~c0_1(a761))) <=> ((~hskp22) | (~c0_1(a761)))),
% 1.99/1.54 inference(rewrite,[status(thm)],[])).
% 1.99/1.54 tff(787,plain,
% 1.99/1.54 (((~c0_1(a761)) | (~hskp22)) <=> ((~hskp22) | (~c0_1(a761)))),
% 1.99/1.54 inference(rewrite,[status(thm)],[])).
% 1.99/1.54 tff(788,axiom,((~c0_1(a761)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause94')).
% 1.99/1.54 tff(789,plain,
% 1.99/1.54 ((~hskp22) | (~c0_1(a761))),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[788, 787])).
% 1.99/1.54 tff(790,plain,
% 1.99/1.54 ((~hskp22) | (~c0_1(a761))),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[789, 786])).
% 1.99/1.54 tff(791,plain,
% 1.99/1.54 (~c0_1(a761)),
% 1.99/1.54 inference(unit_resolution,[status(thm)],[790, 779])).
% 1.99/1.54 tff(792,plain,
% 1.99/1.54 (((~hskp22) | c1_1(a761)) <=> ((~hskp22) | c1_1(a761))),
% 1.99/1.54 inference(rewrite,[status(thm)],[])).
% 1.99/1.54 tff(793,axiom,((~hskp22) | c1_1(a761)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause57')).
% 1.99/1.54 tff(794,plain,
% 1.99/1.54 ((~hskp22) | c1_1(a761)),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[793, 792])).
% 1.99/1.54 tff(795,plain,
% 1.99/1.54 ((~hskp22) | c1_1(a761)),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[794, 792])).
% 1.99/1.54 tff(796,plain,
% 1.99/1.54 ((~hskp22) | c1_1(a761)),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[795, 792])).
% 1.99/1.54 tff(797,plain,
% 1.99/1.54 ((~hskp22) | c1_1(a761)),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[796, 792])).
% 1.99/1.54 tff(798,plain,
% 1.99/1.54 ((~hskp22) | c1_1(a761)),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[797, 792])).
% 1.99/1.54 tff(799,plain,
% 1.99/1.54 ((~hskp22) | c1_1(a761)),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[798, 792])).
% 1.99/1.54 tff(800,plain,
% 1.99/1.54 ((~hskp22) | c1_1(a761)),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[799, 792])).
% 1.99/1.54 tff(801,plain,
% 1.99/1.54 ((~hskp22) | c1_1(a761)),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[800, 792])).
% 1.99/1.54 tff(802,plain,
% 1.99/1.54 (c1_1(a761)),
% 1.99/1.54 inference(unit_resolution,[status(thm)],[801, 779])).
% 1.99/1.54 tff(803,plain,
% 1.99/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a761) | c2_1(a761) | c0_1(a725) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c1_1(a761)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a761) | c2_1(a761) | c0_1(a725) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c1_1(a761)))),
% 1.99/1.54 inference(rewrite,[status(thm)],[])).
% 1.99/1.54 tff(804,plain,
% 1.99/1.54 (((~ndr1_0) | c0_1(a761) | c2_1(a761) | (~c1_1(a761)) | c3_1(a725) | c1_1(a725) | c2_1(a725) | c3_1(a725) | c2_1(a725) | c0_1(a725)) <=> (c0_1(a761) | c2_1(a761) | c0_1(a725) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c1_1(a761)))),
% 1.99/1.54 inference(rewrite,[status(thm)],[])).
% 1.99/1.54 tff(805,plain,
% 1.99/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a761) | c2_1(a761) | (~c1_1(a761)) | c3_1(a725) | c1_1(a725) | c2_1(a725) | c3_1(a725) | c2_1(a725) | c0_1(a725))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a761) | c2_1(a761) | c0_1(a725) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c1_1(a761))))),
% 1.99/1.54 inference(monotonicity,[status(thm)],[804])).
% 1.99/1.54 tff(806,plain,
% 1.99/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a761) | c2_1(a761) | (~c1_1(a761)) | c3_1(a725) | c1_1(a725) | c2_1(a725) | c3_1(a725) | c2_1(a725) | c0_1(a725))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a761) | c2_1(a761) | c0_1(a725) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c1_1(a761)))),
% 1.99/1.54 inference(transitivity,[status(thm)],[805, 803])).
% 1.99/1.54 tff(807,plain,
% 1.99/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a761) | c2_1(a761) | (~c1_1(a761)) | c3_1(a725) | c1_1(a725) | c2_1(a725) | c3_1(a725) | c2_1(a725) | c0_1(a725))),
% 1.99/1.54 inference(quant_inst,[status(thm)],[])).
% 1.99/1.54 tff(808,plain,
% 1.99/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a761) | c2_1(a761) | c0_1(a725) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c1_1(a761))),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[807, 806])).
% 1.99/1.54 tff(809,plain,
% 1.99/1.54 (c2_1(a725)),
% 1.99/1.54 inference(unit_resolution,[status(thm)],[808, 227, 802, 791, 785, 152, 146, 140, 122])).
% 1.99/1.54 tff(810,plain,
% 1.99/1.54 (hskp3),
% 1.99/1.54 inference(unit_resolution,[status(thm)],[554, 809, 176])).
% 1.99/1.54 tff(811,plain,
% 1.99/1.54 (c0_1(a697)),
% 1.99/1.54 inference(unit_resolution,[status(thm)],[508, 810])).
% 1.99/1.54 tff(812,plain,
% 1.99/1.54 (c2_1(a697)),
% 1.99/1.54 inference(unit_resolution,[status(thm)],[527, 810])).
% 1.99/1.54 tff(813,plain,
% 1.99/1.54 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))))),
% 1.99/1.54 inference(bind,[status(th)],[])).
% 1.99/1.54 tff(814,plain,
% 1.99/1.54 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.99/1.54 inference(quant_intro,[status(thm)],[813])).
% 1.99/1.54 tff(815,plain,
% 1.99/1.54 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.99/1.54 inference(rewrite,[status(thm)],[])).
% 1.99/1.54 tff(816,plain,
% 1.99/1.54 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(U)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(U)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(U)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(U)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(U)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(U)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))))),
% 1.99/1.54 inference(bind,[status(th)],[])).
% 1.99/1.54 tff(817,plain,
% 1.99/1.54 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(U)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.99/1.54 inference(quant_intro,[status(thm)],[816])).
% 1.99/1.54 tff(818,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(U)) | c3_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause194')).
% 1.99/1.54 tff(819,plain,
% 1.99/1.54 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[818, 817])).
% 1.99/1.54 tff(820,plain,
% 1.99/1.54 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[819, 815])).
% 1.99/1.54 tff(821,plain,(
% 1.99/1.54 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.99/1.54 inference(skolemize,[status(sab)],[820])).
% 1.99/1.54 tff(822,plain,
% 1.99/1.54 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[821, 814])).
% 1.99/1.54 tff(823,plain,
% 1.99/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a761) | c2_1(a761) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a697)) | (~c1_1(a761)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a761) | c2_1(a761) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a697)) | (~c1_1(a761)))),
% 1.99/1.54 inference(rewrite,[status(thm)],[])).
% 1.99/1.54 tff(824,plain,
% 1.99/1.54 (((~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c2_1(a761) | c0_1(a761) | (~c1_1(a761))) <=> (c0_1(a761) | c2_1(a761) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a697)) | (~c1_1(a761)))),
% 1.99/1.54 inference(rewrite,[status(thm)],[])).
% 1.99/1.54 tff(825,plain,
% 1.99/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c2_1(a761) | c0_1(a761) | (~c1_1(a761)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a761) | c2_1(a761) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a697)) | (~c1_1(a761))))),
% 1.99/1.54 inference(monotonicity,[status(thm)],[824])).
% 1.99/1.54 tff(826,plain,
% 1.99/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c2_1(a761) | c0_1(a761) | (~c1_1(a761)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a761) | c2_1(a761) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a697)) | (~c1_1(a761)))),
% 1.99/1.54 inference(transitivity,[status(thm)],[825, 823])).
% 1.99/1.54 tff(827,plain,
% 1.99/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c2_1(a761) | c0_1(a761) | (~c1_1(a761)))),
% 1.99/1.54 inference(quant_inst,[status(thm)],[])).
% 1.99/1.54 tff(828,plain,
% 1.99/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a761) | c2_1(a761) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a697)) | (~c1_1(a761))),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[827, 826])).
% 1.99/1.54 tff(829,plain,
% 1.99/1.54 ((~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a697))),
% 1.99/1.54 inference(unit_resolution,[status(thm)],[828, 227, 802, 791, 785, 175, 822])).
% 1.99/1.54 tff(830,plain,
% 1.99/1.54 (~c1_1(a697)),
% 1.99/1.54 inference(unit_resolution,[status(thm)],[829, 812, 811])).
% 1.99/1.54 tff(831,plain,
% 1.99/1.54 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))),
% 1.99/1.54 inference(bind,[status(th)],[])).
% 1.99/1.54 tff(832,plain,
% 1.99/1.54 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.99/1.54 inference(quant_intro,[status(thm)],[831])).
% 1.99/1.54 tff(833,plain,
% 1.99/1.54 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.99/1.54 inference(rewrite,[status(thm)],[])).
% 1.99/1.54 tff(834,plain,
% 1.99/1.54 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_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)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_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)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_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)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp0) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp0))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))))),
% 1.99/1.54 inference(bind,[status(th)],[])).
% 1.99/1.54 tff(835,plain,
% 1.99/1.54 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.99/1.54 inference(quant_intro,[status(thm)],[834])).
% 1.99/1.54 tff(836,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause175')).
% 1.99/1.54 tff(837,plain,
% 1.99/1.54 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[836, 835])).
% 1.99/1.54 tff(838,plain,
% 1.99/1.54 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[837, 833])).
% 1.99/1.54 tff(839,plain,(
% 1.99/1.54 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.99/1.54 inference(skolemize,[status(sab)],[838])).
% 1.99/1.54 tff(840,plain,
% 1.99/1.54 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.99/1.54 inference(modus_ponens,[status(thm)],[839, 832])).
% 1.99/1.54 tff(841,plain,
% 1.99/1.54 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp0 | c2_1(a702) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c3_1(a702)) | (~c0_1(a702)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp0 | c2_1(a702) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c3_1(a702)) | (~c0_1(a702)))),
% 1.99/1.54 inference(rewrite,[status(thm)],[])).
% 1.99/1.54 tff(842,plain,
% 1.99/1.54 ((hskp0 | (~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697))) <=> (hskp0 | c2_1(a702) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c3_1(a702)) | (~c0_1(a702)))),
% 1.99/1.54 inference(rewrite,[status(thm)],[])).
% 1.99/1.54 tff(843,plain,
% 1.99/1.54 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp0 | c2_1(a702) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c3_1(a702)) | (~c0_1(a702))))),
% 1.99/1.54 inference(monotonicity,[status(thm)],[842])).
% 1.99/1.54 tff(844,plain,
% 1.99/1.54 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp0 | c2_1(a702) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c3_1(a702)) | (~c0_1(a702)))),
% 1.99/1.54 inference(transitivity,[status(thm)],[843, 841])).
% 1.99/1.54 tff(845,plain,
% 1.99/1.54 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)))),
% 1.99/1.54 inference(quant_inst,[status(thm)],[])).
% 1.99/1.54 tff(846,plain,
% 1.99/1.54 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp0 | c2_1(a702) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c3_1(a702)) | (~c0_1(a702))),
% 1.99/1.55 inference(modus_ponens,[status(thm)],[845, 844])).
% 1.99/1.55 tff(847,plain,
% 1.99/1.55 (hskp0 | (~c0_1(a697)) | c1_1(a697)),
% 1.99/1.55 inference(unit_resolution,[status(thm)],[846, 227, 715, 716, 714, 175, 840])).
% 1.99/1.55 tff(848,plain,
% 1.99/1.55 (hskp0),
% 1.99/1.55 inference(unit_resolution,[status(thm)],[847, 830, 811])).
% 1.99/1.55 tff(849,plain,
% 1.99/1.55 (((~hskp0) | (~c1_1(a692))) <=> ((~hskp0) | (~c1_1(a692)))),
% 1.99/1.55 inference(rewrite,[status(thm)],[])).
% 1.99/1.55 tff(850,plain,
% 1.99/1.55 (((~c1_1(a692)) | (~hskp0)) <=> ((~hskp0) | (~c1_1(a692)))),
% 1.99/1.55 inference(rewrite,[status(thm)],[])).
% 1.99/1.55 tff(851,axiom,((~c1_1(a692)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause132')).
% 1.99/1.55 tff(852,plain,
% 1.99/1.55 ((~hskp0) | (~c1_1(a692))),
% 1.99/1.55 inference(modus_ponens,[status(thm)],[851, 850])).
% 1.99/1.55 tff(853,plain,
% 1.99/1.55 ((~hskp0) | (~c1_1(a692))),
% 1.99/1.55 inference(modus_ponens,[status(thm)],[852, 849])).
% 1.99/1.55 tff(854,plain,
% 1.99/1.55 (~c1_1(a692)),
% 1.99/1.55 inference(unit_resolution,[status(thm)],[853, 848])).
% 1.99/1.55 tff(855,plain,
% 1.99/1.55 (((~hskp0) | (~c0_1(a692))) <=> ((~hskp0) | (~c0_1(a692)))),
% 1.99/1.55 inference(rewrite,[status(thm)],[])).
% 1.99/1.55 tff(856,plain,
% 1.99/1.55 (((~c0_1(a692)) | (~hskp0)) <=> ((~hskp0) | (~c0_1(a692)))),
% 1.99/1.55 inference(rewrite,[status(thm)],[])).
% 1.99/1.55 tff(857,axiom,((~c0_1(a692)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause131')).
% 1.99/1.55 tff(858,plain,
% 1.99/1.55 ((~hskp0) | (~c0_1(a692))),
% 1.99/1.55 inference(modus_ponens,[status(thm)],[857, 856])).
% 1.99/1.55 tff(859,plain,
% 1.99/1.55 ((~hskp0) | (~c0_1(a692))),
% 1.99/1.55 inference(modus_ponens,[status(thm)],[858, 855])).
% 1.99/1.55 tff(860,plain,
% 1.99/1.55 (~c0_1(a692)),
% 1.99/1.55 inference(unit_resolution,[status(thm)],[859, 848])).
% 1.99/1.55 tff(861,plain,
% 1.99/1.55 (hskp14),
% 1.99/1.55 inference(unit_resolution,[status(thm)],[516, 830, 811])).
% 1.99/1.55 tff(862,plain,
% 1.99/1.55 (~c3_1(a730)),
% 1.99/1.55 inference(unit_resolution,[status(thm)],[486, 861])).
% 1.99/1.55 tff(863,plain,
% 1.99/1.55 (((~hskp0) | c2_1(a692)) <=> ((~hskp0) | c2_1(a692))),
% 1.99/1.55 inference(rewrite,[status(thm)],[])).
% 1.99/1.55 tff(864,axiom,((~hskp0) | c2_1(a692)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause86')).
% 1.99/1.55 tff(865,plain,
% 1.99/1.55 ((~hskp0) | c2_1(a692)),
% 1.99/1.55 inference(modus_ponens,[status(thm)],[864, 863])).
% 1.99/1.55 tff(866,plain,
% 1.99/1.55 ((~hskp0) | c2_1(a692)),
% 1.99/1.55 inference(modus_ponens,[status(thm)],[865, 863])).
% 1.99/1.55 tff(867,plain,
% 1.99/1.55 ((~hskp0) | c2_1(a692)),
% 1.99/1.55 inference(modus_ponens,[status(thm)],[866, 863])).
% 1.99/1.55 tff(868,plain,
% 1.99/1.55 ((~hskp0) | c2_1(a692)),
% 1.99/1.55 inference(modus_ponens,[status(thm)],[867, 863])).
% 1.99/1.55 tff(869,plain,
% 1.99/1.55 ((~hskp0) | c2_1(a692)),
% 1.99/1.55 inference(modus_ponens,[status(thm)],[868, 863])).
% 1.99/1.55 tff(870,plain,
% 1.99/1.55 ((~hskp0) | c2_1(a692)),
% 1.99/1.55 inference(modus_ponens,[status(thm)],[869, 863])).
% 1.99/1.55 tff(871,plain,
% 1.99/1.55 ((~hskp0) | c2_1(a692)),
% 1.99/1.55 inference(modus_ponens,[status(thm)],[870, 863])).
% 1.99/1.55 tff(872,plain,
% 1.99/1.55 ((~hskp0) | c2_1(a692)),
% 1.99/1.55 inference(modus_ponens,[status(thm)],[871, 863])).
% 1.99/1.55 tff(873,plain,
% 1.99/1.55 (c2_1(a692)),
% 1.99/1.55 inference(unit_resolution,[status(thm)],[872, 848])).
% 1.99/1.55 tff(874,plain,
% 1.99/1.55 (c1_1(a730)),
% 1.99/1.55 inference(unit_resolution,[status(thm)],[461, 861])).
% 1.99/1.55 tff(875,plain,
% 1.99/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | (c3_1(a730) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a697)) | c1_1(a697) | (~c1_1(a730)) | (~c2_1(a730)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c3_1(a730) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a697)) | c1_1(a697) | (~c1_1(a730)) | (~c2_1(a730)))),
% 1.99/1.55 inference(rewrite,[status(thm)],[])).
% 1.99/1.55 tff(876,plain,
% 1.99/1.55 (((~ndr1_0) | c3_1(a730) | (~c2_1(a730)) | (~c1_1(a730)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692)) <=> (c3_1(a730) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a697)) | c1_1(a697) | (~c1_1(a730)) | (~c2_1(a730)))),
% 1.99/1.55 inference(rewrite,[status(thm)],[])).
% 1.99/1.55 tff(877,plain,
% 1.99/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a730) | (~c2_1(a730)) | (~c1_1(a730)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | (c3_1(a730) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a697)) | c1_1(a697) | (~c1_1(a730)) | (~c2_1(a730))))),
% 1.99/1.55 inference(monotonicity,[status(thm)],[876])).
% 1.99/1.55 tff(878,plain,
% 1.99/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a730) | (~c2_1(a730)) | (~c1_1(a730)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c3_1(a730) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a697)) | c1_1(a697) | (~c1_1(a730)) | (~c2_1(a730)))),
% 1.99/1.55 inference(transitivity,[status(thm)],[877, 875])).
% 1.99/1.55 tff(879,plain,
% 1.99/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a730) | (~c2_1(a730)) | (~c1_1(a730)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692))),
% 1.99/1.55 inference(quant_inst,[status(thm)],[])).
% 1.99/1.55 tff(880,plain,
% 1.99/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c3_1(a730) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a697)) | c1_1(a697) | (~c1_1(a730)) | (~c2_1(a730))),
% 1.99/1.55 inference(modus_ponens,[status(thm)],[879, 878])).
% 1.99/1.55 tff(881,plain,
% 1.99/1.55 (~c2_1(a730)),
% 1.99/1.55 inference(unit_resolution,[status(thm)],[880, 227, 874, 811, 873, 862, 175, 860, 854, 566, 830])).
% 1.99/1.55 tff(882,plain,
% 1.99/1.55 (^[V: $i, U: $i] : refl((hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 1.99/1.55 inference(bind,[status(th)],[])).
% 1.99/1.55 tff(883,plain,
% 1.99/1.55 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.99/1.55 inference(quant_intro,[status(thm)],[882])).
% 1.99/1.55 tff(884,plain,
% 1.99/1.55 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.99/1.55 inference(rewrite,[status(thm)],[])).
% 1.99/1.55 tff(885,plain,
% 1.99/1.55 (^[V: $i, U: $i] : 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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_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)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_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)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_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)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_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)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp27) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp27))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp27) <=> (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 1.99/1.55 inference(bind,[status(th)],[])).
% 1.99/1.55 tff(886,plain,
% 1.99/1.55 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp27) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.99/1.55 inference(quant_intro,[status(thm)],[885])).
% 1.99/1.55 tff(887,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause158')).
% 1.99/1.55 tff(888,plain,
% 1.99/1.55 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.99/1.55 inference(modus_ponens,[status(thm)],[887, 886])).
% 1.99/1.55 tff(889,plain,
% 1.99/1.55 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.99/1.55 inference(modus_ponens,[status(thm)],[888, 884])).
% 1.99/1.55 tff(890,plain,(
% 1.99/1.55 ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.99/1.55 inference(skolemize,[status(sab)],[889])).
% 1.99/1.55 tff(891,plain,
% 1.99/1.55 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.99/1.55 inference(modus_ponens,[status(thm)],[890, 883])).
% 1.99/1.55 tff(892,plain,
% 1.99/1.55 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | c0_1(a761) | c2_1(a761) | c0_1(a725) | c1_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c1_1(a761)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp27 | c0_1(a761) | c2_1(a761) | c0_1(a725) | c1_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c1_1(a761)))),
% 1.99/1.55 inference(rewrite,[status(thm)],[])).
% 1.99/1.55 tff(893,plain,
% 1.99/1.55 ((hskp27 | (~ndr1_0) | c0_1(a761) | c2_1(a761) | (~c1_1(a761)) | c1_1(a725) | c0_1(a725) | (~c2_1(a725))) <=> (hskp27 | c0_1(a761) | c2_1(a761) | c0_1(a725) | c1_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c1_1(a761)))),
% 1.99/1.55 inference(rewrite,[status(thm)],[])).
% 1.99/1.55 tff(894,plain,
% 1.99/1.55 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c0_1(a761) | c2_1(a761) | (~c1_1(a761)) | c1_1(a725) | c0_1(a725) | (~c2_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | c0_1(a761) | c2_1(a761) | c0_1(a725) | c1_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c1_1(a761))))),
% 1.99/1.55 inference(monotonicity,[status(thm)],[893])).
% 1.99/1.55 tff(895,plain,
% 1.99/1.55 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c0_1(a761) | c2_1(a761) | (~c1_1(a761)) | c1_1(a725) | c0_1(a725) | (~c2_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp27 | c0_1(a761) | c2_1(a761) | c0_1(a725) | c1_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c1_1(a761)))),
% 1.99/1.55 inference(transitivity,[status(thm)],[894, 892])).
% 1.99/1.55 tff(896,plain,
% 1.99/1.55 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c0_1(a761) | c2_1(a761) | (~c1_1(a761)) | c1_1(a725) | c0_1(a725) | (~c2_1(a725)))),
% 1.99/1.55 inference(quant_inst,[status(thm)],[])).
% 1.99/1.55 tff(897,plain,
% 1.99/1.55 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp27 | c0_1(a761) | c2_1(a761) | c0_1(a725) | c1_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c1_1(a761))),
% 1.99/1.55 inference(modus_ponens,[status(thm)],[896, 895])).
% 1.99/1.55 tff(898,plain,
% 1.99/1.55 (hskp27),
% 1.99/1.55 inference(unit_resolution,[status(thm)],[897, 227, 802, 791, 785, 152, 146, 891, 809])).
% 1.99/1.55 tff(899,plain,
% 1.99/1.55 (hskp20),
% 1.99/1.55 inference(unit_resolution,[status(thm)],[288, 898, 102])).
% 1.99/1.55 tff(900,plain,
% 1.99/1.55 (~c3_1(a754)),
% 1.99/1.55 inference(unit_resolution,[status(thm)],[668, 899])).
% 1.99/1.55 tff(901,plain,
% 1.99/1.55 (c2_1(a754)),
% 1.99/1.55 inference(unit_resolution,[status(thm)],[190, 899])).
% 1.99/1.55 tff(902,plain,
% 1.99/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | (c3_1(a754) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a697)) | c1_1(a697) | (~c1_1(a754)) | (~c2_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c3_1(a754) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a697)) | c1_1(a697) | (~c1_1(a754)) | (~c2_1(a754)))),
% 1.99/1.55 inference(rewrite,[status(thm)],[])).
% 1.99/1.55 tff(903,plain,
% 1.99/1.55 (((~ndr1_0) | c3_1(a754) | (~c2_1(a754)) | (~c1_1(a754)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692)) <=> (c3_1(a754) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a697)) | c1_1(a697) | (~c1_1(a754)) | (~c2_1(a754)))),
% 1.99/1.55 inference(rewrite,[status(thm)],[])).
% 1.99/1.55 tff(904,plain,
% 1.99/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a754) | (~c2_1(a754)) | (~c1_1(a754)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | (c3_1(a754) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a697)) | c1_1(a697) | (~c1_1(a754)) | (~c2_1(a754))))),
% 1.99/1.55 inference(monotonicity,[status(thm)],[903])).
% 1.99/1.55 tff(905,plain,
% 1.99/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a754) | (~c2_1(a754)) | (~c1_1(a754)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c3_1(a754) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a697)) | c1_1(a697) | (~c1_1(a754)) | (~c2_1(a754)))),
% 1.99/1.55 inference(transitivity,[status(thm)],[904, 902])).
% 1.99/1.55 tff(906,plain,
% 1.99/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a754) | (~c2_1(a754)) | (~c1_1(a754)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692))),
% 1.99/1.55 inference(quant_inst,[status(thm)],[])).
% 1.99/1.55 tff(907,plain,
% 1.99/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c3_1(a754) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a697)) | c1_1(a697) | (~c1_1(a754)) | (~c2_1(a754))),
% 1.99/1.55 inference(modus_ponens,[status(thm)],[906, 905])).
% 1.99/1.55 tff(908,plain,
% 1.99/1.55 (~c1_1(a754)),
% 1.99/1.55 inference(unit_resolution,[status(thm)],[907, 227, 901, 811, 873, 900, 175, 860, 854, 566, 830])).
% 1.99/1.55 tff(909,plain,
% 1.99/1.55 (c0_1(a730)),
% 1.99/1.55 inference(unit_resolution,[status(thm)],[472, 861])).
% 1.99/1.55 tff(910,plain,
% 1.99/1.55 ($false),
% 1.99/1.55 inference(unit_resolution,[status(thm)],[493, 227, 62, 901, 909, 900, 862, 342, 908, 881])).
% 1.99/1.55 tff(911,plain,(hskp4 | hskp28 | c3_1(a697) | hskp30 | c1_1(a693) | c3_1(a693)), inference(lemma,lemma(discharge,[]))).
% 1.99/1.55 tff(912,plain,
% 1.99/1.55 (hskp4),
% 1.99/1.55 inference(unit_resolution,[status(thm)],[911, 175, 62, 102, 164, 153])).
% 1.99/1.55 tff(913,plain,
% 1.99/1.55 (((~hskp4) | (~c0_1(a698))) <=> ((~hskp4) | (~c0_1(a698)))),
% 1.99/1.55 inference(rewrite,[status(thm)],[])).
% 1.99/1.55 tff(914,plain,
% 1.99/1.55 (((~c0_1(a698)) | (~hskp4)) <=> ((~hskp4) | (~c0_1(a698)))),
% 1.99/1.55 inference(rewrite,[status(thm)],[])).
% 1.99/1.55 tff(915,axiom,((~c0_1(a698)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause124')).
% 1.99/1.55 tff(916,plain,
% 1.99/1.55 ((~hskp4) | (~c0_1(a698))),
% 1.99/1.55 inference(modus_ponens,[status(thm)],[915, 914])).
% 1.99/1.55 tff(917,plain,
% 1.99/1.55 ((~hskp4) | (~c0_1(a698))),
% 1.99/1.55 inference(modus_ponens,[status(thm)],[916, 913])).
% 1.99/1.55 tff(918,plain,
% 1.99/1.55 (~c0_1(a698)),
% 1.99/1.55 inference(unit_resolution,[status(thm)],[917, 912])).
% 1.99/1.55 tff(919,plain,
% 1.99/1.55 (((~hskp4) | (~c2_1(a698))) <=> ((~hskp4) | (~c2_1(a698)))),
% 1.99/1.55 inference(rewrite,[status(thm)],[])).
% 1.99/1.55 tff(920,plain,
% 1.99/1.55 (((~c2_1(a698)) | (~hskp4)) <=> ((~hskp4) | (~c2_1(a698)))),
% 1.99/1.55 inference(rewrite,[status(thm)],[])).
% 1.99/1.55 tff(921,axiom,((~c2_1(a698)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause125')).
% 1.99/1.55 tff(922,plain,
% 1.99/1.55 ((~hskp4) | (~c2_1(a698))),
% 1.99/1.55 inference(modus_ponens,[status(thm)],[921, 920])).
% 1.99/1.55 tff(923,plain,
% 1.99/1.55 ((~hskp4) | (~c2_1(a698))),
% 1.99/1.55 inference(modus_ponens,[status(thm)],[922, 919])).
% 1.99/1.55 tff(924,plain,
% 1.99/1.55 (~c2_1(a698)),
% 1.99/1.55 inference(unit_resolution,[status(thm)],[923, 912])).
% 1.99/1.55 tff(925,assumption,(~c2_1(a698)), introduced(assumption)).
% 1.99/1.55 tff(926,assumption,(~c0_1(a698)), introduced(assumption)).
% 1.99/1.55 tff(927,plain,
% 1.99/1.55 (hskp1),
% 1.99/1.55 inference(unit_resolution,[status(thm)],[372, 280, 102])).
% 1.99/1.55 tff(928,plain,
% 1.99/1.55 (c2_1(a693)),
% 1.99/1.55 inference(unit_resolution,[status(thm)],[383, 927])).
% 1.99/1.55 tff(929,plain,
% 1.99/1.55 (~hskp27),
% 1.99/1.55 inference(unit_resolution,[status(thm)],[288, 280, 102])).
% 1.99/1.55 tff(930,plain,
% 1.99/1.55 (~c0_1(a693)),
% 1.99/1.55 inference(unit_resolution,[status(thm)],[677, 929, 164])).
% 1.99/1.55 tff(931,plain,
% 1.99/1.55 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | c0_1(a698) | c2_1(a698) | c1_1(a693) | (~ndr1_0) | (~c1_1(a698)) | c0_1(a693) | (~c2_1(a693)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp27 | c0_1(a698) | c2_1(a698) | c1_1(a693) | (~ndr1_0) | (~c1_1(a698)) | c0_1(a693) | (~c2_1(a693)))),
% 1.99/1.55 inference(rewrite,[status(thm)],[])).
% 1.99/1.55 tff(932,plain,
% 1.99/1.55 ((hskp27 | (~ndr1_0) | c0_1(a698) | c2_1(a698) | (~c1_1(a698)) | c1_1(a693) | c0_1(a693) | (~c2_1(a693))) <=> (hskp27 | c0_1(a698) | c2_1(a698) | c1_1(a693) | (~ndr1_0) | (~c1_1(a698)) | c0_1(a693) | (~c2_1(a693)))),
% 1.99/1.55 inference(rewrite,[status(thm)],[])).
% 1.99/1.55 tff(933,plain,
% 1.99/1.55 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c0_1(a698) | c2_1(a698) | (~c1_1(a698)) | c1_1(a693) | c0_1(a693) | (~c2_1(a693)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | c0_1(a698) | c2_1(a698) | c1_1(a693) | (~ndr1_0) | (~c1_1(a698)) | c0_1(a693) | (~c2_1(a693))))),
% 1.99/1.55 inference(monotonicity,[status(thm)],[932])).
% 1.99/1.55 tff(934,plain,
% 1.99/1.55 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c0_1(a698) | c2_1(a698) | (~c1_1(a698)) | c1_1(a693) | c0_1(a693) | (~c2_1(a693)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp27 | c0_1(a698) | c2_1(a698) | c1_1(a693) | (~ndr1_0) | (~c1_1(a698)) | c0_1(a693) | (~c2_1(a693)))),
% 1.99/1.55 inference(transitivity,[status(thm)],[933, 931])).
% 1.99/1.55 tff(935,plain,
% 1.99/1.55 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c0_1(a698) | c2_1(a698) | (~c1_1(a698)) | c1_1(a693) | c0_1(a693) | (~c2_1(a693)))),
% 1.99/1.55 inference(quant_inst,[status(thm)],[])).
% 1.99/1.55 tff(936,plain,
% 1.99/1.55 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp27 | c0_1(a698) | c2_1(a698) | c1_1(a693) | (~ndr1_0) | (~c1_1(a698)) | c0_1(a693) | (~c2_1(a693))),
% 1.99/1.55 inference(modus_ponens,[status(thm)],[935, 934])).
% 1.99/1.55 tff(937,plain,
% 1.99/1.55 (hskp27 | (~c1_1(a698)) | c0_1(a693) | (~c2_1(a693))),
% 1.99/1.55 inference(unit_resolution,[status(thm)],[936, 227, 926, 925, 164, 891])).
% 1.99/1.55 tff(938,plain,
% 1.99/1.55 (~c1_1(a698)),
% 1.99/1.55 inference(unit_resolution,[status(thm)],[937, 929, 930, 928])).
% 1.99/1.55 tff(939,plain,
% 1.99/1.55 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))))),
% 1.99/1.55 inference(bind,[status(th)],[])).
% 1.99/1.55 tff(940,plain,
% 1.99/1.55 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.99/1.55 inference(quant_intro,[status(thm)],[939])).
% 1.99/1.55 tff(941,plain,
% 1.99/1.55 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.99/1.55 inference(rewrite,[status(thm)],[])).
% 1.99/1.55 tff(942,plain,
% 1.99/1.55 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c3_1(W)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c3_1(W))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c3_1(W)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c3_1(W))))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))))),
% 1.99/1.55 inference(bind,[status(th)],[])).
% 1.99/1.55 tff(943,plain,
% 1.99/1.55 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.99/1.55 inference(quant_intro,[status(thm)],[942])).
% 1.99/1.55 tff(944,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause189')).
% 1.99/1.55 tff(945,plain,
% 1.99/1.55 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.99/1.55 inference(modus_ponens,[status(thm)],[944, 943])).
% 1.99/1.55 tff(946,plain,
% 1.99/1.55 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.99/1.55 inference(modus_ponens,[status(thm)],[945, 941])).
% 1.99/1.55 tff(947,plain,(
% 1.99/1.55 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.99/1.55 inference(skolemize,[status(sab)],[946])).
% 1.99/1.55 tff(948,plain,
% 1.99/1.55 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.99/1.55 inference(modus_ponens,[status(thm)],[947, 940])).
% 1.99/1.55 tff(949,plain,
% 1.99/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a698) | c2_1(a698) | (~c3_1(a698)) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | c1_1(a698) | (~c2_1(a693)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a698) | c2_1(a698) | (~c3_1(a698)) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | c1_1(a698) | (~c2_1(a693)))),
% 1.99/1.55 inference(rewrite,[status(thm)],[])).
% 1.99/1.55 tff(950,plain,
% 1.99/1.55 (((~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c2_1(a693)) | c1_1(a698) | c2_1(a698) | (~c3_1(a698)) | c2_1(a698) | c0_1(a698) | (~c3_1(a698))) <=> (c0_1(a698) | c2_1(a698) | (~c3_1(a698)) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | c1_1(a698) | (~c2_1(a693)))),
% 1.99/1.55 inference(rewrite,[status(thm)],[])).
% 1.99/1.55 tff(951,plain,
% 1.99/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c2_1(a693)) | c1_1(a698) | c2_1(a698) | (~c3_1(a698)) | c2_1(a698) | c0_1(a698) | (~c3_1(a698)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a698) | c2_1(a698) | (~c3_1(a698)) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | c1_1(a698) | (~c2_1(a693))))),
% 1.99/1.55 inference(monotonicity,[status(thm)],[950])).
% 1.99/1.55 tff(952,plain,
% 1.99/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c2_1(a693)) | c1_1(a698) | c2_1(a698) | (~c3_1(a698)) | c2_1(a698) | c0_1(a698) | (~c3_1(a698)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a698) | c2_1(a698) | (~c3_1(a698)) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | c1_1(a698) | (~c2_1(a693)))),
% 1.99/1.55 inference(transitivity,[status(thm)],[951, 949])).
% 1.99/1.55 tff(953,plain,
% 1.99/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c2_1(a693)) | c1_1(a698) | c2_1(a698) | (~c3_1(a698)) | c2_1(a698) | c0_1(a698) | (~c3_1(a698)))),
% 1.99/1.55 inference(quant_inst,[status(thm)],[])).
% 1.99/1.55 tff(954,plain,
% 1.99/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a698) | c2_1(a698) | (~c3_1(a698)) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | c1_1(a698) | (~c2_1(a693))),
% 1.99/1.55 inference(modus_ponens,[status(thm)],[953, 952])).
% 1.99/1.55 tff(955,plain,
% 1.99/1.55 (~c3_1(a698)),
% 1.99/1.55 inference(unit_resolution,[status(thm)],[954, 227, 928, 926, 925, 164, 153, 948, 938])).
% 1.99/1.55 tff(956,plain,
% 1.99/1.55 (((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0))) <=> ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp27 | hskp6 | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0))),
% 1.99/1.55 inference(rewrite,[status(thm)],[])).
% 1.99/1.55 tff(957,plain,
% 1.99/1.55 ((hskp27 | hskp6 | (~ndr1_0) | c3_1(a698) | c0_1(a698) | c2_1(a698)) <=> (hskp27 | hskp6 | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0))),
% 1.99/1.55 inference(rewrite,[status(thm)],[])).
% 1.99/1.55 tff(958,plain,
% 1.99/1.55 (((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | (~ndr1_0) | c3_1(a698) | c0_1(a698) | c2_1(a698))) <=> ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0)))),
% 1.99/1.55 inference(monotonicity,[status(thm)],[957])).
% 1.99/1.55 tff(959,plain,
% 1.99/1.55 (((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | (~ndr1_0) | c3_1(a698) | c0_1(a698) | c2_1(a698))) <=> ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp27 | hskp6 | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0))),
% 1.99/1.55 inference(transitivity,[status(thm)],[958, 956])).
% 1.99/1.56 tff(960,plain,
% 1.99/1.56 ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | (~ndr1_0) | c3_1(a698) | c0_1(a698) | c2_1(a698))),
% 1.99/1.56 inference(quant_inst,[status(thm)],[])).
% 1.99/1.56 tff(961,plain,
% 1.99/1.56 ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp27 | hskp6 | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0)),
% 1.99/1.56 inference(modus_ponens,[status(thm)],[960, 959])).
% 1.99/1.56 tff(962,plain,
% 1.99/1.56 (hskp27 | hskp6 | c0_1(a698) | c3_1(a698)),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[961, 227, 925, 201])).
% 1.99/1.56 tff(963,plain,
% 1.99/1.56 (hskp6),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[962, 955, 926, 929])).
% 1.99/1.56 tff(964,plain,
% 1.99/1.56 (c0_1(a702)),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[90, 963])).
% 1.99/1.56 tff(965,plain,
% 1.99/1.56 (c3_1(a702)),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[79, 963])).
% 1.99/1.56 tff(966,plain,
% 1.99/1.56 (~hskp25),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[763, 965, 964, 717, 62])).
% 1.99/1.56 tff(967,plain,
% 1.99/1.56 (hskp22),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[778, 966, 62])).
% 1.99/1.56 tff(968,plain,
% 1.99/1.56 (~c2_1(a761)),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[784, 967])).
% 1.99/1.56 tff(969,plain,
% 1.99/1.56 (~c0_1(a761)),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[790, 967])).
% 1.99/1.56 tff(970,plain,
% 1.99/1.56 (c1_1(a761)),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[801, 967])).
% 1.99/1.56 tff(971,plain,
% 1.99/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a761) | c2_1(a761) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698) | (~c1_1(a761)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a761) | c2_1(a761) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698) | (~c1_1(a761)))),
% 1.99/1.56 inference(rewrite,[status(thm)],[])).
% 1.99/1.56 tff(972,plain,
% 1.99/1.56 (((~ndr1_0) | c0_1(a761) | c2_1(a761) | (~c1_1(a761)) | c3_1(a698) | c1_1(a698) | c2_1(a698) | c3_1(a698) | c2_1(a698) | c0_1(a698)) <=> (c0_1(a761) | c2_1(a761) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698) | (~c1_1(a761)))),
% 1.99/1.56 inference(rewrite,[status(thm)],[])).
% 1.99/1.56 tff(973,plain,
% 1.99/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a761) | c2_1(a761) | (~c1_1(a761)) | c3_1(a698) | c1_1(a698) | c2_1(a698) | c3_1(a698) | c2_1(a698) | c0_1(a698))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a761) | c2_1(a761) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698) | (~c1_1(a761))))),
% 1.99/1.56 inference(monotonicity,[status(thm)],[972])).
% 1.99/1.56 tff(974,plain,
% 1.99/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a761) | c2_1(a761) | (~c1_1(a761)) | c3_1(a698) | c1_1(a698) | c2_1(a698) | c3_1(a698) | c2_1(a698) | c0_1(a698))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a761) | c2_1(a761) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698) | (~c1_1(a761)))),
% 1.99/1.56 inference(transitivity,[status(thm)],[973, 971])).
% 1.99/1.56 tff(975,plain,
% 1.99/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a761) | c2_1(a761) | (~c1_1(a761)) | c3_1(a698) | c1_1(a698) | c2_1(a698) | c3_1(a698) | c2_1(a698) | c0_1(a698))),
% 1.99/1.56 inference(quant_inst,[status(thm)],[])).
% 1.99/1.56 tff(976,plain,
% 1.99/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a761) | c2_1(a761) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698) | (~c1_1(a761))),
% 1.99/1.56 inference(modus_ponens,[status(thm)],[975, 974])).
% 1.99/1.56 tff(977,plain,
% 1.99/1.56 ($false),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[976, 227, 970, 969, 968, 926, 925, 955, 122, 938])).
% 1.99/1.56 tff(978,plain,(hskp20 | c0_1(a698) | c2_1(a698) | hskp28 | c2_1(a702) | c1_1(a693) | c3_1(a693) | hskp30), inference(lemma,lemma(discharge,[]))).
% 1.99/1.56 tff(979,plain,
% 1.99/1.56 (hskp20),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[978, 717, 925, 62, 926, 164, 153, 102])).
% 1.99/1.56 tff(980,plain,
% 1.99/1.56 (~c0_1(a754)),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[595, 979])).
% 1.99/1.56 tff(981,plain,
% 1.99/1.56 (~c3_1(a754)),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[668, 979])).
% 1.99/1.56 tff(982,assumption,(~hskp9), introduced(assumption)).
% 1.99/1.56 tff(983,plain,
% 1.99/1.56 (hskp1),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[372, 191, 102])).
% 1.99/1.56 tff(984,plain,
% 1.99/1.56 (c2_1(a693)),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[383, 983])).
% 1.99/1.56 tff(985,plain,
% 1.99/1.56 (~c0_1(a754)),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[634, 984, 180])).
% 1.99/1.56 tff(986,plain,
% 1.99/1.56 (hskp6),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[290, 985, 102, 178, 180])).
% 1.99/1.56 tff(987,plain,
% 1.99/1.56 (c0_1(a702)),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[90, 986])).
% 1.99/1.56 tff(988,plain,
% 1.99/1.56 (~hskp27),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[288, 191, 102])).
% 1.99/1.56 tff(989,plain,
% 1.99/1.56 (~c0_1(a693)),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[677, 988, 164])).
% 1.99/1.56 tff(990,plain,
% 1.99/1.56 (c3_1(a702)),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[79, 986])).
% 1.99/1.56 tff(991,plain,
% 1.99/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a754) | c3_1(a754) | c2_1(a702) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c2_1(a693)) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a754) | c3_1(a754) | c2_1(a702) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c2_1(a693)) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a754)))),
% 1.99/1.56 inference(rewrite,[status(thm)],[])).
% 1.99/1.56 tff(992,plain,
% 1.99/1.56 (((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a693) | c0_1(a693) | (~c2_1(a693)) | c3_1(a754) | c0_1(a754) | (~c1_1(a754))) <=> (c0_1(a754) | c3_1(a754) | c2_1(a702) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c2_1(a693)) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a754)))),
% 1.99/1.56 inference(rewrite,[status(thm)],[])).
% 1.99/1.56 tff(993,plain,
% 1.99/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a693) | c0_1(a693) | (~c2_1(a693)) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a754) | c3_1(a754) | c2_1(a702) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c2_1(a693)) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a754))))),
% 1.99/1.56 inference(monotonicity,[status(thm)],[992])).
% 1.99/1.56 tff(994,plain,
% 1.99/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a693) | c0_1(a693) | (~c2_1(a693)) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a754) | c3_1(a754) | c2_1(a702) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c2_1(a693)) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a754)))),
% 1.99/1.56 inference(transitivity,[status(thm)],[993, 991])).
% 1.99/1.56 tff(995,plain,
% 1.99/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a693) | c0_1(a693) | (~c2_1(a693)) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)))),
% 1.99/1.56 inference(quant_inst,[status(thm)],[])).
% 1.99/1.56 tff(996,plain,
% 1.99/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a754) | c3_1(a754) | c2_1(a702) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c2_1(a693)) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a754))),
% 1.99/1.56 inference(modus_ponens,[status(thm)],[995, 994])).
% 1.99/1.56 tff(997,plain,
% 1.99/1.56 (c0_1(a754) | c0_1(a693) | (~c2_1(a693)) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a754))),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[996, 227, 178, 717, 153, 174])).
% 1.99/1.56 tff(998,plain,
% 1.99/1.56 (~c1_1(a754)),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[997, 990, 984, 985, 989, 987])).
% 1.99/1.56 tff(999,plain,
% 1.99/1.56 (^[U: $i] : refl((hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))),
% 1.99/1.56 inference(bind,[status(th)],[])).
% 1.99/1.56 tff(1000,plain,
% 1.99/1.56 (![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> ![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.99/1.56 inference(quant_intro,[status(thm)],[999])).
% 1.99/1.56 tff(1001,plain,
% 1.99/1.56 (![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> ![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.99/1.56 inference(rewrite,[status(thm)],[])).
% 1.99/1.56 tff(1002,plain,
% 1.99/1.56 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_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) | c3_1(U) | c0_1(U) | c2_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp3) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp3))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp3) | hskp9) <=> ((hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp9))), rewrite(((hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp9) <=> (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp3) | hskp9) <=> (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))))),
% 1.99/1.56 inference(bind,[status(th)],[])).
% 1.99/1.56 tff(1003,plain,
% 1.99/1.56 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp3) | hskp9) <=> ![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.99/1.56 inference(quant_intro,[status(thm)],[1002])).
% 1.99/1.56 tff(1004,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp3) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause137')).
% 1.99/1.56 tff(1005,plain,
% 1.99/1.56 (![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.99/1.56 inference(modus_ponens,[status(thm)],[1004, 1003])).
% 1.99/1.56 tff(1006,plain,
% 1.99/1.56 (![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.99/1.56 inference(modus_ponens,[status(thm)],[1005, 1001])).
% 1.99/1.56 tff(1007,plain,(
% 1.99/1.56 ![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.99/1.56 inference(skolemize,[status(sab)],[1006])).
% 1.99/1.56 tff(1008,plain,
% 1.99/1.56 (![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.99/1.56 inference(modus_ponens,[status(thm)],[1007, 1000])).
% 1.99/1.56 tff(1009,plain,
% 1.99/1.56 (((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp9 | hskp3 | c2_1(a754) | c0_1(a754) | c3_1(a754) | (~ndr1_0))) <=> ((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp9 | hskp3 | c2_1(a754) | c0_1(a754) | c3_1(a754) | (~ndr1_0))),
% 1.99/1.56 inference(rewrite,[status(thm)],[])).
% 1.99/1.56 tff(1010,plain,
% 1.99/1.56 ((hskp9 | hskp3 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | c2_1(a754)) <=> (hskp9 | hskp3 | c2_1(a754) | c0_1(a754) | c3_1(a754) | (~ndr1_0))),
% 1.99/1.56 inference(rewrite,[status(thm)],[])).
% 1.99/1.56 tff(1011,plain,
% 1.99/1.56 (((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp9 | hskp3 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | c2_1(a754))) <=> ((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp9 | hskp3 | c2_1(a754) | c0_1(a754) | c3_1(a754) | (~ndr1_0)))),
% 1.99/1.56 inference(monotonicity,[status(thm)],[1010])).
% 1.99/1.56 tff(1012,plain,
% 1.99/1.56 (((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp9 | hskp3 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | c2_1(a754))) <=> ((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp9 | hskp3 | c2_1(a754) | c0_1(a754) | c3_1(a754) | (~ndr1_0))),
% 1.99/1.56 inference(transitivity,[status(thm)],[1011, 1009])).
% 1.99/1.56 tff(1013,plain,
% 1.99/1.56 ((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp9 | hskp3 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | c2_1(a754))),
% 1.99/1.56 inference(quant_inst,[status(thm)],[])).
% 1.99/1.56 tff(1014,plain,
% 1.99/1.56 ((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp9 | hskp3 | c2_1(a754) | c0_1(a754) | c3_1(a754) | (~ndr1_0)),
% 1.99/1.56 inference(modus_ponens,[status(thm)],[1013, 1012])).
% 1.99/1.56 tff(1015,plain,
% 1.99/1.56 (hskp3 | c2_1(a754) | c0_1(a754)),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[1014, 227, 982, 178, 1008])).
% 1.99/1.56 tff(1016,plain,
% 1.99/1.56 (hskp3),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[1015, 985, 180])).
% 1.99/1.56 tff(1017,plain,
% 1.99/1.56 (c0_1(a697)),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[508, 1016])).
% 1.99/1.56 tff(1018,plain,
% 1.99/1.56 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | c0_1(a754) | c3_1(a754) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | c1_1(a754))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp27 | c0_1(a754) | c3_1(a754) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | c1_1(a754))),
% 1.99/1.56 inference(rewrite,[status(thm)],[])).
% 1.99/1.56 tff(1019,plain,
% 1.99/1.56 ((hskp27 | (~ndr1_0) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c3_1(a754) | c1_1(a754) | c0_1(a754)) <=> (hskp27 | c0_1(a754) | c3_1(a754) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | c1_1(a754))),
% 1.99/1.56 inference(rewrite,[status(thm)],[])).
% 1.99/1.56 tff(1020,plain,
% 1.99/1.56 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c3_1(a754) | c1_1(a754) | c0_1(a754))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | c0_1(a754) | c3_1(a754) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | c1_1(a754)))),
% 1.99/1.56 inference(monotonicity,[status(thm)],[1019])).
% 1.99/1.56 tff(1021,plain,
% 1.99/1.56 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c3_1(a754) | c1_1(a754) | c0_1(a754))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp27 | c0_1(a754) | c3_1(a754) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | c1_1(a754))),
% 1.99/1.56 inference(transitivity,[status(thm)],[1020, 1018])).
% 1.99/1.56 tff(1022,plain,
% 1.99/1.56 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c3_1(a754) | c1_1(a754) | c0_1(a754))),
% 1.99/1.56 inference(quant_inst,[status(thm)],[])).
% 1.99/1.56 tff(1023,plain,
% 1.99/1.56 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp27 | c0_1(a754) | c3_1(a754) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | c1_1(a754)),
% 1.99/1.56 inference(modus_ponens,[status(thm)],[1022, 1021])).
% 1.99/1.56 tff(1024,plain,
% 1.99/1.56 (hskp27 | c0_1(a754) | (~c0_1(a697)) | c1_1(a697) | c1_1(a754)),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[1023, 227, 178, 175, 607])).
% 1.99/1.56 tff(1025,plain,
% 1.99/1.56 (c1_1(a697)),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[1024, 1017, 988, 985, 998])).
% 1.99/1.56 tff(1026,plain,
% 1.99/1.56 (~hskp25),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[763, 990, 987, 717, 62])).
% 1.99/1.56 tff(1027,plain,
% 1.99/1.56 (hskp22),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[778, 1026, 62])).
% 1.99/1.56 tff(1028,plain,
% 1.99/1.56 (~c2_1(a761)),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[784, 1027])).
% 1.99/1.56 tff(1029,plain,
% 1.99/1.56 (~c0_1(a761)),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[790, 1027])).
% 1.99/1.56 tff(1030,plain,
% 1.99/1.56 (c2_1(a697)),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[527, 1016])).
% 1.99/1.56 tff(1031,plain,
% 1.99/1.56 (c1_1(a761)),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[801, 1027])).
% 1.99/1.56 tff(1032,plain,
% 1.99/1.56 ($false),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[828, 227, 1031, 1017, 1030, 1029, 1028, 175, 822, 1025])).
% 1.99/1.56 tff(1033,plain,(c2_1(a754) | c3_1(a697) | hskp28 | c3_1(a754) | c2_1(a702) | c3_1(a693) | hskp9 | hskp30 | c1_1(a693)), inference(lemma,lemma(discharge,[]))).
% 1.99/1.56 tff(1034,plain,
% 1.99/1.56 (c2_1(a754)),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[1033, 178, 62, 175, 717, 153, 982, 102, 164])).
% 1.99/1.56 tff(1035,plain,
% 1.99/1.56 (~hskp24),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[385, 177, 62, 164, 153, 102, 178, 179])).
% 1.99/1.56 tff(1036,assumption,(~hskp27), introduced(assumption)).
% 1.99/1.56 tff(1037,assumption,(~c3_1(a725)), introduced(assumption)).
% 1.99/1.56 tff(1038,plain,
% 1.99/1.56 (hskp27 | hskp6 | c2_1(a725)),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[641, 227, 578, 1037, 201])).
% 1.99/1.56 tff(1039,plain,
% 1.99/1.56 (c2_1(a725)),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[1038, 1036, 177])).
% 1.99/1.56 tff(1040,plain,
% 1.99/1.56 (c3_1(a698)),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[962, 1036, 926, 177])).
% 1.99/1.56 tff(1041,plain,
% 1.99/1.56 (((~hskp4) | (~c3_1(a698))) <=> ((~hskp4) | (~c3_1(a698)))),
% 1.99/1.56 inference(rewrite,[status(thm)],[])).
% 1.99/1.56 tff(1042,plain,
% 1.99/1.56 (((~c3_1(a698)) | (~hskp4)) <=> ((~hskp4) | (~c3_1(a698)))),
% 1.99/1.56 inference(rewrite,[status(thm)],[])).
% 1.99/1.56 tff(1043,axiom,((~c3_1(a698)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause126')).
% 1.99/1.56 tff(1044,plain,
% 1.99/1.56 ((~hskp4) | (~c3_1(a698))),
% 1.99/1.56 inference(modus_ponens,[status(thm)],[1043, 1042])).
% 1.99/1.56 tff(1045,plain,
% 1.99/1.56 ((~hskp4) | (~c3_1(a698))),
% 1.99/1.56 inference(modus_ponens,[status(thm)],[1044, 1041])).
% 1.99/1.56 tff(1046,plain,
% 1.99/1.56 (~hskp4),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[1045, 1040])).
% 1.99/1.56 tff(1047,plain,
% 1.99/1.56 (hskp4 | hskp3 | (~c2_1(a725))),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[553, 227, 578, 577, 442])).
% 1.99/1.56 tff(1048,plain,
% 1.99/1.56 (hskp3),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[1047, 1046, 1039])).
% 1.99/1.56 tff(1049,plain,
% 1.99/1.56 (c0_1(a697)),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[508, 1048])).
% 1.99/1.56 tff(1050,plain,
% 1.99/1.56 (hskp27 | (~c0_1(a697)) | c1_1(a697)),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[695, 227, 578, 577, 1037, 175, 607])).
% 1.99/1.56 tff(1051,plain,
% 1.99/1.56 (c1_1(a697)),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[1050, 1049, 1036])).
% 1.99/1.56 tff(1052,plain,
% 1.99/1.56 (c2_1(a697)),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[527, 1048])).
% 1.99/1.56 tff(1053,plain,
% 1.99/1.56 ($false),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[534, 227, 432, 474, 1049, 1052, 163, 1051])).
% 1.99/1.56 tff(1054,plain,(hskp27 | hskp24 | hskp23 | c0_1(a725) | c1_1(a725) | c3_1(a725) | c3_1(a697) | hskp6 | c0_1(a698) | c2_1(a698)), inference(lemma,lemma(discharge,[]))).
% 1.99/1.56 tff(1055,plain,
% 1.99/1.56 (hskp27),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[1054, 474, 1035, 152, 146, 140, 175, 177, 926, 925])).
% 1.99/1.56 tff(1056,plain,
% 1.99/1.56 (c1_1(a691)),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[267, 1055])).
% 1.99/1.56 tff(1057,plain,
% 1.99/1.56 (c0_1(a691)),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[278, 1055])).
% 1.99/1.56 tff(1058,plain,
% 1.99/1.56 (((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a691)) | (~c1_1(a691)) | (~c0_1(a691)))) <=> ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a691)) | (~c1_1(a691)) | (~c0_1(a691)))),
% 1.99/1.56 inference(rewrite,[status(thm)],[])).
% 1.99/1.56 tff(1059,plain,
% 1.99/1.56 ((hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a691)) | (~c0_1(a691)) | (~c1_1(a691))) <=> (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a691)) | (~c1_1(a691)) | (~c0_1(a691)))),
% 1.99/1.56 inference(rewrite,[status(thm)],[])).
% 1.99/1.56 tff(1060,plain,
% 1.99/1.56 (((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a691)) | (~c0_1(a691)) | (~c1_1(a691)))) <=> ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a691)) | (~c1_1(a691)) | (~c0_1(a691))))),
% 1.99/1.56 inference(monotonicity,[status(thm)],[1059])).
% 1.99/1.56 tff(1061,plain,
% 1.99/1.56 (((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a691)) | (~c0_1(a691)) | (~c1_1(a691)))) <=> ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a691)) | (~c1_1(a691)) | (~c0_1(a691)))),
% 1.99/1.56 inference(transitivity,[status(thm)],[1060, 1058])).
% 1.99/1.56 tff(1062,plain,
% 1.99/1.56 ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a691)) | (~c0_1(a691)) | (~c1_1(a691)))),
% 1.99/1.56 inference(quant_inst,[status(thm)],[])).
% 1.99/1.56 tff(1063,plain,
% 1.99/1.56 ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a691)) | (~c1_1(a691)) | (~c0_1(a691))),
% 1.99/1.56 inference(modus_ponens,[status(thm)],[1062, 1061])).
% 1.99/1.56 tff(1064,plain,
% 1.99/1.56 (~c2_1(a691)),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[1063, 227, 1035, 474, 1057, 1056, 163])).
% 1.99/1.56 tff(1065,plain,
% 1.99/1.56 (c3_1(a691)),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[256, 1055])).
% 1.99/1.56 tff(1066,plain,
% 1.99/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754)) | (~c3_1(a691)) | (~c0_1(a691)) | c2_1(a691))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754)) | (~c3_1(a691)) | (~c0_1(a691)) | c2_1(a691))),
% 1.99/1.56 inference(rewrite,[status(thm)],[])).
% 1.99/1.56 tff(1067,plain,
% 1.99/1.56 (((~ndr1_0) | c2_1(a691) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a754) | c0_1(a754) | (~c1_1(a754))) <=> (c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754)) | (~c3_1(a691)) | (~c0_1(a691)) | c2_1(a691))),
% 1.99/1.56 inference(rewrite,[status(thm)],[])).
% 1.99/1.56 tff(1068,plain,
% 1.99/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a691) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754)) | (~c3_1(a691)) | (~c0_1(a691)) | c2_1(a691)))),
% 1.99/1.56 inference(monotonicity,[status(thm)],[1067])).
% 1.99/1.56 tff(1069,plain,
% 1.99/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a691) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754)) | (~c3_1(a691)) | (~c0_1(a691)) | c2_1(a691))),
% 1.99/1.56 inference(transitivity,[status(thm)],[1068, 1066])).
% 1.99/1.56 tff(1070,plain,
% 1.99/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a691) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)))),
% 1.99/1.56 inference(quant_inst,[status(thm)],[])).
% 1.99/1.56 tff(1071,plain,
% 1.99/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754)) | (~c3_1(a691)) | (~c0_1(a691)) | c2_1(a691)),
% 1.99/1.56 inference(modus_ponens,[status(thm)],[1070, 1069])).
% 1.99/1.56 tff(1072,plain,
% 1.99/1.56 (~c1_1(a754)),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[1071, 227, 1057, 1065, 387, 179, 178, 174, 1064])).
% 1.99/1.56 tff(1073,plain,
% 1.99/1.56 (~hskp14),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[495, 1072, 387, 178, 474, 1035, 62])).
% 1.99/1.56 tff(1074,plain,
% 1.99/1.56 (~hskp3),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[536, 1073, 474, 1035, 102, 175])).
% 1.99/1.56 tff(1075,plain,
% 1.99/1.56 (((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp9 | hskp3 | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0))) <=> ((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp9 | hskp3 | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0))),
% 1.99/1.56 inference(rewrite,[status(thm)],[])).
% 1.99/1.56 tff(1076,plain,
% 1.99/1.56 ((hskp9 | hskp3 | (~ndr1_0) | c3_1(a698) | c0_1(a698) | c2_1(a698)) <=> (hskp9 | hskp3 | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0))),
% 1.99/1.56 inference(rewrite,[status(thm)],[])).
% 1.99/1.56 tff(1077,plain,
% 1.99/1.56 (((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp9 | hskp3 | (~ndr1_0) | c3_1(a698) | c0_1(a698) | c2_1(a698))) <=> ((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp9 | hskp3 | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0)))),
% 1.99/1.56 inference(monotonicity,[status(thm)],[1076])).
% 1.99/1.56 tff(1078,plain,
% 1.99/1.56 (((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp9 | hskp3 | (~ndr1_0) | c3_1(a698) | c0_1(a698) | c2_1(a698))) <=> ((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp9 | hskp3 | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0))),
% 1.99/1.56 inference(transitivity,[status(thm)],[1077, 1075])).
% 1.99/1.56 tff(1079,plain,
% 1.99/1.56 ((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp9 | hskp3 | (~ndr1_0) | c3_1(a698) | c0_1(a698) | c2_1(a698))),
% 1.99/1.56 inference(quant_inst,[status(thm)],[])).
% 1.99/1.56 tff(1080,plain,
% 1.99/1.56 ((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp9 | hskp3 | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0)),
% 1.99/1.56 inference(modus_ponens,[status(thm)],[1079, 1078])).
% 1.99/1.56 tff(1081,plain,
% 1.99/1.56 (hskp9 | hskp3 | c0_1(a698) | c3_1(a698)),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[1080, 227, 925, 1008])).
% 1.99/1.56 tff(1082,plain,
% 1.99/1.56 (c3_1(a698)),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[1081, 1074, 926, 982])).
% 1.99/1.56 tff(1083,plain,
% 1.99/1.56 (((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp14 | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)))) <=> ((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp30 | hskp14 | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)))),
% 1.99/1.56 inference(rewrite,[status(thm)],[])).
% 1.99/1.56 tff(1084,plain,
% 1.99/1.56 ((hskp30 | hskp14 | (~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c0_1(a693))) <=> (hskp30 | hskp14 | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)))),
% 1.99/1.56 inference(rewrite,[status(thm)],[])).
% 1.99/1.56 tff(1085,plain,
% 1.99/1.56 (((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp14 | (~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c0_1(a693)))) <=> ((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp14 | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693))))),
% 1.99/1.56 inference(monotonicity,[status(thm)],[1084])).
% 1.99/1.56 tff(1086,plain,
% 1.99/1.56 (((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp14 | (~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c0_1(a693)))) <=> ((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp30 | hskp14 | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)))),
% 1.99/1.56 inference(transitivity,[status(thm)],[1085, 1083])).
% 1.99/1.56 tff(1087,plain,
% 1.99/1.56 ((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp14 | (~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c0_1(a693)))),
% 1.99/1.56 inference(quant_inst,[status(thm)],[])).
% 1.99/1.56 tff(1088,plain,
% 1.99/1.56 ((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp30 | hskp14 | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693))),
% 1.99/1.56 inference(modus_ponens,[status(thm)],[1087, 1086])).
% 1.99/1.56 tff(1089,plain,
% 1.99/1.56 (hskp14 | c1_1(a693) | (~c0_1(a693))),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[1088, 102, 227, 153, 112])).
% 1.99/1.56 tff(1090,plain,
% 1.99/1.56 (~c0_1(a693)),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[1089, 1073, 164])).
% 1.99/1.56 tff(1091,plain,
% 1.99/1.56 (((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp9 | hskp3 | c2_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693))) <=> ((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp9 | hskp3 | c2_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693))),
% 1.99/1.56 inference(rewrite,[status(thm)],[])).
% 1.99/1.56 tff(1092,plain,
% 1.99/1.56 ((hskp9 | hskp3 | (~ndr1_0) | c3_1(a693) | c0_1(a693) | c2_1(a693)) <=> (hskp9 | hskp3 | c2_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693))),
% 1.99/1.56 inference(rewrite,[status(thm)],[])).
% 1.99/1.56 tff(1093,plain,
% 1.99/1.56 (((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp9 | hskp3 | (~ndr1_0) | c3_1(a693) | c0_1(a693) | c2_1(a693))) <=> ((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp9 | hskp3 | c2_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693)))),
% 1.99/1.56 inference(monotonicity,[status(thm)],[1092])).
% 1.99/1.56 tff(1094,plain,
% 1.99/1.56 (((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp9 | hskp3 | (~ndr1_0) | c3_1(a693) | c0_1(a693) | c2_1(a693))) <=> ((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp9 | hskp3 | c2_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693))),
% 1.99/1.56 inference(transitivity,[status(thm)],[1093, 1091])).
% 1.99/1.56 tff(1095,plain,
% 1.99/1.56 ((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp9 | hskp3 | (~ndr1_0) | c3_1(a693) | c0_1(a693) | c2_1(a693))),
% 1.99/1.56 inference(quant_inst,[status(thm)],[])).
% 1.99/1.56 tff(1096,plain,
% 1.99/1.56 ((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp9 | hskp3 | c2_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693)),
% 1.99/1.56 inference(modus_ponens,[status(thm)],[1095, 1094])).
% 1.99/1.56 tff(1097,plain,
% 1.99/1.56 (hskp9 | hskp3 | c2_1(a693) | c0_1(a693)),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[1096, 227, 153, 1008])).
% 1.99/1.56 tff(1098,plain,
% 1.99/1.56 (c2_1(a693)),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[1097, 1074, 982, 1090])).
% 1.99/1.56 tff(1099,plain,
% 1.99/1.56 (hskp4),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[687, 1074, 1098, 1090])).
% 1.99/1.56 tff(1100,plain,
% 1.99/1.56 ($false),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[1045, 1099, 1082])).
% 1.99/1.56 tff(1101,plain,(hskp23 | c1_1(a693) | hskp9 | c3_1(a693) | c0_1(a698) | c2_1(a698) | hskp30 | c3_1(a697) | (~c2_1(a754)) | c3_1(a754) | hskp28 | c0_1(a754) | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.99/1.56 tff(1102,plain,
% 1.99/1.56 (hskp23),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[1101, 177, 982, 153, 926, 925, 102, 175, 387, 178, 62, 179, 164])).
% 1.99/1.56 tff(1103,plain,
% 1.99/1.56 (~c2_1(a725)),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[586, 1102, 152, 146, 62])).
% 1.99/1.56 tff(1104,plain,
% 1.99/1.56 (c1_1(a754)),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[430, 1102, 387, 179, 62])).
% 1.99/1.56 tff(1105,plain,
% 1.99/1.56 (hskp6 | c0_1(a754) | c2_1(a725) | (~c1_1(a754))),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[545, 227, 178, 152, 140, 301])).
% 1.99/1.56 tff(1106,plain,
% 1.99/1.56 ($false),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[1105, 1104, 1103, 179, 177])).
% 1.99/1.56 tff(1107,plain,(hskp6 | c0_1(a754) | c3_1(a754) | (~c2_1(a754)) | hskp28 | hskp9 | c3_1(a693) | c0_1(a698) | c2_1(a698) | hskp30 | c3_1(a697) | c1_1(a693)), inference(lemma,lemma(discharge,[]))).
% 1.99/1.56 tff(1108,plain,
% 1.99/1.56 (hskp6),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[1107, 179, 178, 1034, 62, 982, 153, 926, 925, 102, 175, 164])).
% 1.99/1.56 tff(1109,plain,
% 1.99/1.56 (c0_1(a702)),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[90, 1108])).
% 1.99/1.56 tff(1110,plain,
% 1.99/1.56 (c3_1(a702)),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[79, 1108])).
% 1.99/1.56 tff(1111,plain,
% 1.99/1.56 (~hskp25),
% 1.99/1.56 inference(unit_resolution,[status(thm)],[763, 1110, 1109, 717, 62])).
% 1.99/1.57 tff(1112,plain,
% 1.99/1.57 (hskp22),
% 1.99/1.57 inference(unit_resolution,[status(thm)],[778, 1111, 62])).
% 1.99/1.57 tff(1113,plain,
% 1.99/1.57 (~c2_1(a761)),
% 1.99/1.57 inference(unit_resolution,[status(thm)],[784, 1112])).
% 1.99/1.57 tff(1114,plain,
% 1.99/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a754) | c3_1(a754) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a754)) | (~c2_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a754) | c3_1(a754) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a754)) | (~c2_1(a754)))),
% 1.99/1.57 inference(rewrite,[status(thm)],[])).
% 1.99/1.57 tff(1115,plain,
% 1.99/1.57 (((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a754) | c0_1(a754) | (~c1_1(a754))) <=> (c0_1(a754) | c3_1(a754) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a754)) | (~c2_1(a754)))),
% 1.99/1.57 inference(rewrite,[status(thm)],[])).
% 1.99/1.57 tff(1116,plain,
% 1.99/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a754) | c3_1(a754) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a754)) | (~c2_1(a754))))),
% 1.99/1.57 inference(monotonicity,[status(thm)],[1115])).
% 1.99/1.57 tff(1117,plain,
% 1.99/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a754) | c3_1(a754) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a754)) | (~c2_1(a754)))),
% 1.99/1.57 inference(transitivity,[status(thm)],[1116, 1114])).
% 1.99/1.57 tff(1118,plain,
% 1.99/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)))),
% 1.99/1.57 inference(quant_inst,[status(thm)],[])).
% 1.99/1.57 tff(1119,plain,
% 1.99/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a754) | c3_1(a754) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a754)) | (~c2_1(a754))),
% 1.99/1.57 inference(modus_ponens,[status(thm)],[1118, 1117])).
% 1.99/1.57 tff(1120,plain,
% 1.99/1.57 (c0_1(a754) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a754)) | (~c2_1(a754))),
% 1.99/1.57 inference(unit_resolution,[status(thm)],[1119, 227, 178, 717, 174])).
% 1.99/1.57 tff(1121,plain,
% 1.99/1.57 (~c1_1(a754)),
% 1.99/1.57 inference(unit_resolution,[status(thm)],[1120, 1110, 1034, 179, 1109])).
% 1.99/1.57 tff(1122,plain,
% 1.99/1.57 (c1_1(a761)),
% 1.99/1.57 inference(unit_resolution,[status(thm)],[801, 1112])).
% 1.99/1.57 tff(1123,plain,
% 1.99/1.57 (~c0_1(a761)),
% 1.99/1.57 inference(unit_resolution,[status(thm)],[790, 1112])).
% 1.99/1.57 tff(1124,assumption,(~c2_1(a761)), introduced(assumption)).
% 1.99/1.57 tff(1125,assumption,(~c0_1(a761)), introduced(assumption)).
% 1.99/1.57 tff(1126,assumption,(c1_1(a761)), introduced(assumption)).
% 1.99/1.57 tff(1127,plain,
% 1.99/1.57 (c2_1(a725)),
% 1.99/1.57 inference(unit_resolution,[status(thm)],[808, 227, 1126, 1125, 1124, 152, 146, 140, 122])).
% 1.99/1.57 tff(1128,plain,
% 1.99/1.57 (~hskp23),
% 1.99/1.57 inference(unit_resolution,[status(thm)],[586, 1127, 152, 146, 62])).
% 1.99/1.57 tff(1129,plain,
% 1.99/1.57 (hskp27),
% 1.99/1.57 inference(unit_resolution,[status(thm)],[897, 227, 1126, 1125, 1124, 152, 146, 891, 1127])).
% 1.99/1.57 tff(1130,plain,
% 1.99/1.57 (hskp20),
% 1.99/1.57 inference(unit_resolution,[status(thm)],[288, 1129, 102])).
% 1.99/1.57 tff(1131,plain,
% 1.99/1.57 (~c3_1(a754)),
% 1.99/1.57 inference(unit_resolution,[status(thm)],[668, 1130])).
% 1.99/1.57 tff(1132,plain,
% 1.99/1.57 (c2_1(a754)),
% 1.99/1.57 inference(unit_resolution,[status(thm)],[190, 1130])).
% 1.99/1.57 tff(1133,plain,
% 1.99/1.57 (~hskp14),
% 1.99/1.57 inference(unit_resolution,[status(thm)],[495, 432, 62, 1132, 1131, 388, 1128])).
% 1.99/1.57 tff(1134,plain,
% 1.99/1.57 (~hskp3),
% 1.99/1.57 inference(unit_resolution,[status(thm)],[536, 1133, 1128, 432, 102, 175])).
% 1.99/1.57 tff(1135,plain,
% 1.99/1.57 (c3_1(a698)),
% 1.99/1.57 inference(unit_resolution,[status(thm)],[1081, 1134, 926, 982])).
% 1.99/1.57 tff(1136,plain,
% 1.99/1.57 (~c0_1(a693)),
% 1.99/1.57 inference(unit_resolution,[status(thm)],[1089, 1133, 164])).
% 1.99/1.57 tff(1137,plain,
% 1.99/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a693) | c0_1(a761) | c2_1(a761) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c1_1(a761)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a693) | c0_1(a761) | c2_1(a761) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c1_1(a761)))),
% 1.99/1.57 inference(rewrite,[status(thm)],[])).
% 1.99/1.57 tff(1138,plain,
% 1.99/1.57 (((~ndr1_0) | c0_1(a761) | c2_1(a761) | (~c1_1(a761)) | c3_1(a693) | c1_1(a693) | c2_1(a693) | c3_1(a693) | c2_1(a693) | c0_1(a693)) <=> (c2_1(a693) | c0_1(a761) | c2_1(a761) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c1_1(a761)))),
% 1.99/1.57 inference(rewrite,[status(thm)],[])).
% 1.99/1.57 tff(1139,plain,
% 1.99/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a761) | c2_1(a761) | (~c1_1(a761)) | c3_1(a693) | c1_1(a693) | c2_1(a693) | c3_1(a693) | c2_1(a693) | c0_1(a693))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a693) | c0_1(a761) | c2_1(a761) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c1_1(a761))))),
% 1.99/1.57 inference(monotonicity,[status(thm)],[1138])).
% 1.99/1.57 tff(1140,plain,
% 1.99/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a761) | c2_1(a761) | (~c1_1(a761)) | c3_1(a693) | c1_1(a693) | c2_1(a693) | c3_1(a693) | c2_1(a693) | c0_1(a693))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a693) | c0_1(a761) | c2_1(a761) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c1_1(a761)))),
% 1.99/1.57 inference(transitivity,[status(thm)],[1139, 1137])).
% 1.99/1.57 tff(1141,plain,
% 1.99/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a761) | c2_1(a761) | (~c1_1(a761)) | c3_1(a693) | c1_1(a693) | c2_1(a693) | c3_1(a693) | c2_1(a693) | c0_1(a693))),
% 1.99/1.57 inference(quant_inst,[status(thm)],[])).
% 1.99/1.57 tff(1142,plain,
% 1.99/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a693) | c0_1(a761) | c2_1(a761) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c1_1(a761))),
% 1.99/1.57 inference(modus_ponens,[status(thm)],[1141, 1140])).
% 1.99/1.57 tff(1143,plain,
% 1.99/1.57 (c2_1(a693) | c0_1(a693)),
% 1.99/1.57 inference(unit_resolution,[status(thm)],[1142, 227, 1126, 1125, 1124, 164, 153, 122])).
% 1.99/1.57 tff(1144,plain,
% 1.99/1.57 (c2_1(a693)),
% 1.99/1.57 inference(unit_resolution,[status(thm)],[1143, 1136])).
% 1.99/1.57 tff(1145,plain,
% 1.99/1.57 (hskp4),
% 1.99/1.57 inference(unit_resolution,[status(thm)],[687, 1134, 1144, 1136])).
% 1.99/1.57 tff(1146,plain,
% 1.99/1.57 ($false),
% 1.99/1.57 inference(unit_resolution,[status(thm)],[1045, 1145, 1135])).
% 1.99/1.57 tff(1147,plain,(hskp24 | c1_1(a693) | c0_1(a698) | hskp9 | c2_1(a698) | (~c1_1(a761)) | c0_1(a761) | c2_1(a761) | c3_1(a693) | hskp30 | c3_1(a697) | hskp28 | c1_1(a754)), inference(lemma,lemma(discharge,[]))).
% 1.99/1.57 tff(1148,plain,
% 1.99/1.57 (hskp24),
% 1.99/1.57 inference(unit_resolution,[status(thm)],[1147, 1123, 926, 982, 925, 1122, 1121, 1113, 153, 102, 175, 62, 164])).
% 1.99/1.57 tff(1149,plain,
% 1.99/1.57 (~c3_1(a764)),
% 1.99/1.57 inference(unit_resolution,[status(thm)],[307, 1148])).
% 1.99/1.57 tff(1150,plain,
% 1.99/1.57 (c1_1(a764)),
% 1.99/1.57 inference(unit_resolution,[status(thm)],[324, 1148])).
% 1.99/1.57 tff(1151,plain,
% 1.99/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a764) | c0_1(a754) | c3_1(a754) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c2_1(a754)) | c0_1(a764) | (~c1_1(a764)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a764) | c0_1(a754) | c3_1(a754) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c2_1(a754)) | c0_1(a764) | (~c1_1(a764)))),
% 1.99/1.57 inference(rewrite,[status(thm)],[])).
% 1.99/1.57 tff(1152,plain,
% 1.99/1.57 (((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a764) | c0_1(a764) | (~c1_1(a764))) <=> (c3_1(a764) | c0_1(a754) | c3_1(a754) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c2_1(a754)) | c0_1(a764) | (~c1_1(a764)))),
% 1.99/1.57 inference(rewrite,[status(thm)],[])).
% 1.99/1.57 tff(1153,plain,
% 1.99/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a764) | c0_1(a764) | (~c1_1(a764)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a764) | c0_1(a754) | c3_1(a754) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c2_1(a754)) | c0_1(a764) | (~c1_1(a764))))),
% 1.99/1.57 inference(monotonicity,[status(thm)],[1152])).
% 1.99/1.57 tff(1154,plain,
% 1.99/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a764) | c0_1(a764) | (~c1_1(a764)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a764) | c0_1(a754) | c3_1(a754) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c2_1(a754)) | c0_1(a764) | (~c1_1(a764)))),
% 1.99/1.57 inference(transitivity,[status(thm)],[1153, 1151])).
% 1.99/1.57 tff(1155,plain,
% 1.99/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a764) | c0_1(a764) | (~c1_1(a764)))),
% 1.99/1.57 inference(quant_inst,[status(thm)],[])).
% 1.99/1.57 tff(1156,plain,
% 1.99/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a764) | c0_1(a754) | c3_1(a754) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c2_1(a754)) | c0_1(a764) | (~c1_1(a764))),
% 1.99/1.57 inference(modus_ponens,[status(thm)],[1155, 1154])).
% 1.99/1.57 tff(1157,plain,
% 1.99/1.57 (c0_1(a764)),
% 1.99/1.57 inference(unit_resolution,[status(thm)],[1156, 227, 1150, 1034, 1109, 1110, 1149, 179, 178, 717, 174])).
% 1.99/1.57 tff(1158,plain,
% 1.99/1.57 (~c2_1(a764)),
% 1.99/1.57 inference(unit_resolution,[status(thm)],[313, 1148])).
% 1.99/1.57 tff(1159,plain,
% 1.99/1.57 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754)) | (~c0_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754)) | (~c0_1(a764)))),
% 1.99/1.57 inference(rewrite,[status(thm)],[])).
% 1.99/1.57 tff(1160,plain,
% 1.99/1.57 ((hskp28 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c0_1(a764)) | c3_1(a754) | c1_1(a754) | (~c2_1(a754))) <=> (hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754)) | (~c0_1(a764)))),
% 1.99/1.57 inference(rewrite,[status(thm)],[])).
% 1.99/1.57 tff(1161,plain,
% 1.99/1.57 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c0_1(a764)) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754)) | (~c0_1(a764))))),
% 1.99/1.57 inference(monotonicity,[status(thm)],[1160])).
% 1.99/1.57 tff(1162,plain,
% 1.99/1.57 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c0_1(a764)) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754)) | (~c0_1(a764)))),
% 1.99/1.57 inference(transitivity,[status(thm)],[1161, 1159])).
% 1.99/1.57 tff(1163,plain,
% 1.99/1.57 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c0_1(a764)) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)))),
% 1.99/1.57 inference(quant_inst,[status(thm)],[])).
% 1.99/1.57 tff(1164,plain,
% 1.99/1.57 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754)) | (~c0_1(a764))),
% 1.99/1.57 inference(modus_ponens,[status(thm)],[1163, 1162])).
% 1.99/1.57 tff(1165,plain,
% 1.99/1.57 ($false),
% 1.99/1.57 inference(unit_resolution,[status(thm)],[1164, 227, 62, 1034, 1158, 1149, 178, 342, 1121, 1157])).
% 1.99/1.57 tff(1166,plain,(c0_1(a754) | hskp28 | c3_1(a754) | c2_1(a702) | c0_1(a698) | hskp9 | c2_1(a698) | c3_1(a693) | hskp30 | c3_1(a697) | c1_1(a693)), inference(lemma,lemma(discharge,[]))).
% 1.99/1.57 tff(1167,plain,
% 1.99/1.57 (hskp9),
% 1.99/1.57 inference(unit_resolution,[status(thm)],[1166, 981, 62, 717, 926, 980, 925, 153, 102, 175, 164])).
% 1.99/1.57 tff(1168,plain,
% 1.99/1.57 (((~hskp9) | (~c1_1(a712))) <=> ((~hskp9) | (~c1_1(a712)))),
% 1.99/1.57 inference(rewrite,[status(thm)],[])).
% 1.99/1.57 tff(1169,plain,
% 1.99/1.57 (((~c1_1(a712)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a712)))),
% 1.99/1.57 inference(rewrite,[status(thm)],[])).
% 1.99/1.57 tff(1170,axiom,((~c1_1(a712)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause118')).
% 1.99/1.57 tff(1171,plain,
% 1.99/1.57 ((~hskp9) | (~c1_1(a712))),
% 1.99/1.57 inference(modus_ponens,[status(thm)],[1170, 1169])).
% 1.99/1.57 tff(1172,plain,
% 1.99/1.57 ((~hskp9) | (~c1_1(a712))),
% 1.99/1.57 inference(modus_ponens,[status(thm)],[1171, 1168])).
% 1.99/1.57 tff(1173,plain,
% 1.99/1.57 (~c1_1(a712)),
% 1.99/1.57 inference(unit_resolution,[status(thm)],[1172, 1167])).
% 1.99/1.57 tff(1174,plain,
% 1.99/1.57 (((~hskp9) | (~c0_1(a712))) <=> ((~hskp9) | (~c0_1(a712)))),
% 1.99/1.57 inference(rewrite,[status(thm)],[])).
% 1.99/1.57 tff(1175,plain,
% 1.99/1.57 (((~c0_1(a712)) | (~hskp9)) <=> ((~hskp9) | (~c0_1(a712)))),
% 1.99/1.57 inference(rewrite,[status(thm)],[])).
% 1.99/1.57 tff(1176,axiom,((~c0_1(a712)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause117')).
% 1.99/1.57 tff(1177,plain,
% 1.99/1.57 ((~hskp9) | (~c0_1(a712))),
% 1.99/1.57 inference(modus_ponens,[status(thm)],[1176, 1175])).
% 1.99/1.57 tff(1178,plain,
% 1.99/1.57 ((~hskp9) | (~c0_1(a712))),
% 1.99/1.57 inference(modus_ponens,[status(thm)],[1177, 1174])).
% 1.99/1.57 tff(1179,plain,
% 1.99/1.57 (~c0_1(a712)),
% 1.99/1.57 inference(unit_resolution,[status(thm)],[1178, 1167])).
% 1.99/1.57 tff(1180,plain,
% 1.99/1.57 (((~hskp9) | (~c2_1(a712))) <=> ((~hskp9) | (~c2_1(a712)))),
% 1.99/1.57 inference(rewrite,[status(thm)],[])).
% 1.99/1.57 tff(1181,plain,
% 1.99/1.57 (((~c2_1(a712)) | (~hskp9)) <=> ((~hskp9) | (~c2_1(a712)))),
% 1.99/1.57 inference(rewrite,[status(thm)],[])).
% 1.99/1.57 tff(1182,axiom,((~c2_1(a712)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause119')).
% 1.99/1.57 tff(1183,plain,
% 1.99/1.57 ((~hskp9) | (~c2_1(a712))),
% 1.99/1.57 inference(modus_ponens,[status(thm)],[1182, 1181])).
% 1.99/1.57 tff(1184,plain,
% 1.99/1.57 ((~hskp9) | (~c2_1(a712))),
% 1.99/1.57 inference(modus_ponens,[status(thm)],[1183, 1180])).
% 1.99/1.57 tff(1185,plain,
% 1.99/1.57 (~c2_1(a712)),
% 1.99/1.57 inference(unit_resolution,[status(thm)],[1184, 1167])).
% 1.99/1.57 tff(1186,assumption,(~c2_1(a712)), introduced(assumption)).
% 1.99/1.57 tff(1187,assumption,(~c1_1(a712)), introduced(assumption)).
% 1.99/1.57 tff(1188,assumption,(~c0_1(a712)), introduced(assumption)).
% 1.99/1.57 tff(1189,assumption,(hskp22), introduced(assumption)).
% 1.99/1.57 tff(1190,plain,
% 1.99/1.57 (~c2_1(a761)),
% 1.99/1.57 inference(unit_resolution,[status(thm)],[784, 1189])).
% 1.99/1.57 tff(1191,plain,
% 1.99/1.57 (~c0_1(a761)),
% 1.99/1.57 inference(unit_resolution,[status(thm)],[790, 1189])).
% 1.99/1.57 tff(1192,plain,
% 1.99/1.57 (c1_1(a761)),
% 1.99/1.57 inference(unit_resolution,[status(thm)],[801, 1189])).
% 1.99/1.57 tff(1193,plain,
% 1.99/1.57 (c2_1(a725)),
% 1.99/1.57 inference(unit_resolution,[status(thm)],[808, 227, 1192, 1191, 1190, 578, 577, 1037, 122])).
% 1.99/1.57 tff(1194,plain,
% 1.99/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a725) | c3_1(a725) | c0_1(a712) | c1_1(a712) | c2_1(a712) | (~ndr1_0) | (~c3_1(a712)) | (~c2_1(a725)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a725) | c3_1(a725) | c0_1(a712) | c1_1(a712) | c2_1(a712) | (~ndr1_0) | (~c3_1(a712)) | (~c2_1(a725)))),
% 1.99/1.57 inference(rewrite,[status(thm)],[])).
% 1.99/1.57 tff(1195,plain,
% 1.99/1.57 (((~ndr1_0) | c3_1(a725) | c1_1(a725) | (~c2_1(a725)) | c1_1(a712) | c2_1(a712) | (~c3_1(a712)) | c2_1(a712) | c0_1(a712) | (~c3_1(a712))) <=> (c1_1(a725) | c3_1(a725) | c0_1(a712) | c1_1(a712) | c2_1(a712) | (~ndr1_0) | (~c3_1(a712)) | (~c2_1(a725)))),
% 1.99/1.57 inference(rewrite,[status(thm)],[])).
% 1.99/1.57 tff(1196,plain,
% 1.99/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a725) | c1_1(a725) | (~c2_1(a725)) | c1_1(a712) | c2_1(a712) | (~c3_1(a712)) | c2_1(a712) | c0_1(a712) | (~c3_1(a712)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a725) | c3_1(a725) | c0_1(a712) | c1_1(a712) | c2_1(a712) | (~ndr1_0) | (~c3_1(a712)) | (~c2_1(a725))))),
% 1.99/1.57 inference(monotonicity,[status(thm)],[1195])).
% 1.99/1.57 tff(1197,plain,
% 1.99/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a725) | c1_1(a725) | (~c2_1(a725)) | c1_1(a712) | c2_1(a712) | (~c3_1(a712)) | c2_1(a712) | c0_1(a712) | (~c3_1(a712)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a725) | c3_1(a725) | c0_1(a712) | c1_1(a712) | c2_1(a712) | (~ndr1_0) | (~c3_1(a712)) | (~c2_1(a725)))),
% 1.99/1.57 inference(transitivity,[status(thm)],[1196, 1194])).
% 1.99/1.57 tff(1198,plain,
% 1.99/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a725) | c1_1(a725) | (~c2_1(a725)) | c1_1(a712) | c2_1(a712) | (~c3_1(a712)) | c2_1(a712) | c0_1(a712) | (~c3_1(a712)))),
% 1.99/1.57 inference(quant_inst,[status(thm)],[])).
% 1.99/1.57 tff(1199,plain,
% 1.99/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a725) | c3_1(a725) | c0_1(a712) | c1_1(a712) | c2_1(a712) | (~ndr1_0) | (~c3_1(a712)) | (~c2_1(a725))),
% 1.99/1.57 inference(modus_ponens,[status(thm)],[1198, 1197])).
% 1.99/1.57 tff(1200,plain,
% 1.99/1.57 (c0_1(a712) | (~c3_1(a712)) | (~c2_1(a725))),
% 1.99/1.57 inference(unit_resolution,[status(thm)],[1199, 227, 577, 1037, 1187, 1186, 948])).
% 1.99/1.57 tff(1201,plain,
% 1.99/1.57 (~c3_1(a712)),
% 1.99/1.57 inference(unit_resolution,[status(thm)],[1200, 1193, 1188])).
% 1.99/1.57 tff(1202,plain,
% 1.99/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a761) | c2_1(a761) | c0_1(a712) | c1_1(a712) | c2_1(a712) | (~ndr1_0) | c3_1(a712) | (~c1_1(a761)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a761) | c2_1(a761) | c0_1(a712) | c1_1(a712) | c2_1(a712) | (~ndr1_0) | c3_1(a712) | (~c1_1(a761)))),
% 1.99/1.57 inference(rewrite,[status(thm)],[])).
% 1.99/1.57 tff(1203,plain,
% 1.99/1.57 (((~ndr1_0) | c0_1(a761) | c2_1(a761) | (~c1_1(a761)) | c3_1(a712) | c1_1(a712) | c2_1(a712) | c3_1(a712) | c2_1(a712) | c0_1(a712)) <=> (c0_1(a761) | c2_1(a761) | c0_1(a712) | c1_1(a712) | c2_1(a712) | (~ndr1_0) | c3_1(a712) | (~c1_1(a761)))),
% 1.99/1.57 inference(rewrite,[status(thm)],[])).
% 1.99/1.57 tff(1204,plain,
% 1.99/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a761) | c2_1(a761) | (~c1_1(a761)) | c3_1(a712) | c1_1(a712) | c2_1(a712) | c3_1(a712) | c2_1(a712) | c0_1(a712))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a761) | c2_1(a761) | c0_1(a712) | c1_1(a712) | c2_1(a712) | (~ndr1_0) | c3_1(a712) | (~c1_1(a761))))),
% 1.99/1.57 inference(monotonicity,[status(thm)],[1203])).
% 1.99/1.57 tff(1205,plain,
% 1.99/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a761) | c2_1(a761) | (~c1_1(a761)) | c3_1(a712) | c1_1(a712) | c2_1(a712) | c3_1(a712) | c2_1(a712) | c0_1(a712))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a761) | c2_1(a761) | c0_1(a712) | c1_1(a712) | c2_1(a712) | (~ndr1_0) | c3_1(a712) | (~c1_1(a761)))),
% 1.99/1.57 inference(transitivity,[status(thm)],[1204, 1202])).
% 1.99/1.57 tff(1206,plain,
% 1.99/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a761) | c2_1(a761) | (~c1_1(a761)) | c3_1(a712) | c1_1(a712) | c2_1(a712) | c3_1(a712) | c2_1(a712) | c0_1(a712))),
% 1.99/1.57 inference(quant_inst,[status(thm)],[])).
% 1.99/1.57 tff(1207,plain,
% 1.99/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a761) | c2_1(a761) | c0_1(a712) | c1_1(a712) | c2_1(a712) | (~ndr1_0) | c3_1(a712) | (~c1_1(a761))),
% 1.99/1.57 inference(modus_ponens,[status(thm)],[1206, 1205])).
% 1.99/1.57 tff(1208,plain,
% 1.99/1.57 ($false),
% 1.99/1.57 inference(unit_resolution,[status(thm)],[1207, 227, 1192, 1191, 1190, 1188, 1187, 1186, 122, 1201])).
% 1.99/1.57 tff(1209,plain,((~hskp22) | c0_1(a712) | c1_1(a712) | c2_1(a712) | c1_1(a725) | c3_1(a725) | c0_1(a725)), inference(lemma,lemma(discharge,[]))).
% 1.99/1.57 tff(1210,plain,
% 1.99/1.57 (~hskp22),
% 1.99/1.57 inference(unit_resolution,[status(thm)],[1209, 1188, 1187, 1186, 146, 140, 152])).
% 1.99/1.57 tff(1211,plain,
% 1.99/1.57 (hskp25),
% 1.99/1.57 inference(unit_resolution,[status(thm)],[778, 1210, 62])).
% 1.99/1.57 tff(1212,plain,
% 1.99/1.57 (((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | c0_1(a712) | c2_1(a712) | (~ndr1_0) | c3_1(a712))) <=> ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp27 | hskp6 | c0_1(a712) | c2_1(a712) | (~ndr1_0) | c3_1(a712))),
% 1.99/1.57 inference(rewrite,[status(thm)],[])).
% 1.99/1.57 tff(1213,plain,
% 1.99/1.57 ((hskp27 | hskp6 | (~ndr1_0) | c3_1(a712) | c0_1(a712) | c2_1(a712)) <=> (hskp27 | hskp6 | c0_1(a712) | c2_1(a712) | (~ndr1_0) | c3_1(a712))),
% 1.99/1.57 inference(rewrite,[status(thm)],[])).
% 1.99/1.57 tff(1214,plain,
% 1.99/1.57 (((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | (~ndr1_0) | c3_1(a712) | c0_1(a712) | c2_1(a712))) <=> ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | c0_1(a712) | c2_1(a712) | (~ndr1_0) | c3_1(a712)))),
% 1.99/1.57 inference(monotonicity,[status(thm)],[1213])).
% 1.99/1.57 tff(1215,plain,
% 1.99/1.57 (((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | (~ndr1_0) | c3_1(a712) | c0_1(a712) | c2_1(a712))) <=> ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp27 | hskp6 | c0_1(a712) | c2_1(a712) | (~ndr1_0) | c3_1(a712))),
% 1.99/1.57 inference(transitivity,[status(thm)],[1214, 1212])).
% 1.99/1.57 tff(1216,plain,
% 1.99/1.57 ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | (~ndr1_0) | c3_1(a712) | c0_1(a712) | c2_1(a712))),
% 1.99/1.57 inference(quant_inst,[status(thm)],[])).
% 1.99/1.57 tff(1217,plain,
% 1.99/1.57 ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp27 | hskp6 | c0_1(a712) | c2_1(a712) | (~ndr1_0) | c3_1(a712)),
% 1.99/1.57 inference(modus_ponens,[status(thm)],[1216, 1215])).
% 1.99/1.57 tff(1218,plain,
% 1.99/1.57 (hskp27 | hskp6 | c0_1(a712) | c3_1(a712)),
% 1.99/1.57 inference(unit_resolution,[status(thm)],[1217, 227, 1186, 201])).
% 1.99/1.57 tff(1219,plain,
% 1.99/1.57 (c3_1(a712)),
% 1.99/1.57 inference(unit_resolution,[status(thm)],[1218, 929, 1188, 177])).
% 1.99/1.57 tff(1220,plain,
% 1.99/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a712) | c1_1(a712) | c2_1(a712) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c3_1(a712)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a712) | c1_1(a712) | c2_1(a712) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c3_1(a712)))),
% 1.99/1.57 inference(rewrite,[status(thm)],[])).
% 1.99/1.57 tff(1221,plain,
% 1.99/1.57 (((~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c2_1(a693)) | c1_1(a712) | c2_1(a712) | (~c3_1(a712)) | c2_1(a712) | c0_1(a712) | (~c3_1(a712))) <=> (c0_1(a712) | c1_1(a712) | c2_1(a712) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c3_1(a712)))),
% 1.99/1.57 inference(rewrite,[status(thm)],[])).
% 1.99/1.57 tff(1222,plain,
% 1.99/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c2_1(a693)) | c1_1(a712) | c2_1(a712) | (~c3_1(a712)) | c2_1(a712) | c0_1(a712) | (~c3_1(a712)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a712) | c1_1(a712) | c2_1(a712) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c3_1(a712))))),
% 1.99/1.57 inference(monotonicity,[status(thm)],[1221])).
% 1.99/1.57 tff(1223,plain,
% 1.99/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c2_1(a693)) | c1_1(a712) | c2_1(a712) | (~c3_1(a712)) | c2_1(a712) | c0_1(a712) | (~c3_1(a712)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a712) | c1_1(a712) | c2_1(a712) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c3_1(a712)))),
% 1.99/1.57 inference(transitivity,[status(thm)],[1222, 1220])).
% 1.99/1.57 tff(1224,plain,
% 1.99/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c2_1(a693)) | c1_1(a712) | c2_1(a712) | (~c3_1(a712)) | c2_1(a712) | c0_1(a712) | (~c3_1(a712)))),
% 1.99/1.57 inference(quant_inst,[status(thm)],[])).
% 1.99/1.57 tff(1225,plain,
% 1.99/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a712) | c1_1(a712) | c2_1(a712) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c3_1(a712))),
% 1.99/1.57 inference(modus_ponens,[status(thm)],[1224, 1223])).
% 1.99/1.57 tff(1226,plain,
% 1.99/1.57 (c0_1(a712) | (~c2_1(a693)) | (~c3_1(a712))),
% 1.99/1.57 inference(unit_resolution,[status(thm)],[1225, 227, 1187, 1186, 164, 153, 948])).
% 1.99/1.57 tff(1227,plain,
% 1.99/1.57 ($false),
% 1.99/1.57 inference(unit_resolution,[status(thm)],[1226, 1219, 928, 1188])).
% 1.99/1.57 tff(1228,plain,(hskp20 | c0_1(a712) | c1_1(a712) | c2_1(a712) | c1_1(a693) | c3_1(a693) | hskp6 | hskp30), inference(lemma,lemma(discharge,[]))).
% 1.99/1.57 tff(1229,plain,
% 1.99/1.57 (hskp20),
% 1.99/1.57 inference(unit_resolution,[status(thm)],[1228, 177, 1187, 1186, 164, 153, 1188, 102])).
% 1.99/1.58 tff(1230,plain,
% 1.99/1.58 (~c0_1(a754)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[595, 1229])).
% 1.99/1.58 tff(1231,plain,
% 1.99/1.58 (c2_1(a754)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[190, 1229])).
% 1.99/1.58 tff(1232,plain,
% 1.99/1.58 (~c3_1(a754)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[668, 1229])).
% 1.99/1.58 tff(1233,assumption,(c3_1(a712)), introduced(assumption)).
% 1.99/1.58 tff(1234,plain,
% 1.99/1.58 (~c2_1(a725)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[1200, 1233, 1188])).
% 1.99/1.58 tff(1235,plain,
% 1.99/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a754) | c0_1(a712) | c1_1(a712) | c2_1(a712) | (~ndr1_0) | (~c3_1(a712)) | c1_1(a754) | (~c2_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a754) | c0_1(a712) | c1_1(a712) | c2_1(a712) | (~ndr1_0) | (~c3_1(a712)) | c1_1(a754) | (~c2_1(a754)))),
% 1.99/1.58 inference(rewrite,[status(thm)],[])).
% 1.99/1.58 tff(1236,plain,
% 1.99/1.58 (((~ndr1_0) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)) | c1_1(a712) | c2_1(a712) | (~c3_1(a712)) | c2_1(a712) | c0_1(a712) | (~c3_1(a712))) <=> (c3_1(a754) | c0_1(a712) | c1_1(a712) | c2_1(a712) | (~ndr1_0) | (~c3_1(a712)) | c1_1(a754) | (~c2_1(a754)))),
% 1.99/1.58 inference(rewrite,[status(thm)],[])).
% 1.99/1.58 tff(1237,plain,
% 1.99/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)) | c1_1(a712) | c2_1(a712) | (~c3_1(a712)) | c2_1(a712) | c0_1(a712) | (~c3_1(a712)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a754) | c0_1(a712) | c1_1(a712) | c2_1(a712) | (~ndr1_0) | (~c3_1(a712)) | c1_1(a754) | (~c2_1(a754))))),
% 1.99/1.58 inference(monotonicity,[status(thm)],[1236])).
% 1.99/1.58 tff(1238,plain,
% 1.99/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)) | c1_1(a712) | c2_1(a712) | (~c3_1(a712)) | c2_1(a712) | c0_1(a712) | (~c3_1(a712)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a754) | c0_1(a712) | c1_1(a712) | c2_1(a712) | (~ndr1_0) | (~c3_1(a712)) | c1_1(a754) | (~c2_1(a754)))),
% 1.99/1.58 inference(transitivity,[status(thm)],[1237, 1235])).
% 1.99/1.58 tff(1239,plain,
% 1.99/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)) | c1_1(a712) | c2_1(a712) | (~c3_1(a712)) | c2_1(a712) | c0_1(a712) | (~c3_1(a712)))),
% 1.99/1.58 inference(quant_inst,[status(thm)],[])).
% 1.99/1.58 tff(1240,plain,
% 1.99/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a754) | c0_1(a712) | c1_1(a712) | c2_1(a712) | (~ndr1_0) | (~c3_1(a712)) | c1_1(a754) | (~c2_1(a754))),
% 1.99/1.58 inference(modus_ponens,[status(thm)],[1239, 1238])).
% 1.99/1.58 tff(1241,plain,
% 1.99/1.58 ((~c3_1(a712)) | c1_1(a754)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[1240, 227, 387, 178, 1188, 1187, 1186, 948])).
% 1.99/1.58 tff(1242,plain,
% 1.99/1.58 (c1_1(a754)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[1241, 1233])).
% 1.99/1.58 tff(1243,plain,
% 1.99/1.58 (c2_1(a725) | (~c1_1(a754))),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[545, 227, 177, 179, 178, 578, 1037, 301])).
% 1.99/1.58 tff(1244,plain,
% 1.99/1.58 ($false),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[1243, 1242, 1234])).
% 1.99/1.58 tff(1245,plain,((~c3_1(a712)) | hskp6 | c0_1(a754) | c3_1(a754) | c0_1(a725) | c3_1(a725) | (~c2_1(a754)) | c0_1(a712) | c1_1(a712) | c2_1(a712) | c1_1(a725)), inference(lemma,lemma(discharge,[]))).
% 1.99/1.58 tff(1246,plain,
% 1.99/1.58 (~c3_1(a712)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[1245, 1230, 177, 1232, 152, 140, 1231, 1188, 1187, 1186, 146])).
% 1.99/1.58 tff(1247,plain,
% 1.99/1.58 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | c0_1(a754) | c3_1(a754) | c0_1(a712) | c2_1(a712) | (~ndr1_0) | c3_1(a712) | (~c1_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c0_1(a754) | c3_1(a754) | c0_1(a712) | c2_1(a712) | (~ndr1_0) | c3_1(a712) | (~c1_1(a754)))),
% 1.99/1.58 inference(rewrite,[status(thm)],[])).
% 1.99/1.58 tff(1248,plain,
% 1.99/1.58 ((hskp6 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)) | c3_1(a712) | c0_1(a712) | c2_1(a712)) <=> (hskp6 | c0_1(a754) | c3_1(a754) | c0_1(a712) | c2_1(a712) | (~ndr1_0) | c3_1(a712) | (~c1_1(a754)))),
% 1.99/1.58 inference(rewrite,[status(thm)],[])).
% 1.99/1.58 tff(1249,plain,
% 1.99/1.58 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)) | c3_1(a712) | c0_1(a712) | c2_1(a712))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | c0_1(a754) | c3_1(a754) | c0_1(a712) | c2_1(a712) | (~ndr1_0) | c3_1(a712) | (~c1_1(a754))))),
% 1.99/1.58 inference(monotonicity,[status(thm)],[1248])).
% 1.99/1.58 tff(1250,plain,
% 1.99/1.58 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)) | c3_1(a712) | c0_1(a712) | c2_1(a712))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c0_1(a754) | c3_1(a754) | c0_1(a712) | c2_1(a712) | (~ndr1_0) | c3_1(a712) | (~c1_1(a754)))),
% 1.99/1.58 inference(transitivity,[status(thm)],[1249, 1247])).
% 1.99/1.58 tff(1251,plain,
% 1.99/1.58 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)) | c3_1(a712) | c0_1(a712) | c2_1(a712))),
% 1.99/1.58 inference(quant_inst,[status(thm)],[])).
% 1.99/1.58 tff(1252,plain,
% 1.99/1.58 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c0_1(a754) | c3_1(a754) | c0_1(a712) | c2_1(a712) | (~ndr1_0) | c3_1(a712) | (~c1_1(a754))),
% 1.99/1.58 inference(modus_ponens,[status(thm)],[1251, 1250])).
% 1.99/1.58 tff(1253,plain,
% 1.99/1.58 (~c1_1(a754)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[1252, 227, 177, 1230, 1232, 1188, 1186, 301, 1246])).
% 1.99/1.58 tff(1254,plain,
% 1.99/1.58 (~hskp23),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[430, 1253, 1231, 1230, 62])).
% 1.99/1.58 tff(1255,plain,
% 1.99/1.58 (c3_1(a712)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[1218, 1036, 1188, 177])).
% 1.99/1.58 tff(1256,plain,
% 1.99/1.58 ($false),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[1200, 1039, 1255, 1188])).
% 1.99/1.58 tff(1257,plain,(hskp27 | c0_1(a712) | c1_1(a725) | c3_1(a725) | c1_1(a712) | c2_1(a712) | hskp6 | c0_1(a725)), inference(lemma,lemma(discharge,[]))).
% 1.99/1.58 tff(1258,plain,
% 1.99/1.58 (hskp27),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[1257, 177, 146, 140, 1187, 1186, 1188, 152])).
% 1.99/1.58 tff(1259,plain,
% 1.99/1.58 (c1_1(a691)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[267, 1258])).
% 1.99/1.58 tff(1260,plain,
% 1.99/1.58 (c0_1(a691)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[278, 1258])).
% 1.99/1.58 tff(1261,plain,
% 1.99/1.58 (~hskp24),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[385, 1232, 62, 164, 153, 102, 177, 1230])).
% 1.99/1.58 tff(1262,plain,
% 1.99/1.58 (hskp23 | (~c2_1(a691))),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[1063, 227, 1261, 1260, 1259, 163])).
% 1.99/1.58 tff(1263,plain,
% 1.99/1.58 (~c2_1(a691)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[1262, 1254])).
% 1.99/1.58 tff(1264,plain,
% 1.99/1.58 (c2_1(a773)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[730, 1211])).
% 1.99/1.58 tff(1265,plain,
% 1.99/1.58 (c1_1(a773)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[741, 1211])).
% 1.99/1.58 tff(1266,plain,
% 1.99/1.58 (c3_1(a691)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[256, 1258])).
% 1.99/1.58 tff(1267,plain,
% 1.99/1.58 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c3_1(a773)) | (~c2_1(a773)) | (~c1_1(a773)) | (~c3_1(a691)) | (~c0_1(a691)) | c2_1(a691))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp28 | (~ndr1_0) | (~c3_1(a773)) | (~c2_1(a773)) | (~c1_1(a773)) | (~c3_1(a691)) | (~c0_1(a691)) | c2_1(a691))),
% 1.99/1.58 inference(rewrite,[status(thm)],[])).
% 1.99/1.58 tff(1268,plain,
% 1.99/1.58 ((hskp28 | (~ndr1_0) | (~c2_1(a773)) | (~c3_1(a773)) | (~c1_1(a773)) | c2_1(a691) | (~c3_1(a691)) | (~c0_1(a691))) <=> (hskp28 | (~ndr1_0) | (~c3_1(a773)) | (~c2_1(a773)) | (~c1_1(a773)) | (~c3_1(a691)) | (~c0_1(a691)) | c2_1(a691))),
% 1.99/1.58 inference(rewrite,[status(thm)],[])).
% 1.99/1.58 tff(1269,plain,
% 1.99/1.58 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a773)) | (~c3_1(a773)) | (~c1_1(a773)) | c2_1(a691) | (~c3_1(a691)) | (~c0_1(a691)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c3_1(a773)) | (~c2_1(a773)) | (~c1_1(a773)) | (~c3_1(a691)) | (~c0_1(a691)) | c2_1(a691)))),
% 1.99/1.58 inference(monotonicity,[status(thm)],[1268])).
% 1.99/1.58 tff(1270,plain,
% 1.99/1.58 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a773)) | (~c3_1(a773)) | (~c1_1(a773)) | c2_1(a691) | (~c3_1(a691)) | (~c0_1(a691)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp28 | (~ndr1_0) | (~c3_1(a773)) | (~c2_1(a773)) | (~c1_1(a773)) | (~c3_1(a691)) | (~c0_1(a691)) | c2_1(a691))),
% 1.99/1.58 inference(transitivity,[status(thm)],[1269, 1267])).
% 1.99/1.58 tff(1271,plain,
% 1.99/1.58 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a773)) | (~c3_1(a773)) | (~c1_1(a773)) | c2_1(a691) | (~c3_1(a691)) | (~c0_1(a691)))),
% 1.99/1.58 inference(quant_inst,[status(thm)],[])).
% 1.99/1.58 tff(1272,plain,
% 1.99/1.58 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp28 | (~ndr1_0) | (~c3_1(a773)) | (~c2_1(a773)) | (~c1_1(a773)) | (~c3_1(a691)) | (~c0_1(a691)) | c2_1(a691)),
% 1.99/1.58 inference(modus_ponens,[status(thm)],[1271, 1270])).
% 1.99/1.58 tff(1273,plain,
% 1.99/1.58 (~c3_1(a773)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[1272, 227, 62, 1260, 1266, 1265, 1264, 61, 1263])).
% 1.99/1.58 tff(1274,plain,
% 1.99/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a712) | c1_1(a712) | c2_1(a712) | c0_1(a698) | c2_1(a698) | (~ndr1_0) | (~c1_1(a698)) | c3_1(a712))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a712) | c1_1(a712) | c2_1(a712) | c0_1(a698) | c2_1(a698) | (~ndr1_0) | (~c1_1(a698)) | c3_1(a712))),
% 1.99/1.58 inference(rewrite,[status(thm)],[])).
% 1.99/1.58 tff(1275,plain,
% 1.99/1.58 (((~ndr1_0) | c0_1(a698) | c2_1(a698) | (~c1_1(a698)) | c3_1(a712) | c1_1(a712) | c2_1(a712) | c3_1(a712) | c2_1(a712) | c0_1(a712)) <=> (c0_1(a712) | c1_1(a712) | c2_1(a712) | c0_1(a698) | c2_1(a698) | (~ndr1_0) | (~c1_1(a698)) | c3_1(a712))),
% 1.99/1.58 inference(rewrite,[status(thm)],[])).
% 1.99/1.58 tff(1276,plain,
% 1.99/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a698) | c2_1(a698) | (~c1_1(a698)) | c3_1(a712) | c1_1(a712) | c2_1(a712) | c3_1(a712) | c2_1(a712) | c0_1(a712))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a712) | c1_1(a712) | c2_1(a712) | c0_1(a698) | c2_1(a698) | (~ndr1_0) | (~c1_1(a698)) | c3_1(a712)))),
% 1.99/1.58 inference(monotonicity,[status(thm)],[1275])).
% 1.99/1.58 tff(1277,plain,
% 1.99/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a698) | c2_1(a698) | (~c1_1(a698)) | c3_1(a712) | c1_1(a712) | c2_1(a712) | c3_1(a712) | c2_1(a712) | c0_1(a712))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a712) | c1_1(a712) | c2_1(a712) | c0_1(a698) | c2_1(a698) | (~ndr1_0) | (~c1_1(a698)) | c3_1(a712))),
% 1.99/1.58 inference(transitivity,[status(thm)],[1276, 1274])).
% 1.99/1.58 tff(1278,plain,
% 1.99/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a698) | c2_1(a698) | (~c1_1(a698)) | c3_1(a712) | c1_1(a712) | c2_1(a712) | c3_1(a712) | c2_1(a712) | c0_1(a712))),
% 1.99/1.58 inference(quant_inst,[status(thm)],[])).
% 1.99/1.58 tff(1279,plain,
% 1.99/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a712) | c1_1(a712) | c2_1(a712) | c0_1(a698) | c2_1(a698) | (~ndr1_0) | (~c1_1(a698)) | c3_1(a712)),
% 1.99/1.58 inference(modus_ponens,[status(thm)],[1278, 1277])).
% 1.99/1.58 tff(1280,plain,
% 1.99/1.58 (~c1_1(a698)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[1279, 227, 1188, 1187, 1186, 926, 925, 122, 1246])).
% 1.99/1.58 tff(1281,plain,
% 1.99/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a754) | c0_1(a698) | c2_1(a698) | (~c3_1(a698)) | (~ndr1_0) | c1_1(a698) | c1_1(a754) | (~c2_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a754) | c0_1(a698) | c2_1(a698) | (~c3_1(a698)) | (~ndr1_0) | c1_1(a698) | c1_1(a754) | (~c2_1(a754)))),
% 1.99/1.58 inference(rewrite,[status(thm)],[])).
% 1.99/1.58 tff(1282,plain,
% 1.99/1.58 (((~ndr1_0) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)) | c1_1(a698) | c2_1(a698) | (~c3_1(a698)) | c2_1(a698) | c0_1(a698) | (~c3_1(a698))) <=> (c3_1(a754) | c0_1(a698) | c2_1(a698) | (~c3_1(a698)) | (~ndr1_0) | c1_1(a698) | c1_1(a754) | (~c2_1(a754)))),
% 1.99/1.58 inference(rewrite,[status(thm)],[])).
% 1.99/1.58 tff(1283,plain,
% 1.99/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)) | c1_1(a698) | c2_1(a698) | (~c3_1(a698)) | c2_1(a698) | c0_1(a698) | (~c3_1(a698)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a754) | c0_1(a698) | c2_1(a698) | (~c3_1(a698)) | (~ndr1_0) | c1_1(a698) | c1_1(a754) | (~c2_1(a754))))),
% 1.99/1.58 inference(monotonicity,[status(thm)],[1282])).
% 1.99/1.58 tff(1284,plain,
% 1.99/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)) | c1_1(a698) | c2_1(a698) | (~c3_1(a698)) | c2_1(a698) | c0_1(a698) | (~c3_1(a698)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a754) | c0_1(a698) | c2_1(a698) | (~c3_1(a698)) | (~ndr1_0) | c1_1(a698) | c1_1(a754) | (~c2_1(a754)))),
% 1.99/1.58 inference(transitivity,[status(thm)],[1283, 1281])).
% 1.99/1.58 tff(1285,plain,
% 1.99/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)) | c1_1(a698) | c2_1(a698) | (~c3_1(a698)) | c2_1(a698) | c0_1(a698) | (~c3_1(a698)))),
% 1.99/1.58 inference(quant_inst,[status(thm)],[])).
% 1.99/1.58 tff(1286,plain,
% 1.99/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a754) | c0_1(a698) | c2_1(a698) | (~c3_1(a698)) | (~ndr1_0) | c1_1(a698) | c1_1(a754) | (~c2_1(a754))),
% 1.99/1.58 inference(modus_ponens,[status(thm)],[1285, 1284])).
% 1.99/1.58 tff(1287,plain,
% 1.99/1.58 (~c3_1(a698)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[1286, 227, 1231, 1232, 926, 925, 948, 1280, 1253])).
% 1.99/1.58 tff(1288,plain,
% 1.99/1.58 (~c0_1(a773)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[754, 1211])).
% 1.99/1.58 tff(1289,plain,
% 1.99/1.58 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | c0_1(a773) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c3_1(a773) | (~c1_1(a773)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c0_1(a773) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c3_1(a773) | (~c1_1(a773)))),
% 1.99/1.58 inference(rewrite,[status(thm)],[])).
% 1.99/1.58 tff(1290,plain,
% 1.99/1.58 ((hskp6 | (~ndr1_0) | c3_1(a773) | c0_1(a773) | (~c1_1(a773)) | c3_1(a698) | c0_1(a698) | c2_1(a698)) <=> (hskp6 | c0_1(a773) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c3_1(a773) | (~c1_1(a773)))),
% 1.99/1.58 inference(rewrite,[status(thm)],[])).
% 1.99/1.58 tff(1291,plain,
% 1.99/1.58 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a773) | c0_1(a773) | (~c1_1(a773)) | c3_1(a698) | c0_1(a698) | c2_1(a698))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | c0_1(a773) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c3_1(a773) | (~c1_1(a773))))),
% 1.99/1.58 inference(monotonicity,[status(thm)],[1290])).
% 1.99/1.58 tff(1292,plain,
% 1.99/1.58 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a773) | c0_1(a773) | (~c1_1(a773)) | c3_1(a698) | c0_1(a698) | c2_1(a698))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c0_1(a773) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c3_1(a773) | (~c1_1(a773)))),
% 1.99/1.58 inference(transitivity,[status(thm)],[1291, 1289])).
% 1.99/1.58 tff(1293,plain,
% 1.99/1.58 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a773) | c0_1(a773) | (~c1_1(a773)) | c3_1(a698) | c0_1(a698) | c2_1(a698))),
% 1.99/1.58 inference(quant_inst,[status(thm)],[])).
% 1.99/1.58 tff(1294,plain,
% 1.99/1.58 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c0_1(a773) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c3_1(a773) | (~c1_1(a773))),
% 1.99/1.58 inference(modus_ponens,[status(thm)],[1293, 1292])).
% 1.99/1.58 tff(1295,plain,
% 1.99/1.58 ($false),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[1294, 227, 177, 1265, 1288, 926, 925, 1287, 301, 1273])).
% 1.99/1.58 tff(1296,plain,(hskp6 | c0_1(a698) | c2_1(a698) | hskp28 | c0_1(a712) | c1_1(a712) | c2_1(a712) | c1_1(a693) | c3_1(a693) | hskp30), inference(lemma,lemma(discharge,[]))).
% 1.99/1.58 tff(1297,plain,
% 1.99/1.58 (hskp6),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[1296, 1188, 925, 62, 926, 1187, 1186, 164, 153, 102])).
% 1.99/1.58 tff(1298,plain,
% 1.99/1.58 (c0_1(a702)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[90, 1297])).
% 1.99/1.58 tff(1299,plain,
% 1.99/1.58 (c3_1(a702)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[79, 1297])).
% 1.99/1.58 tff(1300,plain,
% 1.99/1.58 ($false),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[763, 1299, 1298, 1211, 717, 62])).
% 1.99/1.58 tff(1301,plain,(c0_1(a712) | c2_1(a702) | hskp28 | c2_1(a698) | c0_1(a698) | c1_1(a712) | c2_1(a712) | c1_1(a693) | c3_1(a693) | hskp30), inference(lemma,lemma(discharge,[]))).
% 1.99/1.58 tff(1302,plain,
% 1.99/1.58 ($false),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[1301, 1185, 1179, 62, 925, 926, 717, 1173, 164, 153, 102])).
% 1.99/1.58 tff(1303,plain,(c2_1(a702) | hskp28 | c2_1(a698) | c0_1(a698) | c1_1(a693) | c3_1(a693) | hskp30 | c3_1(a697)), inference(lemma,lemma(discharge,[]))).
% 1.99/1.58 tff(1304,plain,
% 1.99/1.58 (c2_1(a702)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[1303, 926, 925, 62, 164, 153, 102, 175])).
% 1.99/1.58 tff(1305,plain,
% 1.99/1.58 (~hskp6),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[68, 1304])).
% 1.99/1.58 tff(1306,assumption,(hskp9), introduced(assumption)).
% 1.99/1.58 tff(1307,plain,
% 1.99/1.58 (~c0_1(a712)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[1178, 1306])).
% 1.99/1.58 tff(1308,plain,
% 1.99/1.58 (~c1_1(a712)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[1172, 1306])).
% 1.99/1.58 tff(1309,plain,
% 1.99/1.58 (~c2_1(a712)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[1184, 1306])).
% 1.99/1.58 tff(1310,plain,
% 1.99/1.58 ($false),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[1296, 1309, 1308, 925, 62, 926, 177, 1307, 164, 153, 102])).
% 1.99/1.58 tff(1311,plain,((~hskp9) | c2_1(a698) | hskp28 | c0_1(a698) | hskp6 | c1_1(a693) | c3_1(a693) | hskp30), inference(lemma,lemma(discharge,[]))).
% 1.99/1.58 tff(1312,plain,
% 1.99/1.58 (~hskp9),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[1311, 926, 62, 925, 1305, 164, 153, 102])).
% 1.99/1.58 tff(1313,plain,
% 1.99/1.58 (c2_1(a754)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[290, 179, 102, 1305, 178])).
% 1.99/1.58 tff(1314,plain,
% 1.99/1.58 ($false),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[1107, 1313, 179, 1305, 1312, 62, 178, 153, 926, 925, 102, 175, 164])).
% 1.99/1.58 tff(1315,plain,(c0_1(a754) | hskp28 | c3_1(a754) | c3_1(a693) | c0_1(a698) | c2_1(a698) | hskp30 | c3_1(a697) | c1_1(a693)), inference(lemma,lemma(discharge,[]))).
% 1.99/1.58 tff(1316,plain,
% 1.99/1.58 (c0_1(a754)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[1315, 178, 62, 153, 926, 925, 102, 175, 164])).
% 1.99/1.58 tff(1317,plain,
% 1.99/1.58 (~hskp20),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[595, 1316])).
% 1.99/1.58 tff(1318,plain,
% 1.99/1.58 (~hskp27),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[288, 1317, 102])).
% 1.99/1.58 tff(1319,plain,
% 1.99/1.58 (c1_1(a754)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[614, 1318, 1316])).
% 1.99/1.58 tff(1320,plain,
% 1.99/1.58 (c2_1(a725)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[642, 1318, 1305])).
% 1.99/1.58 tff(1321,plain,
% 1.99/1.58 (~hskp23),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[586, 1320, 152, 146, 62])).
% 1.99/1.58 tff(1322,plain,
% 1.99/1.58 (hskp24),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[1054, 1321, 1318, 152, 146, 140, 175, 1305, 926, 925])).
% 1.99/1.58 tff(1323,plain,
% 1.99/1.58 (~c3_1(a764)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[307, 1322])).
% 1.99/1.58 tff(1324,plain,
% 1.99/1.58 (~c2_1(a764)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[313, 1322])).
% 1.99/1.58 tff(1325,plain,
% 1.99/1.58 (hskp1),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[372, 1317, 102])).
% 1.99/1.58 tff(1326,plain,
% 1.99/1.58 (c2_1(a693)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[383, 1325])).
% 1.99/1.58 tff(1327,plain,
% 1.99/1.58 (c2_1(a754)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[634, 1326, 1316])).
% 1.99/1.58 tff(1328,plain,
% 1.99/1.58 (c1_1(a764)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[324, 1322])).
% 1.99/1.58 tff(1329,plain,
% 1.99/1.58 ($false),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[660, 227, 62, 1328, 1327, 1324, 1323, 178, 625, 1319])).
% 1.99/1.58 tff(1330,plain,(c3_1(a754) | hskp28 | c3_1(a697) | c0_1(a698) | c2_1(a698) | c1_1(a693) | c3_1(a693) | hskp30), inference(lemma,lemma(discharge,[]))).
% 1.99/1.58 tff(1331,plain,
% 1.99/1.58 (c3_1(a754)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[1330, 926, 175, 62, 925, 164, 153, 102])).
% 1.99/1.58 tff(1332,plain,
% 1.99/1.58 (~hskp20),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[668, 1331])).
% 1.99/1.58 tff(1333,plain,
% 1.99/1.58 (~hskp27),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[288, 1332, 102])).
% 1.99/1.58 tff(1334,plain,
% 1.99/1.58 (c2_1(a725)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[642, 1333, 1305])).
% 1.99/1.58 tff(1335,plain,
% 1.99/1.58 (c3_1(a698)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[962, 1333, 926, 1305])).
% 1.99/1.58 tff(1336,plain,
% 1.99/1.58 (~hskp4),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[1045, 1335])).
% 1.99/1.58 tff(1337,plain,
% 1.99/1.58 (hskp3),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[554, 1336, 1334])).
% 1.99/1.58 tff(1338,plain,
% 1.99/1.58 (c0_1(a697)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[508, 1337])).
% 1.99/1.58 tff(1339,plain,
% 1.99/1.58 (c1_1(a697)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[696, 1338, 1333])).
% 1.99/1.58 tff(1340,plain,
% 1.99/1.58 (~hskp23),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[586, 1334, 152, 146, 62])).
% 1.99/1.58 tff(1341,plain,
% 1.99/1.58 (hskp24),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[1054, 1340, 1333, 152, 146, 140, 175, 1305, 926, 925])).
% 1.99/1.58 tff(1342,plain,
% 1.99/1.58 (~c3_1(a764)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[307, 1341])).
% 1.99/1.58 tff(1343,plain,
% 1.99/1.58 (~c2_1(a764)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[313, 1341])).
% 1.99/1.58 tff(1344,plain,
% 1.99/1.58 (c2_1(a697)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[527, 1337])).
% 1.99/1.58 tff(1345,plain,
% 1.99/1.58 (c1_1(a764)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[324, 1341])).
% 1.99/1.58 tff(1346,plain,
% 1.99/1.58 ($false),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[710, 227, 62, 1345, 1344, 1343, 1342, 175, 625, 1339])).
% 1.99/1.58 tff(1347,plain,(c0_1(a698) | hskp28 | c3_1(a697) | c2_1(a698) | hskp30 | c1_1(a693) | c3_1(a693)), inference(lemma,lemma(discharge,[]))).
% 1.99/1.58 tff(1348,plain,
% 1.99/1.58 ($false),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[1347, 924, 918, 175, 62, 102, 164, 153])).
% 1.99/1.58 tff(1349,plain,(c3_1(a697) | hskp28 | hskp30 | c1_1(a693) | c3_1(a693)), inference(lemma,lemma(discharge,[]))).
% 1.99/1.58 tff(1350,plain,
% 1.99/1.58 (c3_1(a697)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[1349, 164, 102, 62, 153])).
% 1.99/1.58 tff(1351,plain,
% 1.99/1.58 (((~hskp3) | (~c3_1(a697))) <=> ((~hskp3) | (~c3_1(a697)))),
% 1.99/1.58 inference(rewrite,[status(thm)],[])).
% 1.99/1.58 tff(1352,plain,
% 1.99/1.58 (((~c3_1(a697)) | (~hskp3)) <=> ((~hskp3) | (~c3_1(a697)))),
% 1.99/1.58 inference(rewrite,[status(thm)],[])).
% 1.99/1.58 tff(1353,axiom,((~c3_1(a697)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause127')).
% 1.99/1.58 tff(1354,plain,
% 1.99/1.58 ((~hskp3) | (~c3_1(a697))),
% 1.99/1.58 inference(modus_ponens,[status(thm)],[1353, 1352])).
% 1.99/1.58 tff(1355,plain,
% 1.99/1.58 ((~hskp3) | (~c3_1(a697))),
% 1.99/1.58 inference(modus_ponens,[status(thm)],[1354, 1351])).
% 1.99/1.58 tff(1356,plain,
% 1.99/1.58 (~hskp3),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[1355, 1350])).
% 1.99/1.58 tff(1357,assumption,(hskp4), introduced(assumption)).
% 1.99/1.58 tff(1358,plain,
% 1.99/1.58 (~c3_1(a698)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[1045, 1357])).
% 1.99/1.58 tff(1359,plain,
% 1.99/1.58 (~c2_1(a698)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[923, 1357])).
% 1.99/1.58 tff(1360,plain,
% 1.99/1.58 (~c0_1(a698)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[917, 1357])).
% 1.99/1.58 tff(1361,plain,
% 1.99/1.58 (~hskp9),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[1311, 1359, 62, 177, 1360, 164, 153, 102])).
% 1.99/1.58 tff(1362,plain,
% 1.99/1.58 ($false),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[1080, 227, 1361, 1356, 1360, 1359, 1358, 1008])).
% 1.99/1.58 tff(1363,plain,((~hskp4) | hskp28 | hskp6 | c1_1(a693) | c3_1(a693) | hskp30), inference(lemma,lemma(discharge,[]))).
% 1.99/1.58 tff(1364,plain,
% 1.99/1.58 (~hskp4),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[1363, 177, 62, 164, 153, 102])).
% 1.99/1.58 tff(1365,plain,
% 1.99/1.58 (~c2_1(a725)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[554, 1364, 1356])).
% 1.99/1.58 tff(1366,plain,
% 1.99/1.58 (hskp27),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[642, 1365, 177])).
% 1.99/1.58 tff(1367,plain,
% 1.99/1.58 (hskp20),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[288, 1366, 102])).
% 1.99/1.58 tff(1368,plain,
% 1.99/1.58 (~c0_1(a754)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[595, 1367])).
% 1.99/1.58 tff(1369,plain,
% 1.99/1.58 (c0_1(a754)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[290, 180, 102, 177, 178])).
% 1.99/1.58 tff(1370,plain,
% 1.99/1.58 (~c2_1(a693)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[634, 180, 1369])).
% 1.99/1.58 tff(1371,plain,
% 1.99/1.58 ($false),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[383, 983, 1370])).
% 1.99/1.58 tff(1372,plain,(c2_1(a754) | hskp30 | hskp28 | c3_1(a754) | c1_1(a693) | c3_1(a693) | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.99/1.58 tff(1373,plain,
% 1.99/1.58 (c2_1(a754)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[1372, 177, 62, 178, 164, 153, 102])).
% 1.99/1.58 tff(1374,plain,
% 1.99/1.58 (hskp4 | c0_1(a754) | c1_1(a754)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[448, 227, 1356, 1373, 442])).
% 1.99/1.58 tff(1375,plain,
% 1.99/1.58 (c1_1(a754)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[1374, 1368, 1364])).
% 1.99/1.58 tff(1376,plain,
% 1.99/1.58 ($false),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[1105, 1375, 1368, 177, 1365])).
% 1.99/1.58 tff(1377,plain,(hskp6 | c3_1(a754) | hskp30 | hskp28 | c1_1(a693) | c3_1(a693)), inference(lemma,lemma(discharge,[]))).
% 1.99/1.58 tff(1378,plain,
% 1.99/1.58 (hskp6),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[1377, 178, 102, 62, 164, 153])).
% 1.99/1.58 tff(1379,plain,
% 1.99/1.58 (~c2_1(a702)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[68, 1378])).
% 1.99/1.58 tff(1380,plain,
% 1.99/1.58 (c0_1(a702)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[90, 1378])).
% 1.99/1.58 tff(1381,plain,
% 1.99/1.58 (c3_1(a702)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[79, 1378])).
% 1.99/1.58 tff(1382,plain,
% 1.99/1.58 (~hskp25),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[763, 1381, 1380, 1379, 62])).
% 1.99/1.58 tff(1383,plain,
% 1.99/1.58 (hskp22),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[778, 1382, 62])).
% 1.99/1.58 tff(1384,plain,
% 1.99/1.58 (~c2_1(a761)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[784, 1383])).
% 1.99/1.58 tff(1385,plain,
% 1.99/1.58 (~c0_1(a761)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[790, 1383])).
% 1.99/1.58 tff(1386,plain,
% 1.99/1.58 (c1_1(a761)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[801, 1383])).
% 1.99/1.58 tff(1387,plain,
% 1.99/1.58 (c2_1(a725)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[808, 227, 1386, 1385, 1384, 152, 146, 140, 122])).
% 1.99/1.58 tff(1388,plain,
% 1.99/1.58 (hskp4),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[554, 1387, 1356])).
% 1.99/1.58 tff(1389,plain,
% 1.99/1.58 (~c3_1(a698)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[1045, 1388])).
% 1.99/1.58 tff(1390,plain,
% 1.99/1.58 (~c0_1(a698)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[917, 1388])).
% 1.99/1.58 tff(1391,plain,
% 1.99/1.58 (hskp27),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[897, 227, 1386, 1385, 1384, 152, 146, 891, 1387])).
% 1.99/1.58 tff(1392,plain,
% 1.99/1.58 (hskp20),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[288, 1391, 102])).
% 1.99/1.58 tff(1393,plain,
% 1.99/1.58 (~c0_1(a754)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[595, 1392])).
% 1.99/1.58 tff(1394,plain,
% 1.99/1.58 (c2_1(a754)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[190, 1392])).
% 1.99/1.58 tff(1395,plain,
% 1.99/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a754) | c3_1(a754) | c2_1(a702) | c0_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c3_1(a702)) | (~c0_1(a702)) | (~c2_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a754) | c3_1(a754) | c2_1(a702) | c0_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c3_1(a702)) | (~c0_1(a702)) | (~c2_1(a754)))),
% 1.99/1.58 inference(rewrite,[status(thm)],[])).
% 1.99/1.58 tff(1396,plain,
% 1.99/1.58 (((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a698) | c0_1(a698) | (~c1_1(a698))) <=> (c0_1(a754) | c3_1(a754) | c2_1(a702) | c0_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c3_1(a702)) | (~c0_1(a702)) | (~c2_1(a754)))),
% 1.99/1.58 inference(rewrite,[status(thm)],[])).
% 1.99/1.58 tff(1397,plain,
% 1.99/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a698) | c0_1(a698) | (~c1_1(a698)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a754) | c3_1(a754) | c2_1(a702) | c0_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c3_1(a702)) | (~c0_1(a702)) | (~c2_1(a754))))),
% 1.99/1.58 inference(monotonicity,[status(thm)],[1396])).
% 1.99/1.58 tff(1398,plain,
% 1.99/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a698) | c0_1(a698) | (~c1_1(a698)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a754) | c3_1(a754) | c2_1(a702) | c0_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c3_1(a702)) | (~c0_1(a702)) | (~c2_1(a754)))),
% 1.99/1.58 inference(transitivity,[status(thm)],[1397, 1395])).
% 1.99/1.58 tff(1399,plain,
% 1.99/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a698) | c0_1(a698) | (~c1_1(a698)))),
% 1.99/1.58 inference(quant_inst,[status(thm)],[])).
% 1.99/1.58 tff(1400,plain,
% 1.99/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a754) | c3_1(a754) | c2_1(a702) | c0_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c3_1(a702)) | (~c0_1(a702)) | (~c2_1(a754))),
% 1.99/1.58 inference(modus_ponens,[status(thm)],[1399, 1398])).
% 1.99/1.58 tff(1401,plain,
% 1.99/1.58 (~c1_1(a698)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[1400, 227, 1394, 1380, 1381, 1393, 178, 1379, 1390, 1389, 174])).
% 1.99/1.58 tff(1402,plain,
% 1.99/1.58 (~c2_1(a698)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[923, 1388])).
% 1.99/1.58 tff(1403,plain,
% 1.99/1.58 ($false),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[976, 227, 1386, 1385, 1384, 1390, 1402, 1389, 122, 1401])).
% 1.99/1.58 tff(1404,plain,(c3_1(a754) | hskp30 | hskp28 | c1_1(a693) | c3_1(a693)), inference(lemma,lemma(discharge,[]))).
% 1.99/1.58 tff(1405,plain,
% 1.99/1.58 (c3_1(a754)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[1404, 164, 62, 102, 153])).
% 1.99/1.58 tff(1406,plain,
% 1.99/1.58 (~hskp20),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[668, 1405])).
% 1.99/1.58 tff(1407,plain,
% 1.99/1.58 (hskp1),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[372, 1406, 102])).
% 1.99/1.58 tff(1408,plain,
% 1.99/1.58 (c2_1(a693)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[383, 1407])).
% 1.99/1.58 tff(1409,plain,
% 1.99/1.58 (~hskp27),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[288, 1406, 102])).
% 1.99/1.58 tff(1410,plain,
% 1.99/1.58 (~c0_1(a693)),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[677, 1409, 164])).
% 1.99/1.58 tff(1411,plain,
% 1.99/1.58 (hskp4),
% 1.99/1.58 inference(unit_resolution,[status(thm)],[687, 1410, 1356, 1408])).
% 1.99/1.58 tff(1412,plain,
% 1.99/1.58 (hskp6),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[1363, 1411, 62, 164, 153, 102])).
% 1.99/1.59 tff(1413,plain,
% 1.99/1.59 (~c0_1(a698)),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[917, 1411])).
% 1.99/1.59 tff(1414,plain,
% 1.99/1.59 (~c2_1(a698)),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[923, 1411])).
% 1.99/1.59 tff(1415,plain,
% 1.99/1.59 (c2_1(a702)),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[978, 1414, 1406, 62, 1413, 164, 153, 102])).
% 1.99/1.59 tff(1416,plain,
% 1.99/1.59 ($false),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[68, 1415, 1412])).
% 1.99/1.59 tff(1417,plain,(c1_1(a693) | hskp28 | c3_1(a693) | hskp30), inference(lemma,lemma(discharge,[]))).
% 1.99/1.59 tff(1418,plain,
% 1.99/1.59 (c1_1(a693)),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[1417, 153, 62, 102])).
% 1.99/1.59 tff(1419,plain,
% 1.99/1.59 (((~hskp1) | (~c1_1(a693))) <=> ((~hskp1) | (~c1_1(a693)))),
% 1.99/1.59 inference(rewrite,[status(thm)],[])).
% 1.99/1.59 tff(1420,plain,
% 1.99/1.59 (((~c1_1(a693)) | (~hskp1)) <=> ((~hskp1) | (~c1_1(a693)))),
% 1.99/1.59 inference(rewrite,[status(thm)],[])).
% 1.99/1.59 tff(1421,axiom,((~c1_1(a693)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause129')).
% 1.99/1.59 tff(1422,plain,
% 1.99/1.59 ((~hskp1) | (~c1_1(a693))),
% 1.99/1.59 inference(modus_ponens,[status(thm)],[1421, 1420])).
% 1.99/1.59 tff(1423,plain,
% 1.99/1.59 ((~hskp1) | (~c1_1(a693))),
% 1.99/1.59 inference(modus_ponens,[status(thm)],[1422, 1419])).
% 1.99/1.59 tff(1424,plain,
% 1.99/1.59 (~hskp1),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[1423, 1418])).
% 1.99/1.59 tff(1425,plain,
% 1.99/1.59 (hskp20),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[372, 1424, 102])).
% 1.99/1.59 tff(1426,plain,
% 1.99/1.59 (~c3_1(a754)),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[668, 1425])).
% 1.99/1.59 tff(1427,plain,
% 1.99/1.59 (~c0_1(a754)),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[595, 1425])).
% 1.99/1.59 tff(1428,plain,
% 1.99/1.59 (c2_1(a754)),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[190, 1425])).
% 1.99/1.59 tff(1429,assumption,(c1_1(a693)), introduced(assumption)).
% 1.99/1.59 tff(1430,plain,
% 1.99/1.59 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | c2_1(a693) | c0_1(a754) | c3_1(a754) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c2_1(a693) | c0_1(a754) | c3_1(a754) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c2_1(a754)))),
% 1.99/1.59 inference(rewrite,[status(thm)],[])).
% 1.99/1.59 tff(1431,plain,
% 1.99/1.59 ((hskp6 | (~ndr1_0) | c3_1(a693) | c2_1(a693) | (~c1_1(a693)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754))) <=> (hskp6 | c2_1(a693) | c0_1(a754) | c3_1(a754) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c2_1(a754)))),
% 1.99/1.59 inference(rewrite,[status(thm)],[])).
% 1.99/1.59 tff(1432,plain,
% 1.99/1.59 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a693) | c2_1(a693) | (~c1_1(a693)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | c2_1(a693) | c0_1(a754) | c3_1(a754) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c2_1(a754))))),
% 1.99/1.59 inference(monotonicity,[status(thm)],[1431])).
% 1.99/1.59 tff(1433,plain,
% 1.99/1.59 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a693) | c2_1(a693) | (~c1_1(a693)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c2_1(a693) | c0_1(a754) | c3_1(a754) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c2_1(a754)))),
% 1.99/1.59 inference(transitivity,[status(thm)],[1432, 1430])).
% 1.99/1.59 tff(1434,plain,
% 1.99/1.59 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a693) | c2_1(a693) | (~c1_1(a693)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))),
% 1.99/1.59 inference(quant_inst,[status(thm)],[])).
% 1.99/1.59 tff(1435,plain,
% 1.99/1.59 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c2_1(a693) | c0_1(a754) | c3_1(a754) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c2_1(a754))),
% 1.99/1.59 inference(modus_ponens,[status(thm)],[1434, 1433])).
% 1.99/1.59 tff(1436,plain,
% 1.99/1.59 (hskp6 | c2_1(a693)),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[1435, 227, 387, 179, 178, 1429, 153, 101])).
% 1.99/1.59 tff(1437,plain,
% 1.99/1.59 (c2_1(a693)),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[1436, 177])).
% 1.99/1.59 tff(1438,assumption,(c2_1(a693)), introduced(assumption)).
% 1.99/1.59 tff(1439,plain,
% 1.99/1.59 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | c2_1(a764) | c3_1(a764) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c1_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a764) | c3_1(a764) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c1_1(a764)))),
% 1.99/1.59 inference(rewrite,[status(thm)],[])).
% 1.99/1.59 tff(1440,plain,
% 1.99/1.59 ((hskp28 | (~ndr1_0) | c3_1(a693) | (~c2_1(a693)) | (~c1_1(a693)) | c3_1(a764) | c2_1(a764) | (~c1_1(a764))) <=> (hskp28 | c2_1(a764) | c3_1(a764) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c1_1(a764)))),
% 1.99/1.59 inference(rewrite,[status(thm)],[])).
% 1.99/1.59 tff(1441,plain,
% 1.99/1.59 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a693) | (~c2_1(a693)) | (~c1_1(a693)) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | c2_1(a764) | c3_1(a764) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c1_1(a764))))),
% 1.99/1.59 inference(monotonicity,[status(thm)],[1440])).
% 1.99/1.59 tff(1442,plain,
% 1.99/1.59 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a693) | (~c2_1(a693)) | (~c1_1(a693)) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a764) | c3_1(a764) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c1_1(a764)))),
% 1.99/1.59 inference(transitivity,[status(thm)],[1441, 1439])).
% 1.99/1.59 tff(1443,plain,
% 1.99/1.59 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a693) | (~c2_1(a693)) | (~c1_1(a693)) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)))),
% 1.99/1.59 inference(quant_inst,[status(thm)],[])).
% 1.99/1.59 tff(1444,plain,
% 1.99/1.59 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a764) | c3_1(a764) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c1_1(a764))),
% 1.99/1.59 inference(modus_ponens,[status(thm)],[1443, 1442])).
% 1.99/1.59 tff(1445,plain,
% 1.99/1.59 ($false),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[1444, 227, 62, 325, 1438, 314, 308, 1429, 153, 625])).
% 1.99/1.59 tff(1446,plain,((~hskp24) | hskp28 | (~c2_1(a693)) | (~c1_1(a693)) | c3_1(a693)), inference(lemma,lemma(discharge,[]))).
% 1.99/1.59 tff(1447,plain,
% 1.99/1.59 (~hskp24),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[1446, 1437, 62, 1429, 153])).
% 1.99/1.59 tff(1448,plain,
% 1.99/1.59 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | c0_1(a693))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | c0_1(a693))),
% 1.99/1.59 inference(rewrite,[status(thm)],[])).
% 1.99/1.59 tff(1449,plain,
% 1.99/1.59 ((hskp6 | (~ndr1_0) | c3_1(a693) | c0_1(a693) | (~c1_1(a693)) | c3_1(a698) | c0_1(a698) | c2_1(a698)) <=> (hskp6 | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | c0_1(a693))),
% 1.99/1.59 inference(rewrite,[status(thm)],[])).
% 1.99/1.59 tff(1450,plain,
% 1.99/1.59 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a693) | c0_1(a693) | (~c1_1(a693)) | c3_1(a698) | c0_1(a698) | c2_1(a698))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | c0_1(a693)))),
% 1.99/1.59 inference(monotonicity,[status(thm)],[1449])).
% 1.99/1.59 tff(1451,plain,
% 1.99/1.59 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a693) | c0_1(a693) | (~c1_1(a693)) | c3_1(a698) | c0_1(a698) | c2_1(a698))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | c0_1(a693))),
% 1.99/1.59 inference(transitivity,[status(thm)],[1450, 1448])).
% 1.99/1.59 tff(1452,plain,
% 1.99/1.59 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a693) | c0_1(a693) | (~c1_1(a693)) | c3_1(a698) | c0_1(a698) | c2_1(a698))),
% 1.99/1.59 inference(quant_inst,[status(thm)],[])).
% 1.99/1.59 tff(1453,plain,
% 1.99/1.59 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | c0_1(a693)),
% 1.99/1.59 inference(modus_ponens,[status(thm)],[1452, 1451])).
% 1.99/1.59 tff(1454,plain,
% 1.99/1.59 (c0_1(a693)),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[1453, 227, 177, 1360, 1359, 1358, 1429, 153, 301])).
% 1.99/1.59 tff(1455,plain,
% 1.99/1.59 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | c0_1(a754) | c3_1(a754) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c0_1(a754) | c3_1(a754) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a754)))),
% 1.99/1.59 inference(rewrite,[status(thm)],[])).
% 1.99/1.59 tff(1456,plain,
% 1.99/1.59 ((hskp6 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)) | c3_1(a698) | c0_1(a698) | c2_1(a698)) <=> (hskp6 | c0_1(a754) | c3_1(a754) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a754)))),
% 1.99/1.59 inference(rewrite,[status(thm)],[])).
% 1.99/1.59 tff(1457,plain,
% 1.99/1.59 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)) | c3_1(a698) | c0_1(a698) | c2_1(a698))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | c0_1(a754) | c3_1(a754) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a754))))),
% 1.99/1.59 inference(monotonicity,[status(thm)],[1456])).
% 1.99/1.59 tff(1458,plain,
% 1.99/1.59 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)) | c3_1(a698) | c0_1(a698) | c2_1(a698))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c0_1(a754) | c3_1(a754) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a754)))),
% 1.99/1.59 inference(transitivity,[status(thm)],[1457, 1455])).
% 1.99/1.59 tff(1459,plain,
% 1.99/1.59 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)) | c3_1(a698) | c0_1(a698) | c2_1(a698))),
% 1.99/1.59 inference(quant_inst,[status(thm)],[])).
% 1.99/1.59 tff(1460,plain,
% 1.99/1.59 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c0_1(a754) | c3_1(a754) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a754))),
% 1.99/1.59 inference(modus_ponens,[status(thm)],[1459, 1458])).
% 1.99/1.59 tff(1461,plain,
% 1.99/1.59 (~c1_1(a754)),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[1460, 227, 177, 179, 178, 1360, 1359, 1358, 301])).
% 1.99/1.59 tff(1462,plain,
% 1.99/1.59 (~hskp23),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[430, 1461, 387, 179, 62])).
% 1.99/1.59 tff(1463,plain,
% 1.99/1.59 (((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~c1_1(a693)) | (~ndr1_0) | (~c0_1(a693)) | (~c2_1(a693)))) <=> ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp23 | (~c1_1(a693)) | (~ndr1_0) | (~c0_1(a693)) | (~c2_1(a693)))),
% 1.99/1.59 inference(rewrite,[status(thm)],[])).
% 1.99/1.59 tff(1464,plain,
% 1.99/1.59 ((hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a693)) | (~c0_1(a693)) | (~c1_1(a693))) <=> (hskp24 | hskp23 | (~c1_1(a693)) | (~ndr1_0) | (~c0_1(a693)) | (~c2_1(a693)))),
% 1.99/1.59 inference(rewrite,[status(thm)],[])).
% 1.99/1.59 tff(1465,plain,
% 1.99/1.59 (((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a693)) | (~c0_1(a693)) | (~c1_1(a693)))) <=> ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~c1_1(a693)) | (~ndr1_0) | (~c0_1(a693)) | (~c2_1(a693))))),
% 1.99/1.59 inference(monotonicity,[status(thm)],[1464])).
% 1.99/1.59 tff(1466,plain,
% 1.99/1.59 (((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a693)) | (~c0_1(a693)) | (~c1_1(a693)))) <=> ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp23 | (~c1_1(a693)) | (~ndr1_0) | (~c0_1(a693)) | (~c2_1(a693)))),
% 1.99/1.59 inference(transitivity,[status(thm)],[1465, 1463])).
% 1.99/1.59 tff(1467,plain,
% 1.99/1.59 ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a693)) | (~c0_1(a693)) | (~c1_1(a693)))),
% 1.99/1.59 inference(quant_inst,[status(thm)],[])).
% 1.99/1.59 tff(1468,plain,
% 1.99/1.59 ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp23 | (~c1_1(a693)) | (~ndr1_0) | (~c0_1(a693)) | (~c2_1(a693))),
% 1.99/1.59 inference(modus_ponens,[status(thm)],[1467, 1466])).
% 1.99/1.59 tff(1469,plain,
% 1.99/1.59 (hskp24 | hskp23 | (~c0_1(a693)) | (~c2_1(a693))),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[1468, 227, 1429, 163])).
% 1.99/1.59 tff(1470,plain,
% 1.99/1.59 ($false),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[1469, 1462, 1454, 1437, 1447])).
% 1.99/1.59 tff(1471,plain,((~hskp4) | (~c1_1(a693)) | (~c2_1(a754)) | c0_1(a754) | hskp28 | hskp6 | c3_1(a693) | c3_1(a754)), inference(lemma,lemma(discharge,[]))).
% 1.99/1.59 tff(1472,plain,
% 1.99/1.59 (~hskp4),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[1471, 177, 1428, 1427, 62, 1418, 153, 1426])).
% 1.99/1.59 tff(1473,plain,
% 1.99/1.59 (^[U: $i] : refl((hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))),
% 1.99/1.59 inference(bind,[status(th)],[])).
% 1.99/1.59 tff(1474,plain,
% 1.99/1.59 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.99/1.59 inference(quant_intro,[status(thm)],[1473])).
% 1.99/1.59 tff(1475,plain,
% 1.99/1.59 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.99/1.59 inference(rewrite,[status(thm)],[])).
% 1.99/1.59 tff(1476,plain,
% 1.99/1.59 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp0) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp0))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp0) | hskp1) <=> ((hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp1))), rewrite(((hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp1) <=> (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp0) | hskp1) <=> (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))))),
% 1.99/1.59 inference(bind,[status(th)],[])).
% 1.99/1.59 tff(1477,plain,
% 1.99/1.59 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp0) | hskp1) <=> ![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.99/1.59 inference(quant_intro,[status(thm)],[1476])).
% 1.99/1.59 tff(1478,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp0) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause133')).
% 1.99/1.59 tff(1479,plain,
% 1.99/1.59 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.99/1.59 inference(modus_ponens,[status(thm)],[1478, 1477])).
% 1.99/1.59 tff(1480,plain,
% 1.99/1.59 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.99/1.59 inference(modus_ponens,[status(thm)],[1479, 1475])).
% 1.99/1.59 tff(1481,plain,(
% 1.99/1.59 ![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.99/1.59 inference(skolemize,[status(sab)],[1480])).
% 1.99/1.59 tff(1482,plain,
% 1.99/1.59 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.99/1.59 inference(modus_ponens,[status(thm)],[1481, 1474])).
% 1.99/1.59 tff(1483,plain,
% 1.99/1.59 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c0_1(a725) | c1_1(a725) | c3_1(a725) | (~ndr1_0))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a725) | c1_1(a725) | c3_1(a725) | (~ndr1_0))),
% 1.99/1.59 inference(rewrite,[status(thm)],[])).
% 1.99/1.59 tff(1484,plain,
% 1.99/1.59 ((hskp1 | hskp0 | (~ndr1_0) | c3_1(a725) | c1_1(a725) | c0_1(a725)) <=> (hskp1 | hskp0 | c0_1(a725) | c1_1(a725) | c3_1(a725) | (~ndr1_0))),
% 1.99/1.59 inference(rewrite,[status(thm)],[])).
% 1.99/1.59 tff(1485,plain,
% 1.99/1.59 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c3_1(a725) | c1_1(a725) | c0_1(a725))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c0_1(a725) | c1_1(a725) | c3_1(a725) | (~ndr1_0)))),
% 1.99/1.59 inference(monotonicity,[status(thm)],[1484])).
% 1.99/1.59 tff(1486,plain,
% 1.99/1.59 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c3_1(a725) | c1_1(a725) | c0_1(a725))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a725) | c1_1(a725) | c3_1(a725) | (~ndr1_0))),
% 1.99/1.59 inference(transitivity,[status(thm)],[1485, 1483])).
% 1.99/1.59 tff(1487,plain,
% 1.99/1.59 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c3_1(a725) | c1_1(a725) | c0_1(a725))),
% 1.99/1.59 inference(quant_inst,[status(thm)],[])).
% 1.99/1.59 tff(1488,plain,
% 1.99/1.59 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a725) | c1_1(a725) | c3_1(a725) | (~ndr1_0)),
% 1.99/1.59 inference(modus_ponens,[status(thm)],[1487, 1486])).
% 1.99/1.59 tff(1489,plain,
% 1.99/1.59 (hskp1 | hskp0),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[1488, 227, 152, 146, 140, 1482])).
% 1.99/1.59 tff(1490,plain,
% 1.99/1.59 (hskp0),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[1489, 1424])).
% 1.99/1.59 tff(1491,plain,
% 1.99/1.59 (~c1_1(a692)),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[853, 1490])).
% 1.99/1.59 tff(1492,plain,
% 1.99/1.59 (~c0_1(a692)),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[859, 1490])).
% 1.99/1.59 tff(1493,plain,
% 1.99/1.59 (c2_1(a692)),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[872, 1490])).
% 1.99/1.59 tff(1494,plain,
% 1.99/1.59 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)))),
% 1.99/1.59 inference(rewrite,[status(thm)],[])).
% 1.99/1.59 tff(1495,plain,
% 1.99/1.59 ((hskp4 | hskp3 | (~ndr1_0) | c1_1(a692) | c0_1(a692) | (~c2_1(a692))) <=> (hskp4 | hskp3 | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)))),
% 1.99/1.59 inference(rewrite,[status(thm)],[])).
% 1.99/1.59 tff(1496,plain,
% 1.99/1.59 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a692) | c0_1(a692) | (~c2_1(a692)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692))))),
% 1.99/1.59 inference(monotonicity,[status(thm)],[1495])).
% 1.99/1.59 tff(1497,plain,
% 1.99/1.59 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a692) | c0_1(a692) | (~c2_1(a692)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)))),
% 1.99/1.59 inference(transitivity,[status(thm)],[1496, 1494])).
% 1.99/1.59 tff(1498,plain,
% 1.99/1.59 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a692) | c0_1(a692) | (~c2_1(a692)))),
% 1.99/1.59 inference(quant_inst,[status(thm)],[])).
% 1.99/1.59 tff(1499,plain,
% 1.99/1.59 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp4 | hskp3 | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692))),
% 1.99/1.59 inference(modus_ponens,[status(thm)],[1498, 1497])).
% 1.99/1.59 tff(1500,plain,
% 1.99/1.59 (hskp4 | hskp3),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[1499, 227, 1493, 1492, 1491, 442])).
% 1.99/1.59 tff(1501,plain,
% 1.99/1.59 (hskp3),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[1500, 1472])).
% 1.99/1.59 tff(1502,plain,
% 1.99/1.59 (c2_1(a697)),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[527, 1501])).
% 1.99/1.59 tff(1503,plain,
% 1.99/1.59 (c0_1(a697)),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[508, 1501])).
% 1.99/1.59 tff(1504,plain,
% 1.99/1.59 (hskp6 | c2_1(a693)),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[1435, 227, 1428, 1427, 1426, 1418, 153, 101])).
% 1.99/1.59 tff(1505,plain,
% 1.99/1.59 (c2_1(a693)),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[1504, 177])).
% 1.99/1.59 tff(1506,plain,
% 1.99/1.59 (~hskp24),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[1446, 1505, 62, 1418, 153])).
% 1.99/1.59 tff(1507,plain,
% 1.99/1.59 (~c3_1(a697)),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[1355, 1501])).
% 1.99/1.59 tff(1508,plain,
% 1.99/1.59 (c1_1(a754)),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[538, 1507, 102, 1427, 1428, 1426, 62, 1472, 1506])).
% 1.99/1.59 tff(1509,plain,
% 1.99/1.59 (hskp6 | c2_1(a725) | (~c1_1(a754))),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[545, 227, 1427, 1426, 152, 140, 301])).
% 1.99/1.59 tff(1510,plain,
% 1.99/1.59 (c2_1(a725)),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[1509, 1508, 177])).
% 1.99/1.59 tff(1511,plain,
% 1.99/1.59 (~hskp23),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[586, 1510, 152, 146, 62])).
% 1.99/1.59 tff(1512,plain,
% 1.99/1.59 (~c1_1(a697)),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[534, 227, 1506, 1511, 1503, 1502, 163])).
% 1.99/1.59 tff(1513,plain,
% 1.99/1.59 ($false),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[572, 227, 1428, 1503, 1426, 152, 146, 1507, 566, 1510, 1508, 1512])).
% 1.99/1.59 tff(1514,plain,(hskp6 | hskp28 | hskp30 | c3_1(a693)), inference(lemma,lemma(discharge,[]))).
% 1.99/1.59 tff(1515,plain,
% 1.99/1.59 (hskp6),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[1514, 153, 102, 62])).
% 1.99/1.59 tff(1516,plain,
% 1.99/1.59 (~c2_1(a702)),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[68, 1515])).
% 1.99/1.59 tff(1517,plain,
% 1.99/1.59 (c0_1(a702)),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[90, 1515])).
% 1.99/1.59 tff(1518,plain,
% 1.99/1.59 (c3_1(a702)),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[79, 1515])).
% 1.99/1.59 tff(1519,plain,
% 1.99/1.59 (~hskp25),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[763, 1518, 1517, 1516, 62])).
% 1.99/1.59 tff(1520,plain,
% 1.99/1.59 (hskp22),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[778, 1519, 62])).
% 1.99/1.59 tff(1521,plain,
% 1.99/1.59 (~c2_1(a761)),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[784, 1520])).
% 1.99/1.59 tff(1522,plain,
% 1.99/1.59 (~c0_1(a761)),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[790, 1520])).
% 1.99/1.59 tff(1523,plain,
% 1.99/1.59 (c1_1(a761)),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[801, 1520])).
% 1.99/1.59 tff(1524,plain,
% 1.99/1.59 (c2_1(a725)),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[808, 227, 1523, 1522, 1521, 152, 146, 140, 122])).
% 1.99/1.59 tff(1525,plain,
% 1.99/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a754) | c3_1(a754) | c2_1(a702) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c3_1(a702)) | (~c0_1(a702)) | (~c2_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a754) | c3_1(a754) | c2_1(a702) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c3_1(a702)) | (~c0_1(a702)) | (~c2_1(a754)))),
% 1.99/1.59 inference(rewrite,[status(thm)],[])).
% 1.99/1.59 tff(1526,plain,
% 1.99/1.59 (((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a693) | c0_1(a693) | (~c1_1(a693))) <=> (c0_1(a754) | c3_1(a754) | c2_1(a702) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c3_1(a702)) | (~c0_1(a702)) | (~c2_1(a754)))),
% 1.99/1.59 inference(rewrite,[status(thm)],[])).
% 1.99/1.59 tff(1527,plain,
% 1.99/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a693) | c0_1(a693) | (~c1_1(a693)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a754) | c3_1(a754) | c2_1(a702) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c3_1(a702)) | (~c0_1(a702)) | (~c2_1(a754))))),
% 1.99/1.59 inference(monotonicity,[status(thm)],[1526])).
% 1.99/1.59 tff(1528,plain,
% 1.99/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a693) | c0_1(a693) | (~c1_1(a693)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a754) | c3_1(a754) | c2_1(a702) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c3_1(a702)) | (~c0_1(a702)) | (~c2_1(a754)))),
% 1.99/1.59 inference(transitivity,[status(thm)],[1527, 1525])).
% 1.99/1.59 tff(1529,plain,
% 1.99/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a693) | c0_1(a693) | (~c1_1(a693)))),
% 1.99/1.59 inference(quant_inst,[status(thm)],[])).
% 1.99/1.59 tff(1530,plain,
% 1.99/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a754) | c3_1(a754) | c2_1(a702) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c3_1(a702)) | (~c0_1(a702)) | (~c2_1(a754))),
% 1.99/1.59 inference(modus_ponens,[status(thm)],[1529, 1528])).
% 1.99/1.59 tff(1531,plain,
% 1.99/1.59 (c0_1(a693)),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[1530, 227, 1428, 1517, 1518, 1427, 1426, 1516, 1418, 153, 174])).
% 1.99/1.59 tff(1532,plain,
% 1.99/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a761) | c2_1(a761) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)) | (~c2_1(a693)) | (~c1_1(a761)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a761) | c2_1(a761) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)) | (~c2_1(a693)) | (~c1_1(a761)))),
% 1.99/1.59 inference(rewrite,[status(thm)],[])).
% 1.99/1.59 tff(1533,plain,
% 1.99/1.59 (((~ndr1_0) | c3_1(a693) | (~c2_1(a693)) | (~c1_1(a693)) | c3_1(a693) | (~c1_1(a693)) | (~c0_1(a693)) | c2_1(a761) | c0_1(a761) | (~c1_1(a761))) <=> (c0_1(a761) | c2_1(a761) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)) | (~c2_1(a693)) | (~c1_1(a761)))),
% 1.99/1.59 inference(rewrite,[status(thm)],[])).
% 1.99/1.59 tff(1534,plain,
% 1.99/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a693) | (~c2_1(a693)) | (~c1_1(a693)) | c3_1(a693) | (~c1_1(a693)) | (~c0_1(a693)) | c2_1(a761) | c0_1(a761) | (~c1_1(a761)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a761) | c2_1(a761) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)) | (~c2_1(a693)) | (~c1_1(a761))))),
% 1.99/1.59 inference(monotonicity,[status(thm)],[1533])).
% 1.99/1.59 tff(1535,plain,
% 1.99/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a693) | (~c2_1(a693)) | (~c1_1(a693)) | c3_1(a693) | (~c1_1(a693)) | (~c0_1(a693)) | c2_1(a761) | c0_1(a761) | (~c1_1(a761)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a761) | c2_1(a761) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)) | (~c2_1(a693)) | (~c1_1(a761)))),
% 1.99/1.59 inference(transitivity,[status(thm)],[1534, 1532])).
% 1.99/1.59 tff(1536,plain,
% 1.99/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a693) | (~c2_1(a693)) | (~c1_1(a693)) | c3_1(a693) | (~c1_1(a693)) | (~c0_1(a693)) | c2_1(a761) | c0_1(a761) | (~c1_1(a761)))),
% 1.99/1.59 inference(quant_inst,[status(thm)],[])).
% 1.99/1.59 tff(1537,plain,
% 1.99/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a761) | c2_1(a761) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)) | (~c2_1(a693)) | (~c1_1(a761))),
% 1.99/1.59 inference(modus_ponens,[status(thm)],[1536, 1535])).
% 1.99/1.59 tff(1538,plain,
% 1.99/1.59 (~c2_1(a693)),
% 1.99/1.59 inference(unit_resolution,[status(thm)],[1537, 227, 1523, 1522, 1521, 1418, 153, 822, 1531])).
% 1.99/1.59 tff(1539,plain,
% 1.99/1.59 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a693) | c1_1(a725) | c3_1(a725) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)) | (~c2_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a693) | c1_1(a725) | c3_1(a725) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)) | (~c2_1(a725)))),
% 1.99/1.59 inference(rewrite,[status(thm)],[])).
% 1.99/1.59 tff(1540,plain,
% 1.99/1.59 ((hskp28 | (~ndr1_0) | c3_1(a693) | c2_1(a693) | (~c0_1(a693)) | c3_1(a725) | c1_1(a725) | (~c2_1(a725))) <=> (hskp28 | c2_1(a693) | c1_1(a725) | c3_1(a725) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)) | (~c2_1(a725)))),
% 1.99/1.59 inference(rewrite,[status(thm)],[])).
% 1.99/1.59 tff(1541,plain,
% 1.99/1.59 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a693) | c2_1(a693) | (~c0_1(a693)) | c3_1(a725) | c1_1(a725) | (~c2_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a693) | c1_1(a725) | c3_1(a725) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)) | (~c2_1(a725))))),
% 1.99/1.60 inference(monotonicity,[status(thm)],[1540])).
% 1.99/1.60 tff(1542,plain,
% 1.99/1.60 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a693) | c2_1(a693) | (~c0_1(a693)) | c3_1(a725) | c1_1(a725) | (~c2_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a693) | c1_1(a725) | c3_1(a725) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)) | (~c2_1(a725)))),
% 1.99/1.60 inference(transitivity,[status(thm)],[1541, 1539])).
% 1.99/1.60 tff(1543,plain,
% 1.99/1.60 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a693) | c2_1(a693) | (~c0_1(a693)) | c3_1(a725) | c1_1(a725) | (~c2_1(a725)))),
% 1.99/1.60 inference(quant_inst,[status(thm)],[])).
% 1.99/1.60 tff(1544,plain,
% 1.99/1.60 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a693) | c1_1(a725) | c3_1(a725) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)) | (~c2_1(a725))),
% 1.99/1.60 inference(modus_ponens,[status(thm)],[1543, 1542])).
% 1.99/1.60 tff(1545,plain,
% 1.99/1.60 (c2_1(a693) | (~c0_1(a693)) | (~c2_1(a725))),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[1544, 227, 62, 146, 140, 153, 342])).
% 1.99/1.60 tff(1546,plain,
% 1.99/1.60 ($false),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[1545, 1538, 1531, 1524])).
% 1.99/1.60 tff(1547,plain,(c3_1(a693) | hskp28 | hskp30), inference(lemma,lemma(discharge,[]))).
% 1.99/1.60 tff(1548,plain,
% 1.99/1.60 (c3_1(a693)),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[1547, 102, 62])).
% 1.99/1.60 tff(1549,plain,
% 1.99/1.60 (((~hskp1) | (~c3_1(a693))) <=> ((~hskp1) | (~c3_1(a693)))),
% 1.99/1.60 inference(rewrite,[status(thm)],[])).
% 1.99/1.60 tff(1550,plain,
% 1.99/1.60 (((~c3_1(a693)) | (~hskp1)) <=> ((~hskp1) | (~c3_1(a693)))),
% 1.99/1.60 inference(rewrite,[status(thm)],[])).
% 1.99/1.60 tff(1551,axiom,((~c3_1(a693)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause130')).
% 1.99/1.60 tff(1552,plain,
% 1.99/1.60 ((~hskp1) | (~c3_1(a693))),
% 1.99/1.60 inference(modus_ponens,[status(thm)],[1551, 1550])).
% 1.99/1.60 tff(1553,plain,
% 1.99/1.60 ((~hskp1) | (~c3_1(a693))),
% 1.99/1.60 inference(modus_ponens,[status(thm)],[1552, 1549])).
% 1.99/1.60 tff(1554,plain,
% 1.99/1.60 (~hskp1),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[1553, 1548])).
% 1.99/1.60 tff(1555,plain,
% 1.99/1.60 (hskp20),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[372, 1554, 102])).
% 1.99/1.60 tff(1556,plain,
% 1.99/1.60 (~c0_1(a754)),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[595, 1555])).
% 1.99/1.60 tff(1557,plain,
% 1.99/1.60 (~c3_1(a754)),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[668, 1555])).
% 1.99/1.60 tff(1558,plain,
% 1.99/1.60 (c2_1(a754)),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[190, 1555])).
% 1.99/1.60 tff(1559,plain,
% 1.99/1.60 (c0_1(a764)),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[1156, 227, 325, 387, 719, 718, 308, 179, 178, 717, 174])).
% 1.99/1.60 tff(1560,plain,
% 1.99/1.60 (~c1_1(a754)),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[1119, 227, 387, 719, 718, 179, 178, 717, 174])).
% 1.99/1.60 tff(1561,plain,
% 1.99/1.60 ($false),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[1164, 227, 62, 387, 314, 308, 178, 342, 1560, 1559])).
% 1.99/1.60 tff(1562,plain,((~hskp24) | hskp28 | (~c2_1(a754)) | c3_1(a754) | (~c0_1(a702)) | (~c3_1(a702)) | c0_1(a754) | c2_1(a702)), inference(lemma,lemma(discharge,[]))).
% 1.99/1.60 tff(1563,plain,
% 1.99/1.60 (~hskp24),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[1562, 91, 1558, 1557, 62, 80, 1556, 69])).
% 1.99/1.60 tff(1564,plain,
% 1.99/1.60 (~hskp25),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[763, 80, 91, 69, 62])).
% 1.99/1.60 tff(1565,plain,
% 1.99/1.60 (hskp22),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[778, 1564, 62])).
% 1.99/1.60 tff(1566,plain,
% 1.99/1.60 (~c2_1(a761)),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[784, 1565])).
% 1.99/1.60 tff(1567,plain,
% 1.99/1.60 (~c0_1(a761)),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[790, 1565])).
% 1.99/1.60 tff(1568,plain,
% 1.99/1.60 (c1_1(a761)),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[801, 1565])).
% 1.99/1.60 tff(1569,plain,
% 1.99/1.60 (c2_1(a725)),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[808, 227, 1568, 1567, 1566, 152, 146, 140, 122])).
% 1.99/1.60 tff(1570,plain,
% 1.99/1.60 (hskp27),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[897, 227, 1568, 1567, 1566, 152, 146, 891, 1569])).
% 1.99/1.60 tff(1571,plain,
% 1.99/1.60 (c1_1(a691)),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[267, 1570])).
% 1.99/1.60 tff(1572,plain,
% 1.99/1.60 (c0_1(a691)),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[278, 1570])).
% 1.99/1.60 tff(1573,plain,
% 1.99/1.60 (~hskp23),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[586, 1569, 152, 146, 62])).
% 1.99/1.60 tff(1574,plain,
% 1.99/1.60 (hskp24 | (~c2_1(a691))),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[1063, 227, 1573, 1572, 1571, 163])).
% 1.99/1.60 tff(1575,plain,
% 1.99/1.60 (~c2_1(a691)),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[1574, 1563])).
% 1.99/1.60 tff(1576,plain,
% 1.99/1.60 (^[U: $i] : refl((hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))))),
% 1.99/1.60 inference(bind,[status(th)],[])).
% 1.99/1.60 tff(1577,plain,
% 1.99/1.60 (![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.99/1.60 inference(quant_intro,[status(thm)],[1576])).
% 1.99/1.60 tff(1578,plain,
% 1.99/1.60 (![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.99/1.60 inference(rewrite,[status(thm)],[])).
% 1.99/1.60 tff(1579,plain,
% 1.99/1.60 (^[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)) | hskp5) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp5))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp1) <=> ((hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp1))), rewrite(((hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp1) <=> (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp1) <=> (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))))),
% 1.99/1.60 inference(bind,[status(th)],[])).
% 1.99/1.60 tff(1580,plain,
% 1.99/1.60 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp1) <=> ![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.99/1.60 inference(quant_intro,[status(thm)],[1579])).
% 1.99/1.60 tff(1581,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause147')).
% 1.99/1.60 tff(1582,plain,
% 1.99/1.60 (![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.99/1.60 inference(modus_ponens,[status(thm)],[1581, 1580])).
% 1.99/1.60 tff(1583,plain,
% 1.99/1.60 (![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.99/1.60 inference(modus_ponens,[status(thm)],[1582, 1578])).
% 1.99/1.60 tff(1584,plain,(
% 1.99/1.60 ![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.99/1.60 inference(skolemize,[status(sab)],[1583])).
% 1.99/1.60 tff(1585,plain,
% 1.99/1.60 (![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.99/1.60 inference(modus_ponens,[status(thm)],[1584, 1577])).
% 1.99/1.60 tff(1586,plain,
% 1.99/1.60 (((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp5 | hskp1 | (~ndr1_0) | (~c1_1(a691)) | (~c0_1(a691)) | c2_1(a691))) <=> ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp5 | hskp1 | (~ndr1_0) | (~c1_1(a691)) | (~c0_1(a691)) | c2_1(a691))),
% 1.99/1.60 inference(rewrite,[status(thm)],[])).
% 1.99/1.60 tff(1587,plain,
% 1.99/1.60 ((hskp5 | hskp1 | (~ndr1_0) | c2_1(a691) | (~c0_1(a691)) | (~c1_1(a691))) <=> (hskp5 | hskp1 | (~ndr1_0) | (~c1_1(a691)) | (~c0_1(a691)) | c2_1(a691))),
% 1.99/1.60 inference(rewrite,[status(thm)],[])).
% 1.99/1.60 tff(1588,plain,
% 1.99/1.60 (((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp5 | hskp1 | (~ndr1_0) | c2_1(a691) | (~c0_1(a691)) | (~c1_1(a691)))) <=> ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp5 | hskp1 | (~ndr1_0) | (~c1_1(a691)) | (~c0_1(a691)) | c2_1(a691)))),
% 1.99/1.60 inference(monotonicity,[status(thm)],[1587])).
% 1.99/1.60 tff(1589,plain,
% 1.99/1.60 (((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp5 | hskp1 | (~ndr1_0) | c2_1(a691) | (~c0_1(a691)) | (~c1_1(a691)))) <=> ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp5 | hskp1 | (~ndr1_0) | (~c1_1(a691)) | (~c0_1(a691)) | c2_1(a691))),
% 1.99/1.60 inference(transitivity,[status(thm)],[1588, 1586])).
% 1.99/1.60 tff(1590,plain,
% 1.99/1.60 ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp5 | hskp1 | (~ndr1_0) | c2_1(a691) | (~c0_1(a691)) | (~c1_1(a691)))),
% 1.99/1.60 inference(quant_inst,[status(thm)],[])).
% 1.99/1.60 tff(1591,plain,
% 1.99/1.60 ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp5 | hskp1 | (~ndr1_0) | (~c1_1(a691)) | (~c0_1(a691)) | c2_1(a691)),
% 1.99/1.60 inference(modus_ponens,[status(thm)],[1590, 1589])).
% 1.99/1.60 tff(1592,plain,
% 1.99/1.60 (hskp5 | c2_1(a691)),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[1591, 227, 1554, 1572, 1571, 1585])).
% 1.99/1.60 tff(1593,plain,
% 1.99/1.60 (hskp5),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[1592, 1575])).
% 1.99/1.60 tff(1594,plain,
% 1.99/1.60 (~c1_1(a701)),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[28, 1593])).
% 1.99/1.60 tff(1595,plain,
% 1.99/1.60 (c0_1(a701)),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[50, 1593])).
% 1.99/1.60 tff(1596,plain,
% 1.99/1.60 (~c1_1(a754)),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[1119, 227, 1558, 91, 80, 1556, 1557, 69, 174])).
% 1.99/1.60 tff(1597,plain,
% 1.99/1.60 (~hskp14),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[495, 1563, 1558, 1557, 1596, 1573, 62])).
% 1.99/1.60 tff(1598,plain,
% 1.99/1.60 (((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp14 | c1_1(a701) | (~ndr1_0) | c3_1(a701) | (~c0_1(a701)))) <=> ((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp30 | hskp14 | c1_1(a701) | (~ndr1_0) | c3_1(a701) | (~c0_1(a701)))),
% 1.99/1.60 inference(rewrite,[status(thm)],[])).
% 1.99/1.60 tff(1599,plain,
% 1.99/1.60 ((hskp30 | hskp14 | (~ndr1_0) | c3_1(a701) | c1_1(a701) | (~c0_1(a701))) <=> (hskp30 | hskp14 | c1_1(a701) | (~ndr1_0) | c3_1(a701) | (~c0_1(a701)))),
% 1.99/1.60 inference(rewrite,[status(thm)],[])).
% 1.99/1.60 tff(1600,plain,
% 1.99/1.60 (((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp14 | (~ndr1_0) | c3_1(a701) | c1_1(a701) | (~c0_1(a701)))) <=> ((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp14 | c1_1(a701) | (~ndr1_0) | c3_1(a701) | (~c0_1(a701))))),
% 1.99/1.60 inference(monotonicity,[status(thm)],[1599])).
% 1.99/1.60 tff(1601,plain,
% 1.99/1.60 (((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp14 | (~ndr1_0) | c3_1(a701) | c1_1(a701) | (~c0_1(a701)))) <=> ((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp30 | hskp14 | c1_1(a701) | (~ndr1_0) | c3_1(a701) | (~c0_1(a701)))),
% 1.99/1.60 inference(transitivity,[status(thm)],[1600, 1598])).
% 1.99/1.60 tff(1602,plain,
% 1.99/1.60 ((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp14 | (~ndr1_0) | c3_1(a701) | c1_1(a701) | (~c0_1(a701)))),
% 1.99/1.60 inference(quant_inst,[status(thm)],[])).
% 1.99/1.60 tff(1603,plain,
% 1.99/1.60 ((~![U: $i] : (hskp30 | hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp30 | hskp14 | c1_1(a701) | (~ndr1_0) | c3_1(a701) | (~c0_1(a701))),
% 1.99/1.60 inference(modus_ponens,[status(thm)],[1602, 1601])).
% 1.99/1.60 tff(1604,plain,
% 1.99/1.60 (c3_1(a701)),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[1603, 102, 227, 1597, 1595, 1594, 112])).
% 1.99/1.60 tff(1605,plain,
% 1.99/1.60 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))),
% 1.99/1.60 inference(bind,[status(th)],[])).
% 1.99/1.60 tff(1606,plain,
% 1.99/1.60 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.99/1.60 inference(quant_intro,[status(thm)],[1605])).
% 1.99/1.60 tff(1607,plain,
% 1.99/1.60 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.99/1.60 inference(rewrite,[status(thm)],[])).
% 1.99/1.60 tff(1608,plain,
% 1.99/1.60 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) | hskp14) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp14))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp14) <=> (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))))),
% 1.99/1.60 inference(bind,[status(th)],[])).
% 1.99/1.60 tff(1609,plain,
% 1.99/1.60 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.99/1.60 inference(quant_intro,[status(thm)],[1608])).
% 1.99/1.60 tff(1610,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(V)) | c3_1(V)) | hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause180')).
% 1.99/1.60 tff(1611,plain,
% 1.99/1.60 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.99/1.60 inference(modus_ponens,[status(thm)],[1610, 1609])).
% 1.99/1.60 tff(1612,plain,
% 1.99/1.60 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.99/1.60 inference(modus_ponens,[status(thm)],[1611, 1607])).
% 1.99/1.60 tff(1613,plain,(
% 1.99/1.60 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.99/1.60 inference(skolemize,[status(sab)],[1612])).
% 1.99/1.60 tff(1614,plain,
% 1.99/1.60 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.99/1.60 inference(modus_ponens,[status(thm)],[1613, 1606])).
% 1.99/1.60 tff(1615,plain,
% 1.99/1.60 (c2_1(a701)),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[39, 1593])).
% 1.99/1.60 tff(1616,plain,
% 1.99/1.60 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | c3_1(a754) | (~ndr1_0) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c1_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a754) | (~ndr1_0) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c1_1(a754) | (~c2_1(a754)))),
% 1.99/1.60 inference(rewrite,[status(thm)],[])).
% 1.99/1.60 tff(1617,plain,
% 1.99/1.60 ((hskp14 | (~ndr1_0) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c3_1(a754) | c1_1(a754) | (~c2_1(a754))) <=> (hskp14 | c3_1(a754) | (~ndr1_0) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c1_1(a754) | (~c2_1(a754)))),
% 1.99/1.60 inference(rewrite,[status(thm)],[])).
% 1.99/1.60 tff(1618,plain,
% 1.99/1.60 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | c3_1(a754) | (~ndr1_0) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c1_1(a754) | (~c2_1(a754))))),
% 1.99/1.60 inference(monotonicity,[status(thm)],[1617])).
% 1.99/1.60 tff(1619,plain,
% 1.99/1.60 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a754) | (~ndr1_0) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c1_1(a754) | (~c2_1(a754)))),
% 1.99/1.60 inference(transitivity,[status(thm)],[1618, 1616])).
% 1.99/1.60 tff(1620,plain,
% 1.99/1.60 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)))),
% 1.99/1.60 inference(quant_inst,[status(thm)],[])).
% 1.99/1.60 tff(1621,plain,
% 1.99/1.60 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a754) | (~ndr1_0) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c1_1(a754) | (~c2_1(a754))),
% 1.99/1.60 inference(modus_ponens,[status(thm)],[1620, 1619])).
% 1.99/1.60 tff(1622,plain,
% 1.99/1.60 ($false),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[1621, 227, 1597, 1558, 1595, 1615, 1557, 1614, 1596, 1604])).
% 1.99/1.60 tff(1623,plain,((~hskp6) | hskp30 | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.99/1.60 tff(1624,plain,
% 1.99/1.60 (~hskp6),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[1623, 102, 62])).
% 1.99/1.60 tff(1625,plain,
% 1.99/1.60 ($false),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[356, 227, 177, 325, 387, 314, 308, 179, 178, 101])).
% 1.99/1.60 tff(1626,plain,((~hskp24) | hskp6 | (~c2_1(a754)) | c0_1(a754) | c3_1(a754)), inference(lemma,lemma(discharge,[]))).
% 1.99/1.60 tff(1627,plain,
% 1.99/1.60 (~hskp24),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[1626, 177, 1558, 1556, 1557])).
% 1.99/1.60 tff(1628,plain,
% 1.99/1.60 (c1_1(a754)),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[538, 176, 102, 1556, 1558, 1557, 62, 1627, 175])).
% 1.99/1.60 tff(1629,plain,
% 1.99/1.60 (hskp0),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[1489, 1554])).
% 1.99/1.60 tff(1630,plain,
% 1.99/1.60 (~c1_1(a692)),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[853, 1629])).
% 1.99/1.60 tff(1631,plain,
% 1.99/1.60 (~c0_1(a692)),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[859, 1629])).
% 1.99/1.60 tff(1632,plain,
% 1.99/1.60 (c2_1(a692)),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[872, 1629])).
% 1.99/1.60 tff(1633,plain,
% 1.99/1.60 (hskp4 | hskp3),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[1499, 227, 1632, 1631, 1630, 442])).
% 1.99/1.60 tff(1634,plain,
% 1.99/1.60 (hskp3),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[1633, 176])).
% 1.99/1.60 tff(1635,plain,
% 1.99/1.60 (c0_1(a697)),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[508, 1634])).
% 1.99/1.60 tff(1636,plain,
% 1.99/1.60 ((~c0_1(a697)) | c1_1(a697) | (~c1_1(a754))),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[907, 227, 1558, 1632, 1557, 175, 1631, 1630, 566])).
% 1.99/1.60 tff(1637,plain,
% 1.99/1.60 (c1_1(a697)),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[1636, 1635, 1628])).
% 1.99/1.60 tff(1638,plain,
% 1.99/1.60 (c2_1(a697)),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[527, 1634])).
% 1.99/1.60 tff(1639,plain,
% 1.99/1.60 (hskp6 | c2_1(a725) | (~c1_1(a754))),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[545, 227, 1556, 1557, 152, 140, 301])).
% 1.99/1.60 tff(1640,plain,
% 1.99/1.60 (c2_1(a725)),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[1639, 1628, 177])).
% 1.99/1.60 tff(1641,plain,
% 1.99/1.60 (~hskp23),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[586, 1640, 152, 146, 62])).
% 1.99/1.60 tff(1642,plain,
% 1.99/1.60 ($false),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[534, 227, 1627, 1641, 1635, 1638, 163, 1637])).
% 1.99/1.60 tff(1643,plain,(hskp4 | hskp28 | c3_1(a697) | hskp6 | hskp30), inference(lemma,lemma(discharge,[]))).
% 1.99/1.60 tff(1644,plain,
% 1.99/1.60 (hskp4),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[1643, 175, 62, 1624, 102])).
% 1.99/1.60 tff(1645,plain,
% 1.99/1.60 (~c3_1(a698)),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[1045, 1644])).
% 1.99/1.60 tff(1646,plain,
% 1.99/1.60 (~c2_1(a698)),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[923, 1644])).
% 1.99/1.60 tff(1647,plain,
% 1.99/1.60 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | c0_1(a754) | c3_1(a754) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c0_1(a754) | c3_1(a754) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c2_1(a754)))),
% 1.99/1.60 inference(rewrite,[status(thm)],[])).
% 1.99/1.60 tff(1648,plain,
% 1.99/1.60 ((hskp6 | (~ndr1_0) | c3_1(a698) | c2_1(a698) | (~c1_1(a698)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754))) <=> (hskp6 | c0_1(a754) | c3_1(a754) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c2_1(a754)))),
% 1.99/1.60 inference(rewrite,[status(thm)],[])).
% 1.99/1.60 tff(1649,plain,
% 1.99/1.60 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a698) | c2_1(a698) | (~c1_1(a698)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | c0_1(a754) | c3_1(a754) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c2_1(a754))))),
% 1.99/1.60 inference(monotonicity,[status(thm)],[1648])).
% 1.99/1.60 tff(1650,plain,
% 1.99/1.60 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a698) | c2_1(a698) | (~c1_1(a698)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c0_1(a754) | c3_1(a754) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c2_1(a754)))),
% 1.99/1.60 inference(transitivity,[status(thm)],[1649, 1647])).
% 1.99/1.60 tff(1651,plain,
% 1.99/1.60 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a698) | c2_1(a698) | (~c1_1(a698)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))),
% 1.99/1.60 inference(quant_inst,[status(thm)],[])).
% 1.99/1.60 tff(1652,plain,
% 1.99/1.60 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c0_1(a754) | c3_1(a754) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c2_1(a754))),
% 1.99/1.60 inference(modus_ponens,[status(thm)],[1651, 1650])).
% 1.99/1.60 tff(1653,plain,
% 1.99/1.60 (~c1_1(a698)),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[1652, 227, 1624, 1558, 1556, 1557, 1646, 1645, 101])).
% 1.99/1.60 tff(1654,plain,
% 1.99/1.60 (~c0_1(a698)),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[917, 1644])).
% 1.99/1.60 tff(1655,plain,
% 1.99/1.60 (hskp27),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[961, 227, 1624, 1654, 1646, 1645, 201])).
% 1.99/1.60 tff(1656,plain,
% 1.99/1.60 (c1_1(a691)),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[267, 1655])).
% 1.99/1.60 tff(1657,plain,
% 1.99/1.60 (c0_1(a691)),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[278, 1655])).
% 1.99/1.60 tff(1658,plain,
% 1.99/1.60 (~c1_1(a754)),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[1460, 227, 1624, 1556, 1557, 1654, 1646, 1645, 301])).
% 1.99/1.60 tff(1659,plain,
% 1.99/1.60 (~hskp23),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[430, 1658, 1558, 1556, 62])).
% 1.99/1.60 tff(1660,plain,
% 1.99/1.60 (~hskp24),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[1626, 1624, 1558, 1556, 1557])).
% 1.99/1.60 tff(1661,plain,
% 1.99/1.60 (~c2_1(a691)),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[1063, 227, 1660, 1659, 1657, 1656, 163])).
% 1.99/1.60 tff(1662,plain,
% 1.99/1.60 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))),
% 1.99/1.60 inference(bind,[status(th)],[])).
% 1.99/1.60 tff(1663,plain,
% 1.99/1.60 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.99/1.60 inference(quant_intro,[status(thm)],[1662])).
% 1.99/1.60 tff(1664,plain,
% 1.99/1.60 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.99/1.60 inference(rewrite,[status(thm)],[])).
% 1.99/1.60 tff(1665,plain,
% 1.99/1.60 (^[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(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)) | 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))) | (~ndr1_0)) | c2_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))) | (~ndr1_0)) | c2_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)))), 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))) | (~ndr1_0)) | c2_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))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp3) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp3))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))))),
% 1.99/1.60 inference(bind,[status(th)],[])).
% 1.99/1.60 tff(1666,plain,
% 1.99/1.60 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.99/1.60 inference(quant_intro,[status(thm)],[1665])).
% 1.99/1.60 tff(1667,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause166')).
% 1.99/1.60 tff(1668,plain,
% 1.99/1.60 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.99/1.60 inference(modus_ponens,[status(thm)],[1667, 1666])).
% 1.99/1.60 tff(1669,plain,
% 1.99/1.60 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.99/1.60 inference(modus_ponens,[status(thm)],[1668, 1664])).
% 1.99/1.60 tff(1670,plain,(
% 1.99/1.60 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.99/1.60 inference(skolemize,[status(sab)],[1669])).
% 1.99/1.60 tff(1671,plain,
% 1.99/1.60 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.99/1.60 inference(modus_ponens,[status(thm)],[1670, 1663])).
% 1.99/1.60 tff(1672,plain,
% 1.99/1.60 (~hskp14),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[495, 1658, 1558, 1557, 1660, 1659, 62])).
% 1.99/1.60 tff(1673,plain,
% 1.99/1.60 (~hskp3),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[536, 1659, 1660, 175, 102, 1672])).
% 1.99/1.60 tff(1674,plain,
% 1.99/1.60 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp3 | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698) | (~c1_1(a691)) | (~c0_1(a691)) | c2_1(a691))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp3 | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698) | (~c1_1(a691)) | (~c0_1(a691)) | c2_1(a691))),
% 1.99/1.60 inference(rewrite,[status(thm)],[])).
% 1.99/1.60 tff(1675,plain,
% 1.99/1.60 ((hskp3 | (~ndr1_0) | c2_1(a691) | (~c0_1(a691)) | (~c1_1(a691)) | c3_1(a698) | c1_1(a698) | c2_1(a698)) <=> (hskp3 | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698) | (~c1_1(a691)) | (~c0_1(a691)) | c2_1(a691))),
% 1.99/1.60 inference(rewrite,[status(thm)],[])).
% 1.99/1.60 tff(1676,plain,
% 1.99/1.60 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a691) | (~c0_1(a691)) | (~c1_1(a691)) | c3_1(a698) | c1_1(a698) | c2_1(a698))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp3 | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698) | (~c1_1(a691)) | (~c0_1(a691)) | c2_1(a691)))),
% 1.99/1.60 inference(monotonicity,[status(thm)],[1675])).
% 1.99/1.60 tff(1677,plain,
% 1.99/1.60 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a691) | (~c0_1(a691)) | (~c1_1(a691)) | c3_1(a698) | c1_1(a698) | c2_1(a698))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp3 | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698) | (~c1_1(a691)) | (~c0_1(a691)) | c2_1(a691))),
% 1.99/1.60 inference(transitivity,[status(thm)],[1676, 1674])).
% 1.99/1.60 tff(1678,plain,
% 1.99/1.60 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a691) | (~c0_1(a691)) | (~c1_1(a691)) | c3_1(a698) | c1_1(a698) | c2_1(a698))),
% 1.99/1.60 inference(quant_inst,[status(thm)],[])).
% 1.99/1.60 tff(1679,plain,
% 1.99/1.60 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp3 | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698) | (~c1_1(a691)) | (~c0_1(a691)) | c2_1(a691)),
% 1.99/1.60 inference(modus_ponens,[status(thm)],[1678, 1677])).
% 1.99/1.60 tff(1680,plain,
% 1.99/1.60 ($false),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[1679, 227, 1673, 1657, 1656, 1646, 1645, 1671, 1661, 1653])).
% 1.99/1.60 tff(1681,plain,(c3_1(a697) | hskp30 | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.99/1.60 tff(1682,plain,
% 1.99/1.60 (c3_1(a697)),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[1681, 102, 62])).
% 1.99/1.60 tff(1683,plain,
% 1.99/1.60 (~hskp3),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[1355, 1682])).
% 1.99/1.60 tff(1684,plain,
% 1.99/1.60 (hskp4),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[1633, 1683])).
% 1.99/1.60 tff(1685,plain,
% 1.99/1.60 (~c3_1(a698)),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[1045, 1684])).
% 1.99/1.60 tff(1686,plain,
% 1.99/1.60 (~c2_1(a698)),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[923, 1684])).
% 1.99/1.60 tff(1687,plain,
% 1.99/1.60 (~c1_1(a698)),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[1652, 227, 1624, 1558, 1556, 1557, 1686, 1685, 101])).
% 1.99/1.60 tff(1688,plain,
% 1.99/1.60 (~c0_1(a698)),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[917, 1684])).
% 1.99/1.60 tff(1689,plain,
% 1.99/1.60 (hskp27),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[961, 227, 1624, 1688, 1686, 1685, 201])).
% 1.99/1.60 tff(1690,plain,
% 1.99/1.60 (c1_1(a691)),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[267, 1689])).
% 1.99/1.60 tff(1691,plain,
% 1.99/1.60 (c0_1(a691)),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[278, 1689])).
% 1.99/1.60 tff(1692,plain,
% 1.99/1.60 (~c1_1(a754)),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[1460, 227, 1624, 1556, 1557, 1688, 1686, 1685, 301])).
% 1.99/1.60 tff(1693,plain,
% 1.99/1.60 (~hskp23),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[430, 1692, 1558, 1556, 62])).
% 1.99/1.60 tff(1694,plain,
% 1.99/1.60 (~c2_1(a691)),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[1063, 227, 1660, 1693, 1691, 1690, 163])).
% 1.99/1.60 tff(1695,plain,
% 1.99/1.60 ($false),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[1679, 227, 1683, 1691, 1690, 1686, 1685, 1671, 1694, 1687])).
% 1.99/1.60 tff(1696,plain,(hskp30 | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.99/1.60 tff(1697,plain,
% 1.99/1.60 (hskp30),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[1696, 62])).
% 1.99/1.60 tff(1698,plain,
% 1.99/1.60 (((~hskp30) | c3_1(a733)) <=> ((~hskp30) | c3_1(a733))),
% 1.99/1.60 inference(rewrite,[status(thm)],[])).
% 1.99/1.60 tff(1699,axiom,((~hskp30) | c3_1(a733)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause42')).
% 1.99/1.60 tff(1700,plain,
% 1.99/1.60 ((~hskp30) | c3_1(a733)),
% 1.99/1.60 inference(modus_ponens,[status(thm)],[1699, 1698])).
% 1.99/1.60 tff(1701,plain,
% 1.99/1.60 ((~hskp30) | c3_1(a733)),
% 1.99/1.60 inference(modus_ponens,[status(thm)],[1700, 1698])).
% 1.99/1.60 tff(1702,plain,
% 1.99/1.60 ((~hskp30) | c3_1(a733)),
% 1.99/1.60 inference(modus_ponens,[status(thm)],[1701, 1698])).
% 1.99/1.60 tff(1703,plain,
% 1.99/1.60 ((~hskp30) | c3_1(a733)),
% 1.99/1.60 inference(modus_ponens,[status(thm)],[1702, 1698])).
% 1.99/1.60 tff(1704,plain,
% 1.99/1.60 ((~hskp30) | c3_1(a733)),
% 1.99/1.60 inference(modus_ponens,[status(thm)],[1703, 1698])).
% 1.99/1.60 tff(1705,plain,
% 1.99/1.60 ((~hskp30) | c3_1(a733)),
% 1.99/1.60 inference(modus_ponens,[status(thm)],[1704, 1698])).
% 1.99/1.60 tff(1706,plain,
% 1.99/1.60 ((~hskp30) | c3_1(a733)),
% 1.99/1.60 inference(modus_ponens,[status(thm)],[1705, 1698])).
% 1.99/1.60 tff(1707,plain,
% 1.99/1.60 ((~hskp30) | c3_1(a733)),
% 1.99/1.60 inference(modus_ponens,[status(thm)],[1706, 1698])).
% 1.99/1.60 tff(1708,plain,
% 1.99/1.60 (c3_1(a733)),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[1707, 1697])).
% 1.99/1.60 tff(1709,plain,
% 1.99/1.60 (((~hskp30) | c2_1(a733)) <=> ((~hskp30) | c2_1(a733))),
% 1.99/1.60 inference(rewrite,[status(thm)],[])).
% 1.99/1.60 tff(1710,axiom,((~hskp30) | c2_1(a733)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause41')).
% 1.99/1.60 tff(1711,plain,
% 1.99/1.60 ((~hskp30) | c2_1(a733)),
% 1.99/1.60 inference(modus_ponens,[status(thm)],[1710, 1709])).
% 1.99/1.60 tff(1712,plain,
% 1.99/1.60 ((~hskp30) | c2_1(a733)),
% 1.99/1.60 inference(modus_ponens,[status(thm)],[1711, 1709])).
% 1.99/1.60 tff(1713,plain,
% 1.99/1.60 ((~hskp30) | c2_1(a733)),
% 1.99/1.60 inference(modus_ponens,[status(thm)],[1712, 1709])).
% 1.99/1.60 tff(1714,plain,
% 1.99/1.60 ((~hskp30) | c2_1(a733)),
% 1.99/1.60 inference(modus_ponens,[status(thm)],[1713, 1709])).
% 1.99/1.60 tff(1715,plain,
% 1.99/1.60 ((~hskp30) | c2_1(a733)),
% 1.99/1.60 inference(modus_ponens,[status(thm)],[1714, 1709])).
% 1.99/1.60 tff(1716,plain,
% 1.99/1.60 ((~hskp30) | c2_1(a733)),
% 1.99/1.60 inference(modus_ponens,[status(thm)],[1715, 1709])).
% 1.99/1.60 tff(1717,plain,
% 1.99/1.60 ((~hskp30) | c2_1(a733)),
% 1.99/1.60 inference(modus_ponens,[status(thm)],[1716, 1709])).
% 1.99/1.60 tff(1718,plain,
% 1.99/1.60 ((~hskp30) | c2_1(a733)),
% 1.99/1.60 inference(modus_ponens,[status(thm)],[1717, 1709])).
% 1.99/1.60 tff(1719,plain,
% 1.99/1.60 (c2_1(a733)),
% 1.99/1.60 inference(unit_resolution,[status(thm)],[1718, 1697])).
% 1.99/1.61 tff(1720,plain,
% 1.99/1.61 (((~hskp30) | c1_1(a733)) <=> ((~hskp30) | c1_1(a733))),
% 1.99/1.61 inference(rewrite,[status(thm)],[])).
% 1.99/1.61 tff(1721,axiom,((~hskp30) | c1_1(a733)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause40')).
% 1.99/1.61 tff(1722,plain,
% 1.99/1.61 ((~hskp30) | c1_1(a733)),
% 1.99/1.61 inference(modus_ponens,[status(thm)],[1721, 1720])).
% 1.99/1.61 tff(1723,plain,
% 1.99/1.61 ((~hskp30) | c1_1(a733)),
% 1.99/1.61 inference(modus_ponens,[status(thm)],[1722, 1720])).
% 1.99/1.61 tff(1724,plain,
% 1.99/1.61 ((~hskp30) | c1_1(a733)),
% 1.99/1.61 inference(modus_ponens,[status(thm)],[1723, 1720])).
% 1.99/1.61 tff(1725,plain,
% 1.99/1.61 ((~hskp30) | c1_1(a733)),
% 1.99/1.61 inference(modus_ponens,[status(thm)],[1724, 1720])).
% 1.99/1.61 tff(1726,plain,
% 1.99/1.61 ((~hskp30) | c1_1(a733)),
% 1.99/1.61 inference(modus_ponens,[status(thm)],[1725, 1720])).
% 1.99/1.61 tff(1727,plain,
% 1.99/1.61 ((~hskp30) | c1_1(a733)),
% 1.99/1.61 inference(modus_ponens,[status(thm)],[1726, 1720])).
% 1.99/1.61 tff(1728,plain,
% 1.99/1.61 ((~hskp30) | c1_1(a733)),
% 1.99/1.61 inference(modus_ponens,[status(thm)],[1727, 1720])).
% 1.99/1.61 tff(1729,plain,
% 1.99/1.61 ((~hskp30) | c1_1(a733)),
% 1.99/1.61 inference(modus_ponens,[status(thm)],[1728, 1720])).
% 1.99/1.61 tff(1730,plain,
% 1.99/1.61 (c1_1(a733)),
% 1.99/1.61 inference(unit_resolution,[status(thm)],[1729, 1697])).
% 1.99/1.61 tff(1731,plain,
% 1.99/1.61 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | c2_1(a702) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a702)) | (~c0_1(a702)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a702) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a702)) | (~c0_1(a702)))),
% 1.99/1.61 inference(rewrite,[status(thm)],[])).
% 1.99/1.61 tff(1732,plain,
% 1.99/1.61 ((hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702))) <=> (hskp28 | c2_1(a702) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a702)) | (~c0_1(a702)))),
% 1.99/1.61 inference(rewrite,[status(thm)],[])).
% 1.99/1.61 tff(1733,plain,
% 1.99/1.61 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | c2_1(a702) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a702)) | (~c0_1(a702))))),
% 1.99/1.61 inference(monotonicity,[status(thm)],[1732])).
% 1.99/1.61 tff(1734,plain,
% 1.99/1.61 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a702) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a702)) | (~c0_1(a702)))),
% 1.99/1.61 inference(transitivity,[status(thm)],[1733, 1731])).
% 1.99/1.61 tff(1735,plain,
% 1.99/1.61 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)))),
% 1.99/1.61 inference(quant_inst,[status(thm)],[])).
% 1.99/1.61 tff(1736,plain,
% 1.99/1.61 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a702) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a702)) | (~c0_1(a702))),
% 1.99/1.61 inference(modus_ponens,[status(thm)],[1735, 1734])).
% 1.99/1.61 tff(1737,plain,
% 1.99/1.61 ($false),
% 1.99/1.61 inference(unit_resolution,[status(thm)],[1736, 227, 62, 1730, 1719, 1708, 91, 80, 69, 61])).
% 1.99/1.61 tff(1738,plain,((~hskp6) | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.99/1.61 tff(1739,plain,
% 1.99/1.61 (~hskp6),
% 1.99/1.61 inference(unit_resolution,[status(thm)],[1738, 62])).
% 1.99/1.61 tff(1740,plain,
% 1.99/1.61 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))),
% 1.99/1.61 inference(bind,[status(th)],[])).
% 1.99/1.61 tff(1741,plain,
% 1.99/1.61 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.99/1.61 inference(quant_intro,[status(thm)],[1740])).
% 1.99/1.61 tff(1742,plain,
% 1.99/1.61 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.99/1.61 inference(rewrite,[status(thm)],[])).
% 1.99/1.61 tff(1743,plain,
% 1.99/1.61 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp10) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp10))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))))),
% 1.99/1.61 inference(bind,[status(th)],[])).
% 1.99/1.61 tff(1744,plain,
% 1.99/1.61 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.99/1.61 inference(quant_intro,[status(thm)],[1743])).
% 1.99/1.61 tff(1745,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause171')).
% 1.99/1.61 tff(1746,plain,
% 1.99/1.61 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.99/1.61 inference(modus_ponens,[status(thm)],[1745, 1744])).
% 1.99/1.61 tff(1747,plain,
% 1.99/1.61 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.99/1.61 inference(modus_ponens,[status(thm)],[1746, 1742])).
% 1.99/1.61 tff(1748,plain,(
% 1.99/1.61 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.99/1.61 inference(skolemize,[status(sab)],[1747])).
% 1.99/1.61 tff(1749,plain,
% 1.99/1.61 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.99/1.61 inference(modus_ponens,[status(thm)],[1748, 1741])).
% 1.99/1.61 tff(1750,plain,
% 1.99/1.61 (hskp27 | hskp6 | c2_1(a754) | c0_1(a754)),
% 1.99/1.61 inference(unit_resolution,[status(thm)],[233, 227, 178, 201])).
% 1.99/1.61 tff(1751,plain,
% 1.99/1.61 (hskp27),
% 1.99/1.61 inference(unit_resolution,[status(thm)],[1750, 180, 177, 179])).
% 1.99/1.61 tff(1752,plain,
% 1.99/1.61 (c0_1(a691)),
% 1.99/1.61 inference(unit_resolution,[status(thm)],[278, 1751])).
% 1.99/1.61 tff(1753,plain,
% 1.99/1.61 (c3_1(a691)),
% 1.99/1.61 inference(unit_resolution,[status(thm)],[256, 1751])).
% 1.99/1.61 tff(1754,assumption,(~c2_1(a691)), introduced(assumption)).
% 1.99/1.61 tff(1755,assumption,(c3_1(a691)), introduced(assumption)).
% 1.99/1.61 tff(1756,assumption,(c0_1(a691)), introduced(assumption)).
% 1.99/1.61 tff(1757,plain,
% 1.99/1.61 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a691)) | (~c0_1(a691)) | c2_1(a691))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp28 | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a691)) | (~c0_1(a691)) | c2_1(a691))),
% 1.99/1.61 inference(rewrite,[status(thm)],[])).
% 1.99/1.61 tff(1758,plain,
% 1.99/1.61 ((hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c2_1(a691) | (~c3_1(a691)) | (~c0_1(a691))) <=> (hskp28 | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a691)) | (~c0_1(a691)) | c2_1(a691))),
% 1.99/1.61 inference(rewrite,[status(thm)],[])).
% 1.99/1.61 tff(1759,plain,
% 1.99/1.61 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c2_1(a691) | (~c3_1(a691)) | (~c0_1(a691)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a691)) | (~c0_1(a691)) | c2_1(a691)))),
% 1.99/1.61 inference(monotonicity,[status(thm)],[1758])).
% 1.99/1.61 tff(1760,plain,
% 1.99/1.61 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c2_1(a691) | (~c3_1(a691)) | (~c0_1(a691)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp28 | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a691)) | (~c0_1(a691)) | c2_1(a691))),
% 1.99/1.61 inference(transitivity,[status(thm)],[1759, 1757])).
% 1.99/1.61 tff(1761,plain,
% 1.99/1.61 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c2_1(a691) | (~c3_1(a691)) | (~c0_1(a691)))),
% 1.99/1.61 inference(quant_inst,[status(thm)],[])).
% 1.99/1.61 tff(1762,plain,
% 1.99/1.61 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp28 | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a691)) | (~c0_1(a691)) | c2_1(a691)),
% 1.99/1.61 inference(modus_ponens,[status(thm)],[1761, 1760])).
% 1.99/1.61 tff(1763,plain,
% 1.99/1.61 ($false),
% 1.99/1.61 inference(unit_resolution,[status(thm)],[1762, 227, 62, 1730, 1719, 1708, 1756, 1755, 61, 1754])).
% 1.99/1.61 tff(1764,plain,(c2_1(a691) | hskp28 | (~c0_1(a691)) | (~c3_1(a691))), inference(lemma,lemma(discharge,[]))).
% 1.99/1.61 tff(1765,plain,
% 1.99/1.61 (c2_1(a691)),
% 1.99/1.61 inference(unit_resolution,[status(thm)],[1764, 1753, 1752, 62])).
% 1.99/1.61 tff(1766,plain,
% 1.99/1.61 (c1_1(a691)),
% 1.99/1.61 inference(unit_resolution,[status(thm)],[267, 1751])).
% 1.99/1.61 tff(1767,assumption,(c2_1(a691)), introduced(assumption)).
% 1.99/1.61 tff(1768,plain,
% 1.99/1.61 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)))),
% 1.99/1.61 inference(bind,[status(th)],[])).
% 1.99/1.61 tff(1769,plain,
% 1.99/1.61 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.99/1.61 inference(quant_intro,[status(thm)],[1768])).
% 1.99/1.61 tff(1770,plain,
% 1.99/1.61 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.99/1.61 inference(rewrite,[status(thm)],[])).
% 1.99/1.61 tff(1771,plain,
% 1.99/1.61 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(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)) | c3_1(V) | (~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)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~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)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_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))) | (~c1_1(V))) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_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))) | (~c1_1(V))) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))))),
% 1.99/1.61 inference(bind,[status(th)],[])).
% 1.99/1.61 tff(1772,plain,
% 1.99/1.61 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.99/1.61 inference(quant_intro,[status(thm)],[1771])).
% 1.99/1.61 tff(1773,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause193')).
% 1.99/1.61 tff(1774,plain,
% 1.99/1.61 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.99/1.61 inference(modus_ponens,[status(thm)],[1773, 1772])).
% 1.99/1.61 tff(1775,plain,
% 1.99/1.61 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.99/1.61 inference(modus_ponens,[status(thm)],[1774, 1770])).
% 1.99/1.61 tff(1776,plain,(
% 1.99/1.61 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.99/1.61 inference(skolemize,[status(sab)],[1775])).
% 1.99/1.61 tff(1777,plain,
% 1.99/1.61 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.99/1.61 inference(modus_ponens,[status(thm)],[1776, 1769])).
% 1.99/1.61 tff(1778,plain,
% 1.99/1.61 (hskp27),
% 1.99/1.61 inference(unit_resolution,[status(thm)],[1750, 179, 177, 180])).
% 1.99/1.61 tff(1779,plain,
% 1.99/1.61 (c3_1(a691)),
% 1.99/1.61 inference(unit_resolution,[status(thm)],[256, 1778])).
% 1.99/1.61 tff(1780,plain,
% 1.99/1.61 (c0_1(a691)),
% 1.99/1.61 inference(unit_resolution,[status(thm)],[278, 1778])).
% 1.99/1.61 tff(1781,plain,
% 1.99/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a754) | c3_1(a764) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c0_1(a764)) | (~c1_1(a764)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a754) | c3_1(a764) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c0_1(a764)) | (~c1_1(a764)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 1.99/1.61 inference(rewrite,[status(thm)],[])).
% 1.99/1.61 tff(1782,plain,
% 1.99/1.61 (((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764)) | c3_1(a754) | c2_1(a754) | c0_1(a754)) <=> (c2_1(a754) | c3_1(a764) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c0_1(a764)) | (~c1_1(a764)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 1.99/1.61 inference(rewrite,[status(thm)],[])).
% 1.99/1.61 tff(1783,plain,
% 1.99/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764)) | c3_1(a754) | c2_1(a754) | c0_1(a754))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a754) | c3_1(a764) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c0_1(a764)) | (~c1_1(a764)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691))))),
% 1.99/1.61 inference(monotonicity,[status(thm)],[1782])).
% 1.99/1.61 tff(1784,plain,
% 1.99/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764)) | c3_1(a754) | c2_1(a754) | c0_1(a754))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a754) | c3_1(a764) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c0_1(a764)) | (~c1_1(a764)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 1.99/1.61 inference(transitivity,[status(thm)],[1783, 1781])).
% 1.99/1.61 tff(1785,plain,
% 1.99/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764)) | c3_1(a754) | c2_1(a754) | c0_1(a754))),
% 1.99/1.61 inference(quant_inst,[status(thm)],[])).
% 1.99/1.61 tff(1786,plain,
% 1.99/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a754) | c3_1(a764) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c0_1(a764)) | (~c1_1(a764)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691))),
% 1.99/1.61 inference(modus_ponens,[status(thm)],[1785, 1784])).
% 1.99/1.61 tff(1787,plain,
% 1.99/1.61 (~c0_1(a764)),
% 1.99/1.61 inference(unit_resolution,[status(thm)],[1786, 227, 1780, 1779, 325, 180, 308, 179, 178, 1777, 1767])).
% 1.99/1.61 tff(1788,plain,
% 1.99/1.61 ($false),
% 1.99/1.61 inference(unit_resolution,[status(thm)],[331, 227, 177, 325, 314, 308, 301, 1787])).
% 1.99/1.61 tff(1789,plain,((~hskp24) | hskp6 | c2_1(a754) | c0_1(a754) | c3_1(a754) | (~c2_1(a691))), inference(lemma,lemma(discharge,[]))).
% 1.99/1.61 tff(1790,plain,
% 1.99/1.61 (~hskp24),
% 1.99/1.61 inference(unit_resolution,[status(thm)],[1789, 1765, 180, 179, 178, 177])).
% 1.99/1.61 tff(1791,plain,
% 1.99/1.61 (hskp23),
% 1.99/1.61 inference(unit_resolution,[status(thm)],[1063, 227, 1790, 1752, 1766, 163, 1765])).
% 1.99/1.61 tff(1792,plain,
% 1.99/1.61 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | c2_1(a754) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c2_1(a754) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754)))),
% 1.99/1.61 inference(rewrite,[status(thm)],[])).
% 1.99/1.61 tff(1793,plain,
% 1.99/1.61 ((hskp6 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)) | c3_1(a754) | c0_1(a754) | c2_1(a754)) <=> (hskp6 | c2_1(a754) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754)))),
% 1.99/1.61 inference(rewrite,[status(thm)],[])).
% 1.99/1.61 tff(1794,plain,
% 1.99/1.61 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)) | c3_1(a754) | c0_1(a754) | c2_1(a754))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | c2_1(a754) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754))))),
% 1.99/1.61 inference(monotonicity,[status(thm)],[1793])).
% 1.99/1.61 tff(1795,plain,
% 1.99/1.61 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)) | c3_1(a754) | c0_1(a754) | c2_1(a754))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c2_1(a754) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754)))),
% 1.99/1.61 inference(transitivity,[status(thm)],[1794, 1792])).
% 1.99/1.61 tff(1796,plain,
% 1.99/1.61 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)) | c3_1(a754) | c0_1(a754) | c2_1(a754))),
% 1.99/1.61 inference(quant_inst,[status(thm)],[])).
% 1.99/1.61 tff(1797,plain,
% 1.99/1.61 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c2_1(a754) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754))),
% 1.99/1.61 inference(modus_ponens,[status(thm)],[1796, 1795])).
% 1.99/1.61 tff(1798,plain,
% 1.99/1.61 (hskp6 | c2_1(a754) | c0_1(a754) | (~c1_1(a754))),
% 1.99/1.61 inference(unit_resolution,[status(thm)],[1797, 227, 178, 301])).
% 1.99/1.61 tff(1799,plain,
% 1.99/1.61 (~c1_1(a754)),
% 1.99/1.61 inference(unit_resolution,[status(thm)],[1798, 180, 177, 179])).
% 1.99/1.61 tff(1800,plain,
% 1.99/1.61 (~c2_1(a763)),
% 1.99/1.61 inference(unit_resolution,[status(thm)],[404, 1791])).
% 1.99/1.61 tff(1801,plain,
% 1.99/1.61 (~c1_1(a763)),
% 1.99/1.61 inference(unit_resolution,[status(thm)],[410, 1791])).
% 1.99/1.61 tff(1802,plain,
% 1.99/1.61 (c0_1(a763)),
% 1.99/1.61 inference(unit_resolution,[status(thm)],[421, 1791])).
% 1.99/1.61 tff(1803,assumption,(hskp0), introduced(assumption)).
% 1.99/1.61 tff(1804,plain,
% 1.99/1.61 (~c1_1(a692)),
% 1.99/1.61 inference(unit_resolution,[status(thm)],[853, 1803])).
% 1.99/1.61 tff(1805,plain,
% 1.99/1.61 (~c0_1(a692)),
% 1.99/1.61 inference(unit_resolution,[status(thm)],[859, 1803])).
% 1.99/1.61 tff(1806,assumption,(~c2_1(a763)), introduced(assumption)).
% 1.99/1.61 tff(1807,assumption,(~c1_1(a763)), introduced(assumption)).
% 1.99/1.61 tff(1808,plain,
% 1.99/1.61 (c2_1(a692)),
% 1.99/1.61 inference(unit_resolution,[status(thm)],[872, 1803])).
% 1.99/1.61 tff(1809,assumption,(c0_1(a763)), introduced(assumption)).
% 1.99/1.61 tff(1810,plain,
% 1.99/1.61 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | c1_1(a763) | c2_1(a763) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a763)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c1_1(a763) | c2_1(a763) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a763)))),
% 1.99/1.61 inference(rewrite,[status(thm)],[])).
% 1.99/1.61 tff(1811,plain,
% 1.99/1.61 ((hskp28 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c1_1(a692) | c0_1(a692) | (~c2_1(a692))) <=> (hskp28 | c1_1(a763) | c2_1(a763) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a763)))),
% 1.99/1.61 inference(rewrite,[status(thm)],[])).
% 1.99/1.61 tff(1812,plain,
% 1.99/1.61 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c1_1(a692) | c0_1(a692) | (~c2_1(a692)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | c1_1(a763) | c2_1(a763) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a763))))),
% 1.99/1.61 inference(monotonicity,[status(thm)],[1811])).
% 1.99/1.61 tff(1813,plain,
% 1.99/1.61 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c1_1(a692) | c0_1(a692) | (~c2_1(a692)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c1_1(a763) | c2_1(a763) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a763)))),
% 1.99/1.61 inference(transitivity,[status(thm)],[1812, 1810])).
% 1.99/1.61 tff(1814,plain,
% 1.99/1.61 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c1_1(a692) | c0_1(a692) | (~c2_1(a692)))),
% 1.99/1.61 inference(quant_inst,[status(thm)],[])).
% 1.99/1.61 tff(1815,plain,
% 1.99/1.61 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c1_1(a763) | c2_1(a763) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a763))),
% 1.99/1.61 inference(modus_ponens,[status(thm)],[1814, 1813])).
% 1.99/1.61 tff(1816,plain,
% 1.99/1.61 ($false),
% 1.99/1.61 inference(unit_resolution,[status(thm)],[1815, 227, 62, 1809, 1808, 1807, 1806, 1805, 1804, 398])).
% 1.99/1.61 tff(1817,plain,((~hskp0) | hskp28 | (~c0_1(a763)) | c1_1(a763) | c2_1(a763)), inference(lemma,lemma(discharge,[]))).
% 1.99/1.61 tff(1818,plain,
% 1.99/1.61 (~hskp0),
% 1.99/1.61 inference(unit_resolution,[status(thm)],[1817, 1802, 62, 1801, 1800])).
% 1.99/1.61 tff(1819,plain,
% 1.99/1.61 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c0_1(a754) | c3_1(a754) | (~ndr1_0) | c1_1(a754))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a754) | c3_1(a754) | (~ndr1_0) | c1_1(a754))),
% 1.99/1.61 inference(rewrite,[status(thm)],[])).
% 1.99/1.61 tff(1820,plain,
% 1.99/1.61 ((hskp1 | hskp0 | (~ndr1_0) | c3_1(a754) | c1_1(a754) | c0_1(a754)) <=> (hskp1 | hskp0 | c0_1(a754) | c3_1(a754) | (~ndr1_0) | c1_1(a754))),
% 1.99/1.61 inference(rewrite,[status(thm)],[])).
% 1.99/1.61 tff(1821,plain,
% 1.99/1.61 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c3_1(a754) | c1_1(a754) | c0_1(a754))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c0_1(a754) | c3_1(a754) | (~ndr1_0) | c1_1(a754)))),
% 1.99/1.61 inference(monotonicity,[status(thm)],[1820])).
% 1.99/1.61 tff(1822,plain,
% 1.99/1.61 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c3_1(a754) | c1_1(a754) | c0_1(a754))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a754) | c3_1(a754) | (~ndr1_0) | c1_1(a754))),
% 1.99/1.61 inference(transitivity,[status(thm)],[1821, 1819])).
% 1.99/1.61 tff(1823,plain,
% 1.99/1.61 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c3_1(a754) | c1_1(a754) | c0_1(a754))),
% 1.99/1.61 inference(quant_inst,[status(thm)],[])).
% 1.99/1.61 tff(1824,plain,
% 1.99/1.61 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a754) | c3_1(a754) | (~ndr1_0) | c1_1(a754)),
% 1.99/1.61 inference(modus_ponens,[status(thm)],[1823, 1822])).
% 1.99/1.61 tff(1825,plain,
% 1.99/1.61 (hskp1 | hskp0 | c0_1(a754) | c1_1(a754)),
% 1.99/1.61 inference(unit_resolution,[status(thm)],[1824, 227, 178, 1482])).
% 1.99/1.61 tff(1826,plain,
% 1.99/1.61 (hskp1),
% 1.99/1.61 inference(unit_resolution,[status(thm)],[1825, 1818, 179, 1799])).
% 1.99/1.61 tff(1827,plain,
% 1.99/1.61 (~c1_1(a693)),
% 1.99/1.61 inference(unit_resolution,[status(thm)],[1423, 1826])).
% 1.99/1.61 tff(1828,plain,
% 1.99/1.61 (~c3_1(a693)),
% 1.99/1.61 inference(unit_resolution,[status(thm)],[1553, 1826])).
% 1.99/1.61 tff(1829,plain,
% 1.99/1.61 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | c2_1(a763) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a763)) | (~c0_1(a763)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a763) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a763)) | (~c0_1(a763)))),
% 1.99/1.61 inference(rewrite,[status(thm)],[])).
% 1.99/1.61 tff(1830,plain,
% 1.99/1.61 ((hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c2_1(a763) | (~c3_1(a763)) | (~c0_1(a763))) <=> (hskp28 | c2_1(a763) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a763)) | (~c0_1(a763)))),
% 1.99/1.61 inference(rewrite,[status(thm)],[])).
% 1.99/1.61 tff(1831,plain,
% 1.99/1.61 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c2_1(a763) | (~c3_1(a763)) | (~c0_1(a763)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | c2_1(a763) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a763)) | (~c0_1(a763))))),
% 1.99/1.61 inference(monotonicity,[status(thm)],[1830])).
% 1.99/1.61 tff(1832,plain,
% 1.99/1.61 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c2_1(a763) | (~c3_1(a763)) | (~c0_1(a763)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a763) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a763)) | (~c0_1(a763)))),
% 1.99/1.62 inference(transitivity,[status(thm)],[1831, 1829])).
% 1.99/1.62 tff(1833,plain,
% 1.99/1.62 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c2_1(a763) | (~c3_1(a763)) | (~c0_1(a763)))),
% 1.99/1.62 inference(quant_inst,[status(thm)],[])).
% 1.99/1.62 tff(1834,plain,
% 1.99/1.62 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a763) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a763)) | (~c0_1(a763))),
% 1.99/1.62 inference(modus_ponens,[status(thm)],[1833, 1832])).
% 1.99/1.62 tff(1835,plain,
% 1.99/1.62 (~c3_1(a763)),
% 1.99/1.62 inference(unit_resolution,[status(thm)],[1834, 227, 62, 1730, 1719, 1708, 422, 405, 61])).
% 1.99/1.62 tff(1836,plain,
% 1.99/1.62 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a763) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | c3_1(a763) | (~c0_1(a763)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a763) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | c3_1(a763) | (~c0_1(a763)))),
% 1.99/1.62 inference(rewrite,[status(thm)],[])).
% 1.99/1.62 tff(1837,plain,
% 1.99/1.62 ((hskp28 | (~ndr1_0) | c3_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a693) | c1_1(a693) | (~c2_1(a693))) <=> (hskp28 | c2_1(a763) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | c3_1(a763) | (~c0_1(a763)))),
% 1.99/1.62 inference(rewrite,[status(thm)],[])).
% 1.99/1.62 tff(1838,plain,
% 1.99/1.62 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a693) | c1_1(a693) | (~c2_1(a693)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a763) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | c3_1(a763) | (~c0_1(a763))))),
% 1.99/1.62 inference(monotonicity,[status(thm)],[1837])).
% 1.99/1.62 tff(1839,plain,
% 1.99/1.62 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a693) | c1_1(a693) | (~c2_1(a693)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a763) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | c3_1(a763) | (~c0_1(a763)))),
% 1.99/1.62 inference(transitivity,[status(thm)],[1838, 1836])).
% 1.99/1.62 tff(1840,plain,
% 1.99/1.62 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a693) | c1_1(a693) | (~c2_1(a693)))),
% 1.99/1.62 inference(quant_inst,[status(thm)],[])).
% 1.99/1.62 tff(1841,plain,
% 1.99/1.62 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a763) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | c3_1(a763) | (~c0_1(a763))),
% 1.99/1.62 inference(modus_ponens,[status(thm)],[1840, 1839])).
% 1.99/1.62 tff(1842,plain,
% 1.99/1.62 (~c2_1(a693)),
% 1.99/1.62 inference(unit_resolution,[status(thm)],[1841, 227, 62, 422, 405, 164, 153, 342, 1835])).
% 1.99/1.62 tff(1843,plain,
% 1.99/1.62 (~hskp1),
% 1.99/1.62 inference(unit_resolution,[status(thm)],[383, 1842])).
% 1.99/1.62 tff(1844,plain,
% 1.99/1.62 (hskp0),
% 1.99/1.62 inference(unit_resolution,[status(thm)],[1825, 1843, 179, 388])).
% 1.99/1.62 tff(1845,plain,
% 1.99/1.62 (~c1_1(a692)),
% 1.99/1.62 inference(unit_resolution,[status(thm)],[853, 1844])).
% 1.99/1.62 tff(1846,plain,
% 1.99/1.62 (~c0_1(a692)),
% 1.99/1.62 inference(unit_resolution,[status(thm)],[859, 1844])).
% 1.99/1.62 tff(1847,plain,
% 1.99/1.62 (c2_1(a692)),
% 1.99/1.62 inference(unit_resolution,[status(thm)],[872, 1844])).
% 1.99/1.62 tff(1848,plain,
% 1.99/1.62 ($false),
% 1.99/1.62 inference(unit_resolution,[status(thm)],[1815, 227, 62, 422, 1847, 411, 405, 1846, 1845, 398])).
% 1.99/1.62 tff(1849,plain,((~hskp23) | hskp28 | c0_1(a754) | c1_1(a754) | c3_1(a754) | c1_1(a693) | c3_1(a693)), inference(lemma,lemma(discharge,[]))).
% 1.99/1.62 tff(1850,plain,
% 1.99/1.62 ($false),
% 1.99/1.62 inference(unit_resolution,[status(thm)],[1849, 1828, 1827, 179, 1799, 178, 1791, 62])).
% 1.99/1.62 tff(1851,plain,(c2_1(a754) | c0_1(a754) | c3_1(a754) | hskp28 | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.99/1.62 tff(1852,plain,
% 1.99/1.62 (c2_1(a754)),
% 1.99/1.62 inference(unit_resolution,[status(thm)],[1851, 179, 178, 62, 177])).
% 1.99/1.62 tff(1853,plain,
% 1.99/1.62 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))),
% 1.99/1.62 inference(bind,[status(th)],[])).
% 1.99/1.62 tff(1854,plain,
% 1.99/1.62 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.99/1.62 inference(quant_intro,[status(thm)],[1853])).
% 1.99/1.62 tff(1855,plain,
% 1.99/1.62 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.99/1.62 inference(rewrite,[status(thm)],[])).
% 1.99/1.62 tff(1856,plain,
% 1.99/1.62 (^[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)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_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)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_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)) | c3_1(V)) | hskp8) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp8))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_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)) | c3_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))))),
% 1.99/1.62 inference(bind,[status(th)],[])).
% 1.99/1.62 tff(1857,plain,
% 1.99/1.62 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.99/1.62 inference(quant_intro,[status(thm)],[1856])).
% 1.99/1.62 tff(1858,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause178')).
% 1.99/1.62 tff(1859,plain,
% 1.99/1.62 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.99/1.62 inference(modus_ponens,[status(thm)],[1858, 1857])).
% 1.99/1.62 tff(1860,plain,
% 1.99/1.62 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.99/1.62 inference(modus_ponens,[status(thm)],[1859, 1855])).
% 1.99/1.62 tff(1861,plain,(
% 1.99/1.62 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.99/1.62 inference(skolemize,[status(sab)],[1860])).
% 1.99/1.62 tff(1862,plain,
% 1.99/1.62 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.99/1.62 inference(modus_ponens,[status(thm)],[1861, 1854])).
% 1.99/1.62 tff(1863,plain,
% 1.99/1.62 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c2_1(a754)))),
% 1.99/1.62 inference(rewrite,[status(thm)],[])).
% 1.99/1.62 tff(1864,plain,
% 1.99/1.62 ((hskp8 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754))) <=> (hskp8 | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c2_1(a754)))),
% 1.99/1.62 inference(rewrite,[status(thm)],[])).
% 1.99/1.62 tff(1865,plain,
% 1.99/1.62 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c2_1(a754))))),
% 1.99/1.62 inference(monotonicity,[status(thm)],[1864])).
% 1.99/1.62 tff(1866,plain,
% 1.99/1.62 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c2_1(a754)))),
% 1.99/1.62 inference(transitivity,[status(thm)],[1865, 1863])).
% 1.99/1.62 tff(1867,plain,
% 1.99/1.62 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))),
% 1.99/1.62 inference(quant_inst,[status(thm)],[])).
% 1.99/1.62 tff(1868,plain,
% 1.99/1.62 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c2_1(a754))),
% 1.99/1.62 inference(modus_ponens,[status(thm)],[1867, 1866])).
% 1.99/1.62 tff(1869,plain,
% 1.99/1.62 (hskp8 | c0_1(a754) | (~c2_1(a754))),
% 1.99/1.62 inference(unit_resolution,[status(thm)],[1868, 227, 1730, 1719, 1708, 178, 1862])).
% 1.99/1.62 tff(1870,plain,
% 1.99/1.62 (hskp8),
% 1.99/1.62 inference(unit_resolution,[status(thm)],[1869, 1852, 179])).
% 1.99/1.62 tff(1871,plain,
% 1.99/1.62 (((~hskp8) | (~c0_1(a710))) <=> ((~hskp8) | (~c0_1(a710)))),
% 1.99/1.62 inference(rewrite,[status(thm)],[])).
% 1.99/1.62 tff(1872,plain,
% 1.99/1.62 (((~c0_1(a710)) | (~hskp8)) <=> ((~hskp8) | (~c0_1(a710)))),
% 1.99/1.62 inference(rewrite,[status(thm)],[])).
% 1.99/1.62 tff(1873,axiom,((~c0_1(a710)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause120')).
% 1.99/1.62 tff(1874,plain,
% 1.99/1.62 ((~hskp8) | (~c0_1(a710))),
% 1.99/1.62 inference(modus_ponens,[status(thm)],[1873, 1872])).
% 1.99/1.62 tff(1875,plain,
% 1.99/1.62 ((~hskp8) | (~c0_1(a710))),
% 1.99/1.62 inference(modus_ponens,[status(thm)],[1874, 1871])).
% 1.99/1.62 tff(1876,plain,
% 1.99/1.62 (~c0_1(a710)),
% 1.99/1.62 inference(unit_resolution,[status(thm)],[1875, 1870])).
% 1.99/1.62 tff(1877,plain,
% 1.99/1.62 (((~hskp8) | c3_1(a710)) <=> ((~hskp8) | c3_1(a710))),
% 1.99/1.62 inference(rewrite,[status(thm)],[])).
% 1.99/1.62 tff(1878,axiom,((~hskp8) | c3_1(a710)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause74')).
% 1.99/1.62 tff(1879,plain,
% 1.99/1.62 ((~hskp8) | c3_1(a710)),
% 1.99/1.62 inference(modus_ponens,[status(thm)],[1878, 1877])).
% 1.99/1.62 tff(1880,plain,
% 1.99/1.62 ((~hskp8) | c3_1(a710)),
% 1.99/1.62 inference(modus_ponens,[status(thm)],[1879, 1877])).
% 1.99/1.62 tff(1881,plain,
% 1.99/1.62 ((~hskp8) | c3_1(a710)),
% 1.99/1.62 inference(modus_ponens,[status(thm)],[1880, 1877])).
% 1.99/1.62 tff(1882,plain,
% 1.99/1.62 ((~hskp8) | c3_1(a710)),
% 1.99/1.62 inference(modus_ponens,[status(thm)],[1881, 1877])).
% 1.99/1.62 tff(1883,plain,
% 1.99/1.62 ((~hskp8) | c3_1(a710)),
% 1.99/1.62 inference(modus_ponens,[status(thm)],[1882, 1877])).
% 1.99/1.62 tff(1884,plain,
% 1.99/1.62 ((~hskp8) | c3_1(a710)),
% 1.99/1.62 inference(modus_ponens,[status(thm)],[1883, 1877])).
% 1.99/1.62 tff(1885,plain,
% 1.99/1.62 ((~hskp8) | c3_1(a710)),
% 1.99/1.62 inference(modus_ponens,[status(thm)],[1884, 1877])).
% 1.99/1.62 tff(1886,plain,
% 1.99/1.62 ((~hskp8) | c3_1(a710)),
% 1.99/1.62 inference(modus_ponens,[status(thm)],[1885, 1877])).
% 1.99/1.62 tff(1887,plain,
% 1.99/1.62 (c3_1(a710)),
% 1.99/1.62 inference(unit_resolution,[status(thm)],[1886, 1870])).
% 1.99/1.62 tff(1888,assumption,(hskp10), introduced(assumption)).
% 1.99/1.62 tff(1889,plain,
% 1.99/1.62 (((~hskp10) | (~c2_1(a717))) <=> ((~hskp10) | (~c2_1(a717)))),
% 1.99/1.62 inference(rewrite,[status(thm)],[])).
% 1.99/1.62 tff(1890,plain,
% 1.99/1.62 (((~c2_1(a717)) | (~hskp10)) <=> ((~hskp10) | (~c2_1(a717)))),
% 1.99/1.62 inference(rewrite,[status(thm)],[])).
% 1.99/1.62 tff(1891,axiom,((~c2_1(a717)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause116')).
% 1.99/1.62 tff(1892,plain,
% 1.99/1.62 ((~hskp10) | (~c2_1(a717))),
% 1.99/1.62 inference(modus_ponens,[status(thm)],[1891, 1890])).
% 1.99/1.62 tff(1893,plain,
% 1.99/1.62 ((~hskp10) | (~c2_1(a717))),
% 1.99/1.62 inference(modus_ponens,[status(thm)],[1892, 1889])).
% 1.99/1.62 tff(1894,plain,
% 1.99/1.62 (~c2_1(a717)),
% 1.99/1.62 inference(unit_resolution,[status(thm)],[1893, 1888])).
% 1.99/1.62 tff(1895,plain,
% 1.99/1.62 (((~hskp10) | c3_1(a717)) <=> ((~hskp10) | c3_1(a717))),
% 1.99/1.62 inference(rewrite,[status(thm)],[])).
% 1.99/1.62 tff(1896,axiom,((~hskp10) | c3_1(a717)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause72')).
% 1.99/1.62 tff(1897,plain,
% 1.99/1.62 ((~hskp10) | c3_1(a717)),
% 1.99/1.62 inference(modus_ponens,[status(thm)],[1896, 1895])).
% 1.99/1.62 tff(1898,plain,
% 1.99/1.62 ((~hskp10) | c3_1(a717)),
% 1.99/1.62 inference(modus_ponens,[status(thm)],[1897, 1895])).
% 1.99/1.62 tff(1899,plain,
% 1.99/1.62 ((~hskp10) | c3_1(a717)),
% 1.99/1.62 inference(modus_ponens,[status(thm)],[1898, 1895])).
% 1.99/1.62 tff(1900,plain,
% 1.99/1.62 ((~hskp10) | c3_1(a717)),
% 1.99/1.62 inference(modus_ponens,[status(thm)],[1899, 1895])).
% 1.99/1.62 tff(1901,plain,
% 1.99/1.62 ((~hskp10) | c3_1(a717)),
% 1.99/1.62 inference(modus_ponens,[status(thm)],[1900, 1895])).
% 1.99/1.62 tff(1902,plain,
% 1.99/1.62 ((~hskp10) | c3_1(a717)),
% 1.99/1.62 inference(modus_ponens,[status(thm)],[1901, 1895])).
% 1.99/1.62 tff(1903,plain,
% 1.99/1.62 ((~hskp10) | c3_1(a717)),
% 1.99/1.62 inference(modus_ponens,[status(thm)],[1902, 1895])).
% 1.99/1.62 tff(1904,plain,
% 1.99/1.62 ((~hskp10) | c3_1(a717)),
% 1.99/1.62 inference(modus_ponens,[status(thm)],[1903, 1895])).
% 1.99/1.62 tff(1905,plain,
% 1.99/1.62 (c3_1(a717)),
% 1.99/1.62 inference(unit_resolution,[status(thm)],[1904, 1888])).
% 1.99/1.62 tff(1906,plain,
% 1.99/1.62 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | c2_1(a717) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a717)) | (~c0_1(a717)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a717) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a717)) | (~c0_1(a717)))),
% 1.99/1.62 inference(rewrite,[status(thm)],[])).
% 1.99/1.62 tff(1907,plain,
% 1.99/1.62 ((hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c2_1(a717) | (~c3_1(a717)) | (~c0_1(a717))) <=> (hskp28 | c2_1(a717) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a717)) | (~c0_1(a717)))),
% 1.99/1.62 inference(rewrite,[status(thm)],[])).
% 1.99/1.62 tff(1908,plain,
% 1.99/1.62 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c2_1(a717) | (~c3_1(a717)) | (~c0_1(a717)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | c2_1(a717) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a717)) | (~c0_1(a717))))),
% 1.99/1.62 inference(monotonicity,[status(thm)],[1907])).
% 1.99/1.62 tff(1909,plain,
% 1.99/1.62 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c2_1(a717) | (~c3_1(a717)) | (~c0_1(a717)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a717) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a717)) | (~c0_1(a717)))),
% 1.99/1.62 inference(transitivity,[status(thm)],[1908, 1906])).
% 1.99/1.62 tff(1910,plain,
% 1.99/1.62 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c2_1(a717) | (~c3_1(a717)) | (~c0_1(a717)))),
% 1.99/1.62 inference(quant_inst,[status(thm)],[])).
% 1.99/1.62 tff(1911,plain,
% 1.99/1.62 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a717) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a717)) | (~c0_1(a717))),
% 1.99/1.62 inference(modus_ponens,[status(thm)],[1910, 1909])).
% 1.99/1.62 tff(1912,plain,
% 1.99/1.62 (~c0_1(a717)),
% 1.99/1.62 inference(unit_resolution,[status(thm)],[1911, 227, 62, 1730, 1719, 1708, 1905, 1894, 61])).
% 1.99/1.62 tff(1913,plain,
% 1.99/1.62 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))),
% 1.99/1.62 inference(bind,[status(th)],[])).
% 1.99/1.62 tff(1914,plain,
% 1.99/1.62 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.99/1.62 inference(quant_intro,[status(thm)],[1913])).
% 1.99/1.62 tff(1915,plain,
% 1.99/1.62 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.99/1.62 inference(rewrite,[status(thm)],[])).
% 1.99/1.62 tff(1916,plain,
% 1.99/1.62 (^[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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp28) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp28))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp28) <=> (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))))),
% 1.99/1.62 inference(bind,[status(th)],[])).
% 1.99/1.62 tff(1917,plain,
% 1.99/1.62 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.99/1.62 inference(quant_intro,[status(thm)],[1916])).
% 1.99/1.62 tff(1918,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause177')).
% 1.99/1.62 tff(1919,plain,
% 1.99/1.62 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.99/1.62 inference(modus_ponens,[status(thm)],[1918, 1917])).
% 1.99/1.62 tff(1920,plain,
% 1.99/1.62 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.99/1.62 inference(modus_ponens,[status(thm)],[1919, 1915])).
% 1.99/1.62 tff(1921,plain,(
% 1.99/1.62 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.99/1.62 inference(skolemize,[status(sab)],[1920])).
% 1.99/1.62 tff(1922,plain,
% 1.99/1.62 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.99/1.62 inference(modus_ponens,[status(thm)],[1921, 1914])).
% 1.99/1.62 tff(1923,plain,
% 1.99/1.62 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | c2_1(a717) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a717)) | c0_1(a717))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp28 | c2_1(a717) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a717)) | c0_1(a717))),
% 1.99/1.62 inference(rewrite,[status(thm)],[])).
% 1.99/1.62 tff(1924,plain,
% 1.99/1.62 ((hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a717) | c2_1(a717) | (~c3_1(a717))) <=> (hskp28 | c2_1(a717) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a717)) | c0_1(a717))),
% 1.99/1.62 inference(rewrite,[status(thm)],[])).
% 1.99/1.62 tff(1925,plain,
% 1.99/1.62 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a717) | c2_1(a717) | (~c3_1(a717)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | c2_1(a717) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a717)) | c0_1(a717)))),
% 1.99/1.62 inference(monotonicity,[status(thm)],[1924])).
% 1.99/1.62 tff(1926,plain,
% 1.99/1.62 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a717) | c2_1(a717) | (~c3_1(a717)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp28 | c2_1(a717) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a717)) | c0_1(a717))),
% 1.99/1.62 inference(transitivity,[status(thm)],[1925, 1923])).
% 1.99/1.62 tff(1927,plain,
% 1.99/1.62 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a717) | c2_1(a717) | (~c3_1(a717)))),
% 1.99/1.62 inference(quant_inst,[status(thm)],[])).
% 1.99/1.62 tff(1928,plain,
% 1.99/1.62 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp28 | c2_1(a717) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a717)) | c0_1(a717)),
% 1.99/1.62 inference(modus_ponens,[status(thm)],[1927, 1926])).
% 1.99/1.62 tff(1929,plain,
% 1.99/1.62 ($false),
% 1.99/1.62 inference(unit_resolution,[status(thm)],[1928, 227, 62, 1730, 1719, 1708, 1905, 1894, 1922, 1912])).
% 1.99/1.62 tff(1930,plain,((~hskp10) | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.99/1.62 tff(1931,plain,
% 1.99/1.62 (~hskp10),
% 1.99/1.62 inference(unit_resolution,[status(thm)],[1930, 62])).
% 1.99/1.62 tff(1932,plain,
% 1.99/1.62 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c0_1(a754) | c3_1(a754) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c1_1(a710)) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a754) | c3_1(a754) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c1_1(a710)) | (~c2_1(a754)))),
% 1.99/1.62 inference(rewrite,[status(thm)],[])).
% 1.99/1.62 tff(1933,plain,
% 1.99/1.62 ((hskp10 | (~ndr1_0) | c0_1(a710) | (~c3_1(a710)) | (~c1_1(a710)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754))) <=> (hskp10 | c0_1(a754) | c3_1(a754) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c1_1(a710)) | (~c2_1(a754)))),
% 1.99/1.62 inference(rewrite,[status(thm)],[])).
% 1.99/1.62 tff(1934,plain,
% 1.99/1.62 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a710) | (~c3_1(a710)) | (~c1_1(a710)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c0_1(a754) | c3_1(a754) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c1_1(a710)) | (~c2_1(a754))))),
% 1.99/1.62 inference(monotonicity,[status(thm)],[1933])).
% 1.99/1.62 tff(1935,plain,
% 1.99/1.62 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a710) | (~c3_1(a710)) | (~c1_1(a710)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a754) | c3_1(a754) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c1_1(a710)) | (~c2_1(a754)))),
% 1.99/1.62 inference(transitivity,[status(thm)],[1934, 1932])).
% 1.99/1.62 tff(1936,plain,
% 1.99/1.62 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a710) | (~c3_1(a710)) | (~c1_1(a710)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))),
% 1.99/1.62 inference(quant_inst,[status(thm)],[])).
% 1.99/1.62 tff(1937,plain,
% 1.99/1.62 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a754) | c3_1(a754) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c1_1(a710)) | (~c2_1(a754))),
% 1.99/1.62 inference(modus_ponens,[status(thm)],[1936, 1935])).
% 1.99/1.62 tff(1938,plain,
% 1.99/1.62 (~c1_1(a710)),
% 1.99/1.62 inference(unit_resolution,[status(thm)],[1937, 227, 1931, 1852, 1887, 179, 178, 1876, 1749])).
% 1.99/1.62 tff(1939,plain,
% 1.99/1.62 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 1.99/1.62 inference(bind,[status(th)],[])).
% 1.99/1.62 tff(1940,plain,
% 1.99/1.62 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.99/1.62 inference(quant_intro,[status(thm)],[1939])).
% 1.99/1.62 tff(1941,plain,
% 1.99/1.62 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.99/1.62 inference(rewrite,[status(thm)],[])).
% 1.99/1.62 tff(1942,plain,
% 1.99/1.62 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp2) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp2))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 1.99/1.62 inference(bind,[status(th)],[])).
% 1.99/1.62 tff(1943,plain,
% 1.99/1.62 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.99/1.62 inference(quant_intro,[status(thm)],[1942])).
% 1.99/1.62 tff(1944,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause169')).
% 1.99/1.62 tff(1945,plain,
% 1.99/1.62 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.99/1.62 inference(modus_ponens,[status(thm)],[1944, 1943])).
% 1.99/1.62 tff(1946,plain,
% 1.99/1.62 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.99/1.62 inference(modus_ponens,[status(thm)],[1945, 1941])).
% 1.99/1.62 tff(1947,plain,(
% 1.99/1.62 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.99/1.62 inference(skolemize,[status(sab)],[1946])).
% 1.99/1.62 tff(1948,plain,
% 1.99/1.62 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.99/1.62 inference(modus_ponens,[status(thm)],[1947, 1940])).
% 1.99/1.62 tff(1949,plain,
% 1.99/1.62 (((~hskp8) | c2_1(a710)) <=> ((~hskp8) | c2_1(a710))),
% 1.99/1.62 inference(rewrite,[status(thm)],[])).
% 1.99/1.62 tff(1950,axiom,((~hskp8) | c2_1(a710)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause73')).
% 1.99/1.62 tff(1951,plain,
% 1.99/1.62 ((~hskp8) | c2_1(a710)),
% 1.99/1.62 inference(modus_ponens,[status(thm)],[1950, 1949])).
% 1.99/1.62 tff(1952,plain,
% 1.99/1.62 ((~hskp8) | c2_1(a710)),
% 1.99/1.62 inference(modus_ponens,[status(thm)],[1951, 1949])).
% 1.99/1.62 tff(1953,plain,
% 1.99/1.62 ((~hskp8) | c2_1(a710)),
% 1.99/1.62 inference(modus_ponens,[status(thm)],[1952, 1949])).
% 1.99/1.62 tff(1954,plain,
% 1.99/1.62 ((~hskp8) | c2_1(a710)),
% 1.99/1.62 inference(modus_ponens,[status(thm)],[1953, 1949])).
% 1.99/1.62 tff(1955,plain,
% 1.99/1.62 ((~hskp8) | c2_1(a710)),
% 1.99/1.62 inference(modus_ponens,[status(thm)],[1954, 1949])).
% 1.99/1.62 tff(1956,plain,
% 1.99/1.62 ((~hskp8) | c2_1(a710)),
% 1.99/1.62 inference(modus_ponens,[status(thm)],[1955, 1949])).
% 1.99/1.62 tff(1957,plain,
% 1.99/1.62 ((~hskp8) | c2_1(a710)),
% 1.99/1.62 inference(modus_ponens,[status(thm)],[1956, 1949])).
% 1.99/1.62 tff(1958,plain,
% 1.99/1.62 ((~hskp8) | c2_1(a710)),
% 1.99/1.62 inference(modus_ponens,[status(thm)],[1957, 1949])).
% 1.99/1.62 tff(1959,plain,
% 1.99/1.62 (c2_1(a710)),
% 1.99/1.62 inference(unit_resolution,[status(thm)],[1958, 1870])).
% 1.99/1.62 tff(1960,plain,
% 1.99/1.62 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp2 | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | c1_1(a710))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp2 | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | c1_1(a710))),
% 1.99/1.62 inference(rewrite,[status(thm)],[])).
% 1.99/1.62 tff(1961,plain,
% 1.99/1.62 ((hskp2 | (~ndr1_0) | c1_1(a710) | (~c2_1(a710)) | (~c3_1(a710)) | c1_1(a710) | c0_1(a710) | (~c2_1(a710))) <=> (hskp2 | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | c1_1(a710))),
% 1.99/1.62 inference(rewrite,[status(thm)],[])).
% 1.99/1.62 tff(1962,plain,
% 1.99/1.62 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a710) | (~c2_1(a710)) | (~c3_1(a710)) | c1_1(a710) | c0_1(a710) | (~c2_1(a710)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp2 | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | c1_1(a710)))),
% 1.99/1.62 inference(monotonicity,[status(thm)],[1961])).
% 1.99/1.62 tff(1963,plain,
% 1.99/1.62 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a710) | (~c2_1(a710)) | (~c3_1(a710)) | c1_1(a710) | c0_1(a710) | (~c2_1(a710)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp2 | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | c1_1(a710))),
% 1.99/1.62 inference(transitivity,[status(thm)],[1962, 1960])).
% 1.99/1.62 tff(1964,plain,
% 1.99/1.62 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a710) | (~c2_1(a710)) | (~c3_1(a710)) | c1_1(a710) | c0_1(a710) | (~c2_1(a710)))),
% 1.99/1.62 inference(quant_inst,[status(thm)],[])).
% 1.99/1.62 tff(1965,plain,
% 1.99/1.62 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp2 | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | c1_1(a710)),
% 1.99/1.63 inference(modus_ponens,[status(thm)],[1964, 1963])).
% 1.99/1.63 tff(1966,plain,
% 1.99/1.63 (hskp2),
% 1.99/1.63 inference(unit_resolution,[status(thm)],[1965, 227, 1959, 1887, 1876, 1948, 1938])).
% 1.99/1.63 tff(1967,plain,
% 1.99/1.63 (((~hskp2) | (~c2_1(a696))) <=> ((~hskp2) | (~c2_1(a696)))),
% 1.99/1.63 inference(rewrite,[status(thm)],[])).
% 1.99/1.63 tff(1968,plain,
% 1.99/1.63 (((~c2_1(a696)) | (~hskp2)) <=> ((~hskp2) | (~c2_1(a696)))),
% 1.99/1.63 inference(rewrite,[status(thm)],[])).
% 1.99/1.63 tff(1969,axiom,((~c2_1(a696)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause128')).
% 1.99/1.63 tff(1970,plain,
% 1.99/1.63 ((~hskp2) | (~c2_1(a696))),
% 1.99/1.63 inference(modus_ponens,[status(thm)],[1969, 1968])).
% 1.99/1.63 tff(1971,plain,
% 1.99/1.63 ((~hskp2) | (~c2_1(a696))),
% 1.99/1.63 inference(modus_ponens,[status(thm)],[1970, 1967])).
% 1.99/1.63 tff(1972,plain,
% 1.99/1.63 (~c2_1(a696)),
% 1.99/1.63 inference(unit_resolution,[status(thm)],[1971, 1966])).
% 1.99/1.63 tff(1973,plain,
% 1.99/1.63 (((~hskp2) | c0_1(a696)) <=> ((~hskp2) | c0_1(a696))),
% 1.99/1.63 inference(rewrite,[status(thm)],[])).
% 1.99/1.63 tff(1974,axiom,((~hskp2) | c0_1(a696)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause83')).
% 1.99/1.63 tff(1975,plain,
% 1.99/1.63 ((~hskp2) | c0_1(a696)),
% 1.99/1.63 inference(modus_ponens,[status(thm)],[1974, 1973])).
% 1.99/1.63 tff(1976,plain,
% 1.99/1.63 ((~hskp2) | c0_1(a696)),
% 1.99/1.63 inference(modus_ponens,[status(thm)],[1975, 1973])).
% 1.99/1.63 tff(1977,plain,
% 1.99/1.63 ((~hskp2) | c0_1(a696)),
% 1.99/1.63 inference(modus_ponens,[status(thm)],[1976, 1973])).
% 1.99/1.63 tff(1978,plain,
% 1.99/1.63 ((~hskp2) | c0_1(a696)),
% 1.99/1.63 inference(modus_ponens,[status(thm)],[1977, 1973])).
% 1.99/1.63 tff(1979,plain,
% 1.99/1.63 ((~hskp2) | c0_1(a696)),
% 1.99/1.63 inference(modus_ponens,[status(thm)],[1978, 1973])).
% 1.99/1.63 tff(1980,plain,
% 1.99/1.63 ((~hskp2) | c0_1(a696)),
% 1.99/1.63 inference(modus_ponens,[status(thm)],[1979, 1973])).
% 1.99/1.63 tff(1981,plain,
% 1.99/1.63 ((~hskp2) | c0_1(a696)),
% 1.99/1.63 inference(modus_ponens,[status(thm)],[1980, 1973])).
% 1.99/1.63 tff(1982,plain,
% 1.99/1.63 ((~hskp2) | c0_1(a696)),
% 1.99/1.63 inference(modus_ponens,[status(thm)],[1981, 1973])).
% 1.99/1.63 tff(1983,plain,
% 1.99/1.63 (c0_1(a696)),
% 1.99/1.63 inference(unit_resolution,[status(thm)],[1982, 1966])).
% 1.99/1.63 tff(1984,plain,
% 1.99/1.63 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | c2_1(a696) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a696)) | (~c0_1(a696)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a696) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a696)) | (~c0_1(a696)))),
% 1.99/1.63 inference(rewrite,[status(thm)],[])).
% 1.99/1.63 tff(1985,plain,
% 1.99/1.63 ((hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c2_1(a696) | (~c3_1(a696)) | (~c0_1(a696))) <=> (hskp28 | c2_1(a696) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a696)) | (~c0_1(a696)))),
% 1.99/1.63 inference(rewrite,[status(thm)],[])).
% 1.99/1.63 tff(1986,plain,
% 1.99/1.63 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c2_1(a696) | (~c3_1(a696)) | (~c0_1(a696)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | c2_1(a696) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a696)) | (~c0_1(a696))))),
% 1.99/1.63 inference(monotonicity,[status(thm)],[1985])).
% 1.99/1.63 tff(1987,plain,
% 1.99/1.63 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c2_1(a696) | (~c3_1(a696)) | (~c0_1(a696)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a696) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a696)) | (~c0_1(a696)))),
% 1.99/1.63 inference(transitivity,[status(thm)],[1986, 1984])).
% 1.99/1.63 tff(1988,plain,
% 1.99/1.63 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c2_1(a696) | (~c3_1(a696)) | (~c0_1(a696)))),
% 2.09/1.63 inference(quant_inst,[status(thm)],[])).
% 2.09/1.63 tff(1989,plain,
% 2.09/1.63 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a696) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a696)) | (~c0_1(a696))),
% 2.09/1.63 inference(modus_ponens,[status(thm)],[1988, 1987])).
% 2.09/1.63 tff(1990,plain,
% 2.09/1.63 (~c3_1(a696)),
% 2.09/1.63 inference(unit_resolution,[status(thm)],[1989, 227, 62, 1730, 1719, 1708, 1983, 1972, 61])).
% 2.09/1.63 tff(1991,plain,
% 2.09/1.63 (((~hskp2) | c1_1(a696)) <=> ((~hskp2) | c1_1(a696))),
% 2.09/1.63 inference(rewrite,[status(thm)],[])).
% 2.09/1.63 tff(1992,axiom,((~hskp2) | c1_1(a696)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause84')).
% 2.09/1.63 tff(1993,plain,
% 2.09/1.63 ((~hskp2) | c1_1(a696)),
% 2.09/1.63 inference(modus_ponens,[status(thm)],[1992, 1991])).
% 2.09/1.63 tff(1994,plain,
% 2.09/1.63 ((~hskp2) | c1_1(a696)),
% 2.09/1.63 inference(modus_ponens,[status(thm)],[1993, 1991])).
% 2.09/1.63 tff(1995,plain,
% 2.09/1.63 ((~hskp2) | c1_1(a696)),
% 2.09/1.63 inference(modus_ponens,[status(thm)],[1994, 1991])).
% 2.09/1.63 tff(1996,plain,
% 2.09/1.63 ((~hskp2) | c1_1(a696)),
% 2.09/1.63 inference(modus_ponens,[status(thm)],[1995, 1991])).
% 2.09/1.63 tff(1997,plain,
% 2.09/1.63 ((~hskp2) | c1_1(a696)),
% 2.09/1.63 inference(modus_ponens,[status(thm)],[1996, 1991])).
% 2.09/1.63 tff(1998,plain,
% 2.09/1.63 ((~hskp2) | c1_1(a696)),
% 2.09/1.63 inference(modus_ponens,[status(thm)],[1997, 1991])).
% 2.09/1.63 tff(1999,plain,
% 2.09/1.63 ((~hskp2) | c1_1(a696)),
% 2.09/1.63 inference(modus_ponens,[status(thm)],[1998, 1991])).
% 2.09/1.63 tff(2000,plain,
% 2.09/1.63 ((~hskp2) | c1_1(a696)),
% 2.09/1.63 inference(modus_ponens,[status(thm)],[1999, 1991])).
% 2.09/1.63 tff(2001,plain,
% 2.09/1.63 (c1_1(a696)),
% 2.09/1.63 inference(unit_resolution,[status(thm)],[2000, 1966])).
% 2.09/1.63 tff(2002,plain,
% 2.09/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a710) | c2_1(a696) | (~ndr1_0) | c3_1(a696) | (~c1_1(a696)) | (~c3_1(a710)) | (~c2_1(a710)) | c1_1(a710))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a710) | c2_1(a696) | (~ndr1_0) | c3_1(a696) | (~c1_1(a696)) | (~c3_1(a710)) | (~c2_1(a710)) | c1_1(a710))),
% 2.09/1.63 inference(rewrite,[status(thm)],[])).
% 2.09/1.63 tff(2003,plain,
% 2.09/1.63 (((~ndr1_0) | c3_1(a696) | c2_1(a696) | (~c1_1(a696)) | c1_1(a710) | (~c2_1(a710)) | (~c3_1(a710)) | c0_1(a710) | (~c3_1(a710)) | (~c2_1(a710))) <=> (c0_1(a710) | c2_1(a696) | (~ndr1_0) | c3_1(a696) | (~c1_1(a696)) | (~c3_1(a710)) | (~c2_1(a710)) | c1_1(a710))),
% 2.09/1.63 inference(rewrite,[status(thm)],[])).
% 2.09/1.63 tff(2004,plain,
% 2.09/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a696) | c2_1(a696) | (~c1_1(a696)) | c1_1(a710) | (~c2_1(a710)) | (~c3_1(a710)) | c0_1(a710) | (~c3_1(a710)) | (~c2_1(a710)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a710) | c2_1(a696) | (~ndr1_0) | c3_1(a696) | (~c1_1(a696)) | (~c3_1(a710)) | (~c2_1(a710)) | c1_1(a710)))),
% 2.09/1.63 inference(monotonicity,[status(thm)],[2003])).
% 2.09/1.63 tff(2005,plain,
% 2.09/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a696) | c2_1(a696) | (~c1_1(a696)) | c1_1(a710) | (~c2_1(a710)) | (~c3_1(a710)) | c0_1(a710) | (~c3_1(a710)) | (~c2_1(a710)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a710) | c2_1(a696) | (~ndr1_0) | c3_1(a696) | (~c1_1(a696)) | (~c3_1(a710)) | (~c2_1(a710)) | c1_1(a710))),
% 2.09/1.63 inference(transitivity,[status(thm)],[2004, 2002])).
% 2.09/1.63 tff(2006,plain,
% 2.09/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a696) | c2_1(a696) | (~c1_1(a696)) | c1_1(a710) | (~c2_1(a710)) | (~c3_1(a710)) | c0_1(a710) | (~c3_1(a710)) | (~c2_1(a710)))),
% 2.09/1.63 inference(quant_inst,[status(thm)],[])).
% 2.09/1.63 tff(2007,plain,
% 2.09/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a710) | c2_1(a696) | (~ndr1_0) | c3_1(a696) | (~c1_1(a696)) | (~c3_1(a710)) | (~c2_1(a710)) | c1_1(a710)),
% 2.09/1.63 inference(modus_ponens,[status(thm)],[2006, 2005])).
% 2.09/1.63 tff(2008,plain,
% 2.09/1.63 ($false),
% 2.09/1.63 inference(unit_resolution,[status(thm)],[2007, 227, 1959, 1887, 2001, 1876, 1972, 10, 1990, 1938])).
% 2.09/1.63 tff(2009,plain,(c0_1(a754) | hskp28 | c3_1(a754) | hskp6), inference(lemma,lemma(discharge,[]))).
% 2.09/1.63 tff(2010,plain,
% 2.09/1.63 (c0_1(a754)),
% 2.09/1.63 inference(unit_resolution,[status(thm)],[2009, 177, 178, 62])).
% 2.09/1.63 tff(2011,plain,
% 2.09/1.63 (~hskp20),
% 2.09/1.63 inference(unit_resolution,[status(thm)],[595, 2010])).
% 2.09/1.63 tff(2012,assumption,(~c3_1(a764)), introduced(assumption)).
% 2.09/1.63 tff(2013,assumption,(~c2_1(a764)), introduced(assumption)).
% 2.09/1.63 tff(2014,assumption,(c1_1(a764)), introduced(assumption)).
% 2.09/1.63 tff(2015,plain,
% 2.09/1.63 (c0_1(a764)),
% 2.09/1.63 inference(unit_resolution,[status(thm)],[331, 227, 177, 2014, 2013, 2012, 301])).
% 2.09/1.63 tff(2016,assumption,(hskp13), introduced(assumption)).
% 2.09/1.63 tff(2017,plain,
% 2.09/1.63 (((~hskp13) | (~c3_1(a726))) <=> ((~hskp13) | (~c3_1(a726)))),
% 2.09/1.63 inference(rewrite,[status(thm)],[])).
% 2.09/1.63 tff(2018,plain,
% 2.09/1.63 (((~c3_1(a726)) | (~hskp13)) <=> ((~hskp13) | (~c3_1(a726)))),
% 2.09/1.63 inference(rewrite,[status(thm)],[])).
% 2.09/1.63 tff(2019,axiom,((~c3_1(a726)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause111')).
% 2.09/1.63 tff(2020,plain,
% 2.09/1.63 ((~hskp13) | (~c3_1(a726))),
% 2.09/1.63 inference(modus_ponens,[status(thm)],[2019, 2018])).
% 2.09/1.63 tff(2021,plain,
% 2.09/1.63 ((~hskp13) | (~c3_1(a726))),
% 2.09/1.63 inference(modus_ponens,[status(thm)],[2020, 2017])).
% 2.09/1.63 tff(2022,plain,
% 2.09/1.63 (~c3_1(a726)),
% 2.09/1.63 inference(unit_resolution,[status(thm)],[2021, 2016])).
% 2.09/1.63 tff(2023,plain,
% 2.09/1.63 (((~hskp13) | (~c0_1(a726))) <=> ((~hskp13) | (~c0_1(a726)))),
% 2.09/1.63 inference(rewrite,[status(thm)],[])).
% 2.09/1.63 tff(2024,plain,
% 2.09/1.63 (((~c0_1(a726)) | (~hskp13)) <=> ((~hskp13) | (~c0_1(a726)))),
% 2.09/1.63 inference(rewrite,[status(thm)],[])).
% 2.09/1.63 tff(2025,axiom,((~c0_1(a726)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause110')).
% 2.09/1.63 tff(2026,plain,
% 2.09/1.63 ((~hskp13) | (~c0_1(a726))),
% 2.09/1.63 inference(modus_ponens,[status(thm)],[2025, 2024])).
% 2.09/1.63 tff(2027,plain,
% 2.09/1.63 ((~hskp13) | (~c0_1(a726))),
% 2.09/1.63 inference(modus_ponens,[status(thm)],[2026, 2023])).
% 2.09/1.63 tff(2028,plain,
% 2.09/1.63 (~c0_1(a726)),
% 2.09/1.63 inference(unit_resolution,[status(thm)],[2027, 2016])).
% 2.09/1.63 tff(2029,plain,
% 2.09/1.63 (((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | c2_1(a726))) <=> ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp27 | hskp6 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | c2_1(a726))),
% 2.09/1.63 inference(rewrite,[status(thm)],[])).
% 2.09/1.63 tff(2030,plain,
% 2.09/1.63 ((hskp27 | hskp6 | (~ndr1_0) | c3_1(a726) | c0_1(a726) | c2_1(a726)) <=> (hskp27 | hskp6 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | c2_1(a726))),
% 2.09/1.63 inference(rewrite,[status(thm)],[])).
% 2.09/1.63 tff(2031,plain,
% 2.09/1.63 (((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | (~ndr1_0) | c3_1(a726) | c0_1(a726) | c2_1(a726))) <=> ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | c2_1(a726)))),
% 2.09/1.63 inference(monotonicity,[status(thm)],[2030])).
% 2.09/1.63 tff(2032,plain,
% 2.09/1.63 (((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | (~ndr1_0) | c3_1(a726) | c0_1(a726) | c2_1(a726))) <=> ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp27 | hskp6 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | c2_1(a726))),
% 2.09/1.63 inference(transitivity,[status(thm)],[2031, 2029])).
% 2.09/1.63 tff(2033,plain,
% 2.09/1.63 ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | (~ndr1_0) | c3_1(a726) | c0_1(a726) | c2_1(a726))),
% 2.09/1.63 inference(quant_inst,[status(thm)],[])).
% 2.09/1.63 tff(2034,plain,
% 2.09/1.63 ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp27 | hskp6 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | c2_1(a726)),
% 2.09/1.63 inference(modus_ponens,[status(thm)],[2033, 2032])).
% 2.09/1.63 tff(2035,plain,
% 2.09/1.63 (c2_1(a726)),
% 2.09/1.63 inference(unit_resolution,[status(thm)],[2034, 227, 1036, 177, 2028, 2022, 201])).
% 2.09/1.63 tff(2036,plain,
% 2.09/1.63 (((~hskp13) | c1_1(a726)) <=> ((~hskp13) | c1_1(a726))),
% 2.09/1.63 inference(rewrite,[status(thm)],[])).
% 2.09/1.63 tff(2037,axiom,((~hskp13) | c1_1(a726)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause68')).
% 2.09/1.63 tff(2038,plain,
% 2.09/1.63 ((~hskp13) | c1_1(a726)),
% 2.09/1.63 inference(modus_ponens,[status(thm)],[2037, 2036])).
% 2.09/1.63 tff(2039,plain,
% 2.09/1.63 ((~hskp13) | c1_1(a726)),
% 2.09/1.63 inference(modus_ponens,[status(thm)],[2038, 2036])).
% 2.09/1.63 tff(2040,plain,
% 2.09/1.63 ((~hskp13) | c1_1(a726)),
% 2.09/1.63 inference(modus_ponens,[status(thm)],[2039, 2036])).
% 2.09/1.63 tff(2041,plain,
% 2.09/1.63 ((~hskp13) | c1_1(a726)),
% 2.09/1.63 inference(modus_ponens,[status(thm)],[2040, 2036])).
% 2.09/1.63 tff(2042,plain,
% 2.09/1.63 ((~hskp13) | c1_1(a726)),
% 2.09/1.63 inference(modus_ponens,[status(thm)],[2041, 2036])).
% 2.09/1.63 tff(2043,plain,
% 2.09/1.63 ((~hskp13) | c1_1(a726)),
% 2.09/1.63 inference(modus_ponens,[status(thm)],[2042, 2036])).
% 2.09/1.63 tff(2044,plain,
% 2.09/1.63 ((~hskp13) | c1_1(a726)),
% 2.09/1.63 inference(modus_ponens,[status(thm)],[2043, 2036])).
% 2.09/1.63 tff(2045,plain,
% 2.09/1.63 ((~hskp13) | c1_1(a726)),
% 2.09/1.63 inference(modus_ponens,[status(thm)],[2044, 2036])).
% 2.09/1.63 tff(2046,plain,
% 2.09/1.63 (c1_1(a726)),
% 2.09/1.63 inference(unit_resolution,[status(thm)],[2045, 2016])).
% 2.09/1.63 tff(2047,plain,
% 2.09/1.63 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | (~c2_1(a726)) | (~c1_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | (~c2_1(a726)) | (~c1_1(a764)))),
% 2.09/1.63 inference(rewrite,[status(thm)],[])).
% 2.09/1.63 tff(2048,plain,
% 2.09/1.63 ((hskp28 | (~ndr1_0) | c3_1(a726) | (~c2_1(a726)) | (~c1_1(a726)) | c3_1(a764) | c2_1(a764) | (~c1_1(a764))) <=> (hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | (~c2_1(a726)) | (~c1_1(a764)))),
% 2.09/1.63 inference(rewrite,[status(thm)],[])).
% 2.09/1.63 tff(2049,plain,
% 2.09/1.63 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a726) | (~c2_1(a726)) | (~c1_1(a726)) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | (~c2_1(a726)) | (~c1_1(a764))))),
% 2.09/1.63 inference(monotonicity,[status(thm)],[2048])).
% 2.09/1.63 tff(2050,plain,
% 2.09/1.63 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a726) | (~c2_1(a726)) | (~c1_1(a726)) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | (~c2_1(a726)) | (~c1_1(a764)))),
% 2.09/1.63 inference(transitivity,[status(thm)],[2049, 2047])).
% 2.09/1.63 tff(2051,plain,
% 2.09/1.63 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a726) | (~c2_1(a726)) | (~c1_1(a726)) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)))),
% 2.09/1.63 inference(quant_inst,[status(thm)],[])).
% 2.09/1.63 tff(2052,plain,
% 2.09/1.63 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a764) | c3_1(a764) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | (~c2_1(a726)) | (~c1_1(a764))),
% 2.09/1.63 inference(modus_ponens,[status(thm)],[2051, 2050])).
% 2.09/1.63 tff(2053,plain,
% 2.09/1.63 ($false),
% 2.09/1.63 inference(unit_resolution,[status(thm)],[2052, 227, 62, 2014, 2046, 2013, 2012, 2022, 625, 2035])).
% 2.09/1.63 tff(2054,plain,((~hskp13) | hskp28 | (~c1_1(a764)) | c2_1(a764) | c3_1(a764) | hskp27 | hskp6), inference(lemma,lemma(discharge,[]))).
% 2.09/1.63 tff(2055,plain,
% 2.09/1.63 (~hskp13),
% 2.09/1.63 inference(unit_resolution,[status(thm)],[2054, 1036, 2014, 2013, 2012, 62, 177])).
% 2.09/1.63 tff(2056,plain,
% 2.09/1.63 ((hskp20 | hskp13 | hskp12) <=> (hskp20 | hskp13 | hskp12)),
% 2.09/1.63 inference(rewrite,[status(thm)],[])).
% 2.09/1.63 tff(2057,plain,
% 2.09/1.63 (((hskp13 | hskp20) | hskp12) <=> (hskp20 | hskp13 | hskp12)),
% 2.09/1.63 inference(rewrite,[status(thm)],[])).
% 2.09/1.63 tff(2058,axiom,((hskp13 | hskp20) | hskp12), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause39')).
% 2.09/1.63 tff(2059,plain,
% 2.09/1.63 (hskp20 | hskp13 | hskp12),
% 2.09/1.63 inference(modus_ponens,[status(thm)],[2058, 2057])).
% 2.09/1.63 tff(2060,plain,
% 2.09/1.63 (hskp20 | hskp13 | hskp12),
% 2.09/1.63 inference(modus_ponens,[status(thm)],[2059, 2056])).
% 2.09/1.63 tff(2061,plain,
% 2.09/1.63 (hskp20 | hskp13 | hskp12),
% 2.09/1.63 inference(modus_ponens,[status(thm)],[2060, 2056])).
% 2.09/1.63 tff(2062,plain,
% 2.09/1.63 (hskp20 | hskp13 | hskp12),
% 2.09/1.63 inference(modus_ponens,[status(thm)],[2061, 2056])).
% 2.09/1.63 tff(2063,plain,
% 2.09/1.63 (hskp20 | hskp13 | hskp12),
% 2.09/1.63 inference(modus_ponens,[status(thm)],[2062, 2056])).
% 2.09/1.63 tff(2064,plain,
% 2.09/1.63 (hskp20 | hskp13 | hskp12),
% 2.09/1.63 inference(modus_ponens,[status(thm)],[2063, 2056])).
% 2.09/1.63 tff(2065,plain,
% 2.09/1.63 (hskp20 | hskp13 | hskp12),
% 2.09/1.63 inference(modus_ponens,[status(thm)],[2064, 2056])).
% 2.09/1.63 tff(2066,plain,
% 2.09/1.63 (hskp20 | hskp13 | hskp12),
% 2.09/1.63 inference(modus_ponens,[status(thm)],[2065, 2056])).
% 2.09/1.63 tff(2067,plain,
% 2.09/1.63 (hskp12),
% 2.09/1.63 inference(unit_resolution,[status(thm)],[2066, 2055, 280])).
% 2.09/1.63 tff(2068,plain,
% 2.09/1.63 (~c3_1(a725)),
% 2.09/1.63 inference(unit_resolution,[status(thm)],[139, 2067])).
% 2.09/1.63 tff(2069,plain,
% 2.09/1.63 (~c0_1(a725)),
% 2.09/1.63 inference(unit_resolution,[status(thm)],[151, 2067])).
% 2.09/1.63 tff(2070,plain,
% 2.09/1.63 (c2_1(a725)),
% 2.09/1.63 inference(unit_resolution,[status(thm)],[641, 227, 1036, 177, 2069, 2068, 201])).
% 2.09/1.63 tff(2071,plain,
% 2.09/1.63 (~c1_1(a725)),
% 2.09/1.63 inference(unit_resolution,[status(thm)],[145, 2067])).
% 2.09/1.63 tff(2072,plain,
% 2.09/1.63 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a764) | c3_1(a764) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a764) | c3_1(a764) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a764)))),
% 2.09/1.63 inference(rewrite,[status(thm)],[])).
% 2.09/1.63 tff(2073,plain,
% 2.09/1.63 ((hskp28 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c0_1(a764)) | c3_1(a725) | c1_1(a725) | (~c2_1(a725))) <=> (hskp28 | c2_1(a764) | c3_1(a764) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a764)))),
% 2.09/1.63 inference(rewrite,[status(thm)],[])).
% 2.09/1.63 tff(2074,plain,
% 2.09/1.63 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c0_1(a764)) | c3_1(a725) | c1_1(a725) | (~c2_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a764) | c3_1(a764) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a764))))),
% 2.09/1.63 inference(monotonicity,[status(thm)],[2073])).
% 2.09/1.63 tff(2075,plain,
% 2.09/1.63 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c0_1(a764)) | c3_1(a725) | c1_1(a725) | (~c2_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a764) | c3_1(a764) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a764)))),
% 2.09/1.63 inference(transitivity,[status(thm)],[2074, 2072])).
% 2.09/1.63 tff(2076,plain,
% 2.09/1.63 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c0_1(a764)) | c3_1(a725) | c1_1(a725) | (~c2_1(a725)))),
% 2.09/1.63 inference(quant_inst,[status(thm)],[])).
% 2.09/1.63 tff(2077,plain,
% 2.09/1.63 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a764) | c3_1(a764) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a764))),
% 2.09/1.63 inference(modus_ponens,[status(thm)],[2076, 2075])).
% 2.09/1.63 tff(2078,plain,
% 2.09/1.63 ($false),
% 2.09/1.63 inference(unit_resolution,[status(thm)],[2077, 227, 62, 2013, 2012, 2071, 2068, 342, 2070, 2015])).
% 2.09/1.63 tff(2079,plain,(hskp27 | hskp28 | c2_1(a764) | c3_1(a764) | hskp6 | hskp20 | (~c1_1(a764))), inference(lemma,lemma(discharge,[]))).
% 2.09/1.63 tff(2080,plain,
% 2.09/1.63 (hskp27),
% 2.09/1.63 inference(unit_resolution,[status(thm)],[2079, 314, 62, 308, 177, 280, 325])).
% 2.09/1.63 tff(2081,plain,
% 2.09/1.63 (c3_1(a691)),
% 2.09/1.63 inference(unit_resolution,[status(thm)],[256, 2080])).
% 2.09/1.63 tff(2082,plain,
% 2.09/1.63 (c0_1(a691)),
% 2.09/1.63 inference(unit_resolution,[status(thm)],[278, 2080])).
% 2.09/1.63 tff(2083,plain,
% 2.09/1.63 (c2_1(a691)),
% 2.09/1.63 inference(unit_resolution,[status(thm)],[1764, 2081, 2082, 62])).
% 2.09/1.63 tff(2084,assumption,(c0_1(a764)), introduced(assumption)).
% 2.09/1.63 tff(2085,plain,
% 2.09/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c3_1(a764) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | c2_1(a726) | (~c0_1(a764)) | (~c1_1(a764)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a764) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | c2_1(a726) | (~c0_1(a764)) | (~c1_1(a764)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 2.09/1.63 inference(rewrite,[status(thm)],[])).
% 2.09/1.63 tff(2086,plain,
% 2.09/1.63 (((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764)) | c3_1(a726) | c2_1(a726) | c0_1(a726)) <=> (c3_1(a764) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | c2_1(a726) | (~c0_1(a764)) | (~c1_1(a764)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 2.09/1.63 inference(rewrite,[status(thm)],[])).
% 2.09/1.63 tff(2087,plain,
% 2.09/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764)) | c3_1(a726) | c2_1(a726) | c0_1(a726))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c3_1(a764) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | c2_1(a726) | (~c0_1(a764)) | (~c1_1(a764)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691))))),
% 2.09/1.63 inference(monotonicity,[status(thm)],[2086])).
% 2.09/1.63 tff(2088,plain,
% 2.09/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764)) | c3_1(a726) | c2_1(a726) | c0_1(a726))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a764) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | c2_1(a726) | (~c0_1(a764)) | (~c1_1(a764)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 2.09/1.63 inference(transitivity,[status(thm)],[2087, 2085])).
% 2.09/1.63 tff(2089,plain,
% 2.09/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764)) | c3_1(a726) | c2_1(a726) | c0_1(a726))),
% 2.09/1.63 inference(quant_inst,[status(thm)],[])).
% 2.09/1.63 tff(2090,plain,
% 2.09/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a764) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | c2_1(a726) | (~c0_1(a764)) | (~c1_1(a764)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691))),
% 2.09/1.63 inference(modus_ponens,[status(thm)],[2089, 2088])).
% 2.09/1.63 tff(2091,plain,
% 2.09/1.63 (c2_1(a726)),
% 2.09/1.63 inference(unit_resolution,[status(thm)],[2090, 227, 1756, 1755, 2014, 2012, 2028, 2022, 1777, 1767, 2084])).
% 2.09/1.63 tff(2092,plain,
% 2.09/1.63 (^[V: $i, U: $i] : refl((hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V))))),
% 2.09/1.63 inference(bind,[status(th)],[])).
% 2.09/1.63 tff(2093,plain,
% 2.09/1.63 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.09/1.63 inference(quant_intro,[status(thm)],[2092])).
% 2.09/1.63 tff(2094,plain,
% 2.09/1.63 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.09/1.63 inference(rewrite,[status(thm)],[])).
% 2.09/1.63 tff(2095,plain,
% 2.09/1.63 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp20) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp20))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp20) <=> (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp20) <=> (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))))),
% 2.09/1.63 inference(bind,[status(th)],[])).
% 2.09/1.63 tff(2096,plain,
% 2.09/1.63 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp20) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.09/1.64 inference(quant_intro,[status(thm)],[2095])).
% 2.09/1.64 tff(2097,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause188')).
% 2.09/1.64 tff(2098,plain,
% 2.09/1.64 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.09/1.64 inference(modus_ponens,[status(thm)],[2097, 2096])).
% 2.09/1.64 tff(2099,plain,
% 2.09/1.64 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.09/1.64 inference(modus_ponens,[status(thm)],[2098, 2094])).
% 2.09/1.64 tff(2100,plain,(
% 2.09/1.64 ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.09/1.64 inference(skolemize,[status(sab)],[2099])).
% 2.09/1.64 tff(2101,plain,
% 2.09/1.64 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.09/1.64 inference(modus_ponens,[status(thm)],[2100, 2093])).
% 2.09/1.64 tff(2102,plain,
% 2.09/1.64 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | (~c2_1(a726)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | (~c2_1(a726)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 2.09/1.64 inference(rewrite,[status(thm)],[])).
% 2.09/1.64 tff(2103,plain,
% 2.09/1.64 ((hskp20 | (~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a726) | (~c2_1(a726)) | (~c1_1(a726))) <=> (hskp20 | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | (~c2_1(a726)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 2.09/1.64 inference(rewrite,[status(thm)],[])).
% 2.09/1.64 tff(2104,plain,
% 2.09/1.64 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a726) | (~c2_1(a726)) | (~c1_1(a726)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | (~c2_1(a726)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691))))),
% 2.09/1.64 inference(monotonicity,[status(thm)],[2103])).
% 2.09/1.64 tff(2105,plain,
% 2.09/1.64 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a726) | (~c2_1(a726)) | (~c1_1(a726)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | (~c2_1(a726)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 2.09/1.64 inference(transitivity,[status(thm)],[2104, 2102])).
% 2.09/1.64 tff(2106,plain,
% 2.09/1.64 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a726) | (~c2_1(a726)) | (~c1_1(a726)))),
% 2.09/1.64 inference(quant_inst,[status(thm)],[])).
% 2.09/1.64 tff(2107,plain,
% 2.09/1.64 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | (~c2_1(a726)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691))),
% 2.09/1.64 inference(modus_ponens,[status(thm)],[2106, 2105])).
% 2.09/1.64 tff(2108,plain,
% 2.09/1.64 ($false),
% 2.09/1.64 inference(unit_resolution,[status(thm)],[2107, 227, 280, 1756, 1755, 2046, 2022, 2101, 1767, 2091])).
% 2.09/1.64 tff(2109,plain,((~hskp13) | hskp20 | (~c0_1(a691)) | (~c3_1(a691)) | (~c2_1(a691)) | (~c1_1(a764)) | c3_1(a764) | (~c0_1(a764))), inference(lemma,lemma(discharge,[]))).
% 2.09/1.64 tff(2110,plain,
% 2.09/1.64 (~hskp13),
% 2.09/1.64 inference(unit_resolution,[status(thm)],[2109, 2082, 280, 2081, 2083, 325, 308, 332])).
% 2.09/1.64 tff(2111,plain,
% 2.09/1.64 (hskp12),
% 2.09/1.64 inference(unit_resolution,[status(thm)],[2066, 2110, 280])).
% 2.09/1.64 tff(2112,plain,
% 2.09/1.64 (~c0_1(a725)),
% 2.09/1.64 inference(unit_resolution,[status(thm)],[151, 2111])).
% 2.09/1.64 tff(2113,plain,
% 2.09/1.64 (~c1_1(a725)),
% 2.09/1.64 inference(unit_resolution,[status(thm)],[145, 2111])).
% 2.09/1.64 tff(2114,plain,
% 2.09/1.64 (c2_1(a691)),
% 2.09/1.64 inference(unit_resolution,[status(thm)],[1764, 1755, 1756, 62])).
% 2.09/1.64 tff(2115,plain,
% 2.09/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c3_1(a764) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c0_1(a764)) | (~c1_1(a764)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a764) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c0_1(a764)) | (~c1_1(a764)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 2.09/1.64 inference(rewrite,[status(thm)],[])).
% 2.09/1.64 tff(2116,plain,
% 2.09/1.64 (((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764)) | c3_1(a725) | c2_1(a725) | c0_1(a725)) <=> (c3_1(a764) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c0_1(a764)) | (~c1_1(a764)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 2.09/1.64 inference(rewrite,[status(thm)],[])).
% 2.09/1.64 tff(2117,plain,
% 2.09/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764)) | c3_1(a725) | c2_1(a725) | c0_1(a725))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c3_1(a764) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c0_1(a764)) | (~c1_1(a764)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691))))),
% 2.09/1.64 inference(monotonicity,[status(thm)],[2116])).
% 2.09/1.64 tff(2118,plain,
% 2.09/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764)) | c3_1(a725) | c2_1(a725) | c0_1(a725))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a764) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c0_1(a764)) | (~c1_1(a764)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 2.09/1.64 inference(transitivity,[status(thm)],[2117, 2115])).
% 2.09/1.64 tff(2119,plain,
% 2.09/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764)) | c3_1(a725) | c2_1(a725) | c0_1(a725))),
% 2.09/1.64 inference(quant_inst,[status(thm)],[])).
% 2.09/1.64 tff(2120,plain,
% 2.09/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a764) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c0_1(a764)) | (~c1_1(a764)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691))),
% 2.09/1.64 inference(modus_ponens,[status(thm)],[2119, 2118])).
% 2.09/1.64 tff(2121,plain,
% 2.09/1.64 (c2_1(a725)),
% 2.09/1.64 inference(unit_resolution,[status(thm)],[2120, 227, 1756, 1755, 2014, 2012, 578, 1037, 1777, 2114, 2084])).
% 2.09/1.64 tff(2122,plain,
% 2.09/1.64 ($false),
% 2.09/1.64 inference(unit_resolution,[status(thm)],[2077, 227, 62, 2013, 2012, 577, 1037, 342, 2121, 2084])).
% 2.09/1.64 tff(2123,plain,(c3_1(a725) | hskp28 | c2_1(a764) | c3_1(a764) | c1_1(a725) | (~c0_1(a764)) | (~c0_1(a691)) | (~c3_1(a691)) | (~c1_1(a764)) | c0_1(a725)), inference(lemma,lemma(discharge,[]))).
% 2.09/1.64 tff(2124,plain,
% 2.09/1.64 (c3_1(a725)),
% 2.09/1.64 inference(unit_resolution,[status(thm)],[2123, 577, 2013, 2012, 62, 2084, 1756, 1755, 2014, 578])).
% 2.09/1.64 tff(2125,plain,
% 2.09/1.64 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | c0_1(a725) | (~c3_1(a725)) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | c2_1(a725))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp28 | c0_1(a725) | (~c3_1(a725)) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | c2_1(a725))),
% 2.09/1.64 inference(rewrite,[status(thm)],[])).
% 2.09/1.64 tff(2126,plain,
% 2.09/1.64 ((hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a725) | c2_1(a725) | (~c3_1(a725))) <=> (hskp28 | c0_1(a725) | (~c3_1(a725)) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | c2_1(a725))),
% 2.09/1.64 inference(rewrite,[status(thm)],[])).
% 2.09/1.64 tff(2127,plain,
% 2.09/1.64 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a725) | c2_1(a725) | (~c3_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | c0_1(a725) | (~c3_1(a725)) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | c2_1(a725)))),
% 2.09/1.64 inference(monotonicity,[status(thm)],[2126])).
% 2.09/1.64 tff(2128,plain,
% 2.09/1.64 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a725) | c2_1(a725) | (~c3_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp28 | c0_1(a725) | (~c3_1(a725)) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | c2_1(a725))),
% 2.09/1.64 inference(transitivity,[status(thm)],[2127, 2125])).
% 2.09/1.64 tff(2129,plain,
% 2.09/1.64 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a725) | c2_1(a725) | (~c3_1(a725)))),
% 2.09/1.64 inference(quant_inst,[status(thm)],[])).
% 2.09/1.64 tff(2130,plain,
% 2.09/1.64 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp28 | c0_1(a725) | (~c3_1(a725)) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | c2_1(a725)),
% 2.09/1.64 inference(modus_ponens,[status(thm)],[2129, 2128])).
% 2.09/1.64 tff(2131,plain,
% 2.09/1.64 ((~c3_1(a725)) | c2_1(a725)),
% 2.09/1.64 inference(unit_resolution,[status(thm)],[2130, 227, 62, 1730, 1719, 1708, 578, 1922])).
% 2.09/1.64 tff(2132,plain,
% 2.09/1.64 (c2_1(a725)),
% 2.09/1.64 inference(unit_resolution,[status(thm)],[2131, 2124])).
% 2.09/1.64 tff(2133,plain,
% 2.09/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a764) | c3_1(a764) | c0_1(a725) | c1_1(a725) | (~c3_1(a725)) | (~ndr1_0) | (~c2_1(a725)) | (~c1_1(a764)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a764) | c3_1(a764) | c0_1(a725) | c1_1(a725) | (~c3_1(a725)) | (~ndr1_0) | (~c2_1(a725)) | (~c1_1(a764)))),
% 2.09/1.64 inference(rewrite,[status(thm)],[])).
% 2.09/1.64 tff(2134,plain,
% 2.09/1.64 (((~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c1_1(a725) | (~c2_1(a725)) | (~c3_1(a725)) | c0_1(a725) | (~c3_1(a725)) | (~c2_1(a725))) <=> (c2_1(a764) | c3_1(a764) | c0_1(a725) | c1_1(a725) | (~c3_1(a725)) | (~ndr1_0) | (~c2_1(a725)) | (~c1_1(a764)))),
% 2.09/1.64 inference(rewrite,[status(thm)],[])).
% 2.09/1.64 tff(2135,plain,
% 2.09/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c1_1(a725) | (~c2_1(a725)) | (~c3_1(a725)) | c0_1(a725) | (~c3_1(a725)) | (~c2_1(a725)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a764) | c3_1(a764) | c0_1(a725) | c1_1(a725) | (~c3_1(a725)) | (~ndr1_0) | (~c2_1(a725)) | (~c1_1(a764))))),
% 2.09/1.64 inference(monotonicity,[status(thm)],[2134])).
% 2.09/1.64 tff(2136,plain,
% 2.09/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c1_1(a725) | (~c2_1(a725)) | (~c3_1(a725)) | c0_1(a725) | (~c3_1(a725)) | (~c2_1(a725)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a764) | c3_1(a764) | c0_1(a725) | c1_1(a725) | (~c3_1(a725)) | (~ndr1_0) | (~c2_1(a725)) | (~c1_1(a764)))),
% 2.09/1.64 inference(transitivity,[status(thm)],[2135, 2133])).
% 2.09/1.64 tff(2137,plain,
% 2.09/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c1_1(a725) | (~c2_1(a725)) | (~c3_1(a725)) | c0_1(a725) | (~c3_1(a725)) | (~c2_1(a725)))),
% 2.09/1.64 inference(quant_inst,[status(thm)],[])).
% 2.09/1.64 tff(2138,plain,
% 2.09/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a764) | c3_1(a764) | c0_1(a725) | c1_1(a725) | (~c3_1(a725)) | (~ndr1_0) | (~c2_1(a725)) | (~c1_1(a764))),
% 2.09/1.64 inference(modus_ponens,[status(thm)],[2137, 2136])).
% 2.09/1.64 tff(2139,plain,
% 2.09/1.64 ((~c3_1(a725)) | (~c2_1(a725))),
% 2.09/1.64 inference(unit_resolution,[status(thm)],[2138, 227, 2014, 2013, 2012, 578, 577, 10])).
% 2.09/1.64 tff(2140,plain,
% 2.09/1.64 ($false),
% 2.09/1.64 inference(unit_resolution,[status(thm)],[2139, 2132, 2124])).
% 2.09/1.64 tff(2141,plain,(c1_1(a725) | (~c1_1(a764)) | c2_1(a764) | c3_1(a764) | c0_1(a725) | hskp28 | (~c0_1(a764)) | (~c0_1(a691)) | (~c3_1(a691))), inference(lemma,lemma(discharge,[]))).
% 2.09/1.64 tff(2142,plain,
% 2.09/1.64 ($false),
% 2.09/1.64 inference(unit_resolution,[status(thm)],[2141, 2113, 2112, 314, 308, 325, 62, 332, 2082, 2081])).
% 2.09/1.64 tff(2143,plain,((~hskp24) | hskp28 | hskp20 | hskp6), inference(lemma,lemma(discharge,[]))).
% 2.09/1.64 tff(2144,plain,
% 2.09/1.64 (~hskp24),
% 2.09/1.64 inference(unit_resolution,[status(thm)],[2143, 2011, 62, 177])).
% 2.09/1.64 tff(2145,plain,
% 2.09/1.64 (c2_1(a691)),
% 2.09/1.64 inference(unit_resolution,[status(thm)],[1764, 257, 279, 62])).
% 2.09/1.64 tff(2146,plain,
% 2.09/1.64 ($false),
% 2.09/1.64 inference(unit_resolution,[status(thm)],[1063, 227, 432, 474, 279, 268, 163, 2145])).
% 2.09/1.64 tff(2147,plain,((~hskp27) | hskp24 | hskp23 | hskp28), inference(lemma,lemma(discharge,[]))).
% 2.09/1.64 tff(2148,plain,
% 2.09/1.64 (~hskp27),
% 2.09/1.64 inference(unit_resolution,[status(thm)],[2147, 474, 432, 62])).
% 2.09/1.64 tff(2149,plain,
% 2.09/1.64 ($false),
% 2.09/1.64 inference(unit_resolution,[status(thm)],[961, 227, 1036, 177, 1360, 1359, 1358, 201])).
% 2.09/1.64 tff(2150,plain,((~hskp4) | hskp27 | hskp6), inference(lemma,lemma(discharge,[]))).
% 2.09/1.64 tff(2151,plain,
% 2.09/1.64 (~hskp4),
% 2.09/1.64 inference(unit_resolution,[status(thm)],[2150, 2148, 177])).
% 2.09/1.64 tff(2152,plain,
% 2.09/1.64 (((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)))) <=> ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)))),
% 2.09/1.64 inference(rewrite,[status(thm)],[])).
% 2.09/1.64 tff(2153,plain,
% 2.09/1.64 ((hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a733)) | (~c0_1(a733)) | (~c1_1(a733))) <=> (hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)))),
% 2.09/1.64 inference(rewrite,[status(thm)],[])).
% 2.09/1.64 tff(2154,plain,
% 2.09/1.64 (((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a733)) | (~c0_1(a733)) | (~c1_1(a733)))) <=> ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a733)) | (~c1_1(a733)) | (~c2_1(a733))))),
% 2.09/1.64 inference(monotonicity,[status(thm)],[2153])).
% 2.09/1.64 tff(2155,plain,
% 2.09/1.64 (((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a733)) | (~c0_1(a733)) | (~c1_1(a733)))) <=> ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)))),
% 2.09/1.64 inference(transitivity,[status(thm)],[2154, 2152])).
% 2.09/1.64 tff(2156,plain,
% 2.09/1.64 ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a733)) | (~c0_1(a733)) | (~c1_1(a733)))),
% 2.09/1.64 inference(quant_inst,[status(thm)],[])).
% 2.09/1.64 tff(2157,plain,
% 2.09/1.64 ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a733)) | (~c1_1(a733)) | (~c2_1(a733))),
% 2.09/1.64 inference(modus_ponens,[status(thm)],[2156, 2155])).
% 2.09/1.64 tff(2158,plain,
% 2.09/1.64 (hskp24 | hskp23 | (~c0_1(a733))),
% 2.09/1.64 inference(unit_resolution,[status(thm)],[2157, 227, 1730, 1719, 163])).
% 2.09/1.64 tff(2159,plain,
% 2.09/1.64 (~c0_1(a733)),
% 2.09/1.64 inference(unit_resolution,[status(thm)],[2158, 474, 432])).
% 2.09/1.64 tff(2160,plain,
% 2.09/1.64 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 2.09/1.64 inference(bind,[status(th)],[])).
% 2.09/1.64 tff(2161,plain,
% 2.09/1.64 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.09/1.64 inference(quant_intro,[status(thm)],[2160])).
% 2.09/1.64 tff(2162,plain,
% 2.09/1.64 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.09/1.64 inference(rewrite,[status(thm)],[])).
% 2.09/1.64 tff(2163,plain,
% 2.09/1.64 (^[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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp4) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp4))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 2.09/1.64 inference(bind,[status(th)],[])).
% 2.09/1.64 tff(2164,plain,
% 2.09/1.64 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.09/1.64 inference(quant_intro,[status(thm)],[2163])).
% 2.09/1.64 tff(2165,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause172')).
% 2.09/1.64 tff(2166,plain,
% 2.09/1.64 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.09/1.64 inference(modus_ponens,[status(thm)],[2165, 2164])).
% 2.09/1.64 tff(2167,plain,
% 2.09/1.64 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.09/1.64 inference(modus_ponens,[status(thm)],[2166, 2162])).
% 2.09/1.64 tff(2168,plain,(
% 2.09/1.64 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.09/1.64 inference(skolemize,[status(sab)],[2167])).
% 2.09/1.64 tff(2169,plain,
% 2.09/1.64 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.09/1.64 inference(modus_ponens,[status(thm)],[2168, 2161])).
% 2.09/1.64 tff(2170,plain,
% 2.09/1.64 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))),
% 2.09/1.64 inference(bind,[status(th)],[])).
% 2.09/1.64 tff(2171,plain,
% 2.09/1.64 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 2.09/1.64 inference(quant_intro,[status(thm)],[2170])).
% 2.09/1.64 tff(2172,plain,
% 2.09/1.64 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 2.09/1.64 inference(rewrite,[status(thm)],[])).
% 2.09/1.64 tff(2173,plain,
% 2.09/1.64 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp11) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp11))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))))),
% 2.09/1.64 inference(bind,[status(th)],[])).
% 2.09/1.64 tff(2174,plain,
% 2.09/1.64 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 2.09/1.64 inference(quant_intro,[status(thm)],[2173])).
% 2.09/1.64 tff(2175,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause173')).
% 2.09/1.64 tff(2176,plain,
% 2.09/1.64 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 2.09/1.64 inference(modus_ponens,[status(thm)],[2175, 2174])).
% 2.09/1.64 tff(2177,plain,
% 2.09/1.64 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 2.09/1.64 inference(modus_ponens,[status(thm)],[2176, 2172])).
% 2.09/1.64 tff(2178,plain,(
% 2.09/1.64 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 2.09/1.64 inference(skolemize,[status(sab)],[2177])).
% 2.09/1.64 tff(2179,plain,
% 2.09/1.64 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 2.09/1.64 inference(modus_ponens,[status(thm)],[2178, 2171])).
% 2.09/1.64 tff(2180,plain,
% 2.09/1.64 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp11 | c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733)))),
% 2.09/1.64 inference(rewrite,[status(thm)],[])).
% 2.09/1.64 tff(2181,plain,
% 2.09/1.64 ((hskp11 | (~ndr1_0) | c3_1(a754) | c2_1(a754) | (~c0_1(a754)) | c0_1(a733) | (~c2_1(a733)) | (~c3_1(a733))) <=> (hskp11 | c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733)))),
% 2.09/1.64 inference(rewrite,[status(thm)],[])).
% 2.09/1.64 tff(2182,plain,
% 2.09/1.64 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a754) | c2_1(a754) | (~c0_1(a754)) | c0_1(a733) | (~c2_1(a733)) | (~c3_1(a733)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733))))),
% 2.09/1.64 inference(monotonicity,[status(thm)],[2181])).
% 2.09/1.64 tff(2183,plain,
% 2.09/1.64 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a754) | c2_1(a754) | (~c0_1(a754)) | c0_1(a733) | (~c2_1(a733)) | (~c3_1(a733)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp11 | c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733)))),
% 2.09/1.64 inference(transitivity,[status(thm)],[2182, 2180])).
% 2.09/1.64 tff(2184,plain,
% 2.09/1.64 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a754) | c2_1(a754) | (~c0_1(a754)) | c0_1(a733) | (~c2_1(a733)) | (~c3_1(a733)))),
% 2.09/1.64 inference(quant_inst,[status(thm)],[])).
% 2.09/1.64 tff(2185,plain,
% 2.09/1.64 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp11 | c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733))),
% 2.09/1.64 inference(modus_ponens,[status(thm)],[2184, 2183])).
% 2.09/1.64 tff(2186,plain,
% 2.09/1.64 (hskp11),
% 2.09/1.64 inference(unit_resolution,[status(thm)],[2185, 227, 1719, 1708, 180, 2010, 178, 2179, 2159])).
% 2.09/1.64 tff(2187,plain,
% 2.09/1.64 (((~hskp11) | (~c1_1(a722))) <=> ((~hskp11) | (~c1_1(a722)))),
% 2.09/1.64 inference(rewrite,[status(thm)],[])).
% 2.09/1.64 tff(2188,plain,
% 2.09/1.64 (((~c1_1(a722)) | (~hskp11)) <=> ((~hskp11) | (~c1_1(a722)))),
% 2.09/1.64 inference(rewrite,[status(thm)],[])).
% 2.09/1.64 tff(2189,axiom,((~c1_1(a722)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause115')).
% 2.09/1.64 tff(2190,plain,
% 2.09/1.64 ((~hskp11) | (~c1_1(a722))),
% 2.09/1.64 inference(modus_ponens,[status(thm)],[2189, 2188])).
% 2.09/1.64 tff(2191,plain,
% 2.09/1.64 ((~hskp11) | (~c1_1(a722))),
% 2.09/1.64 inference(modus_ponens,[status(thm)],[2190, 2187])).
% 2.09/1.64 tff(2192,plain,
% 2.09/1.64 (~c1_1(a722)),
% 2.09/1.64 inference(unit_resolution,[status(thm)],[2191, 2186])).
% 2.09/1.64 tff(2193,plain,
% 2.09/1.64 (((~hskp11) | c0_1(a722)) <=> ((~hskp11) | c0_1(a722))),
% 2.09/1.64 inference(rewrite,[status(thm)],[])).
% 2.09/1.64 tff(2194,axiom,((~hskp11) | c0_1(a722)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause69')).
% 2.09/1.64 tff(2195,plain,
% 2.09/1.64 ((~hskp11) | c0_1(a722)),
% 2.09/1.64 inference(modus_ponens,[status(thm)],[2194, 2193])).
% 2.09/1.64 tff(2196,plain,
% 2.09/1.64 ((~hskp11) | c0_1(a722)),
% 2.09/1.64 inference(modus_ponens,[status(thm)],[2195, 2193])).
% 2.09/1.64 tff(2197,plain,
% 2.09/1.64 ((~hskp11) | c0_1(a722)),
% 2.09/1.64 inference(modus_ponens,[status(thm)],[2196, 2193])).
% 2.09/1.64 tff(2198,plain,
% 2.09/1.64 ((~hskp11) | c0_1(a722)),
% 2.09/1.64 inference(modus_ponens,[status(thm)],[2197, 2193])).
% 2.09/1.64 tff(2199,plain,
% 2.09/1.64 ((~hskp11) | c0_1(a722)),
% 2.09/1.64 inference(modus_ponens,[status(thm)],[2198, 2193])).
% 2.09/1.64 tff(2200,plain,
% 2.09/1.64 ((~hskp11) | c0_1(a722)),
% 2.09/1.64 inference(modus_ponens,[status(thm)],[2199, 2193])).
% 2.09/1.64 tff(2201,plain,
% 2.09/1.64 ((~hskp11) | c0_1(a722)),
% 2.09/1.64 inference(modus_ponens,[status(thm)],[2200, 2193])).
% 2.09/1.64 tff(2202,plain,
% 2.09/1.64 ((~hskp11) | c0_1(a722)),
% 2.09/1.64 inference(modus_ponens,[status(thm)],[2201, 2193])).
% 2.09/1.64 tff(2203,plain,
% 2.09/1.64 (c0_1(a722)),
% 2.09/1.64 inference(unit_resolution,[status(thm)],[2202, 2186])).
% 2.09/1.64 tff(2204,plain,
% 2.09/1.64 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c1_1(a722) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | c2_1(a722) | (~c0_1(a722)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a722) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | c2_1(a722) | (~c0_1(a722)))),
% 2.09/1.64 inference(rewrite,[status(thm)],[])).
% 2.09/1.64 tff(2205,plain,
% 2.09/1.64 ((hskp4 | (~ndr1_0) | c1_1(a722) | c2_1(a722) | (~c0_1(a722)) | c0_1(a733) | (~c3_1(a733)) | (~c1_1(a733))) <=> (hskp4 | c1_1(a722) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | c2_1(a722) | (~c0_1(a722)))),
% 2.09/1.64 inference(rewrite,[status(thm)],[])).
% 2.09/1.64 tff(2206,plain,
% 2.09/1.64 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a722) | c2_1(a722) | (~c0_1(a722)) | c0_1(a733) | (~c3_1(a733)) | (~c1_1(a733)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c1_1(a722) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | c2_1(a722) | (~c0_1(a722))))),
% 2.09/1.65 inference(monotonicity,[status(thm)],[2205])).
% 2.09/1.65 tff(2207,plain,
% 2.09/1.65 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a722) | c2_1(a722) | (~c0_1(a722)) | c0_1(a733) | (~c3_1(a733)) | (~c1_1(a733)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a722) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | c2_1(a722) | (~c0_1(a722)))),
% 2.09/1.65 inference(transitivity,[status(thm)],[2206, 2204])).
% 2.09/1.65 tff(2208,plain,
% 2.09/1.65 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a722) | c2_1(a722) | (~c0_1(a722)) | c0_1(a733) | (~c3_1(a733)) | (~c1_1(a733)))),
% 2.09/1.65 inference(quant_inst,[status(thm)],[])).
% 2.09/1.65 tff(2209,plain,
% 2.09/1.65 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a722) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | c2_1(a722) | (~c0_1(a722))),
% 2.09/1.65 inference(modus_ponens,[status(thm)],[2208, 2207])).
% 2.09/1.65 tff(2210,plain,
% 2.09/1.65 (hskp4 | c2_1(a722)),
% 2.09/1.65 inference(unit_resolution,[status(thm)],[2209, 227, 1730, 1708, 2203, 2192, 2169, 2159])).
% 2.09/1.65 tff(2211,plain,
% 2.09/1.65 (c2_1(a722)),
% 2.09/1.65 inference(unit_resolution,[status(thm)],[2210, 2151])).
% 2.09/1.65 tff(2212,assumption,(c0_1(a754)), introduced(assumption)).
% 2.09/1.65 tff(2213,plain,
% 2.09/1.65 (c1_1(a693) | (~c2_1(a693))),
% 2.09/1.65 inference(unit_resolution,[status(thm)],[633, 227, 62, 180, 2212, 178, 153, 342])).
% 2.09/1.65 tff(2214,plain,
% 2.09/1.65 (~c2_1(a693)),
% 2.09/1.65 inference(unit_resolution,[status(thm)],[2213, 164])).
% 2.09/1.65 tff(2215,plain,
% 2.09/1.65 (~hskp1),
% 2.09/1.65 inference(unit_resolution,[status(thm)],[383, 2214])).
% 2.09/1.65 tff(2216,assumption,(~hskp0), introduced(assumption)).
% 2.09/1.65 tff(2217,plain,
% 2.09/1.65 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c1_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c1_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693))),
% 2.09/1.65 inference(rewrite,[status(thm)],[])).
% 2.09/1.65 tff(2218,plain,
% 2.09/1.65 ((hskp1 | hskp0 | (~ndr1_0) | c3_1(a693) | c1_1(a693) | c0_1(a693)) <=> (hskp1 | hskp0 | c1_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693))),
% 2.09/1.65 inference(rewrite,[status(thm)],[])).
% 2.09/1.65 tff(2219,plain,
% 2.09/1.65 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c3_1(a693) | c1_1(a693) | c0_1(a693))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c1_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693)))),
% 2.09/1.65 inference(monotonicity,[status(thm)],[2218])).
% 2.09/1.65 tff(2220,plain,
% 2.09/1.65 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c3_1(a693) | c1_1(a693) | c0_1(a693))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c1_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693))),
% 2.09/1.65 inference(transitivity,[status(thm)],[2219, 2217])).
% 2.09/1.65 tff(2221,plain,
% 2.09/1.65 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c3_1(a693) | c1_1(a693) | c0_1(a693))),
% 2.09/1.65 inference(quant_inst,[status(thm)],[])).
% 2.09/1.65 tff(2222,plain,
% 2.09/1.65 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c1_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693)),
% 2.09/1.65 inference(modus_ponens,[status(thm)],[2221, 2220])).
% 2.09/1.65 tff(2223,plain,
% 2.09/1.65 (hskp1 | hskp0 | c1_1(a693) | c0_1(a693)),
% 2.09/1.65 inference(unit_resolution,[status(thm)],[2222, 227, 153, 1482])).
% 2.09/1.65 tff(2224,plain,
% 2.09/1.65 (c0_1(a693)),
% 2.09/1.65 inference(unit_resolution,[status(thm)],[2223, 2216, 164, 2215])).
% 2.09/1.65 tff(2225,plain,
% 2.09/1.65 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 2.09/1.65 inference(bind,[status(th)],[])).
% 2.09/1.65 tff(2226,plain,
% 2.09/1.65 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 2.09/1.65 inference(quant_intro,[status(thm)],[2225])).
% 2.09/1.65 tff(2227,plain,
% 2.09/1.65 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 2.09/1.65 inference(rewrite,[status(thm)],[])).
% 2.09/1.65 tff(2228,plain,
% 2.09/1.65 (^[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))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp3) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp3))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 2.09/1.65 inference(bind,[status(th)],[])).
% 2.09/1.65 tff(2229,plain,
% 2.09/1.65 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 2.09/1.65 inference(quant_intro,[status(thm)],[2228])).
% 2.09/1.65 tff(2230,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause187')).
% 2.09/1.65 tff(2231,plain,
% 2.09/1.65 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 2.09/1.65 inference(modus_ponens,[status(thm)],[2230, 2229])).
% 2.09/1.65 tff(2232,plain,
% 2.09/1.65 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 2.09/1.65 inference(modus_ponens,[status(thm)],[2231, 2227])).
% 2.09/1.65 tff(2233,plain,(
% 2.09/1.65 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 2.09/1.65 inference(skolemize,[status(sab)],[2232])).
% 2.09/1.65 tff(2234,plain,
% 2.09/1.65 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 2.09/1.65 inference(modus_ponens,[status(thm)],[2233, 2226])).
% 2.09/1.65 tff(2235,assumption,(c0_1(a693)), introduced(assumption)).
% 2.09/1.65 tff(2236,assumption,(~hskp3), introduced(assumption)).
% 2.09/1.65 tff(2237,plain,
% 2.09/1.65 (^[U: $i] : refl((hskp14 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp14 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))),
% 2.09/1.65 inference(bind,[status(th)],[])).
% 2.09/1.65 tff(2238,plain,
% 2.09/1.65 (![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 2.09/1.65 inference(quant_intro,[status(thm)],[2237])).
% 2.09/1.65 tff(2239,plain,
% 2.09/1.65 (![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 2.09/1.65 inference(rewrite,[status(thm)],[])).
% 2.09/1.65 tff(2240,plain,
% 2.09/1.65 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp14) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp14))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp14) | hskp3) <=> ((hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp3))), rewrite(((hskp14 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp3) <=> (hskp14 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp14) | hskp3) <=> (hskp14 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))))),
% 2.09/1.65 inference(bind,[status(th)],[])).
% 2.09/1.65 tff(2241,plain,
% 2.09/1.65 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp14) | hskp3) <=> ![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 2.09/1.65 inference(quant_intro,[status(thm)],[2240])).
% 2.09/1.65 tff(2242,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp14) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause141')).
% 2.09/1.65 tff(2243,plain,
% 2.09/1.65 (![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 2.09/1.65 inference(modus_ponens,[status(thm)],[2242, 2241])).
% 2.09/1.65 tff(2244,plain,
% 2.09/1.65 (![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 2.09/1.65 inference(modus_ponens,[status(thm)],[2243, 2239])).
% 2.09/1.65 tff(2245,plain,(
% 2.09/1.65 ![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 2.09/1.65 inference(skolemize,[status(sab)],[2244])).
% 2.09/1.65 tff(2246,plain,
% 2.09/1.65 (![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 2.09/1.65 inference(modus_ponens,[status(thm)],[2245, 2238])).
% 2.09/1.65 tff(2247,plain,
% 2.09/1.65 (((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp14 | hskp3 | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)))) <=> ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp14 | hskp3 | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)))),
% 2.09/1.65 inference(rewrite,[status(thm)],[])).
% 2.09/1.65 tff(2248,plain,
% 2.09/1.65 ((hskp14 | hskp3 | (~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c0_1(a693))) <=> (hskp14 | hskp3 | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)))),
% 2.09/1.65 inference(rewrite,[status(thm)],[])).
% 2.09/1.65 tff(2249,plain,
% 2.09/1.65 (((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp14 | hskp3 | (~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c0_1(a693)))) <=> ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp14 | hskp3 | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693))))),
% 2.09/1.65 inference(monotonicity,[status(thm)],[2248])).
% 2.09/1.65 tff(2250,plain,
% 2.09/1.65 (((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp14 | hskp3 | (~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c0_1(a693)))) <=> ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp14 | hskp3 | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)))),
% 2.09/1.65 inference(transitivity,[status(thm)],[2249, 2247])).
% 2.09/1.65 tff(2251,plain,
% 2.09/1.65 ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp14 | hskp3 | (~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c0_1(a693)))),
% 2.09/1.65 inference(quant_inst,[status(thm)],[])).
% 2.09/1.65 tff(2252,plain,
% 2.09/1.65 ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp14 | hskp3 | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693))),
% 2.09/1.65 inference(modus_ponens,[status(thm)],[2251, 2250])).
% 2.09/1.65 tff(2253,plain,
% 2.09/1.65 (hskp14 | hskp3 | c1_1(a693) | (~c0_1(a693))),
% 2.09/1.65 inference(unit_resolution,[status(thm)],[2252, 227, 153, 2246])).
% 2.09/1.65 tff(2254,plain,
% 2.09/1.65 (hskp14),
% 2.09/1.65 inference(unit_resolution,[status(thm)],[2253, 2236, 164, 2235])).
% 2.09/1.65 tff(2255,plain,
% 2.09/1.65 (~c3_1(a730)),
% 2.09/1.65 inference(unit_resolution,[status(thm)],[486, 2254])).
% 2.09/1.65 tff(2256,plain,
% 2.09/1.65 (c0_1(a730)),
% 2.09/1.65 inference(unit_resolution,[status(thm)],[472, 2254])).
% 2.09/1.65 tff(2257,assumption,(c3_1(a733)), introduced(assumption)).
% 2.09/1.65 tff(2258,assumption,(c2_1(a733)), introduced(assumption)).
% 2.09/1.65 tff(2259,assumption,(c1_1(a733)), introduced(assumption)).
% 2.09/1.65 tff(2260,plain,
% 2.09/1.65 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | c3_1(a730) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c0_1(a730)) | (~c2_1(a730)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp3 | c3_1(a730) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c0_1(a730)) | (~c2_1(a730)))),
% 2.09/1.65 inference(rewrite,[status(thm)],[])).
% 2.09/1.65 tff(2261,plain,
% 2.09/1.65 ((hskp3 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a730) | (~c2_1(a730)) | (~c0_1(a730))) <=> (hskp3 | c3_1(a730) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c0_1(a730)) | (~c2_1(a730)))),
% 2.09/1.65 inference(rewrite,[status(thm)],[])).
% 2.09/1.65 tff(2262,plain,
% 2.09/1.65 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a730) | (~c2_1(a730)) | (~c0_1(a730)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | c3_1(a730) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c0_1(a730)) | (~c2_1(a730))))),
% 2.09/1.65 inference(monotonicity,[status(thm)],[2261])).
% 2.09/1.65 tff(2263,plain,
% 2.09/1.65 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a730) | (~c2_1(a730)) | (~c0_1(a730)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp3 | c3_1(a730) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c0_1(a730)) | (~c2_1(a730)))),
% 2.09/1.65 inference(transitivity,[status(thm)],[2262, 2260])).
% 2.09/1.65 tff(2264,plain,
% 2.09/1.65 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a730) | (~c2_1(a730)) | (~c0_1(a730)))),
% 2.09/1.65 inference(quant_inst,[status(thm)],[])).
% 2.09/1.65 tff(2265,plain,
% 2.09/1.65 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp3 | c3_1(a730) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c0_1(a730)) | (~c2_1(a730))),
% 2.09/1.65 inference(modus_ponens,[status(thm)],[2264, 2263])).
% 2.09/1.65 tff(2266,plain,
% 2.09/1.65 (~c2_1(a730)),
% 2.09/1.65 inference(unit_resolution,[status(thm)],[2265, 227, 2236, 2259, 2258, 2257, 2256, 2255, 2234])).
% 2.09/1.65 tff(2267,assumption,(~c2_1(a693)), introduced(assumption)).
% 2.09/1.65 tff(2268,plain,
% 2.09/1.65 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp3 | c2_1(a754) | c2_1(a693) | (~c0_1(a754)) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c1_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp3 | c2_1(a754) | c2_1(a693) | (~c0_1(a754)) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c1_1(a754)))),
% 2.09/1.65 inference(rewrite,[status(thm)],[])).
% 2.09/1.65 tff(2269,plain,
% 2.09/1.65 ((hskp3 | (~ndr1_0) | c2_1(a754) | (~c0_1(a754)) | (~c1_1(a754)) | c3_1(a693) | c1_1(a693) | c2_1(a693)) <=> (hskp3 | c2_1(a754) | c2_1(a693) | (~c0_1(a754)) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c1_1(a754)))),
% 2.09/1.65 inference(rewrite,[status(thm)],[])).
% 2.09/1.65 tff(2270,plain,
% 2.09/1.65 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a754) | (~c0_1(a754)) | (~c1_1(a754)) | c3_1(a693) | c1_1(a693) | c2_1(a693))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp3 | c2_1(a754) | c2_1(a693) | (~c0_1(a754)) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c1_1(a754))))),
% 2.09/1.65 inference(monotonicity,[status(thm)],[2269])).
% 2.09/1.65 tff(2271,plain,
% 2.09/1.65 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a754) | (~c0_1(a754)) | (~c1_1(a754)) | c3_1(a693) | c1_1(a693) | c2_1(a693))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp3 | c2_1(a754) | c2_1(a693) | (~c0_1(a754)) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c1_1(a754)))),
% 2.09/1.65 inference(transitivity,[status(thm)],[2270, 2268])).
% 2.09/1.65 tff(2272,plain,
% 2.09/1.65 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a754) | (~c0_1(a754)) | (~c1_1(a754)) | c3_1(a693) | c1_1(a693) | c2_1(a693))),
% 2.09/1.65 inference(quant_inst,[status(thm)],[])).
% 2.09/1.65 tff(2273,plain,
% 2.09/1.65 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp3 | c2_1(a754) | c2_1(a693) | (~c0_1(a754)) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c1_1(a754))),
% 2.09/1.65 inference(modus_ponens,[status(thm)],[2272, 2271])).
% 2.09/1.65 tff(2274,plain,
% 2.09/1.65 (hskp3 | c2_1(a693) | c1_1(a693) | (~c1_1(a754))),
% 2.09/1.65 inference(unit_resolution,[status(thm)],[2273, 227, 180, 2212, 153, 1671])).
% 2.09/1.65 tff(2275,plain,
% 2.09/1.65 (~c1_1(a754)),
% 2.09/1.65 inference(unit_resolution,[status(thm)],[2274, 2236, 164, 2267])).
% 2.09/1.65 tff(2276,plain,
% 2.09/1.65 (c1_1(a730)),
% 2.09/1.65 inference(unit_resolution,[status(thm)],[461, 2254])).
% 2.09/1.65 tff(2277,plain,
% 2.09/1.65 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp3 | c2_1(a754) | c3_1(a754) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | c2_1(a730) | c1_1(a754))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp3 | c2_1(a754) | c3_1(a754) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | c2_1(a730) | c1_1(a754))),
% 2.09/1.65 inference(rewrite,[status(thm)],[])).
% 2.09/1.65 tff(2278,plain,
% 2.09/1.65 ((hskp3 | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c1_1(a730)) | c3_1(a754) | c1_1(a754) | c2_1(a754)) <=> (hskp3 | c2_1(a754) | c3_1(a754) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | c2_1(a730) | c1_1(a754))),
% 2.09/1.65 inference(rewrite,[status(thm)],[])).
% 2.09/1.65 tff(2279,plain,
% 2.09/1.65 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c1_1(a730)) | c3_1(a754) | c1_1(a754) | c2_1(a754))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp3 | c2_1(a754) | c3_1(a754) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | c2_1(a730) | c1_1(a754)))),
% 2.09/1.65 inference(monotonicity,[status(thm)],[2278])).
% 2.09/1.65 tff(2280,plain,
% 2.09/1.65 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c1_1(a730)) | c3_1(a754) | c1_1(a754) | c2_1(a754))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp3 | c2_1(a754) | c3_1(a754) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | c2_1(a730) | c1_1(a754))),
% 2.09/1.65 inference(transitivity,[status(thm)],[2279, 2277])).
% 2.09/1.65 tff(2281,plain,
% 2.09/1.65 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a730) | (~c0_1(a730)) | (~c1_1(a730)) | c3_1(a754) | c1_1(a754) | c2_1(a754))),
% 2.09/1.65 inference(quant_inst,[status(thm)],[])).
% 2.09/1.65 tff(2282,plain,
% 2.09/1.65 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp3 | c2_1(a754) | c3_1(a754) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | c2_1(a730) | c1_1(a754)),
% 2.09/1.65 inference(modus_ponens,[status(thm)],[2281, 2280])).
% 2.09/1.65 tff(2283,plain,
% 2.09/1.65 ($false),
% 2.09/1.65 inference(unit_resolution,[status(thm)],[2282, 227, 2236, 180, 2256, 2276, 178, 1671, 2275, 2266])).
% 2.09/1.65 tff(2284,plain,(hskp3 | c2_1(a754) | c3_1(a754) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a733)) | c1_1(a693) | (~c0_1(a693)) | c3_1(a693) | c2_1(a693) | (~c0_1(a754))), inference(lemma,lemma(discharge,[]))).
% 2.09/1.65 tff(2285,plain,
% 2.09/1.65 (hskp3),
% 2.09/1.65 inference(unit_resolution,[status(thm)],[2284, 2224, 178, 1730, 1719, 1708, 164, 180, 153, 2214, 2212])).
% 2.09/1.65 tff(2286,plain,
% 2.09/1.65 (~c3_1(a697)),
% 2.09/1.65 inference(unit_resolution,[status(thm)],[1355, 2285])).
% 2.09/1.65 tff(2287,plain,
% 2.09/1.65 (c2_1(a697)),
% 2.09/1.65 inference(unit_resolution,[status(thm)],[527, 2285])).
% 2.09/1.65 tff(2288,plain,
% 2.09/1.65 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | c3_1(a697) | (~ndr1_0) | c1_1(a697) | (~c2_1(a697)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | c3_1(a697) | (~ndr1_0) | c1_1(a697) | (~c2_1(a697)))),
% 2.09/1.65 inference(rewrite,[status(thm)],[])).
% 2.09/1.65 tff(2289,plain,
% 2.09/1.65 ((hskp28 | (~ndr1_0) | c3_1(a754) | c2_1(a754) | (~c0_1(a754)) | c3_1(a697) | c1_1(a697) | (~c2_1(a697))) <=> (hskp28 | c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | c3_1(a697) | (~ndr1_0) | c1_1(a697) | (~c2_1(a697)))),
% 2.09/1.65 inference(rewrite,[status(thm)],[])).
% 2.09/1.65 tff(2290,plain,
% 2.09/1.65 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a754) | c2_1(a754) | (~c0_1(a754)) | c3_1(a697) | c1_1(a697) | (~c2_1(a697)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | c3_1(a697) | (~ndr1_0) | c1_1(a697) | (~c2_1(a697))))),
% 2.09/1.65 inference(monotonicity,[status(thm)],[2289])).
% 2.09/1.65 tff(2291,plain,
% 2.09/1.65 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a754) | c2_1(a754) | (~c0_1(a754)) | c3_1(a697) | c1_1(a697) | (~c2_1(a697)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | c3_1(a697) | (~ndr1_0) | c1_1(a697) | (~c2_1(a697)))),
% 2.09/1.65 inference(transitivity,[status(thm)],[2290, 2288])).
% 2.09/1.65 tff(2292,plain,
% 2.09/1.65 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a754) | c2_1(a754) | (~c0_1(a754)) | c3_1(a697) | c1_1(a697) | (~c2_1(a697)))),
% 2.09/1.65 inference(quant_inst,[status(thm)],[])).
% 2.09/1.65 tff(2293,plain,
% 2.09/1.65 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | c3_1(a697) | (~ndr1_0) | c1_1(a697) | (~c2_1(a697))),
% 2.09/1.65 inference(modus_ponens,[status(thm)],[2292, 2291])).
% 2.09/1.65 tff(2294,plain,
% 2.09/1.65 (c1_1(a697)),
% 2.09/1.65 inference(unit_resolution,[status(thm)],[2293, 227, 62, 180, 2287, 2212, 178, 2286, 342])).
% 2.09/1.65 tff(2295,plain,
% 2.09/1.65 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | c2_1(a754) | c3_1(a754) | c3_1(a697) | (~ndr1_0) | (~c1_1(a697)) | (~c2_1(a697)) | (~c1_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a754) | c3_1(a754) | c3_1(a697) | (~ndr1_0) | (~c1_1(a697)) | (~c2_1(a697)) | (~c1_1(a754)))),
% 2.09/1.65 inference(rewrite,[status(thm)],[])).
% 2.09/1.65 tff(2296,plain,
% 2.09/1.65 ((hskp28 | (~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a754) | c2_1(a754) | (~c1_1(a754))) <=> (hskp28 | c2_1(a754) | c3_1(a754) | c3_1(a697) | (~ndr1_0) | (~c1_1(a697)) | (~c2_1(a697)) | (~c1_1(a754)))),
% 2.09/1.65 inference(rewrite,[status(thm)],[])).
% 2.09/1.65 tff(2297,plain,
% 2.09/1.65 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a754) | c2_1(a754) | (~c1_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | c2_1(a754) | c3_1(a754) | c3_1(a697) | (~ndr1_0) | (~c1_1(a697)) | (~c2_1(a697)) | (~c1_1(a754))))),
% 2.09/1.65 inference(monotonicity,[status(thm)],[2296])).
% 2.09/1.65 tff(2298,plain,
% 2.09/1.65 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a754) | c2_1(a754) | (~c1_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a754) | c3_1(a754) | c3_1(a697) | (~ndr1_0) | (~c1_1(a697)) | (~c2_1(a697)) | (~c1_1(a754)))),
% 2.09/1.65 inference(transitivity,[status(thm)],[2297, 2295])).
% 2.09/1.65 tff(2299,plain,
% 2.09/1.65 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a754) | c2_1(a754) | (~c1_1(a754)))),
% 2.09/1.65 inference(quant_inst,[status(thm)],[])).
% 2.09/1.65 tff(2300,plain,
% 2.09/1.65 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp28 | c2_1(a754) | c3_1(a754) | c3_1(a697) | (~ndr1_0) | (~c1_1(a697)) | (~c2_1(a697)) | (~c1_1(a754))),
% 2.09/1.65 inference(modus_ponens,[status(thm)],[2299, 2298])).
% 2.09/1.65 tff(2301,plain,
% 2.09/1.65 ((~c1_1(a697)) | (~c1_1(a754))),
% 2.09/1.65 inference(unit_resolution,[status(thm)],[2300, 227, 62, 180, 2287, 178, 2286, 625])).
% 2.09/1.65 tff(2302,plain,
% 2.09/1.65 (~c1_1(a754)),
% 2.09/1.65 inference(unit_resolution,[status(thm)],[2301, 2294])).
% 2.09/1.65 tff(2303,plain,
% 2.09/1.65 (~hskp20),
% 2.09/1.65 inference(unit_resolution,[status(thm)],[595, 2212])).
% 2.09/1.65 tff(2304,plain,
% 2.09/1.65 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | c3_1(a697) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a697)) | (~c2_1(a697)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a697) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a697)) | (~c2_1(a697)))),
% 2.09/1.66 inference(rewrite,[status(thm)],[])).
% 2.09/1.66 tff(2305,plain,
% 2.09/1.66 ((hskp20 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697))) <=> (hskp20 | c3_1(a697) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a697)) | (~c2_1(a697)))),
% 2.09/1.66 inference(rewrite,[status(thm)],[])).
% 2.09/1.66 tff(2306,plain,
% 2.09/1.66 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | c3_1(a697) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a697)) | (~c2_1(a697))))),
% 2.09/1.66 inference(monotonicity,[status(thm)],[2305])).
% 2.09/1.66 tff(2307,plain,
% 2.09/1.66 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a697) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a697)) | (~c2_1(a697)))),
% 2.09/1.66 inference(transitivity,[status(thm)],[2306, 2304])).
% 2.09/1.66 tff(2308,plain,
% 2.09/1.66 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)))),
% 2.09/1.66 inference(quant_inst,[status(thm)],[])).
% 2.09/1.66 tff(2309,plain,
% 2.09/1.66 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a697) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a697)) | (~c2_1(a697))),
% 2.09/1.66 inference(modus_ponens,[status(thm)],[2308, 2307])).
% 2.09/1.66 tff(2310,plain,
% 2.09/1.66 ((~c0_1(a733)) | (~c1_1(a697))),
% 2.09/1.66 inference(unit_resolution,[status(thm)],[2309, 227, 2303, 1719, 1708, 2287, 2286, 2101])).
% 2.09/1.66 tff(2311,plain,
% 2.09/1.66 (~c0_1(a733)),
% 2.09/1.66 inference(unit_resolution,[status(thm)],[2310, 2294])).
% 2.09/1.66 tff(2312,plain,
% 2.09/1.66 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c2_1(a754) | (~c0_1(a754)) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | c1_1(a754))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c2_1(a754) | (~c0_1(a754)) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | c1_1(a754))),
% 2.09/1.66 inference(rewrite,[status(thm)],[])).
% 2.09/1.66 tff(2313,plain,
% 2.09/1.66 ((hskp4 | (~ndr1_0) | c1_1(a754) | c2_1(a754) | (~c0_1(a754)) | c0_1(a733) | (~c3_1(a733)) | (~c1_1(a733))) <=> (hskp4 | c2_1(a754) | (~c0_1(a754)) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | c1_1(a754))),
% 2.09/1.66 inference(rewrite,[status(thm)],[])).
% 2.09/1.66 tff(2314,plain,
% 2.09/1.66 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a754) | c2_1(a754) | (~c0_1(a754)) | c0_1(a733) | (~c3_1(a733)) | (~c1_1(a733)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c2_1(a754) | (~c0_1(a754)) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | c1_1(a754)))),
% 2.09/1.66 inference(monotonicity,[status(thm)],[2313])).
% 2.09/1.66 tff(2315,plain,
% 2.09/1.66 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a754) | c2_1(a754) | (~c0_1(a754)) | c0_1(a733) | (~c3_1(a733)) | (~c1_1(a733)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c2_1(a754) | (~c0_1(a754)) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | c1_1(a754))),
% 2.09/1.66 inference(transitivity,[status(thm)],[2314, 2312])).
% 2.09/1.66 tff(2316,plain,
% 2.09/1.66 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a754) | c2_1(a754) | (~c0_1(a754)) | c0_1(a733) | (~c3_1(a733)) | (~c1_1(a733)))),
% 2.09/1.66 inference(quant_inst,[status(thm)],[])).
% 2.09/1.66 tff(2317,plain,
% 2.09/1.66 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c2_1(a754) | (~c0_1(a754)) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | c1_1(a754)),
% 2.09/1.66 inference(modus_ponens,[status(thm)],[2316, 2315])).
% 2.09/1.66 tff(2318,plain,
% 2.09/1.66 (hskp4),
% 2.09/1.66 inference(unit_resolution,[status(thm)],[2317, 227, 1730, 1708, 180, 2212, 2169, 2302, 2311])).
% 2.09/1.66 tff(2319,plain,
% 2.09/1.66 (~c3_1(a698)),
% 2.09/1.66 inference(unit_resolution,[status(thm)],[1045, 2318])).
% 2.09/1.66 tff(2320,plain,
% 2.09/1.66 (~c2_1(a698)),
% 2.09/1.66 inference(unit_resolution,[status(thm)],[923, 2318])).
% 2.09/1.66 tff(2321,plain,
% 2.09/1.66 (~c0_1(a698)),
% 2.09/1.66 inference(unit_resolution,[status(thm)],[917, 2318])).
% 2.09/1.66 tff(2322,plain,
% 2.09/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a754) | c3_1(a754) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a698)) | c1_1(a754))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a754) | c3_1(a754) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a698)) | c1_1(a754))),
% 2.09/1.66 inference(rewrite,[status(thm)],[])).
% 2.09/1.66 tff(2323,plain,
% 2.09/1.66 (((~ndr1_0) | c0_1(a698) | c2_1(a698) | (~c1_1(a698)) | c3_1(a754) | c1_1(a754) | c2_1(a754) | c3_1(a698) | c2_1(a698) | c0_1(a698)) <=> (c2_1(a754) | c3_1(a754) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a698)) | c1_1(a754))),
% 2.09/1.66 inference(rewrite,[status(thm)],[])).
% 2.09/1.66 tff(2324,plain,
% 2.09/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a698) | c2_1(a698) | (~c1_1(a698)) | c3_1(a754) | c1_1(a754) | c2_1(a754) | c3_1(a698) | c2_1(a698) | c0_1(a698))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a754) | c3_1(a754) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a698)) | c1_1(a754)))),
% 2.09/1.66 inference(monotonicity,[status(thm)],[2323])).
% 2.09/1.66 tff(2325,plain,
% 2.09/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a698) | c2_1(a698) | (~c1_1(a698)) | c3_1(a754) | c1_1(a754) | c2_1(a754) | c3_1(a698) | c2_1(a698) | c0_1(a698))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a754) | c3_1(a754) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a698)) | c1_1(a754))),
% 2.09/1.66 inference(transitivity,[status(thm)],[2324, 2322])).
% 2.09/1.66 tff(2326,plain,
% 2.09/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a698) | c2_1(a698) | (~c1_1(a698)) | c3_1(a754) | c1_1(a754) | c2_1(a754) | c3_1(a698) | c2_1(a698) | c0_1(a698))),
% 2.09/1.66 inference(quant_inst,[status(thm)],[])).
% 2.09/1.66 tff(2327,plain,
% 2.09/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a754) | c3_1(a754) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c1_1(a698)) | c1_1(a754)),
% 2.09/1.66 inference(modus_ponens,[status(thm)],[2326, 2325])).
% 2.09/1.66 tff(2328,plain,
% 2.09/1.66 (~c1_1(a698)),
% 2.09/1.66 inference(unit_resolution,[status(thm)],[2327, 227, 180, 178, 2321, 2320, 2319, 122, 2302])).
% 2.09/1.66 tff(2329,plain,
% 2.09/1.66 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c0_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698))),
% 2.09/1.66 inference(rewrite,[status(thm)],[])).
% 2.09/1.66 tff(2330,plain,
% 2.09/1.66 ((hskp1 | hskp0 | (~ndr1_0) | c3_1(a698) | c1_1(a698) | c0_1(a698)) <=> (hskp1 | hskp0 | c0_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698))),
% 2.09/1.66 inference(rewrite,[status(thm)],[])).
% 2.09/1.66 tff(2331,plain,
% 2.09/1.66 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c3_1(a698) | c1_1(a698) | c0_1(a698))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c0_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698)))),
% 2.09/1.66 inference(monotonicity,[status(thm)],[2330])).
% 2.09/1.66 tff(2332,plain,
% 2.09/1.66 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c3_1(a698) | c1_1(a698) | c0_1(a698))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698))),
% 2.09/1.66 inference(transitivity,[status(thm)],[2331, 2329])).
% 2.09/1.66 tff(2333,plain,
% 2.09/1.66 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c3_1(a698) | c1_1(a698) | c0_1(a698))),
% 2.09/1.66 inference(quant_inst,[status(thm)],[])).
% 2.09/1.66 tff(2334,plain,
% 2.09/1.66 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698)),
% 2.09/1.66 inference(modus_ponens,[status(thm)],[2333, 2332])).
% 2.09/1.66 tff(2335,plain,
% 2.09/1.66 ($false),
% 2.09/1.66 inference(unit_resolution,[status(thm)],[2334, 227, 2215, 2216, 2321, 2319, 1482, 2328])).
% 2.09/1.66 tff(2336,plain,(hskp0 | c2_1(a754) | c3_1(a754) | (~c0_1(a754)) | hskp28 | c1_1(a693) | c3_1(a693)), inference(lemma,lemma(discharge,[]))).
% 2.09/1.66 tff(2337,plain,
% 2.09/1.66 (hskp0),
% 2.09/1.66 inference(unit_resolution,[status(thm)],[2336, 164, 178, 2010, 62, 180, 153])).
% 2.09/1.66 tff(2338,plain,
% 2.09/1.66 (~c1_1(a692)),
% 2.09/1.66 inference(unit_resolution,[status(thm)],[853, 2337])).
% 2.09/1.66 tff(2339,plain,
% 2.09/1.66 (~c0_1(a692)),
% 2.09/1.66 inference(unit_resolution,[status(thm)],[859, 2337])).
% 2.09/1.66 tff(2340,plain,
% 2.09/1.66 (c2_1(a692)),
% 2.09/1.66 inference(unit_resolution,[status(thm)],[872, 2337])).
% 2.09/1.66 tff(2341,plain,
% 2.09/1.66 (c1_1(a693) | (~c2_1(a693))),
% 2.09/1.66 inference(unit_resolution,[status(thm)],[633, 227, 62, 180, 2010, 178, 153, 342])).
% 2.09/1.66 tff(2342,plain,
% 2.09/1.66 (~c2_1(a693)),
% 2.09/1.66 inference(unit_resolution,[status(thm)],[2341, 164])).
% 2.09/1.66 tff(2343,plain,
% 2.09/1.66 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a693) | c1_1(a693) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a693)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a693) | c1_1(a693) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a693)))),
% 2.09/1.66 inference(rewrite,[status(thm)],[])).
% 2.09/1.66 tff(2344,plain,
% 2.09/1.66 ((hskp28 | (~ndr1_0) | c1_1(a693) | c2_1(a693) | (~c0_1(a693)) | c1_1(a692) | c0_1(a692) | (~c2_1(a692))) <=> (hskp28 | c2_1(a693) | c1_1(a693) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a693)))),
% 2.09/1.66 inference(rewrite,[status(thm)],[])).
% 2.09/1.66 tff(2345,plain,
% 2.09/1.66 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a693) | c2_1(a693) | (~c0_1(a693)) | c1_1(a692) | c0_1(a692) | (~c2_1(a692)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a693) | c1_1(a693) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a693))))),
% 2.09/1.66 inference(monotonicity,[status(thm)],[2344])).
% 2.09/1.66 tff(2346,plain,
% 2.09/1.66 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a693) | c2_1(a693) | (~c0_1(a693)) | c1_1(a692) | c0_1(a692) | (~c2_1(a692)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a693) | c1_1(a693) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a693)))),
% 2.09/1.66 inference(transitivity,[status(thm)],[2345, 2343])).
% 2.09/1.66 tff(2347,plain,
% 2.09/1.66 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a693) | c2_1(a693) | (~c0_1(a693)) | c1_1(a692) | c0_1(a692) | (~c2_1(a692)))),
% 2.09/1.66 inference(quant_inst,[status(thm)],[])).
% 2.09/1.66 tff(2348,plain,
% 2.09/1.66 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a693) | c1_1(a693) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c0_1(a693))),
% 2.09/1.66 inference(modus_ponens,[status(thm)],[2347, 2346])).
% 2.09/1.66 tff(2349,plain,
% 2.09/1.66 (~c0_1(a693)),
% 2.09/1.66 inference(unit_resolution,[status(thm)],[2348, 227, 62, 2342, 2340, 164, 2339, 2338, 398])).
% 2.09/1.66 tff(2350,plain,
% 2.09/1.66 (((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | c2_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693))) <=> ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp27 | hskp6 | c2_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693))),
% 2.09/1.66 inference(rewrite,[status(thm)],[])).
% 2.09/1.66 tff(2351,plain,
% 2.09/1.66 ((hskp27 | hskp6 | (~ndr1_0) | c3_1(a693) | c0_1(a693) | c2_1(a693)) <=> (hskp27 | hskp6 | c2_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693))),
% 2.09/1.66 inference(rewrite,[status(thm)],[])).
% 2.09/1.66 tff(2352,plain,
% 2.09/1.66 (((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | (~ndr1_0) | c3_1(a693) | c0_1(a693) | c2_1(a693))) <=> ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | c2_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693)))),
% 2.09/1.66 inference(monotonicity,[status(thm)],[2351])).
% 2.09/1.66 tff(2353,plain,
% 2.09/1.66 (((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | (~ndr1_0) | c3_1(a693) | c0_1(a693) | c2_1(a693))) <=> ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp27 | hskp6 | c2_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693))),
% 2.09/1.66 inference(transitivity,[status(thm)],[2352, 2350])).
% 2.09/1.66 tff(2354,plain,
% 2.09/1.66 ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | (~ndr1_0) | c3_1(a693) | c0_1(a693) | c2_1(a693))),
% 2.09/1.66 inference(quant_inst,[status(thm)],[])).
% 2.09/1.66 tff(2355,plain,
% 2.09/1.66 ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp27 | hskp6 | c2_1(a693) | c3_1(a693) | (~ndr1_0) | c0_1(a693)),
% 2.09/1.66 inference(modus_ponens,[status(thm)],[2354, 2353])).
% 2.09/1.66 tff(2356,plain,
% 2.09/1.66 (hskp27 | c2_1(a693) | c0_1(a693)),
% 2.09/1.66 inference(unit_resolution,[status(thm)],[2355, 227, 177, 153, 201])).
% 2.09/1.66 tff(2357,plain,
% 2.09/1.66 (hskp27),
% 2.09/1.66 inference(unit_resolution,[status(thm)],[2356, 2349, 2342])).
% 2.09/1.66 tff(2358,plain,
% 2.09/1.66 (c0_1(a691)),
% 2.09/1.66 inference(unit_resolution,[status(thm)],[278, 2357])).
% 2.09/1.66 tff(2359,plain,
% 2.09/1.66 (c3_1(a691)),
% 2.09/1.66 inference(unit_resolution,[status(thm)],[256, 2357])).
% 2.09/1.66 tff(2360,plain,
% 2.09/1.66 (c2_1(a691)),
% 2.09/1.66 inference(unit_resolution,[status(thm)],[1764, 2359, 2358, 62])).
% 2.09/1.66 tff(2361,plain,
% 2.09/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a693) | (~c0_1(a754)) | c3_1(a754) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c1_1(a754)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a693) | (~c0_1(a754)) | c3_1(a754) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c1_1(a754)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 2.09/1.66 inference(rewrite,[status(thm)],[])).
% 2.09/1.66 tff(2362,plain,
% 2.09/1.66 (((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a754) | (~c1_1(a754)) | (~c0_1(a754)) | c3_1(a693) | c2_1(a693) | c0_1(a693)) <=> (c2_1(a693) | (~c0_1(a754)) | c3_1(a754) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c1_1(a754)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 2.09/1.66 inference(rewrite,[status(thm)],[])).
% 2.09/1.66 tff(2363,plain,
% 2.09/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a754) | (~c1_1(a754)) | (~c0_1(a754)) | c3_1(a693) | c2_1(a693) | c0_1(a693))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a693) | (~c0_1(a754)) | c3_1(a754) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c1_1(a754)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691))))),
% 2.09/1.66 inference(monotonicity,[status(thm)],[2362])).
% 2.09/1.66 tff(2364,plain,
% 2.09/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a754) | (~c1_1(a754)) | (~c0_1(a754)) | c3_1(a693) | c2_1(a693) | c0_1(a693))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a693) | (~c0_1(a754)) | c3_1(a754) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c1_1(a754)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 2.09/1.66 inference(transitivity,[status(thm)],[2363, 2361])).
% 2.09/1.66 tff(2365,plain,
% 2.09/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a754) | (~c1_1(a754)) | (~c0_1(a754)) | c3_1(a693) | c2_1(a693) | c0_1(a693))),
% 2.09/1.66 inference(quant_inst,[status(thm)],[])).
% 2.09/1.66 tff(2366,plain,
% 2.09/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a693) | (~c0_1(a754)) | c3_1(a754) | c3_1(a693) | (~ndr1_0) | c0_1(a693) | (~c1_1(a754)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691))),
% 2.09/1.66 inference(modus_ponens,[status(thm)],[2365, 2364])).
% 2.09/1.66 tff(2367,plain,
% 2.09/1.66 (~c1_1(a754)),
% 2.09/1.66 inference(unit_resolution,[status(thm)],[2366, 227, 2358, 2359, 2342, 2010, 178, 153, 1777, 2360, 2349])).
% 2.09/1.66 tff(2368,plain,
% 2.09/1.66 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a754) | (~c0_1(a754)) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | c1_1(a754))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a754) | (~c0_1(a754)) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | c1_1(a754))),
% 2.09/1.66 inference(rewrite,[status(thm)],[])).
% 2.09/1.66 tff(2369,plain,
% 2.09/1.66 ((hskp28 | (~ndr1_0) | c1_1(a754) | c2_1(a754) | (~c0_1(a754)) | c1_1(a692) | c0_1(a692) | (~c2_1(a692))) <=> (hskp28 | c2_1(a754) | (~c0_1(a754)) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | c1_1(a754))),
% 2.09/1.66 inference(rewrite,[status(thm)],[])).
% 2.09/1.66 tff(2370,plain,
% 2.09/1.66 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a754) | c2_1(a754) | (~c0_1(a754)) | c1_1(a692) | c0_1(a692) | (~c2_1(a692)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a754) | (~c0_1(a754)) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | c1_1(a754)))),
% 2.09/1.66 inference(monotonicity,[status(thm)],[2369])).
% 2.09/1.66 tff(2371,plain,
% 2.09/1.66 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a754) | c2_1(a754) | (~c0_1(a754)) | c1_1(a692) | c0_1(a692) | (~c2_1(a692)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a754) | (~c0_1(a754)) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | c1_1(a754))),
% 2.09/1.66 inference(transitivity,[status(thm)],[2370, 2368])).
% 2.09/1.66 tff(2372,plain,
% 2.09/1.66 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c1_1(a754) | c2_1(a754) | (~c0_1(a754)) | c1_1(a692) | c0_1(a692) | (~c2_1(a692)))),
% 2.09/1.66 inference(quant_inst,[status(thm)],[])).
% 2.09/1.66 tff(2373,plain,
% 2.09/1.66 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a754) | (~c0_1(a754)) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | c1_1(a754)),
% 2.09/1.66 inference(modus_ponens,[status(thm)],[2372, 2371])).
% 2.09/1.66 tff(2374,plain,
% 2.09/1.66 ($false),
% 2.09/1.66 inference(unit_resolution,[status(thm)],[2373, 227, 62, 180, 2340, 2010, 2339, 2338, 398, 2367])).
% 2.09/1.66 tff(2375,plain,(c1_1(a693) | hskp28 | c2_1(a754) | c3_1(a754) | c3_1(a693) | hskp6), inference(lemma,lemma(discharge,[]))).
% 2.09/1.66 tff(2376,plain,
% 2.09/1.66 (c1_1(a693)),
% 2.09/1.66 inference(unit_resolution,[status(thm)],[2375, 153, 180, 178, 62, 177])).
% 2.09/1.66 tff(2377,plain,
% 2.09/1.66 (((~hskp11) | c3_1(a722)) <=> ((~hskp11) | c3_1(a722))),
% 2.09/1.66 inference(rewrite,[status(thm)],[])).
% 2.09/1.66 tff(2378,axiom,((~hskp11) | c3_1(a722)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause70')).
% 2.09/1.66 tff(2379,plain,
% 2.09/1.66 ((~hskp11) | c3_1(a722)),
% 2.09/1.66 inference(modus_ponens,[status(thm)],[2378, 2377])).
% 2.09/1.66 tff(2380,plain,
% 2.09/1.66 ((~hskp11) | c3_1(a722)),
% 2.09/1.66 inference(modus_ponens,[status(thm)],[2379, 2377])).
% 2.09/1.66 tff(2381,plain,
% 2.09/1.66 ((~hskp11) | c3_1(a722)),
% 2.09/1.66 inference(modus_ponens,[status(thm)],[2380, 2377])).
% 2.09/1.66 tff(2382,plain,
% 2.09/1.66 ((~hskp11) | c3_1(a722)),
% 2.09/1.66 inference(modus_ponens,[status(thm)],[2381, 2377])).
% 2.09/1.66 tff(2383,plain,
% 2.09/1.66 ((~hskp11) | c3_1(a722)),
% 2.09/1.66 inference(modus_ponens,[status(thm)],[2382, 2377])).
% 2.09/1.66 tff(2384,plain,
% 2.09/1.66 ((~hskp11) | c3_1(a722)),
% 2.09/1.66 inference(modus_ponens,[status(thm)],[2383, 2377])).
% 2.09/1.66 tff(2385,plain,
% 2.09/1.66 ((~hskp11) | c3_1(a722)),
% 2.09/1.66 inference(modus_ponens,[status(thm)],[2384, 2377])).
% 2.09/1.66 tff(2386,plain,
% 2.09/1.66 ((~hskp11) | c3_1(a722)),
% 2.09/1.66 inference(modus_ponens,[status(thm)],[2385, 2377])).
% 2.09/1.66 tff(2387,plain,
% 2.09/1.66 (c3_1(a722)),
% 2.09/1.66 inference(unit_resolution,[status(thm)],[2386, 2186])).
% 2.09/1.66 tff(2388,plain,
% 2.09/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a693) | c1_1(a722) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733)) | (~c2_1(a722)) | (~c3_1(a722)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a693) | c1_1(a722) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733)) | (~c2_1(a722)) | (~c3_1(a722)))),
% 2.09/1.66 inference(rewrite,[status(thm)],[])).
% 2.09/1.66 tff(2389,plain,
% 2.09/1.66 (((~ndr1_0) | c3_1(a693) | c2_1(a693) | (~c1_1(a693)) | c1_1(a722) | (~c2_1(a722)) | (~c3_1(a722)) | c0_1(a733) | (~c3_1(a733)) | (~c2_1(a733))) <=> (c2_1(a693) | c1_1(a722) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733)) | (~c2_1(a722)) | (~c3_1(a722)))),
% 2.09/1.66 inference(rewrite,[status(thm)],[])).
% 2.09/1.66 tff(2390,plain,
% 2.09/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a693) | c2_1(a693) | (~c1_1(a693)) | c1_1(a722) | (~c2_1(a722)) | (~c3_1(a722)) | c0_1(a733) | (~c3_1(a733)) | (~c2_1(a733)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a693) | c1_1(a722) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733)) | (~c2_1(a722)) | (~c3_1(a722))))),
% 2.09/1.66 inference(monotonicity,[status(thm)],[2389])).
% 2.09/1.66 tff(2391,plain,
% 2.09/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a693) | c2_1(a693) | (~c1_1(a693)) | c1_1(a722) | (~c2_1(a722)) | (~c3_1(a722)) | c0_1(a733) | (~c3_1(a733)) | (~c2_1(a733)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a693) | c1_1(a722) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733)) | (~c2_1(a722)) | (~c3_1(a722)))),
% 2.09/1.66 inference(transitivity,[status(thm)],[2390, 2388])).
% 2.09/1.66 tff(2392,plain,
% 2.09/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a693) | c2_1(a693) | (~c1_1(a693)) | c1_1(a722) | (~c2_1(a722)) | (~c3_1(a722)) | c0_1(a733) | (~c3_1(a733)) | (~c2_1(a733)))),
% 2.09/1.66 inference(quant_inst,[status(thm)],[])).
% 2.09/1.66 tff(2393,plain,
% 2.09/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a693) | c1_1(a722) | (~c1_1(a693)) | c3_1(a693) | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733)) | (~c2_1(a722)) | (~c3_1(a722))),
% 2.09/1.66 inference(modus_ponens,[status(thm)],[2392, 2391])).
% 2.09/1.66 tff(2394,plain,
% 2.09/1.66 (c2_1(a693) | (~c2_1(a722))),
% 2.09/1.66 inference(unit_resolution,[status(thm)],[2393, 227, 1719, 1708, 2387, 2192, 2376, 153, 10, 2159])).
% 2.09/1.66 tff(2395,plain,
% 2.09/1.66 (c2_1(a693)),
% 2.09/1.66 inference(unit_resolution,[status(thm)],[2394, 2211])).
% 2.09/1.66 tff(2396,plain,
% 2.09/1.66 (hskp24 | hskp23 | (~c0_1(a693)) | (~c2_1(a693))),
% 2.09/1.66 inference(unit_resolution,[status(thm)],[1468, 227, 2376, 163])).
% 2.09/1.66 tff(2397,plain,
% 2.09/1.66 (~c0_1(a693)),
% 2.09/1.66 inference(unit_resolution,[status(thm)],[2396, 2395, 432, 474])).
% 2.09/1.66 tff(2398,plain,
% 2.09/1.66 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c3_1(a693) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | c0_1(a693) | (~c2_1(a693)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c3_1(a693) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | c0_1(a693) | (~c2_1(a693)))),
% 2.09/1.66 inference(rewrite,[status(thm)],[])).
% 2.09/1.66 tff(2399,plain,
% 2.09/1.66 ((hskp10 | (~ndr1_0) | c0_1(a733) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a693) | c0_1(a693) | (~c2_1(a693))) <=> (hskp10 | c3_1(a693) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | c0_1(a693) | (~c2_1(a693)))),
% 2.09/1.66 inference(rewrite,[status(thm)],[])).
% 2.09/1.66 tff(2400,plain,
% 2.09/1.66 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a733) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a693) | c0_1(a693) | (~c2_1(a693)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c3_1(a693) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | c0_1(a693) | (~c2_1(a693))))),
% 2.09/1.66 inference(monotonicity,[status(thm)],[2399])).
% 2.09/1.66 tff(2401,plain,
% 2.09/1.66 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a733) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a693) | c0_1(a693) | (~c2_1(a693)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c3_1(a693) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | c0_1(a693) | (~c2_1(a693)))),
% 2.09/1.66 inference(transitivity,[status(thm)],[2400, 2398])).
% 2.09/1.66 tff(2402,plain,
% 2.09/1.66 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a733) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a693) | c0_1(a693) | (~c2_1(a693)))),
% 2.09/1.66 inference(quant_inst,[status(thm)],[])).
% 2.09/1.66 tff(2403,plain,
% 2.09/1.66 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c3_1(a693) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | c0_1(a693) | (~c2_1(a693))),
% 2.09/1.66 inference(modus_ponens,[status(thm)],[2402, 2401])).
% 2.09/1.66 tff(2404,plain,
% 2.09/1.66 (c0_1(a693) | (~c2_1(a693))),
% 2.09/1.66 inference(unit_resolution,[status(thm)],[2403, 227, 1931, 1730, 1708, 153, 1749, 2159])).
% 2.09/1.66 tff(2405,plain,
% 2.09/1.66 ($false),
% 2.09/1.66 inference(unit_resolution,[status(thm)],[2404, 2397, 2395])).
% 2.09/1.66 tff(2406,plain,(hskp23 | c3_1(a693) | hskp24 | hskp6 | c2_1(a754) | c3_1(a754) | hskp28), inference(lemma,lemma(discharge,[]))).
% 2.09/1.66 tff(2407,plain,
% 2.09/1.66 (hskp23),
% 2.09/1.66 inference(unit_resolution,[status(thm)],[2406, 153, 2144, 177, 180, 178, 62])).
% 2.09/1.66 tff(2408,plain,
% 2.09/1.66 (~hskp1),
% 2.09/1.66 inference(unit_resolution,[status(thm)],[1423, 2376])).
% 2.09/1.66 tff(2409,assumption,(~hskp1), introduced(assumption)).
% 2.09/1.66 tff(2410,plain,
% 2.09/1.66 (~hskp0),
% 2.09/1.66 inference(unit_resolution,[status(thm)],[1817, 411, 62, 422, 405])).
% 2.09/1.66 tff(2411,assumption,(hskp12), introduced(assumption)).
% 2.09/1.66 tff(2412,plain,
% 2.09/1.66 (~c3_1(a725)),
% 2.09/1.66 inference(unit_resolution,[status(thm)],[139, 2411])).
% 2.09/1.66 tff(2413,plain,
% 2.09/1.66 (~c1_1(a725)),
% 2.09/1.66 inference(unit_resolution,[status(thm)],[145, 2411])).
% 2.09/1.66 tff(2414,plain,
% 2.09/1.66 (~c0_1(a725)),
% 2.09/1.66 inference(unit_resolution,[status(thm)],[151, 2411])).
% 2.09/1.66 tff(2415,plain,
% 2.09/1.66 ($false),
% 2.09/1.66 inference(unit_resolution,[status(thm)],[1488, 227, 2409, 2216, 2414, 2413, 2412, 1482])).
% 2.09/1.66 tff(2416,plain,((~hskp12) | hskp1 | hskp0), inference(lemma,lemma(discharge,[]))).
% 2.09/1.66 tff(2417,plain,
% 2.09/1.66 (~hskp12),
% 2.09/1.66 inference(unit_resolution,[status(thm)],[2416, 2410, 2409])).
% 2.09/1.66 tff(2418,plain,
% 2.09/1.66 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))))),
% 2.09/1.66 inference(bind,[status(th)],[])).
% 2.09/1.66 tff(2419,plain,
% 2.09/1.66 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 2.09/1.66 inference(quant_intro,[status(thm)],[2418])).
% 2.09/1.66 tff(2420,plain,
% 2.09/1.66 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 2.09/1.67 inference(rewrite,[status(thm)],[])).
% 2.09/1.67 tff(2421,plain,
% 2.09/1.67 (^[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))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_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))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_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))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_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(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp12) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) | hskp12))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))))),
% 2.09/1.67 inference(bind,[status(th)],[])).
% 2.09/1.67 tff(2422,plain,
% 2.09/1.67 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 2.09/1.67 inference(quant_intro,[status(thm)],[2421])).
% 2.09/1.67 tff(2423,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause174')).
% 2.09/1.67 tff(2424,plain,
% 2.09/1.67 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 2.09/1.67 inference(modus_ponens,[status(thm)],[2423, 2422])).
% 2.09/1.67 tff(2425,plain,
% 2.09/1.67 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 2.09/1.67 inference(modus_ponens,[status(thm)],[2424, 2420])).
% 2.09/1.67 tff(2426,plain,(
% 2.09/1.67 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 2.09/1.67 inference(skolemize,[status(sab)],[2425])).
% 2.09/1.67 tff(2427,plain,
% 2.09/1.67 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 2.09/1.67 inference(modus_ponens,[status(thm)],[2426, 2419])).
% 2.09/1.67 tff(2428,plain,
% 2.09/1.67 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp12 | c2_1(a754) | c1_1(a763) | c2_1(a763) | (~c0_1(a754)) | (~ndr1_0) | (~c1_1(a754)) | (~c0_1(a763)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp12 | c2_1(a754) | c1_1(a763) | c2_1(a763) | (~c0_1(a754)) | (~ndr1_0) | (~c1_1(a754)) | (~c0_1(a763)))),
% 2.09/1.67 inference(rewrite,[status(thm)],[])).
% 2.09/1.67 tff(2429,plain,
% 2.09/1.67 ((hskp12 | (~ndr1_0) | c2_1(a754) | (~c0_1(a754)) | (~c1_1(a754)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763))) <=> (hskp12 | c2_1(a754) | c1_1(a763) | c2_1(a763) | (~c0_1(a754)) | (~ndr1_0) | (~c1_1(a754)) | (~c0_1(a763)))),
% 2.09/1.67 inference(rewrite,[status(thm)],[])).
% 2.09/1.67 tff(2430,plain,
% 2.09/1.67 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a754) | (~c0_1(a754)) | (~c1_1(a754)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp12 | c2_1(a754) | c1_1(a763) | c2_1(a763) | (~c0_1(a754)) | (~ndr1_0) | (~c1_1(a754)) | (~c0_1(a763))))),
% 2.09/1.67 inference(monotonicity,[status(thm)],[2429])).
% 2.09/1.67 tff(2431,plain,
% 2.09/1.67 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a754) | (~c0_1(a754)) | (~c1_1(a754)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp12 | c2_1(a754) | c1_1(a763) | c2_1(a763) | (~c0_1(a754)) | (~ndr1_0) | (~c1_1(a754)) | (~c0_1(a763)))),
% 2.09/1.67 inference(transitivity,[status(thm)],[2430, 2428])).
% 2.09/1.67 tff(2432,plain,
% 2.09/1.67 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a754) | (~c0_1(a754)) | (~c1_1(a754)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)))),
% 2.09/1.67 inference(quant_inst,[status(thm)],[])).
% 2.09/1.67 tff(2433,plain,
% 2.09/1.67 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp12 | c2_1(a754) | c1_1(a763) | c2_1(a763) | (~c0_1(a754)) | (~ndr1_0) | (~c1_1(a754)) | (~c0_1(a763))),
% 2.09/1.67 inference(modus_ponens,[status(thm)],[2432, 2431])).
% 2.09/1.67 tff(2434,plain,
% 2.09/1.67 (hskp12 | (~c1_1(a754))),
% 2.09/1.67 inference(unit_resolution,[status(thm)],[2433, 227, 422, 180, 411, 405, 2212, 2427])).
% 2.09/1.67 tff(2435,plain,
% 2.09/1.67 (~c1_1(a754)),
% 2.09/1.67 inference(unit_resolution,[status(thm)],[2434, 2417])).
% 2.09/1.67 tff(2436,plain,
% 2.09/1.67 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))))),
% 2.09/1.67 inference(bind,[status(th)],[])).
% 2.09/1.67 tff(2437,plain,
% 2.09/1.67 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 2.09/1.67 inference(quant_intro,[status(thm)],[2436])).
% 2.09/1.67 tff(2438,plain,
% 2.09/1.67 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 2.09/1.67 inference(rewrite,[status(thm)],[])).
% 2.09/1.67 tff(2439,plain,
% 2.09/1.67 (^[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(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))))),
% 2.09/1.67 inference(bind,[status(th)],[])).
% 2.09/1.67 tff(2440,plain,
% 2.09/1.67 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 2.09/1.67 inference(quant_intro,[status(thm)],[2439])).
% 2.09/1.67 tff(2441,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause190')).
% 2.09/1.67 tff(2442,plain,
% 2.09/1.67 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 2.09/1.67 inference(modus_ponens,[status(thm)],[2441, 2440])).
% 2.09/1.67 tff(2443,plain,
% 2.09/1.67 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 2.09/1.67 inference(modus_ponens,[status(thm)],[2442, 2438])).
% 2.09/1.67 tff(2444,plain,(
% 2.09/1.67 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 2.09/1.67 inference(skolemize,[status(sab)],[2443])).
% 2.09/1.67 tff(2445,plain,
% 2.09/1.67 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 2.09/1.67 inference(modus_ponens,[status(thm)],[2444, 2437])).
% 2.09/1.67 tff(2446,plain,
% 2.09/1.67 (hskp13),
% 2.09/1.67 inference(unit_resolution,[status(thm)],[2066, 2417, 2303])).
% 2.09/1.67 tff(2447,plain,
% 2.09/1.67 (~c3_1(a726)),
% 2.09/1.67 inference(unit_resolution,[status(thm)],[2021, 2446])).
% 2.09/1.67 tff(2448,plain,
% 2.09/1.67 (~c0_1(a726)),
% 2.09/1.67 inference(unit_resolution,[status(thm)],[2027, 2446])).
% 2.09/1.67 tff(2449,plain,
% 2.09/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | c1_1(a754))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | c1_1(a754))),
% 2.09/1.67 inference(rewrite,[status(thm)],[])).
% 2.09/1.67 tff(2450,plain,
% 2.09/1.67 (((~ndr1_0) | c3_1(a754) | c2_1(a754) | (~c0_1(a754)) | c1_1(a754) | c2_1(a754) | (~c0_1(a754)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726))) <=> (c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | c1_1(a754))),
% 2.09/1.67 inference(rewrite,[status(thm)],[])).
% 2.09/1.67 tff(2451,plain,
% 2.09/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a754) | c2_1(a754) | (~c0_1(a754)) | c1_1(a754) | c2_1(a754) | (~c0_1(a754)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | c1_1(a754)))),
% 2.09/1.67 inference(monotonicity,[status(thm)],[2450])).
% 2.09/1.67 tff(2452,plain,
% 2.09/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a754) | c2_1(a754) | (~c0_1(a754)) | c1_1(a754) | c2_1(a754) | (~c0_1(a754)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | c1_1(a754))),
% 2.09/1.67 inference(transitivity,[status(thm)],[2451, 2449])).
% 2.09/1.67 tff(2453,plain,
% 2.09/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a754) | c2_1(a754) | (~c0_1(a754)) | c1_1(a754) | c2_1(a754) | (~c0_1(a754)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726)))),
% 2.09/1.67 inference(quant_inst,[status(thm)],[])).
% 2.09/1.67 tff(2454,plain,
% 2.09/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a754) | (~c0_1(a754)) | c3_1(a754) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | c1_1(a754)),
% 2.09/1.67 inference(modus_ponens,[status(thm)],[2453, 2452])).
% 2.09/1.67 tff(2455,plain,
% 2.09/1.67 (~c2_1(a726)),
% 2.09/1.67 inference(unit_resolution,[status(thm)],[2454, 227, 180, 2212, 178, 2448, 2447, 2445, 2435])).
% 2.09/1.67 tff(2456,plain,
% 2.09/1.67 (c1_1(a726)),
% 2.09/1.67 inference(unit_resolution,[status(thm)],[2045, 2446])).
% 2.09/1.67 tff(2457,plain,
% 2.09/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a754) | c3_1(a754) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726) | c1_1(a754))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a754) | c3_1(a754) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726) | c1_1(a754))),
% 2.09/1.67 inference(rewrite,[status(thm)],[])).
% 2.09/1.67 tff(2458,plain,
% 2.09/1.67 (((~ndr1_0) | c0_1(a726) | c2_1(a726) | (~c1_1(a726)) | c3_1(a754) | c1_1(a754) | c2_1(a754) | c3_1(a726) | c2_1(a726) | c0_1(a726)) <=> (c2_1(a754) | c3_1(a754) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726) | c1_1(a754))),
% 2.09/1.67 inference(rewrite,[status(thm)],[])).
% 2.09/1.67 tff(2459,plain,
% 2.09/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a726) | c2_1(a726) | (~c1_1(a726)) | c3_1(a754) | c1_1(a754) | c2_1(a754) | c3_1(a726) | c2_1(a726) | c0_1(a726))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a754) | c3_1(a754) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726) | c1_1(a754)))),
% 2.09/1.67 inference(monotonicity,[status(thm)],[2458])).
% 2.09/1.67 tff(2460,plain,
% 2.09/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a726) | c2_1(a726) | (~c1_1(a726)) | c3_1(a754) | c1_1(a754) | c2_1(a754) | c3_1(a726) | c2_1(a726) | c0_1(a726))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a754) | c3_1(a754) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726) | c1_1(a754))),
% 2.09/1.67 inference(transitivity,[status(thm)],[2459, 2457])).
% 2.09/1.67 tff(2461,plain,
% 2.09/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a726) | c2_1(a726) | (~c1_1(a726)) | c3_1(a754) | c1_1(a754) | c2_1(a754) | c3_1(a726) | c2_1(a726) | c0_1(a726))),
% 2.09/1.67 inference(quant_inst,[status(thm)],[])).
% 2.09/1.67 tff(2462,plain,
% 2.09/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a754) | c3_1(a754) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726) | c1_1(a754)),
% 2.09/1.67 inference(modus_ponens,[status(thm)],[2461, 2460])).
% 2.09/1.67 tff(2463,plain,
% 2.09/1.67 ($false),
% 2.09/1.67 inference(unit_resolution,[status(thm)],[2462, 227, 180, 2456, 178, 2448, 2447, 122, 2435, 2455])).
% 2.09/1.67 tff(2464,plain,((~hskp23) | c2_1(a754) | c3_1(a754) | (~c0_1(a754)) | hskp1 | hskp28), inference(lemma,lemma(discharge,[]))).
% 2.09/1.67 tff(2465,plain,
% 2.09/1.67 ($false),
% 2.09/1.67 inference(unit_resolution,[status(thm)],[2464, 2408, 2407, 178, 2010, 180, 62])).
% 2.09/1.67 tff(2466,plain,(c3_1(a693) | c3_1(a754) | c2_1(a754) | hskp28 | hskp6), inference(lemma,lemma(discharge,[]))).
% 2.09/1.67 tff(2467,plain,
% 2.09/1.67 (c3_1(a693)),
% 2.09/1.67 inference(unit_resolution,[status(thm)],[2466, 180, 178, 62, 177])).
% 2.09/1.67 tff(2468,plain,
% 2.09/1.67 (~hskp1),
% 2.09/1.67 inference(unit_resolution,[status(thm)],[1553, 2467])).
% 2.09/1.67 tff(2469,plain,
% 2.09/1.67 (~hskp23),
% 2.09/1.67 inference(unit_resolution,[status(thm)],[2464, 2468, 178, 2010, 180, 62])).
% 2.09/1.67 tff(2470,plain,
% 2.09/1.67 (~c0_1(a733)),
% 2.09/1.67 inference(unit_resolution,[status(thm)],[2158, 2469, 2144])).
% 2.09/1.67 tff(2471,plain,
% 2.09/1.67 (hskp11),
% 2.09/1.67 inference(unit_resolution,[status(thm)],[2185, 227, 1719, 1708, 180, 2010, 178, 2179, 2470])).
% 2.09/1.67 tff(2472,plain,
% 2.09/1.67 (~c1_1(a722)),
% 2.09/1.67 inference(unit_resolution,[status(thm)],[2191, 2471])).
% 2.09/1.67 tff(2473,plain,
% 2.09/1.67 (c0_1(a722)),
% 2.09/1.67 inference(unit_resolution,[status(thm)],[2202, 2471])).
% 2.09/1.67 tff(2474,plain,
% 2.09/1.67 (~hskp27),
% 2.09/1.67 inference(unit_resolution,[status(thm)],[2147, 2469, 2144, 62])).
% 2.09/1.67 tff(2475,plain,
% 2.09/1.67 (~hskp4),
% 2.09/1.67 inference(unit_resolution,[status(thm)],[2150, 2474, 177])).
% 2.09/1.67 tff(2476,plain,
% 2.09/1.67 (c2_1(a722)),
% 2.09/1.67 inference(unit_resolution,[status(thm)],[2209, 227, 2475, 1730, 1708, 2473, 2472, 2169, 2470])).
% 2.09/1.67 tff(2477,plain,
% 2.09/1.67 (c3_1(a722)),
% 2.09/1.67 inference(unit_resolution,[status(thm)],[2386, 2471])).
% 2.09/1.67 tff(2478,plain,
% 2.09/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a754) | c3_1(a754) | c1_1(a722) | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733)) | (~c2_1(a722)) | (~c3_1(a722)) | (~c1_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a754) | c3_1(a754) | c1_1(a722) | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733)) | (~c2_1(a722)) | (~c3_1(a722)) | (~c1_1(a754)))),
% 2.09/1.67 inference(rewrite,[status(thm)],[])).
% 2.09/1.67 tff(2479,plain,
% 2.09/1.67 (((~ndr1_0) | c3_1(a754) | c2_1(a754) | (~c1_1(a754)) | c1_1(a722) | (~c2_1(a722)) | (~c3_1(a722)) | c0_1(a733) | (~c3_1(a733)) | (~c2_1(a733))) <=> (c2_1(a754) | c3_1(a754) | c1_1(a722) | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733)) | (~c2_1(a722)) | (~c3_1(a722)) | (~c1_1(a754)))),
% 2.09/1.67 inference(rewrite,[status(thm)],[])).
% 2.09/1.67 tff(2480,plain,
% 2.09/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a754) | c2_1(a754) | (~c1_1(a754)) | c1_1(a722) | (~c2_1(a722)) | (~c3_1(a722)) | c0_1(a733) | (~c3_1(a733)) | (~c2_1(a733)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a754) | c3_1(a754) | c1_1(a722) | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733)) | (~c2_1(a722)) | (~c3_1(a722)) | (~c1_1(a754))))),
% 2.09/1.67 inference(monotonicity,[status(thm)],[2479])).
% 2.09/1.67 tff(2481,plain,
% 2.09/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a754) | c2_1(a754) | (~c1_1(a754)) | c1_1(a722) | (~c2_1(a722)) | (~c3_1(a722)) | c0_1(a733) | (~c3_1(a733)) | (~c2_1(a733)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a754) | c3_1(a754) | c1_1(a722) | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733)) | (~c2_1(a722)) | (~c3_1(a722)) | (~c1_1(a754)))),
% 2.09/1.67 inference(transitivity,[status(thm)],[2480, 2478])).
% 2.09/1.67 tff(2482,plain,
% 2.09/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a754) | c2_1(a754) | (~c1_1(a754)) | c1_1(a722) | (~c2_1(a722)) | (~c3_1(a722)) | c0_1(a733) | (~c3_1(a733)) | (~c2_1(a733)))),
% 2.09/1.67 inference(quant_inst,[status(thm)],[])).
% 2.09/1.67 tff(2483,plain,
% 2.09/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a754) | c3_1(a754) | c1_1(a722) | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733)) | (~c2_1(a722)) | (~c3_1(a722)) | (~c1_1(a754))),
% 2.09/1.67 inference(modus_ponens,[status(thm)],[2482, 2481])).
% 2.09/1.67 tff(2484,plain,
% 2.09/1.67 ((~c2_1(a722)) | (~c1_1(a754))),
% 2.09/1.67 inference(unit_resolution,[status(thm)],[2483, 227, 1719, 1708, 180, 2477, 178, 2472, 10, 2470])).
% 2.09/1.67 tff(2485,plain,
% 2.09/1.67 (~c1_1(a754)),
% 2.09/1.67 inference(unit_resolution,[status(thm)],[2484, 2476])).
% 2.09/1.67 tff(2486,plain,
% 2.09/1.67 ($false),
% 2.09/1.67 inference(unit_resolution,[status(thm)],[2317, 227, 2475, 1730, 1708, 180, 2010, 2169, 2485, 2470])).
% 2.09/1.67 tff(2487,plain,(c2_1(a754) | c3_1(a754) | hskp6 | hskp28), inference(lemma,lemma(discharge,[]))).
% 2.09/1.67 tff(2488,plain,
% 2.09/1.67 (c2_1(a754)),
% 2.09/1.67 inference(unit_resolution,[status(thm)],[2487, 177, 178, 62])).
% 2.09/1.67 tff(2489,plain,
% 2.09/1.67 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~c0_1(a754)) | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp3 | (~c0_1(a754)) | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c2_1(a754)))),
% 2.09/1.67 inference(rewrite,[status(thm)],[])).
% 2.09/1.67 tff(2490,plain,
% 2.09/1.67 ((hskp3 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a754) | (~c2_1(a754)) | (~c0_1(a754))) <=> (hskp3 | (~c0_1(a754)) | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c2_1(a754)))),
% 2.09/1.67 inference(rewrite,[status(thm)],[])).
% 2.09/1.67 tff(2491,plain,
% 2.09/1.67 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a754) | (~c2_1(a754)) | (~c0_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~c0_1(a754)) | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c2_1(a754))))),
% 2.09/1.67 inference(monotonicity,[status(thm)],[2490])).
% 2.09/1.67 tff(2492,plain,
% 2.09/1.67 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a754) | (~c2_1(a754)) | (~c0_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp3 | (~c0_1(a754)) | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c2_1(a754)))),
% 2.09/1.67 inference(transitivity,[status(thm)],[2491, 2489])).
% 2.09/1.67 tff(2493,plain,
% 2.09/1.67 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a754) | (~c2_1(a754)) | (~c0_1(a754)))),
% 2.09/1.67 inference(quant_inst,[status(thm)],[])).
% 2.09/1.67 tff(2494,plain,
% 2.09/1.67 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp3 | (~c0_1(a754)) | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c2_1(a754))),
% 2.09/1.67 inference(modus_ponens,[status(thm)],[2493, 2492])).
% 2.09/1.67 tff(2495,plain,
% 2.09/1.67 (hskp3 | (~c0_1(a754)) | (~c2_1(a754))),
% 2.09/1.67 inference(unit_resolution,[status(thm)],[2494, 227, 1730, 1719, 1708, 178, 2234])).
% 2.09/1.67 tff(2496,plain,
% 2.09/1.67 (hskp3),
% 2.09/1.67 inference(unit_resolution,[status(thm)],[2495, 2488, 2010])).
% 2.09/1.67 tff(2497,plain,
% 2.09/1.67 (~c3_1(a697)),
% 2.09/1.67 inference(unit_resolution,[status(thm)],[1355, 2496])).
% 2.09/1.67 tff(2498,plain,
% 2.09/1.67 (c2_1(a697)),
% 2.09/1.67 inference(unit_resolution,[status(thm)],[527, 2496])).
% 2.09/1.67 tff(2499,assumption,(c0_1(a733)), introduced(assumption)).
% 2.09/1.67 tff(2500,assumption,(c2_1(a697)), introduced(assumption)).
% 2.09/1.67 tff(2501,plain,
% 2.09/1.67 ((~c0_1(a733)) | (~c1_1(a697))),
% 2.09/1.67 inference(unit_resolution,[status(thm)],[2309, 227, 280, 1719, 1708, 2500, 175, 2101])).
% 2.09/1.67 tff(2502,plain,
% 2.09/1.67 (~c1_1(a697)),
% 2.09/1.67 inference(unit_resolution,[status(thm)],[2501, 2499])).
% 2.09/1.67 tff(2503,plain,
% 2.09/1.67 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | c3_1(a697) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | c1_1(a697) | (~c2_1(a697)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a697) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | c1_1(a697) | (~c2_1(a697)))),
% 2.09/1.67 inference(rewrite,[status(thm)],[])).
% 2.09/1.67 tff(2504,plain,
% 2.09/1.67 ((hskp14 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a697) | c1_1(a697) | (~c2_1(a697))) <=> (hskp14 | c3_1(a697) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | c1_1(a697) | (~c2_1(a697)))),
% 2.09/1.67 inference(rewrite,[status(thm)],[])).
% 2.09/1.67 tff(2505,plain,
% 2.09/1.67 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a697) | c1_1(a697) | (~c2_1(a697)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | c3_1(a697) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | c1_1(a697) | (~c2_1(a697))))),
% 2.09/1.67 inference(monotonicity,[status(thm)],[2504])).
% 2.09/1.67 tff(2506,plain,
% 2.09/1.67 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a697) | c1_1(a697) | (~c2_1(a697)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a697) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | c1_1(a697) | (~c2_1(a697)))),
% 2.09/1.67 inference(transitivity,[status(thm)],[2505, 2503])).
% 2.09/1.67 tff(2507,plain,
% 2.09/1.67 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a697) | c1_1(a697) | (~c2_1(a697)))),
% 2.09/1.67 inference(quant_inst,[status(thm)],[])).
% 2.09/1.67 tff(2508,plain,
% 2.09/1.67 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a697) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | c1_1(a697) | (~c2_1(a697))),
% 2.09/1.67 inference(modus_ponens,[status(thm)],[2507, 2506])).
% 2.09/1.67 tff(2509,plain,
% 2.09/1.67 (hskp14 | (~c0_1(a733)) | c1_1(a697)),
% 2.09/1.67 inference(unit_resolution,[status(thm)],[2508, 227, 1719, 1708, 2500, 175, 1614])).
% 2.09/1.67 tff(2510,plain,
% 2.09/1.67 (hskp14),
% 2.09/1.67 inference(unit_resolution,[status(thm)],[2509, 2499, 2502])).
% 2.09/1.67 tff(2511,plain,
% 2.09/1.67 (~c3_1(a730)),
% 2.09/1.67 inference(unit_resolution,[status(thm)],[486, 2510])).
% 2.09/1.67 tff(2512,plain,
% 2.09/1.67 (c1_1(a730)),
% 2.09/1.67 inference(unit_resolution,[status(thm)],[461, 2510])).
% 2.09/1.67 tff(2513,plain,
% 2.09/1.67 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | c3_1(a730) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a730)) | (~c2_1(a730)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a730) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a730)) | (~c2_1(a730)))),
% 2.09/1.67 inference(rewrite,[status(thm)],[])).
% 2.09/1.67 tff(2514,plain,
% 2.09/1.67 ((hskp20 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a730) | (~c2_1(a730)) | (~c1_1(a730))) <=> (hskp20 | c3_1(a730) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a730)) | (~c2_1(a730)))),
% 2.09/1.68 inference(rewrite,[status(thm)],[])).
% 2.09/1.68 tff(2515,plain,
% 2.09/1.68 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a730) | (~c2_1(a730)) | (~c1_1(a730)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | c3_1(a730) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a730)) | (~c2_1(a730))))),
% 2.09/1.68 inference(monotonicity,[status(thm)],[2514])).
% 2.09/1.68 tff(2516,plain,
% 2.09/1.68 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a730) | (~c2_1(a730)) | (~c1_1(a730)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a730) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a730)) | (~c2_1(a730)))),
% 2.09/1.68 inference(transitivity,[status(thm)],[2515, 2513])).
% 2.09/1.68 tff(2517,plain,
% 2.09/1.68 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a730) | (~c2_1(a730)) | (~c1_1(a730)))),
% 2.09/1.68 inference(quant_inst,[status(thm)],[])).
% 2.09/1.68 tff(2518,plain,
% 2.09/1.68 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a730) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a730)) | (~c2_1(a730))),
% 2.09/1.68 inference(modus_ponens,[status(thm)],[2517, 2516])).
% 2.09/1.68 tff(2519,plain,
% 2.09/1.68 (~c2_1(a730)),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[2518, 227, 280, 1719, 1708, 2512, 2511, 2101, 2499])).
% 2.09/1.68 tff(2520,plain,
% 2.09/1.68 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a754)) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a754)) | (~c2_1(a754)))),
% 2.09/1.68 inference(rewrite,[status(thm)],[])).
% 2.09/1.68 tff(2521,plain,
% 2.09/1.68 ((hskp20 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a754) | (~c2_1(a754)) | (~c1_1(a754))) <=> (hskp20 | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a754)) | (~c2_1(a754)))),
% 2.09/1.68 inference(rewrite,[status(thm)],[])).
% 2.09/1.68 tff(2522,plain,
% 2.09/1.68 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a754) | (~c2_1(a754)) | (~c1_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a754)) | (~c2_1(a754))))),
% 2.09/1.68 inference(monotonicity,[status(thm)],[2521])).
% 2.09/1.68 tff(2523,plain,
% 2.09/1.68 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a754) | (~c2_1(a754)) | (~c1_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a754)) | (~c2_1(a754)))),
% 2.09/1.68 inference(transitivity,[status(thm)],[2522, 2520])).
% 2.09/1.68 tff(2524,plain,
% 2.09/1.68 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a754) | (~c2_1(a754)) | (~c1_1(a754)))),
% 2.09/1.68 inference(quant_inst,[status(thm)],[])).
% 2.09/1.68 tff(2525,plain,
% 2.09/1.68 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a754) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a754)) | (~c2_1(a754))),
% 2.09/1.68 inference(modus_ponens,[status(thm)],[2524, 2523])).
% 2.09/1.68 tff(2526,plain,
% 2.09/1.68 (hskp20 | (~c0_1(a733)) | (~c1_1(a754)) | (~c2_1(a754))),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[2525, 227, 1719, 1708, 178, 2101])).
% 2.09/1.68 tff(2527,plain,
% 2.09/1.68 (~c1_1(a754)),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[2526, 2499, 280, 387])).
% 2.09/1.68 tff(2528,plain,
% 2.09/1.68 (c0_1(a730)),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[472, 2510])).
% 2.09/1.68 tff(2529,plain,
% 2.09/1.68 ($false),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[493, 227, 62, 387, 2528, 178, 2511, 342, 2527, 2519])).
% 2.09/1.68 tff(2530,plain,((~c0_1(a733)) | hskp28 | (~c2_1(a754)) | c3_1(a754) | hskp20 | (~c2_1(a697)) | c3_1(a697)), inference(lemma,lemma(discharge,[]))).
% 2.09/1.68 tff(2531,plain,
% 2.09/1.68 (~c0_1(a733)),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[2530, 2488, 62, 178, 2011, 2498, 2497])).
% 2.09/1.68 tff(2532,assumption,(~c0_1(a733)), introduced(assumption)).
% 2.09/1.68 tff(2533,assumption,(~hskp10), introduced(assumption)).
% 2.09/1.68 tff(2534,plain,
% 2.09/1.68 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | (~c2_1(a726)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | (~c2_1(a726)))),
% 2.09/1.68 inference(rewrite,[status(thm)],[])).
% 2.09/1.68 tff(2535,plain,
% 2.09/1.68 ((hskp10 | (~ndr1_0) | c0_1(a733) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726))) <=> (hskp10 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | (~c2_1(a726)))),
% 2.09/1.68 inference(rewrite,[status(thm)],[])).
% 2.09/1.68 tff(2536,plain,
% 2.09/1.68 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a733) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | (~c2_1(a726))))),
% 2.09/1.68 inference(monotonicity,[status(thm)],[2535])).
% 2.09/1.68 tff(2537,plain,
% 2.09/1.68 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a733) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | (~c2_1(a726)))),
% 2.09/1.68 inference(transitivity,[status(thm)],[2536, 2534])).
% 2.09/1.68 tff(2538,plain,
% 2.09/1.68 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a733) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726)))),
% 2.09/1.68 inference(quant_inst,[status(thm)],[])).
% 2.09/1.68 tff(2539,plain,
% 2.09/1.68 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | (~c2_1(a726))),
% 2.09/1.68 inference(modus_ponens,[status(thm)],[2538, 2537])).
% 2.09/1.68 tff(2540,plain,
% 2.09/1.68 (~c2_1(a726)),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[2539, 227, 2533, 2259, 2257, 2028, 2022, 1749, 2532])).
% 2.09/1.68 tff(2541,plain,
% 2.09/1.68 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726))),
% 2.09/1.68 inference(rewrite,[status(thm)],[])).
% 2.09/1.68 tff(2542,plain,
% 2.09/1.68 ((hskp6 | (~ndr1_0) | c3_1(a726) | c0_1(a726) | (~c1_1(a726)) | c3_1(a726) | c0_1(a726) | c2_1(a726)) <=> (hskp6 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726))),
% 2.09/1.68 inference(rewrite,[status(thm)],[])).
% 2.09/1.68 tff(2543,plain,
% 2.09/1.68 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a726) | c0_1(a726) | (~c1_1(a726)) | c3_1(a726) | c0_1(a726) | c2_1(a726))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726)))),
% 2.09/1.68 inference(monotonicity,[status(thm)],[2542])).
% 2.09/1.68 tff(2544,plain,
% 2.09/1.68 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a726) | c0_1(a726) | (~c1_1(a726)) | c3_1(a726) | c0_1(a726) | c2_1(a726))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726))),
% 2.09/1.68 inference(transitivity,[status(thm)],[2543, 2541])).
% 2.09/1.68 tff(2545,plain,
% 2.09/1.68 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp6 | (~ndr1_0) | c3_1(a726) | c0_1(a726) | (~c1_1(a726)) | c3_1(a726) | c0_1(a726) | c2_1(a726))),
% 2.09/1.68 inference(quant_inst,[status(thm)],[])).
% 2.09/1.68 tff(2546,plain,
% 2.09/1.68 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp6 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726)),
% 2.09/1.68 inference(modus_ponens,[status(thm)],[2545, 2544])).
% 2.09/1.68 tff(2547,plain,
% 2.09/1.68 ($false),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[2546, 227, 177, 2046, 2028, 2022, 301, 2540])).
% 2.09/1.68 tff(2548,plain,((~hskp13) | hskp6 | hskp10 | (~c1_1(a733)) | (~c3_1(a733)) | c0_1(a733)), inference(lemma,lemma(discharge,[]))).
% 2.09/1.68 tff(2549,plain,
% 2.09/1.68 (~hskp13),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[2548, 2531, 1931, 1730, 1708, 177])).
% 2.09/1.68 tff(2550,plain,
% 2.09/1.68 (hskp12),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[2066, 2549, 2011])).
% 2.09/1.68 tff(2551,plain,
% 2.09/1.68 (~hskp13),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[2548, 2532, 2533, 2259, 2257, 177])).
% 2.09/1.68 tff(2552,plain,
% 2.09/1.68 (hskp12),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[2066, 2551, 280])).
% 2.09/1.68 tff(2553,plain,
% 2.09/1.68 (~c0_1(a725)),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[151, 2552])).
% 2.09/1.68 tff(2554,plain,
% 2.09/1.68 (~c3_1(a725)),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[139, 2552])).
% 2.09/1.68 tff(2555,plain,
% 2.09/1.68 (c3_1(a725) | c2_1(a725)),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[641, 227, 1036, 177, 578, 201])).
% 2.09/1.68 tff(2556,plain,
% 2.09/1.68 (c2_1(a725)),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[2555, 1037])).
% 2.09/1.68 tff(2557,plain,
% 2.09/1.68 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | (~c2_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | (~c2_1(a725)))),
% 2.09/1.68 inference(rewrite,[status(thm)],[])).
% 2.09/1.68 tff(2558,plain,
% 2.09/1.68 ((hskp10 | (~ndr1_0) | c0_1(a733) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725))) <=> (hskp10 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | (~c2_1(a725)))),
% 2.09/1.68 inference(rewrite,[status(thm)],[])).
% 2.09/1.68 tff(2559,plain,
% 2.09/1.68 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a733) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | (~c2_1(a725))))),
% 2.09/1.68 inference(monotonicity,[status(thm)],[2558])).
% 2.09/1.68 tff(2560,plain,
% 2.09/1.68 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a733) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | (~c2_1(a725)))),
% 2.09/1.68 inference(transitivity,[status(thm)],[2559, 2557])).
% 2.09/1.68 tff(2561,plain,
% 2.09/1.68 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a733) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))),
% 2.09/1.68 inference(quant_inst,[status(thm)],[])).
% 2.09/1.68 tff(2562,plain,
% 2.09/1.68 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | c0_1(a733) | (~c2_1(a725))),
% 2.09/1.68 inference(modus_ponens,[status(thm)],[2561, 2560])).
% 2.09/1.68 tff(2563,plain,
% 2.09/1.68 ($false),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[2562, 227, 2533, 2259, 2257, 578, 1037, 1749, 2556, 2532])).
% 2.09/1.68 tff(2564,plain,(c3_1(a725) | hskp10 | (~c1_1(a733)) | (~c3_1(a733)) | c0_1(a725) | c0_1(a733) | hskp27 | hskp6), inference(lemma,lemma(discharge,[]))).
% 2.09/1.68 tff(2565,plain,
% 2.09/1.68 ($false),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[2564, 2554, 2553, 2259, 2257, 2533, 2532, 1036, 177])).
% 2.09/1.68 tff(2566,plain,(c0_1(a733) | (~c1_1(a733)) | (~c3_1(a733)) | hskp10 | hskp27 | hskp6 | hskp20), inference(lemma,lemma(discharge,[]))).
% 2.09/1.68 tff(2567,plain,
% 2.09/1.68 (hskp27),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[2566, 2531, 1708, 1931, 1730, 177, 2011])).
% 2.09/1.68 tff(2568,plain,
% 2.09/1.68 (hskp23),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[2147, 2567, 2144, 62])).
% 2.09/1.68 tff(2569,plain,
% 2.09/1.68 (~c2_1(a763)),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[404, 2568])).
% 2.09/1.68 tff(2570,plain,
% 2.09/1.68 (c0_1(a763)),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[421, 2568])).
% 2.09/1.68 tff(2571,plain,
% 2.09/1.68 (~c1_1(a763)),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[410, 2568])).
% 2.09/1.68 tff(2572,plain,
% 2.09/1.68 (~hskp0),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[1817, 2571, 62, 2570, 2569])).
% 2.09/1.68 tff(2573,plain,
% 2.09/1.68 (hskp1),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[2416, 2572, 2550])).
% 2.09/1.68 tff(2574,plain,
% 2.09/1.68 (~c3_1(a693)),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[1553, 2573])).
% 2.09/1.68 tff(2575,plain,
% 2.09/1.68 (c2_1(a693)),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[383, 2573])).
% 2.09/1.68 tff(2576,plain,
% 2.09/1.68 (c0_1(a693)),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[2403, 227, 1931, 1730, 1708, 2575, 2574, 1749, 2531])).
% 2.09/1.68 tff(2577,plain,
% 2.09/1.68 (^[V: $i, U: $i] : refl((hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))))),
% 2.09/1.68 inference(bind,[status(th)],[])).
% 2.09/1.68 tff(2578,plain,
% 2.09/1.68 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 2.09/1.68 inference(quant_intro,[status(thm)],[2577])).
% 2.09/1.68 tff(2579,plain,
% 2.09/1.68 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 2.09/1.68 inference(rewrite,[status(thm)],[])).
% 2.09/1.68 tff(2580,plain,
% 2.09/1.68 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp13) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | hskp13))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | hskp13) <=> (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))))),
% 2.09/1.68 inference(bind,[status(th)],[])).
% 2.09/1.68 tff(2581,plain,
% 2.09/1.68 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp13) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 2.09/1.68 inference(quant_intro,[status(thm)],[2580])).
% 2.09/1.68 tff(2582,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause167')).
% 2.09/1.68 tff(2583,plain,
% 2.09/1.68 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 2.09/1.68 inference(modus_ponens,[status(thm)],[2582, 2581])).
% 2.09/1.68 tff(2584,plain,
% 2.09/1.68 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 2.09/1.68 inference(modus_ponens,[status(thm)],[2583, 2579])).
% 2.09/1.68 tff(2585,plain,(
% 2.09/1.68 ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 2.09/1.68 inference(skolemize,[status(sab)],[2584])).
% 2.09/1.68 tff(2586,plain,
% 2.09/1.68 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 2.09/1.68 inference(modus_ponens,[status(thm)],[2585, 2578])).
% 2.09/1.68 tff(2587,plain,
% 2.09/1.68 (~c1_1(a693)),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[1423, 2573])).
% 2.09/1.68 tff(2588,plain,
% 2.09/1.68 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp13 | c1_1(a763) | c2_1(a763) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)) | (~c3_1(a763)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp13 | c1_1(a763) | c2_1(a763) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)) | (~c3_1(a763)))),
% 2.09/1.68 inference(rewrite,[status(thm)],[])).
% 2.09/1.68 tff(2589,plain,
% 2.09/1.68 ((hskp13 | (~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c0_1(a693)) | c1_1(a763) | c2_1(a763) | (~c3_1(a763))) <=> (hskp13 | c1_1(a763) | c2_1(a763) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)) | (~c3_1(a763)))),
% 2.09/1.68 inference(rewrite,[status(thm)],[])).
% 2.09/1.68 tff(2590,plain,
% 2.09/1.68 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c0_1(a693)) | c1_1(a763) | c2_1(a763) | (~c3_1(a763)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp13 | c1_1(a763) | c2_1(a763) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)) | (~c3_1(a763))))),
% 2.09/1.68 inference(monotonicity,[status(thm)],[2589])).
% 2.09/1.68 tff(2591,plain,
% 2.09/1.68 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c0_1(a693)) | c1_1(a763) | c2_1(a763) | (~c3_1(a763)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp13 | c1_1(a763) | c2_1(a763) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)) | (~c3_1(a763)))),
% 2.09/1.68 inference(transitivity,[status(thm)],[2590, 2588])).
% 2.09/1.68 tff(2592,plain,
% 2.09/1.68 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c0_1(a693)) | c1_1(a763) | c2_1(a763) | (~c3_1(a763)))),
% 2.09/1.68 inference(quant_inst,[status(thm)],[])).
% 2.09/1.68 tff(2593,plain,
% 2.09/1.68 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp13 | c1_1(a763) | c2_1(a763) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c0_1(a693)) | (~c3_1(a763))),
% 2.09/1.68 inference(modus_ponens,[status(thm)],[2592, 2591])).
% 2.09/1.68 tff(2594,plain,
% 2.09/1.68 (~c3_1(a763)),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[2593, 227, 2549, 2571, 2569, 2587, 2574, 2586, 2576])).
% 2.09/1.68 tff(2595,plain,
% 2.09/1.68 (c0_1(a691)),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[278, 2567])).
% 2.09/1.68 tff(2596,plain,
% 2.09/1.68 (c3_1(a691)),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[256, 2567])).
% 2.09/1.68 tff(2597,plain,
% 2.09/1.68 (c2_1(a691)),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[1764, 2596, 2595, 62])).
% 2.09/1.68 tff(2598,plain,
% 2.09/1.68 (~c0_1(a725)),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[151, 2550])).
% 2.09/1.68 tff(2599,plain,
% 2.09/1.68 (~c1_1(a725)),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[145, 2550])).
% 2.09/1.68 tff(2600,plain,
% 2.09/1.68 (~c2_1(a725)),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[586, 2599, 2568, 2598, 62])).
% 2.09/1.68 tff(2601,plain,
% 2.09/1.68 (~c3_1(a725)),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[139, 2550])).
% 2.09/1.68 tff(2602,plain,
% 2.09/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~c0_1(a754)) | c3_1(a754) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c1_1(a754)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (~c0_1(a754)) | c3_1(a754) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c1_1(a754)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 2.09/1.68 inference(rewrite,[status(thm)],[])).
% 2.09/1.68 tff(2603,plain,
% 2.09/1.68 (((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a754) | (~c1_1(a754)) | (~c0_1(a754)) | c3_1(a725) | c2_1(a725) | c0_1(a725)) <=> ((~c0_1(a754)) | c3_1(a754) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c1_1(a754)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 2.09/1.68 inference(rewrite,[status(thm)],[])).
% 2.09/1.68 tff(2604,plain,
% 2.09/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a754) | (~c1_1(a754)) | (~c0_1(a754)) | c3_1(a725) | c2_1(a725) | c0_1(a725))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~c0_1(a754)) | c3_1(a754) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c1_1(a754)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691))))),
% 2.09/1.68 inference(monotonicity,[status(thm)],[2603])).
% 2.09/1.68 tff(2605,plain,
% 2.09/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a754) | (~c1_1(a754)) | (~c0_1(a754)) | c3_1(a725) | c2_1(a725) | c0_1(a725))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (~c0_1(a754)) | c3_1(a754) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c1_1(a754)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 2.09/1.68 inference(transitivity,[status(thm)],[2604, 2602])).
% 2.09/1.68 tff(2606,plain,
% 2.09/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a754) | (~c1_1(a754)) | (~c0_1(a754)) | c3_1(a725) | c2_1(a725) | c0_1(a725))),
% 2.09/1.68 inference(quant_inst,[status(thm)],[])).
% 2.09/1.68 tff(2607,plain,
% 2.09/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (~c0_1(a754)) | c3_1(a754) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725) | (~c1_1(a754)) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691))),
% 2.09/1.68 inference(modus_ponens,[status(thm)],[2606, 2605])).
% 2.09/1.68 tff(2608,plain,
% 2.09/1.68 (~c1_1(a754)),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[2607, 227, 2595, 2596, 2010, 178, 2598, 2601, 1777, 2600, 2597])).
% 2.09/1.68 tff(2609,plain,
% 2.09/1.68 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a763) | c3_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754)) | c3_1(a763) | (~c0_1(a763)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a763) | c3_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754)) | c3_1(a763) | (~c0_1(a763)))),
% 2.09/1.68 inference(rewrite,[status(thm)],[])).
% 2.09/1.68 tff(2610,plain,
% 2.09/1.68 ((hskp28 | (~ndr1_0) | c3_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a754) | c1_1(a754) | (~c2_1(a754))) <=> (hskp28 | c2_1(a763) | c3_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754)) | c3_1(a763) | (~c0_1(a763)))),
% 2.09/1.68 inference(rewrite,[status(thm)],[])).
% 2.09/1.68 tff(2611,plain,
% 2.09/1.68 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a763) | c3_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754)) | c3_1(a763) | (~c0_1(a763))))),
% 2.09/1.68 inference(monotonicity,[status(thm)],[2610])).
% 2.09/1.68 tff(2612,plain,
% 2.09/1.68 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a763) | c3_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754)) | c3_1(a763) | (~c0_1(a763)))),
% 2.09/1.68 inference(transitivity,[status(thm)],[2611, 2609])).
% 2.09/1.68 tff(2613,plain,
% 2.09/1.68 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)))),
% 2.09/1.68 inference(quant_inst,[status(thm)],[])).
% 2.09/1.68 tff(2614,plain,
% 2.09/1.68 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a763) | c3_1(a754) | (~ndr1_0) | c1_1(a754) | (~c2_1(a754)) | c3_1(a763) | (~c0_1(a763))),
% 2.09/1.68 inference(modus_ponens,[status(thm)],[2613, 2612])).
% 2.09/1.68 tff(2615,plain,
% 2.09/1.68 ($false),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[2614, 227, 62, 2570, 2488, 2569, 178, 342, 2608, 2594])).
% 2.09/1.68 tff(2616,plain,(hskp6 | hskp28 | c3_1(a754)), inference(lemma,lemma(discharge,[]))).
% 2.09/1.68 tff(2617,plain,
% 2.09/1.68 (c3_1(a754)),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[2616, 1739, 62])).
% 2.09/1.68 tff(2618,plain,
% 2.09/1.68 (~hskp20),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[668, 2617])).
% 2.09/1.68 tff(2619,plain,
% 2.09/1.68 (~hskp24),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[2143, 2618, 62, 1739])).
% 2.09/1.68 tff(2620,plain,
% 2.09/1.68 (c0_1(a733)),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[2566, 1036, 1708, 1931, 1730, 1739, 2618])).
% 2.09/1.68 tff(2621,plain,
% 2.09/1.68 (hskp23),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[2158, 2620, 2619])).
% 2.09/1.68 tff(2622,plain,
% 2.09/1.68 (~c2_1(a763)),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[404, 2621])).
% 2.09/1.68 tff(2623,plain,
% 2.09/1.68 (c0_1(a763)),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[421, 2621])).
% 2.09/1.68 tff(2624,plain,
% 2.09/1.68 (~c3_1(a763)),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[1834, 227, 62, 1730, 1719, 1708, 2623, 2622, 61])).
% 2.09/1.68 tff(2625,plain,
% 2.09/1.68 (^[U: $i] : refl((hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) <=> (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))))),
% 2.09/1.68 inference(bind,[status(th)],[])).
% 2.09/1.68 tff(2626,plain,
% 2.09/1.68 (![U: $i] : (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 2.09/1.68 inference(quant_intro,[status(thm)],[2625])).
% 2.09/1.68 tff(2627,plain,
% 2.09/1.68 (![U: $i] : (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 2.09/1.68 inference(rewrite,[status(thm)],[])).
% 2.09/1.68 tff(2628,plain,
% 2.09/1.68 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp27))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) <=> (hskp27 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp18) <=> ((hskp27 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp18))), rewrite(((hskp27 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp18) <=> (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp18) <=> (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))))),
% 2.09/1.68 inference(bind,[status(th)],[])).
% 2.09/1.68 tff(2629,plain,
% 2.09/1.68 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp18) <=> ![U: $i] : (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 2.09/1.68 inference(quant_intro,[status(thm)],[2628])).
% 2.09/1.68 tff(2630,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause154')).
% 2.09/1.68 tff(2631,plain,
% 2.09/1.68 (![U: $i] : (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 2.09/1.68 inference(modus_ponens,[status(thm)],[2630, 2629])).
% 2.09/1.68 tff(2632,plain,
% 2.09/1.68 (![U: $i] : (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 2.09/1.68 inference(modus_ponens,[status(thm)],[2631, 2627])).
% 2.09/1.68 tff(2633,plain,(
% 2.09/1.68 ![U: $i] : (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 2.09/1.68 inference(skolemize,[status(sab)],[2632])).
% 2.09/1.68 tff(2634,plain,
% 2.09/1.68 (![U: $i] : (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 2.09/1.68 inference(modus_ponens,[status(thm)],[2633, 2626])).
% 2.09/1.68 tff(2635,plain,
% 2.09/1.68 (((~![U: $i] : (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c1_1(a733)))) <=> ((~![U: $i] : (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp27 | hskp18 | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c1_1(a733)))),
% 2.09/1.68 inference(rewrite,[status(thm)],[])).
% 2.09/1.68 tff(2636,plain,
% 2.09/1.68 ((~![U: $i] : (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c1_1(a733)))),
% 2.09/1.68 inference(quant_inst,[status(thm)],[])).
% 2.09/1.68 tff(2637,plain,
% 2.09/1.68 ((~![U: $i] : (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp27 | hskp18 | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c1_1(a733))),
% 2.09/1.68 inference(modus_ponens,[status(thm)],[2636, 2635])).
% 2.09/1.68 tff(2638,plain,
% 2.09/1.68 (hskp27 | hskp18 | (~c0_1(a733))),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[2637, 227, 1730, 1708, 2634])).
% 2.09/1.68 tff(2639,plain,
% 2.09/1.68 (hskp18),
% 2.09/1.68 inference(unit_resolution,[status(thm)],[2638, 2620, 1036])).
% 2.09/1.68 tff(2640,plain,
% 2.09/1.68 (((~hskp18) | (~c3_1(a751))) <=> ((~hskp18) | (~c3_1(a751)))),
% 2.09/1.68 inference(rewrite,[status(thm)],[])).
% 2.09/1.68 tff(2641,plain,
% 2.09/1.68 (((~c3_1(a751)) | (~hskp18)) <=> ((~hskp18) | (~c3_1(a751)))),
% 2.09/1.68 inference(rewrite,[status(thm)],[])).
% 2.09/1.68 tff(2642,axiom,((~c3_1(a751)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause102')).
% 2.09/1.68 tff(2643,plain,
% 2.09/1.68 ((~hskp18) | (~c3_1(a751))),
% 2.09/1.68 inference(modus_ponens,[status(thm)],[2642, 2641])).
% 2.09/1.68 tff(2644,plain,
% 2.09/1.69 ((~hskp18) | (~c3_1(a751))),
% 2.09/1.69 inference(modus_ponens,[status(thm)],[2643, 2640])).
% 2.09/1.69 tff(2645,plain,
% 2.09/1.69 (~c3_1(a751)),
% 2.09/1.69 inference(unit_resolution,[status(thm)],[2644, 2639])).
% 2.09/1.69 tff(2646,plain,
% 2.09/1.69 (((~hskp18) | (~c1_1(a751))) <=> ((~hskp18) | (~c1_1(a751)))),
% 2.09/1.69 inference(rewrite,[status(thm)],[])).
% 2.09/1.69 tff(2647,plain,
% 2.09/1.69 (((~c1_1(a751)) | (~hskp18)) <=> ((~hskp18) | (~c1_1(a751)))),
% 2.09/1.69 inference(rewrite,[status(thm)],[])).
% 2.09/1.69 tff(2648,axiom,((~c1_1(a751)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause101')).
% 2.09/1.69 tff(2649,plain,
% 2.09/1.69 ((~hskp18) | (~c1_1(a751))),
% 2.09/1.69 inference(modus_ponens,[status(thm)],[2648, 2647])).
% 2.09/1.69 tff(2650,plain,
% 2.09/1.69 ((~hskp18) | (~c1_1(a751))),
% 2.09/1.69 inference(modus_ponens,[status(thm)],[2649, 2646])).
% 2.09/1.69 tff(2651,plain,
% 2.09/1.69 (~c1_1(a751)),
% 2.09/1.69 inference(unit_resolution,[status(thm)],[2650, 2639])).
% 2.09/1.69 tff(2652,plain,
% 2.09/1.69 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a763) | c1_1(a751) | c3_1(a751) | (~ndr1_0) | (~c2_1(a751)) | c3_1(a763) | (~c0_1(a763)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a763) | c1_1(a751) | c3_1(a751) | (~ndr1_0) | (~c2_1(a751)) | c3_1(a763) | (~c0_1(a763)))),
% 2.09/1.69 inference(rewrite,[status(thm)],[])).
% 2.09/1.69 tff(2653,plain,
% 2.09/1.69 ((hskp28 | (~ndr1_0) | c3_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a751) | c1_1(a751) | (~c2_1(a751))) <=> (hskp28 | c2_1(a763) | c1_1(a751) | c3_1(a751) | (~ndr1_0) | (~c2_1(a751)) | c3_1(a763) | (~c0_1(a763)))),
% 2.09/1.69 inference(rewrite,[status(thm)],[])).
% 2.09/1.69 tff(2654,plain,
% 2.09/1.69 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a751) | c1_1(a751) | (~c2_1(a751)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | c2_1(a763) | c1_1(a751) | c3_1(a751) | (~ndr1_0) | (~c2_1(a751)) | c3_1(a763) | (~c0_1(a763))))),
% 2.09/1.69 inference(monotonicity,[status(thm)],[2653])).
% 2.09/1.69 tff(2655,plain,
% 2.09/1.69 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a751) | c1_1(a751) | (~c2_1(a751)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a763) | c1_1(a751) | c3_1(a751) | (~ndr1_0) | (~c2_1(a751)) | c3_1(a763) | (~c0_1(a763)))),
% 2.09/1.69 inference(transitivity,[status(thm)],[2654, 2652])).
% 2.09/1.69 tff(2656,plain,
% 2.09/1.69 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a751) | c1_1(a751) | (~c2_1(a751)))),
% 2.09/1.69 inference(quant_inst,[status(thm)],[])).
% 2.09/1.69 tff(2657,plain,
% 2.09/1.69 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp28 | c2_1(a763) | c1_1(a751) | c3_1(a751) | (~ndr1_0) | (~c2_1(a751)) | c3_1(a763) | (~c0_1(a763))),
% 2.09/1.69 inference(modus_ponens,[status(thm)],[2656, 2655])).
% 2.09/1.69 tff(2658,plain,
% 2.09/1.69 (~c2_1(a751)),
% 2.09/1.69 inference(unit_resolution,[status(thm)],[2657, 227, 62, 2623, 2622, 2651, 2645, 342, 2624])).
% 2.09/1.69 tff(2659,plain,
% 2.09/1.69 (~c1_1(a763)),
% 2.09/1.69 inference(unit_resolution,[status(thm)],[410, 2621])).
% 2.09/1.69 tff(2660,plain,
% 2.09/1.69 (((~hskp18) | c0_1(a751)) <=> ((~hskp18) | c0_1(a751))),
% 2.09/1.69 inference(rewrite,[status(thm)],[])).
% 2.09/1.69 tff(2661,axiom,((~hskp18) | c0_1(a751)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause62')).
% 2.09/1.69 tff(2662,plain,
% 2.09/1.69 ((~hskp18) | c0_1(a751)),
% 2.09/1.69 inference(modus_ponens,[status(thm)],[2661, 2660])).
% 2.09/1.69 tff(2663,plain,
% 2.09/1.69 ((~hskp18) | c0_1(a751)),
% 2.09/1.69 inference(modus_ponens,[status(thm)],[2662, 2660])).
% 2.09/1.69 tff(2664,plain,
% 2.09/1.69 ((~hskp18) | c0_1(a751)),
% 2.09/1.69 inference(modus_ponens,[status(thm)],[2663, 2660])).
% 2.09/1.69 tff(2665,plain,
% 2.09/1.69 ((~hskp18) | c0_1(a751)),
% 2.09/1.69 inference(modus_ponens,[status(thm)],[2664, 2660])).
% 2.09/1.69 tff(2666,plain,
% 2.09/1.69 ((~hskp18) | c0_1(a751)),
% 2.09/1.69 inference(modus_ponens,[status(thm)],[2665, 2660])).
% 2.09/1.69 tff(2667,plain,
% 2.09/1.69 ((~hskp18) | c0_1(a751)),
% 2.09/1.69 inference(modus_ponens,[status(thm)],[2666, 2660])).
% 2.09/1.69 tff(2668,plain,
% 2.09/1.69 ((~hskp18) | c0_1(a751)),
% 2.09/1.69 inference(modus_ponens,[status(thm)],[2667, 2660])).
% 2.09/1.69 tff(2669,plain,
% 2.09/1.69 ((~hskp18) | c0_1(a751)),
% 2.09/1.69 inference(modus_ponens,[status(thm)],[2668, 2660])).
% 2.09/1.69 tff(2670,plain,
% 2.09/1.69 (c0_1(a751)),
% 2.09/1.69 inference(unit_resolution,[status(thm)],[2669, 2639])).
% 2.09/1.69 tff(2671,assumption,(~c2_1(a751)), introduced(assumption)).
% 2.09/1.69 tff(2672,assumption,(~c3_1(a751)), introduced(assumption)).
% 2.09/1.69 tff(2673,assumption,(c0_1(a751)), introduced(assumption)).
% 2.09/1.69 tff(2674,plain,
% 2.09/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a763) | c2_1(a763) | c3_1(a751) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a751)) | c2_1(a751) | (~c0_1(a763)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a763) | c2_1(a763) | c3_1(a751) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a751)) | c2_1(a751) | (~c0_1(a763)))),
% 2.15/1.69 inference(rewrite,[status(thm)],[])).
% 2.15/1.69 tff(2675,plain,
% 2.15/1.69 (((~ndr1_0) | c3_1(a751) | c2_1(a751) | (~c0_1(a751)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725))) <=> (c1_1(a763) | c2_1(a763) | c3_1(a751) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a751)) | c2_1(a751) | (~c0_1(a763)))),
% 2.15/1.69 inference(rewrite,[status(thm)],[])).
% 2.15/1.69 tff(2676,plain,
% 2.15/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a751) | c2_1(a751) | (~c0_1(a751)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a763) | c2_1(a763) | c3_1(a751) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a751)) | c2_1(a751) | (~c0_1(a763))))),
% 2.15/1.69 inference(monotonicity,[status(thm)],[2675])).
% 2.15/1.69 tff(2677,plain,
% 2.15/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a751) | c2_1(a751) | (~c0_1(a751)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a763) | c2_1(a763) | c3_1(a751) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a751)) | c2_1(a751) | (~c0_1(a763)))),
% 2.15/1.69 inference(transitivity,[status(thm)],[2676, 2674])).
% 2.15/1.69 tff(2678,plain,
% 2.15/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a751) | c2_1(a751) | (~c0_1(a751)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))),
% 2.15/1.69 inference(quant_inst,[status(thm)],[])).
% 2.15/1.69 tff(2679,plain,
% 2.15/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a763) | c2_1(a763) | c3_1(a751) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a751)) | c2_1(a751) | (~c0_1(a763))),
% 2.15/1.69 inference(modus_ponens,[status(thm)],[2678, 2677])).
% 2.15/1.69 tff(2680,plain,
% 2.15/1.69 ($false),
% 2.15/1.69 inference(unit_resolution,[status(thm)],[2679, 227, 1809, 2673, 1807, 1806, 2672, 578, 1037, 2445, 2556, 2671])).
% 2.15/1.69 tff(2681,plain,(c3_1(a725) | (~c0_1(a763)) | (~c0_1(a751)) | c1_1(a763) | c2_1(a763) | c3_1(a751) | c0_1(a725) | c2_1(a751) | hskp27 | hskp6), inference(lemma,lemma(discharge,[]))).
% 2.15/1.69 tff(2682,plain,
% 2.15/1.69 (c3_1(a725)),
% 2.15/1.69 inference(unit_resolution,[status(thm)],[2681, 578, 2670, 2659, 2622, 2645, 2623, 2658, 1036, 1739])).
% 2.15/1.69 tff(2683,plain,
% 2.15/1.69 (c2_1(a725)),
% 2.15/1.69 inference(unit_resolution,[status(thm)],[2131, 2682])).
% 2.15/1.69 tff(2684,plain,
% 2.15/1.69 (~hskp4),
% 2.15/1.69 inference(unit_resolution,[status(thm)],[2150, 1036, 1739])).
% 2.15/1.69 tff(2685,plain,
% 2.15/1.69 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a725) | (~c1_1(a725)) | (~c3_1(a725)) | (~ndr1_0) | (~c0_1(a763)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a725) | (~c1_1(a725)) | (~c3_1(a725)) | (~ndr1_0) | (~c0_1(a763)))),
% 2.15/1.69 inference(rewrite,[status(thm)],[])).
% 2.15/1.69 tff(2686,plain,
% 2.15/1.69 ((hskp4 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c0_1(a725) | (~c3_1(a725)) | (~c1_1(a725))) <=> (hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a725) | (~c1_1(a725)) | (~c3_1(a725)) | (~ndr1_0) | (~c0_1(a763)))),
% 2.15/1.69 inference(rewrite,[status(thm)],[])).
% 2.15/1.69 tff(2687,plain,
% 2.15/1.69 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c0_1(a725) | (~c3_1(a725)) | (~c1_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a725) | (~c1_1(a725)) | (~c3_1(a725)) | (~ndr1_0) | (~c0_1(a763))))),
% 2.15/1.69 inference(monotonicity,[status(thm)],[2686])).
% 2.15/1.69 tff(2688,plain,
% 2.15/1.69 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c0_1(a725) | (~c3_1(a725)) | (~c1_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a725) | (~c1_1(a725)) | (~c3_1(a725)) | (~ndr1_0) | (~c0_1(a763)))),
% 2.15/1.69 inference(transitivity,[status(thm)],[2687, 2685])).
% 2.15/1.69 tff(2689,plain,
% 2.15/1.69 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c0_1(a725) | (~c3_1(a725)) | (~c1_1(a725)))),
% 2.15/1.69 inference(quant_inst,[status(thm)],[])).
% 2.15/1.69 tff(2690,plain,
% 2.15/1.69 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a725) | (~c1_1(a725)) | (~c3_1(a725)) | (~ndr1_0) | (~c0_1(a763))),
% 2.15/1.69 inference(modus_ponens,[status(thm)],[2689, 2688])).
% 2.15/1.69 tff(2691,plain,
% 2.15/1.69 ((~c1_1(a725)) | (~c3_1(a725))),
% 2.15/1.69 inference(unit_resolution,[status(thm)],[2690, 227, 2684, 2623, 2659, 2622, 578, 2169])).
% 2.15/1.69 tff(2692,plain,
% 2.15/1.69 (~c1_1(a725)),
% 2.15/1.69 inference(unit_resolution,[status(thm)],[2691, 2682])).
% 2.15/1.69 tff(2693,plain,
% 2.15/1.69 ($false),
% 2.15/1.69 inference(unit_resolution,[status(thm)],[586, 2692, 2683, 2621, 578, 62])).
% 2.15/1.69 tff(2694,plain,(c0_1(a725) | hskp28 | hskp27), inference(lemma,lemma(discharge,[]))).
% 2.15/1.69 tff(2695,plain,
% 2.15/1.69 (c0_1(a725)),
% 2.15/1.69 inference(unit_resolution,[status(thm)],[2694, 1036, 62])).
% 2.15/1.69 tff(2696,plain,
% 2.15/1.69 (~hskp12),
% 2.15/1.69 inference(unit_resolution,[status(thm)],[151, 2695])).
% 2.15/1.69 tff(2697,plain,
% 2.15/1.69 (hskp13),
% 2.15/1.69 inference(unit_resolution,[status(thm)],[2066, 2696, 2618])).
% 2.15/1.69 tff(2698,plain,
% 2.15/1.69 (~c3_1(a726)),
% 2.15/1.69 inference(unit_resolution,[status(thm)],[2021, 2697])).
% 2.15/1.69 tff(2699,plain,
% 2.15/1.69 (~c0_1(a726)),
% 2.15/1.69 inference(unit_resolution,[status(thm)],[2027, 2697])).
% 2.15/1.69 tff(2700,plain,
% 2.15/1.69 (c1_1(a726)),
% 2.15/1.69 inference(unit_resolution,[status(thm)],[2045, 2697])).
% 2.15/1.69 tff(2701,plain,
% 2.15/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c1_1(a751) | c3_1(a751) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726) | c2_1(a751))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c1_1(a751) | c3_1(a751) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726) | c2_1(a751))),
% 2.15/1.69 inference(rewrite,[status(thm)],[])).
% 2.15/1.69 tff(2702,plain,
% 2.15/1.69 (((~ndr1_0) | c0_1(a726) | c2_1(a726) | (~c1_1(a726)) | c3_1(a751) | c1_1(a751) | c2_1(a751) | c3_1(a726) | c2_1(a726) | c0_1(a726)) <=> (c1_1(a751) | c3_1(a751) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726) | c2_1(a751))),
% 2.15/1.69 inference(rewrite,[status(thm)],[])).
% 2.15/1.69 tff(2703,plain,
% 2.15/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a726) | c2_1(a726) | (~c1_1(a726)) | c3_1(a751) | c1_1(a751) | c2_1(a751) | c3_1(a726) | c2_1(a726) | c0_1(a726))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c1_1(a751) | c3_1(a751) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726) | c2_1(a751)))),
% 2.15/1.69 inference(monotonicity,[status(thm)],[2702])).
% 2.15/1.69 tff(2704,plain,
% 2.15/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a726) | c2_1(a726) | (~c1_1(a726)) | c3_1(a751) | c1_1(a751) | c2_1(a751) | c3_1(a726) | c2_1(a726) | c0_1(a726))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c1_1(a751) | c3_1(a751) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726) | c2_1(a751))),
% 2.15/1.69 inference(transitivity,[status(thm)],[2703, 2701])).
% 2.15/1.69 tff(2705,plain,
% 2.15/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a726) | c2_1(a726) | (~c1_1(a726)) | c3_1(a751) | c1_1(a751) | c2_1(a751) | c3_1(a726) | c2_1(a726) | c0_1(a726))),
% 2.15/1.69 inference(quant_inst,[status(thm)],[])).
% 2.15/1.69 tff(2706,plain,
% 2.15/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c1_1(a751) | c3_1(a751) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726) | c2_1(a751)),
% 2.15/1.69 inference(modus_ponens,[status(thm)],[2705, 2704])).
% 2.15/1.69 tff(2707,plain,
% 2.15/1.69 (c2_1(a726)),
% 2.15/1.69 inference(unit_resolution,[status(thm)],[2706, 227, 2700, 2651, 2645, 2699, 2698, 122, 2658])).
% 2.15/1.69 tff(2708,plain,
% 2.15/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a763) | c2_1(a763) | c3_1(a751) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | (~c0_1(a751)) | c2_1(a751) | (~c0_1(a763)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a763) | c2_1(a763) | c3_1(a751) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | (~c0_1(a751)) | c2_1(a751) | (~c0_1(a763)))),
% 2.15/1.69 inference(rewrite,[status(thm)],[])).
% 2.15/1.69 tff(2709,plain,
% 2.15/1.69 (((~ndr1_0) | c3_1(a751) | c2_1(a751) | (~c0_1(a751)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726))) <=> (c1_1(a763) | c2_1(a763) | c3_1(a751) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | (~c0_1(a751)) | c2_1(a751) | (~c0_1(a763)))),
% 2.15/1.69 inference(rewrite,[status(thm)],[])).
% 2.15/1.69 tff(2710,plain,
% 2.15/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a751) | c2_1(a751) | (~c0_1(a751)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a763) | c2_1(a763) | c3_1(a751) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | (~c0_1(a751)) | c2_1(a751) | (~c0_1(a763))))),
% 2.15/1.69 inference(monotonicity,[status(thm)],[2709])).
% 2.15/1.69 tff(2711,plain,
% 2.15/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a751) | c2_1(a751) | (~c0_1(a751)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a763) | c2_1(a763) | c3_1(a751) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | (~c0_1(a751)) | c2_1(a751) | (~c0_1(a763)))),
% 2.15/1.69 inference(transitivity,[status(thm)],[2710, 2708])).
% 2.15/1.69 tff(2712,plain,
% 2.15/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a751) | c2_1(a751) | (~c0_1(a751)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726)))),
% 2.15/1.69 inference(quant_inst,[status(thm)],[])).
% 2.15/1.69 tff(2713,plain,
% 2.15/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a763) | c2_1(a763) | c3_1(a751) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | (~c0_1(a751)) | c2_1(a751) | (~c0_1(a763))),
% 2.15/1.69 inference(modus_ponens,[status(thm)],[2712, 2711])).
% 2.15/1.69 tff(2714,plain,
% 2.15/1.69 ($false),
% 2.15/1.69 inference(unit_resolution,[status(thm)],[2713, 227, 2623, 2670, 2659, 2622, 2645, 2699, 2698, 2445, 2658, 2707])).
% 2.15/1.69 tff(2715,plain,(hskp27 | hskp28), inference(lemma,lemma(discharge,[]))).
% 2.15/1.69 tff(2716,plain,
% 2.15/1.69 (hskp27),
% 2.15/1.69 inference(unit_resolution,[status(thm)],[2715, 62])).
% 2.15/1.69 tff(2717,plain,
% 2.15/1.69 (hskp23),
% 2.15/1.69 inference(unit_resolution,[status(thm)],[2147, 2716, 2619, 62])).
% 2.15/1.69 tff(2718,plain,
% 2.15/1.69 (~c2_1(a763)),
% 2.15/1.69 inference(unit_resolution,[status(thm)],[404, 2717])).
% 2.15/1.69 tff(2719,plain,
% 2.15/1.69 (c0_1(a763)),
% 2.15/1.69 inference(unit_resolution,[status(thm)],[421, 2717])).
% 2.15/1.69 tff(2720,plain,
% 2.15/1.69 (~c3_1(a763)),
% 2.15/1.69 inference(unit_resolution,[status(thm)],[1834, 227, 62, 1730, 1719, 1708, 2719, 2718, 61])).
% 2.15/1.69 tff(2721,plain,
% 2.15/1.69 (~c1_1(a763)),
% 2.15/1.69 inference(unit_resolution,[status(thm)],[410, 2717])).
% 2.15/1.69 tff(2722,plain,
% 2.15/1.69 (~hskp0),
% 2.15/1.69 inference(unit_resolution,[status(thm)],[1817, 2721, 62, 2719, 2718])).
% 2.15/1.69 tff(2723,assumption,(hskp1), introduced(assumption)).
% 2.15/1.69 tff(2724,plain,
% 2.15/1.69 (~c3_1(a693)),
% 2.15/1.69 inference(unit_resolution,[status(thm)],[1553, 2723])).
% 2.15/1.69 tff(2725,plain,
% 2.15/1.69 (~c1_1(a693)),
% 2.15/1.69 inference(unit_resolution,[status(thm)],[1423, 2723])).
% 2.15/1.69 tff(2726,plain,
% 2.15/1.69 (c2_1(a693)),
% 2.15/1.69 inference(unit_resolution,[status(thm)],[383, 2723])).
% 2.15/1.69 tff(2727,plain,
% 2.15/1.69 ($false),
% 2.15/1.69 inference(unit_resolution,[status(thm)],[1841, 227, 62, 2719, 2726, 2718, 2725, 2724, 342, 2720])).
% 2.15/1.69 tff(2728,plain,((~hskp1) | hskp28), inference(lemma,lemma(discharge,[]))).
% 2.15/1.69 tff(2729,plain,
% 2.15/1.69 (~hskp1),
% 2.15/1.69 inference(unit_resolution,[status(thm)],[2728, 62])).
% 2.15/1.69 tff(2730,plain,
% 2.15/1.69 (~hskp12),
% 2.15/1.69 inference(unit_resolution,[status(thm)],[2416, 2729, 2722])).
% 2.15/1.69 tff(2731,plain,
% 2.15/1.69 (hskp13),
% 2.15/1.69 inference(unit_resolution,[status(thm)],[2066, 2730, 2618])).
% 2.15/1.69 tff(2732,plain,
% 2.15/1.69 (~c3_1(a726)),
% 2.15/1.69 inference(unit_resolution,[status(thm)],[2021, 2731])).
% 2.15/1.69 tff(2733,plain,
% 2.15/1.69 (~c0_1(a726)),
% 2.15/1.69 inference(unit_resolution,[status(thm)],[2027, 2731])).
% 2.15/1.69 tff(2734,plain,
% 2.15/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a763) | c2_1(a763) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | c3_1(a763) | (~c0_1(a763)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a763) | c2_1(a763) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | c3_1(a763) | (~c0_1(a763)))),
% 2.15/1.69 inference(rewrite,[status(thm)],[])).
% 2.15/1.69 tff(2735,plain,
% 2.15/1.69 (((~ndr1_0) | c3_1(a763) | c2_1(a763) | (~c0_1(a763)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726))) <=> (c1_1(a763) | c2_1(a763) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | c3_1(a763) | (~c0_1(a763)))),
% 2.15/1.69 inference(rewrite,[status(thm)],[])).
% 2.15/1.69 tff(2736,plain,
% 2.15/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a763) | c2_1(a763) | (~c0_1(a763)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a763) | c2_1(a763) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | c3_1(a763) | (~c0_1(a763))))),
% 2.15/1.69 inference(monotonicity,[status(thm)],[2735])).
% 2.15/1.69 tff(2737,plain,
% 2.15/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a763) | c2_1(a763) | (~c0_1(a763)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a763) | c2_1(a763) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | c3_1(a763) | (~c0_1(a763)))),
% 2.15/1.69 inference(transitivity,[status(thm)],[2736, 2734])).
% 2.15/1.69 tff(2738,plain,
% 2.15/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a763) | c2_1(a763) | (~c0_1(a763)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726)))),
% 2.15/1.69 inference(quant_inst,[status(thm)],[])).
% 2.15/1.69 tff(2739,plain,
% 2.15/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a763) | c2_1(a763) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | c3_1(a763) | (~c0_1(a763))),
% 2.15/1.69 inference(modus_ponens,[status(thm)],[2738, 2737])).
% 2.15/1.69 tff(2740,plain,
% 2.15/1.69 (~c2_1(a726)),
% 2.15/1.69 inference(unit_resolution,[status(thm)],[2739, 227, 2719, 2721, 2718, 2733, 2732, 2445, 2720])).
% 2.15/1.69 tff(2741,plain,
% 2.15/1.69 (c1_1(a726)),
% 2.15/1.69 inference(unit_resolution,[status(thm)],[2045, 2731])).
% 2.15/1.69 tff(2742,plain,
% 2.15/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c1_1(a763) | c2_1(a763) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726) | c3_1(a763))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c1_1(a763) | c2_1(a763) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726) | c3_1(a763))),
% 2.15/1.69 inference(rewrite,[status(thm)],[])).
% 2.15/1.69 tff(2743,plain,
% 2.15/1.69 (((~ndr1_0) | c0_1(a726) | c2_1(a726) | (~c1_1(a726)) | c3_1(a763) | c1_1(a763) | c2_1(a763) | c3_1(a726) | c2_1(a726) | c0_1(a726)) <=> (c1_1(a763) | c2_1(a763) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726) | c3_1(a763))),
% 2.15/1.69 inference(rewrite,[status(thm)],[])).
% 2.15/1.69 tff(2744,plain,
% 2.15/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a726) | c2_1(a726) | (~c1_1(a726)) | c3_1(a763) | c1_1(a763) | c2_1(a763) | c3_1(a726) | c2_1(a726) | c0_1(a726))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c1_1(a763) | c2_1(a763) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726) | c3_1(a763)))),
% 2.15/1.69 inference(monotonicity,[status(thm)],[2743])).
% 2.15/1.69 tff(2745,plain,
% 2.15/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a726) | c2_1(a726) | (~c1_1(a726)) | c3_1(a763) | c1_1(a763) | c2_1(a763) | c3_1(a726) | c2_1(a726) | c0_1(a726))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c1_1(a763) | c2_1(a763) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726) | c3_1(a763))),
% 2.15/1.69 inference(transitivity,[status(thm)],[2744, 2742])).
% 2.15/1.69 tff(2746,plain,
% 2.15/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a726) | c2_1(a726) | (~c1_1(a726)) | c3_1(a763) | c1_1(a763) | c2_1(a763) | c3_1(a726) | c2_1(a726) | c0_1(a726))),
% 2.15/1.69 inference(quant_inst,[status(thm)],[])).
% 2.15/1.69 tff(2747,plain,
% 2.15/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c1_1(a763) | c2_1(a763) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c1_1(a726)) | c2_1(a726) | c3_1(a763)),
% 2.15/1.69 inference(modus_ponens,[status(thm)],[2746, 2745])).
% 2.15/1.69 tff(2748,plain,
% 2.15/1.69 ($false),
% 2.15/1.69 inference(unit_resolution,[status(thm)],[2747, 227, 2741, 2721, 2718, 2733, 2732, 122, 2720, 2740])).
% 2.15/1.69 tff(2749,plain,(hskp28), inference(lemma,lemma(discharge,[]))).
% 2.15/1.69 tff(2750,plain,
% 2.15/1.69 (((~hskp28) | c2_1(a695)) <=> ((~hskp28) | c2_1(a695))),
% 2.15/1.69 inference(rewrite,[status(thm)],[])).
% 2.15/1.69 tff(2751,axiom,((~hskp28) | c2_1(a695)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause48')).
% 2.15/1.69 tff(2752,plain,
% 2.15/1.69 ((~hskp28) | c2_1(a695)),
% 2.15/1.69 inference(modus_ponens,[status(thm)],[2751, 2750])).
% 2.15/1.69 tff(2753,plain,
% 2.15/1.69 ((~hskp28) | c2_1(a695)),
% 2.15/1.69 inference(modus_ponens,[status(thm)],[2752, 2750])).
% 2.15/1.69 tff(2754,plain,
% 2.15/1.69 ((~hskp28) | c2_1(a695)),
% 2.15/1.69 inference(modus_ponens,[status(thm)],[2753, 2750])).
% 2.15/1.69 tff(2755,plain,
% 2.15/1.69 ((~hskp28) | c2_1(a695)),
% 2.15/1.69 inference(modus_ponens,[status(thm)],[2754, 2750])).
% 2.15/1.69 tff(2756,plain,
% 2.15/1.69 ((~hskp28) | c2_1(a695)),
% 2.15/1.69 inference(modus_ponens,[status(thm)],[2755, 2750])).
% 2.15/1.69 tff(2757,plain,
% 2.15/1.69 ((~hskp28) | c2_1(a695)),
% 2.15/1.69 inference(modus_ponens,[status(thm)],[2756, 2750])).
% 2.15/1.69 tff(2758,plain,
% 2.15/1.69 ((~hskp28) | c2_1(a695)),
% 2.15/1.69 inference(modus_ponens,[status(thm)],[2757, 2750])).
% 2.15/1.69 tff(2759,plain,
% 2.15/1.69 ((~hskp28) | c2_1(a695)),
% 2.15/1.69 inference(modus_ponens,[status(thm)],[2758, 2750])).
% 2.15/1.69 tff(2760,plain,
% 2.15/1.69 (c2_1(a695)),
% 2.15/1.69 inference(unit_resolution,[status(thm)],[2759, 2749])).
% 2.15/1.69 tff(2761,plain,
% 2.15/1.69 (((~hskp28) | c1_1(a695)) <=> ((~hskp28) | c1_1(a695))),
% 2.15/1.69 inference(rewrite,[status(thm)],[])).
% 2.15/1.69 tff(2762,axiom,((~hskp28) | c1_1(a695)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause47')).
% 2.15/1.69 tff(2763,plain,
% 2.15/1.69 ((~hskp28) | c1_1(a695)),
% 2.15/1.69 inference(modus_ponens,[status(thm)],[2762, 2761])).
% 2.15/1.69 tff(2764,plain,
% 2.15/1.69 ((~hskp28) | c1_1(a695)),
% 2.15/1.69 inference(modus_ponens,[status(thm)],[2763, 2761])).
% 2.15/1.69 tff(2765,plain,
% 2.15/1.69 ((~hskp28) | c1_1(a695)),
% 2.15/1.69 inference(modus_ponens,[status(thm)],[2764, 2761])).
% 2.15/1.69 tff(2766,plain,
% 2.15/1.69 ((~hskp28) | c1_1(a695)),
% 2.15/1.69 inference(modus_ponens,[status(thm)],[2765, 2761])).
% 2.15/1.69 tff(2767,plain,
% 2.15/1.69 ((~hskp28) | c1_1(a695)),
% 2.15/1.69 inference(modus_ponens,[status(thm)],[2766, 2761])).
% 2.15/1.69 tff(2768,plain,
% 2.15/1.69 ((~hskp28) | c1_1(a695)),
% 2.15/1.69 inference(modus_ponens,[status(thm)],[2767, 2761])).
% 2.15/1.69 tff(2769,plain,
% 2.15/1.69 ((~hskp28) | c1_1(a695)),
% 2.15/1.69 inference(modus_ponens,[status(thm)],[2768, 2761])).
% 2.15/1.69 tff(2770,plain,
% 2.15/1.69 ((~hskp28) | c1_1(a695)),
% 2.15/1.69 inference(modus_ponens,[status(thm)],[2769, 2761])).
% 2.15/1.69 tff(2771,plain,
% 2.15/1.69 (c1_1(a695)),
% 2.15/1.69 inference(unit_resolution,[status(thm)],[2770, 2749])).
% 2.15/1.69 tff(2772,plain,
% 2.15/1.69 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp16 | c1_1(a701) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | (~c2_1(a701)) | (~c0_1(a701)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp16 | c1_1(a701) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | (~c2_1(a701)) | (~c0_1(a701)))),
% 2.15/1.69 inference(rewrite,[status(thm)],[])).
% 2.15/1.69 tff(2773,plain,
% 2.15/1.69 ((hskp16 | (~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c1_1(a701) | (~c2_1(a701)) | (~c0_1(a701))) <=> (hskp16 | c1_1(a701) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | (~c2_1(a701)) | (~c0_1(a701)))),
% 2.15/1.69 inference(rewrite,[status(thm)],[])).
% 2.15/1.69 tff(2774,plain,
% 2.15/1.69 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c1_1(a701) | (~c2_1(a701)) | (~c0_1(a701)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp16 | c1_1(a701) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | (~c2_1(a701)) | (~c0_1(a701))))),
% 2.15/1.69 inference(monotonicity,[status(thm)],[2773])).
% 2.15/1.69 tff(2775,plain,
% 2.15/1.69 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c1_1(a701) | (~c2_1(a701)) | (~c0_1(a701)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp16 | c1_1(a701) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | (~c2_1(a701)) | (~c0_1(a701)))),
% 2.15/1.69 inference(transitivity,[status(thm)],[2774, 2772])).
% 2.15/1.70 tff(2776,plain,
% 2.15/1.70 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c1_1(a701) | (~c2_1(a701)) | (~c0_1(a701)))),
% 2.15/1.70 inference(quant_inst,[status(thm)],[])).
% 2.15/1.70 tff(2777,plain,
% 2.15/1.70 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp16 | c1_1(a701) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | (~c2_1(a701)) | (~c0_1(a701))),
% 2.15/1.70 inference(modus_ponens,[status(thm)],[2776, 2775])).
% 2.15/1.70 tff(2778,plain,
% 2.15/1.70 ($false),
% 2.15/1.70 inference(unit_resolution,[status(thm)],[2777, 227, 12, 2771, 2760, 51, 40, 29, 22, 11])).
% 2.15/1.70 tff(2779,plain,((~hskp5) | hskp16 | c3_1(a695)), inference(lemma,lemma(discharge,[]))).
% 2.15/1.70 tff(2780,plain,
% 2.15/1.70 (~hskp5),
% 2.15/1.70 inference(unit_resolution,[status(thm)],[2779, 12, 11])).
% 2.15/1.70 tff(2781,assumption,(~hskp21), introduced(assumption)).
% 2.15/1.70 tff(2782,plain,
% 2.15/1.70 (^[U: $i] : refl((hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 2.15/1.70 inference(bind,[status(th)],[])).
% 2.15/1.70 tff(2783,plain,
% 2.15/1.70 (![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 2.15/1.70 inference(quant_intro,[status(thm)],[2782])).
% 2.15/1.70 tff(2784,plain,
% 2.15/1.70 (![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 2.15/1.70 inference(rewrite,[status(thm)],[])).
% 2.15/1.70 tff(2785,plain,
% 2.15/1.70 (^[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)) | hskp21) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp21))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp21) | hskp22) <=> ((hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp22))), rewrite(((hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp22) <=> (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp21) | hskp22) <=> (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 2.15/1.70 inference(bind,[status(th)],[])).
% 2.15/1.70 tff(2786,plain,
% 2.15/1.70 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp21) | hskp22) <=> ![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 2.15/1.70 inference(quant_intro,[status(thm)],[2785])).
% 2.15/1.70 tff(2787,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp21) | hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause152')).
% 2.15/1.70 tff(2788,plain,
% 2.15/1.70 (![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 2.15/1.70 inference(modus_ponens,[status(thm)],[2787, 2786])).
% 2.15/1.70 tff(2789,plain,
% 2.15/1.70 (![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 2.15/1.70 inference(modus_ponens,[status(thm)],[2788, 2784])).
% 2.15/1.70 tff(2790,plain,(
% 2.15/1.70 ![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 2.15/1.70 inference(skolemize,[status(sab)],[2789])).
% 2.15/1.70 tff(2791,plain,
% 2.15/1.70 (![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 2.15/1.70 inference(modus_ponens,[status(thm)],[2790, 2783])).
% 2.15/1.70 tff(2792,plain,
% 2.15/1.70 (((~hskp28) | c0_1(a695)) <=> ((~hskp28) | c0_1(a695))),
% 2.15/1.70 inference(rewrite,[status(thm)],[])).
% 2.15/1.70 tff(2793,axiom,((~hskp28) | c0_1(a695)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause46')).
% 2.15/1.70 tff(2794,plain,
% 2.15/1.70 ((~hskp28) | c0_1(a695)),
% 2.15/1.70 inference(modus_ponens,[status(thm)],[2793, 2792])).
% 2.15/1.70 tff(2795,plain,
% 2.15/1.70 ((~hskp28) | c0_1(a695)),
% 2.15/1.70 inference(modus_ponens,[status(thm)],[2794, 2792])).
% 2.15/1.70 tff(2796,plain,
% 2.15/1.70 ((~hskp28) | c0_1(a695)),
% 2.15/1.70 inference(modus_ponens,[status(thm)],[2795, 2792])).
% 2.15/1.70 tff(2797,plain,
% 2.15/1.70 ((~hskp28) | c0_1(a695)),
% 2.15/1.70 inference(modus_ponens,[status(thm)],[2796, 2792])).
% 2.15/1.70 tff(2798,plain,
% 2.15/1.70 ((~hskp28) | c0_1(a695)),
% 2.15/1.70 inference(modus_ponens,[status(thm)],[2797, 2792])).
% 2.15/1.70 tff(2799,plain,
% 2.15/1.70 ((~hskp28) | c0_1(a695)),
% 2.15/1.70 inference(modus_ponens,[status(thm)],[2798, 2792])).
% 2.15/1.70 tff(2800,plain,
% 2.15/1.70 ((~hskp28) | c0_1(a695)),
% 2.15/1.70 inference(modus_ponens,[status(thm)],[2799, 2792])).
% 2.15/1.70 tff(2801,plain,
% 2.15/1.70 ((~hskp28) | c0_1(a695)),
% 2.15/1.70 inference(modus_ponens,[status(thm)],[2800, 2792])).
% 2.15/1.70 tff(2802,plain,
% 2.15/1.70 (c0_1(a695)),
% 2.15/1.70 inference(unit_resolution,[status(thm)],[2801, 2749])).
% 2.15/1.70 tff(2803,plain,
% 2.15/1.70 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c2_1(a695)))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp22 | hskp21 | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c2_1(a695)))),
% 2.15/1.70 inference(rewrite,[status(thm)],[])).
% 2.15/1.70 tff(2804,plain,
% 2.15/1.70 ((hskp22 | hskp21 | (~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c0_1(a695))) <=> (hskp22 | hskp21 | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c2_1(a695)))),
% 2.15/1.70 inference(rewrite,[status(thm)],[])).
% 2.15/1.70 tff(2805,plain,
% 2.15/1.70 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c0_1(a695)))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c2_1(a695))))),
% 2.15/1.70 inference(monotonicity,[status(thm)],[2804])).
% 2.15/1.70 tff(2806,plain,
% 2.15/1.70 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c0_1(a695)))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp22 | hskp21 | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c2_1(a695)))),
% 2.15/1.70 inference(transitivity,[status(thm)],[2805, 2803])).
% 2.15/1.70 tff(2807,plain,
% 2.15/1.70 ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c0_1(a695)))),
% 2.15/1.70 inference(quant_inst,[status(thm)],[])).
% 2.15/1.70 tff(2808,plain,
% 2.15/1.70 ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp22 | hskp21 | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c2_1(a695))),
% 2.15/1.70 inference(modus_ponens,[status(thm)],[2807, 2806])).
% 2.15/1.70 tff(2809,plain,
% 2.15/1.70 (hskp22 | hskp21 | c3_1(a695)),
% 2.15/1.70 inference(unit_resolution,[status(thm)],[2808, 227, 2802, 2760, 2791])).
% 2.15/1.70 tff(2810,plain,
% 2.15/1.70 (hskp22),
% 2.15/1.70 inference(unit_resolution,[status(thm)],[2809, 11, 2781])).
% 2.15/1.70 tff(2811,plain,
% 2.15/1.70 (~c2_1(a761)),
% 2.15/1.70 inference(unit_resolution,[status(thm)],[784, 2810])).
% 2.15/1.70 tff(2812,plain,
% 2.15/1.70 (~c0_1(a761)),
% 2.15/1.70 inference(unit_resolution,[status(thm)],[790, 2810])).
% 2.15/1.70 tff(2813,plain,
% 2.15/1.70 (c1_1(a761)),
% 2.15/1.70 inference(unit_resolution,[status(thm)],[801, 2810])).
% 2.15/1.70 tff(2814,plain,
% 2.15/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a761) | c2_1(a761) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | (~c1_1(a761)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a761) | c2_1(a761) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | (~c1_1(a761)))),
% 2.15/1.70 inference(rewrite,[status(thm)],[])).
% 2.15/1.70 tff(2815,plain,
% 2.15/1.70 (((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c2_1(a761) | c0_1(a761) | (~c1_1(a761))) <=> (c0_1(a761) | c2_1(a761) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | (~c1_1(a761)))),
% 2.15/1.70 inference(rewrite,[status(thm)],[])).
% 2.15/1.70 tff(2816,plain,
% 2.15/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c2_1(a761) | c0_1(a761) | (~c1_1(a761)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a761) | c2_1(a761) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | (~c1_1(a761))))),
% 2.15/1.70 inference(monotonicity,[status(thm)],[2815])).
% 2.15/1.70 tff(2817,plain,
% 2.15/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c2_1(a761) | c0_1(a761) | (~c1_1(a761)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a761) | c2_1(a761) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | (~c1_1(a761)))),
% 2.15/1.70 inference(transitivity,[status(thm)],[2816, 2814])).
% 2.15/1.70 tff(2818,plain,
% 2.15/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c2_1(a761) | c0_1(a761) | (~c1_1(a761)))),
% 2.15/1.70 inference(quant_inst,[status(thm)],[])).
% 2.15/1.70 tff(2819,plain,
% 2.15/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a761) | c2_1(a761) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | (~c1_1(a761))),
% 2.15/1.70 inference(modus_ponens,[status(thm)],[2818, 2817])).
% 2.15/1.70 tff(2820,plain,
% 2.15/1.70 ($false),
% 2.15/1.70 inference(unit_resolution,[status(thm)],[2819, 227, 2802, 2771, 2760, 2813, 2812, 2811, 822, 11])).
% 2.15/1.70 tff(2821,plain,(c3_1(a695) | hskp21), inference(lemma,lemma(discharge,[]))).
% 2.15/1.70 tff(2822,plain,
% 2.15/1.70 (hskp21),
% 2.15/1.70 inference(unit_resolution,[status(thm)],[2821, 11])).
% 2.15/1.70 tff(2823,plain,
% 2.15/1.70 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))),
% 2.15/1.70 inference(bind,[status(th)],[])).
% 2.15/1.70 tff(2824,plain,
% 2.15/1.70 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 2.15/1.70 inference(quant_intro,[status(thm)],[2823])).
% 2.15/1.70 tff(2825,plain,
% 2.15/1.70 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 2.15/1.70 inference(rewrite,[status(thm)],[])).
% 2.15/1.70 tff(2826,plain,
% 2.15/1.70 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp0) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | hskp0))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))))),
% 2.15/1.70 inference(bind,[status(th)],[])).
% 2.15/1.70 tff(2827,plain,
% 2.15/1.70 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 2.15/1.70 inference(quant_intro,[status(thm)],[2826])).
% 2.15/1.70 tff(2828,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause162')).
% 2.15/1.70 tff(2829,plain,
% 2.15/1.70 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 2.15/1.70 inference(modus_ponens,[status(thm)],[2828, 2827])).
% 2.15/1.70 tff(2830,plain,
% 2.15/1.70 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 2.15/1.70 inference(modus_ponens,[status(thm)],[2829, 2825])).
% 2.15/1.70 tff(2831,plain,(
% 2.15/1.70 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 2.15/1.70 inference(skolemize,[status(sab)],[2830])).
% 2.15/1.70 tff(2832,plain,
% 2.15/1.70 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 2.15/1.70 inference(modus_ponens,[status(thm)],[2831, 2824])).
% 2.15/1.70 tff(2833,plain,
% 2.15/1.70 (^[U: $i] : refl((hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))),
% 2.15/1.70 inference(bind,[status(th)],[])).
% 2.15/1.70 tff(2834,plain,
% 2.15/1.70 (![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 2.15/1.70 inference(quant_intro,[status(thm)],[2833])).
% 2.15/1.70 tff(2835,plain,
% 2.15/1.70 (![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 2.15/1.70 inference(rewrite,[status(thm)],[])).
% 2.15/1.70 tff(2836,plain,
% 2.15/1.70 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp7) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp7))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp7) <=> (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp7) | hskp13) <=> ((hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp13))), rewrite(((hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp13) <=> (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp7) | hskp13) <=> (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))))),
% 2.15/1.70 inference(bind,[status(th)],[])).
% 2.15/1.70 tff(2837,plain,
% 2.15/1.70 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp7) | hskp13) <=> ![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 2.15/1.70 inference(quant_intro,[status(thm)],[2836])).
% 2.15/1.70 tff(2838,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp7) | hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause146')).
% 2.15/1.70 tff(2839,plain,
% 2.15/1.70 (![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 2.15/1.70 inference(modus_ponens,[status(thm)],[2838, 2837])).
% 2.15/1.70 tff(2840,plain,
% 2.15/1.70 (![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 2.15/1.70 inference(modus_ponens,[status(thm)],[2839, 2835])).
% 2.15/1.70 tff(2841,plain,(
% 2.15/1.70 ![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 2.15/1.70 inference(skolemize,[status(sab)],[2840])).
% 2.15/1.70 tff(2842,plain,
% 2.15/1.70 (![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 2.15/1.70 inference(modus_ponens,[status(thm)],[2841, 2834])).
% 2.15/1.70 tff(2843,plain,
% 2.15/1.70 (c2_1(a726)),
% 2.15/1.70 inference(unit_resolution,[status(thm)],[2546, 227, 177, 2046, 2028, 2022, 301])).
% 2.15/1.70 tff(2844,plain,
% 2.15/1.70 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | c3_1(a726) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c1_1(a726)) | (~c2_1(a726)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a726) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c1_1(a726)) | (~c2_1(a726)))),
% 2.15/1.70 inference(rewrite,[status(thm)],[])).
% 2.15/1.70 tff(2845,plain,
% 2.15/1.70 ((hskp20 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a726) | (~c2_1(a726)) | (~c1_1(a726))) <=> (hskp20 | c3_1(a726) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c1_1(a726)) | (~c2_1(a726)))),
% 2.15/1.70 inference(rewrite,[status(thm)],[])).
% 2.15/1.70 tff(2846,plain,
% 2.15/1.70 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a726) | (~c2_1(a726)) | (~c1_1(a726)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | c3_1(a726) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c1_1(a726)) | (~c2_1(a726))))),
% 2.15/1.70 inference(monotonicity,[status(thm)],[2845])).
% 2.15/1.70 tff(2847,plain,
% 2.15/1.70 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a726) | (~c2_1(a726)) | (~c1_1(a726)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a726) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c1_1(a726)) | (~c2_1(a726)))),
% 2.15/1.70 inference(transitivity,[status(thm)],[2846, 2844])).
% 2.15/1.70 tff(2848,plain,
% 2.15/1.70 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a726) | (~c2_1(a726)) | (~c1_1(a726)))),
% 2.15/1.70 inference(quant_inst,[status(thm)],[])).
% 2.15/1.70 tff(2849,plain,
% 2.15/1.70 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a726) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c1_1(a726)) | (~c2_1(a726))),
% 2.15/1.70 inference(modus_ponens,[status(thm)],[2848, 2847])).
% 2.15/1.70 tff(2850,plain,
% 2.15/1.70 ((~c3_1(a695)) | (~c2_1(a726))),
% 2.15/1.70 inference(unit_resolution,[status(thm)],[2849, 227, 280, 2802, 2760, 2046, 2022, 2101])).
% 2.15/1.70 tff(2851,plain,
% 2.15/1.70 (~c3_1(a695)),
% 2.15/1.70 inference(unit_resolution,[status(thm)],[2850, 2843])).
% 2.15/1.70 tff(2852,plain,
% 2.15/1.70 (~hskp4),
% 2.15/1.70 inference(unit_resolution,[status(thm)],[2150, 1036, 177])).
% 2.15/1.70 tff(2853,plain,
% 2.15/1.70 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | c2_1(a764) | c3_1(a764) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c1_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c2_1(a764) | c3_1(a764) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c1_1(a764)))),
% 2.15/1.70 inference(rewrite,[status(thm)],[])).
% 2.15/1.70 tff(2854,plain,
% 2.15/1.70 ((hskp6 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725))) <=> (hskp6 | c2_1(a764) | c3_1(a764) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c1_1(a764)))),
% 2.15/1.70 inference(rewrite,[status(thm)],[])).
% 2.15/1.70 tff(2855,plain,
% 2.15/1.70 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | c2_1(a764) | c3_1(a764) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c1_1(a764))))),
% 2.15/1.70 inference(monotonicity,[status(thm)],[2854])).
% 2.15/1.70 tff(2856,plain,
% 2.15/1.70 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c2_1(a764) | c3_1(a764) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c1_1(a764)))),
% 2.15/1.70 inference(transitivity,[status(thm)],[2855, 2853])).
% 2.15/1.70 tff(2857,plain,
% 2.15/1.70 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))),
% 2.15/1.70 inference(quant_inst,[status(thm)],[])).
% 2.15/1.70 tff(2858,plain,
% 2.15/1.70 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c2_1(a764) | c3_1(a764) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c1_1(a764))),
% 2.15/1.70 inference(modus_ponens,[status(thm)],[2857, 2856])).
% 2.15/1.70 tff(2859,plain,
% 2.15/1.70 ($false),
% 2.15/1.70 inference(unit_resolution,[status(thm)],[2858, 227, 177, 2014, 2013, 2012, 578, 1037, 101, 2556])).
% 2.15/1.70 tff(2860,plain,(c3_1(a725) | hskp6 | (~c1_1(a764)) | c2_1(a764) | c3_1(a764) | c0_1(a725) | hskp27), inference(lemma,lemma(discharge,[]))).
% 2.15/1.70 tff(2861,plain,
% 2.15/1.70 ($false),
% 2.15/1.70 inference(unit_resolution,[status(thm)],[2860, 2412, 2414, 2014, 2013, 2012, 177, 1036])).
% 2.15/1.70 tff(2862,plain,((~hskp12) | (~c1_1(a764)) | c2_1(a764) | c3_1(a764) | hskp6 | hskp27), inference(lemma,lemma(discharge,[]))).
% 2.15/1.70 tff(2863,plain,
% 2.15/1.70 (~hskp12),
% 2.15/1.70 inference(unit_resolution,[status(thm)],[2862, 325, 314, 308, 177, 1036])).
% 2.15/1.70 tff(2864,plain,
% 2.15/1.70 (hskp13),
% 2.15/1.70 inference(unit_resolution,[status(thm)],[2066, 2863, 280])).
% 2.15/1.70 tff(2865,plain,
% 2.15/1.70 (~c3_1(a726)),
% 2.15/1.70 inference(unit_resolution,[status(thm)],[2021, 2864])).
% 2.15/1.70 tff(2866,plain,
% 2.15/1.70 (~c0_1(a726)),
% 2.15/1.70 inference(unit_resolution,[status(thm)],[2027, 2864])).
% 2.15/1.70 tff(2867,plain,
% 2.15/1.70 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | c2_1(a764) | c3_1(a764) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | (~c1_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c2_1(a764) | c3_1(a764) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | (~c1_1(a764)))),
% 2.15/1.70 inference(rewrite,[status(thm)],[])).
% 2.15/1.70 tff(2868,plain,
% 2.15/1.70 ((hskp6 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726))) <=> (hskp6 | c2_1(a764) | c3_1(a764) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | (~c1_1(a764)))),
% 2.15/1.70 inference(rewrite,[status(thm)],[])).
% 2.15/1.70 tff(2869,plain,
% 2.15/1.70 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | c2_1(a764) | c3_1(a764) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | (~c1_1(a764))))),
% 2.15/1.70 inference(monotonicity,[status(thm)],[2868])).
% 2.15/1.70 tff(2870,plain,
% 2.15/1.70 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c2_1(a764) | c3_1(a764) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | (~c1_1(a764)))),
% 2.15/1.70 inference(transitivity,[status(thm)],[2869, 2867])).
% 2.15/1.70 tff(2871,plain,
% 2.15/1.70 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726)))),
% 2.15/1.70 inference(quant_inst,[status(thm)],[])).
% 2.15/1.70 tff(2872,plain,
% 2.15/1.70 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c2_1(a764) | c3_1(a764) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c2_1(a726)) | (~c1_1(a764))),
% 2.15/1.70 inference(modus_ponens,[status(thm)],[2871, 2870])).
% 2.15/1.70 tff(2873,plain,
% 2.15/1.70 (~c2_1(a726)),
% 2.15/1.70 inference(unit_resolution,[status(thm)],[2872, 227, 177, 325, 314, 308, 2866, 2865, 101])).
% 2.15/1.70 tff(2874,plain,
% 2.15/1.70 (c1_1(a726)),
% 2.15/1.70 inference(unit_resolution,[status(thm)],[2045, 2864])).
% 2.15/1.70 tff(2875,plain,
% 2.15/1.70 ($false),
% 2.15/1.70 inference(unit_resolution,[status(thm)],[2546, 227, 177, 2874, 2866, 2865, 301, 2873])).
% 2.15/1.70 tff(2876,plain,((~hskp24) | hskp6 | hskp20 | hskp27), inference(lemma,lemma(discharge,[]))).
% 2.15/1.70 tff(2877,plain,
% 2.15/1.70 (~hskp24),
% 2.15/1.70 inference(unit_resolution,[status(thm)],[2876, 280, 177, 1036])).
% 2.15/1.70 tff(2878,plain,
% 2.15/1.70 (((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a695)) | (~c1_1(a695)) | (~c2_1(a695)))) <=> ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a695)) | (~c1_1(a695)) | (~c2_1(a695)))),
% 2.15/1.70 inference(rewrite,[status(thm)],[])).
% 2.15/1.70 tff(2879,plain,
% 2.15/1.70 ((hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a695)) | (~c0_1(a695)) | (~c1_1(a695))) <=> (hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a695)) | (~c1_1(a695)) | (~c2_1(a695)))),
% 2.15/1.70 inference(rewrite,[status(thm)],[])).
% 2.15/1.70 tff(2880,plain,
% 2.15/1.70 (((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a695)) | (~c0_1(a695)) | (~c1_1(a695)))) <=> ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a695)) | (~c1_1(a695)) | (~c2_1(a695))))),
% 2.15/1.70 inference(monotonicity,[status(thm)],[2879])).
% 2.15/1.70 tff(2881,plain,
% 2.15/1.70 (((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a695)) | (~c0_1(a695)) | (~c1_1(a695)))) <=> ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a695)) | (~c1_1(a695)) | (~c2_1(a695)))),
% 2.15/1.71 inference(transitivity,[status(thm)],[2880, 2878])).
% 2.15/1.71 tff(2882,plain,
% 2.15/1.71 ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(a695)) | (~c0_1(a695)) | (~c1_1(a695)))),
% 2.15/1.71 inference(quant_inst,[status(thm)],[])).
% 2.15/1.71 tff(2883,plain,
% 2.15/1.71 ((~![U: $i] : (hskp24 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp24 | hskp23 | (~ndr1_0) | (~c0_1(a695)) | (~c1_1(a695)) | (~c2_1(a695))),
% 2.15/1.71 inference(modus_ponens,[status(thm)],[2882, 2881])).
% 2.15/1.71 tff(2884,plain,
% 2.15/1.71 (hskp24 | hskp23),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[2883, 227, 2802, 2771, 2760, 163])).
% 2.15/1.71 tff(2885,plain,
% 2.15/1.71 (hskp23),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[2884, 2877])).
% 2.15/1.71 tff(2886,plain,
% 2.15/1.71 (~c2_1(a763)),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[404, 2885])).
% 2.15/1.71 tff(2887,plain,
% 2.15/1.71 (~c1_1(a763)),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[410, 2885])).
% 2.15/1.71 tff(2888,plain,
% 2.15/1.71 (c0_1(a763)),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[421, 2885])).
% 2.15/1.71 tff(2889,plain,
% 2.15/1.71 (((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | c0_1(a761) | c2_1(a761) | (~ndr1_0) | c3_1(a761))) <=> ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp27 | hskp6 | c0_1(a761) | c2_1(a761) | (~ndr1_0) | c3_1(a761))),
% 2.15/1.71 inference(rewrite,[status(thm)],[])).
% 2.15/1.71 tff(2890,plain,
% 2.15/1.71 ((hskp27 | hskp6 | (~ndr1_0) | c3_1(a761) | c0_1(a761) | c2_1(a761)) <=> (hskp27 | hskp6 | c0_1(a761) | c2_1(a761) | (~ndr1_0) | c3_1(a761))),
% 2.15/1.71 inference(rewrite,[status(thm)],[])).
% 2.15/1.71 tff(2891,plain,
% 2.15/1.71 (((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | (~ndr1_0) | c3_1(a761) | c0_1(a761) | c2_1(a761))) <=> ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | c0_1(a761) | c2_1(a761) | (~ndr1_0) | c3_1(a761)))),
% 2.15/1.71 inference(monotonicity,[status(thm)],[2890])).
% 2.15/1.71 tff(2892,plain,
% 2.15/1.71 (((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | (~ndr1_0) | c3_1(a761) | c0_1(a761) | c2_1(a761))) <=> ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp27 | hskp6 | c0_1(a761) | c2_1(a761) | (~ndr1_0) | c3_1(a761))),
% 2.15/1.71 inference(transitivity,[status(thm)],[2891, 2889])).
% 2.15/1.71 tff(2893,plain,
% 2.15/1.71 ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp27 | hskp6 | (~ndr1_0) | c3_1(a761) | c0_1(a761) | c2_1(a761))),
% 2.15/1.71 inference(quant_inst,[status(thm)],[])).
% 2.15/1.71 tff(2894,plain,
% 2.15/1.71 ((~![U: $i] : (hskp27 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp27 | hskp6 | c0_1(a761) | c2_1(a761) | (~ndr1_0) | c3_1(a761)),
% 2.15/1.71 inference(modus_ponens,[status(thm)],[2893, 2892])).
% 2.15/1.71 tff(2895,plain,
% 2.15/1.71 (c3_1(a761)),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[2894, 227, 1036, 177, 1191, 1190, 201])).
% 2.15/1.71 tff(2896,plain,
% 2.15/1.71 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a761) | (~ndr1_0) | (~c3_1(a761)) | (~c1_1(a761)) | (~c0_1(a763)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a761) | (~ndr1_0) | (~c3_1(a761)) | (~c1_1(a761)) | (~c0_1(a763)))),
% 2.15/1.71 inference(rewrite,[status(thm)],[])).
% 2.15/1.71 tff(2897,plain,
% 2.15/1.71 ((hskp4 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c0_1(a761) | (~c3_1(a761)) | (~c1_1(a761))) <=> (hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a761) | (~ndr1_0) | (~c3_1(a761)) | (~c1_1(a761)) | (~c0_1(a763)))),
% 2.15/1.71 inference(rewrite,[status(thm)],[])).
% 2.15/1.71 tff(2898,plain,
% 2.15/1.71 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c0_1(a761) | (~c3_1(a761)) | (~c1_1(a761)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a761) | (~ndr1_0) | (~c3_1(a761)) | (~c1_1(a761)) | (~c0_1(a763))))),
% 2.15/1.71 inference(monotonicity,[status(thm)],[2897])).
% 2.15/1.71 tff(2899,plain,
% 2.15/1.71 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c0_1(a761) | (~c3_1(a761)) | (~c1_1(a761)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a761) | (~ndr1_0) | (~c3_1(a761)) | (~c1_1(a761)) | (~c0_1(a763)))),
% 2.15/1.71 inference(transitivity,[status(thm)],[2898, 2896])).
% 2.15/1.71 tff(2900,plain,
% 2.15/1.71 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c0_1(a761) | (~c3_1(a761)) | (~c1_1(a761)))),
% 2.15/1.71 inference(quant_inst,[status(thm)],[])).
% 2.15/1.71 tff(2901,plain,
% 2.15/1.71 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a761) | (~ndr1_0) | (~c3_1(a761)) | (~c1_1(a761)) | (~c0_1(a763))),
% 2.15/1.71 inference(modus_ponens,[status(thm)],[2900, 2899])).
% 2.15/1.71 tff(2902,plain,
% 2.15/1.71 ($false),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[2901, 227, 2852, 1809, 1192, 1807, 1806, 1191, 2169, 2895])).
% 2.15/1.71 tff(2903,plain,((~hskp22) | (~c0_1(a763)) | c1_1(a763) | c2_1(a763) | hskp27 | hskp6), inference(lemma,lemma(discharge,[]))).
% 2.15/1.71 tff(2904,plain,
% 2.15/1.71 (~hskp22),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[2903, 2888, 2887, 2886, 1036, 177])).
% 2.15/1.71 tff(2905,assumption,(hskp21), introduced(assumption)).
% 2.15/1.71 tff(2906,plain,
% 2.15/1.71 (((~hskp21) | (~c0_1(a760))) <=> ((~hskp21) | (~c0_1(a760)))),
% 2.15/1.71 inference(rewrite,[status(thm)],[])).
% 2.15/1.71 tff(2907,plain,
% 2.15/1.71 (((~c0_1(a760)) | (~hskp21)) <=> ((~hskp21) | (~c0_1(a760)))),
% 2.15/1.71 inference(rewrite,[status(thm)],[])).
% 2.15/1.71 tff(2908,axiom,((~c0_1(a760)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause96')).
% 2.15/1.71 tff(2909,plain,
% 2.15/1.71 ((~hskp21) | (~c0_1(a760))),
% 2.15/1.71 inference(modus_ponens,[status(thm)],[2908, 2907])).
% 2.15/1.71 tff(2910,plain,
% 2.15/1.71 ((~hskp21) | (~c0_1(a760))),
% 2.15/1.71 inference(modus_ponens,[status(thm)],[2909, 2906])).
% 2.15/1.71 tff(2911,plain,
% 2.15/1.71 (~c0_1(a760)),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[2910, 2905])).
% 2.15/1.71 tff(2912,plain,
% 2.15/1.71 (((~hskp21) | c3_1(a760)) <=> ((~hskp21) | c3_1(a760))),
% 2.15/1.71 inference(rewrite,[status(thm)],[])).
% 2.15/1.71 tff(2913,axiom,((~hskp21) | c3_1(a760)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause59')).
% 2.15/1.71 tff(2914,plain,
% 2.15/1.71 ((~hskp21) | c3_1(a760)),
% 2.15/1.71 inference(modus_ponens,[status(thm)],[2913, 2912])).
% 2.15/1.71 tff(2915,plain,
% 2.15/1.71 ((~hskp21) | c3_1(a760)),
% 2.15/1.71 inference(modus_ponens,[status(thm)],[2914, 2912])).
% 2.15/1.71 tff(2916,plain,
% 2.15/1.71 ((~hskp21) | c3_1(a760)),
% 2.15/1.71 inference(modus_ponens,[status(thm)],[2915, 2912])).
% 2.15/1.71 tff(2917,plain,
% 2.15/1.71 ((~hskp21) | c3_1(a760)),
% 2.15/1.71 inference(modus_ponens,[status(thm)],[2916, 2912])).
% 2.15/1.71 tff(2918,plain,
% 2.15/1.71 ((~hskp21) | c3_1(a760)),
% 2.15/1.71 inference(modus_ponens,[status(thm)],[2917, 2912])).
% 2.15/1.71 tff(2919,plain,
% 2.15/1.71 ((~hskp21) | c3_1(a760)),
% 2.15/1.71 inference(modus_ponens,[status(thm)],[2918, 2912])).
% 2.15/1.71 tff(2920,plain,
% 2.15/1.71 ((~hskp21) | c3_1(a760)),
% 2.15/1.71 inference(modus_ponens,[status(thm)],[2919, 2912])).
% 2.15/1.71 tff(2921,plain,
% 2.15/1.71 ((~hskp21) | c3_1(a760)),
% 2.15/1.71 inference(modus_ponens,[status(thm)],[2920, 2912])).
% 2.15/1.71 tff(2922,plain,
% 2.15/1.71 (c3_1(a760)),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[2921, 2905])).
% 2.15/1.71 tff(2923,plain,
% 2.15/1.71 (((~hskp21) | c1_1(a760)) <=> ((~hskp21) | c1_1(a760))),
% 2.15/1.71 inference(rewrite,[status(thm)],[])).
% 2.15/1.71 tff(2924,axiom,((~hskp21) | c1_1(a760)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause58')).
% 2.15/1.71 tff(2925,plain,
% 2.15/1.71 ((~hskp21) | c1_1(a760)),
% 2.15/1.71 inference(modus_ponens,[status(thm)],[2924, 2923])).
% 2.15/1.71 tff(2926,plain,
% 2.15/1.71 ((~hskp21) | c1_1(a760)),
% 2.15/1.71 inference(modus_ponens,[status(thm)],[2925, 2923])).
% 2.15/1.71 tff(2927,plain,
% 2.15/1.71 ((~hskp21) | c1_1(a760)),
% 2.15/1.71 inference(modus_ponens,[status(thm)],[2926, 2923])).
% 2.15/1.71 tff(2928,plain,
% 2.15/1.71 ((~hskp21) | c1_1(a760)),
% 2.15/1.71 inference(modus_ponens,[status(thm)],[2927, 2923])).
% 2.15/1.71 tff(2929,plain,
% 2.15/1.71 ((~hskp21) | c1_1(a760)),
% 2.15/1.71 inference(modus_ponens,[status(thm)],[2928, 2923])).
% 2.15/1.71 tff(2930,plain,
% 2.15/1.71 ((~hskp21) | c1_1(a760)),
% 2.15/1.71 inference(modus_ponens,[status(thm)],[2929, 2923])).
% 2.15/1.71 tff(2931,plain,
% 2.15/1.71 ((~hskp21) | c1_1(a760)),
% 2.15/1.71 inference(modus_ponens,[status(thm)],[2930, 2923])).
% 2.15/1.71 tff(2932,plain,
% 2.15/1.71 ((~hskp21) | c1_1(a760)),
% 2.15/1.71 inference(modus_ponens,[status(thm)],[2931, 2923])).
% 2.15/1.71 tff(2933,plain,
% 2.15/1.71 (c1_1(a760)),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[2932, 2905])).
% 2.15/1.71 tff(2934,plain,
% 2.15/1.71 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a760) | (~ndr1_0) | (~c3_1(a760)) | (~c1_1(a760)) | (~c0_1(a763)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a760) | (~ndr1_0) | (~c3_1(a760)) | (~c1_1(a760)) | (~c0_1(a763)))),
% 2.15/1.71 inference(rewrite,[status(thm)],[])).
% 2.15/1.71 tff(2935,plain,
% 2.15/1.71 ((hskp4 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c0_1(a760) | (~c3_1(a760)) | (~c1_1(a760))) <=> (hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a760) | (~ndr1_0) | (~c3_1(a760)) | (~c1_1(a760)) | (~c0_1(a763)))),
% 2.15/1.71 inference(rewrite,[status(thm)],[])).
% 2.15/1.71 tff(2936,plain,
% 2.15/1.71 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c0_1(a760) | (~c3_1(a760)) | (~c1_1(a760)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a760) | (~ndr1_0) | (~c3_1(a760)) | (~c1_1(a760)) | (~c0_1(a763))))),
% 2.15/1.71 inference(monotonicity,[status(thm)],[2935])).
% 2.15/1.71 tff(2937,plain,
% 2.15/1.71 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c0_1(a760) | (~c3_1(a760)) | (~c1_1(a760)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a760) | (~ndr1_0) | (~c3_1(a760)) | (~c1_1(a760)) | (~c0_1(a763)))),
% 2.15/1.71 inference(transitivity,[status(thm)],[2936, 2934])).
% 2.15/1.71 tff(2938,plain,
% 2.15/1.71 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c0_1(a760) | (~c3_1(a760)) | (~c1_1(a760)))),
% 2.15/1.71 inference(quant_inst,[status(thm)],[])).
% 2.15/1.71 tff(2939,plain,
% 2.15/1.71 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a760) | (~ndr1_0) | (~c3_1(a760)) | (~c1_1(a760)) | (~c0_1(a763))),
% 2.15/1.71 inference(modus_ponens,[status(thm)],[2938, 2937])).
% 2.15/1.71 tff(2940,plain,
% 2.15/1.71 ($false),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[2939, 227, 176, 1809, 2933, 2922, 1807, 1806, 2911, 2169])).
% 2.15/1.71 tff(2941,plain,((~hskp21) | hskp4 | (~c0_1(a763)) | c1_1(a763) | c2_1(a763)), inference(lemma,lemma(discharge,[]))).
% 2.15/1.71 tff(2942,plain,
% 2.15/1.71 ($false),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[2941, 411, 422, 176, 2905, 405])).
% 2.15/1.71 tff(2943,plain,((~hskp23) | hskp4 | (~hskp21)), inference(lemma,lemma(discharge,[]))).
% 2.15/1.71 tff(2944,plain,
% 2.15/1.71 (~hskp21),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[2943, 2885, 2852])).
% 2.15/1.71 tff(2945,plain,
% 2.15/1.71 (c3_1(a695)),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[2821, 2944])).
% 2.15/1.71 tff(2946,plain,
% 2.15/1.71 (((~![U: $i] : (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp27 | hskp18 | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c1_1(a695)))) <=> ((~![U: $i] : (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp27 | hskp18 | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c1_1(a695)))),
% 2.15/1.71 inference(rewrite,[status(thm)],[])).
% 2.15/1.71 tff(2947,plain,
% 2.15/1.71 ((hskp27 | hskp18 | (~ndr1_0) | (~c3_1(a695)) | (~c0_1(a695)) | (~c1_1(a695))) <=> (hskp27 | hskp18 | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c1_1(a695)))),
% 2.15/1.71 inference(rewrite,[status(thm)],[])).
% 2.15/1.71 tff(2948,plain,
% 2.15/1.71 (((~![U: $i] : (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(a695)) | (~c0_1(a695)) | (~c1_1(a695)))) <=> ((~![U: $i] : (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp27 | hskp18 | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c1_1(a695))))),
% 2.15/1.71 inference(monotonicity,[status(thm)],[2947])).
% 2.15/1.71 tff(2949,plain,
% 2.15/1.71 (((~![U: $i] : (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(a695)) | (~c0_1(a695)) | (~c1_1(a695)))) <=> ((~![U: $i] : (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp27 | hskp18 | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c1_1(a695)))),
% 2.15/1.71 inference(transitivity,[status(thm)],[2948, 2946])).
% 2.15/1.71 tff(2950,plain,
% 2.15/1.71 ((~![U: $i] : (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(a695)) | (~c0_1(a695)) | (~c1_1(a695)))),
% 2.15/1.71 inference(quant_inst,[status(thm)],[])).
% 2.15/1.71 tff(2951,plain,
% 2.15/1.71 ((~![U: $i] : (hskp27 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp27 | hskp18 | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c1_1(a695))),
% 2.15/1.71 inference(modus_ponens,[status(thm)],[2950, 2949])).
% 2.15/1.71 tff(2952,plain,
% 2.15/1.71 (hskp27 | hskp18 | (~c3_1(a695))),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[2951, 227, 2802, 2771, 2634])).
% 2.15/1.71 tff(2953,plain,
% 2.15/1.71 (hskp18),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[2952, 2945, 1036])).
% 2.15/1.71 tff(2954,plain,
% 2.15/1.71 (~c3_1(a751)),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[2644, 2953])).
% 2.15/1.71 tff(2955,plain,
% 2.15/1.71 (c0_1(a751)),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[2669, 2953])).
% 2.15/1.71 tff(2956,plain,
% 2.15/1.71 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp21 | c3_1(a751) | (~ndr1_0) | (~c0_1(a751)) | (~c2_1(a751)))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp22 | hskp21 | c3_1(a751) | (~ndr1_0) | (~c0_1(a751)) | (~c2_1(a751)))),
% 2.15/1.71 inference(rewrite,[status(thm)],[])).
% 2.15/1.71 tff(2957,plain,
% 2.15/1.71 ((hskp22 | hskp21 | (~ndr1_0) | c3_1(a751) | (~c2_1(a751)) | (~c0_1(a751))) <=> (hskp22 | hskp21 | c3_1(a751) | (~ndr1_0) | (~c0_1(a751)) | (~c2_1(a751)))),
% 2.15/1.71 inference(rewrite,[status(thm)],[])).
% 2.15/1.71 tff(2958,plain,
% 2.15/1.71 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c3_1(a751) | (~c2_1(a751)) | (~c0_1(a751)))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp21 | c3_1(a751) | (~ndr1_0) | (~c0_1(a751)) | (~c2_1(a751))))),
% 2.15/1.71 inference(monotonicity,[status(thm)],[2957])).
% 2.15/1.71 tff(2959,plain,
% 2.15/1.71 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c3_1(a751) | (~c2_1(a751)) | (~c0_1(a751)))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp22 | hskp21 | c3_1(a751) | (~ndr1_0) | (~c0_1(a751)) | (~c2_1(a751)))),
% 2.15/1.71 inference(transitivity,[status(thm)],[2958, 2956])).
% 2.15/1.71 tff(2960,plain,
% 2.15/1.71 ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c3_1(a751) | (~c2_1(a751)) | (~c0_1(a751)))),
% 2.15/1.71 inference(quant_inst,[status(thm)],[])).
% 2.15/1.71 tff(2961,plain,
% 2.15/1.71 ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp22 | hskp21 | c3_1(a751) | (~ndr1_0) | (~c0_1(a751)) | (~c2_1(a751))),
% 2.15/1.71 inference(modus_ponens,[status(thm)],[2960, 2959])).
% 2.15/1.71 tff(2962,plain,
% 2.15/1.71 (hskp22 | (~c2_1(a751))),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[2961, 227, 2944, 2955, 2954, 2791])).
% 2.15/1.71 tff(2963,plain,
% 2.15/1.71 (~c2_1(a751)),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[2962, 2904])).
% 2.15/1.71 tff(2964,plain,
% 2.15/1.71 (~c1_1(a751)),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[2650, 2953])).
% 2.15/1.71 tff(2965,plain,
% 2.15/1.71 (~c2_1(a726)),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[2713, 227, 1809, 2673, 1807, 1806, 2672, 2028, 2022, 2445, 2671])).
% 2.15/1.71 tff(2966,assumption,(~c1_1(a751)), introduced(assumption)).
% 2.15/1.71 tff(2967,plain,
% 2.15/1.71 ($false),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[2706, 227, 2046, 2966, 2672, 2028, 2022, 122, 2671, 2965])).
% 2.15/1.71 tff(2968,plain,((~hskp13) | c1_1(a751) | c3_1(a751) | c2_1(a751) | (~c0_1(a763)) | (~c0_1(a751)) | c1_1(a763) | c2_1(a763)), inference(lemma,lemma(discharge,[]))).
% 2.15/1.71 tff(2969,plain,
% 2.15/1.71 (~hskp13),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[2968, 2964, 2954, 2963, 2888, 2955, 2887, 2886])).
% 2.15/1.71 tff(2970,plain,
% 2.15/1.71 (hskp12),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[2066, 2969, 280])).
% 2.15/1.71 tff(2971,plain,
% 2.15/1.71 (~c0_1(a725)),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[151, 2970])).
% 2.15/1.71 tff(2972,plain,
% 2.15/1.71 (~c3_1(a725)),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[139, 2970])).
% 2.15/1.71 tff(2973,plain,
% 2.15/1.71 ($false),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[2681, 2972, 2971, 177, 2888, 2886, 2887, 2955, 2954, 1036, 2963])).
% 2.15/1.71 tff(2974,plain,(hskp20 | hskp6 | hskp27), inference(lemma,lemma(discharge,[]))).
% 2.15/1.71 tff(2975,plain,
% 2.15/1.71 (hskp20),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[2974, 1036, 177])).
% 2.15/1.71 tff(2976,plain,
% 2.15/1.71 (~c0_1(a754)),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[595, 2975])).
% 2.15/1.71 tff(2977,plain,
% 2.15/1.71 (~c3_1(a754)),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[668, 2975])).
% 2.15/1.71 tff(2978,plain,
% 2.15/1.71 (c2_1(a754)),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[190, 2975])).
% 2.15/1.71 tff(2979,plain,
% 2.15/1.71 (~hskp24),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[1626, 2978, 177, 2977, 2976])).
% 2.15/1.71 tff(2980,plain,
% 2.15/1.71 (hskp23),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[2884, 2979])).
% 2.15/1.71 tff(2981,plain,
% 2.15/1.71 (~hskp21),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[2943, 2980, 2852])).
% 2.15/1.71 tff(2982,plain,
% 2.15/1.71 (c3_1(a695)),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[2821, 2981])).
% 2.15/1.71 tff(2983,plain,
% 2.15/1.71 (hskp18),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[2952, 2982, 1036])).
% 2.15/1.71 tff(2984,plain,
% 2.15/1.71 (~c3_1(a751)),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[2644, 2983])).
% 2.15/1.71 tff(2985,plain,
% 2.15/1.71 (c0_1(a751)),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[2669, 2983])).
% 2.15/1.71 tff(2986,plain,
% 2.15/1.71 (~c2_1(a763)),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[404, 2980])).
% 2.15/1.71 tff(2987,plain,
% 2.15/1.71 (~c1_1(a763)),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[410, 2980])).
% 2.15/1.71 tff(2988,plain,
% 2.15/1.71 (c0_1(a763)),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[421, 2980])).
% 2.15/1.71 tff(2989,plain,
% 2.15/1.71 (~hskp22),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[2903, 2988, 2987, 2986, 1036, 177])).
% 2.15/1.71 tff(2990,plain,
% 2.15/1.71 (~c2_1(a751)),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[2961, 227, 2989, 2981, 2985, 2984, 2791])).
% 2.15/1.71 tff(2991,plain,
% 2.15/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a763) | c2_1(a763) | c0_1(a754) | c3_1(a754) | c3_1(a751) | (~ndr1_0) | (~c0_1(a751)) | c2_1(a751) | (~c2_1(a754)) | (~c0_1(a763)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a763) | c2_1(a763) | c0_1(a754) | c3_1(a754) | c3_1(a751) | (~ndr1_0) | (~c0_1(a751)) | c2_1(a751) | (~c2_1(a754)) | (~c0_1(a763)))),
% 2.15/1.71 inference(rewrite,[status(thm)],[])).
% 2.15/1.71 tff(2992,plain,
% 2.15/1.71 (((~ndr1_0) | c3_1(a751) | c2_1(a751) | (~c0_1(a751)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754))) <=> (c1_1(a763) | c2_1(a763) | c0_1(a754) | c3_1(a754) | c3_1(a751) | (~ndr1_0) | (~c0_1(a751)) | c2_1(a751) | (~c2_1(a754)) | (~c0_1(a763)))),
% 2.15/1.71 inference(rewrite,[status(thm)],[])).
% 2.15/1.71 tff(2993,plain,
% 2.15/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a751) | c2_1(a751) | (~c0_1(a751)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a763) | c2_1(a763) | c0_1(a754) | c3_1(a754) | c3_1(a751) | (~ndr1_0) | (~c0_1(a751)) | c2_1(a751) | (~c2_1(a754)) | (~c0_1(a763))))),
% 2.15/1.71 inference(monotonicity,[status(thm)],[2992])).
% 2.15/1.71 tff(2994,plain,
% 2.15/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a751) | c2_1(a751) | (~c0_1(a751)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a763) | c2_1(a763) | c0_1(a754) | c3_1(a754) | c3_1(a751) | (~ndr1_0) | (~c0_1(a751)) | c2_1(a751) | (~c2_1(a754)) | (~c0_1(a763)))),
% 2.15/1.71 inference(transitivity,[status(thm)],[2993, 2991])).
% 2.15/1.71 tff(2995,plain,
% 2.15/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a751) | c2_1(a751) | (~c0_1(a751)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))),
% 2.15/1.71 inference(quant_inst,[status(thm)],[])).
% 2.15/1.71 tff(2996,plain,
% 2.15/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a763) | c2_1(a763) | c0_1(a754) | c3_1(a754) | c3_1(a751) | (~ndr1_0) | (~c0_1(a751)) | c2_1(a751) | (~c2_1(a754)) | (~c0_1(a763))),
% 2.15/1.71 inference(modus_ponens,[status(thm)],[2995, 2994])).
% 2.15/1.71 tff(2997,plain,
% 2.15/1.71 ($false),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[2996, 227, 2988, 2978, 2985, 2987, 2986, 2976, 2977, 2984, 2445, 2990])).
% 2.15/1.71 tff(2998,plain,(hskp27 | hskp6), inference(lemma,lemma(discharge,[]))).
% 2.15/1.71 tff(2999,plain,
% 2.15/1.71 (hskp27),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[2998, 177])).
% 2.15/1.71 tff(3000,plain,
% 2.15/1.71 (hskp30),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[288, 280, 2999])).
% 2.15/1.71 tff(3001,plain,
% 2.15/1.71 (c3_1(a733)),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[1707, 3000])).
% 2.15/1.71 tff(3002,plain,
% 2.15/1.71 (c1_1(a733)),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[1729, 3000])).
% 2.15/1.71 tff(3003,plain,
% 2.15/1.71 (c2_1(a733)),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[1718, 3000])).
% 2.15/1.71 tff(3004,plain,
% 2.15/1.71 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | c3_1(a726) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a726)) | (~c2_1(a726)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a726) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a726)) | (~c2_1(a726)))),
% 2.15/1.71 inference(rewrite,[status(thm)],[])).
% 2.15/1.71 tff(3005,plain,
% 2.15/1.71 ((hskp20 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a726) | (~c2_1(a726)) | (~c1_1(a726))) <=> (hskp20 | c3_1(a726) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a726)) | (~c2_1(a726)))),
% 2.15/1.71 inference(rewrite,[status(thm)],[])).
% 2.15/1.71 tff(3006,plain,
% 2.15/1.71 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a726) | (~c2_1(a726)) | (~c1_1(a726)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | c3_1(a726) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a726)) | (~c2_1(a726))))),
% 2.15/1.71 inference(monotonicity,[status(thm)],[3005])).
% 2.15/1.71 tff(3007,plain,
% 2.15/1.71 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a726) | (~c2_1(a726)) | (~c1_1(a726)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a726) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a726)) | (~c2_1(a726)))),
% 2.15/1.71 inference(transitivity,[status(thm)],[3006, 3004])).
% 2.15/1.71 tff(3008,plain,
% 2.15/1.71 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a726) | (~c2_1(a726)) | (~c1_1(a726)))),
% 2.15/1.71 inference(quant_inst,[status(thm)],[])).
% 2.15/1.71 tff(3009,plain,
% 2.15/1.71 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a726) | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | (~c1_1(a726)) | (~c2_1(a726))),
% 2.15/1.71 inference(modus_ponens,[status(thm)],[3008, 3007])).
% 2.15/1.71 tff(3010,plain,
% 2.15/1.71 ((~c0_1(a733)) | (~c2_1(a726))),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[3009, 227, 280, 3003, 3001, 2046, 2022, 2101])).
% 2.15/1.71 tff(3011,plain,
% 2.15/1.71 (~c0_1(a733)),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[3010, 2843])).
% 2.15/1.71 tff(3012,plain,
% 2.15/1.71 (hskp10),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[2548, 3011, 2016, 3002, 3001, 177])).
% 2.15/1.71 tff(3013,plain,
% 2.15/1.71 (~c2_1(a717)),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[1893, 3012])).
% 2.15/1.71 tff(3014,plain,
% 2.15/1.71 (((~hskp10) | c1_1(a717)) <=> ((~hskp10) | c1_1(a717))),
% 2.15/1.71 inference(rewrite,[status(thm)],[])).
% 2.15/1.71 tff(3015,axiom,((~hskp10) | c1_1(a717)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause71')).
% 2.15/1.71 tff(3016,plain,
% 2.15/1.71 ((~hskp10) | c1_1(a717)),
% 2.15/1.71 inference(modus_ponens,[status(thm)],[3015, 3014])).
% 2.15/1.71 tff(3017,plain,
% 2.15/1.71 ((~hskp10) | c1_1(a717)),
% 2.15/1.71 inference(modus_ponens,[status(thm)],[3016, 3014])).
% 2.15/1.71 tff(3018,plain,
% 2.15/1.71 ((~hskp10) | c1_1(a717)),
% 2.15/1.71 inference(modus_ponens,[status(thm)],[3017, 3014])).
% 2.15/1.71 tff(3019,plain,
% 2.15/1.71 ((~hskp10) | c1_1(a717)),
% 2.15/1.71 inference(modus_ponens,[status(thm)],[3018, 3014])).
% 2.15/1.71 tff(3020,plain,
% 2.15/1.71 ((~hskp10) | c1_1(a717)),
% 2.15/1.71 inference(modus_ponens,[status(thm)],[3019, 3014])).
% 2.15/1.71 tff(3021,plain,
% 2.15/1.71 ((~hskp10) | c1_1(a717)),
% 2.15/1.71 inference(modus_ponens,[status(thm)],[3020, 3014])).
% 2.15/1.71 tff(3022,plain,
% 2.15/1.71 ((~hskp10) | c1_1(a717)),
% 2.15/1.71 inference(modus_ponens,[status(thm)],[3021, 3014])).
% 2.15/1.71 tff(3023,plain,
% 2.15/1.71 ((~hskp10) | c1_1(a717)),
% 2.15/1.71 inference(modus_ponens,[status(thm)],[3022, 3014])).
% 2.15/1.71 tff(3024,plain,
% 2.15/1.71 (c1_1(a717)),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[3023, 3012])).
% 2.15/1.71 tff(3025,plain,
% 2.15/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a726) | c2_1(a717) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | c0_1(a717) | (~c1_1(a717)) | (~c1_1(a726)) | (~c2_1(a726)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a726) | c2_1(a717) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | c0_1(a717) | (~c1_1(a717)) | (~c1_1(a726)) | (~c2_1(a726)))),
% 2.15/1.71 inference(rewrite,[status(thm)],[])).
% 2.15/1.71 tff(3026,plain,
% 2.15/1.71 (((~ndr1_0) | c3_1(a726) | (~c2_1(a726)) | (~c1_1(a726)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c2_1(a717) | c0_1(a717) | (~c1_1(a717))) <=> (c3_1(a726) | c2_1(a717) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | c0_1(a717) | (~c1_1(a717)) | (~c1_1(a726)) | (~c2_1(a726)))),
% 2.15/1.71 inference(rewrite,[status(thm)],[])).
% 2.15/1.71 tff(3027,plain,
% 2.15/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a726) | (~c2_1(a726)) | (~c1_1(a726)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c2_1(a717) | c0_1(a717) | (~c1_1(a717)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a726) | c2_1(a717) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | c0_1(a717) | (~c1_1(a717)) | (~c1_1(a726)) | (~c2_1(a726))))),
% 2.15/1.71 inference(monotonicity,[status(thm)],[3026])).
% 2.15/1.71 tff(3028,plain,
% 2.15/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a726) | (~c2_1(a726)) | (~c1_1(a726)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c2_1(a717) | c0_1(a717) | (~c1_1(a717)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a726) | c2_1(a717) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | c0_1(a717) | (~c1_1(a717)) | (~c1_1(a726)) | (~c2_1(a726)))),
% 2.15/1.71 inference(transitivity,[status(thm)],[3027, 3025])).
% 2.15/1.71 tff(3029,plain,
% 2.15/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a726) | (~c2_1(a726)) | (~c1_1(a726)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c2_1(a717) | c0_1(a717) | (~c1_1(a717)))),
% 2.15/1.71 inference(quant_inst,[status(thm)],[])).
% 2.15/1.71 tff(3030,plain,
% 2.15/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a726) | c2_1(a717) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | c0_1(a717) | (~c1_1(a717)) | (~c1_1(a726)) | (~c2_1(a726))),
% 2.15/1.71 inference(modus_ponens,[status(thm)],[3029, 3028])).
% 2.15/1.71 tff(3031,plain,
% 2.15/1.71 (c0_1(a717)),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[3030, 227, 2802, 2771, 2046, 3024, 2022, 3013, 822, 2851, 2843])).
% 2.15/1.71 tff(3032,plain,
% 2.15/1.71 (c3_1(a717)),
% 2.15/1.71 inference(unit_resolution,[status(thm)],[1904, 3012])).
% 2.15/1.71 tff(3033,plain,
% 2.15/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a726) | c3_1(a726) | c2_1(a717) | (~ndr1_0) | (~c3_1(a717)) | (~c0_1(a717)) | (~c1_1(a726)) | (~c2_1(a726)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a726) | c3_1(a726) | c2_1(a717) | (~ndr1_0) | (~c3_1(a717)) | (~c0_1(a717)) | (~c1_1(a726)) | (~c2_1(a726)))),
% 2.15/1.71 inference(rewrite,[status(thm)],[])).
% 2.15/1.71 tff(3034,plain,
% 2.15/1.71 (((~ndr1_0) | c2_1(a717) | (~c3_1(a717)) | (~c0_1(a717)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726)) | c3_1(a726) | c0_1(a726) | (~c1_1(a726))) <=> (c0_1(a726) | c3_1(a726) | c2_1(a717) | (~ndr1_0) | (~c3_1(a717)) | (~c0_1(a717)) | (~c1_1(a726)) | (~c2_1(a726)))),
% 2.15/1.71 inference(rewrite,[status(thm)],[])).
% 2.15/1.71 tff(3035,plain,
% 2.15/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a717) | (~c3_1(a717)) | (~c0_1(a717)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726)) | c3_1(a726) | c0_1(a726) | (~c1_1(a726)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a726) | c3_1(a726) | c2_1(a717) | (~ndr1_0) | (~c3_1(a717)) | (~c0_1(a717)) | (~c1_1(a726)) | (~c2_1(a726))))),
% 2.15/1.71 inference(monotonicity,[status(thm)],[3034])).
% 2.15/1.71 tff(3036,plain,
% 2.15/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a717) | (~c3_1(a717)) | (~c0_1(a717)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726)) | c3_1(a726) | c0_1(a726) | (~c1_1(a726)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a726) | c3_1(a726) | c2_1(a717) | (~ndr1_0) | (~c3_1(a717)) | (~c0_1(a717)) | (~c1_1(a726)) | (~c2_1(a726)))),
% 2.15/1.71 inference(transitivity,[status(thm)],[3035, 3033])).
% 2.15/1.71 tff(3037,plain,
% 2.15/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a717) | (~c3_1(a717)) | (~c0_1(a717)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726)) | c3_1(a726) | c0_1(a726) | (~c1_1(a726)))),
% 2.15/1.72 inference(quant_inst,[status(thm)],[])).
% 2.15/1.72 tff(3038,plain,
% 2.15/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a726) | c3_1(a726) | c2_1(a717) | (~ndr1_0) | (~c3_1(a717)) | (~c0_1(a717)) | (~c1_1(a726)) | (~c2_1(a726))),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3037, 3036])).
% 2.15/1.72 tff(3039,plain,
% 2.15/1.72 ($false),
% 2.15/1.72 inference(unit_resolution,[status(thm)],[3038, 227, 2046, 3032, 2028, 2022, 3013, 174, 2843, 3031])).
% 2.15/1.72 tff(3040,plain,((~hskp13) | hskp6 | hskp20), inference(lemma,lemma(discharge,[]))).
% 2.15/1.72 tff(3041,plain,
% 2.15/1.72 (~hskp13),
% 2.15/1.72 inference(unit_resolution,[status(thm)],[3040, 280, 177])).
% 2.15/1.72 tff(3042,plain,
% 2.15/1.72 (c0_1(a691)),
% 2.15/1.72 inference(unit_resolution,[status(thm)],[278, 2999])).
% 2.15/1.72 tff(3043,plain,
% 2.15/1.72 (c3_1(a691)),
% 2.15/1.72 inference(unit_resolution,[status(thm)],[256, 2999])).
% 2.15/1.72 tff(3044,plain,
% 2.15/1.72 (c1_1(a691)),
% 2.15/1.72 inference(unit_resolution,[status(thm)],[267, 2999])).
% 2.15/1.72 tff(3045,assumption,(c1_1(a691)), introduced(assumption)).
% 2.15/1.72 tff(3046,assumption,(~hskp13), introduced(assumption)).
% 2.15/1.72 tff(3047,assumption,(~c2_1(a725)), introduced(assumption)).
% 2.15/1.72 tff(3048,plain,
% 2.15/1.72 (hskp12),
% 2.15/1.72 inference(unit_resolution,[status(thm)],[2066, 3046, 280])).
% 2.15/1.72 tff(3049,plain,
% 2.15/1.72 (~c3_1(a725)),
% 2.15/1.72 inference(unit_resolution,[status(thm)],[139, 3048])).
% 2.15/1.72 tff(3050,plain,
% 2.15/1.72 (~c0_1(a725)),
% 2.15/1.72 inference(unit_resolution,[status(thm)],[151, 3048])).
% 2.15/1.72 tff(3051,plain,
% 2.15/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | c2_1(a725) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | c2_1(a725) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 2.15/1.72 inference(rewrite,[status(thm)],[])).
% 2.15/1.72 tff(3052,plain,
% 2.15/1.72 (((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c3_1(a725) | c2_1(a725) | c0_1(a725)) <=> (c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | c2_1(a725) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 2.15/1.72 inference(rewrite,[status(thm)],[])).
% 2.15/1.72 tff(3053,plain,
% 2.15/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c3_1(a725) | c2_1(a725) | c0_1(a725))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | c2_1(a725) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691))))),
% 2.15/1.72 inference(monotonicity,[status(thm)],[3052])).
% 2.15/1.72 tff(3054,plain,
% 2.15/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c3_1(a725) | c2_1(a725) | c0_1(a725))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | c2_1(a725) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 2.15/1.72 inference(transitivity,[status(thm)],[3053, 3051])).
% 2.15/1.72 tff(3055,plain,
% 2.15/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c3_1(a725) | c2_1(a725) | c0_1(a725))),
% 2.15/1.72 inference(quant_inst,[status(thm)],[])).
% 2.15/1.72 tff(3056,plain,
% 2.15/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | c2_1(a725) | (~c2_1(a691)) | (~c3_1(a691)) | (~c0_1(a691))),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3055, 3054])).
% 2.15/1.72 tff(3057,plain,
% 2.15/1.72 ($false),
% 2.15/1.72 inference(unit_resolution,[status(thm)],[3056, 227, 2802, 2771, 1756, 1755, 578, 1037, 1777, 3047, 1767, 11])).
% 2.15/1.72 tff(3058,plain,((~c2_1(a691)) | (~c0_1(a691)) | (~c3_1(a691)) | c0_1(a725) | c3_1(a725) | c2_1(a725) | c3_1(a695)), inference(lemma,lemma(discharge,[]))).
% 2.15/1.72 tff(3059,plain,
% 2.15/1.72 (~c2_1(a691)),
% 2.15/1.72 inference(unit_resolution,[status(thm)],[3058, 3047, 1755, 3050, 3049, 1756, 11])).
% 2.15/1.72 tff(3060,plain,
% 2.15/1.72 (^[U: $i] : refl((hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 2.15/1.72 inference(bind,[status(th)],[])).
% 2.15/1.72 tff(3061,plain,
% 2.15/1.72 (![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.15/1.72 inference(quant_intro,[status(thm)],[3060])).
% 2.15/1.72 tff(3062,plain,
% 2.15/1.72 (![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.15/1.72 inference(rewrite,[status(thm)],[])).
% 2.15/1.72 tff(3063,plain,
% 2.15/1.72 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp16) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp16))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp16) <=> (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp16) <=> (hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp16) | hskp20) <=> ((hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp20))), rewrite(((hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp20) <=> (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp16) | hskp20) <=> (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 2.15/1.72 inference(bind,[status(th)],[])).
% 2.15/1.72 tff(3064,plain,
% 2.15/1.72 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp16) | hskp20) <=> ![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.15/1.72 inference(quant_intro,[status(thm)],[3063])).
% 2.15/1.72 tff(3065,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp16) | hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause149')).
% 2.15/1.72 tff(3066,plain,
% 2.15/1.72 (![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3065, 3064])).
% 2.15/1.72 tff(3067,plain,
% 2.15/1.72 (![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3066, 3062])).
% 2.15/1.72 tff(3068,plain,(
% 2.15/1.72 ![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.15/1.72 inference(skolemize,[status(sab)],[3067])).
% 2.15/1.72 tff(3069,plain,
% 2.15/1.72 (![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3068, 3061])).
% 2.15/1.72 tff(3070,plain,
% 2.15/1.72 (((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp16 | (~ndr1_0) | (~c1_1(a691)) | (~c3_1(a691)) | c2_1(a691))) <=> ((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp16 | (~ndr1_0) | (~c1_1(a691)) | (~c3_1(a691)) | c2_1(a691))),
% 2.15/1.72 inference(rewrite,[status(thm)],[])).
% 2.15/1.72 tff(3071,plain,
% 2.15/1.72 ((hskp20 | hskp16 | (~ndr1_0) | c2_1(a691) | (~c3_1(a691)) | (~c1_1(a691))) <=> (hskp20 | hskp16 | (~ndr1_0) | (~c1_1(a691)) | (~c3_1(a691)) | c2_1(a691))),
% 2.15/1.72 inference(rewrite,[status(thm)],[])).
% 2.15/1.72 tff(3072,plain,
% 2.15/1.72 (((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp16 | (~ndr1_0) | c2_1(a691) | (~c3_1(a691)) | (~c1_1(a691)))) <=> ((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp16 | (~ndr1_0) | (~c1_1(a691)) | (~c3_1(a691)) | c2_1(a691)))),
% 2.15/1.72 inference(monotonicity,[status(thm)],[3071])).
% 2.15/1.72 tff(3073,plain,
% 2.15/1.72 (((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp16 | (~ndr1_0) | c2_1(a691) | (~c3_1(a691)) | (~c1_1(a691)))) <=> ((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp16 | (~ndr1_0) | (~c1_1(a691)) | (~c3_1(a691)) | c2_1(a691))),
% 2.15/1.72 inference(transitivity,[status(thm)],[3072, 3070])).
% 2.15/1.72 tff(3074,plain,
% 2.15/1.72 ((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp16 | (~ndr1_0) | c2_1(a691) | (~c3_1(a691)) | (~c1_1(a691)))),
% 2.15/1.72 inference(quant_inst,[status(thm)],[])).
% 2.15/1.72 tff(3075,plain,
% 2.15/1.72 ((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp16 | (~ndr1_0) | (~c1_1(a691)) | (~c3_1(a691)) | c2_1(a691)),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3074, 3073])).
% 2.15/1.72 tff(3076,plain,
% 2.15/1.72 (hskp20 | hskp16 | c2_1(a691)),
% 2.15/1.72 inference(unit_resolution,[status(thm)],[3075, 227, 3045, 1755, 3069])).
% 2.15/1.72 tff(3077,plain,
% 2.15/1.72 (hskp16),
% 2.15/1.72 inference(unit_resolution,[status(thm)],[3076, 3059, 280])).
% 2.15/1.72 tff(3078,plain,
% 2.15/1.72 (((~hskp16) | c3_1(a738)) <=> ((~hskp16) | c3_1(a738))),
% 2.15/1.72 inference(rewrite,[status(thm)],[])).
% 2.15/1.72 tff(3079,axiom,((~hskp16) | c3_1(a738)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause64')).
% 2.15/1.72 tff(3080,plain,
% 2.15/1.72 ((~hskp16) | c3_1(a738)),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3079, 3078])).
% 2.15/1.72 tff(3081,plain,
% 2.15/1.72 ((~hskp16) | c3_1(a738)),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3080, 3078])).
% 2.15/1.72 tff(3082,plain,
% 2.15/1.72 ((~hskp16) | c3_1(a738)),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3081, 3078])).
% 2.15/1.72 tff(3083,plain,
% 2.15/1.72 ((~hskp16) | c3_1(a738)),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3082, 3078])).
% 2.15/1.72 tff(3084,plain,
% 2.15/1.72 ((~hskp16) | c3_1(a738)),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3083, 3078])).
% 2.15/1.72 tff(3085,plain,
% 2.15/1.72 ((~hskp16) | c3_1(a738)),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3084, 3078])).
% 2.15/1.72 tff(3086,plain,
% 2.15/1.72 ((~hskp16) | c3_1(a738)),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3085, 3078])).
% 2.15/1.72 tff(3087,plain,
% 2.15/1.72 ((~hskp16) | c3_1(a738)),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3086, 3078])).
% 2.15/1.72 tff(3088,plain,
% 2.15/1.72 (c3_1(a738)),
% 2.15/1.72 inference(unit_resolution,[status(thm)],[3087, 3077])).
% 2.15/1.72 tff(3089,plain,
% 2.15/1.72 (((~hskp16) | c2_1(a738)) <=> ((~hskp16) | c2_1(a738))),
% 2.15/1.72 inference(rewrite,[status(thm)],[])).
% 2.15/1.72 tff(3090,axiom,((~hskp16) | c2_1(a738)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause63')).
% 2.15/1.72 tff(3091,plain,
% 2.15/1.72 ((~hskp16) | c2_1(a738)),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3090, 3089])).
% 2.15/1.72 tff(3092,plain,
% 2.15/1.72 ((~hskp16) | c2_1(a738)),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3091, 3089])).
% 2.15/1.72 tff(3093,plain,
% 2.15/1.72 ((~hskp16) | c2_1(a738)),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3092, 3089])).
% 2.15/1.72 tff(3094,plain,
% 2.15/1.72 ((~hskp16) | c2_1(a738)),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3093, 3089])).
% 2.15/1.72 tff(3095,plain,
% 2.15/1.72 ((~hskp16) | c2_1(a738)),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3094, 3089])).
% 2.15/1.72 tff(3096,plain,
% 2.15/1.72 ((~hskp16) | c2_1(a738)),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3095, 3089])).
% 2.15/1.72 tff(3097,plain,
% 2.15/1.72 ((~hskp16) | c2_1(a738)),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3096, 3089])).
% 2.15/1.72 tff(3098,plain,
% 2.15/1.72 ((~hskp16) | c2_1(a738)),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3097, 3089])).
% 2.15/1.72 tff(3099,plain,
% 2.15/1.72 (c2_1(a738)),
% 2.15/1.72 inference(unit_resolution,[status(thm)],[3098, 3077])).
% 2.15/1.72 tff(3100,plain,
% 2.15/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | c2_1(a725) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a738)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | c2_1(a725) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a738)))),
% 2.15/1.72 inference(rewrite,[status(thm)],[])).
% 2.15/1.72 tff(3101,plain,
% 2.15/1.72 (((~ndr1_0) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a738)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c3_1(a725) | c2_1(a725) | c0_1(a725)) <=> (c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | c2_1(a725) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a738)))),
% 2.15/1.72 inference(rewrite,[status(thm)],[])).
% 2.15/1.72 tff(3102,plain,
% 2.15/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a738)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c3_1(a725) | c2_1(a725) | c0_1(a725))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | c2_1(a725) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a738))))),
% 2.15/1.72 inference(monotonicity,[status(thm)],[3101])).
% 2.15/1.72 tff(3103,plain,
% 2.15/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a738)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c3_1(a725) | c2_1(a725) | c0_1(a725))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | c2_1(a725) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a738)))),
% 2.15/1.72 inference(transitivity,[status(thm)],[3102, 3100])).
% 2.15/1.72 tff(3104,plain,
% 2.15/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a738)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c3_1(a725) | c2_1(a725) | c0_1(a725))),
% 2.15/1.72 inference(quant_inst,[status(thm)],[])).
% 2.15/1.72 tff(3105,plain,
% 2.15/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | c2_1(a725) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a738))),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3104, 3103])).
% 2.15/1.72 tff(3106,plain,
% 2.15/1.72 (~c0_1(a738)),
% 2.15/1.72 inference(unit_resolution,[status(thm)],[3105, 227, 2802, 2771, 3099, 3088, 3050, 3049, 1777, 3047, 11])).
% 2.15/1.72 tff(3107,plain,
% 2.15/1.72 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W)))),
% 2.15/1.72 inference(bind,[status(th)],[])).
% 2.15/1.72 tff(3108,plain,
% 2.15/1.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))),
% 2.15/1.72 inference(quant_intro,[status(thm)],[3107])).
% 2.15/1.72 tff(3109,plain,
% 2.15/1.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))),
% 2.15/1.72 inference(rewrite,[status(thm)],[])).
% 2.15/1.72 tff(3110,plain,
% 2.15/1.72 (^[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))) | (~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)) | (~c2_1(V)) | (~c3_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))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | c1_1(W))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | c1_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | c1_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))))),
% 2.15/1.72 inference(bind,[status(th)],[])).
% 2.15/1.72 tff(3111,plain,
% 2.15/1.72 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))),
% 2.15/1.72 inference(quant_intro,[status(thm)],[3110])).
% 2.15/1.72 tff(3112,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause196')).
% 2.15/1.72 tff(3113,plain,
% 2.15/1.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3112, 3111])).
% 2.15/1.72 tff(3114,plain,
% 2.15/1.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3113, 3109])).
% 2.15/1.72 tff(3115,plain,(
% 2.15/1.72 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))),
% 2.15/1.72 inference(skolemize,[status(sab)],[3114])).
% 2.15/1.72 tff(3116,plain,
% 2.15/1.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3115, 3108])).
% 2.15/1.72 tff(3117,plain,
% 2.15/1.72 (((~hskp16) | (~c1_1(a738))) <=> ((~hskp16) | (~c1_1(a738)))),
% 2.15/1.72 inference(rewrite,[status(thm)],[])).
% 2.15/1.72 tff(3118,plain,
% 2.15/1.72 (((~c1_1(a738)) | (~hskp16)) <=> ((~hskp16) | (~c1_1(a738)))),
% 2.15/1.72 inference(rewrite,[status(thm)],[])).
% 2.15/1.72 tff(3119,axiom,((~c1_1(a738)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause106')).
% 2.15/1.72 tff(3120,plain,
% 2.15/1.72 ((~hskp16) | (~c1_1(a738))),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3119, 3118])).
% 2.15/1.72 tff(3121,plain,
% 2.15/1.72 ((~hskp16) | (~c1_1(a738))),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3120, 3117])).
% 2.15/1.72 tff(3122,plain,
% 2.15/1.72 (~c1_1(a738)),
% 2.15/1.72 inference(unit_resolution,[status(thm)],[3121, 3077])).
% 2.15/1.72 tff(3123,plain,
% 2.15/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c1_1(a763) | c2_1(a763) | c1_1(a738) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a763)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c1_1(a763) | c2_1(a763) | c1_1(a738) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a763)))),
% 2.15/1.72 inference(rewrite,[status(thm)],[])).
% 2.15/1.72 tff(3124,plain,
% 2.15/1.72 (((~ndr1_0) | c3_1(a695) | (~c0_1(a695)) | (~c1_1(a695)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c2_1(a763) | (~c3_1(a763)) | c1_1(a763)) <=> (c1_1(a763) | c2_1(a763) | c1_1(a738) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a763)))),
% 2.15/1.72 inference(rewrite,[status(thm)],[])).
% 2.15/1.72 tff(3125,plain,
% 2.15/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a695) | (~c0_1(a695)) | (~c1_1(a695)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c2_1(a763) | (~c3_1(a763)) | c1_1(a763))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c1_1(a763) | c2_1(a763) | c1_1(a738) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a763))))),
% 2.15/1.72 inference(monotonicity,[status(thm)],[3124])).
% 2.15/1.72 tff(3126,plain,
% 2.15/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a695) | (~c0_1(a695)) | (~c1_1(a695)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c2_1(a763) | (~c3_1(a763)) | c1_1(a763))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c1_1(a763) | c2_1(a763) | c1_1(a738) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a763)))),
% 2.15/1.72 inference(transitivity,[status(thm)],[3125, 3123])).
% 2.15/1.72 tff(3127,plain,
% 2.15/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a695) | (~c0_1(a695)) | (~c1_1(a695)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c2_1(a763) | (~c3_1(a763)) | c1_1(a763))),
% 2.15/1.72 inference(quant_inst,[status(thm)],[])).
% 2.15/1.72 tff(3128,plain,
% 2.15/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c1_1(a763) | c2_1(a763) | c1_1(a738) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a763))),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3127, 3126])).
% 2.15/1.72 tff(3129,plain,
% 2.15/1.72 (~c3_1(a763)),
% 2.15/1.72 inference(unit_resolution,[status(thm)],[3128, 227, 2802, 2771, 3099, 3088, 1807, 1806, 3122, 3116, 11])).
% 2.15/1.72 tff(3130,plain,
% 2.15/1.72 (((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | c1_1(a738) | (~ndr1_0) | (~c2_1(a738)) | (~c3_1(a738)))) <=> ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp13 | hskp7 | c1_1(a738) | (~ndr1_0) | (~c2_1(a738)) | (~c3_1(a738)))),
% 2.15/1.72 inference(rewrite,[status(thm)],[])).
% 2.15/1.72 tff(3131,plain,
% 2.15/1.72 ((hskp13 | hskp7 | (~ndr1_0) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738))) <=> (hskp13 | hskp7 | c1_1(a738) | (~ndr1_0) | (~c2_1(a738)) | (~c3_1(a738)))),
% 2.15/1.72 inference(rewrite,[status(thm)],[])).
% 2.15/1.72 tff(3132,plain,
% 2.15/1.72 (((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | (~ndr1_0) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)))) <=> ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | c1_1(a738) | (~ndr1_0) | (~c2_1(a738)) | (~c3_1(a738))))),
% 2.15/1.72 inference(monotonicity,[status(thm)],[3131])).
% 2.15/1.72 tff(3133,plain,
% 2.15/1.72 (((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | (~ndr1_0) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)))) <=> ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp13 | hskp7 | c1_1(a738) | (~ndr1_0) | (~c2_1(a738)) | (~c3_1(a738)))),
% 2.15/1.72 inference(transitivity,[status(thm)],[3132, 3130])).
% 2.15/1.72 tff(3134,plain,
% 2.15/1.72 ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | (~ndr1_0) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)))),
% 2.15/1.72 inference(quant_inst,[status(thm)],[])).
% 2.15/1.72 tff(3135,plain,
% 2.15/1.72 ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp13 | hskp7 | c1_1(a738) | (~ndr1_0) | (~c2_1(a738)) | (~c3_1(a738))),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3134, 3133])).
% 2.15/1.72 tff(3136,plain,
% 2.15/1.72 (hskp7),
% 2.15/1.72 inference(unit_resolution,[status(thm)],[3135, 227, 3046, 3099, 3088, 3122, 2842])).
% 2.15/1.72 tff(3137,plain,
% 2.15/1.72 (((~hskp7) | (~c3_1(a708))) <=> ((~hskp7) | (~c3_1(a708)))),
% 2.15/1.72 inference(rewrite,[status(thm)],[])).
% 2.15/1.72 tff(3138,plain,
% 2.15/1.72 (((~c3_1(a708)) | (~hskp7)) <=> ((~hskp7) | (~c3_1(a708)))),
% 2.15/1.72 inference(rewrite,[status(thm)],[])).
% 2.15/1.72 tff(3139,axiom,((~c3_1(a708)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause121')).
% 2.15/1.72 tff(3140,plain,
% 2.15/1.72 ((~hskp7) | (~c3_1(a708))),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3139, 3138])).
% 2.15/1.72 tff(3141,plain,
% 2.15/1.72 ((~hskp7) | (~c3_1(a708))),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3140, 3137])).
% 2.15/1.72 tff(3142,plain,
% 2.15/1.72 (~c3_1(a708)),
% 2.15/1.72 inference(unit_resolution,[status(thm)],[3141, 3136])).
% 2.15/1.72 tff(3143,plain,
% 2.15/1.72 (((~hskp7) | c2_1(a708)) <=> ((~hskp7) | c2_1(a708))),
% 2.15/1.72 inference(rewrite,[status(thm)],[])).
% 2.15/1.72 tff(3144,axiom,((~hskp7) | c2_1(a708)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause76')).
% 2.15/1.72 tff(3145,plain,
% 2.15/1.72 ((~hskp7) | c2_1(a708)),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3144, 3143])).
% 2.15/1.72 tff(3146,plain,
% 2.15/1.72 ((~hskp7) | c2_1(a708)),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3145, 3143])).
% 2.15/1.72 tff(3147,plain,
% 2.15/1.72 ((~hskp7) | c2_1(a708)),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3146, 3143])).
% 2.15/1.72 tff(3148,plain,
% 2.15/1.72 ((~hskp7) | c2_1(a708)),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3147, 3143])).
% 2.15/1.72 tff(3149,plain,
% 2.15/1.72 ((~hskp7) | c2_1(a708)),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3148, 3143])).
% 2.15/1.72 tff(3150,plain,
% 2.15/1.72 ((~hskp7) | c2_1(a708)),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3149, 3143])).
% 2.15/1.72 tff(3151,plain,
% 2.15/1.72 ((~hskp7) | c2_1(a708)),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3150, 3143])).
% 2.15/1.72 tff(3152,plain,
% 2.15/1.72 ((~hskp7) | c2_1(a708)),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3151, 3143])).
% 2.15/1.72 tff(3153,plain,
% 2.15/1.72 (c2_1(a708)),
% 2.15/1.72 inference(unit_resolution,[status(thm)],[3152, 3136])).
% 2.15/1.72 tff(3154,plain,
% 2.15/1.72 (((~hskp7) | c1_1(a708)) <=> ((~hskp7) | c1_1(a708))),
% 2.15/1.72 inference(rewrite,[status(thm)],[])).
% 2.15/1.72 tff(3155,axiom,((~hskp7) | c1_1(a708)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause75')).
% 2.15/1.72 tff(3156,plain,
% 2.15/1.72 ((~hskp7) | c1_1(a708)),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3155, 3154])).
% 2.15/1.72 tff(3157,plain,
% 2.15/1.72 ((~hskp7) | c1_1(a708)),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3156, 3154])).
% 2.15/1.72 tff(3158,plain,
% 2.15/1.72 ((~hskp7) | c1_1(a708)),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3157, 3154])).
% 2.15/1.72 tff(3159,plain,
% 2.15/1.72 ((~hskp7) | c1_1(a708)),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3158, 3154])).
% 2.15/1.72 tff(3160,plain,
% 2.15/1.72 ((~hskp7) | c1_1(a708)),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3159, 3154])).
% 2.15/1.72 tff(3161,plain,
% 2.15/1.72 ((~hskp7) | c1_1(a708)),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3160, 3154])).
% 2.15/1.72 tff(3162,plain,
% 2.15/1.72 ((~hskp7) | c1_1(a708)),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3161, 3154])).
% 2.15/1.72 tff(3163,plain,
% 2.15/1.72 ((~hskp7) | c1_1(a708)),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3162, 3154])).
% 2.15/1.72 tff(3164,plain,
% 2.15/1.72 (c1_1(a708)),
% 2.15/1.72 inference(unit_resolution,[status(thm)],[3163, 3136])).
% 2.15/1.72 tff(3165,plain,
% 2.15/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | (c1_1(a763) | c1_1(a738) | c3_1(a708) | (~ndr1_0) | (~c1_1(a708)) | (~c2_1(a708)) | (~c2_1(a738)) | c0_1(a738) | c3_1(a763) | (~c0_1(a763)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c1_1(a763) | c1_1(a738) | c3_1(a708) | (~ndr1_0) | (~c1_1(a708)) | (~c2_1(a708)) | (~c2_1(a738)) | c0_1(a738) | c3_1(a763) | (~c0_1(a763)))),
% 2.15/1.72 inference(rewrite,[status(thm)],[])).
% 2.15/1.72 tff(3166,plain,
% 2.15/1.72 (((~ndr1_0) | c3_1(a708) | (~c2_1(a708)) | (~c1_1(a708)) | c3_1(a763) | c1_1(a763) | (~c0_1(a763)) | c0_1(a738) | (~c2_1(a738)) | c1_1(a738)) <=> (c1_1(a763) | c1_1(a738) | c3_1(a708) | (~ndr1_0) | (~c1_1(a708)) | (~c2_1(a708)) | (~c2_1(a738)) | c0_1(a738) | c3_1(a763) | (~c0_1(a763)))),
% 2.15/1.72 inference(rewrite,[status(thm)],[])).
% 2.15/1.72 tff(3167,plain,
% 2.15/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a708) | (~c2_1(a708)) | (~c1_1(a708)) | c3_1(a763) | c1_1(a763) | (~c0_1(a763)) | c0_1(a738) | (~c2_1(a738)) | c1_1(a738))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | (c1_1(a763) | c1_1(a738) | c3_1(a708) | (~ndr1_0) | (~c1_1(a708)) | (~c2_1(a708)) | (~c2_1(a738)) | c0_1(a738) | c3_1(a763) | (~c0_1(a763))))),
% 2.15/1.72 inference(monotonicity,[status(thm)],[3166])).
% 2.15/1.72 tff(3168,plain,
% 2.15/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a708) | (~c2_1(a708)) | (~c1_1(a708)) | c3_1(a763) | c1_1(a763) | (~c0_1(a763)) | c0_1(a738) | (~c2_1(a738)) | c1_1(a738))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c1_1(a763) | c1_1(a738) | c3_1(a708) | (~ndr1_0) | (~c1_1(a708)) | (~c2_1(a708)) | (~c2_1(a738)) | c0_1(a738) | c3_1(a763) | (~c0_1(a763)))),
% 2.15/1.72 inference(transitivity,[status(thm)],[3167, 3165])).
% 2.15/1.72 tff(3169,plain,
% 2.15/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a708) | (~c2_1(a708)) | (~c1_1(a708)) | c3_1(a763) | c1_1(a763) | (~c0_1(a763)) | c0_1(a738) | (~c2_1(a738)) | c1_1(a738))),
% 2.15/1.72 inference(quant_inst,[status(thm)],[])).
% 2.15/1.72 tff(3170,plain,
% 2.15/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c1_1(a763) | c1_1(a738) | c3_1(a708) | (~ndr1_0) | (~c1_1(a708)) | (~c2_1(a708)) | (~c2_1(a738)) | c0_1(a738) | c3_1(a763) | (~c0_1(a763))),
% 2.15/1.72 inference(modus_ponens,[status(thm)],[3169, 3168])).
% 2.15/1.72 tff(3171,plain,
% 2.15/1.72 ($false),
% 2.15/1.72 inference(unit_resolution,[status(thm)],[3170, 227, 1809, 3099, 3164, 3153, 1807, 3122, 3142, 566, 3129, 3106])).
% 2.15/1.72 tff(3172,plain,(c2_1(a725) | (~c0_1(a763)) | c1_1(a763) | c2_1(a763) | c3_1(a695) | hskp13 | hskp20 | (~c1_1(a691)) | (~c3_1(a691)) | (~c0_1(a691))), inference(lemma,lemma(discharge,[]))).
% 2.15/1.72 tff(3173,plain,
% 2.15/1.72 (c2_1(a725)),
% 2.15/1.72 inference(unit_resolution,[status(thm)],[3172, 11, 411, 1806, 1809, 3046, 280, 3045, 1755, 1756])).
% 2.15/1.73 tff(3174,plain,
% 2.15/1.73 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c0_1(a695)) | c3_1(a695) | (~c2_1(a695)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp3 | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c0_1(a695)) | c3_1(a695) | (~c2_1(a695)))),
% 2.15/1.73 inference(rewrite,[status(thm)],[])).
% 2.15/1.73 tff(3175,plain,
% 2.15/1.73 ((hskp3 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a695) | (~c2_1(a695)) | (~c0_1(a695))) <=> (hskp3 | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c0_1(a695)) | c3_1(a695) | (~c2_1(a695)))),
% 2.15/1.73 inference(rewrite,[status(thm)],[])).
% 2.15/1.73 tff(3176,plain,
% 2.15/1.73 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a695) | (~c2_1(a695)) | (~c0_1(a695)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c0_1(a695)) | c3_1(a695) | (~c2_1(a695))))),
% 2.15/1.73 inference(monotonicity,[status(thm)],[3175])).
% 2.15/1.73 tff(3177,plain,
% 2.15/1.73 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a695) | (~c2_1(a695)) | (~c0_1(a695)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp3 | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c0_1(a695)) | c3_1(a695) | (~c2_1(a695)))),
% 2.15/1.73 inference(transitivity,[status(thm)],[3176, 3174])).
% 2.15/1.73 tff(3178,plain,
% 2.15/1.73 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c1_1(a733)) | c3_1(a695) | (~c2_1(a695)) | (~c0_1(a695)))),
% 2.15/1.73 inference(quant_inst,[status(thm)],[])).
% 2.15/1.73 tff(3179,plain,
% 2.15/1.73 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp3 | (~ndr1_0) | (~c3_1(a733)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c0_1(a695)) | c3_1(a695) | (~c2_1(a695))),
% 2.15/1.73 inference(modus_ponens,[status(thm)],[3178, 3177])).
% 2.15/1.73 tff(3180,plain,
% 2.15/1.73 (hskp3),
% 2.15/1.73 inference(unit_resolution,[status(thm)],[3179, 227, 2259, 2258, 2257, 2802, 2760, 2234, 11])).
% 2.15/1.73 tff(3181,plain,
% 2.15/1.73 (~c3_1(a697)),
% 2.15/1.73 inference(unit_resolution,[status(thm)],[1355, 3180])).
% 2.15/1.73 tff(3182,plain,
% 2.15/1.73 (~c1_1(a725)),
% 2.15/1.73 inference(unit_resolution,[status(thm)],[145, 3048])).
% 2.15/1.73 tff(3183,plain,
% 2.15/1.73 (c0_1(a697)),
% 2.15/1.73 inference(unit_resolution,[status(thm)],[508, 3180])).
% 2.15/1.73 tff(3184,plain,
% 2.15/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | (c0_1(a725) | c1_1(a725) | c3_1(a697) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a725)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c0_1(a725) | c1_1(a725) | c3_1(a697) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a725)))),
% 2.15/1.73 inference(rewrite,[status(thm)],[])).
% 2.15/1.73 tff(3185,plain,
% 2.15/1.73 (((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a725) | (~c2_1(a725)) | c1_1(a725)) <=> (c0_1(a725) | c1_1(a725) | c3_1(a697) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a725)))),
% 2.15/1.73 inference(rewrite,[status(thm)],[])).
% 2.15/1.73 tff(3186,plain,
% 2.15/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a725) | (~c2_1(a725)) | c1_1(a725))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | (c0_1(a725) | c1_1(a725) | c3_1(a697) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a725))))),
% 2.15/1.73 inference(monotonicity,[status(thm)],[3185])).
% 2.15/1.73 tff(3187,plain,
% 2.15/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a725) | (~c2_1(a725)) | c1_1(a725))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c0_1(a725) | c1_1(a725) | c3_1(a697) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a725)))),
% 2.15/1.73 inference(transitivity,[status(thm)],[3186, 3184])).
% 2.15/1.73 tff(3188,plain,
% 2.15/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a725) | (~c2_1(a725)) | c1_1(a725))),
% 2.15/1.73 inference(quant_inst,[status(thm)],[])).
% 2.15/1.73 tff(3189,plain,
% 2.15/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c0_1(a725) | c1_1(a725) | c3_1(a697) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a725))),
% 2.15/1.73 inference(modus_ponens,[status(thm)],[3188, 3187])).
% 2.15/1.73 tff(3190,plain,
% 2.15/1.73 (c1_1(a697) | (~c2_1(a725))),
% 2.15/1.73 inference(unit_resolution,[status(thm)],[3189, 227, 2771, 2760, 3183, 3050, 3182, 3181, 566, 11])).
% 2.15/1.73 tff(3191,plain,
% 2.15/1.73 (c1_1(a697)),
% 2.15/1.73 inference(unit_resolution,[status(thm)],[3190, 3173])).
% 2.15/1.73 tff(3192,plain,
% 2.15/1.73 (~c0_1(a760)),
% 2.15/1.73 inference(unit_resolution,[status(thm)],[2910, 2822])).
% 2.15/1.73 tff(3193,plain,
% 2.15/1.73 (c3_1(a760)),
% 2.15/1.73 inference(unit_resolution,[status(thm)],[2921, 2822])).
% 2.15/1.73 tff(3194,plain,
% 2.15/1.73 (c1_1(a760)),
% 2.15/1.73 inference(unit_resolution,[status(thm)],[2932, 2822])).
% 2.15/1.73 tff(3195,plain,
% 2.15/1.73 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c0_1(a760) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c3_1(a760)) | (~c1_1(a760)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a760) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c3_1(a760)) | (~c1_1(a760)))),
% 2.15/1.73 inference(rewrite,[status(thm)],[])).
% 2.15/1.73 tff(3196,plain,
% 2.15/1.73 ((hskp10 | (~ndr1_0) | c0_1(a760) | (~c3_1(a760)) | (~c1_1(a760)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725))) <=> (hskp10 | c0_1(a760) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c3_1(a760)) | (~c1_1(a760)))),
% 2.15/1.73 inference(rewrite,[status(thm)],[])).
% 2.15/1.73 tff(3197,plain,
% 2.15/1.73 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a760) | (~c3_1(a760)) | (~c1_1(a760)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c0_1(a760) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c3_1(a760)) | (~c1_1(a760))))),
% 2.15/1.73 inference(monotonicity,[status(thm)],[3196])).
% 2.15/1.73 tff(3198,plain,
% 2.15/1.73 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a760) | (~c3_1(a760)) | (~c1_1(a760)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a760) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c3_1(a760)) | (~c1_1(a760)))),
% 2.15/1.73 inference(transitivity,[status(thm)],[3197, 3195])).
% 2.15/1.73 tff(3199,plain,
% 2.15/1.73 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a760) | (~c3_1(a760)) | (~c1_1(a760)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))),
% 2.15/1.73 inference(quant_inst,[status(thm)],[])).
% 2.15/1.73 tff(3200,plain,
% 2.15/1.73 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a760) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c3_1(a760)) | (~c1_1(a760))),
% 2.15/1.73 inference(modus_ponens,[status(thm)],[3199, 3198])).
% 2.15/1.73 tff(3201,plain,
% 2.15/1.73 (hskp10 | (~c2_1(a725))),
% 2.15/1.73 inference(unit_resolution,[status(thm)],[3200, 227, 3194, 3193, 3192, 3050, 3049, 1749])).
% 2.15/1.73 tff(3202,plain,
% 2.15/1.73 (hskp10),
% 2.15/1.73 inference(unit_resolution,[status(thm)],[3201, 3173])).
% 2.15/1.73 tff(3203,plain,
% 2.15/1.73 (~c2_1(a717)),
% 2.15/1.73 inference(unit_resolution,[status(thm)],[1893, 3202])).
% 2.15/1.73 tff(3204,plain,
% 2.15/1.73 (c2_1(a697)),
% 2.15/1.73 inference(unit_resolution,[status(thm)],[527, 3180])).
% 2.15/1.73 tff(3205,plain,
% 2.15/1.73 (c1_1(a717)),
% 2.15/1.73 inference(unit_resolution,[status(thm)],[3023, 3202])).
% 2.15/1.73 tff(3206,plain,
% 2.15/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a717) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a697)) | c0_1(a717) | (~c1_1(a717)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a717) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a697)) | c0_1(a717) | (~c1_1(a717)))),
% 2.15/1.73 inference(rewrite,[status(thm)],[])).
% 2.15/1.73 tff(3207,plain,
% 2.15/1.73 (((~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c2_1(a717) | c0_1(a717) | (~c1_1(a717))) <=> (c2_1(a717) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a697)) | c0_1(a717) | (~c1_1(a717)))),
% 2.15/1.73 inference(rewrite,[status(thm)],[])).
% 2.15/1.73 tff(3208,plain,
% 2.15/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c2_1(a717) | c0_1(a717) | (~c1_1(a717)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a717) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a697)) | c0_1(a717) | (~c1_1(a717))))),
% 2.15/1.73 inference(monotonicity,[status(thm)],[3207])).
% 2.15/1.73 tff(3209,plain,
% 2.15/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c2_1(a717) | c0_1(a717) | (~c1_1(a717)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a717) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a697)) | c0_1(a717) | (~c1_1(a717)))),
% 2.15/1.73 inference(transitivity,[status(thm)],[3208, 3206])).
% 2.15/1.73 tff(3210,plain,
% 2.15/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c2_1(a717) | c0_1(a717) | (~c1_1(a717)))),
% 2.15/1.73 inference(quant_inst,[status(thm)],[])).
% 2.15/1.73 tff(3211,plain,
% 2.15/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a717) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a697)) | c0_1(a717) | (~c1_1(a717))),
% 2.15/1.73 inference(modus_ponens,[status(thm)],[3210, 3209])).
% 2.15/1.73 tff(3212,plain,
% 2.15/1.73 (c0_1(a717)),
% 2.15/1.73 inference(unit_resolution,[status(thm)],[3211, 227, 3205, 3183, 3204, 3203, 3181, 822, 3191])).
% 2.15/1.73 tff(3213,plain,
% 2.15/1.73 (hskp4),
% 2.15/1.73 inference(unit_resolution,[status(thm)],[2943, 2822, 399])).
% 2.15/1.73 tff(3214,plain,
% 2.15/1.73 (~c3_1(a698)),
% 2.15/1.73 inference(unit_resolution,[status(thm)],[1045, 3213])).
% 2.15/1.73 tff(3215,plain,
% 2.15/1.73 (~c2_1(a698)),
% 2.15/1.73 inference(unit_resolution,[status(thm)],[923, 3213])).
% 2.15/1.73 tff(3216,plain,
% 2.15/1.73 (~c0_1(a698)),
% 2.15/1.73 inference(unit_resolution,[status(thm)],[917, 3213])).
% 2.15/1.73 tff(3217,plain,
% 2.15/1.73 (c3_1(a717)),
% 2.15/1.73 inference(unit_resolution,[status(thm)],[1904, 3202])).
% 2.15/1.73 tff(3218,plain,
% 2.15/1.73 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c2_1(a717) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c3_1(a717)) | (~c0_1(a717)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c2_1(a717) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c3_1(a717)) | (~c0_1(a717)))),
% 2.15/1.73 inference(rewrite,[status(thm)],[])).
% 2.15/1.73 tff(3219,plain,
% 2.15/1.73 ((hskp0 | (~ndr1_0) | c2_1(a717) | (~c3_1(a717)) | (~c0_1(a717)) | c3_1(a698) | c0_1(a698) | c2_1(a698)) <=> (hskp0 | c2_1(a717) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c3_1(a717)) | (~c0_1(a717)))),
% 2.15/1.73 inference(rewrite,[status(thm)],[])).
% 2.15/1.73 tff(3220,plain,
% 2.15/1.73 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a717) | (~c3_1(a717)) | (~c0_1(a717)) | c3_1(a698) | c0_1(a698) | c2_1(a698))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c2_1(a717) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c3_1(a717)) | (~c0_1(a717))))),
% 2.15/1.73 inference(monotonicity,[status(thm)],[3219])).
% 2.15/1.73 tff(3221,plain,
% 2.15/1.73 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a717) | (~c3_1(a717)) | (~c0_1(a717)) | c3_1(a698) | c0_1(a698) | c2_1(a698))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c2_1(a717) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c3_1(a717)) | (~c0_1(a717)))),
% 2.15/1.73 inference(transitivity,[status(thm)],[3220, 3218])).
% 2.15/1.73 tff(3222,plain,
% 2.15/1.73 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a717) | (~c3_1(a717)) | (~c0_1(a717)) | c3_1(a698) | c0_1(a698) | c2_1(a698))),
% 2.15/1.73 inference(quant_inst,[status(thm)],[])).
% 2.15/1.73 tff(3223,plain,
% 2.15/1.73 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c2_1(a717) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c3_1(a717)) | (~c0_1(a717))),
% 2.15/1.73 inference(modus_ponens,[status(thm)],[3222, 3221])).
% 2.15/1.73 tff(3224,plain,
% 2.15/1.73 (hskp0),
% 2.15/1.73 inference(unit_resolution,[status(thm)],[3223, 227, 3217, 3203, 3216, 3215, 3214, 2832, 3212])).
% 2.15/1.73 tff(3225,plain,
% 2.15/1.73 (~c1_1(a692)),
% 2.15/1.73 inference(unit_resolution,[status(thm)],[853, 3224])).
% 2.15/1.73 tff(3226,plain,
% 2.15/1.73 (~c0_1(a692)),
% 2.15/1.73 inference(unit_resolution,[status(thm)],[859, 3224])).
% 2.15/1.73 tff(3227,plain,
% 2.15/1.73 (^[V: $i, U: $i] : refl((hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 2.15/1.73 inference(bind,[status(th)],[])).
% 2.15/1.73 tff(3228,plain,
% 2.15/1.73 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.15/1.73 inference(quant_intro,[status(thm)],[3227])).
% 2.15/1.73 tff(3229,plain,
% 2.15/1.73 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.15/1.73 inference(rewrite,[status(thm)],[])).
% 2.15/1.73 tff(3230,plain,
% 2.15/1.73 (^[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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp17) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp17))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp17) <=> (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 2.15/1.73 inference(bind,[status(th)],[])).
% 2.15/1.73 tff(3231,plain,
% 2.15/1.73 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp17) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.15/1.73 inference(quant_intro,[status(thm)],[3230])).
% 2.15/1.73 tff(3232,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause183')).
% 2.15/1.73 tff(3233,plain,
% 2.15/1.73 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.15/1.73 inference(modus_ponens,[status(thm)],[3232, 3231])).
% 2.15/1.73 tff(3234,plain,
% 2.15/1.73 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.15/1.73 inference(modus_ponens,[status(thm)],[3233, 3229])).
% 2.15/1.73 tff(3235,plain,(
% 2.15/1.73 ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.15/1.73 inference(skolemize,[status(sab)],[3234])).
% 2.15/1.73 tff(3236,plain,
% 2.15/1.73 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.15/1.73 inference(modus_ponens,[status(thm)],[3235, 3228])).
% 2.15/1.73 tff(3237,plain,
% 2.15/1.73 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c2_1(a717) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c3_1(a717)) | (~c1_1(a717)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c2_1(a717) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c3_1(a717)) | (~c1_1(a717)))),
% 2.15/1.73 inference(rewrite,[status(thm)],[])).
% 2.15/1.73 tff(3238,plain,
% 2.15/1.73 ((hskp17 | (~ndr1_0) | c3_1(a697) | (~c0_1(a697)) | (~c1_1(a697)) | c2_1(a717) | (~c3_1(a717)) | (~c1_1(a717))) <=> (hskp17 | c2_1(a717) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c3_1(a717)) | (~c1_1(a717)))),
% 2.15/1.73 inference(rewrite,[status(thm)],[])).
% 2.15/1.73 tff(3239,plain,
% 2.15/1.73 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a697) | (~c0_1(a697)) | (~c1_1(a697)) | c2_1(a717) | (~c3_1(a717)) | (~c1_1(a717)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c2_1(a717) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c3_1(a717)) | (~c1_1(a717))))),
% 2.15/1.73 inference(monotonicity,[status(thm)],[3238])).
% 2.15/1.73 tff(3240,plain,
% 2.15/1.73 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a697) | (~c0_1(a697)) | (~c1_1(a697)) | c2_1(a717) | (~c3_1(a717)) | (~c1_1(a717)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c2_1(a717) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c3_1(a717)) | (~c1_1(a717)))),
% 2.15/1.73 inference(transitivity,[status(thm)],[3239, 3237])).
% 2.15/1.73 tff(3241,plain,
% 2.15/1.73 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a697) | (~c0_1(a697)) | (~c1_1(a697)) | c2_1(a717) | (~c3_1(a717)) | (~c1_1(a717)))),
% 2.15/1.73 inference(quant_inst,[status(thm)],[])).
% 2.15/1.73 tff(3242,plain,
% 2.15/1.73 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c2_1(a717) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c3_1(a717)) | (~c1_1(a717))),
% 2.15/1.73 inference(modus_ponens,[status(thm)],[3241, 3240])).
% 2.15/1.73 tff(3243,plain,
% 2.15/1.73 (hskp17),
% 2.15/1.73 inference(unit_resolution,[status(thm)],[3242, 227, 3205, 3217, 3183, 3203, 3181, 3236, 3191])).
% 2.15/1.73 tff(3244,plain,
% 2.15/1.73 (((~hskp17) | (~c3_1(a744))) <=> ((~hskp17) | (~c3_1(a744)))),
% 2.15/1.73 inference(rewrite,[status(thm)],[])).
% 2.15/1.73 tff(3245,plain,
% 2.15/1.73 (((~c3_1(a744)) | (~hskp17)) <=> ((~hskp17) | (~c3_1(a744)))),
% 2.15/1.73 inference(rewrite,[status(thm)],[])).
% 2.15/1.73 tff(3246,axiom,((~c3_1(a744)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause105')).
% 2.15/1.73 tff(3247,plain,
% 2.15/1.73 ((~hskp17) | (~c3_1(a744))),
% 2.15/1.73 inference(modus_ponens,[status(thm)],[3246, 3245])).
% 2.15/1.73 tff(3248,plain,
% 2.15/1.73 ((~hskp17) | (~c3_1(a744))),
% 2.15/1.73 inference(modus_ponens,[status(thm)],[3247, 3244])).
% 2.15/1.73 tff(3249,plain,
% 2.15/1.73 (~c3_1(a744)),
% 2.15/1.73 inference(unit_resolution,[status(thm)],[3248, 3243])).
% 2.15/1.73 tff(3250,plain,
% 2.15/1.73 (((~hskp17) | (~c1_1(a744))) <=> ((~hskp17) | (~c1_1(a744)))),
% 2.15/1.73 inference(rewrite,[status(thm)],[])).
% 2.15/1.73 tff(3251,plain,
% 2.15/1.73 (((~c1_1(a744)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a744)))),
% 2.15/1.73 inference(rewrite,[status(thm)],[])).
% 2.15/1.73 tff(3252,axiom,((~c1_1(a744)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause103')).
% 2.15/1.73 tff(3253,plain,
% 2.15/1.73 ((~hskp17) | (~c1_1(a744))),
% 2.15/1.73 inference(modus_ponens,[status(thm)],[3252, 3251])).
% 2.15/1.73 tff(3254,plain,
% 2.15/1.73 ((~hskp17) | (~c1_1(a744))),
% 2.15/1.73 inference(modus_ponens,[status(thm)],[3253, 3250])).
% 2.15/1.73 tff(3255,plain,
% 2.15/1.73 (~c1_1(a744)),
% 2.15/1.73 inference(unit_resolution,[status(thm)],[3254, 3243])).
% 2.15/1.73 tff(3256,plain,
% 2.15/1.73 (c2_1(a692)),
% 2.15/1.73 inference(unit_resolution,[status(thm)],[872, 3224])).
% 2.15/1.73 tff(3257,plain,
% 2.15/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | (c1_1(a744) | c3_1(a744) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c1_1(a697)) | (~c2_1(a697)) | (~c0_1(a744)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c1_1(a744) | c3_1(a744) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c1_1(a697)) | (~c2_1(a697)) | (~c0_1(a744)))),
% 2.15/1.73 inference(rewrite,[status(thm)],[])).
% 2.15/1.73 tff(3258,plain,
% 2.15/1.73 (((~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a744) | c1_1(a744) | (~c0_1(a744)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692)) <=> (c1_1(a744) | c3_1(a744) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c1_1(a697)) | (~c2_1(a697)) | (~c0_1(a744)))),
% 2.15/1.73 inference(rewrite,[status(thm)],[])).
% 2.15/1.73 tff(3259,plain,
% 2.15/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a744) | c1_1(a744) | (~c0_1(a744)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | (c1_1(a744) | c3_1(a744) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c1_1(a697)) | (~c2_1(a697)) | (~c0_1(a744))))),
% 2.15/1.73 inference(monotonicity,[status(thm)],[3258])).
% 2.15/1.73 tff(3260,plain,
% 2.15/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a744) | c1_1(a744) | (~c0_1(a744)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c1_1(a744) | c3_1(a744) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c1_1(a697)) | (~c2_1(a697)) | (~c0_1(a744)))),
% 2.15/1.73 inference(transitivity,[status(thm)],[3259, 3257])).
% 2.15/1.73 tff(3261,plain,
% 2.15/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a744) | c1_1(a744) | (~c0_1(a744)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692))),
% 2.15/1.73 inference(quant_inst,[status(thm)],[])).
% 2.15/1.73 tff(3262,plain,
% 2.15/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c1_1(a744) | c3_1(a744) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c1_1(a697)) | (~c2_1(a697)) | (~c0_1(a744))),
% 2.15/1.73 inference(modus_ponens,[status(thm)],[3261, 3260])).
% 2.15/1.73 tff(3263,plain,
% 2.15/1.73 (~c0_1(a744)),
% 2.15/1.73 inference(unit_resolution,[status(thm)],[3262, 227, 3204, 3256, 3255, 3249, 3181, 3226, 3225, 566, 3191])).
% 2.15/1.73 tff(3264,plain,
% 2.15/1.73 (((~hskp17) | (~c2_1(a744))) <=> ((~hskp17) | (~c2_1(a744)))),
% 2.15/1.73 inference(rewrite,[status(thm)],[])).
% 2.15/1.73 tff(3265,plain,
% 2.15/1.73 (((~c2_1(a744)) | (~hskp17)) <=> ((~hskp17) | (~c2_1(a744)))),
% 2.15/1.73 inference(rewrite,[status(thm)],[])).
% 2.15/1.73 tff(3266,axiom,((~c2_1(a744)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause104')).
% 2.15/1.73 tff(3267,plain,
% 2.15/1.73 ((~hskp17) | (~c2_1(a744))),
% 2.15/1.73 inference(modus_ponens,[status(thm)],[3266, 3265])).
% 2.15/1.73 tff(3268,plain,
% 2.15/1.73 ((~hskp17) | (~c2_1(a744))),
% 2.15/1.73 inference(modus_ponens,[status(thm)],[3267, 3264])).
% 2.15/1.73 tff(3269,plain,
% 2.15/1.73 (~c2_1(a744)),
% 2.15/1.73 inference(unit_resolution,[status(thm)],[3268, 3243])).
% 2.15/1.73 tff(3270,plain,
% 2.15/1.73 (((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp16 | c2_1(a717) | (~ndr1_0) | (~c3_1(a717)) | (~c1_1(a717)))) <=> ((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp16 | c2_1(a717) | (~ndr1_0) | (~c3_1(a717)) | (~c1_1(a717)))),
% 2.15/1.73 inference(rewrite,[status(thm)],[])).
% 2.15/1.73 tff(3271,plain,
% 2.15/1.73 ((hskp20 | hskp16 | (~ndr1_0) | c2_1(a717) | (~c3_1(a717)) | (~c1_1(a717))) <=> (hskp20 | hskp16 | c2_1(a717) | (~ndr1_0) | (~c3_1(a717)) | (~c1_1(a717)))),
% 2.15/1.73 inference(rewrite,[status(thm)],[])).
% 2.15/1.73 tff(3272,plain,
% 2.15/1.73 (((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp16 | (~ndr1_0) | c2_1(a717) | (~c3_1(a717)) | (~c1_1(a717)))) <=> ((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp16 | c2_1(a717) | (~ndr1_0) | (~c3_1(a717)) | (~c1_1(a717))))),
% 2.15/1.73 inference(monotonicity,[status(thm)],[3271])).
% 2.15/1.73 tff(3273,plain,
% 2.15/1.73 (((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp16 | (~ndr1_0) | c2_1(a717) | (~c3_1(a717)) | (~c1_1(a717)))) <=> ((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp16 | c2_1(a717) | (~ndr1_0) | (~c3_1(a717)) | (~c1_1(a717)))),
% 2.15/1.73 inference(transitivity,[status(thm)],[3272, 3270])).
% 2.15/1.73 tff(3274,plain,
% 2.15/1.73 ((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp16 | (~ndr1_0) | c2_1(a717) | (~c3_1(a717)) | (~c1_1(a717)))),
% 2.15/1.73 inference(quant_inst,[status(thm)],[])).
% 2.15/1.73 tff(3275,plain,
% 2.15/1.73 ((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp16 | c2_1(a717) | (~ndr1_0) | (~c3_1(a717)) | (~c1_1(a717))),
% 2.15/1.73 inference(modus_ponens,[status(thm)],[3274, 3273])).
% 2.15/1.73 tff(3276,plain,
% 2.15/1.73 (hskp16),
% 2.15/1.73 inference(unit_resolution,[status(thm)],[3275, 227, 280, 3205, 3217, 3203, 3069])).
% 2.15/1.73 tff(3277,plain,
% 2.15/1.73 (c3_1(a738)),
% 2.15/1.73 inference(unit_resolution,[status(thm)],[3087, 3276])).
% 2.15/1.73 tff(3278,plain,
% 2.15/1.73 (c2_1(a738)),
% 2.15/1.73 inference(unit_resolution,[status(thm)],[3098, 3276])).
% 2.15/1.73 tff(3279,plain,
% 2.15/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a744) | c3_1(a744) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a738)) | c0_1(a744))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a744) | c3_1(a744) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a738)) | c0_1(a744))),
% 2.15/1.74 inference(rewrite,[status(thm)],[])).
% 2.15/1.74 tff(3280,plain,
% 2.15/1.74 (((~ndr1_0) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a738)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c3_1(a744) | c2_1(a744) | c0_1(a744)) <=> (c2_1(a744) | c3_1(a744) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a738)) | c0_1(a744))),
% 2.15/1.74 inference(rewrite,[status(thm)],[])).
% 2.15/1.74 tff(3281,plain,
% 2.15/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a738)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c3_1(a744) | c2_1(a744) | c0_1(a744))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a744) | c3_1(a744) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a738)) | c0_1(a744)))),
% 2.15/1.74 inference(monotonicity,[status(thm)],[3280])).
% 2.15/1.74 tff(3282,plain,
% 2.15/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a738)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c3_1(a744) | c2_1(a744) | c0_1(a744))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a744) | c3_1(a744) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a738)) | c0_1(a744))),
% 2.15/1.74 inference(transitivity,[status(thm)],[3281, 3279])).
% 2.15/1.74 tff(3283,plain,
% 2.15/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a738)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c3_1(a744) | c2_1(a744) | c0_1(a744))),
% 2.15/1.74 inference(quant_inst,[status(thm)],[])).
% 2.15/1.74 tff(3284,plain,
% 2.15/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a744) | c3_1(a744) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a738)) | c0_1(a744)),
% 2.15/1.74 inference(modus_ponens,[status(thm)],[3283, 3282])).
% 2.15/1.74 tff(3285,plain,
% 2.15/1.74 (~c0_1(a738)),
% 2.15/1.74 inference(unit_resolution,[status(thm)],[3284, 227, 3278, 3277, 3183, 3269, 3249, 3181, 1777, 3263, 3191])).
% 2.15/1.74 tff(3286,plain,
% 2.15/1.74 (~c1_1(a738)),
% 2.15/1.74 inference(unit_resolution,[status(thm)],[3121, 3276])).
% 2.15/1.74 tff(3287,plain,
% 2.15/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c1_1(a763) | c2_1(a763) | c1_1(a738) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a763)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c1_1(a763) | c2_1(a763) | c1_1(a738) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a763)))),
% 2.15/1.74 inference(rewrite,[status(thm)],[])).
% 2.15/1.74 tff(3288,plain,
% 2.15/1.74 (((~ndr1_0) | c3_1(a697) | (~c0_1(a697)) | (~c1_1(a697)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c2_1(a763) | (~c3_1(a763)) | c1_1(a763)) <=> (c1_1(a763) | c2_1(a763) | c1_1(a738) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a763)))),
% 2.15/1.74 inference(rewrite,[status(thm)],[])).
% 2.15/1.74 tff(3289,plain,
% 2.15/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a697) | (~c0_1(a697)) | (~c1_1(a697)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c2_1(a763) | (~c3_1(a763)) | c1_1(a763))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c1_1(a763) | c2_1(a763) | c1_1(a738) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a763))))),
% 2.15/1.74 inference(monotonicity,[status(thm)],[3288])).
% 2.15/1.74 tff(3290,plain,
% 2.15/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a697) | (~c0_1(a697)) | (~c1_1(a697)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c2_1(a763) | (~c3_1(a763)) | c1_1(a763))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c1_1(a763) | c2_1(a763) | c1_1(a738) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a763)))),
% 2.15/1.74 inference(transitivity,[status(thm)],[3289, 3287])).
% 2.15/1.74 tff(3291,plain,
% 2.15/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a697) | (~c0_1(a697)) | (~c1_1(a697)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c2_1(a763) | (~c3_1(a763)) | c1_1(a763))),
% 2.15/1.74 inference(quant_inst,[status(thm)],[])).
% 2.15/1.74 tff(3292,plain,
% 2.15/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c1_1(a763) | c2_1(a763) | c1_1(a738) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a763))),
% 2.15/1.74 inference(modus_ponens,[status(thm)],[3291, 3290])).
% 2.15/1.74 tff(3293,plain,
% 2.15/1.74 (~c3_1(a763)),
% 2.15/1.74 inference(unit_resolution,[status(thm)],[3292, 227, 3278, 3277, 3183, 411, 1806, 3286, 3181, 3116, 3191])).
% 2.15/1.74 tff(3294,plain,
% 2.15/1.74 (hskp7),
% 2.15/1.74 inference(unit_resolution,[status(thm)],[3135, 227, 3046, 3278, 3277, 3286, 2842])).
% 2.15/1.74 tff(3295,plain,
% 2.15/1.74 (~c3_1(a708)),
% 2.15/1.74 inference(unit_resolution,[status(thm)],[3141, 3294])).
% 2.15/1.74 tff(3296,plain,
% 2.15/1.74 (c2_1(a708)),
% 2.15/1.74 inference(unit_resolution,[status(thm)],[3152, 3294])).
% 2.15/1.74 tff(3297,plain,
% 2.15/1.74 (c1_1(a708)),
% 2.15/1.74 inference(unit_resolution,[status(thm)],[3163, 3294])).
% 2.15/1.74 tff(3298,plain,
% 2.15/1.74 ($false),
% 2.15/1.74 inference(unit_resolution,[status(thm)],[3170, 227, 1809, 3278, 3297, 3296, 411, 3286, 3295, 566, 3293, 3285])).
% 2.15/1.74 tff(3299,plain,(c3_1(a695) | (~c0_1(a763)) | c2_1(a763) | hskp13 | hskp20 | (~c1_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a733)) | (~hskp23)), inference(lemma,lemma(discharge,[]))).
% 2.15/1.74 tff(3300,plain,
% 2.15/1.74 (c3_1(a695)),
% 2.15/1.74 inference(unit_resolution,[status(thm)],[3299, 3046, 1806, 1809, 280, 3045, 1755, 1756, 2259, 2258, 2257, 399])).
% 2.15/1.74 tff(3301,assumption,(c3_1(a695)), introduced(assumption)).
% 2.15/1.74 tff(3302,assumption,(hskp7), introduced(assumption)).
% 2.15/1.74 tff(3303,plain,
% 2.15/1.74 (~c3_1(a708)),
% 2.15/1.74 inference(unit_resolution,[status(thm)],[3141, 3302])).
% 2.15/1.74 tff(3304,plain,
% 2.15/1.74 (c2_1(a708)),
% 2.15/1.74 inference(unit_resolution,[status(thm)],[3152, 3302])).
% 2.15/1.74 tff(3305,plain,
% 2.15/1.74 (c1_1(a708)),
% 2.15/1.74 inference(unit_resolution,[status(thm)],[3163, 3302])).
% 2.15/1.74 tff(3306,plain,
% 2.15/1.74 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | c3_1(a708) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c1_1(a708)) | (~c2_1(a708)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a708) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c1_1(a708)) | (~c2_1(a708)))),
% 2.15/1.74 inference(rewrite,[status(thm)],[])).
% 2.15/1.74 tff(3307,plain,
% 2.15/1.74 ((hskp20 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a708) | (~c2_1(a708)) | (~c1_1(a708))) <=> (hskp20 | c3_1(a708) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c1_1(a708)) | (~c2_1(a708)))),
% 2.15/1.74 inference(rewrite,[status(thm)],[])).
% 2.15/1.74 tff(3308,plain,
% 2.15/1.74 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a708) | (~c2_1(a708)) | (~c1_1(a708)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | c3_1(a708) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c1_1(a708)) | (~c2_1(a708))))),
% 2.15/1.74 inference(monotonicity,[status(thm)],[3307])).
% 2.15/1.74 tff(3309,plain,
% 2.15/1.74 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a708) | (~c2_1(a708)) | (~c1_1(a708)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a708) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c1_1(a708)) | (~c2_1(a708)))),
% 2.15/1.74 inference(transitivity,[status(thm)],[3308, 3306])).
% 2.15/1.74 tff(3310,plain,
% 2.15/1.74 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a708) | (~c2_1(a708)) | (~c1_1(a708)))),
% 2.15/1.74 inference(quant_inst,[status(thm)],[])).
% 2.15/1.74 tff(3311,plain,
% 2.15/1.74 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a708) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c1_1(a708)) | (~c2_1(a708))),
% 2.15/1.74 inference(modus_ponens,[status(thm)],[3310, 3309])).
% 2.15/1.74 tff(3312,plain,
% 2.15/1.74 ($false),
% 2.15/1.74 inference(unit_resolution,[status(thm)],[3311, 227, 280, 2802, 2760, 3305, 3304, 3303, 2101, 3301])).
% 2.15/1.74 tff(3313,plain,((~hskp7) | hskp20 | (~c3_1(a695))), inference(lemma,lemma(discharge,[]))).
% 2.15/1.74 tff(3314,plain,
% 2.15/1.74 (~hskp7),
% 2.15/1.74 inference(unit_resolution,[status(thm)],[3313, 3300, 280])).
% 2.15/1.74 tff(3315,assumption,(hskp16), introduced(assumption)).
% 2.15/1.74 tff(3316,plain,
% 2.15/1.74 (~c1_1(a738)),
% 2.15/1.74 inference(unit_resolution,[status(thm)],[3121, 3315])).
% 2.15/1.74 tff(3317,plain,
% 2.15/1.74 (c3_1(a738)),
% 2.15/1.74 inference(unit_resolution,[status(thm)],[3087, 3315])).
% 2.15/1.74 tff(3318,plain,
% 2.15/1.74 (c2_1(a738)),
% 2.15/1.74 inference(unit_resolution,[status(thm)],[3098, 3315])).
% 2.15/1.74 tff(3319,assumption,(~hskp7), introduced(assumption)).
% 2.15/1.74 tff(3320,plain,
% 2.15/1.74 ($false),
% 2.15/1.74 inference(unit_resolution,[status(thm)],[3135, 227, 3046, 3319, 3318, 3317, 3316, 2842])).
% 2.15/1.74 tff(3321,plain,((~hskp16) | hskp13 | hskp7), inference(lemma,lemma(discharge,[]))).
% 2.15/1.74 tff(3322,plain,
% 2.15/1.74 (~hskp16),
% 2.15/1.74 inference(unit_resolution,[status(thm)],[3321, 3046, 3314])).
% 2.15/1.74 tff(3323,plain,
% 2.15/1.74 (^[U: $i] : refl((hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))),
% 2.15/1.74 inference(bind,[status(th)],[])).
% 2.15/1.74 tff(3324,plain,
% 2.15/1.74 (![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> ![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 2.15/1.74 inference(quant_intro,[status(thm)],[3323])).
% 2.15/1.74 tff(3325,plain,
% 2.15/1.74 (![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> ![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 2.15/1.74 inference(rewrite,[status(thm)],[])).
% 2.15/1.74 tff(3326,plain,
% 2.15/1.74 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_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) | c3_1(U) | c0_1(U) | c2_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp2) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp2))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp2) | hskp7) <=> ((hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp7))), rewrite(((hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp7) <=> (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp2) | hskp7) <=> (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))))),
% 2.15/1.74 inference(bind,[status(th)],[])).
% 2.15/1.74 tff(3327,plain,
% 2.15/1.74 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp2) | hskp7) <=> ![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 2.15/1.74 inference(quant_intro,[status(thm)],[3326])).
% 2.15/1.74 tff(3328,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp2) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause135')).
% 2.15/1.74 tff(3329,plain,
% 2.15/1.74 (![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 2.15/1.74 inference(modus_ponens,[status(thm)],[3328, 3327])).
% 2.15/1.74 tff(3330,plain,
% 2.15/1.74 (![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 2.15/1.74 inference(modus_ponens,[status(thm)],[3329, 3325])).
% 2.15/1.74 tff(3331,plain,(
% 2.15/1.74 ![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 2.15/1.74 inference(skolemize,[status(sab)],[3330])).
% 2.15/1.74 tff(3332,plain,
% 2.15/1.74 (![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 2.15/1.74 inference(modus_ponens,[status(thm)],[3331, 3324])).
% 2.15/1.74 tff(3333,plain,
% 2.15/1.74 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp7 | hskp2 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp7 | hskp2 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725))),
% 2.15/1.74 inference(rewrite,[status(thm)],[])).
% 2.15/1.74 tff(3334,plain,
% 2.15/1.74 ((hskp7 | hskp2 | (~ndr1_0) | c3_1(a725) | c0_1(a725) | c2_1(a725)) <=> (hskp7 | hskp2 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725))),
% 2.15/1.74 inference(rewrite,[status(thm)],[])).
% 2.15/1.74 tff(3335,plain,
% 2.15/1.74 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp7 | hskp2 | (~ndr1_0) | c3_1(a725) | c0_1(a725) | c2_1(a725))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp7 | hskp2 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725)))),
% 2.15/1.74 inference(monotonicity,[status(thm)],[3334])).
% 2.15/1.74 tff(3336,plain,
% 2.15/1.74 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp7 | hskp2 | (~ndr1_0) | c3_1(a725) | c0_1(a725) | c2_1(a725))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp7 | hskp2 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725))),
% 2.15/1.74 inference(transitivity,[status(thm)],[3335, 3333])).
% 2.15/1.74 tff(3337,plain,
% 2.15/1.74 ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp7 | hskp2 | (~ndr1_0) | c3_1(a725) | c0_1(a725) | c2_1(a725))),
% 2.15/1.74 inference(quant_inst,[status(thm)],[])).
% 2.15/1.74 tff(3338,plain,
% 2.15/1.74 ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp7 | hskp2 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a725)),
% 2.15/1.74 inference(modus_ponens,[status(thm)],[3337, 3336])).
% 2.15/1.74 tff(3339,plain,
% 2.15/1.74 (hskp7 | hskp2 | c2_1(a725)),
% 2.15/1.74 inference(unit_resolution,[status(thm)],[3338, 227, 578, 1037, 3332])).
% 2.15/1.74 tff(3340,plain,
% 2.15/1.74 (hskp2),
% 2.15/1.74 inference(unit_resolution,[status(thm)],[3339, 3047, 3319])).
% 2.15/1.74 tff(3341,plain,
% 2.15/1.74 (~c3_1(a697)),
% 2.15/1.74 inference(unit_resolution,[status(thm)],[1355, 498])).
% 2.15/1.74 tff(3342,plain,
% 2.15/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a725) | c3_1(a725) | c3_1(a697) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c0_1(a697)) | (~c1_1(a697)) | c2_1(a725))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a725) | c3_1(a725) | c3_1(a697) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c0_1(a697)) | (~c1_1(a697)) | c2_1(a725))),
% 2.15/1.74 inference(rewrite,[status(thm)],[])).
% 2.15/1.74 tff(3343,plain,
% 2.15/1.74 (((~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c3_1(a725) | c2_1(a725) | c0_1(a725)) <=> (c0_1(a725) | c3_1(a725) | c3_1(a697) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c0_1(a697)) | (~c1_1(a697)) | c2_1(a725))),
% 2.15/1.74 inference(rewrite,[status(thm)],[])).
% 2.15/1.74 tff(3344,plain,
% 2.15/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c3_1(a725) | c2_1(a725) | c0_1(a725))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a725) | c3_1(a725) | c3_1(a697) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c0_1(a697)) | (~c1_1(a697)) | c2_1(a725)))),
% 2.15/1.74 inference(monotonicity,[status(thm)],[3343])).
% 2.15/1.74 tff(3345,plain,
% 2.15/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c3_1(a725) | c2_1(a725) | c0_1(a725))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a725) | c3_1(a725) | c3_1(a697) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c0_1(a697)) | (~c1_1(a697)) | c2_1(a725))),
% 2.15/1.74 inference(transitivity,[status(thm)],[3344, 3342])).
% 2.15/1.74 tff(3346,plain,
% 2.15/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c3_1(a725) | c2_1(a725) | c0_1(a725))),
% 2.15/1.74 inference(quant_inst,[status(thm)],[])).
% 2.15/1.74 tff(3347,plain,
% 2.15/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a725) | c3_1(a725) | c3_1(a697) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c0_1(a697)) | (~c1_1(a697)) | c2_1(a725)),
% 2.15/1.74 inference(modus_ponens,[status(thm)],[3346, 3345])).
% 2.15/1.74 tff(3348,plain,
% 2.15/1.74 (~c1_1(a697)),
% 2.15/1.74 inference(unit_resolution,[status(thm)],[3347, 227, 2802, 2760, 509, 578, 1037, 3341, 1777, 3047, 3301])).
% 2.15/1.74 tff(3349,plain,
% 2.15/1.74 (^[U: $i] : refl((hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 2.15/1.74 inference(bind,[status(th)],[])).
% 2.15/1.74 tff(3350,plain,
% 2.15/1.74 (![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 2.15/1.74 inference(quant_intro,[status(thm)],[3349])).
% 2.15/1.74 tff(3351,plain,
% 2.15/1.74 (![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 2.15/1.74 inference(rewrite,[status(thm)],[])).
% 2.15/1.74 tff(3352,plain,
% 2.15/1.74 (^[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)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp7) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp7))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp7) <=> (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp7) | hskp16) <=> ((hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp16))), rewrite(((hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp16) <=> (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp7) | hskp16) <=> (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 2.15/1.74 inference(bind,[status(th)],[])).
% 2.15/1.74 tff(3353,plain,
% 2.15/1.74 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp7) | hskp16) <=> ![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 2.15/1.74 inference(quant_intro,[status(thm)],[3352])).
% 2.15/1.74 tff(3354,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp7) | hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause145')).
% 2.15/1.74 tff(3355,plain,
% 2.15/1.74 (![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 2.15/1.74 inference(modus_ponens,[status(thm)],[3354, 3353])).
% 2.15/1.74 tff(3356,plain,
% 2.15/1.74 (![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 2.15/1.74 inference(modus_ponens,[status(thm)],[3355, 3351])).
% 2.15/1.74 tff(3357,plain,(
% 2.15/1.74 ![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 2.15/1.74 inference(skolemize,[status(sab)],[3356])).
% 2.15/1.74 tff(3358,plain,
% 2.15/1.74 (![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 2.15/1.74 inference(modus_ponens,[status(thm)],[3357, 3350])).
% 2.15/1.74 tff(3359,plain,
% 2.15/1.74 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a697)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a697)))),
% 2.15/1.74 inference(rewrite,[status(thm)],[])).
% 2.15/1.74 tff(3360,plain,
% 2.15/1.74 ((hskp16 | hskp7 | (~ndr1_0) | c1_1(a697) | (~c2_1(a697)) | (~c0_1(a697))) <=> (hskp16 | hskp7 | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a697)))),
% 2.15/1.74 inference(rewrite,[status(thm)],[])).
% 2.15/1.74 tff(3361,plain,
% 2.15/1.74 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c1_1(a697) | (~c2_1(a697)) | (~c0_1(a697)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a697))))),
% 2.15/1.74 inference(monotonicity,[status(thm)],[3360])).
% 2.15/1.74 tff(3362,plain,
% 2.15/1.74 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c1_1(a697) | (~c2_1(a697)) | (~c0_1(a697)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a697)))),
% 2.15/1.74 inference(transitivity,[status(thm)],[3361, 3359])).
% 2.15/1.74 tff(3363,plain,
% 2.15/1.74 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c1_1(a697) | (~c2_1(a697)) | (~c0_1(a697)))),
% 2.15/1.74 inference(quant_inst,[status(thm)],[])).
% 2.15/1.74 tff(3364,plain,
% 2.15/1.74 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a697))),
% 2.15/1.74 inference(modus_ponens,[status(thm)],[3363, 3362])).
% 2.15/1.74 tff(3365,plain,
% 2.15/1.74 (hskp7 | c1_1(a697)),
% 2.15/1.74 inference(unit_resolution,[status(thm)],[3364, 227, 12, 509, 528, 3358])).
% 2.15/1.74 tff(3366,plain,
% 2.15/1.74 (hskp7),
% 2.15/1.74 inference(unit_resolution,[status(thm)],[3365, 3348])).
% 2.15/1.74 tff(3367,plain,
% 2.15/1.74 (~c3_1(a708)),
% 2.15/1.74 inference(unit_resolution,[status(thm)],[3141, 3366])).
% 2.15/1.74 tff(3368,plain,
% 2.15/1.74 (c2_1(a708)),
% 2.15/1.74 inference(unit_resolution,[status(thm)],[3152, 3366])).
% 2.15/1.74 tff(3369,plain,
% 2.15/1.74 (c1_1(a708)),
% 2.15/1.74 inference(unit_resolution,[status(thm)],[3163, 3366])).
% 2.15/1.74 tff(3370,plain,
% 2.15/1.74 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp16 | c3_1(a708) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a697)) | (~c1_1(a708)) | (~c2_1(a708)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp16 | c3_1(a708) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a697)) | (~c1_1(a708)) | (~c2_1(a708)))),
% 2.15/1.74 inference(rewrite,[status(thm)],[])).
% 2.15/1.74 tff(3371,plain,
% 2.15/1.74 ((hskp16 | (~ndr1_0) | c3_1(a708) | (~c2_1(a708)) | (~c1_1(a708)) | c1_1(a697) | (~c2_1(a697)) | (~c0_1(a697))) <=> (hskp16 | c3_1(a708) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a697)) | (~c1_1(a708)) | (~c2_1(a708)))),
% 2.15/1.74 inference(rewrite,[status(thm)],[])).
% 2.15/1.74 tff(3372,plain,
% 2.15/1.74 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a708) | (~c2_1(a708)) | (~c1_1(a708)) | c1_1(a697) | (~c2_1(a697)) | (~c0_1(a697)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp16 | c3_1(a708) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a697)) | (~c1_1(a708)) | (~c2_1(a708))))),
% 2.15/1.74 inference(monotonicity,[status(thm)],[3371])).
% 2.15/1.74 tff(3373,plain,
% 2.15/1.74 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a708) | (~c2_1(a708)) | (~c1_1(a708)) | c1_1(a697) | (~c2_1(a697)) | (~c0_1(a697)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp16 | c3_1(a708) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a697)) | (~c1_1(a708)) | (~c2_1(a708)))),
% 2.15/1.74 inference(transitivity,[status(thm)],[3372, 3370])).
% 2.15/1.74 tff(3374,plain,
% 2.15/1.74 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a708) | (~c2_1(a708)) | (~c1_1(a708)) | c1_1(a697) | (~c2_1(a697)) | (~c0_1(a697)))),
% 2.15/1.74 inference(quant_inst,[status(thm)],[])).
% 2.15/1.74 tff(3375,plain,
% 2.15/1.74 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp16 | c3_1(a708) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c2_1(a697)) | (~c1_1(a708)) | (~c2_1(a708))),
% 2.15/1.74 inference(modus_ponens,[status(thm)],[3374, 3373])).
% 2.15/1.74 tff(3376,plain,
% 2.15/1.74 ($false),
% 2.15/1.74 inference(unit_resolution,[status(thm)],[3375, 227, 12, 3369, 3368, 509, 528, 3367, 22, 3348])).
% 2.15/1.74 tff(3377,plain,((~hskp3) | hskp16 | c0_1(a725) | c3_1(a725) | c2_1(a725) | (~c3_1(a695))), inference(lemma,lemma(discharge,[]))).
% 2.15/1.74 tff(3378,plain,
% 2.15/1.74 (~hskp3),
% 2.15/1.74 inference(unit_resolution,[status(thm)],[3377, 3047, 578, 1037, 12, 3301])).
% 2.15/1.74 tff(3379,assumption,(hskp2), introduced(assumption)).
% 2.15/1.74 tff(3380,plain,
% 2.15/1.74 (~c2_1(a696)),
% 2.15/1.74 inference(unit_resolution,[status(thm)],[1971, 3379])).
% 2.15/1.74 tff(3381,plain,
% 2.15/1.74 (c1_1(a696)),
% 2.15/1.74 inference(unit_resolution,[status(thm)],[2000, 3379])).
% 2.15/1.74 tff(3382,plain,
% 2.15/1.74 (c0_1(a696)),
% 2.15/1.74 inference(unit_resolution,[status(thm)],[1982, 3379])).
% 2.15/1.74 tff(3383,plain,
% 2.15/1.74 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp3 | c1_1(a725) | c3_1(a725) | c2_1(a696) | (~ndr1_0) | (~c1_1(a696)) | (~c0_1(a696)) | c2_1(a725))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp3 | c1_1(a725) | c3_1(a725) | c2_1(a696) | (~ndr1_0) | (~c1_1(a696)) | (~c0_1(a696)) | c2_1(a725))),
% 2.15/1.74 inference(rewrite,[status(thm)],[])).
% 2.15/1.75 tff(3384,plain,
% 2.15/1.75 ((hskp3 | (~ndr1_0) | c2_1(a696) | (~c0_1(a696)) | (~c1_1(a696)) | c3_1(a725) | c1_1(a725) | c2_1(a725)) <=> (hskp3 | c1_1(a725) | c3_1(a725) | c2_1(a696) | (~ndr1_0) | (~c1_1(a696)) | (~c0_1(a696)) | c2_1(a725))),
% 2.15/1.75 inference(rewrite,[status(thm)],[])).
% 2.15/1.75 tff(3385,plain,
% 2.15/1.75 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a696) | (~c0_1(a696)) | (~c1_1(a696)) | c3_1(a725) | c1_1(a725) | c2_1(a725))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp3 | c1_1(a725) | c3_1(a725) | c2_1(a696) | (~ndr1_0) | (~c1_1(a696)) | (~c0_1(a696)) | c2_1(a725)))),
% 2.15/1.75 inference(monotonicity,[status(thm)],[3384])).
% 2.15/1.75 tff(3386,plain,
% 2.15/1.75 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a696) | (~c0_1(a696)) | (~c1_1(a696)) | c3_1(a725) | c1_1(a725) | c2_1(a725))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp3 | c1_1(a725) | c3_1(a725) | c2_1(a696) | (~ndr1_0) | (~c1_1(a696)) | (~c0_1(a696)) | c2_1(a725))),
% 2.15/1.75 inference(transitivity,[status(thm)],[3385, 3383])).
% 2.15/1.75 tff(3387,plain,
% 2.15/1.75 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a696) | (~c0_1(a696)) | (~c1_1(a696)) | c3_1(a725) | c1_1(a725) | c2_1(a725))),
% 2.15/1.75 inference(quant_inst,[status(thm)],[])).
% 2.15/1.75 tff(3388,plain,
% 2.15/1.75 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp3 | c1_1(a725) | c3_1(a725) | c2_1(a696) | (~ndr1_0) | (~c1_1(a696)) | (~c0_1(a696)) | c2_1(a725)),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3387, 3386])).
% 2.15/1.75 tff(3389,plain,
% 2.15/1.75 ($false),
% 2.15/1.75 inference(unit_resolution,[status(thm)],[3388, 227, 2236, 3382, 3381, 577, 1037, 3380, 1671, 3047])).
% 2.15/1.75 tff(3390,plain,((~hskp2) | hskp3 | c1_1(a725) | c3_1(a725) | c2_1(a725)), inference(lemma,lemma(discharge,[]))).
% 2.15/1.75 tff(3391,plain,
% 2.15/1.75 ($false),
% 2.15/1.75 inference(unit_resolution,[status(thm)],[3390, 3378, 3340, 577, 1037, 3047])).
% 2.15/1.75 tff(3392,plain,(c2_1(a725) | c1_1(a725) | c3_1(a725) | c0_1(a725) | hskp16 | (~c3_1(a695)) | hskp7), inference(lemma,lemma(discharge,[]))).
% 2.15/1.75 tff(3393,plain,
% 2.15/1.75 (c2_1(a725)),
% 2.15/1.75 inference(unit_resolution,[status(thm)],[3392, 3182, 3049, 3050, 3322, 3300, 3314])).
% 2.15/1.75 tff(3394,plain,
% 2.15/1.75 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c2_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c2_1(a725)))),
% 2.15/1.75 inference(rewrite,[status(thm)],[])).
% 2.15/1.75 tff(3395,plain,
% 2.15/1.75 ((hskp14 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a725) | c1_1(a725) | (~c2_1(a725))) <=> (hskp14 | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c2_1(a725)))),
% 2.15/1.75 inference(rewrite,[status(thm)],[])).
% 2.15/1.75 tff(3396,plain,
% 2.15/1.75 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a725) | c1_1(a725) | (~c2_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c2_1(a725))))),
% 2.15/1.75 inference(monotonicity,[status(thm)],[3395])).
% 2.15/1.75 tff(3397,plain,
% 2.15/1.75 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a725) | c1_1(a725) | (~c2_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c2_1(a725)))),
% 2.15/1.75 inference(transitivity,[status(thm)],[3396, 3394])).
% 2.15/1.75 tff(3398,plain,
% 2.15/1.75 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a725) | c1_1(a725) | (~c2_1(a725)))),
% 2.15/1.75 inference(quant_inst,[status(thm)],[])).
% 2.15/1.75 tff(3399,plain,
% 2.15/1.75 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c2_1(a725))),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3398, 3397])).
% 2.15/1.75 tff(3400,plain,
% 2.15/1.75 (hskp14 | (~c3_1(a695)) | (~c2_1(a725))),
% 2.15/1.75 inference(unit_resolution,[status(thm)],[3399, 227, 2802, 2760, 3182, 3049, 1614])).
% 2.15/1.75 tff(3401,plain,
% 2.15/1.75 (hskp14),
% 2.15/1.75 inference(unit_resolution,[status(thm)],[3400, 3393, 3300])).
% 2.15/1.75 tff(3402,plain,
% 2.15/1.75 (~c3_1(a730)),
% 2.15/1.75 inference(unit_resolution,[status(thm)],[486, 3401])).
% 2.15/1.75 tff(3403,plain,
% 2.15/1.75 (c0_1(a730)),
% 2.15/1.75 inference(unit_resolution,[status(thm)],[472, 3401])).
% 2.15/1.75 tff(3404,plain,
% 2.15/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a763) | c2_1(a763) | c3_1(a730) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a730)) | c2_1(a730) | (~c0_1(a763)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a763) | c2_1(a763) | c3_1(a730) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a730)) | c2_1(a730) | (~c0_1(a763)))),
% 2.15/1.75 inference(rewrite,[status(thm)],[])).
% 2.15/1.75 tff(3405,plain,
% 2.15/1.75 (((~ndr1_0) | c3_1(a730) | c2_1(a730) | (~c0_1(a730)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725))) <=> (c1_1(a763) | c2_1(a763) | c3_1(a730) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a730)) | c2_1(a730) | (~c0_1(a763)))),
% 2.15/1.75 inference(rewrite,[status(thm)],[])).
% 2.15/1.75 tff(3406,plain,
% 2.15/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a730) | c2_1(a730) | (~c0_1(a730)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a763) | c2_1(a763) | c3_1(a730) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a730)) | c2_1(a730) | (~c0_1(a763))))),
% 2.15/1.75 inference(monotonicity,[status(thm)],[3405])).
% 2.15/1.75 tff(3407,plain,
% 2.15/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a730) | c2_1(a730) | (~c0_1(a730)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a763) | c2_1(a763) | c3_1(a730) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a730)) | c2_1(a730) | (~c0_1(a763)))),
% 2.15/1.75 inference(transitivity,[status(thm)],[3406, 3404])).
% 2.15/1.75 tff(3408,plain,
% 2.15/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a730) | c2_1(a730) | (~c0_1(a730)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))),
% 2.15/1.75 inference(quant_inst,[status(thm)],[])).
% 2.15/1.75 tff(3409,plain,
% 2.15/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a763) | c2_1(a763) | c3_1(a730) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a730)) | c2_1(a730) | (~c0_1(a763))),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3408, 3407])).
% 2.15/1.75 tff(3410,plain,
% 2.15/1.75 (c2_1(a730)),
% 2.15/1.75 inference(unit_resolution,[status(thm)],[3409, 227, 1809, 3403, 411, 1806, 3402, 3050, 3049, 2445, 3393])).
% 2.15/1.75 tff(3411,plain,
% 2.15/1.75 (c1_1(a730)),
% 2.15/1.75 inference(unit_resolution,[status(thm)],[461, 3401])).
% 2.15/1.75 tff(3412,plain,
% 2.15/1.75 ((hskp29 | hskp13 | hskp7) <=> (hskp29 | hskp13 | hskp7)),
% 2.15/1.75 inference(rewrite,[status(thm)],[])).
% 2.15/1.75 tff(3413,plain,
% 2.15/1.75 (((hskp29 | hskp7) | hskp13) <=> (hskp29 | hskp13 | hskp7)),
% 2.15/1.75 inference(rewrite,[status(thm)],[])).
% 2.15/1.75 tff(3414,axiom,((hskp29 | hskp7) | hskp13), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause35')).
% 2.15/1.75 tff(3415,plain,
% 2.15/1.75 (hskp29 | hskp13 | hskp7),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3414, 3413])).
% 2.15/1.75 tff(3416,plain,
% 2.15/1.75 (hskp29 | hskp13 | hskp7),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3415, 3412])).
% 2.15/1.75 tff(3417,plain,
% 2.15/1.75 (hskp29 | hskp13 | hskp7),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3416, 3412])).
% 2.15/1.75 tff(3418,plain,
% 2.15/1.75 (hskp29 | hskp13 | hskp7),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3417, 3412])).
% 2.15/1.75 tff(3419,plain,
% 2.15/1.75 (hskp29 | hskp13 | hskp7),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3418, 3412])).
% 2.15/1.75 tff(3420,plain,
% 2.15/1.75 (hskp29 | hskp13 | hskp7),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3419, 3412])).
% 2.15/1.75 tff(3421,plain,
% 2.15/1.75 (hskp29 | hskp13 | hskp7),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3420, 3412])).
% 2.15/1.75 tff(3422,plain,
% 2.15/1.75 (hskp29 | hskp13 | hskp7),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3421, 3412])).
% 2.15/1.75 tff(3423,plain,
% 2.15/1.75 (hskp29),
% 2.15/1.75 inference(unit_resolution,[status(thm)],[3422, 3314, 3046])).
% 2.15/1.75 tff(3424,plain,
% 2.15/1.75 (((~hskp29) | c3_1(a713)) <=> ((~hskp29) | c3_1(a713))),
% 2.15/1.75 inference(rewrite,[status(thm)],[])).
% 2.15/1.75 tff(3425,axiom,((~hskp29) | c3_1(a713)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause45')).
% 2.15/1.75 tff(3426,plain,
% 2.15/1.75 ((~hskp29) | c3_1(a713)),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3425, 3424])).
% 2.15/1.75 tff(3427,plain,
% 2.15/1.75 ((~hskp29) | c3_1(a713)),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3426, 3424])).
% 2.15/1.75 tff(3428,plain,
% 2.15/1.75 ((~hskp29) | c3_1(a713)),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3427, 3424])).
% 2.15/1.75 tff(3429,plain,
% 2.15/1.75 ((~hskp29) | c3_1(a713)),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3428, 3424])).
% 2.15/1.75 tff(3430,plain,
% 2.15/1.75 ((~hskp29) | c3_1(a713)),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3429, 3424])).
% 2.15/1.75 tff(3431,plain,
% 2.15/1.75 ((~hskp29) | c3_1(a713)),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3430, 3424])).
% 2.15/1.75 tff(3432,plain,
% 2.15/1.75 ((~hskp29) | c3_1(a713)),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3431, 3424])).
% 2.15/1.75 tff(3433,plain,
% 2.15/1.75 ((~hskp29) | c3_1(a713)),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3432, 3424])).
% 2.15/1.75 tff(3434,plain,
% 2.15/1.75 (c3_1(a713)),
% 2.15/1.75 inference(unit_resolution,[status(thm)],[3433, 3423])).
% 2.15/1.75 tff(3435,plain,
% 2.15/1.75 (((~hskp29) | c2_1(a713)) <=> ((~hskp29) | c2_1(a713))),
% 2.15/1.75 inference(rewrite,[status(thm)],[])).
% 2.15/1.75 tff(3436,axiom,((~hskp29) | c2_1(a713)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause44')).
% 2.15/1.75 tff(3437,plain,
% 2.15/1.75 ((~hskp29) | c2_1(a713)),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3436, 3435])).
% 2.15/1.75 tff(3438,plain,
% 2.15/1.75 ((~hskp29) | c2_1(a713)),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3437, 3435])).
% 2.15/1.75 tff(3439,plain,
% 2.15/1.75 ((~hskp29) | c2_1(a713)),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3438, 3435])).
% 2.15/1.75 tff(3440,plain,
% 2.15/1.75 ((~hskp29) | c2_1(a713)),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3439, 3435])).
% 2.15/1.75 tff(3441,plain,
% 2.15/1.75 ((~hskp29) | c2_1(a713)),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3440, 3435])).
% 2.15/1.75 tff(3442,plain,
% 2.15/1.75 ((~hskp29) | c2_1(a713)),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3441, 3435])).
% 2.15/1.75 tff(3443,plain,
% 2.15/1.75 ((~hskp29) | c2_1(a713)),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3442, 3435])).
% 2.15/1.75 tff(3444,plain,
% 2.15/1.75 ((~hskp29) | c2_1(a713)),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3443, 3435])).
% 2.15/1.75 tff(3445,plain,
% 2.15/1.75 (c2_1(a713)),
% 2.15/1.75 inference(unit_resolution,[status(thm)],[3444, 3423])).
% 2.15/1.75 tff(3446,plain,
% 2.15/1.75 (((~hskp29) | c0_1(a713)) <=> ((~hskp29) | c0_1(a713))),
% 2.15/1.75 inference(rewrite,[status(thm)],[])).
% 2.15/1.75 tff(3447,axiom,((~hskp29) | c0_1(a713)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause43')).
% 2.15/1.75 tff(3448,plain,
% 2.15/1.75 ((~hskp29) | c0_1(a713)),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3447, 3446])).
% 2.15/1.75 tff(3449,plain,
% 2.15/1.75 ((~hskp29) | c0_1(a713)),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3448, 3446])).
% 2.15/1.75 tff(3450,plain,
% 2.15/1.75 ((~hskp29) | c0_1(a713)),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3449, 3446])).
% 2.15/1.75 tff(3451,plain,
% 2.15/1.75 ((~hskp29) | c0_1(a713)),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3450, 3446])).
% 2.15/1.75 tff(3452,plain,
% 2.15/1.75 ((~hskp29) | c0_1(a713)),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3451, 3446])).
% 2.15/1.75 tff(3453,plain,
% 2.15/1.75 ((~hskp29) | c0_1(a713)),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3452, 3446])).
% 2.15/1.75 tff(3454,plain,
% 2.15/1.75 ((~hskp29) | c0_1(a713)),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3453, 3446])).
% 2.15/1.75 tff(3455,plain,
% 2.15/1.75 ((~hskp29) | c0_1(a713)),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3454, 3446])).
% 2.15/1.75 tff(3456,plain,
% 2.15/1.75 (c0_1(a713)),
% 2.15/1.75 inference(unit_resolution,[status(thm)],[3455, 3423])).
% 2.15/1.75 tff(3457,plain,
% 2.15/1.75 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | c3_1(a730) | (~ndr1_0) | (~c1_1(a730)) | (~c2_1(a730)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a730) | (~ndr1_0) | (~c1_1(a730)) | (~c2_1(a730)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713)))),
% 2.15/1.75 inference(rewrite,[status(thm)],[])).
% 2.15/1.75 tff(3458,plain,
% 2.15/1.75 ((hskp20 | (~ndr1_0) | (~c2_1(a713)) | (~c3_1(a713)) | (~c0_1(a713)) | c3_1(a730) | (~c2_1(a730)) | (~c1_1(a730))) <=> (hskp20 | c3_1(a730) | (~ndr1_0) | (~c1_1(a730)) | (~c2_1(a730)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713)))),
% 2.15/1.75 inference(rewrite,[status(thm)],[])).
% 2.15/1.75 tff(3459,plain,
% 2.15/1.75 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a713)) | (~c3_1(a713)) | (~c0_1(a713)) | c3_1(a730) | (~c2_1(a730)) | (~c1_1(a730)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | c3_1(a730) | (~ndr1_0) | (~c1_1(a730)) | (~c2_1(a730)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713))))),
% 2.15/1.75 inference(monotonicity,[status(thm)],[3458])).
% 2.15/1.75 tff(3460,plain,
% 2.15/1.75 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a713)) | (~c3_1(a713)) | (~c0_1(a713)) | c3_1(a730) | (~c2_1(a730)) | (~c1_1(a730)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a730) | (~ndr1_0) | (~c1_1(a730)) | (~c2_1(a730)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713)))),
% 2.15/1.75 inference(transitivity,[status(thm)],[3459, 3457])).
% 2.15/1.75 tff(3461,plain,
% 2.15/1.75 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a713)) | (~c3_1(a713)) | (~c0_1(a713)) | c3_1(a730) | (~c2_1(a730)) | (~c1_1(a730)))),
% 2.15/1.75 inference(quant_inst,[status(thm)],[])).
% 2.15/1.75 tff(3462,plain,
% 2.15/1.75 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | c3_1(a730) | (~ndr1_0) | (~c1_1(a730)) | (~c2_1(a730)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713))),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3461, 3460])).
% 2.15/1.75 tff(3463,plain,
% 2.15/1.75 ($false),
% 2.15/1.75 inference(unit_resolution,[status(thm)],[3462, 227, 280, 3456, 3445, 3434, 3411, 3402, 2101, 3410])).
% 2.15/1.75 tff(3464,plain,(hskp13 | hskp20 | (~c0_1(a763)) | c2_1(a763) | (~c1_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a733)) | (~hskp23)), inference(lemma,lemma(discharge,[]))).
% 2.15/1.75 tff(3465,plain,
% 2.15/1.75 ($false),
% 2.15/1.75 inference(unit_resolution,[status(thm)],[3464, 422, 399, 3046, 405, 3045, 1755, 1756, 2259, 2258, 2257, 280])).
% 2.15/1.75 tff(3466,plain,((~hskp23) | hskp13 | (~c1_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)) | (~c1_1(a733)) | (~c2_1(a733)) | (~c3_1(a733)) | hskp20), inference(lemma,lemma(discharge,[]))).
% 2.15/1.75 tff(3467,plain,
% 2.15/1.75 (~hskp23),
% 2.15/1.75 inference(unit_resolution,[status(thm)],[3466, 3041, 3044, 3043, 3042, 3002, 3003, 3001, 280])).
% 2.15/1.75 tff(3468,plain,
% 2.15/1.75 ((hskp23 | hskp13 | hskp11) <=> (hskp23 | hskp13 | hskp11)),
% 2.15/1.75 inference(rewrite,[status(thm)],[])).
% 2.15/1.75 tff(3469,plain,
% 2.15/1.75 (((hskp11 | hskp23) | hskp13) <=> (hskp23 | hskp13 | hskp11)),
% 2.15/1.75 inference(rewrite,[status(thm)],[])).
% 2.15/1.75 tff(3470,axiom,((hskp11 | hskp23) | hskp13), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause36')).
% 2.15/1.75 tff(3471,plain,
% 2.15/1.75 (hskp23 | hskp13 | hskp11),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3470, 3469])).
% 2.15/1.75 tff(3472,plain,
% 2.15/1.75 (hskp23 | hskp13 | hskp11),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3471, 3468])).
% 2.15/1.75 tff(3473,plain,
% 2.15/1.75 (hskp23 | hskp13 | hskp11),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3472, 3468])).
% 2.15/1.75 tff(3474,plain,
% 2.15/1.75 (hskp23 | hskp13 | hskp11),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3473, 3468])).
% 2.15/1.75 tff(3475,plain,
% 2.15/1.75 (hskp23 | hskp13 | hskp11),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3474, 3468])).
% 2.15/1.75 tff(3476,plain,
% 2.15/1.75 (hskp23 | hskp13 | hskp11),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3475, 3468])).
% 2.15/1.75 tff(3477,plain,
% 2.15/1.75 (hskp23 | hskp13 | hskp11),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3476, 3468])).
% 2.15/1.75 tff(3478,plain,
% 2.15/1.75 (hskp23 | hskp13 | hskp11),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3477, 3468])).
% 2.15/1.75 tff(3479,plain,
% 2.15/1.75 (hskp11),
% 2.15/1.75 inference(unit_resolution,[status(thm)],[3478, 3467, 3041])).
% 2.15/1.75 tff(3480,plain,
% 2.15/1.75 (~c1_1(a722)),
% 2.15/1.75 inference(unit_resolution,[status(thm)],[2191, 3479])).
% 2.15/1.75 tff(3481,plain,
% 2.15/1.75 (c3_1(a722)),
% 2.15/1.75 inference(unit_resolution,[status(thm)],[2386, 3479])).
% 2.15/1.75 tff(3482,plain,
% 2.15/1.75 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)))),
% 2.15/1.75 inference(rewrite,[status(thm)],[])).
% 2.15/1.75 tff(3483,plain,
% 2.15/1.75 ((hskp20 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695))) <=> (hskp20 | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)))),
% 2.15/1.75 inference(rewrite,[status(thm)],[])).
% 2.15/1.75 tff(3484,plain,
% 2.15/1.75 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695))))),
% 2.15/1.75 inference(monotonicity,[status(thm)],[3483])).
% 2.15/1.75 tff(3485,plain,
% 2.15/1.75 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)))),
% 2.15/1.75 inference(transitivity,[status(thm)],[3484, 3482])).
% 2.15/1.75 tff(3486,plain,
% 2.15/1.75 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a733)) | (~c3_1(a733)) | (~c0_1(a733)) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)))),
% 2.15/1.75 inference(quant_inst,[status(thm)],[])).
% 2.15/1.75 tff(3487,plain,
% 2.15/1.75 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp20 | (~ndr1_0) | (~c3_1(a733)) | (~c0_1(a733)) | (~c2_1(a733)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695))),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3486, 3485])).
% 2.15/1.75 tff(3488,plain,
% 2.15/1.75 (~c0_1(a733)),
% 2.15/1.75 inference(unit_resolution,[status(thm)],[3487, 227, 280, 3003, 3001, 2771, 2760, 2101, 11])).
% 2.15/1.75 tff(3489,plain,
% 2.15/1.75 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))),
% 2.15/1.75 inference(bind,[status(th)],[])).
% 2.15/1.75 tff(3490,plain,
% 2.15/1.75 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 2.15/1.75 inference(quant_intro,[status(thm)],[3489])).
% 2.15/1.75 tff(3491,plain,
% 2.15/1.75 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 2.15/1.75 inference(rewrite,[status(thm)],[])).
% 2.15/1.75 tff(3492,plain,
% 2.15/1.75 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp8) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp8))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))))),
% 2.15/1.75 inference(bind,[status(th)],[])).
% 2.15/1.75 tff(3493,plain,
% 2.15/1.75 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 2.15/1.75 inference(quant_intro,[status(thm)],[3492])).
% 2.15/1.75 tff(3494,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause185')).
% 2.15/1.75 tff(3495,plain,
% 2.15/1.75 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3494, 3493])).
% 2.15/1.75 tff(3496,plain,
% 2.15/1.75 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3495, 3491])).
% 2.15/1.75 tff(3497,plain,(
% 2.15/1.75 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 2.15/1.75 inference(skolemize,[status(sab)],[3496])).
% 2.15/1.75 tff(3498,plain,
% 2.15/1.75 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3497, 3490])).
% 2.15/1.75 tff(3499,plain,
% 2.15/1.75 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733)) | (~c1_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp8 | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733)) | (~c1_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 2.15/1.75 inference(rewrite,[status(thm)],[])).
% 2.15/1.75 tff(3500,plain,
% 2.15/1.75 ((hskp8 | (~ndr1_0) | (~c3_1(a691)) | (~c0_1(a691)) | (~c1_1(a691)) | c0_1(a733) | (~c2_1(a733)) | (~c3_1(a733))) <=> (hskp8 | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733)) | (~c1_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 2.15/1.75 inference(rewrite,[status(thm)],[])).
% 2.15/1.75 tff(3501,plain,
% 2.15/1.75 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a691)) | (~c0_1(a691)) | (~c1_1(a691)) | c0_1(a733) | (~c2_1(a733)) | (~c3_1(a733)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733)) | (~c1_1(a691)) | (~c3_1(a691)) | (~c0_1(a691))))),
% 2.15/1.75 inference(monotonicity,[status(thm)],[3500])).
% 2.15/1.75 tff(3502,plain,
% 2.15/1.75 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a691)) | (~c0_1(a691)) | (~c1_1(a691)) | c0_1(a733) | (~c2_1(a733)) | (~c3_1(a733)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp8 | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733)) | (~c1_1(a691)) | (~c3_1(a691)) | (~c0_1(a691)))),
% 2.15/1.75 inference(transitivity,[status(thm)],[3501, 3499])).
% 2.15/1.75 tff(3503,plain,
% 2.15/1.75 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a691)) | (~c0_1(a691)) | (~c1_1(a691)) | c0_1(a733) | (~c2_1(a733)) | (~c3_1(a733)))),
% 2.15/1.75 inference(quant_inst,[status(thm)],[])).
% 2.15/1.75 tff(3504,plain,
% 2.15/1.75 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp8 | (~ndr1_0) | (~c3_1(a733)) | c0_1(a733) | (~c2_1(a733)) | (~c1_1(a691)) | (~c3_1(a691)) | (~c0_1(a691))),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3503, 3502])).
% 2.15/1.75 tff(3505,plain,
% 2.15/1.75 (hskp8),
% 2.15/1.75 inference(unit_resolution,[status(thm)],[3504, 227, 3003, 3001, 3042, 3044, 3043, 3498, 3488])).
% 2.15/1.75 tff(3506,plain,
% 2.15/1.75 (~c0_1(a710)),
% 2.15/1.75 inference(unit_resolution,[status(thm)],[1875, 3505])).
% 2.15/1.75 tff(3507,plain,
% 2.15/1.75 (hskp11),
% 2.15/1.75 inference(unit_resolution,[status(thm)],[3478, 474, 3041])).
% 2.15/1.75 tff(3508,plain,
% 2.15/1.75 (~c1_1(a722)),
% 2.15/1.75 inference(unit_resolution,[status(thm)],[2191, 3507])).
% 2.15/1.75 tff(3509,plain,
% 2.15/1.75 (hskp24),
% 2.15/1.75 inference(unit_resolution,[status(thm)],[2884, 474])).
% 2.15/1.75 tff(3510,plain,
% 2.15/1.75 (~c3_1(a764)),
% 2.15/1.75 inference(unit_resolution,[status(thm)],[307, 3509])).
% 2.15/1.75 tff(3511,plain,
% 2.15/1.75 (~c2_1(a764)),
% 2.15/1.75 inference(unit_resolution,[status(thm)],[313, 3509])).
% 2.15/1.75 tff(3512,plain,
% 2.15/1.75 (c3_1(a710)),
% 2.15/1.75 inference(unit_resolution,[status(thm)],[1886, 3505])).
% 2.15/1.75 tff(3513,plain,
% 2.15/1.75 (c2_1(a710)),
% 2.15/1.75 inference(unit_resolution,[status(thm)],[1958, 3505])).
% 2.15/1.75 tff(3514,plain,
% 2.15/1.75 (c3_1(a722)),
% 2.15/1.75 inference(unit_resolution,[status(thm)],[2386, 3507])).
% 2.15/1.75 tff(3515,plain,
% 2.15/1.75 (c1_1(a764)),
% 2.15/1.75 inference(unit_resolution,[status(thm)],[324, 3509])).
% 2.15/1.75 tff(3516,plain,
% 2.15/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a764) | c3_1(a764) | c1_1(a722) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | (~c2_1(a722)) | (~c3_1(a722)) | (~c1_1(a764)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a764) | c3_1(a764) | c1_1(a722) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | (~c2_1(a722)) | (~c3_1(a722)) | (~c1_1(a764)))),
% 2.15/1.75 inference(rewrite,[status(thm)],[])).
% 2.15/1.75 tff(3517,plain,
% 2.15/1.75 (((~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c1_1(a722) | (~c2_1(a722)) | (~c3_1(a722)) | c0_1(a710) | (~c3_1(a710)) | (~c2_1(a710))) <=> (c2_1(a764) | c3_1(a764) | c1_1(a722) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | (~c2_1(a722)) | (~c3_1(a722)) | (~c1_1(a764)))),
% 2.15/1.75 inference(rewrite,[status(thm)],[])).
% 2.15/1.75 tff(3518,plain,
% 2.15/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c1_1(a722) | (~c2_1(a722)) | (~c3_1(a722)) | c0_1(a710) | (~c3_1(a710)) | (~c2_1(a710)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a764) | c3_1(a764) | c1_1(a722) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | (~c2_1(a722)) | (~c3_1(a722)) | (~c1_1(a764))))),
% 2.15/1.75 inference(monotonicity,[status(thm)],[3517])).
% 2.15/1.75 tff(3519,plain,
% 2.15/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c1_1(a722) | (~c2_1(a722)) | (~c3_1(a722)) | c0_1(a710) | (~c3_1(a710)) | (~c2_1(a710)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a764) | c3_1(a764) | c1_1(a722) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | (~c2_1(a722)) | (~c3_1(a722)) | (~c1_1(a764)))),
% 2.15/1.75 inference(transitivity,[status(thm)],[3518, 3516])).
% 2.15/1.75 tff(3520,plain,
% 2.15/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c1_1(a722) | (~c2_1(a722)) | (~c3_1(a722)) | c0_1(a710) | (~c3_1(a710)) | (~c2_1(a710)))),
% 2.15/1.75 inference(quant_inst,[status(thm)],[])).
% 2.15/1.75 tff(3521,plain,
% 2.15/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a764) | c3_1(a764) | c1_1(a722) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | (~c2_1(a722)) | (~c3_1(a722)) | (~c1_1(a764))),
% 2.15/1.75 inference(modus_ponens,[status(thm)],[3520, 3519])).
% 2.15/1.75 tff(3522,plain,
% 2.15/1.75 (~c2_1(a722)),
% 2.15/1.75 inference(unit_resolution,[status(thm)],[3521, 227, 3515, 3514, 3513, 3512, 3511, 3510, 3508, 3506, 10])).
% 2.15/1.75 tff(3523,plain,
% 2.15/1.75 (c0_1(a764)),
% 2.15/1.75 inference(unit_resolution,[status(thm)],[331, 227, 177, 3515, 3511, 3510, 301])).
% 2.15/1.76 tff(3524,plain,
% 2.15/1.76 (hskp12),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[2066, 3041, 280])).
% 2.15/1.76 tff(3525,plain,
% 2.15/1.76 (~c3_1(a725)),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[139, 3524])).
% 2.15/1.76 tff(3526,plain,
% 2.15/1.76 (~c0_1(a725)),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[151, 3524])).
% 2.15/1.76 tff(3527,plain,
% 2.15/1.76 (~c2_1(a725)),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[2858, 227, 177, 3515, 3511, 3510, 3526, 3525, 101])).
% 2.15/1.76 tff(3528,plain,
% 2.15/1.76 (~c2_1(a691)),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[3058, 3527, 3043, 3526, 3525, 3042, 11])).
% 2.15/1.76 tff(3529,plain,
% 2.15/1.76 (hskp20 | hskp16 | c2_1(a691)),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[3075, 227, 3044, 3043, 3069])).
% 2.15/1.76 tff(3530,plain,
% 2.15/1.76 (hskp16),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[3529, 3528, 280])).
% 2.15/1.76 tff(3531,plain,
% 2.15/1.76 (~c1_1(a738)),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[3121, 3530])).
% 2.15/1.76 tff(3532,plain,
% 2.15/1.76 (c3_1(a738)),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[3087, 3530])).
% 2.15/1.76 tff(3533,plain,
% 2.15/1.76 (c2_1(a738)),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[3098, 3530])).
% 2.15/1.76 tff(3534,plain,
% 2.15/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c3_1(a764) | c1_1(a738) | c1_1(a722) | (~ndr1_0) | c2_1(a722) | (~c3_1(a722)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a764)) | (~c1_1(a764)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c3_1(a764) | c1_1(a738) | c1_1(a722) | (~ndr1_0) | c2_1(a722) | (~c3_1(a722)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a764)) | (~c1_1(a764)))),
% 2.15/1.76 inference(rewrite,[status(thm)],[])).
% 2.15/1.76 tff(3535,plain,
% 2.15/1.76 (((~ndr1_0) | c3_1(a764) | (~c0_1(a764)) | (~c1_1(a764)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c2_1(a722) | (~c3_1(a722)) | c1_1(a722)) <=> (c3_1(a764) | c1_1(a738) | c1_1(a722) | (~ndr1_0) | c2_1(a722) | (~c3_1(a722)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a764)) | (~c1_1(a764)))),
% 2.15/1.76 inference(rewrite,[status(thm)],[])).
% 2.15/1.76 tff(3536,plain,
% 2.15/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a764) | (~c0_1(a764)) | (~c1_1(a764)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c2_1(a722) | (~c3_1(a722)) | c1_1(a722))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c3_1(a764) | c1_1(a738) | c1_1(a722) | (~ndr1_0) | c2_1(a722) | (~c3_1(a722)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a764)) | (~c1_1(a764))))),
% 2.15/1.76 inference(monotonicity,[status(thm)],[3535])).
% 2.15/1.76 tff(3537,plain,
% 2.15/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a764) | (~c0_1(a764)) | (~c1_1(a764)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c2_1(a722) | (~c3_1(a722)) | c1_1(a722))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c3_1(a764) | c1_1(a738) | c1_1(a722) | (~ndr1_0) | c2_1(a722) | (~c3_1(a722)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a764)) | (~c1_1(a764)))),
% 2.15/1.76 inference(transitivity,[status(thm)],[3536, 3534])).
% 2.15/1.76 tff(3538,plain,
% 2.15/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a764) | (~c0_1(a764)) | (~c1_1(a764)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c2_1(a722) | (~c3_1(a722)) | c1_1(a722))),
% 2.15/1.76 inference(quant_inst,[status(thm)],[])).
% 2.15/1.76 tff(3539,plain,
% 2.15/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c3_1(a764) | c1_1(a738) | c1_1(a722) | (~ndr1_0) | c2_1(a722) | (~c3_1(a722)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c0_1(a764)) | (~c1_1(a764))),
% 2.15/1.76 inference(modus_ponens,[status(thm)],[3538, 3537])).
% 2.15/1.76 tff(3540,plain,
% 2.15/1.76 ($false),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[3539, 227, 3515, 3533, 3532, 3514, 3510, 3531, 3508, 3116, 3523, 3522])).
% 2.15/1.76 tff(3541,plain,(hskp23 | hskp20 | c3_1(a695) | hskp6), inference(lemma,lemma(discharge,[]))).
% 2.15/1.76 tff(3542,plain,
% 2.15/1.76 (c3_1(a695)),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[3541, 3467, 280, 177])).
% 2.15/1.76 tff(3543,plain,
% 2.15/1.76 (~hskp7),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[3313, 3542, 280])).
% 2.15/1.76 tff(3544,plain,
% 2.15/1.76 (((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | c1_1(a722) | (~ndr1_0) | (~c2_1(a722)) | (~c3_1(a722)))) <=> ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp13 | hskp7 | c1_1(a722) | (~ndr1_0) | (~c2_1(a722)) | (~c3_1(a722)))),
% 2.15/1.76 inference(rewrite,[status(thm)],[])).
% 2.15/1.76 tff(3545,plain,
% 2.15/1.76 ((hskp13 | hskp7 | (~ndr1_0) | c1_1(a722) | (~c2_1(a722)) | (~c3_1(a722))) <=> (hskp13 | hskp7 | c1_1(a722) | (~ndr1_0) | (~c2_1(a722)) | (~c3_1(a722)))),
% 2.15/1.76 inference(rewrite,[status(thm)],[])).
% 2.15/1.76 tff(3546,plain,
% 2.15/1.76 (((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | (~ndr1_0) | c1_1(a722) | (~c2_1(a722)) | (~c3_1(a722)))) <=> ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | c1_1(a722) | (~ndr1_0) | (~c2_1(a722)) | (~c3_1(a722))))),
% 2.15/1.76 inference(monotonicity,[status(thm)],[3545])).
% 2.15/1.76 tff(3547,plain,
% 2.15/1.76 (((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | (~ndr1_0) | c1_1(a722) | (~c2_1(a722)) | (~c3_1(a722)))) <=> ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp13 | hskp7 | c1_1(a722) | (~ndr1_0) | (~c2_1(a722)) | (~c3_1(a722)))),
% 2.15/1.76 inference(transitivity,[status(thm)],[3546, 3544])).
% 2.15/1.76 tff(3548,plain,
% 2.15/1.76 ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | (~ndr1_0) | c1_1(a722) | (~c2_1(a722)) | (~c3_1(a722)))),
% 2.15/1.76 inference(quant_inst,[status(thm)],[])).
% 2.15/1.76 tff(3549,plain,
% 2.15/1.76 ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp13 | hskp7 | c1_1(a722) | (~ndr1_0) | (~c2_1(a722)) | (~c3_1(a722))),
% 2.15/1.76 inference(modus_ponens,[status(thm)],[3548, 3547])).
% 2.15/1.76 tff(3550,plain,
% 2.15/1.76 (~c2_1(a722)),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[3549, 227, 3041, 3543, 3481, 3480, 2842])).
% 2.15/1.76 tff(3551,plain,
% 2.15/1.76 (~c1_1(a725)),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[145, 3524])).
% 2.15/1.76 tff(3552,plain,
% 2.15/1.76 (~hskp16),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[3321, 3543, 3041])).
% 2.15/1.76 tff(3553,plain,
% 2.15/1.76 (c2_1(a725)),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[3392, 3552, 3525, 3526, 3551, 3542, 3543])).
% 2.15/1.76 tff(3554,plain,
% 2.15/1.76 (hskp14 | (~c3_1(a695)) | (~c2_1(a725))),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[3399, 227, 2802, 2760, 3551, 3525, 1614])).
% 2.15/1.76 tff(3555,plain,
% 2.15/1.76 (hskp14),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[3554, 3553, 3542])).
% 2.15/1.76 tff(3556,plain,
% 2.15/1.76 (~c3_1(a730)),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[486, 3555])).
% 2.15/1.76 tff(3557,plain,
% 2.15/1.76 (hskp24),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[2884, 3467])).
% 2.15/1.76 tff(3558,plain,
% 2.15/1.76 (~c3_1(a764)),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[307, 3557])).
% 2.15/1.76 tff(3559,plain,
% 2.15/1.76 (~c2_1(a764)),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[313, 3557])).
% 2.15/1.76 tff(3560,plain,
% 2.15/1.76 (c1_1(a730)),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[461, 3555])).
% 2.15/1.76 tff(3561,plain,
% 2.15/1.76 (c0_1(a730)),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[472, 3555])).
% 2.15/1.76 tff(3562,plain,
% 2.15/1.76 (hskp29),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[3422, 3543, 3041])).
% 2.15/1.76 tff(3563,plain,
% 2.15/1.76 (c3_1(a713)),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[3433, 3562])).
% 2.15/1.76 tff(3564,plain,
% 2.15/1.76 (c2_1(a713)),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[3444, 3562])).
% 2.15/1.76 tff(3565,plain,
% 2.15/1.76 (c0_1(a713)),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[3455, 3562])).
% 2.15/1.76 tff(3566,plain,
% 2.15/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a764) | c3_1(a764) | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713)) | c0_1(a764))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a764) | c3_1(a764) | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713)) | c0_1(a764))),
% 2.15/1.76 inference(rewrite,[status(thm)],[])).
% 2.15/1.76 tff(3567,plain,
% 2.15/1.76 (((~ndr1_0) | (~c2_1(a713)) | (~c3_1(a713)) | (~c0_1(a713)) | c3_1(a730) | (~c1_1(a730)) | (~c0_1(a730)) | c3_1(a764) | c2_1(a764) | c0_1(a764)) <=> (c2_1(a764) | c3_1(a764) | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713)) | c0_1(a764))),
% 2.15/1.76 inference(rewrite,[status(thm)],[])).
% 2.15/1.76 tff(3568,plain,
% 2.15/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a713)) | (~c3_1(a713)) | (~c0_1(a713)) | c3_1(a730) | (~c1_1(a730)) | (~c0_1(a730)) | c3_1(a764) | c2_1(a764) | c0_1(a764))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a764) | c3_1(a764) | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713)) | c0_1(a764)))),
% 2.15/1.76 inference(monotonicity,[status(thm)],[3567])).
% 2.15/1.76 tff(3569,plain,
% 2.15/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a713)) | (~c3_1(a713)) | (~c0_1(a713)) | c3_1(a730) | (~c1_1(a730)) | (~c0_1(a730)) | c3_1(a764) | c2_1(a764) | c0_1(a764))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a764) | c3_1(a764) | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713)) | c0_1(a764))),
% 2.15/1.76 inference(transitivity,[status(thm)],[3568, 3566])).
% 2.15/1.76 tff(3570,plain,
% 2.15/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a713)) | (~c3_1(a713)) | (~c0_1(a713)) | c3_1(a730) | (~c1_1(a730)) | (~c0_1(a730)) | c3_1(a764) | c2_1(a764) | c0_1(a764))),
% 2.15/1.76 inference(quant_inst,[status(thm)],[])).
% 2.15/1.76 tff(3571,plain,
% 2.15/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a764) | c3_1(a764) | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713)) | c0_1(a764)),
% 2.15/1.76 inference(modus_ponens,[status(thm)],[3570, 3569])).
% 2.15/1.76 tff(3572,plain,
% 2.15/1.76 (c0_1(a764)),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[3571, 227, 3565, 3564, 3563, 3561, 3560, 3559, 3558, 3556, 1777])).
% 2.15/1.76 tff(3573,plain,
% 2.15/1.76 (c0_1(a722)),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[2202, 3479])).
% 2.15/1.76 tff(3574,plain,
% 2.15/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a764) | c3_1(a764) | c0_1(a725) | c3_1(a725) | c1_1(a722) | (~ndr1_0) | c2_1(a722) | (~c0_1(a722)) | (~c2_1(a725)) | (~c0_1(a764)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a764) | c3_1(a764) | c0_1(a725) | c3_1(a725) | c1_1(a722) | (~ndr1_0) | c2_1(a722) | (~c0_1(a722)) | (~c2_1(a725)) | (~c0_1(a764)))),
% 2.15/1.76 inference(rewrite,[status(thm)],[])).
% 2.15/1.76 tff(3575,plain,
% 2.15/1.76 (((~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c0_1(a764)) | c1_1(a722) | c2_1(a722) | (~c0_1(a722)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725))) <=> (c2_1(a764) | c3_1(a764) | c0_1(a725) | c3_1(a725) | c1_1(a722) | (~ndr1_0) | c2_1(a722) | (~c0_1(a722)) | (~c2_1(a725)) | (~c0_1(a764)))),
% 2.15/1.76 inference(rewrite,[status(thm)],[])).
% 2.15/1.76 tff(3576,plain,
% 2.15/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c0_1(a764)) | c1_1(a722) | c2_1(a722) | (~c0_1(a722)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a764) | c3_1(a764) | c0_1(a725) | c3_1(a725) | c1_1(a722) | (~ndr1_0) | c2_1(a722) | (~c0_1(a722)) | (~c2_1(a725)) | (~c0_1(a764))))),
% 2.15/1.76 inference(monotonicity,[status(thm)],[3575])).
% 2.15/1.76 tff(3577,plain,
% 2.15/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c0_1(a764)) | c1_1(a722) | c2_1(a722) | (~c0_1(a722)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a764) | c3_1(a764) | c0_1(a725) | c3_1(a725) | c1_1(a722) | (~ndr1_0) | c2_1(a722) | (~c0_1(a722)) | (~c2_1(a725)) | (~c0_1(a764)))),
% 2.15/1.76 inference(transitivity,[status(thm)],[3576, 3574])).
% 2.15/1.76 tff(3578,plain,
% 2.15/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c0_1(a764)) | c1_1(a722) | c2_1(a722) | (~c0_1(a722)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))),
% 2.15/1.76 inference(quant_inst,[status(thm)],[])).
% 2.15/1.76 tff(3579,plain,
% 2.15/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a764) | c3_1(a764) | c0_1(a725) | c3_1(a725) | c1_1(a722) | (~ndr1_0) | c2_1(a722) | (~c0_1(a722)) | (~c2_1(a725)) | (~c0_1(a764))),
% 2.15/1.76 inference(modus_ponens,[status(thm)],[3578, 3577])).
% 2.15/1.76 tff(3580,plain,
% 2.15/1.76 ($false),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[3579, 227, 3573, 3559, 3558, 3526, 3525, 3480, 2445, 3553, 3572, 3550])).
% 2.15/1.76 tff(3581,plain,(hskp20 | hskp6), inference(lemma,lemma(discharge,[]))).
% 2.15/1.76 tff(3582,plain,
% 2.15/1.76 (hskp20),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[3581, 177])).
% 2.15/1.76 tff(3583,plain,
% 2.15/1.76 (~c3_1(a754)),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[668, 3582])).
% 2.15/1.76 tff(3584,plain,
% 2.15/1.76 (~c0_1(a754)),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[595, 3582])).
% 2.15/1.76 tff(3585,plain,
% 2.15/1.76 (c2_1(a754)),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[190, 3582])).
% 2.15/1.76 tff(3586,plain,
% 2.15/1.76 (~hskp24),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[1626, 3584, 177, 3585, 3583])).
% 2.15/1.76 tff(3587,plain,
% 2.15/1.76 (hskp23),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[2884, 3586])).
% 2.15/1.76 tff(3588,plain,
% 2.15/1.76 (~c2_1(a763)),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[404, 3587])).
% 2.15/1.76 tff(3589,plain,
% 2.15/1.76 (~c1_1(a763)),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[410, 3587])).
% 2.15/1.76 tff(3590,plain,
% 2.15/1.76 (c0_1(a763)),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[421, 3587])).
% 2.15/1.76 tff(3591,assumption,(~c3_1(a763)), introduced(assumption)).
% 2.15/1.76 tff(3592,plain,
% 2.15/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a763) | c2_1(a763) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c2_1(a754)) | c3_1(a763) | (~c0_1(a763)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a763) | c2_1(a763) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c2_1(a754)) | c3_1(a763) | (~c0_1(a763)))),
% 2.15/1.76 inference(rewrite,[status(thm)],[])).
% 2.15/1.76 tff(3593,plain,
% 2.15/1.76 (((~ndr1_0) | c3_1(a763) | c2_1(a763) | (~c0_1(a763)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754))) <=> (c1_1(a763) | c2_1(a763) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c2_1(a754)) | c3_1(a763) | (~c0_1(a763)))),
% 2.15/1.76 inference(rewrite,[status(thm)],[])).
% 2.15/1.76 tff(3594,plain,
% 2.15/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a763) | c2_1(a763) | (~c0_1(a763)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a763) | c2_1(a763) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c2_1(a754)) | c3_1(a763) | (~c0_1(a763))))),
% 2.15/1.76 inference(monotonicity,[status(thm)],[3593])).
% 2.15/1.76 tff(3595,plain,
% 2.15/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a763) | c2_1(a763) | (~c0_1(a763)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a763) | c2_1(a763) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c2_1(a754)) | c3_1(a763) | (~c0_1(a763)))),
% 2.15/1.76 inference(transitivity,[status(thm)],[3594, 3592])).
% 2.15/1.76 tff(3596,plain,
% 2.15/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a763) | c2_1(a763) | (~c0_1(a763)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))),
% 2.15/1.76 inference(quant_inst,[status(thm)],[])).
% 2.15/1.76 tff(3597,plain,
% 2.15/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a763) | c2_1(a763) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c2_1(a754)) | c3_1(a763) | (~c0_1(a763))),
% 2.15/1.76 inference(modus_ponens,[status(thm)],[3596, 3595])).
% 2.15/1.76 tff(3598,plain,
% 2.15/1.76 ($false),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[3597, 227, 1809, 387, 1807, 1806, 179, 178, 2445, 3591])).
% 2.15/1.76 tff(3599,plain,(c3_1(a763) | (~c0_1(a763)) | (~c2_1(a754)) | c1_1(a763) | c2_1(a763) | c0_1(a754) | c3_1(a754)), inference(lemma,lemma(discharge,[]))).
% 2.15/1.76 tff(3600,plain,
% 2.15/1.76 (c3_1(a763)),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[3599, 3590, 3585, 3589, 3588, 3584, 3583])).
% 2.15/1.76 tff(3601,plain,
% 2.15/1.76 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c0_1(a760) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c2_1(a754)) | (~c3_1(a760)) | (~c1_1(a760)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a760) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c2_1(a754)) | (~c3_1(a760)) | (~c1_1(a760)))),
% 2.15/1.76 inference(rewrite,[status(thm)],[])).
% 2.15/1.76 tff(3602,plain,
% 2.15/1.76 ((hskp10 | (~ndr1_0) | c0_1(a760) | (~c3_1(a760)) | (~c1_1(a760)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754))) <=> (hskp10 | c0_1(a760) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c2_1(a754)) | (~c3_1(a760)) | (~c1_1(a760)))),
% 2.15/1.76 inference(rewrite,[status(thm)],[])).
% 2.15/1.76 tff(3603,plain,
% 2.15/1.76 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a760) | (~c3_1(a760)) | (~c1_1(a760)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c0_1(a760) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c2_1(a754)) | (~c3_1(a760)) | (~c1_1(a760))))),
% 2.15/1.76 inference(monotonicity,[status(thm)],[3602])).
% 2.15/1.76 tff(3604,plain,
% 2.15/1.76 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a760) | (~c3_1(a760)) | (~c1_1(a760)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a760) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c2_1(a754)) | (~c3_1(a760)) | (~c1_1(a760)))),
% 2.15/1.76 inference(transitivity,[status(thm)],[3603, 3601])).
% 2.15/1.76 tff(3605,plain,
% 2.15/1.76 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a760) | (~c3_1(a760)) | (~c1_1(a760)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))),
% 2.15/1.76 inference(quant_inst,[status(thm)],[])).
% 2.15/1.76 tff(3606,plain,
% 2.15/1.76 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a760) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c2_1(a754)) | (~c3_1(a760)) | (~c1_1(a760))),
% 2.15/1.76 inference(modus_ponens,[status(thm)],[3605, 3604])).
% 2.15/1.76 tff(3607,plain,
% 2.15/1.76 (hskp10),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[3606, 227, 3194, 3193, 3585, 3192, 3584, 3583, 1749])).
% 2.15/1.76 tff(3608,plain,
% 2.15/1.76 (~c2_1(a717)),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[1893, 3607])).
% 2.15/1.76 tff(3609,plain,
% 2.15/1.76 (c1_1(a717)),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[3023, 3607])).
% 2.15/1.76 tff(3610,plain,
% 2.15/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a717) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | c0_1(a717) | (~c1_1(a717)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a717) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | c0_1(a717) | (~c1_1(a717)))),
% 2.15/1.76 inference(rewrite,[status(thm)],[])).
% 2.15/1.76 tff(3611,plain,
% 2.15/1.76 (((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c2_1(a717) | c0_1(a717) | (~c1_1(a717))) <=> (c2_1(a717) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | c0_1(a717) | (~c1_1(a717)))),
% 2.15/1.76 inference(rewrite,[status(thm)],[])).
% 2.15/1.76 tff(3612,plain,
% 2.15/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c2_1(a717) | c0_1(a717) | (~c1_1(a717)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a717) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | c0_1(a717) | (~c1_1(a717))))),
% 2.15/1.76 inference(monotonicity,[status(thm)],[3611])).
% 2.15/1.76 tff(3613,plain,
% 2.15/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c2_1(a717) | c0_1(a717) | (~c1_1(a717)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a717) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | c0_1(a717) | (~c1_1(a717)))),
% 2.15/1.76 inference(transitivity,[status(thm)],[3612, 3610])).
% 2.15/1.76 tff(3614,plain,
% 2.15/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c2_1(a717) | c0_1(a717) | (~c1_1(a717)))),
% 2.15/1.76 inference(quant_inst,[status(thm)],[])).
% 2.15/1.76 tff(3615,plain,
% 2.15/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a717) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | c0_1(a717) | (~c1_1(a717))),
% 2.15/1.76 inference(modus_ponens,[status(thm)],[3614, 3613])).
% 2.15/1.76 tff(3616,plain,
% 2.15/1.76 (c0_1(a717)),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[3615, 227, 2802, 2771, 2760, 3609, 3608, 822, 11])).
% 2.15/1.76 tff(3617,plain,
% 2.15/1.76 (hskp4),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[2943, 2822, 3587])).
% 2.15/1.76 tff(3618,plain,
% 2.15/1.76 (~c3_1(a698)),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[1045, 3617])).
% 2.15/1.76 tff(3619,plain,
% 2.15/1.76 (~c2_1(a698)),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[923, 3617])).
% 2.15/1.76 tff(3620,plain,
% 2.15/1.76 (~c0_1(a698)),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[917, 3617])).
% 2.15/1.76 tff(3621,plain,
% 2.15/1.76 (c3_1(a717)),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[1904, 3607])).
% 2.15/1.76 tff(3622,plain,
% 2.15/1.76 (hskp0),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[3223, 227, 3621, 3608, 3620, 3619, 3618, 2832, 3616])).
% 2.15/1.76 tff(3623,plain,
% 2.15/1.76 (~c1_1(a692)),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[853, 3622])).
% 2.15/1.76 tff(3624,plain,
% 2.15/1.76 (~c0_1(a692)),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[859, 3622])).
% 2.15/1.76 tff(3625,plain,
% 2.15/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a698) | c2_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a698) | c2_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)))),
% 2.15/1.76 inference(rewrite,[status(thm)],[])).
% 2.15/1.76 tff(3626,plain,
% 2.15/1.76 (((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c2_1(a698) | c0_1(a698) | (~c1_1(a698))) <=> (c0_1(a698) | c2_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)))),
% 2.15/1.76 inference(rewrite,[status(thm)],[])).
% 2.15/1.76 tff(3627,plain,
% 2.15/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c2_1(a698) | c0_1(a698) | (~c1_1(a698)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a698) | c2_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695))))),
% 2.15/1.76 inference(monotonicity,[status(thm)],[3626])).
% 2.15/1.76 tff(3628,plain,
% 2.15/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c2_1(a698) | c0_1(a698) | (~c1_1(a698)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a698) | c2_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)))),
% 2.15/1.76 inference(transitivity,[status(thm)],[3627, 3625])).
% 2.15/1.76 tff(3629,plain,
% 2.15/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c2_1(a698) | c0_1(a698) | (~c1_1(a698)))),
% 2.15/1.76 inference(quant_inst,[status(thm)],[])).
% 2.15/1.76 tff(3630,plain,
% 2.15/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a698) | c2_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695))),
% 2.15/1.76 inference(modus_ponens,[status(thm)],[3629, 3628])).
% 2.15/1.76 tff(3631,plain,
% 2.15/1.76 (~c1_1(a698)),
% 2.15/1.76 inference(unit_resolution,[status(thm)],[3630, 227, 2802, 2771, 2760, 3620, 3619, 822, 11])).
% 2.15/1.76 tff(3632,plain,
% 2.15/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a760) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698) | c2_1(a760) | (~c1_1(a760)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a760) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698) | c2_1(a760) | (~c1_1(a760)))),
% 2.15/1.77 inference(rewrite,[status(thm)],[])).
% 2.15/1.77 tff(3633,plain,
% 2.15/1.77 (((~ndr1_0) | c0_1(a760) | c2_1(a760) | (~c1_1(a760)) | c3_1(a698) | c1_1(a698) | c2_1(a698) | c3_1(a698) | c2_1(a698) | c0_1(a698)) <=> (c0_1(a760) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698) | c2_1(a760) | (~c1_1(a760)))),
% 2.15/1.77 inference(rewrite,[status(thm)],[])).
% 2.15/1.77 tff(3634,plain,
% 2.15/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a760) | c2_1(a760) | (~c1_1(a760)) | c3_1(a698) | c1_1(a698) | c2_1(a698) | c3_1(a698) | c2_1(a698) | c0_1(a698))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a760) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698) | c2_1(a760) | (~c1_1(a760))))),
% 2.15/1.77 inference(monotonicity,[status(thm)],[3633])).
% 2.15/1.77 tff(3635,plain,
% 2.15/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a760) | c2_1(a760) | (~c1_1(a760)) | c3_1(a698) | c1_1(a698) | c2_1(a698) | c3_1(a698) | c2_1(a698) | c0_1(a698))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a760) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698) | c2_1(a760) | (~c1_1(a760)))),
% 2.15/1.77 inference(transitivity,[status(thm)],[3634, 3632])).
% 2.15/1.77 tff(3636,plain,
% 2.15/1.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a760) | c2_1(a760) | (~c1_1(a760)) | c3_1(a698) | c1_1(a698) | c2_1(a698) | c3_1(a698) | c2_1(a698) | c0_1(a698))),
% 2.15/1.77 inference(quant_inst,[status(thm)],[])).
% 2.15/1.77 tff(3637,plain,
% 2.15/1.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a760) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | c1_1(a698) | c2_1(a760) | (~c1_1(a760))),
% 2.15/1.77 inference(modus_ponens,[status(thm)],[3636, 3635])).
% 2.15/1.77 tff(3638,plain,
% 2.15/1.77 (c2_1(a760)),
% 2.15/1.77 inference(unit_resolution,[status(thm)],[3637, 227, 3194, 3192, 3620, 3619, 3618, 122, 3631])).
% 2.15/1.77 tff(3639,plain,
% 2.15/1.77 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c2_1(a695)) | (~c3_1(a760)) | (~c2_1(a760)) | (~c1_1(a760)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp3 | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c2_1(a695)) | (~c3_1(a760)) | (~c2_1(a760)) | (~c1_1(a760)))),
% 2.15/1.77 inference(rewrite,[status(thm)],[])).
% 2.15/1.77 tff(3640,plain,
% 2.15/1.77 ((hskp3 | (~ndr1_0) | (~c2_1(a760)) | (~c3_1(a760)) | (~c1_1(a760)) | c3_1(a695) | (~c2_1(a695)) | (~c0_1(a695))) <=> (hskp3 | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c2_1(a695)) | (~c3_1(a760)) | (~c2_1(a760)) | (~c1_1(a760)))),
% 2.15/1.77 inference(rewrite,[status(thm)],[])).
% 2.15/1.77 tff(3641,plain,
% 2.15/1.77 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a760)) | (~c3_1(a760)) | (~c1_1(a760)) | c3_1(a695) | (~c2_1(a695)) | (~c0_1(a695)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c2_1(a695)) | (~c3_1(a760)) | (~c2_1(a760)) | (~c1_1(a760))))),
% 2.15/1.77 inference(monotonicity,[status(thm)],[3640])).
% 2.15/1.77 tff(3642,plain,
% 2.15/1.77 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a760)) | (~c3_1(a760)) | (~c1_1(a760)) | c3_1(a695) | (~c2_1(a695)) | (~c0_1(a695)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp3 | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c2_1(a695)) | (~c3_1(a760)) | (~c2_1(a760)) | (~c1_1(a760)))),
% 2.15/1.77 inference(transitivity,[status(thm)],[3641, 3639])).
% 2.15/1.77 tff(3643,plain,
% 2.15/1.77 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a760)) | (~c3_1(a760)) | (~c1_1(a760)) | c3_1(a695) | (~c2_1(a695)) | (~c0_1(a695)))),
% 2.15/1.77 inference(quant_inst,[status(thm)],[])).
% 2.15/1.77 tff(3644,plain,
% 2.15/1.77 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp3 | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c2_1(a695)) | (~c3_1(a760)) | (~c2_1(a760)) | (~c1_1(a760))),
% 2.15/1.77 inference(modus_ponens,[status(thm)],[3643, 3642])).
% 2.15/1.77 tff(3645,plain,
% 2.15/1.77 (hskp3),
% 2.15/1.77 inference(unit_resolution,[status(thm)],[3644, 227, 2802, 2760, 3194, 3193, 2234, 11, 3638])).
% 2.15/1.77 tff(3646,plain,
% 2.15/1.77 (~c3_1(a697)),
% 2.15/1.77 inference(unit_resolution,[status(thm)],[1355, 3645])).
% 2.15/1.77 tff(3647,plain,
% 2.15/1.77 (c2_1(a692)),
% 2.15/1.77 inference(unit_resolution,[status(thm)],[872, 3622])).
% 2.15/1.77 tff(3648,plain,
% 2.15/1.77 (c0_1(a697)),
% 2.15/1.77 inference(unit_resolution,[status(thm)],[508, 3645])).
% 2.15/1.77 tff(3649,plain,
% 2.15/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | (c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a692)) | (~c2_1(a695)) | (~c0_1(a697)) | c1_1(a697))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a692)) | (~c2_1(a695)) | (~c0_1(a697)) | c1_1(a697))),
% 2.15/1.77 inference(rewrite,[status(thm)],[])).
% 2.15/1.77 tff(3650,plain,
% 2.15/1.77 (((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692)) <=> (c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a692)) | (~c2_1(a695)) | (~c0_1(a697)) | c1_1(a697))),
% 2.15/1.77 inference(rewrite,[status(thm)],[])).
% 2.15/1.77 tff(3651,plain,
% 2.15/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | (c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a692)) | (~c2_1(a695)) | (~c0_1(a697)) | c1_1(a697)))),
% 2.15/1.77 inference(monotonicity,[status(thm)],[3650])).
% 2.15/1.77 tff(3652,plain,
% 2.15/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a692)) | (~c2_1(a695)) | (~c0_1(a697)) | c1_1(a697))),
% 2.15/1.77 inference(transitivity,[status(thm)],[3651, 3649])).
% 2.15/1.77 tff(3653,plain,
% 2.15/1.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692))),
% 2.15/1.77 inference(quant_inst,[status(thm)],[])).
% 2.15/1.77 tff(3654,plain,
% 2.15/1.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a692)) | (~c2_1(a695)) | (~c0_1(a697)) | c1_1(a697)),
% 2.15/1.77 inference(modus_ponens,[status(thm)],[3653, 3652])).
% 2.15/1.77 tff(3655,plain,
% 2.15/1.77 (c1_1(a697)),
% 2.15/1.77 inference(unit_resolution,[status(thm)],[3654, 227, 2771, 2760, 3648, 3647, 3646, 3624, 3623, 566, 11])).
% 2.15/1.77 tff(3656,plain,
% 2.15/1.77 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c2_1(a717) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c3_1(a717)) | (~c1_1(a717)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c2_1(a717) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c3_1(a717)) | (~c1_1(a717)))),
% 2.15/1.77 inference(rewrite,[status(thm)],[])).
% 2.15/1.77 tff(3657,plain,
% 2.15/1.77 ((hskp17 | (~ndr1_0) | c3_1(a695) | (~c0_1(a695)) | (~c1_1(a695)) | c2_1(a717) | (~c3_1(a717)) | (~c1_1(a717))) <=> (hskp17 | c2_1(a717) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c3_1(a717)) | (~c1_1(a717)))),
% 2.15/1.77 inference(rewrite,[status(thm)],[])).
% 2.15/1.77 tff(3658,plain,
% 2.15/1.77 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a695) | (~c0_1(a695)) | (~c1_1(a695)) | c2_1(a717) | (~c3_1(a717)) | (~c1_1(a717)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c2_1(a717) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c3_1(a717)) | (~c1_1(a717))))),
% 2.15/1.77 inference(monotonicity,[status(thm)],[3657])).
% 2.15/1.77 tff(3659,plain,
% 2.15/1.77 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a695) | (~c0_1(a695)) | (~c1_1(a695)) | c2_1(a717) | (~c3_1(a717)) | (~c1_1(a717)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c2_1(a717) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c3_1(a717)) | (~c1_1(a717)))),
% 2.15/1.77 inference(transitivity,[status(thm)],[3658, 3656])).
% 2.15/1.77 tff(3660,plain,
% 2.15/1.77 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a695) | (~c0_1(a695)) | (~c1_1(a695)) | c2_1(a717) | (~c3_1(a717)) | (~c1_1(a717)))),
% 2.15/1.77 inference(quant_inst,[status(thm)],[])).
% 2.15/1.77 tff(3661,plain,
% 2.15/1.77 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c2_1(a717) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c3_1(a717)) | (~c1_1(a717))),
% 2.15/1.77 inference(modus_ponens,[status(thm)],[3660, 3659])).
% 2.15/1.77 tff(3662,plain,
% 2.15/1.77 (hskp17),
% 2.15/1.77 inference(unit_resolution,[status(thm)],[3661, 227, 2802, 2771, 3609, 3621, 3608, 3236, 11])).
% 2.15/1.77 tff(3663,plain,
% 2.15/1.77 (~c3_1(a744)),
% 2.15/1.77 inference(unit_resolution,[status(thm)],[3248, 3662])).
% 2.15/1.77 tff(3664,plain,
% 2.15/1.77 (~c1_1(a744)),
% 2.15/1.77 inference(unit_resolution,[status(thm)],[3254, 3662])).
% 2.15/1.77 tff(3665,plain,
% 2.15/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | (c1_1(a744) | c3_1(a744) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a692)) | (~c2_1(a695)) | (~c0_1(a744)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c1_1(a744) | c3_1(a744) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a692)) | (~c2_1(a695)) | (~c0_1(a744)))),
% 2.15/1.77 inference(rewrite,[status(thm)],[])).
% 2.15/1.77 tff(3666,plain,
% 2.15/1.77 (((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a744) | c1_1(a744) | (~c0_1(a744)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692)) <=> (c1_1(a744) | c3_1(a744) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a692)) | (~c2_1(a695)) | (~c0_1(a744)))),
% 2.15/1.77 inference(rewrite,[status(thm)],[])).
% 2.15/1.77 tff(3667,plain,
% 2.15/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a744) | c1_1(a744) | (~c0_1(a744)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | (c1_1(a744) | c3_1(a744) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a692)) | (~c2_1(a695)) | (~c0_1(a744))))),
% 2.15/1.77 inference(monotonicity,[status(thm)],[3666])).
% 2.15/1.77 tff(3668,plain,
% 2.15/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a744) | c1_1(a744) | (~c0_1(a744)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c1_1(a744) | c3_1(a744) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a692)) | (~c2_1(a695)) | (~c0_1(a744)))),
% 2.15/1.77 inference(transitivity,[status(thm)],[3667, 3665])).
% 2.15/1.77 tff(3669,plain,
% 2.15/1.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a744) | c1_1(a744) | (~c0_1(a744)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692))),
% 2.15/1.77 inference(quant_inst,[status(thm)],[])).
% 2.15/1.77 tff(3670,plain,
% 2.15/1.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c1_1(a744) | c3_1(a744) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a692)) | (~c2_1(a695)) | (~c0_1(a744))),
% 2.15/1.77 inference(modus_ponens,[status(thm)],[3669, 3668])).
% 2.15/1.77 tff(3671,plain,
% 2.15/1.77 (~c0_1(a744)),
% 2.15/1.77 inference(unit_resolution,[status(thm)],[3670, 227, 2771, 2760, 3647, 3664, 3663, 3624, 3623, 566, 11])).
% 2.15/1.77 tff(3672,plain,
% 2.15/1.77 (~c2_1(a744)),
% 2.15/1.77 inference(unit_resolution,[status(thm)],[3268, 3662])).
% 2.15/1.77 tff(3673,plain,
% 2.15/1.77 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))),
% 2.15/1.77 inference(bind,[status(th)],[])).
% 2.15/1.77 tff(3674,plain,
% 2.15/1.77 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.15/1.77 inference(quant_intro,[status(thm)],[3673])).
% 2.15/1.77 tff(3675,plain,
% 2.15/1.77 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.15/1.77 inference(rewrite,[status(thm)],[])).
% 2.15/1.77 tff(3676,plain,
% 2.15/1.77 (^[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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | hskp5) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp5))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))))),
% 2.22/1.77 inference(bind,[status(th)],[])).
% 2.22/1.77 tff(3677,plain,
% 2.22/1.77 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.22/1.77 inference(quant_intro,[status(thm)],[3676])).
% 2.22/1.77 tff(3678,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause179')).
% 2.22/1.77 tff(3679,plain,
% 2.22/1.77 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.22/1.77 inference(modus_ponens,[status(thm)],[3678, 3677])).
% 2.22/1.77 tff(3680,plain,
% 2.22/1.77 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.22/1.77 inference(modus_ponens,[status(thm)],[3679, 3675])).
% 2.22/1.77 tff(3681,plain,(
% 2.22/1.77 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.22/1.77 inference(skolemize,[status(sab)],[3680])).
% 2.22/1.77 tff(3682,plain,
% 2.22/1.77 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.22/1.77 inference(modus_ponens,[status(thm)],[3681, 3674])).
% 2.22/1.77 tff(3683,plain,
% 2.22/1.77 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp5 | c0_1(a760) | c2_1(a717) | (~ndr1_0) | (~c1_1(a717)) | (~c0_1(a717)) | (~c2_1(a760)) | (~c1_1(a760)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp5 | c0_1(a760) | c2_1(a717) | (~ndr1_0) | (~c1_1(a717)) | (~c0_1(a717)) | (~c2_1(a760)) | (~c1_1(a760)))),
% 2.22/1.77 inference(rewrite,[status(thm)],[])).
% 2.22/1.77 tff(3684,plain,
% 2.22/1.77 ((hskp5 | (~ndr1_0) | c2_1(a717) | (~c0_1(a717)) | (~c1_1(a717)) | c0_1(a760) | (~c2_1(a760)) | (~c1_1(a760))) <=> (hskp5 | c0_1(a760) | c2_1(a717) | (~ndr1_0) | (~c1_1(a717)) | (~c0_1(a717)) | (~c2_1(a760)) | (~c1_1(a760)))),
% 2.22/1.77 inference(rewrite,[status(thm)],[])).
% 2.22/1.77 tff(3685,plain,
% 2.22/1.77 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a717) | (~c0_1(a717)) | (~c1_1(a717)) | c0_1(a760) | (~c2_1(a760)) | (~c1_1(a760)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp5 | c0_1(a760) | c2_1(a717) | (~ndr1_0) | (~c1_1(a717)) | (~c0_1(a717)) | (~c2_1(a760)) | (~c1_1(a760))))),
% 2.22/1.77 inference(monotonicity,[status(thm)],[3684])).
% 2.22/1.77 tff(3686,plain,
% 2.22/1.77 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a717) | (~c0_1(a717)) | (~c1_1(a717)) | c0_1(a760) | (~c2_1(a760)) | (~c1_1(a760)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp5 | c0_1(a760) | c2_1(a717) | (~ndr1_0) | (~c1_1(a717)) | (~c0_1(a717)) | (~c2_1(a760)) | (~c1_1(a760)))),
% 2.22/1.77 inference(transitivity,[status(thm)],[3685, 3683])).
% 2.22/1.77 tff(3687,plain,
% 2.22/1.77 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a717) | (~c0_1(a717)) | (~c1_1(a717)) | c0_1(a760) | (~c2_1(a760)) | (~c1_1(a760)))),
% 2.22/1.77 inference(quant_inst,[status(thm)],[])).
% 2.22/1.77 tff(3688,plain,
% 2.22/1.77 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp5 | c0_1(a760) | c2_1(a717) | (~ndr1_0) | (~c1_1(a717)) | (~c0_1(a717)) | (~c2_1(a760)) | (~c1_1(a760))),
% 2.22/1.77 inference(modus_ponens,[status(thm)],[3687, 3686])).
% 2.22/1.77 tff(3689,plain,
% 2.22/1.77 (hskp5),
% 2.22/1.77 inference(unit_resolution,[status(thm)],[3688, 227, 3194, 3609, 3192, 3608, 3682, 3638, 3616])).
% 2.22/1.77 tff(3690,plain,
% 2.22/1.77 (c2_1(a701)),
% 2.22/1.77 inference(unit_resolution,[status(thm)],[39, 3689])).
% 2.22/1.77 tff(3691,plain,
% 2.22/1.77 (c0_1(a701)),
% 2.22/1.77 inference(unit_resolution,[status(thm)],[50, 3689])).
% 2.22/1.77 tff(3692,plain,
% 2.22/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a744) | c3_1(a744) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c0_1(a744))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a744) | c3_1(a744) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c0_1(a744))),
% 2.22/1.77 inference(rewrite,[status(thm)],[])).
% 2.22/1.77 tff(3693,plain,
% 2.22/1.77 (((~ndr1_0) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c3_1(a744) | c2_1(a744) | c0_1(a744)) <=> (c2_1(a744) | c3_1(a744) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c0_1(a744))),
% 2.22/1.77 inference(rewrite,[status(thm)],[])).
% 2.22/1.77 tff(3694,plain,
% 2.22/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c3_1(a744) | c2_1(a744) | c0_1(a744))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a744) | c3_1(a744) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c0_1(a744)))),
% 2.22/1.77 inference(monotonicity,[status(thm)],[3693])).
% 2.22/1.77 tff(3695,plain,
% 2.22/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c3_1(a744) | c2_1(a744) | c0_1(a744))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a744) | c3_1(a744) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c0_1(a744))),
% 2.22/1.77 inference(transitivity,[status(thm)],[3694, 3692])).
% 2.22/1.77 tff(3696,plain,
% 2.22/1.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c3_1(a744) | c2_1(a744) | c0_1(a744))),
% 2.22/1.77 inference(quant_inst,[status(thm)],[])).
% 2.22/1.77 tff(3697,plain,
% 2.22/1.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a744) | c3_1(a744) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c0_1(a744)),
% 2.22/1.77 inference(modus_ponens,[status(thm)],[3696, 3695])).
% 2.22/1.77 tff(3698,plain,
% 2.22/1.77 (~c3_1(a701)),
% 2.22/1.77 inference(unit_resolution,[status(thm)],[3697, 227, 3691, 3690, 3648, 3672, 3663, 3646, 1777, 3671, 3655])).
% 2.22/1.77 tff(3699,plain,
% 2.22/1.77 (~c1_1(a754)),
% 2.22/1.77 inference(unit_resolution,[status(thm)],[1460, 227, 177, 3584, 3583, 3620, 3619, 3618, 301])).
% 2.22/1.77 tff(3700,plain,
% 2.22/1.77 (~c1_1(a701)),
% 2.22/1.77 inference(unit_resolution,[status(thm)],[28, 3689])).
% 2.22/1.77 tff(3701,plain,
% 2.22/1.77 (c2_1(a697)),
% 2.22/1.77 inference(unit_resolution,[status(thm)],[527, 3645])).
% 2.22/1.77 tff(3702,plain,
% 2.22/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | (c0_1(a754) | c1_1(a701) | c3_1(a697) | (~ndr1_0) | (~c1_1(a697)) | (~c2_1(a697)) | c3_1(a701) | (~c0_1(a701)) | c1_1(a754) | (~c2_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c0_1(a754) | c1_1(a701) | c3_1(a697) | (~ndr1_0) | (~c1_1(a697)) | (~c2_1(a697)) | c3_1(a701) | (~c0_1(a701)) | c1_1(a754) | (~c2_1(a754)))),
% 2.22/1.77 inference(rewrite,[status(thm)],[])).
% 2.22/1.77 tff(3703,plain,
% 2.22/1.77 (((~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a701) | c1_1(a701) | (~c0_1(a701)) | c0_1(a754) | (~c2_1(a754)) | c1_1(a754)) <=> (c0_1(a754) | c1_1(a701) | c3_1(a697) | (~ndr1_0) | (~c1_1(a697)) | (~c2_1(a697)) | c3_1(a701) | (~c0_1(a701)) | c1_1(a754) | (~c2_1(a754)))),
% 2.22/1.77 inference(rewrite,[status(thm)],[])).
% 2.22/1.77 tff(3704,plain,
% 2.22/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a701) | c1_1(a701) | (~c0_1(a701)) | c0_1(a754) | (~c2_1(a754)) | c1_1(a754))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | (c0_1(a754) | c1_1(a701) | c3_1(a697) | (~ndr1_0) | (~c1_1(a697)) | (~c2_1(a697)) | c3_1(a701) | (~c0_1(a701)) | c1_1(a754) | (~c2_1(a754))))),
% 2.22/1.77 inference(monotonicity,[status(thm)],[3703])).
% 2.22/1.77 tff(3705,plain,
% 2.22/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a701) | c1_1(a701) | (~c0_1(a701)) | c0_1(a754) | (~c2_1(a754)) | c1_1(a754))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c0_1(a754) | c1_1(a701) | c3_1(a697) | (~ndr1_0) | (~c1_1(a697)) | (~c2_1(a697)) | c3_1(a701) | (~c0_1(a701)) | c1_1(a754) | (~c2_1(a754)))),
% 2.22/1.77 inference(transitivity,[status(thm)],[3704, 3702])).
% 2.22/1.77 tff(3706,plain,
% 2.22/1.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a701) | c1_1(a701) | (~c0_1(a701)) | c0_1(a754) | (~c2_1(a754)) | c1_1(a754))),
% 2.22/1.77 inference(quant_inst,[status(thm)],[])).
% 2.22/1.77 tff(3707,plain,
% 2.22/1.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c0_1(a754) | c1_1(a701) | c3_1(a697) | (~ndr1_0) | (~c1_1(a697)) | (~c2_1(a697)) | c3_1(a701) | (~c0_1(a701)) | c1_1(a754) | (~c2_1(a754))),
% 2.22/1.78 inference(modus_ponens,[status(thm)],[3706, 3705])).
% 2.22/1.78 tff(3708,plain,
% 2.22/1.78 ($false),
% 2.22/1.78 inference(unit_resolution,[status(thm)],[3707, 227, 3585, 3691, 3701, 3584, 3700, 3646, 566, 3699, 3655, 3698])).
% 2.22/1.78 tff(3709,plain,(c3_1(a695) | hskp6), inference(lemma,lemma(discharge,[]))).
% 2.22/1.78 tff(3710,plain,
% 2.22/1.78 (c3_1(a695)),
% 2.22/1.78 inference(unit_resolution,[status(thm)],[3709, 177])).
% 2.22/1.78 tff(3711,plain,
% 2.22/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a763) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754)) | (~c3_1(a763)) | (~c0_1(a763)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a763) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754)) | (~c3_1(a763)) | (~c0_1(a763)))),
% 2.22/1.78 inference(rewrite,[status(thm)],[])).
% 2.22/1.78 tff(3712,plain,
% 2.22/1.78 (((~ndr1_0) | c2_1(a763) | (~c3_1(a763)) | (~c0_1(a763)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a754) | c0_1(a754) | (~c1_1(a754))) <=> (c2_1(a763) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754)) | (~c3_1(a763)) | (~c0_1(a763)))),
% 2.22/1.78 inference(rewrite,[status(thm)],[])).
% 2.22/1.78 tff(3713,plain,
% 2.22/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a763) | (~c3_1(a763)) | (~c0_1(a763)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a763) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754)) | (~c3_1(a763)) | (~c0_1(a763))))),
% 2.22/1.78 inference(monotonicity,[status(thm)],[3712])).
% 2.22/1.78 tff(3714,plain,
% 2.22/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a763) | (~c3_1(a763)) | (~c0_1(a763)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a763) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754)) | (~c3_1(a763)) | (~c0_1(a763)))),
% 2.22/1.78 inference(transitivity,[status(thm)],[3713, 3711])).
% 2.22/1.78 tff(3715,plain,
% 2.22/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a763) | (~c3_1(a763)) | (~c0_1(a763)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a754) | c0_1(a754) | (~c1_1(a754)))),
% 2.22/1.78 inference(quant_inst,[status(thm)],[])).
% 2.22/1.78 tff(3716,plain,
% 2.22/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a763) | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c1_1(a754)) | (~c2_1(a754)) | (~c3_1(a763)) | (~c0_1(a763))),
% 2.22/1.78 inference(modus_ponens,[status(thm)],[3715, 3714])).
% 2.22/1.78 tff(3717,plain,
% 2.22/1.78 ((~c1_1(a754)) | (~c3_1(a763))),
% 2.22/1.78 inference(unit_resolution,[status(thm)],[3716, 227, 3590, 3585, 3588, 3584, 3583, 174])).
% 2.22/1.78 tff(3718,plain,
% 2.22/1.78 (~c1_1(a754)),
% 2.22/1.78 inference(unit_resolution,[status(thm)],[3717, 3600])).
% 2.22/1.78 tff(3719,plain,
% 2.22/1.78 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | c3_1(a754) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | c1_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a754) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | c1_1(a754) | (~c2_1(a754)))),
% 2.22/1.78 inference(rewrite,[status(thm)],[])).
% 2.22/1.78 tff(3720,plain,
% 2.22/1.78 ((hskp14 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a754) | c1_1(a754) | (~c2_1(a754))) <=> (hskp14 | c3_1(a754) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | c1_1(a754) | (~c2_1(a754)))),
% 2.22/1.78 inference(rewrite,[status(thm)],[])).
% 2.22/1.78 tff(3721,plain,
% 2.22/1.78 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | c3_1(a754) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | c1_1(a754) | (~c2_1(a754))))),
% 2.22/1.78 inference(monotonicity,[status(thm)],[3720])).
% 2.22/1.78 tff(3722,plain,
% 2.22/1.78 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a754) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | c1_1(a754) | (~c2_1(a754)))),
% 2.22/1.78 inference(transitivity,[status(thm)],[3721, 3719])).
% 2.22/1.78 tff(3723,plain,
% 2.22/1.78 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)))),
% 2.22/1.78 inference(quant_inst,[status(thm)],[])).
% 2.22/1.78 tff(3724,plain,
% 2.22/1.78 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a754) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | c1_1(a754) | (~c2_1(a754))),
% 2.22/1.78 inference(modus_ponens,[status(thm)],[3723, 3722])).
% 2.22/1.78 tff(3725,plain,
% 2.22/1.78 (hskp14 | (~c3_1(a695)) | c1_1(a754)),
% 2.22/1.78 inference(unit_resolution,[status(thm)],[3724, 227, 2802, 2760, 3585, 3583, 1614])).
% 2.22/1.78 tff(3726,plain,
% 2.22/1.78 (hskp14),
% 2.22/1.78 inference(unit_resolution,[status(thm)],[3725, 3718, 3710])).
% 2.22/1.78 tff(3727,plain,
% 2.22/1.78 (~c3_1(a730)),
% 2.22/1.78 inference(unit_resolution,[status(thm)],[486, 3726])).
% 2.22/1.78 tff(3728,plain,
% 2.22/1.78 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c3_1(a695)) | (~c1_1(a695)) | (~c2_1(a695)) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c3_1(a695)) | (~c1_1(a695)) | (~c2_1(a695)) | (~c2_1(a754)))),
% 2.22/1.78 inference(rewrite,[status(thm)],[])).
% 2.22/1.78 tff(3729,plain,
% 2.22/1.78 ((hskp8 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c1_1(a695)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754))) <=> (hskp8 | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c3_1(a695)) | (~c1_1(a695)) | (~c2_1(a695)) | (~c2_1(a754)))),
% 2.22/1.78 inference(rewrite,[status(thm)],[])).
% 2.22/1.78 tff(3730,plain,
% 2.22/1.78 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c1_1(a695)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c3_1(a695)) | (~c1_1(a695)) | (~c2_1(a695)) | (~c2_1(a754))))),
% 2.22/1.78 inference(monotonicity,[status(thm)],[3729])).
% 2.22/1.78 tff(3731,plain,
% 2.22/1.78 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c1_1(a695)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c3_1(a695)) | (~c1_1(a695)) | (~c2_1(a695)) | (~c2_1(a754)))),
% 2.22/1.78 inference(transitivity,[status(thm)],[3730, 3728])).
% 2.22/1.78 tff(3732,plain,
% 2.22/1.78 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c1_1(a695)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))),
% 2.22/1.78 inference(quant_inst,[status(thm)],[])).
% 2.22/1.78 tff(3733,plain,
% 2.22/1.78 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c0_1(a754) | c3_1(a754) | (~ndr1_0) | (~c3_1(a695)) | (~c1_1(a695)) | (~c2_1(a695)) | (~c2_1(a754))),
% 2.22/1.78 inference(modus_ponens,[status(thm)],[3732, 3731])).
% 2.22/1.78 tff(3734,plain,
% 2.22/1.78 (hskp8 | (~c3_1(a695))),
% 2.22/1.78 inference(unit_resolution,[status(thm)],[3733, 227, 2771, 2760, 3585, 3584, 3583, 1862])).
% 2.22/1.78 tff(3735,plain,
% 2.22/1.78 (hskp8),
% 2.22/1.78 inference(unit_resolution,[status(thm)],[3734, 3710])).
% 2.22/1.78 tff(3736,plain,
% 2.22/1.78 (c2_1(a710)),
% 2.22/1.78 inference(unit_resolution,[status(thm)],[1958, 3735])).
% 2.22/1.78 tff(3737,plain,
% 2.22/1.78 (~c0_1(a710)),
% 2.22/1.78 inference(unit_resolution,[status(thm)],[1875, 3735])).
% 2.22/1.78 tff(3738,plain,
% 2.22/1.78 (c3_1(a710)),
% 2.22/1.78 inference(unit_resolution,[status(thm)],[1886, 3735])).
% 2.22/1.78 tff(3739,plain,
% 2.22/1.78 (^[U: $i] : refl((hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))))),
% 2.22/1.78 inference(bind,[status(th)],[])).
% 2.22/1.78 tff(3740,plain,
% 2.22/1.78 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 2.22/1.78 inference(quant_intro,[status(thm)],[3739])).
% 2.22/1.78 tff(3741,plain,
% 2.22/1.78 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 2.22/1.78 inference(rewrite,[status(thm)],[])).
% 2.22/1.78 tff(3742,plain,
% 2.22/1.78 (^[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)) | 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)) | hskp16) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp16))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp16) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp16) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp16) | hskp15) <=> ((hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp15))), rewrite(((hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp15) <=> (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp16) | hskp15) <=> (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))))),
% 2.22/1.78 inference(bind,[status(th)],[])).
% 2.22/1.78 tff(3743,plain,
% 2.22/1.78 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp16) | hskp15) <=> ![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 2.22/1.78 inference(quant_intro,[status(thm)],[3742])).
% 2.22/1.78 tff(3744,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp16) | hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause151')).
% 2.22/1.78 tff(3745,plain,
% 2.22/1.78 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 2.22/1.78 inference(modus_ponens,[status(thm)],[3744, 3743])).
% 2.22/1.78 tff(3746,plain,
% 2.22/1.78 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 2.22/1.78 inference(modus_ponens,[status(thm)],[3745, 3741])).
% 2.22/1.78 tff(3747,plain,(
% 2.22/1.78 ![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 2.22/1.78 inference(skolemize,[status(sab)],[3746])).
% 2.22/1.78 tff(3748,plain,
% 2.22/1.78 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 2.24/1.78 inference(modus_ponens,[status(thm)],[3747, 3740])).
% 2.24/1.78 tff(3749,plain,
% 2.24/1.78 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp16 | hskp15 | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp16 | hskp15 | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)))),
% 2.24/1.78 inference(rewrite,[status(thm)],[])).
% 2.24/1.78 tff(3750,plain,
% 2.24/1.78 ((hskp16 | hskp15 | (~ndr1_0) | c3_1(a730) | (~c0_1(a730)) | (~c1_1(a730))) <=> (hskp16 | hskp15 | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)))),
% 2.24/1.78 inference(rewrite,[status(thm)],[])).
% 2.24/1.78 tff(3751,plain,
% 2.24/1.78 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c3_1(a730) | (~c0_1(a730)) | (~c1_1(a730)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp16 | hskp15 | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730))))),
% 2.24/1.78 inference(monotonicity,[status(thm)],[3750])).
% 2.24/1.78 tff(3752,plain,
% 2.24/1.78 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c3_1(a730) | (~c0_1(a730)) | (~c1_1(a730)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp16 | hskp15 | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)))),
% 2.24/1.78 inference(transitivity,[status(thm)],[3751, 3749])).
% 2.24/1.78 tff(3753,plain,
% 2.24/1.78 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c3_1(a730) | (~c0_1(a730)) | (~c1_1(a730)))),
% 2.24/1.78 inference(quant_inst,[status(thm)],[])).
% 2.24/1.78 tff(3754,plain,
% 2.24/1.78 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp16 | hskp15 | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730))),
% 2.24/1.78 inference(modus_ponens,[status(thm)],[3753, 3752])).
% 2.24/1.78 tff(3755,plain,
% 2.24/1.78 (hskp15),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[3754, 227, 12, 473, 462, 487, 3748])).
% 2.24/1.78 tff(3756,plain,
% 2.24/1.78 (((~hskp15) | (~c2_1(a734))) <=> ((~hskp15) | (~c2_1(a734)))),
% 2.24/1.78 inference(rewrite,[status(thm)],[])).
% 2.24/1.78 tff(3757,plain,
% 2.24/1.78 (((~c2_1(a734)) | (~hskp15)) <=> ((~hskp15) | (~c2_1(a734)))),
% 2.24/1.78 inference(rewrite,[status(thm)],[])).
% 2.24/1.78 tff(3758,axiom,((~c2_1(a734)) | (~hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause108')).
% 2.24/1.78 tff(3759,plain,
% 2.24/1.78 ((~hskp15) | (~c2_1(a734))),
% 2.24/1.78 inference(modus_ponens,[status(thm)],[3758, 3757])).
% 2.24/1.78 tff(3760,plain,
% 2.24/1.78 ((~hskp15) | (~c2_1(a734))),
% 2.24/1.78 inference(modus_ponens,[status(thm)],[3759, 3756])).
% 2.24/1.78 tff(3761,plain,
% 2.24/1.78 (~c2_1(a734)),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[3760, 3755])).
% 2.24/1.78 tff(3762,plain,
% 2.24/1.78 (((~hskp15) | (~c1_1(a734))) <=> ((~hskp15) | (~c1_1(a734)))),
% 2.24/1.78 inference(rewrite,[status(thm)],[])).
% 2.24/1.78 tff(3763,plain,
% 2.24/1.78 (((~c1_1(a734)) | (~hskp15)) <=> ((~hskp15) | (~c1_1(a734)))),
% 2.24/1.78 inference(rewrite,[status(thm)],[])).
% 2.24/1.78 tff(3764,axiom,((~c1_1(a734)) | (~hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause107')).
% 2.24/1.78 tff(3765,plain,
% 2.24/1.78 ((~hskp15) | (~c1_1(a734))),
% 2.24/1.78 inference(modus_ponens,[status(thm)],[3764, 3763])).
% 2.24/1.78 tff(3766,plain,
% 2.24/1.78 ((~hskp15) | (~c1_1(a734))),
% 2.24/1.78 inference(modus_ponens,[status(thm)],[3765, 3762])).
% 2.24/1.78 tff(3767,plain,
% 2.24/1.78 (~c1_1(a734)),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[3766, 3755])).
% 2.24/1.78 tff(3768,assumption,(c3_1(a710)), introduced(assumption)).
% 2.24/1.78 tff(3769,assumption,(c2_1(a710)), introduced(assumption)).
% 2.24/1.78 tff(3770,plain,
% 2.24/1.78 (((~hskp15) | c3_1(a734)) <=> ((~hskp15) | c3_1(a734))),
% 2.24/1.78 inference(rewrite,[status(thm)],[])).
% 2.24/1.78 tff(3771,axiom,((~hskp15) | c3_1(a734)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause65')).
% 2.24/1.78 tff(3772,plain,
% 2.24/1.78 ((~hskp15) | c3_1(a734)),
% 2.24/1.78 inference(modus_ponens,[status(thm)],[3771, 3770])).
% 2.24/1.78 tff(3773,plain,
% 2.24/1.78 ((~hskp15) | c3_1(a734)),
% 2.24/1.78 inference(modus_ponens,[status(thm)],[3772, 3770])).
% 2.24/1.78 tff(3774,plain,
% 2.24/1.78 ((~hskp15) | c3_1(a734)),
% 2.24/1.78 inference(modus_ponens,[status(thm)],[3773, 3770])).
% 2.24/1.78 tff(3775,plain,
% 2.24/1.78 ((~hskp15) | c3_1(a734)),
% 2.24/1.78 inference(modus_ponens,[status(thm)],[3774, 3770])).
% 2.24/1.78 tff(3776,plain,
% 2.24/1.78 ((~hskp15) | c3_1(a734)),
% 2.24/1.78 inference(modus_ponens,[status(thm)],[3775, 3770])).
% 2.24/1.78 tff(3777,plain,
% 2.24/1.78 ((~hskp15) | c3_1(a734)),
% 2.24/1.78 inference(modus_ponens,[status(thm)],[3776, 3770])).
% 2.24/1.78 tff(3778,plain,
% 2.24/1.78 ((~hskp15) | c3_1(a734)),
% 2.24/1.78 inference(modus_ponens,[status(thm)],[3777, 3770])).
% 2.24/1.78 tff(3779,plain,
% 2.24/1.78 ((~hskp15) | c3_1(a734)),
% 2.24/1.78 inference(modus_ponens,[status(thm)],[3778, 3770])).
% 2.24/1.78 tff(3780,plain,
% 2.24/1.78 (c3_1(a734)),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[3779, 3755])).
% 2.24/1.78 tff(3781,assumption,(~c1_1(a710)), introduced(assumption)).
% 2.24/1.78 tff(3782,assumption,(~c3_1(a730)), introduced(assumption)).
% 2.24/1.78 tff(3783,assumption,(~c2_1(a734)), introduced(assumption)).
% 2.24/1.78 tff(3784,assumption,(~c1_1(a734)), introduced(assumption)).
% 2.24/1.78 tff(3785,assumption,(c1_1(a730)), introduced(assumption)).
% 2.24/1.78 tff(3786,assumption,(c0_1(a730)), introduced(assumption)).
% 2.24/1.78 tff(3787,assumption,(c3_1(a734)), introduced(assumption)).
% 2.24/1.78 tff(3788,plain,
% 2.24/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c1_1(a734) | c2_1(a734) | c3_1(a730) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | c1_1(a710) | (~c0_1(a730)) | (~c1_1(a730)) | (~c3_1(a734)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c1_1(a734) | c2_1(a734) | c3_1(a730) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | c1_1(a710) | (~c0_1(a730)) | (~c1_1(a730)) | (~c3_1(a734)))),
% 2.24/1.78 inference(rewrite,[status(thm)],[])).
% 2.24/1.78 tff(3789,plain,
% 2.24/1.78 (((~ndr1_0) | c3_1(a730) | (~c0_1(a730)) | (~c1_1(a730)) | c1_1(a710) | (~c2_1(a710)) | (~c3_1(a710)) | c2_1(a734) | (~c3_1(a734)) | c1_1(a734)) <=> (c1_1(a734) | c2_1(a734) | c3_1(a730) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | c1_1(a710) | (~c0_1(a730)) | (~c1_1(a730)) | (~c3_1(a734)))),
% 2.24/1.78 inference(rewrite,[status(thm)],[])).
% 2.24/1.78 tff(3790,plain,
% 2.24/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a730) | (~c0_1(a730)) | (~c1_1(a730)) | c1_1(a710) | (~c2_1(a710)) | (~c3_1(a710)) | c2_1(a734) | (~c3_1(a734)) | c1_1(a734))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c1_1(a734) | c2_1(a734) | c3_1(a730) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | c1_1(a710) | (~c0_1(a730)) | (~c1_1(a730)) | (~c3_1(a734))))),
% 2.24/1.78 inference(monotonicity,[status(thm)],[3789])).
% 2.24/1.78 tff(3791,plain,
% 2.24/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a730) | (~c0_1(a730)) | (~c1_1(a730)) | c1_1(a710) | (~c2_1(a710)) | (~c3_1(a710)) | c2_1(a734) | (~c3_1(a734)) | c1_1(a734))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c1_1(a734) | c2_1(a734) | c3_1(a730) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | c1_1(a710) | (~c0_1(a730)) | (~c1_1(a730)) | (~c3_1(a734)))),
% 2.24/1.78 inference(transitivity,[status(thm)],[3790, 3788])).
% 2.24/1.78 tff(3792,plain,
% 2.24/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a730) | (~c0_1(a730)) | (~c1_1(a730)) | c1_1(a710) | (~c2_1(a710)) | (~c3_1(a710)) | c2_1(a734) | (~c3_1(a734)) | c1_1(a734))),
% 2.24/1.78 inference(quant_inst,[status(thm)],[])).
% 2.24/1.78 tff(3793,plain,
% 2.24/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c1_1(a734) | c2_1(a734) | c3_1(a730) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | c1_1(a710) | (~c0_1(a730)) | (~c1_1(a730)) | (~c3_1(a734))),
% 2.24/1.78 inference(modus_ponens,[status(thm)],[3792, 3791])).
% 2.24/1.78 tff(3794,plain,
% 2.24/1.78 ($false),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[3793, 227, 3787, 3786, 3785, 3769, 3768, 3784, 3783, 3782, 3116, 3781])).
% 2.24/1.78 tff(3795,plain,(c1_1(a710) | (~c3_1(a734)) | (~c0_1(a730)) | (~c1_1(a730)) | (~c2_1(a710)) | (~c3_1(a710)) | c1_1(a734) | c2_1(a734) | c3_1(a730)), inference(lemma,lemma(discharge,[]))).
% 2.24/1.78 tff(3796,plain,
% 2.24/1.78 (c1_1(a710)),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[3795, 3780, 473, 462, 3769, 3768, 3767, 3761, 487])).
% 2.24/1.78 tff(3797,assumption,(~c0_1(a710)), introduced(assumption)).
% 2.24/1.78 tff(3798,plain,
% 2.24/1.78 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c1_1(a710)) | (~c0_1(a763)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c1_1(a710)) | (~c0_1(a763)))),
% 2.24/1.78 inference(rewrite,[status(thm)],[])).
% 2.24/1.78 tff(3799,plain,
% 2.24/1.78 ((hskp4 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c0_1(a710) | (~c3_1(a710)) | (~c1_1(a710))) <=> (hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c1_1(a710)) | (~c0_1(a763)))),
% 2.24/1.78 inference(rewrite,[status(thm)],[])).
% 2.24/1.78 tff(3800,plain,
% 2.24/1.78 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c0_1(a710) | (~c3_1(a710)) | (~c1_1(a710)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c1_1(a710)) | (~c0_1(a763))))),
% 2.24/1.78 inference(monotonicity,[status(thm)],[3799])).
% 2.24/1.78 tff(3801,plain,
% 2.24/1.78 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c0_1(a710) | (~c3_1(a710)) | (~c1_1(a710)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c1_1(a710)) | (~c0_1(a763)))),
% 2.24/1.78 inference(transitivity,[status(thm)],[3800, 3798])).
% 2.24/1.78 tff(3802,plain,
% 2.24/1.78 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)) | c0_1(a710) | (~c3_1(a710)) | (~c1_1(a710)))),
% 2.24/1.78 inference(quant_inst,[status(thm)],[])).
% 2.24/1.78 tff(3803,plain,
% 2.24/1.78 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp4 | c1_1(a763) | c2_1(a763) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c1_1(a710)) | (~c0_1(a763))),
% 2.24/1.78 inference(modus_ponens,[status(thm)],[3802, 3801])).
% 2.24/1.78 tff(3804,plain,
% 2.24/1.78 (hskp4 | (~c1_1(a710))),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[3803, 227, 1809, 3768, 1807, 1806, 3797, 2169])).
% 2.24/1.78 tff(3805,plain,
% 2.24/1.78 (hskp4),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[3804, 3796])).
% 2.24/1.78 tff(3806,plain,
% 2.24/1.78 (~c3_1(a698)),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[1045, 3805])).
% 2.24/1.78 tff(3807,plain,
% 2.24/1.78 (~c2_1(a698)),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[923, 3805])).
% 2.24/1.78 tff(3808,plain,
% 2.24/1.78 (~c0_1(a698)),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[917, 3805])).
% 2.24/1.78 tff(3809,plain,
% 2.24/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c3_1(a730) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c0_1(a730)) | (~c1_1(a730)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a730) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c0_1(a730)) | (~c1_1(a730)))),
% 2.24/1.78 inference(rewrite,[status(thm)],[])).
% 2.24/1.78 tff(3810,plain,
% 2.24/1.78 (((~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a730) | (~c1_1(a730)) | (~c0_1(a730)) | c3_1(a698) | c2_1(a698) | c0_1(a698)) <=> (c3_1(a730) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c0_1(a730)) | (~c1_1(a730)))),
% 2.24/1.78 inference(rewrite,[status(thm)],[])).
% 2.24/1.78 tff(3811,plain,
% 2.24/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a730) | (~c1_1(a730)) | (~c0_1(a730)) | c3_1(a698) | c2_1(a698) | c0_1(a698))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c3_1(a730) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c0_1(a730)) | (~c1_1(a730))))),
% 2.24/1.78 inference(monotonicity,[status(thm)],[3810])).
% 2.24/1.78 tff(3812,plain,
% 2.24/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a730) | (~c1_1(a730)) | (~c0_1(a730)) | c3_1(a698) | c2_1(a698) | c0_1(a698))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a730) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c0_1(a730)) | (~c1_1(a730)))),
% 2.24/1.78 inference(transitivity,[status(thm)],[3811, 3809])).
% 2.24/1.78 tff(3813,plain,
% 2.24/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a730) | (~c1_1(a730)) | (~c0_1(a730)) | c3_1(a698) | c2_1(a698) | c0_1(a698))),
% 2.24/1.78 inference(quant_inst,[status(thm)],[])).
% 2.24/1.78 tff(3814,plain,
% 2.24/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a730) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c0_1(a730)) | (~c1_1(a730))),
% 2.24/1.78 inference(modus_ponens,[status(thm)],[3813, 3812])).
% 2.24/1.78 tff(3815,plain,
% 2.24/1.78 ($false),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[3814, 227, 2802, 2760, 473, 462, 487, 3808, 3807, 3806, 1777, 3301])).
% 2.24/1.78 tff(3816,plain,((~hskp14) | (~c3_1(a695)) | (~c0_1(a763)) | (~c3_1(a710)) | c1_1(a763) | c2_1(a763) | c0_1(a710) | (~c2_1(a710)) | hskp16), inference(lemma,lemma(discharge,[]))).
% 2.24/1.78 tff(3817,plain,
% 2.24/1.78 (hskp16),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[3816, 3726, 3590, 3738, 3589, 3588, 3737, 3736, 3710])).
% 2.24/1.78 tff(3818,plain,
% 2.24/1.78 (~c1_1(a738)),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[3121, 3817])).
% 2.24/1.78 tff(3819,plain,
% 2.24/1.78 (c1_1(a730)),
% 2.24/1.78 inference(unit_resolution,[status(thm)],[461, 3726])).
% 2.24/1.78 tff(3820,plain,
% 2.24/1.79 (c0_1(a730)),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[472, 3726])).
% 2.24/1.79 tff(3821,plain,
% 2.24/1.79 (c3_1(a738)),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[3087, 3817])).
% 2.24/1.79 tff(3822,plain,
% 2.24/1.79 (c2_1(a738)),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[3098, 3817])).
% 2.24/1.79 tff(3823,plain,
% 2.24/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c1_1(a763) | c2_1(a763) | c1_1(a738) | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a763)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c1_1(a763) | c2_1(a763) | c1_1(a738) | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a763)))),
% 2.24/1.79 inference(rewrite,[status(thm)],[])).
% 2.24/1.79 tff(3824,plain,
% 2.24/1.79 (((~ndr1_0) | c3_1(a730) | (~c0_1(a730)) | (~c1_1(a730)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c2_1(a763) | (~c3_1(a763)) | c1_1(a763)) <=> (c1_1(a763) | c2_1(a763) | c1_1(a738) | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a763)))),
% 2.24/1.79 inference(rewrite,[status(thm)],[])).
% 2.24/1.79 tff(3825,plain,
% 2.24/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a730) | (~c0_1(a730)) | (~c1_1(a730)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c2_1(a763) | (~c3_1(a763)) | c1_1(a763))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c1_1(a763) | c2_1(a763) | c1_1(a738) | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a763))))),
% 2.24/1.79 inference(monotonicity,[status(thm)],[3824])).
% 2.24/1.79 tff(3826,plain,
% 2.24/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a730) | (~c0_1(a730)) | (~c1_1(a730)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c2_1(a763) | (~c3_1(a763)) | c1_1(a763))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c1_1(a763) | c2_1(a763) | c1_1(a738) | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a763)))),
% 2.24/1.79 inference(transitivity,[status(thm)],[3825, 3823])).
% 2.24/1.79 tff(3827,plain,
% 2.24/1.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a730) | (~c0_1(a730)) | (~c1_1(a730)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c2_1(a763) | (~c3_1(a763)) | c1_1(a763))),
% 2.24/1.79 inference(quant_inst,[status(thm)],[])).
% 2.24/1.79 tff(3828,plain,
% 2.24/1.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c1_1(a763) | c2_1(a763) | c1_1(a738) | c3_1(a730) | (~ndr1_0) | (~c0_1(a730)) | (~c1_1(a730)) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a763))),
% 2.24/1.79 inference(modus_ponens,[status(thm)],[3827, 3826])).
% 2.24/1.79 tff(3829,plain,
% 2.24/1.79 ($false),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[3828, 227, 3822, 3821, 3820, 3819, 3589, 3588, 3818, 3727, 3116, 3600])).
% 2.24/1.79 tff(3830,plain,(hskp6), inference(lemma,lemma(discharge,[]))).
% 2.24/1.79 tff(3831,plain,
% 2.24/1.79 (~c2_1(a702)),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[68, 3830])).
% 2.24/1.79 tff(3832,plain,
% 2.24/1.79 (c3_1(a702)),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[79, 3830])).
% 2.24/1.79 tff(3833,plain,
% 2.24/1.79 (c0_1(a702)),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[90, 3830])).
% 2.24/1.79 tff(3834,plain,
% 2.24/1.79 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c2_1(a702) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c2_1(a702) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)))),
% 2.24/1.79 inference(rewrite,[status(thm)],[])).
% 2.24/1.79 tff(3835,plain,
% 2.24/1.79 ((hskp0 | (~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a698) | c0_1(a698) | c2_1(a698)) <=> (hskp0 | c2_1(a702) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)))),
% 2.24/1.79 inference(rewrite,[status(thm)],[])).
% 2.24/1.79 tff(3836,plain,
% 2.24/1.79 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a698) | c0_1(a698) | c2_1(a698))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c2_1(a702) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702))))),
% 2.24/1.79 inference(monotonicity,[status(thm)],[3835])).
% 2.24/1.79 tff(3837,plain,
% 2.24/1.79 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a698) | c0_1(a698) | c2_1(a698))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c2_1(a702) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)))),
% 2.24/1.79 inference(transitivity,[status(thm)],[3836, 3834])).
% 2.24/1.79 tff(3838,plain,
% 2.24/1.79 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a698) | c0_1(a698) | c2_1(a698))),
% 2.24/1.79 inference(quant_inst,[status(thm)],[])).
% 2.24/1.79 tff(3839,plain,
% 2.24/1.79 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c2_1(a702) | c0_1(a698) | c2_1(a698) | c3_1(a698) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702))),
% 2.24/1.79 inference(modus_ponens,[status(thm)],[3838, 3837])).
% 2.24/1.79 tff(3840,plain,
% 2.24/1.79 (hskp0),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[3839, 227, 3833, 3832, 3831, 1360, 1359, 1358, 2832])).
% 2.24/1.79 tff(3841,plain,
% 2.24/1.79 (~c1_1(a692)),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[853, 3840])).
% 2.24/1.79 tff(3842,plain,
% 2.24/1.79 (~c0_1(a692)),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[859, 3840])).
% 2.24/1.79 tff(3843,plain,
% 2.24/1.79 (~c1_1(a698)),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[3630, 227, 2802, 2771, 2760, 1360, 1359, 822, 11])).
% 2.24/1.79 tff(3844,plain,
% 2.24/1.79 (c2_1(a760)),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[3637, 227, 3194, 3192, 1360, 1359, 1358, 122, 3843])).
% 2.24/1.79 tff(3845,plain,
% 2.24/1.79 (hskp3),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[3644, 227, 2802, 2760, 3194, 3193, 2234, 11, 3844])).
% 2.24/1.79 tff(3846,plain,
% 2.24/1.79 (~c3_1(a697)),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[1355, 3845])).
% 2.24/1.79 tff(3847,plain,
% 2.24/1.79 (c2_1(a692)),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[872, 3840])).
% 2.24/1.79 tff(3848,plain,
% 2.24/1.79 (c0_1(a697)),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[508, 3845])).
% 2.24/1.79 tff(3849,plain,
% 2.24/1.79 (c1_1(a697)),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[3654, 227, 2771, 2760, 3848, 3847, 3846, 3842, 3841, 566, 11])).
% 2.24/1.79 tff(3850,assumption,(~c1_1(a692)), introduced(assumption)).
% 2.24/1.79 tff(3851,assumption,(~c0_1(a692)), introduced(assumption)).
% 2.24/1.79 tff(3852,assumption,(c2_1(a760)), introduced(assumption)).
% 2.24/1.79 tff(3853,plain,
% 2.24/1.79 (hskp3),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[3644, 227, 2802, 2760, 3194, 3193, 2234, 11, 3852])).
% 2.24/1.79 tff(3854,plain,
% 2.24/1.79 (~c3_1(a697)),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[1355, 3853])).
% 2.24/1.79 tff(3855,assumption,(c2_1(a692)), introduced(assumption)).
% 2.24/1.79 tff(3856,plain,
% 2.24/1.79 (c0_1(a697)),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[508, 3853])).
% 2.24/1.79 tff(3857,plain,
% 2.24/1.79 (c1_1(a697)),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[3654, 227, 2771, 2760, 3856, 3855, 3854, 3851, 3850, 566, 11])).
% 2.24/1.79 tff(3858,assumption,(~hskp5), introduced(assumption)).
% 2.24/1.79 tff(3859,plain,
% 2.24/1.79 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp5 | c0_1(a760) | c2_1(a702) | (~ndr1_0) | (~c1_1(a702)) | (~c0_1(a702)) | (~c2_1(a760)) | (~c1_1(a760)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp5 | c0_1(a760) | c2_1(a702) | (~ndr1_0) | (~c1_1(a702)) | (~c0_1(a702)) | (~c2_1(a760)) | (~c1_1(a760)))),
% 2.24/1.79 inference(rewrite,[status(thm)],[])).
% 2.24/1.79 tff(3860,plain,
% 2.24/1.79 ((hskp5 | (~ndr1_0) | c2_1(a702) | (~c0_1(a702)) | (~c1_1(a702)) | c0_1(a760) | (~c2_1(a760)) | (~c1_1(a760))) <=> (hskp5 | c0_1(a760) | c2_1(a702) | (~ndr1_0) | (~c1_1(a702)) | (~c0_1(a702)) | (~c2_1(a760)) | (~c1_1(a760)))),
% 2.24/1.79 inference(rewrite,[status(thm)],[])).
% 2.24/1.79 tff(3861,plain,
% 2.24/1.79 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a702) | (~c0_1(a702)) | (~c1_1(a702)) | c0_1(a760) | (~c2_1(a760)) | (~c1_1(a760)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp5 | c0_1(a760) | c2_1(a702) | (~ndr1_0) | (~c1_1(a702)) | (~c0_1(a702)) | (~c2_1(a760)) | (~c1_1(a760))))),
% 2.24/1.79 inference(monotonicity,[status(thm)],[3860])).
% 2.24/1.79 tff(3862,plain,
% 2.24/1.79 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a702) | (~c0_1(a702)) | (~c1_1(a702)) | c0_1(a760) | (~c2_1(a760)) | (~c1_1(a760)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp5 | c0_1(a760) | c2_1(a702) | (~ndr1_0) | (~c1_1(a702)) | (~c0_1(a702)) | (~c2_1(a760)) | (~c1_1(a760)))),
% 2.24/1.79 inference(transitivity,[status(thm)],[3861, 3859])).
% 2.24/1.79 tff(3863,plain,
% 2.24/1.79 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a702) | (~c0_1(a702)) | (~c1_1(a702)) | c0_1(a760) | (~c2_1(a760)) | (~c1_1(a760)))),
% 2.24/1.79 inference(quant_inst,[status(thm)],[])).
% 2.24/1.79 tff(3864,plain,
% 2.24/1.79 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp5 | c0_1(a760) | c2_1(a702) | (~ndr1_0) | (~c1_1(a702)) | (~c0_1(a702)) | (~c2_1(a760)) | (~c1_1(a760))),
% 2.24/1.79 inference(modus_ponens,[status(thm)],[3863, 3862])).
% 2.24/1.79 tff(3865,plain,
% 2.24/1.79 (hskp5 | (~c1_1(a702)) | (~c2_1(a760))),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[3864, 227, 3194, 3833, 3192, 3831, 3682])).
% 2.24/1.79 tff(3866,plain,
% 2.24/1.79 (~c1_1(a702)),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[3865, 3858, 3852])).
% 2.24/1.79 tff(3867,plain,
% 2.24/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c2_1(a702) | c1_1(a692) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a692)) | (~c3_1(a692)) | (~c3_1(a702)) | c1_1(a702))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c2_1(a702) | c1_1(a692) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a692)) | (~c3_1(a692)) | (~c3_1(a702)) | c1_1(a702))),
% 2.24/1.79 inference(rewrite,[status(thm)],[])).
% 2.24/1.79 tff(3868,plain,
% 2.24/1.79 (((~ndr1_0) | c3_1(a695) | (~c0_1(a695)) | (~c1_1(a695)) | c1_1(a692) | (~c2_1(a692)) | (~c3_1(a692)) | c2_1(a702) | (~c3_1(a702)) | c1_1(a702)) <=> (c2_1(a702) | c1_1(a692) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a692)) | (~c3_1(a692)) | (~c3_1(a702)) | c1_1(a702))),
% 2.24/1.79 inference(rewrite,[status(thm)],[])).
% 2.24/1.79 tff(3869,plain,
% 2.24/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a695) | (~c0_1(a695)) | (~c1_1(a695)) | c1_1(a692) | (~c2_1(a692)) | (~c3_1(a692)) | c2_1(a702) | (~c3_1(a702)) | c1_1(a702))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c2_1(a702) | c1_1(a692) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a692)) | (~c3_1(a692)) | (~c3_1(a702)) | c1_1(a702)))),
% 2.24/1.79 inference(monotonicity,[status(thm)],[3868])).
% 2.24/1.79 tff(3870,plain,
% 2.24/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a695) | (~c0_1(a695)) | (~c1_1(a695)) | c1_1(a692) | (~c2_1(a692)) | (~c3_1(a692)) | c2_1(a702) | (~c3_1(a702)) | c1_1(a702))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c2_1(a702) | c1_1(a692) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a692)) | (~c3_1(a692)) | (~c3_1(a702)) | c1_1(a702))),
% 2.24/1.79 inference(transitivity,[status(thm)],[3869, 3867])).
% 2.24/1.79 tff(3871,plain,
% 2.24/1.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a695) | (~c0_1(a695)) | (~c1_1(a695)) | c1_1(a692) | (~c2_1(a692)) | (~c3_1(a692)) | c2_1(a702) | (~c3_1(a702)) | c1_1(a702))),
% 2.24/1.79 inference(quant_inst,[status(thm)],[])).
% 2.24/1.79 tff(3872,plain,
% 2.24/1.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c2_1(a702) | c1_1(a692) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a692)) | (~c3_1(a692)) | (~c3_1(a702)) | c1_1(a702)),
% 2.24/1.79 inference(modus_ponens,[status(thm)],[3871, 3870])).
% 2.24/1.79 tff(3873,plain,
% 2.24/1.79 ((~c3_1(a692)) | c1_1(a702)),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[3872, 227, 2802, 2771, 3832, 3855, 3831, 3850, 3116, 11])).
% 2.24/1.79 tff(3874,plain,
% 2.24/1.79 (~c3_1(a692)),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[3873, 3866])).
% 2.24/1.79 tff(3875,plain,
% 2.24/1.79 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c0_1(a760) | c0_1(a692) | (~ndr1_0) | (~c2_1(a692)) | c3_1(a692) | (~c3_1(a760)) | (~c1_1(a760)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a760) | c0_1(a692) | (~ndr1_0) | (~c2_1(a692)) | c3_1(a692) | (~c3_1(a760)) | (~c1_1(a760)))),
% 2.24/1.79 inference(rewrite,[status(thm)],[])).
% 2.24/1.79 tff(3876,plain,
% 2.24/1.79 ((hskp10 | (~ndr1_0) | c0_1(a760) | (~c3_1(a760)) | (~c1_1(a760)) | c3_1(a692) | c0_1(a692) | (~c2_1(a692))) <=> (hskp10 | c0_1(a760) | c0_1(a692) | (~ndr1_0) | (~c2_1(a692)) | c3_1(a692) | (~c3_1(a760)) | (~c1_1(a760)))),
% 2.24/1.79 inference(rewrite,[status(thm)],[])).
% 2.24/1.79 tff(3877,plain,
% 2.24/1.79 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a760) | (~c3_1(a760)) | (~c1_1(a760)) | c3_1(a692) | c0_1(a692) | (~c2_1(a692)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c0_1(a760) | c0_1(a692) | (~ndr1_0) | (~c2_1(a692)) | c3_1(a692) | (~c3_1(a760)) | (~c1_1(a760))))),
% 2.24/1.79 inference(monotonicity,[status(thm)],[3876])).
% 2.24/1.79 tff(3878,plain,
% 2.24/1.79 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a760) | (~c3_1(a760)) | (~c1_1(a760)) | c3_1(a692) | c0_1(a692) | (~c2_1(a692)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a760) | c0_1(a692) | (~ndr1_0) | (~c2_1(a692)) | c3_1(a692) | (~c3_1(a760)) | (~c1_1(a760)))),
% 2.24/1.79 inference(transitivity,[status(thm)],[3877, 3875])).
% 2.24/1.79 tff(3879,plain,
% 2.24/1.79 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c0_1(a760) | (~c3_1(a760)) | (~c1_1(a760)) | c3_1(a692) | c0_1(a692) | (~c2_1(a692)))),
% 2.24/1.79 inference(quant_inst,[status(thm)],[])).
% 2.24/1.79 tff(3880,plain,
% 2.24/1.79 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a760) | c0_1(a692) | (~ndr1_0) | (~c2_1(a692)) | c3_1(a692) | (~c3_1(a760)) | (~c1_1(a760))),
% 2.24/1.79 inference(modus_ponens,[status(thm)],[3879, 3878])).
% 2.24/1.79 tff(3881,plain,
% 2.24/1.79 (hskp10),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[3880, 227, 3194, 3193, 3855, 3192, 3851, 1749, 3874])).
% 2.24/1.79 tff(3882,plain,
% 2.24/1.79 (~c2_1(a717)),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[1893, 3881])).
% 2.24/1.79 tff(3883,plain,
% 2.24/1.79 (c2_1(a697)),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[527, 3853])).
% 2.24/1.79 tff(3884,plain,
% 2.24/1.79 (c1_1(a717)),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[3023, 3881])).
% 2.24/1.79 tff(3885,plain,
% 2.24/1.79 (c0_1(a717)),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[3211, 227, 3884, 3856, 3883, 3882, 3854, 822, 3857])).
% 2.24/1.79 tff(3886,plain,
% 2.24/1.79 ($false),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[3688, 227, 3858, 3194, 3884, 3192, 3882, 3682, 3852, 3885])).
% 2.24/1.79 tff(3887,plain,(hskp5 | (~c2_1(a760)) | (~c2_1(a692)) | c0_1(a692) | c1_1(a692) | c3_1(a695)), inference(lemma,lemma(discharge,[]))).
% 2.24/1.79 tff(3888,plain,
% 2.24/1.79 (hskp5),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[3887, 3844, 3847, 3842, 3841, 11])).
% 2.24/1.79 tff(3889,plain,
% 2.24/1.79 (c2_1(a701)),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[39, 3888])).
% 2.24/1.79 tff(3890,plain,
% 2.24/1.79 (c0_1(a701)),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[50, 3888])).
% 2.24/1.79 tff(3891,plain,
% 2.24/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a698) | c2_1(a698) | c3_1(a698) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a698) | c2_1(a698) | c3_1(a698) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)))),
% 2.24/1.79 inference(rewrite,[status(thm)],[])).
% 2.24/1.79 tff(3892,plain,
% 2.24/1.79 (((~ndr1_0) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c3_1(a698) | c2_1(a698) | c0_1(a698)) <=> (c0_1(a698) | c2_1(a698) | c3_1(a698) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)))),
% 2.24/1.79 inference(rewrite,[status(thm)],[])).
% 2.24/1.79 tff(3893,plain,
% 2.24/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c3_1(a698) | c2_1(a698) | c0_1(a698))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a698) | c2_1(a698) | c3_1(a698) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701))))),
% 2.24/1.79 inference(monotonicity,[status(thm)],[3892])).
% 2.24/1.79 tff(3894,plain,
% 2.24/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c3_1(a698) | c2_1(a698) | c0_1(a698))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a698) | c2_1(a698) | c3_1(a698) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)))),
% 2.24/1.79 inference(transitivity,[status(thm)],[3893, 3891])).
% 2.24/1.79 tff(3895,plain,
% 2.24/1.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c3_1(a698) | c2_1(a698) | c0_1(a698))),
% 2.24/1.79 inference(quant_inst,[status(thm)],[])).
% 2.24/1.79 tff(3896,plain,
% 2.24/1.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a698) | c2_1(a698) | c3_1(a698) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | (~c1_1(a697)) | (~c2_1(a701)) | (~c3_1(a701)) | (~c0_1(a701))),
% 2.24/1.79 inference(modus_ponens,[status(thm)],[3895, 3894])).
% 2.24/1.79 tff(3897,plain,
% 2.24/1.79 (~c3_1(a701)),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[3896, 227, 3890, 3889, 3848, 1360, 1359, 1358, 3846, 1777, 3849])).
% 2.24/1.79 tff(3898,plain,
% 2.24/1.79 (~c1_1(a701)),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[28, 3888])).
% 2.24/1.79 tff(3899,plain,
% 2.24/1.79 (c2_1(a697)),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[527, 3845])).
% 2.24/1.79 tff(3900,plain,
% 2.24/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | (c1_1(a701) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c1_1(a697)) | (~c2_1(a697)) | c3_1(a701) | (~c0_1(a701)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c1_1(a701) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c1_1(a697)) | (~c2_1(a697)) | c3_1(a701) | (~c0_1(a701)))),
% 2.24/1.79 inference(rewrite,[status(thm)],[])).
% 2.24/1.79 tff(3901,plain,
% 2.24/1.79 (((~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a701) | c1_1(a701) | (~c0_1(a701)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692)) <=> (c1_1(a701) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c1_1(a697)) | (~c2_1(a697)) | c3_1(a701) | (~c0_1(a701)))),
% 2.24/1.79 inference(rewrite,[status(thm)],[])).
% 2.24/1.79 tff(3902,plain,
% 2.24/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a701) | c1_1(a701) | (~c0_1(a701)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | (c1_1(a701) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c1_1(a697)) | (~c2_1(a697)) | c3_1(a701) | (~c0_1(a701))))),
% 2.24/1.79 inference(monotonicity,[status(thm)],[3901])).
% 2.24/1.79 tff(3903,plain,
% 2.24/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a701) | c1_1(a701) | (~c0_1(a701)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c1_1(a701) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c1_1(a697)) | (~c2_1(a697)) | c3_1(a701) | (~c0_1(a701)))),
% 2.24/1.79 inference(transitivity,[status(thm)],[3902, 3900])).
% 2.24/1.79 tff(3904,plain,
% 2.24/1.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a697) | (~c2_1(a697)) | (~c1_1(a697)) | c3_1(a701) | c1_1(a701) | (~c0_1(a701)) | c0_1(a692) | (~c2_1(a692)) | c1_1(a692))),
% 2.24/1.79 inference(quant_inst,[status(thm)],[])).
% 2.24/1.79 tff(3905,plain,
% 2.24/1.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c1_1(a701) | c3_1(a697) | c0_1(a692) | c1_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c1_1(a697)) | (~c2_1(a697)) | c3_1(a701) | (~c0_1(a701))),
% 2.24/1.79 inference(modus_ponens,[status(thm)],[3904, 3903])).
% 2.24/1.79 tff(3906,plain,
% 2.24/1.79 ($false),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[3905, 227, 3890, 3899, 3847, 3898, 3846, 3842, 3841, 566, 3849, 3897])).
% 2.24/1.79 tff(3907,plain,((~hskp4) | c3_1(a695)), inference(lemma,lemma(discharge,[]))).
% 2.24/1.79 tff(3908,plain,
% 2.24/1.79 (~hskp4),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[3907, 11])).
% 2.24/1.79 tff(3909,plain,
% 2.24/1.79 (~hskp23),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[2943, 3908, 2822])).
% 2.24/1.79 tff(3910,plain,
% 2.24/1.79 (hskp24),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[2884, 3909])).
% 2.24/1.79 tff(3911,plain,
% 2.24/1.79 (~c2_1(a764)),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[313, 3910])).
% 2.24/1.79 tff(3912,plain,
% 2.24/1.79 (c1_1(a764)),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[324, 3910])).
% 2.24/1.79 tff(3913,plain,
% 2.24/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a764) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | c0_1(a764) | (~c1_1(a764)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a764) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | c0_1(a764) | (~c1_1(a764)))),
% 2.24/1.79 inference(rewrite,[status(thm)],[])).
% 2.24/1.79 tff(3914,plain,
% 2.24/1.79 (((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c2_1(a764) | c0_1(a764) | (~c1_1(a764))) <=> (c2_1(a764) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | c0_1(a764) | (~c1_1(a764)))),
% 2.24/1.79 inference(rewrite,[status(thm)],[])).
% 2.24/1.79 tff(3915,plain,
% 2.24/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c2_1(a764) | c0_1(a764) | (~c1_1(a764)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a764) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | c0_1(a764) | (~c1_1(a764))))),
% 2.24/1.79 inference(monotonicity,[status(thm)],[3914])).
% 2.24/1.79 tff(3916,plain,
% 2.24/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c2_1(a764) | c0_1(a764) | (~c1_1(a764)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a764) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | c0_1(a764) | (~c1_1(a764)))),
% 2.24/1.79 inference(transitivity,[status(thm)],[3915, 3913])).
% 2.24/1.79 tff(3917,plain,
% 2.24/1.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c0_1(a695)) | c2_1(a764) | c0_1(a764) | (~c1_1(a764)))),
% 2.24/1.79 inference(quant_inst,[status(thm)],[])).
% 2.24/1.79 tff(3918,plain,
% 2.24/1.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a764) | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | c0_1(a764) | (~c1_1(a764))),
% 2.24/1.79 inference(modus_ponens,[status(thm)],[3917, 3916])).
% 2.24/1.79 tff(3919,plain,
% 2.24/1.79 (c0_1(a764)),
% 2.24/1.79 inference(unit_resolution,[status(thm)],[3918, 227, 2802, 2771, 2760, 3912, 3911, 822, 11])).
% 2.24/1.79 tff(3920,plain,
% 2.24/1.79 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp5 | c2_1(a764) | c0_1(a760) | (~ndr1_0) | (~c2_1(a760)) | (~c1_1(a760)) | (~c0_1(a764)) | (~c1_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp5 | c2_1(a764) | c0_1(a760) | (~ndr1_0) | (~c2_1(a760)) | (~c1_1(a760)) | (~c0_1(a764)) | (~c1_1(a764)))),
% 2.24/1.79 inference(rewrite,[status(thm)],[])).
% 2.24/1.79 tff(3921,plain,
% 2.24/1.79 ((hskp5 | (~ndr1_0) | c2_1(a764) | (~c0_1(a764)) | (~c1_1(a764)) | c0_1(a760) | (~c2_1(a760)) | (~c1_1(a760))) <=> (hskp5 | c2_1(a764) | c0_1(a760) | (~ndr1_0) | (~c2_1(a760)) | (~c1_1(a760)) | (~c0_1(a764)) | (~c1_1(a764)))),
% 2.24/1.79 inference(rewrite,[status(thm)],[])).
% 2.24/1.79 tff(3922,plain,
% 2.24/1.79 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a764) | (~c0_1(a764)) | (~c1_1(a764)) | c0_1(a760) | (~c2_1(a760)) | (~c1_1(a760)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp5 | c2_1(a764) | c0_1(a760) | (~ndr1_0) | (~c2_1(a760)) | (~c1_1(a760)) | (~c0_1(a764)) | (~c1_1(a764))))),
% 2.24/1.79 inference(monotonicity,[status(thm)],[3921])).
% 2.24/1.79 tff(3923,plain,
% 2.24/1.79 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a764) | (~c0_1(a764)) | (~c1_1(a764)) | c0_1(a760) | (~c2_1(a760)) | (~c1_1(a760)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp5 | c2_1(a764) | c0_1(a760) | (~ndr1_0) | (~c2_1(a760)) | (~c1_1(a760)) | (~c0_1(a764)) | (~c1_1(a764)))),
% 2.24/1.79 inference(transitivity,[status(thm)],[3922, 3920])).
% 2.24/1.80 tff(3924,plain,
% 2.24/1.80 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a764) | (~c0_1(a764)) | (~c1_1(a764)) | c0_1(a760) | (~c2_1(a760)) | (~c1_1(a760)))),
% 2.24/1.80 inference(quant_inst,[status(thm)],[])).
% 2.24/1.80 tff(3925,plain,
% 2.24/1.80 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp5 | c2_1(a764) | c0_1(a760) | (~ndr1_0) | (~c2_1(a760)) | (~c1_1(a760)) | (~c0_1(a764)) | (~c1_1(a764))),
% 2.24/1.80 inference(modus_ponens,[status(thm)],[3924, 3923])).
% 2.24/1.80 tff(3926,plain,
% 2.24/1.80 (hskp5 | (~c2_1(a760))),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[3925, 227, 3912, 3194, 3911, 3192, 3682, 3919])).
% 2.24/1.80 tff(3927,plain,
% 2.24/1.80 (~c2_1(a760)),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[3926, 2780])).
% 2.24/1.80 tff(3928,plain,
% 2.24/1.80 (((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp5 | hskp1 | c2_1(a764) | (~ndr1_0) | (~c0_1(a764)) | (~c1_1(a764)))) <=> ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp5 | hskp1 | c2_1(a764) | (~ndr1_0) | (~c0_1(a764)) | (~c1_1(a764)))),
% 2.24/1.80 inference(rewrite,[status(thm)],[])).
% 2.24/1.80 tff(3929,plain,
% 2.24/1.80 ((hskp5 | hskp1 | (~ndr1_0) | c2_1(a764) | (~c0_1(a764)) | (~c1_1(a764))) <=> (hskp5 | hskp1 | c2_1(a764) | (~ndr1_0) | (~c0_1(a764)) | (~c1_1(a764)))),
% 2.24/1.80 inference(rewrite,[status(thm)],[])).
% 2.24/1.80 tff(3930,plain,
% 2.24/1.80 (((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp5 | hskp1 | (~ndr1_0) | c2_1(a764) | (~c0_1(a764)) | (~c1_1(a764)))) <=> ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp5 | hskp1 | c2_1(a764) | (~ndr1_0) | (~c0_1(a764)) | (~c1_1(a764))))),
% 2.24/1.80 inference(monotonicity,[status(thm)],[3929])).
% 2.24/1.80 tff(3931,plain,
% 2.24/1.80 (((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp5 | hskp1 | (~ndr1_0) | c2_1(a764) | (~c0_1(a764)) | (~c1_1(a764)))) <=> ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp5 | hskp1 | c2_1(a764) | (~ndr1_0) | (~c0_1(a764)) | (~c1_1(a764)))),
% 2.24/1.80 inference(transitivity,[status(thm)],[3930, 3928])).
% 2.24/1.80 tff(3932,plain,
% 2.24/1.80 ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp5 | hskp1 | (~ndr1_0) | c2_1(a764) | (~c0_1(a764)) | (~c1_1(a764)))),
% 2.24/1.80 inference(quant_inst,[status(thm)],[])).
% 2.24/1.80 tff(3933,plain,
% 2.24/1.80 ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp5 | hskp1 | c2_1(a764) | (~ndr1_0) | (~c0_1(a764)) | (~c1_1(a764))),
% 2.24/1.80 inference(modus_ponens,[status(thm)],[3932, 3931])).
% 2.24/1.80 tff(3934,plain,
% 2.24/1.80 (hskp5 | hskp1 | (~c0_1(a764))),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[3933, 227, 3912, 3911, 1585])).
% 2.24/1.80 tff(3935,plain,
% 2.24/1.80 (hskp1),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[3934, 2780, 3919])).
% 2.24/1.80 tff(3936,plain,
% 2.24/1.80 (~c3_1(a693)),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[1553, 3935])).
% 2.24/1.80 tff(3937,plain,
% 2.24/1.80 (~c1_1(a693)),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[1423, 3935])).
% 2.24/1.80 tff(3938,plain,
% 2.24/1.80 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp16 | hskp15 | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)))),
% 2.24/1.80 inference(rewrite,[status(thm)],[])).
% 2.24/1.80 tff(3939,plain,
% 2.24/1.80 ((hskp16 | hskp15 | (~ndr1_0) | c3_1(a695) | (~c0_1(a695)) | (~c1_1(a695))) <=> (hskp16 | hskp15 | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)))),
% 2.24/1.80 inference(rewrite,[status(thm)],[])).
% 2.24/1.80 tff(3940,plain,
% 2.24/1.80 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c3_1(a695) | (~c0_1(a695)) | (~c1_1(a695)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695))))),
% 2.24/1.80 inference(monotonicity,[status(thm)],[3939])).
% 2.24/1.80 tff(3941,plain,
% 2.24/1.80 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c3_1(a695) | (~c0_1(a695)) | (~c1_1(a695)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp16 | hskp15 | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695)))),
% 2.24/1.80 inference(transitivity,[status(thm)],[3940, 3938])).
% 2.24/1.80 tff(3942,plain,
% 2.24/1.80 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c3_1(a695) | (~c0_1(a695)) | (~c1_1(a695)))),
% 2.24/1.80 inference(quant_inst,[status(thm)],[])).
% 2.24/1.80 tff(3943,plain,
% 2.24/1.80 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp16 | hskp15 | (~ndr1_0) | (~c0_1(a695)) | c3_1(a695) | (~c1_1(a695))),
% 2.24/1.80 inference(modus_ponens,[status(thm)],[3942, 3941])).
% 2.24/1.80 tff(3944,plain,
% 2.24/1.80 (hskp16 | hskp15 | c3_1(a695)),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[3943, 227, 2802, 2771, 3748])).
% 2.24/1.80 tff(3945,plain,
% 2.24/1.80 (hskp15),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[3944, 12, 11])).
% 2.24/1.80 tff(3946,plain,
% 2.24/1.80 (~c2_1(a734)),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[3760, 3945])).
% 2.24/1.80 tff(3947,plain,
% 2.24/1.80 (~c1_1(a734)),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[3766, 3945])).
% 2.24/1.80 tff(3948,plain,
% 2.24/1.80 (c2_1(a693)),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[383, 3935])).
% 2.24/1.80 tff(3949,plain,
% 2.24/1.80 (c3_1(a734)),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[3779, 3945])).
% 2.24/1.80 tff(3950,plain,
% 2.24/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a760) | c1_1(a734) | c2_1(a734) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c3_1(a734)) | (~c3_1(a760)) | c2_1(a760))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a760) | c1_1(a734) | c2_1(a734) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c3_1(a734)) | (~c3_1(a760)) | c2_1(a760))),
% 2.24/1.80 inference(rewrite,[status(thm)],[])).
% 2.24/1.80 tff(3951,plain,
% 2.24/1.80 (((~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c2_1(a693)) | c1_1(a734) | c2_1(a734) | (~c3_1(a734)) | c2_1(a760) | c0_1(a760) | (~c3_1(a760))) <=> (c0_1(a760) | c1_1(a734) | c2_1(a734) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c3_1(a734)) | (~c3_1(a760)) | c2_1(a760))),
% 2.24/1.80 inference(rewrite,[status(thm)],[])).
% 2.24/1.80 tff(3952,plain,
% 2.24/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c2_1(a693)) | c1_1(a734) | c2_1(a734) | (~c3_1(a734)) | c2_1(a760) | c0_1(a760) | (~c3_1(a760)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a760) | c1_1(a734) | c2_1(a734) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c3_1(a734)) | (~c3_1(a760)) | c2_1(a760)))),
% 2.24/1.80 inference(monotonicity,[status(thm)],[3951])).
% 2.24/1.80 tff(3953,plain,
% 2.24/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c2_1(a693)) | c1_1(a734) | c2_1(a734) | (~c3_1(a734)) | c2_1(a760) | c0_1(a760) | (~c3_1(a760)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a760) | c1_1(a734) | c2_1(a734) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c3_1(a734)) | (~c3_1(a760)) | c2_1(a760))),
% 2.24/1.80 inference(transitivity,[status(thm)],[3952, 3950])).
% 2.24/1.80 tff(3954,plain,
% 2.24/1.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a693) | c1_1(a693) | (~c2_1(a693)) | c1_1(a734) | c2_1(a734) | (~c3_1(a734)) | c2_1(a760) | c0_1(a760) | (~c3_1(a760)))),
% 2.24/1.80 inference(quant_inst,[status(thm)],[])).
% 2.24/1.80 tff(3955,plain,
% 2.24/1.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a760) | c1_1(a734) | c2_1(a734) | c1_1(a693) | c3_1(a693) | (~ndr1_0) | (~c2_1(a693)) | (~c3_1(a734)) | (~c3_1(a760)) | c2_1(a760)),
% 2.24/1.80 inference(modus_ponens,[status(thm)],[3954, 3953])).
% 2.24/1.80 tff(3956,plain,
% 2.24/1.80 ($false),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[3955, 227, 3193, 3949, 3948, 3192, 3947, 3946, 3937, 3936, 948, 3927])).
% 2.24/1.80 tff(3957,plain,(hskp16 | c3_1(a695)), inference(lemma,lemma(discharge,[]))).
% 2.24/1.80 tff(3958,plain,
% 2.24/1.80 (hskp16),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[3957, 11])).
% 2.24/1.80 tff(3959,plain,
% 2.24/1.80 (~c1_1(a738)),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[3121, 3958])).
% 2.24/1.80 tff(3960,plain,
% 2.24/1.80 (~c3_1(a764)),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[307, 3910])).
% 2.24/1.80 tff(3961,plain,
% 2.24/1.80 (c3_1(a738)),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[3087, 3958])).
% 2.24/1.80 tff(3962,plain,
% 2.24/1.80 (c2_1(a738)),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[3098, 3958])).
% 2.24/1.80 tff(3963,plain,
% 2.24/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a764) | c3_1(a764) | c0_1(a760) | c1_1(a738) | (~ndr1_0) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a760)) | (~c2_1(a760)) | (~c1_1(a764)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a764) | c3_1(a764) | c0_1(a760) | c1_1(a738) | (~ndr1_0) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a760)) | (~c2_1(a760)) | (~c1_1(a764)))),
% 2.24/1.80 inference(rewrite,[status(thm)],[])).
% 2.24/1.80 tff(3964,plain,
% 2.24/1.80 (((~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c0_1(a760) | (~c3_1(a760)) | (~c2_1(a760))) <=> (c2_1(a764) | c3_1(a764) | c0_1(a760) | c1_1(a738) | (~ndr1_0) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a760)) | (~c2_1(a760)) | (~c1_1(a764)))),
% 2.24/1.80 inference(rewrite,[status(thm)],[])).
% 2.24/1.80 tff(3965,plain,
% 2.24/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c0_1(a760) | (~c3_1(a760)) | (~c2_1(a760)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a764) | c3_1(a764) | c0_1(a760) | c1_1(a738) | (~ndr1_0) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a760)) | (~c2_1(a760)) | (~c1_1(a764))))),
% 2.24/1.80 inference(monotonicity,[status(thm)],[3964])).
% 2.24/1.80 tff(3966,plain,
% 2.24/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c0_1(a760) | (~c3_1(a760)) | (~c2_1(a760)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a764) | c3_1(a764) | c0_1(a760) | c1_1(a738) | (~ndr1_0) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a760)) | (~c2_1(a760)) | (~c1_1(a764)))),
% 2.24/1.80 inference(transitivity,[status(thm)],[3965, 3963])).
% 2.24/1.80 tff(3967,plain,
% 2.24/1.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c1_1(a764)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c0_1(a760) | (~c3_1(a760)) | (~c2_1(a760)))),
% 2.24/1.80 inference(quant_inst,[status(thm)],[])).
% 2.24/1.80 tff(3968,plain,
% 2.24/1.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a764) | c3_1(a764) | c0_1(a760) | c1_1(a738) | (~ndr1_0) | (~c2_1(a738)) | (~c3_1(a738)) | (~c3_1(a760)) | (~c2_1(a760)) | (~c1_1(a764))),
% 2.24/1.80 inference(modus_ponens,[status(thm)],[3967, 3966])).
% 2.24/1.80 tff(3969,plain,
% 2.24/1.80 (~c2_1(a760)),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[3968, 227, 3912, 3193, 3962, 3961, 3911, 3960, 3192, 3959, 10])).
% 2.24/1.80 tff(3970,plain,
% 2.24/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a764) | c0_1(a760) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | c2_1(a760) | (~c1_1(a760)) | (~c0_1(a764)) | (~c1_1(a764)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a764) | c0_1(a760) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | c2_1(a760) | (~c1_1(a760)) | (~c0_1(a764)) | (~c1_1(a764)))),
% 2.24/1.80 inference(rewrite,[status(thm)],[])).
% 2.24/1.80 tff(3971,plain,
% 2.24/1.80 (((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764)) | c2_1(a760) | c0_1(a760) | (~c1_1(a760))) <=> (c3_1(a764) | c0_1(a760) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | c2_1(a760) | (~c1_1(a760)) | (~c0_1(a764)) | (~c1_1(a764)))),
% 2.24/1.80 inference(rewrite,[status(thm)],[])).
% 2.24/1.80 tff(3972,plain,
% 2.24/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764)) | c2_1(a760) | c0_1(a760) | (~c1_1(a760)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a764) | c0_1(a760) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | c2_1(a760) | (~c1_1(a760)) | (~c0_1(a764)) | (~c1_1(a764))))),
% 2.24/1.80 inference(monotonicity,[status(thm)],[3971])).
% 2.24/1.80 tff(3973,plain,
% 2.24/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764)) | c2_1(a760) | c0_1(a760) | (~c1_1(a760)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a764) | c0_1(a760) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | c2_1(a760) | (~c1_1(a760)) | (~c0_1(a764)) | (~c1_1(a764)))),
% 2.24/1.80 inference(transitivity,[status(thm)],[3972, 3970])).
% 2.24/1.80 tff(3974,plain,
% 2.24/1.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764)) | c2_1(a760) | c0_1(a760) | (~c1_1(a760)))),
% 2.24/1.80 inference(quant_inst,[status(thm)],[])).
% 2.24/1.80 tff(3975,plain,
% 2.24/1.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a764) | c0_1(a760) | (~ndr1_0) | c3_1(a695) | (~c1_1(a695)) | (~c2_1(a695)) | c2_1(a760) | (~c1_1(a760)) | (~c0_1(a764)) | (~c1_1(a764))),
% 2.24/1.80 inference(modus_ponens,[status(thm)],[3974, 3973])).
% 2.24/1.80 tff(3976,plain,
% 2.24/1.80 ($false),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[3975, 227, 2771, 2760, 3912, 3194, 3960, 3192, 822, 3919, 11, 3969])).
% 2.24/1.80 tff(3977,plain,(c3_1(a695)), inference(lemma,lemma(discharge,[]))).
% 2.24/1.80 tff(3978,plain,
% 2.24/1.80 (~hskp7),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[3313, 280, 3977])).
% 2.24/1.80 tff(3979,plain,
% 2.24/1.80 (hskp29),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[3422, 3046, 3978])).
% 2.24/1.80 tff(3980,plain,
% 2.24/1.80 (c2_1(a713)),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[3444, 3979])).
% 2.24/1.80 tff(3981,plain,
% 2.24/1.80 (c0_1(a713)),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[3455, 3979])).
% 2.24/1.80 tff(3982,plain,
% 2.24/1.80 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | (~c0_1(a713)) | (~c2_1(a713)) | c1_1(a713))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | (~ndr1_0) | (~c0_1(a713)) | (~c2_1(a713)) | c1_1(a713))),
% 2.24/1.80 inference(rewrite,[status(thm)],[])).
% 2.24/1.80 tff(3983,plain,
% 2.24/1.80 ((hskp16 | hskp7 | (~ndr1_0) | c1_1(a713) | (~c2_1(a713)) | (~c0_1(a713))) <=> (hskp16 | hskp7 | (~ndr1_0) | (~c0_1(a713)) | (~c2_1(a713)) | c1_1(a713))),
% 2.24/1.80 inference(rewrite,[status(thm)],[])).
% 2.24/1.80 tff(3984,plain,
% 2.24/1.80 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c1_1(a713) | (~c2_1(a713)) | (~c0_1(a713)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | (~c0_1(a713)) | (~c2_1(a713)) | c1_1(a713)))),
% 2.24/1.80 inference(monotonicity,[status(thm)],[3983])).
% 2.24/1.80 tff(3985,plain,
% 2.24/1.80 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c1_1(a713) | (~c2_1(a713)) | (~c0_1(a713)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | (~ndr1_0) | (~c0_1(a713)) | (~c2_1(a713)) | c1_1(a713))),
% 2.24/1.80 inference(transitivity,[status(thm)],[3984, 3982])).
% 2.24/1.80 tff(3986,plain,
% 2.24/1.80 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c1_1(a713) | (~c2_1(a713)) | (~c0_1(a713)))),
% 2.24/1.80 inference(quant_inst,[status(thm)],[])).
% 2.24/1.80 tff(3987,plain,
% 2.24/1.80 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | (~ndr1_0) | (~c0_1(a713)) | (~c2_1(a713)) | c1_1(a713)),
% 2.24/1.80 inference(modus_ponens,[status(thm)],[3986, 3985])).
% 2.24/1.80 tff(3988,plain,
% 2.24/1.80 (c1_1(a713)),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[3987, 227, 12, 3978, 3981, 3980, 3358])).
% 2.24/1.80 tff(3989,plain,
% 2.24/1.80 (c2_1(a725)),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[3392, 3049, 3977, 3978, 12, 3050, 3182])).
% 2.24/1.80 tff(3990,plain,
% 2.24/1.80 (c3_1(a713)),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[3433, 3979])).
% 2.24/1.80 tff(3991,plain,
% 2.24/1.80 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c2_1(a713)) | (~c1_1(a713)) | (~c3_1(a713)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c2_1(a713)) | (~c1_1(a713)) | (~c3_1(a713)))),
% 2.24/1.80 inference(rewrite,[status(thm)],[])).
% 2.24/1.80 tff(3992,plain,
% 2.24/1.80 ((hskp8 | (~ndr1_0) | (~c2_1(a713)) | (~c3_1(a713)) | (~c1_1(a713)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725))) <=> (hskp8 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c2_1(a713)) | (~c1_1(a713)) | (~c3_1(a713)))),
% 2.24/1.80 inference(rewrite,[status(thm)],[])).
% 2.24/1.80 tff(3993,plain,
% 2.24/1.80 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a713)) | (~c3_1(a713)) | (~c1_1(a713)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c2_1(a713)) | (~c1_1(a713)) | (~c3_1(a713))))),
% 2.24/1.80 inference(monotonicity,[status(thm)],[3992])).
% 2.24/1.80 tff(3994,plain,
% 2.24/1.80 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a713)) | (~c3_1(a713)) | (~c1_1(a713)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c2_1(a713)) | (~c1_1(a713)) | (~c3_1(a713)))),
% 2.24/1.80 inference(transitivity,[status(thm)],[3993, 3991])).
% 2.24/1.80 tff(3995,plain,
% 2.24/1.80 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a713)) | (~c3_1(a713)) | (~c1_1(a713)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))),
% 2.24/1.80 inference(quant_inst,[status(thm)],[])).
% 2.24/1.80 tff(3996,plain,
% 2.24/1.80 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c0_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c2_1(a713)) | (~c1_1(a713)) | (~c3_1(a713))),
% 2.24/1.80 inference(modus_ponens,[status(thm)],[3995, 3994])).
% 2.24/1.80 tff(3997,plain,
% 2.24/1.80 (hskp8),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[3996, 227, 3980, 3990, 3050, 3049, 1862, 3989, 3988])).
% 2.24/1.80 tff(3998,plain,
% 2.24/1.80 (c3_1(a710)),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[1886, 3997])).
% 2.24/1.80 tff(3999,plain,
% 2.24/1.80 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713)))),
% 2.24/1.80 inference(rewrite,[status(thm)],[])).
% 2.24/1.80 tff(4000,plain,
% 2.24/1.80 ((hskp14 | (~ndr1_0) | (~c2_1(a713)) | (~c3_1(a713)) | (~c0_1(a713)) | c3_1(a725) | c1_1(a725) | (~c2_1(a725))) <=> (hskp14 | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713)))),
% 2.24/1.80 inference(rewrite,[status(thm)],[])).
% 2.24/1.80 tff(4001,plain,
% 2.24/1.80 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a713)) | (~c3_1(a713)) | (~c0_1(a713)) | c3_1(a725) | c1_1(a725) | (~c2_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713))))),
% 2.24/1.80 inference(monotonicity,[status(thm)],[4000])).
% 2.24/1.80 tff(4002,plain,
% 2.24/1.80 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a713)) | (~c3_1(a713)) | (~c0_1(a713)) | c3_1(a725) | c1_1(a725) | (~c2_1(a725)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713)))),
% 2.24/1.80 inference(transitivity,[status(thm)],[4001, 3999])).
% 2.24/1.80 tff(4003,plain,
% 2.24/1.80 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | (~c2_1(a713)) | (~c3_1(a713)) | (~c0_1(a713)) | c3_1(a725) | c1_1(a725) | (~c2_1(a725)))),
% 2.24/1.80 inference(quant_inst,[status(thm)],[])).
% 2.24/1.80 tff(4004,plain,
% 2.24/1.80 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp14 | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713))),
% 2.24/1.80 inference(modus_ponens,[status(thm)],[4003, 4002])).
% 2.24/1.80 tff(4005,plain,
% 2.24/1.80 (hskp14),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[4004, 227, 3981, 3980, 3990, 3182, 3049, 1614, 3989])).
% 2.24/1.80 tff(4006,assumption,(hskp20), introduced(assumption)).
% 2.24/1.80 tff(4007,plain,
% 2.24/1.80 (~c3_1(a754)),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[668, 4006])).
% 2.24/1.80 tff(4008,plain,
% 2.24/1.80 (~c0_1(a754)),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[595, 4006])).
% 2.24/1.80 tff(4009,plain,
% 2.24/1.80 (c2_1(a754)),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[190, 4006])).
% 2.24/1.80 tff(4010,plain,
% 2.24/1.80 (c0_1(a764)),
% 2.24/1.80 inference(unit_resolution,[status(thm)],[1156, 227, 2014, 4009, 3833, 3832, 2012, 4008, 4007, 3831, 174])).
% 2.24/1.80 tff(4011,plain,
% 2.24/1.80 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp16 | hskp15 | c3_1(a764) | (~ndr1_0) | (~c0_1(a764)) | (~c1_1(a764)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp16 | hskp15 | c3_1(a764) | (~ndr1_0) | (~c0_1(a764)) | (~c1_1(a764)))),
% 2.24/1.80 inference(rewrite,[status(thm)],[])).
% 2.24/1.80 tff(4012,plain,
% 2.24/1.80 ((hskp16 | hskp15 | (~ndr1_0) | c3_1(a764) | (~c0_1(a764)) | (~c1_1(a764))) <=> (hskp16 | hskp15 | c3_1(a764) | (~ndr1_0) | (~c0_1(a764)) | (~c1_1(a764)))),
% 2.24/1.81 inference(rewrite,[status(thm)],[])).
% 2.24/1.81 tff(4013,plain,
% 2.24/1.81 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c3_1(a764) | (~c0_1(a764)) | (~c1_1(a764)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp16 | hskp15 | c3_1(a764) | (~ndr1_0) | (~c0_1(a764)) | (~c1_1(a764))))),
% 2.24/1.81 inference(monotonicity,[status(thm)],[4012])).
% 2.24/1.81 tff(4014,plain,
% 2.24/1.81 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c3_1(a764) | (~c0_1(a764)) | (~c1_1(a764)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp16 | hskp15 | c3_1(a764) | (~ndr1_0) | (~c0_1(a764)) | (~c1_1(a764)))),
% 2.24/1.81 inference(transitivity,[status(thm)],[4013, 4011])).
% 2.24/1.81 tff(4015,plain,
% 2.24/1.81 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c3_1(a764) | (~c0_1(a764)) | (~c1_1(a764)))),
% 2.24/1.81 inference(quant_inst,[status(thm)],[])).
% 2.24/1.81 tff(4016,plain,
% 2.24/1.81 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp16 | hskp15 | c3_1(a764) | (~ndr1_0) | (~c0_1(a764)) | (~c1_1(a764))),
% 2.24/1.81 inference(modus_ponens,[status(thm)],[4015, 4014])).
% 2.24/1.81 tff(4017,plain,
% 2.24/1.81 (hskp15 | (~c0_1(a764))),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[4016, 227, 12, 2014, 2012, 3748])).
% 2.24/1.81 tff(4018,plain,
% 2.24/1.81 (hskp15),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[4017, 4010])).
% 2.24/1.81 tff(4019,plain,
% 2.24/1.81 (~c2_1(a734)),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[3760, 4018])).
% 2.24/1.81 tff(4020,plain,
% 2.24/1.81 (~c1_1(a734)),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[3766, 4018])).
% 2.24/1.81 tff(4021,plain,
% 2.24/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a764) | c3_1(a764) | c0_1(a754) | c3_1(a754) | c1_1(a734) | c2_1(a734) | (~ndr1_0) | (~c0_1(a734)) | (~c2_1(a754)) | (~c0_1(a764)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a764) | c3_1(a764) | c0_1(a754) | c3_1(a754) | c1_1(a734) | c2_1(a734) | (~ndr1_0) | (~c0_1(a734)) | (~c2_1(a754)) | (~c0_1(a764)))),
% 2.24/1.81 inference(rewrite,[status(thm)],[])).
% 2.24/1.81 tff(4022,plain,
% 2.24/1.81 (((~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c0_1(a764)) | c1_1(a734) | c2_1(a734) | (~c0_1(a734)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754))) <=> (c2_1(a764) | c3_1(a764) | c0_1(a754) | c3_1(a754) | c1_1(a734) | c2_1(a734) | (~ndr1_0) | (~c0_1(a734)) | (~c2_1(a754)) | (~c0_1(a764)))),
% 2.24/1.81 inference(rewrite,[status(thm)],[])).
% 2.24/1.81 tff(4023,plain,
% 2.24/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c0_1(a764)) | c1_1(a734) | c2_1(a734) | (~c0_1(a734)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a764) | c3_1(a764) | c0_1(a754) | c3_1(a754) | c1_1(a734) | c2_1(a734) | (~ndr1_0) | (~c0_1(a734)) | (~c2_1(a754)) | (~c0_1(a764))))),
% 2.24/1.81 inference(monotonicity,[status(thm)],[4022])).
% 2.24/1.81 tff(4024,plain,
% 2.24/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c0_1(a764)) | c1_1(a734) | c2_1(a734) | (~c0_1(a734)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a764) | c3_1(a764) | c0_1(a754) | c3_1(a754) | c1_1(a734) | c2_1(a734) | (~ndr1_0) | (~c0_1(a734)) | (~c2_1(a754)) | (~c0_1(a764)))),
% 2.24/1.81 inference(transitivity,[status(thm)],[4023, 4021])).
% 2.24/1.81 tff(4025,plain,
% 2.24/1.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a764) | c2_1(a764) | (~c0_1(a764)) | c1_1(a734) | c2_1(a734) | (~c0_1(a734)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))),
% 2.24/1.81 inference(quant_inst,[status(thm)],[])).
% 2.24/1.81 tff(4026,plain,
% 2.24/1.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a764) | c3_1(a764) | c0_1(a754) | c3_1(a754) | c1_1(a734) | c2_1(a734) | (~ndr1_0) | (~c0_1(a734)) | (~c2_1(a754)) | (~c0_1(a764))),
% 2.24/1.81 inference(modus_ponens,[status(thm)],[4025, 4024])).
% 2.24/1.81 tff(4027,plain,
% 2.24/1.81 (~c0_1(a734)),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[4026, 227, 4009, 2013, 2012, 4008, 4007, 4020, 4019, 2445, 4010])).
% 2.24/1.81 tff(4028,plain,
% 2.24/1.81 (~c1_1(a754)),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[1119, 227, 4009, 3833, 3832, 4008, 4007, 3831, 174])).
% 2.24/1.81 tff(4029,plain,
% 2.24/1.81 (c3_1(a734)),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[3779, 4018])).
% 2.24/1.81 tff(4030,plain,
% 2.24/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a754) | c1_1(a734) | c2_1(a734) | (~ndr1_0) | (~c3_1(a734)) | c0_1(a734) | c1_1(a754) | (~c2_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a754) | c1_1(a734) | c2_1(a734) | (~ndr1_0) | (~c3_1(a734)) | c0_1(a734) | c1_1(a754) | (~c2_1(a754)))),
% 2.24/1.81 inference(rewrite,[status(thm)],[])).
% 2.24/1.81 tff(4031,plain,
% 2.24/1.81 (((~ndr1_0) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)) | c1_1(a734) | c2_1(a734) | (~c3_1(a734)) | c2_1(a734) | c0_1(a734) | (~c3_1(a734))) <=> (c3_1(a754) | c1_1(a734) | c2_1(a734) | (~ndr1_0) | (~c3_1(a734)) | c0_1(a734) | c1_1(a754) | (~c2_1(a754)))),
% 2.24/1.81 inference(rewrite,[status(thm)],[])).
% 2.24/1.81 tff(4032,plain,
% 2.24/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)) | c1_1(a734) | c2_1(a734) | (~c3_1(a734)) | c2_1(a734) | c0_1(a734) | (~c3_1(a734)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a754) | c1_1(a734) | c2_1(a734) | (~ndr1_0) | (~c3_1(a734)) | c0_1(a734) | c1_1(a754) | (~c2_1(a754))))),
% 2.24/1.81 inference(monotonicity,[status(thm)],[4031])).
% 2.24/1.81 tff(4033,plain,
% 2.24/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)) | c1_1(a734) | c2_1(a734) | (~c3_1(a734)) | c2_1(a734) | c0_1(a734) | (~c3_1(a734)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a754) | c1_1(a734) | c2_1(a734) | (~ndr1_0) | (~c3_1(a734)) | c0_1(a734) | c1_1(a754) | (~c2_1(a754)))),
% 2.24/1.81 inference(transitivity,[status(thm)],[4032, 4030])).
% 2.24/1.81 tff(4034,plain,
% 2.24/1.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a754) | c1_1(a754) | (~c2_1(a754)) | c1_1(a734) | c2_1(a734) | (~c3_1(a734)) | c2_1(a734) | c0_1(a734) | (~c3_1(a734)))),
% 2.24/1.81 inference(quant_inst,[status(thm)],[])).
% 2.24/1.81 tff(4035,plain,
% 2.24/1.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a754) | c1_1(a734) | c2_1(a734) | (~ndr1_0) | (~c3_1(a734)) | c0_1(a734) | c1_1(a754) | (~c2_1(a754))),
% 2.24/1.81 inference(modus_ponens,[status(thm)],[4034, 4033])).
% 2.24/1.81 tff(4036,plain,
% 2.24/1.81 ($false),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[4035, 227, 4009, 4029, 4007, 4020, 4019, 948, 4028, 4027])).
% 2.24/1.81 tff(4037,plain,((~hskp20) | c2_1(a764) | c3_1(a764) | hskp16 | (~c1_1(a764))), inference(lemma,lemma(discharge,[]))).
% 2.24/1.81 tff(4038,plain,
% 2.24/1.81 (~hskp20),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[4037, 3511, 3510, 12, 3515])).
% 2.24/1.81 tff(4039,plain,
% 2.24/1.81 (hskp11),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[3478, 3046, 474])).
% 2.24/1.81 tff(4040,plain,
% 2.24/1.81 (c3_1(a722)),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[2386, 4039])).
% 2.24/1.81 tff(4041,plain,
% 2.24/1.81 (c0_1(a722)),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[2202, 4039])).
% 2.24/1.81 tff(4042,plain,
% 2.24/1.81 (~c1_1(a722)),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[2191, 4039])).
% 2.24/1.81 tff(4043,assumption,(~c1_1(a722)), introduced(assumption)).
% 2.24/1.81 tff(4044,assumption,(c0_1(a722)), introduced(assumption)).
% 2.24/1.81 tff(4045,plain,
% 2.24/1.81 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | c1_1(a722) | (~ndr1_0) | (~c2_1(a722)) | (~c0_1(a722)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | c1_1(a722) | (~ndr1_0) | (~c2_1(a722)) | (~c0_1(a722)))),
% 2.24/1.81 inference(rewrite,[status(thm)],[])).
% 2.24/1.81 tff(4046,plain,
% 2.24/1.81 ((hskp16 | hskp7 | (~ndr1_0) | c1_1(a722) | (~c2_1(a722)) | (~c0_1(a722))) <=> (hskp16 | hskp7 | c1_1(a722) | (~ndr1_0) | (~c2_1(a722)) | (~c0_1(a722)))),
% 2.24/1.81 inference(rewrite,[status(thm)],[])).
% 2.24/1.81 tff(4047,plain,
% 2.24/1.81 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c1_1(a722) | (~c2_1(a722)) | (~c0_1(a722)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | c1_1(a722) | (~ndr1_0) | (~c2_1(a722)) | (~c0_1(a722))))),
% 2.24/1.81 inference(monotonicity,[status(thm)],[4046])).
% 2.24/1.81 tff(4048,plain,
% 2.24/1.81 (((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c1_1(a722) | (~c2_1(a722)) | (~c0_1(a722)))) <=> ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | c1_1(a722) | (~ndr1_0) | (~c2_1(a722)) | (~c0_1(a722)))),
% 2.24/1.81 inference(transitivity,[status(thm)],[4047, 4045])).
% 2.24/1.81 tff(4049,plain,
% 2.24/1.81 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp7 | (~ndr1_0) | c1_1(a722) | (~c2_1(a722)) | (~c0_1(a722)))),
% 2.24/1.81 inference(quant_inst,[status(thm)],[])).
% 2.24/1.81 tff(4050,plain,
% 2.24/1.81 ((~![U: $i] : (hskp16 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp7 | c1_1(a722) | (~ndr1_0) | (~c2_1(a722)) | (~c0_1(a722))),
% 2.24/1.81 inference(modus_ponens,[status(thm)],[4049, 4048])).
% 2.24/1.81 tff(4051,plain,
% 2.24/1.81 (hskp7 | (~c2_1(a722))),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[4050, 227, 12, 4044, 4043, 3358])).
% 2.24/1.81 tff(4052,plain,
% 2.24/1.81 (~c2_1(a722)),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[4051, 3978])).
% 2.24/1.81 tff(4053,plain,
% 2.24/1.81 (hskp12),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[2066, 280, 3046])).
% 2.24/1.81 tff(4054,plain,
% 2.24/1.81 (~c1_1(a725)),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[145, 4053])).
% 2.24/1.81 tff(4055,plain,
% 2.24/1.81 (~c0_1(a725)),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[151, 4053])).
% 2.24/1.81 tff(4056,plain,
% 2.24/1.81 (~c3_1(a725)),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[139, 4053])).
% 2.24/1.81 tff(4057,plain,
% 2.24/1.81 (c2_1(a725)),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[3392, 4056, 3977, 3978, 12, 4055, 4054])).
% 2.24/1.81 tff(4058,assumption,(c3_1(a722)), introduced(assumption)).
% 2.24/1.81 tff(4059,plain,
% 2.24/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a764) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a722) | (~c3_1(a722)) | (~c0_1(a722)) | (~c2_1(a725)) | c0_1(a764) | (~c1_1(a764)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a764) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a722) | (~c3_1(a722)) | (~c0_1(a722)) | (~c2_1(a725)) | c0_1(a764) | (~c1_1(a764)))),
% 2.24/1.81 inference(rewrite,[status(thm)],[])).
% 2.24/1.81 tff(4060,plain,
% 2.24/1.81 (((~ndr1_0) | c2_1(a722) | (~c3_1(a722)) | (~c0_1(a722)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)) | c3_1(a764) | c0_1(a764) | (~c1_1(a764))) <=> (c3_1(a764) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a722) | (~c3_1(a722)) | (~c0_1(a722)) | (~c2_1(a725)) | c0_1(a764) | (~c1_1(a764)))),
% 2.24/1.81 inference(rewrite,[status(thm)],[])).
% 2.24/1.81 tff(4061,plain,
% 2.24/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a722) | (~c3_1(a722)) | (~c0_1(a722)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)) | c3_1(a764) | c0_1(a764) | (~c1_1(a764)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a764) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a722) | (~c3_1(a722)) | (~c0_1(a722)) | (~c2_1(a725)) | c0_1(a764) | (~c1_1(a764))))),
% 2.24/1.81 inference(monotonicity,[status(thm)],[4060])).
% 2.24/1.81 tff(4062,plain,
% 2.24/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a722) | (~c3_1(a722)) | (~c0_1(a722)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)) | c3_1(a764) | c0_1(a764) | (~c1_1(a764)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a764) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a722) | (~c3_1(a722)) | (~c0_1(a722)) | (~c2_1(a725)) | c0_1(a764) | (~c1_1(a764)))),
% 2.24/1.81 inference(transitivity,[status(thm)],[4061, 4059])).
% 2.24/1.81 tff(4063,plain,
% 2.24/1.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a722) | (~c3_1(a722)) | (~c0_1(a722)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)) | c3_1(a764) | c0_1(a764) | (~c1_1(a764)))),
% 2.24/1.81 inference(quant_inst,[status(thm)],[])).
% 2.24/1.81 tff(4064,plain,
% 2.24/1.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a764) | c0_1(a725) | c3_1(a725) | (~ndr1_0) | c2_1(a722) | (~c3_1(a722)) | (~c0_1(a722)) | (~c2_1(a725)) | c0_1(a764) | (~c1_1(a764))),
% 2.24/1.81 inference(modus_ponens,[status(thm)],[4063, 4062])).
% 2.24/1.81 tff(4065,plain,
% 2.24/1.81 (c0_1(a764)),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[4064, 227, 2014, 4044, 4058, 2012, 4055, 4056, 174, 4057, 4052])).
% 2.24/1.81 tff(4066,plain,
% 2.24/1.81 ($false),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[3579, 227, 4044, 2013, 2012, 4055, 4056, 4043, 2445, 4057, 4065, 4052])).
% 2.24/1.81 tff(4067,plain,(hskp20 | (~c0_1(a722)) | c2_1(a764) | c3_1(a764) | c1_1(a722) | (~c1_1(a764)) | (~c3_1(a722)) | hskp16 | hskp13), inference(lemma,lemma(discharge,[]))).
% 2.24/1.81 tff(4068,plain,
% 2.24/1.81 ($false),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[4067, 4042, 4041, 3511, 3510, 4038, 3515, 4040, 12, 3046])).
% 2.24/1.81 tff(4069,plain,(hskp13 | hskp16 | hskp23), inference(lemma,lemma(discharge,[]))).
% 2.24/1.81 tff(4070,plain,
% 2.24/1.81 (hskp13),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[4069, 474, 12])).
% 2.24/1.81 tff(4071,plain,
% 2.24/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c3_1(a764) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | c2_1(a726) | (~c0_1(a764)) | (~c1_1(a764)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a764) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | c2_1(a726) | (~c0_1(a764)) | (~c1_1(a764)))),
% 2.24/1.81 inference(rewrite,[status(thm)],[])).
% 2.24/1.81 tff(4072,plain,
% 2.24/1.81 (((~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764)) | c3_1(a726) | c2_1(a726) | c0_1(a726)) <=> (c3_1(a764) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | c2_1(a726) | (~c0_1(a764)) | (~c1_1(a764)))),
% 2.24/1.81 inference(rewrite,[status(thm)],[])).
% 2.24/1.81 tff(4073,plain,
% 2.24/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764)) | c3_1(a726) | c2_1(a726) | c0_1(a726))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c3_1(a764) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | c2_1(a726) | (~c0_1(a764)) | (~c1_1(a764))))),
% 2.24/1.81 inference(monotonicity,[status(thm)],[4072])).
% 2.24/1.81 tff(4074,plain,
% 2.24/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764)) | c3_1(a726) | c2_1(a726) | c0_1(a726))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a764) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | c2_1(a726) | (~c0_1(a764)) | (~c1_1(a764)))),
% 2.24/1.81 inference(transitivity,[status(thm)],[4073, 4071])).
% 2.24/1.81 tff(4075,plain,
% 2.24/1.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a764) | (~c1_1(a764)) | (~c0_1(a764)) | c3_1(a726) | c2_1(a726) | c0_1(a726))),
% 2.24/1.81 inference(quant_inst,[status(thm)],[])).
% 2.24/1.81 tff(4076,plain,
% 2.24/1.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c3_1(a764) | c0_1(a726) | c3_1(a726) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | c2_1(a726) | (~c0_1(a764)) | (~c1_1(a764))),
% 2.24/1.81 inference(modus_ponens,[status(thm)],[4075, 4074])).
% 2.24/1.81 tff(4077,plain,
% 2.24/1.81 (c2_1(a726)),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[4076, 227, 2802, 2760, 2014, 2012, 2028, 2022, 1777, 2084, 3301])).
% 2.24/1.81 tff(4078,plain,
% 2.24/1.81 ($false),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[2849, 227, 280, 2802, 2760, 2046, 2022, 2101, 3301, 4077])).
% 2.24/1.81 tff(4079,plain,((~hskp13) | hskp20 | (~c3_1(a695)) | (~c1_1(a764)) | c3_1(a764) | (~c0_1(a764))), inference(lemma,lemma(discharge,[]))).
% 2.24/1.81 tff(4080,plain,
% 2.24/1.81 (~c0_1(a764)),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[4079, 4070, 3515, 3977, 3510, 4038])).
% 2.24/1.81 tff(4081,plain,
% 2.24/1.81 (~hskp7),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[3313, 4038, 3977])).
% 2.24/1.81 tff(4082,plain,
% 2.24/1.81 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp7 | hskp2 | c2_1(a764) | c3_1(a764) | (~ndr1_0) | c0_1(a764))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp7 | hskp2 | c2_1(a764) | c3_1(a764) | (~ndr1_0) | c0_1(a764))),
% 2.24/1.81 inference(rewrite,[status(thm)],[])).
% 2.24/1.81 tff(4083,plain,
% 2.24/1.81 ((hskp7 | hskp2 | (~ndr1_0) | c3_1(a764) | c0_1(a764) | c2_1(a764)) <=> (hskp7 | hskp2 | c2_1(a764) | c3_1(a764) | (~ndr1_0) | c0_1(a764))),
% 2.24/1.81 inference(rewrite,[status(thm)],[])).
% 2.24/1.81 tff(4084,plain,
% 2.24/1.81 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp7 | hskp2 | (~ndr1_0) | c3_1(a764) | c0_1(a764) | c2_1(a764))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp7 | hskp2 | c2_1(a764) | c3_1(a764) | (~ndr1_0) | c0_1(a764)))),
% 2.24/1.81 inference(monotonicity,[status(thm)],[4083])).
% 2.24/1.81 tff(4085,plain,
% 2.24/1.81 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp7 | hskp2 | (~ndr1_0) | c3_1(a764) | c0_1(a764) | c2_1(a764))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp7 | hskp2 | c2_1(a764) | c3_1(a764) | (~ndr1_0) | c0_1(a764))),
% 2.24/1.81 inference(transitivity,[status(thm)],[4084, 4082])).
% 2.24/1.81 tff(4086,plain,
% 2.24/1.81 ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp7 | hskp2 | (~ndr1_0) | c3_1(a764) | c0_1(a764) | c2_1(a764))),
% 2.24/1.81 inference(quant_inst,[status(thm)],[])).
% 2.24/1.81 tff(4087,plain,
% 2.24/1.81 ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp7 | hskp2 | c2_1(a764) | c3_1(a764) | (~ndr1_0) | c0_1(a764)),
% 2.24/1.81 inference(modus_ponens,[status(thm)],[4086, 4085])).
% 2.24/1.81 tff(4088,plain,
% 2.24/1.81 (hskp7 | hskp2 | c0_1(a764)),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[4087, 227, 3511, 3510, 3332])).
% 2.24/1.81 tff(4089,plain,
% 2.24/1.81 (hskp2),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[4088, 4080, 4081])).
% 2.24/1.81 tff(4090,plain,
% 2.24/1.81 (~c2_1(a696)),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[1971, 4089])).
% 2.24/1.81 tff(4091,plain,
% 2.24/1.81 (c1_1(a696)),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[2000, 4089])).
% 2.24/1.81 tff(4092,plain,
% 2.24/1.81 (((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp16 | c2_1(a696) | (~ndr1_0) | (~c3_1(a696)) | (~c1_1(a696)))) <=> ((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp16 | c2_1(a696) | (~ndr1_0) | (~c3_1(a696)) | (~c1_1(a696)))),
% 2.24/1.81 inference(rewrite,[status(thm)],[])).
% 2.24/1.81 tff(4093,plain,
% 2.24/1.81 ((hskp20 | hskp16 | (~ndr1_0) | c2_1(a696) | (~c3_1(a696)) | (~c1_1(a696))) <=> (hskp20 | hskp16 | c2_1(a696) | (~ndr1_0) | (~c3_1(a696)) | (~c1_1(a696)))),
% 2.24/1.81 inference(rewrite,[status(thm)],[])).
% 2.24/1.81 tff(4094,plain,
% 2.24/1.81 (((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp16 | (~ndr1_0) | c2_1(a696) | (~c3_1(a696)) | (~c1_1(a696)))) <=> ((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp16 | c2_1(a696) | (~ndr1_0) | (~c3_1(a696)) | (~c1_1(a696))))),
% 2.24/1.81 inference(monotonicity,[status(thm)],[4093])).
% 2.24/1.81 tff(4095,plain,
% 2.24/1.81 (((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp16 | (~ndr1_0) | c2_1(a696) | (~c3_1(a696)) | (~c1_1(a696)))) <=> ((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp16 | c2_1(a696) | (~ndr1_0) | (~c3_1(a696)) | (~c1_1(a696)))),
% 2.24/1.81 inference(transitivity,[status(thm)],[4094, 4092])).
% 2.24/1.81 tff(4096,plain,
% 2.24/1.81 ((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp16 | (~ndr1_0) | c2_1(a696) | (~c3_1(a696)) | (~c1_1(a696)))),
% 2.24/1.81 inference(quant_inst,[status(thm)],[])).
% 2.24/1.81 tff(4097,plain,
% 2.24/1.81 ((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp16 | c2_1(a696) | (~ndr1_0) | (~c3_1(a696)) | (~c1_1(a696))),
% 2.24/1.81 inference(modus_ponens,[status(thm)],[4096, 4095])).
% 2.24/1.81 tff(4098,plain,
% 2.24/1.81 (~c3_1(a696)),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[4097, 227, 4038, 12, 4091, 4090, 3069])).
% 2.24/1.81 tff(4099,plain,
% 2.24/1.81 (c0_1(a696)),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[1982, 4089])).
% 2.24/1.81 tff(4100,plain,
% 2.24/1.81 (((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp16 | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c1_1(a702)))) <=> ((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp16 | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c1_1(a702)))),
% 2.24/1.81 inference(rewrite,[status(thm)],[])).
% 2.24/1.81 tff(4101,plain,
% 2.24/1.81 ((hskp20 | hskp16 | (~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c1_1(a702))) <=> (hskp20 | hskp16 | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c1_1(a702)))),
% 2.24/1.81 inference(rewrite,[status(thm)],[])).
% 2.24/1.81 tff(4102,plain,
% 2.24/1.81 (((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp16 | (~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c1_1(a702)))) <=> ((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp16 | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c1_1(a702))))),
% 2.24/1.81 inference(monotonicity,[status(thm)],[4101])).
% 2.24/1.81 tff(4103,plain,
% 2.24/1.81 (((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp16 | (~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c1_1(a702)))) <=> ((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp16 | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c1_1(a702)))),
% 2.24/1.81 inference(transitivity,[status(thm)],[4102, 4100])).
% 2.24/1.81 tff(4104,plain,
% 2.24/1.81 ((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp20 | hskp16 | (~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c1_1(a702)))),
% 2.24/1.81 inference(quant_inst,[status(thm)],[])).
% 2.24/1.81 tff(4105,plain,
% 2.24/1.81 ((~![U: $i] : (hskp20 | hskp16 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp20 | hskp16 | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c1_1(a702))),
% 2.24/1.81 inference(modus_ponens,[status(thm)],[4104, 4103])).
% 2.24/1.81 tff(4106,plain,
% 2.24/1.81 (hskp20 | hskp16 | (~c1_1(a702))),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[4105, 227, 3832, 3831, 3069])).
% 2.24/1.81 tff(4107,plain,
% 2.24/1.81 (~c1_1(a702)),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[4106, 4038, 12])).
% 2.24/1.81 tff(4108,plain,
% 2.24/1.81 (^[V: $i, U: $i] : refl((hskp29 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp29 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))),
% 2.24/1.81 inference(bind,[status(th)],[])).
% 2.24/1.81 tff(4109,plain,
% 2.24/1.81 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 2.24/1.81 inference(quant_intro,[status(thm)],[4108])).
% 2.24/1.81 tff(4110,plain,
% 2.24/1.81 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 2.24/1.81 inference(rewrite,[status(thm)],[])).
% 2.24/1.81 tff(4111,plain,
% 2.24/1.81 (^[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(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | (~c1_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | (~c1_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_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)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_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)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp29) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp29))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp29) <=> (hskp29 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp29) <=> (hskp29 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))))),
% 2.24/1.81 inference(bind,[status(th)],[])).
% 2.24/1.81 tff(4112,plain,
% 2.24/1.81 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp29) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 2.24/1.81 inference(quant_intro,[status(thm)],[4111])).
% 2.24/1.81 tff(4113,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause163')).
% 2.24/1.81 tff(4114,plain,
% 2.24/1.81 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 2.24/1.81 inference(modus_ponens,[status(thm)],[4113, 4112])).
% 2.24/1.81 tff(4115,plain,
% 2.24/1.81 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 2.24/1.81 inference(modus_ponens,[status(thm)],[4114, 4110])).
% 2.24/1.81 tff(4116,plain,(
% 2.24/1.81 ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 2.24/1.81 inference(skolemize,[status(sab)],[4115])).
% 2.24/1.81 tff(4117,plain,
% 2.24/1.81 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 2.24/1.81 inference(modus_ponens,[status(thm)],[4116, 4109])).
% 2.24/1.81 tff(4118,plain,
% 2.24/1.81 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp29 | c2_1(a764) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | c1_1(a702) | c0_1(a764) | (~c1_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp29 | c2_1(a764) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | c1_1(a702) | c0_1(a764) | (~c1_1(a764)))),
% 2.24/1.81 inference(rewrite,[status(thm)],[])).
% 2.24/1.81 tff(4119,plain,
% 2.24/1.81 ((hskp29 | (~ndr1_0) | c1_1(a702) | c2_1(a702) | (~c3_1(a702)) | c0_1(a764) | c2_1(a764) | (~c1_1(a764))) <=> (hskp29 | c2_1(a764) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | c1_1(a702) | c0_1(a764) | (~c1_1(a764)))),
% 2.24/1.81 inference(rewrite,[status(thm)],[])).
% 2.24/1.81 tff(4120,plain,
% 2.24/1.81 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a702) | c2_1(a702) | (~c3_1(a702)) | c0_1(a764) | c2_1(a764) | (~c1_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp29 | c2_1(a764) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | c1_1(a702) | c0_1(a764) | (~c1_1(a764))))),
% 2.24/1.81 inference(monotonicity,[status(thm)],[4119])).
% 2.24/1.81 tff(4121,plain,
% 2.24/1.81 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a702) | c2_1(a702) | (~c3_1(a702)) | c0_1(a764) | c2_1(a764) | (~c1_1(a764)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp29 | c2_1(a764) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | c1_1(a702) | c0_1(a764) | (~c1_1(a764)))),
% 2.24/1.81 inference(transitivity,[status(thm)],[4120, 4118])).
% 2.24/1.81 tff(4122,plain,
% 2.24/1.81 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a702) | c2_1(a702) | (~c3_1(a702)) | c0_1(a764) | c2_1(a764) | (~c1_1(a764)))),
% 2.24/1.81 inference(quant_inst,[status(thm)],[])).
% 2.24/1.81 tff(4123,plain,
% 2.24/1.81 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp29 | c2_1(a764) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | c1_1(a702) | c0_1(a764) | (~c1_1(a764))),
% 2.24/1.81 inference(modus_ponens,[status(thm)],[4122, 4121])).
% 2.24/1.81 tff(4124,plain,
% 2.24/1.81 (hskp29),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[4123, 227, 3515, 3832, 3511, 3831, 4117, 4080, 4107])).
% 2.24/1.81 tff(4125,plain,
% 2.24/1.81 (c3_1(a713)),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[3433, 4124])).
% 2.24/1.81 tff(4126,plain,
% 2.24/1.81 (c2_1(a713)),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[3444, 4124])).
% 2.24/1.81 tff(4127,plain,
% 2.24/1.81 (c0_1(a713)),
% 2.24/1.81 inference(unit_resolution,[status(thm)],[3455, 4124])).
% 2.24/1.82 tff(4128,plain,
% 2.24/1.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a764) | c3_1(a764) | (~ndr1_0) | c3_1(a696) | (~c1_1(a696)) | (~c0_1(a696)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713)) | c0_1(a764))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a764) | c3_1(a764) | (~ndr1_0) | c3_1(a696) | (~c1_1(a696)) | (~c0_1(a696)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713)) | c0_1(a764))),
% 2.24/1.82 inference(rewrite,[status(thm)],[])).
% 2.24/1.82 tff(4129,plain,
% 2.24/1.82 (((~ndr1_0) | (~c2_1(a713)) | (~c3_1(a713)) | (~c0_1(a713)) | c3_1(a696) | (~c1_1(a696)) | (~c0_1(a696)) | c3_1(a764) | c2_1(a764) | c0_1(a764)) <=> (c2_1(a764) | c3_1(a764) | (~ndr1_0) | c3_1(a696) | (~c1_1(a696)) | (~c0_1(a696)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713)) | c0_1(a764))),
% 2.24/1.82 inference(rewrite,[status(thm)],[])).
% 2.24/1.82 tff(4130,plain,
% 2.24/1.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a713)) | (~c3_1(a713)) | (~c0_1(a713)) | c3_1(a696) | (~c1_1(a696)) | (~c0_1(a696)) | c3_1(a764) | c2_1(a764) | c0_1(a764))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a764) | c3_1(a764) | (~ndr1_0) | c3_1(a696) | (~c1_1(a696)) | (~c0_1(a696)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713)) | c0_1(a764)))),
% 2.24/1.82 inference(monotonicity,[status(thm)],[4129])).
% 2.24/1.82 tff(4131,plain,
% 2.24/1.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a713)) | (~c3_1(a713)) | (~c0_1(a713)) | c3_1(a696) | (~c1_1(a696)) | (~c0_1(a696)) | c3_1(a764) | c2_1(a764) | c0_1(a764))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a764) | c3_1(a764) | (~ndr1_0) | c3_1(a696) | (~c1_1(a696)) | (~c0_1(a696)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713)) | c0_1(a764))),
% 2.24/1.82 inference(transitivity,[status(thm)],[4130, 4128])).
% 2.24/1.82 tff(4132,plain,
% 2.24/1.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a713)) | (~c3_1(a713)) | (~c0_1(a713)) | c3_1(a696) | (~c1_1(a696)) | (~c0_1(a696)) | c3_1(a764) | c2_1(a764) | c0_1(a764))),
% 2.24/1.82 inference(quant_inst,[status(thm)],[])).
% 2.24/1.82 tff(4133,plain,
% 2.24/1.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a764) | c3_1(a764) | (~ndr1_0) | c3_1(a696) | (~c1_1(a696)) | (~c0_1(a696)) | (~c0_1(a713)) | (~c2_1(a713)) | (~c3_1(a713)) | c0_1(a764)),
% 2.24/1.82 inference(modus_ponens,[status(thm)],[4132, 4131])).
% 2.24/1.82 tff(4134,plain,
% 2.24/1.82 ($false),
% 2.24/1.82 inference(unit_resolution,[status(thm)],[4133, 227, 4127, 4126, 4125, 4099, 4091, 3511, 3510, 1777, 4098, 4080])).
% 2.24/1.82 tff(4135,plain,(hskp23 | hskp16), inference(lemma,lemma(discharge,[]))).
% 2.24/1.82 tff(4136,plain,
% 2.24/1.82 (hskp23),
% 2.24/1.82 inference(unit_resolution,[status(thm)],[4135, 12])).
% 2.24/1.82 tff(4137,plain,
% 2.24/1.82 (c0_1(a763)),
% 2.24/1.82 inference(unit_resolution,[status(thm)],[421, 4136])).
% 2.24/1.82 tff(4138,plain,
% 2.24/1.82 (~c2_1(a763)),
% 2.24/1.82 inference(unit_resolution,[status(thm)],[404, 4136])).
% 2.24/1.82 tff(4139,plain,
% 2.24/1.82 (~c1_1(a763)),
% 2.24/1.82 inference(unit_resolution,[status(thm)],[410, 4136])).
% 2.24/1.82 tff(4140,plain,
% 2.24/1.82 (c2_1(a710)),
% 2.24/1.82 inference(unit_resolution,[status(thm)],[1958, 3997])).
% 2.24/1.82 tff(4141,plain,
% 2.24/1.82 (~c0_1(a710)),
% 2.24/1.82 inference(unit_resolution,[status(thm)],[1875, 3997])).
% 2.24/1.82 tff(4142,plain,
% 2.24/1.82 ($false),
% 2.24/1.82 inference(unit_resolution,[status(thm)],[3816, 4141, 4140, 3977, 12, 4139, 4138, 4137, 4005, 3998])).
% 2.24/1.82 tff(4143,plain,(hskp13 | hskp16 | hskp20), inference(lemma,lemma(discharge,[]))).
% 2.24/1.82 tff(4144,plain,
% 2.24/1.82 (hskp13),
% 2.24/1.82 inference(unit_resolution,[status(thm)],[4143, 280, 12])).
% 2.24/1.82 tff(4145,plain,
% 2.24/1.82 (~c3_1(a726)),
% 2.24/1.82 inference(unit_resolution,[status(thm)],[2021, 4144])).
% 2.24/1.82 tff(4146,plain,
% 2.24/1.82 (~c0_1(a726)),
% 2.24/1.82 inference(unit_resolution,[status(thm)],[2027, 4144])).
% 2.24/1.82 tff(4147,plain,
% 2.24/1.82 (c1_1(a726)),
% 2.24/1.82 inference(unit_resolution,[status(thm)],[2045, 4144])).
% 2.24/1.82 tff(4148,plain,
% 2.24/1.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a726) | c3_1(a726) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a726)) | (~c2_1(a726)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a726) | c3_1(a726) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a726)) | (~c2_1(a726)))),
% 2.24/1.82 inference(rewrite,[status(thm)],[])).
% 2.24/1.82 tff(4149,plain,
% 2.24/1.82 (((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726)) | c3_1(a726) | c0_1(a726) | (~c1_1(a726))) <=> (c0_1(a726) | c3_1(a726) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a726)) | (~c2_1(a726)))),
% 2.24/1.82 inference(rewrite,[status(thm)],[])).
% 2.24/1.82 tff(4150,plain,
% 2.24/1.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726)) | c3_1(a726) | c0_1(a726) | (~c1_1(a726)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a726) | c3_1(a726) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a726)) | (~c2_1(a726))))),
% 2.24/1.82 inference(monotonicity,[status(thm)],[4149])).
% 2.24/1.82 tff(4151,plain,
% 2.24/1.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726)) | c3_1(a726) | c0_1(a726) | (~c1_1(a726)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a726) | c3_1(a726) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a726)) | (~c2_1(a726)))),
% 2.24/1.82 inference(transitivity,[status(thm)],[4150, 4148])).
% 2.24/1.82 tff(4152,plain,
% 2.24/1.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a726) | c0_1(a726) | (~c2_1(a726)) | c3_1(a726) | c0_1(a726) | (~c1_1(a726)))),
% 2.24/1.82 inference(quant_inst,[status(thm)],[])).
% 2.24/1.82 tff(4153,plain,
% 2.24/1.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a726) | c3_1(a726) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a726)) | (~c2_1(a726))),
% 2.24/1.82 inference(modus_ponens,[status(thm)],[4152, 4151])).
% 2.24/1.82 tff(4154,plain,
% 2.24/1.82 (~c2_1(a726)),
% 2.24/1.82 inference(unit_resolution,[status(thm)],[4153, 227, 4147, 3833, 3832, 4146, 4145, 3831, 174])).
% 2.24/1.82 tff(4155,plain,
% 2.24/1.82 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp7 | hskp2 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | c2_1(a726))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp7 | hskp2 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | c2_1(a726))),
% 2.24/1.82 inference(rewrite,[status(thm)],[])).
% 2.24/1.82 tff(4156,plain,
% 2.24/1.82 ((hskp7 | hskp2 | (~ndr1_0) | c3_1(a726) | c0_1(a726) | c2_1(a726)) <=> (hskp7 | hskp2 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | c2_1(a726))),
% 2.24/1.82 inference(rewrite,[status(thm)],[])).
% 2.24/1.82 tff(4157,plain,
% 2.24/1.82 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp7 | hskp2 | (~ndr1_0) | c3_1(a726) | c0_1(a726) | c2_1(a726))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp7 | hskp2 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | c2_1(a726)))),
% 2.24/1.82 inference(monotonicity,[status(thm)],[4156])).
% 2.24/1.82 tff(4158,plain,
% 2.24/1.82 (((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp7 | hskp2 | (~ndr1_0) | c3_1(a726) | c0_1(a726) | c2_1(a726))) <=> ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp7 | hskp2 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | c2_1(a726))),
% 2.24/1.82 inference(transitivity,[status(thm)],[4157, 4155])).
% 2.24/1.82 tff(4159,plain,
% 2.24/1.82 ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp7 | hskp2 | (~ndr1_0) | c3_1(a726) | c0_1(a726) | c2_1(a726))),
% 2.24/1.82 inference(quant_inst,[status(thm)],[])).
% 2.24/1.82 tff(4160,plain,
% 2.24/1.82 ((~![U: $i] : (hskp7 | hskp2 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp7 | hskp2 | c0_1(a726) | c3_1(a726) | (~ndr1_0) | c2_1(a726)),
% 2.24/1.82 inference(modus_ponens,[status(thm)],[4159, 4158])).
% 2.24/1.82 tff(4161,plain,
% 2.24/1.82 (hskp2 | c2_1(a726)),
% 2.28/1.82 inference(unit_resolution,[status(thm)],[4160, 227, 3978, 4146, 4145, 3332])).
% 2.28/1.82 tff(4162,plain,
% 2.28/1.82 (hskp2),
% 2.28/1.82 inference(unit_resolution,[status(thm)],[4161, 4154])).
% 2.28/1.82 tff(4163,plain,
% 2.28/1.82 (~c2_1(a696)),
% 2.28/1.82 inference(unit_resolution,[status(thm)],[1971, 4162])).
% 2.28/1.82 tff(4164,plain,
% 2.28/1.82 (c1_1(a696)),
% 2.28/1.82 inference(unit_resolution,[status(thm)],[2000, 4162])).
% 2.28/1.82 tff(4165,plain,
% 2.28/1.82 (~c3_1(a696)),
% 2.28/1.82 inference(unit_resolution,[status(thm)],[4097, 227, 280, 12, 4164, 4163, 3069])).
% 2.28/1.82 tff(4166,plain,
% 2.28/1.82 (c0_1(a696)),
% 2.28/1.82 inference(unit_resolution,[status(thm)],[1982, 4162])).
% 2.28/1.82 tff(4167,plain,
% 2.28/1.82 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp12 | c1_1(a763) | c2_1(a763) | c2_1(a696) | (~ndr1_0) | (~c1_1(a696)) | (~c0_1(a696)) | (~c0_1(a763)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp12 | c1_1(a763) | c2_1(a763) | c2_1(a696) | (~ndr1_0) | (~c1_1(a696)) | (~c0_1(a696)) | (~c0_1(a763)))),
% 2.28/1.82 inference(rewrite,[status(thm)],[])).
% 2.28/1.82 tff(4168,plain,
% 2.28/1.82 ((hskp12 | (~ndr1_0) | c2_1(a696) | (~c0_1(a696)) | (~c1_1(a696)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763))) <=> (hskp12 | c1_1(a763) | c2_1(a763) | c2_1(a696) | (~ndr1_0) | (~c1_1(a696)) | (~c0_1(a696)) | (~c0_1(a763)))),
% 2.28/1.82 inference(rewrite,[status(thm)],[])).
% 2.28/1.82 tff(4169,plain,
% 2.28/1.82 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a696) | (~c0_1(a696)) | (~c1_1(a696)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp12 | c1_1(a763) | c2_1(a763) | c2_1(a696) | (~ndr1_0) | (~c1_1(a696)) | (~c0_1(a696)) | (~c0_1(a763))))),
% 2.28/1.82 inference(monotonicity,[status(thm)],[4168])).
% 2.28/1.82 tff(4170,plain,
% 2.28/1.82 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a696) | (~c0_1(a696)) | (~c1_1(a696)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp12 | c1_1(a763) | c2_1(a763) | c2_1(a696) | (~ndr1_0) | (~c1_1(a696)) | (~c0_1(a696)) | (~c0_1(a763)))),
% 2.28/1.82 inference(transitivity,[status(thm)],[4169, 4167])).
% 2.28/1.82 tff(4171,plain,
% 2.28/1.82 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a696) | (~c0_1(a696)) | (~c1_1(a696)) | c1_1(a763) | c2_1(a763) | (~c0_1(a763)))),
% 2.28/1.82 inference(quant_inst,[status(thm)],[])).
% 2.28/1.82 tff(4172,plain,
% 2.28/1.82 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp12 | c1_1(a763) | c2_1(a763) | c2_1(a696) | (~ndr1_0) | (~c1_1(a696)) | (~c0_1(a696)) | (~c0_1(a763))),
% 2.28/1.82 inference(modus_ponens,[status(thm)],[4171, 4170])).
% 2.28/1.82 tff(4173,plain,
% 2.28/1.82 (hskp12),
% 2.28/1.82 inference(unit_resolution,[status(thm)],[4172, 227, 4137, 4166, 4164, 4139, 4138, 4163, 2427])).
% 2.28/1.82 tff(4174,plain,
% 2.28/1.82 (~c1_1(a725)),
% 2.28/1.82 inference(unit_resolution,[status(thm)],[145, 4173])).
% 2.28/1.82 tff(4175,plain,
% 2.28/1.82 (~c0_1(a725)),
% 2.28/1.82 inference(unit_resolution,[status(thm)],[151, 4173])).
% 2.28/1.82 tff(4176,plain,
% 2.28/1.82 (~c3_1(a725)),
% 2.28/1.82 inference(unit_resolution,[status(thm)],[139, 4173])).
% 2.28/1.82 tff(4177,plain,
% 2.28/1.82 (c2_1(a725)),
% 2.28/1.82 inference(unit_resolution,[status(thm)],[3392, 4176, 3977, 3978, 12, 4175, 4174])).
% 2.28/1.82 tff(4178,plain,
% 2.28/1.82 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c3_1(a696) | (~c1_1(a696)) | (~c0_1(a696)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp16 | hskp15 | (~ndr1_0) | c3_1(a696) | (~c1_1(a696)) | (~c0_1(a696)))),
% 2.28/1.82 inference(rewrite,[status(thm)],[])).
% 2.28/1.82 tff(4179,plain,
% 2.28/1.82 ((hskp16 | hskp15 | (~ndr1_0) | c3_1(a696) | (~c0_1(a696)) | (~c1_1(a696))) <=> (hskp16 | hskp15 | (~ndr1_0) | c3_1(a696) | (~c1_1(a696)) | (~c0_1(a696)))),
% 2.28/1.82 inference(rewrite,[status(thm)],[])).
% 2.28/1.82 tff(4180,plain,
% 2.28/1.82 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c3_1(a696) | (~c0_1(a696)) | (~c1_1(a696)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c3_1(a696) | (~c1_1(a696)) | (~c0_1(a696))))),
% 2.28/1.82 inference(monotonicity,[status(thm)],[4179])).
% 2.28/1.82 tff(4181,plain,
% 2.28/1.82 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c3_1(a696) | (~c0_1(a696)) | (~c1_1(a696)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp16 | hskp15 | (~ndr1_0) | c3_1(a696) | (~c1_1(a696)) | (~c0_1(a696)))),
% 2.28/1.82 inference(transitivity,[status(thm)],[4180, 4178])).
% 2.28/1.82 tff(4182,plain,
% 2.28/1.82 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c3_1(a696) | (~c0_1(a696)) | (~c1_1(a696)))),
% 2.28/1.82 inference(quant_inst,[status(thm)],[])).
% 2.28/1.82 tff(4183,plain,
% 2.28/1.82 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp16 | hskp15 | (~ndr1_0) | c3_1(a696) | (~c1_1(a696)) | (~c0_1(a696))),
% 2.28/1.82 inference(modus_ponens,[status(thm)],[4182, 4181])).
% 2.28/1.82 tff(4184,plain,
% 2.28/1.82 (hskp15),
% 2.28/1.82 inference(unit_resolution,[status(thm)],[4183, 227, 12, 4166, 4164, 3748, 4165])).
% 2.28/1.82 tff(4185,plain,
% 2.28/1.82 (~c2_1(a734)),
% 2.28/1.82 inference(unit_resolution,[status(thm)],[3760, 4184])).
% 2.28/1.82 tff(4186,plain,
% 2.28/1.82 (~c1_1(a734)),
% 2.28/1.82 inference(unit_resolution,[status(thm)],[3766, 4184])).
% 2.28/1.82 tff(4187,plain,
% 2.28/1.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a734) | c2_1(a734) | c0_1(a725) | c3_1(a725) | c2_1(a696) | (~ndr1_0) | c3_1(a696) | (~c0_1(a696)) | (~c2_1(a725)) | (~c0_1(a734)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a734) | c2_1(a734) | c0_1(a725) | c3_1(a725) | c2_1(a696) | (~ndr1_0) | c3_1(a696) | (~c0_1(a696)) | (~c2_1(a725)) | (~c0_1(a734)))),
% 2.28/1.82 inference(rewrite,[status(thm)],[])).
% 2.28/1.82 tff(4188,plain,
% 2.28/1.82 (((~ndr1_0) | c3_1(a696) | c2_1(a696) | (~c0_1(a696)) | c1_1(a734) | c2_1(a734) | (~c0_1(a734)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725))) <=> (c1_1(a734) | c2_1(a734) | c0_1(a725) | c3_1(a725) | c2_1(a696) | (~ndr1_0) | c3_1(a696) | (~c0_1(a696)) | (~c2_1(a725)) | (~c0_1(a734)))),
% 2.28/1.82 inference(rewrite,[status(thm)],[])).
% 2.28/1.82 tff(4189,plain,
% 2.28/1.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a696) | c2_1(a696) | (~c0_1(a696)) | c1_1(a734) | c2_1(a734) | (~c0_1(a734)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a734) | c2_1(a734) | c0_1(a725) | c3_1(a725) | c2_1(a696) | (~ndr1_0) | c3_1(a696) | (~c0_1(a696)) | (~c2_1(a725)) | (~c0_1(a734))))),
% 2.28/1.82 inference(monotonicity,[status(thm)],[4188])).
% 2.28/1.82 tff(4190,plain,
% 2.28/1.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a696) | c2_1(a696) | (~c0_1(a696)) | c1_1(a734) | c2_1(a734) | (~c0_1(a734)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a734) | c2_1(a734) | c0_1(a725) | c3_1(a725) | c2_1(a696) | (~ndr1_0) | c3_1(a696) | (~c0_1(a696)) | (~c2_1(a725)) | (~c0_1(a734)))),
% 2.28/1.82 inference(transitivity,[status(thm)],[4189, 4187])).
% 2.28/1.82 tff(4191,plain,
% 2.28/1.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a696) | c2_1(a696) | (~c0_1(a696)) | c1_1(a734) | c2_1(a734) | (~c0_1(a734)) | c3_1(a725) | c0_1(a725) | (~c2_1(a725)))),
% 2.28/1.82 inference(quant_inst,[status(thm)],[])).
% 2.28/1.82 tff(4192,plain,
% 2.28/1.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a734) | c2_1(a734) | c0_1(a725) | c3_1(a725) | c2_1(a696) | (~ndr1_0) | c3_1(a696) | (~c0_1(a696)) | (~c2_1(a725)) | (~c0_1(a734))),
% 2.28/1.82 inference(modus_ponens,[status(thm)],[4191, 4190])).
% 2.28/1.82 tff(4193,plain,
% 2.28/1.82 (~c0_1(a734)),
% 2.28/1.82 inference(unit_resolution,[status(thm)],[4192, 227, 4166, 4186, 4185, 4175, 4176, 4163, 2445, 4177, 4165])).
% 2.28/1.82 tff(4194,plain,
% 2.28/1.82 (c3_1(a734)),
% 2.28/1.82 inference(unit_resolution,[status(thm)],[3779, 4184])).
% 2.28/1.82 tff(4195,plain,
% 2.28/1.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a734) | c2_1(a734) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c3_1(a734)) | c0_1(a734))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a734) | c2_1(a734) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c3_1(a734)) | c0_1(a734))),
% 2.28/1.82 inference(rewrite,[status(thm)],[])).
% 2.28/1.82 tff(4196,plain,
% 2.28/1.82 (((~ndr1_0) | c3_1(a725) | c1_1(a725) | (~c2_1(a725)) | c1_1(a734) | c2_1(a734) | (~c3_1(a734)) | c2_1(a734) | c0_1(a734) | (~c3_1(a734))) <=> (c1_1(a734) | c2_1(a734) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c3_1(a734)) | c0_1(a734))),
% 2.28/1.82 inference(rewrite,[status(thm)],[])).
% 2.28/1.82 tff(4197,plain,
% 2.28/1.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a725) | c1_1(a725) | (~c2_1(a725)) | c1_1(a734) | c2_1(a734) | (~c3_1(a734)) | c2_1(a734) | c0_1(a734) | (~c3_1(a734)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a734) | c2_1(a734) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c3_1(a734)) | c0_1(a734)))),
% 2.28/1.82 inference(monotonicity,[status(thm)],[4196])).
% 2.28/1.82 tff(4198,plain,
% 2.28/1.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a725) | c1_1(a725) | (~c2_1(a725)) | c1_1(a734) | c2_1(a734) | (~c3_1(a734)) | c2_1(a734) | c0_1(a734) | (~c3_1(a734)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a734) | c2_1(a734) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c3_1(a734)) | c0_1(a734))),
% 2.28/1.82 inference(transitivity,[status(thm)],[4197, 4195])).
% 2.28/1.82 tff(4199,plain,
% 2.28/1.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a725) | c1_1(a725) | (~c2_1(a725)) | c1_1(a734) | c2_1(a734) | (~c3_1(a734)) | c2_1(a734) | c0_1(a734) | (~c3_1(a734)))),
% 2.28/1.82 inference(quant_inst,[status(thm)],[])).
% 2.28/1.82 tff(4200,plain,
% 2.28/1.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a734) | c2_1(a734) | c1_1(a725) | c3_1(a725) | (~ndr1_0) | (~c2_1(a725)) | (~c3_1(a734)) | c0_1(a734)),
% 2.28/1.82 inference(modus_ponens,[status(thm)],[4199, 4198])).
% 2.28/1.82 tff(4201,plain,
% 2.28/1.82 ($false),
% 2.28/1.82 inference(unit_resolution,[status(thm)],[4200, 227, 4194, 4186, 4185, 4174, 4176, 948, 4177, 4193])).
% 2.28/1.82 tff(4202,plain,(hskp20 | hskp16), inference(lemma,lemma(discharge,[]))).
% 2.28/1.82 tff(4203,plain,
% 2.28/1.82 (hskp20),
% 2.28/1.82 inference(unit_resolution,[status(thm)],[4202, 12])).
% 2.28/1.82 tff(4204,plain,
% 2.28/1.82 (~c3_1(a754)),
% 2.28/1.82 inference(unit_resolution,[status(thm)],[668, 4203])).
% 2.28/1.82 tff(4205,plain,
% 2.28/1.82 (~c0_1(a754)),
% 2.28/1.82 inference(unit_resolution,[status(thm)],[595, 4203])).
% 2.28/1.82 tff(4206,plain,
% 2.28/1.82 (c2_1(a754)),
% 2.28/1.82 inference(unit_resolution,[status(thm)],[190, 4203])).
% 2.28/1.82 tff(4207,plain,
% 2.28/1.82 (hskp8),
% 2.28/1.82 inference(unit_resolution,[status(thm)],[3733, 227, 2771, 2760, 4206, 4205, 4204, 1862, 3977])).
% 2.28/1.82 tff(4208,plain,
% 2.28/1.82 (c3_1(a710)),
% 2.28/1.82 inference(unit_resolution,[status(thm)],[1886, 4207])).
% 2.28/1.82 tff(4209,plain,
% 2.28/1.82 (c3_1(a763)),
% 2.28/1.82 inference(unit_resolution,[status(thm)],[3599, 4205, 4139, 4137, 4138, 4206, 4204])).
% 2.28/1.82 tff(4210,plain,
% 2.28/1.82 (~c1_1(a754)),
% 2.28/1.82 inference(unit_resolution,[status(thm)],[3716, 227, 4137, 4206, 4138, 4205, 4204, 174, 4209])).
% 2.28/1.82 tff(4211,plain,
% 2.28/1.82 (hskp14),
% 2.28/1.82 inference(unit_resolution,[status(thm)],[3724, 227, 2802, 2760, 4206, 4204, 1614, 4210, 3977])).
% 2.28/1.82 tff(4212,plain,
% 2.28/1.82 (c2_1(a710)),
% 2.28/1.82 inference(unit_resolution,[status(thm)],[1958, 4207])).
% 2.28/1.82 tff(4213,plain,
% 2.28/1.82 (~c0_1(a710)),
% 2.28/1.82 inference(unit_resolution,[status(thm)],[1875, 4207])).
% 2.28/1.82 tff(4214,plain,
% 2.28/1.82 ($false),
% 2.28/1.82 inference(unit_resolution,[status(thm)],[3816, 4213, 4212, 3977, 12, 4139, 4138, 4137, 4211, 4208])).
% 2.28/1.82 tff(4215,plain,(hskp16), inference(lemma,lemma(discharge,[]))).
% 2.28/1.82 tff(4216,plain,
% 2.28/1.82 (~c2_1(a726)),
% 2.28/1.82 inference(unit_resolution,[status(thm)],[4153, 227, 2046, 3833, 3832, 2028, 2022, 3831, 174])).
% 2.28/1.82 tff(4217,plain,
% 2.28/1.82 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c0_1(a726) | c3_1(a726) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | c2_1(a726))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a726) | c3_1(a726) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | c2_1(a726))),
% 2.28/1.82 inference(rewrite,[status(thm)],[])).
% 2.28/1.82 tff(4218,plain,
% 2.28/1.82 ((hskp0 | (~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a726) | c0_1(a726) | c2_1(a726)) <=> (hskp0 | c0_1(a726) | c3_1(a726) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | c2_1(a726))),
% 2.28/1.82 inference(rewrite,[status(thm)],[])).
% 2.28/1.82 tff(4219,plain,
% 2.28/1.82 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a726) | c0_1(a726) | c2_1(a726))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c0_1(a726) | c3_1(a726) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | c2_1(a726)))),
% 2.28/1.82 inference(monotonicity,[status(thm)],[4218])).
% 2.28/1.82 tff(4220,plain,
% 2.28/1.82 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a726) | c0_1(a726) | c2_1(a726))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a726) | c3_1(a726) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | c2_1(a726))),
% 2.28/1.82 inference(transitivity,[status(thm)],[4219, 4217])).
% 2.28/1.82 tff(4221,plain,
% 2.28/1.82 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a726) | c0_1(a726) | c2_1(a726))),
% 2.28/1.82 inference(quant_inst,[status(thm)],[])).
% 2.28/1.82 tff(4222,plain,
% 2.28/1.82 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a726) | c3_1(a726) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | c2_1(a726)),
% 2.28/1.82 inference(modus_ponens,[status(thm)],[4221, 4220])).
% 2.28/1.82 tff(4223,plain,
% 2.28/1.82 (hskp0),
% 2.28/1.82 inference(unit_resolution,[status(thm)],[4222, 227, 3833, 3832, 2028, 2022, 3831, 2832, 4216])).
% 2.28/1.82 tff(4224,plain,
% 2.28/1.82 (~c0_1(a692)),
% 2.28/1.82 inference(unit_resolution,[status(thm)],[859, 4223])).
% 2.28/1.82 tff(4225,plain,
% 2.28/1.82 (~c1_1(a738)),
% 2.28/1.82 inference(unit_resolution,[status(thm)],[3121, 4215])).
% 2.28/1.82 tff(4226,plain,
% 2.28/1.82 (c2_1(a692)),
% 2.28/1.82 inference(unit_resolution,[status(thm)],[872, 4223])).
% 2.28/1.82 tff(4227,plain,
% 2.28/1.82 (c3_1(a738)),
% 2.28/1.82 inference(unit_resolution,[status(thm)],[3087, 4215])).
% 2.28/1.82 tff(4228,plain,
% 2.28/1.82 (c2_1(a738)),
% 2.28/1.82 inference(unit_resolution,[status(thm)],[3098, 4215])).
% 2.28/1.82 tff(4229,plain,
% 2.28/1.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a738) | c3_1(a726) | c0_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c3_1(a692)) | (~c1_1(a726)) | c2_1(a726) | (~c2_1(a738)) | (~c3_1(a738)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a738) | c3_1(a726) | c0_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c3_1(a692)) | (~c1_1(a726)) | c2_1(a726) | (~c2_1(a738)) | (~c3_1(a738)))),
% 2.28/1.82 inference(rewrite,[status(thm)],[])).
% 2.28/1.82 tff(4230,plain,
% 2.28/1.82 (((~ndr1_0) | c3_1(a726) | c2_1(a726) | (~c1_1(a726)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c0_1(a692) | (~c3_1(a692)) | (~c2_1(a692))) <=> (c1_1(a738) | c3_1(a726) | c0_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c3_1(a692)) | (~c1_1(a726)) | c2_1(a726) | (~c2_1(a738)) | (~c3_1(a738)))),
% 2.28/1.82 inference(rewrite,[status(thm)],[])).
% 2.28/1.82 tff(4231,plain,
% 2.28/1.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a726) | c2_1(a726) | (~c1_1(a726)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c0_1(a692) | (~c3_1(a692)) | (~c2_1(a692)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a738) | c3_1(a726) | c0_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c3_1(a692)) | (~c1_1(a726)) | c2_1(a726) | (~c2_1(a738)) | (~c3_1(a738))))),
% 2.28/1.82 inference(monotonicity,[status(thm)],[4230])).
% 2.28/1.82 tff(4232,plain,
% 2.28/1.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a726) | c2_1(a726) | (~c1_1(a726)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c0_1(a692) | (~c3_1(a692)) | (~c2_1(a692)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a738) | c3_1(a726) | c0_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c3_1(a692)) | (~c1_1(a726)) | c2_1(a726) | (~c2_1(a738)) | (~c3_1(a738)))),
% 2.28/1.82 inference(transitivity,[status(thm)],[4231, 4229])).
% 2.28/1.82 tff(4233,plain,
% 2.28/1.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a726) | c2_1(a726) | (~c1_1(a726)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c0_1(a692) | (~c3_1(a692)) | (~c2_1(a692)))),
% 2.28/1.82 inference(quant_inst,[status(thm)],[])).
% 2.28/1.82 tff(4234,plain,
% 2.28/1.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a738) | c3_1(a726) | c0_1(a692) | (~ndr1_0) | (~c2_1(a692)) | (~c3_1(a692)) | (~c1_1(a726)) | c2_1(a726) | (~c2_1(a738)) | (~c3_1(a738))),
% 2.28/1.82 inference(modus_ponens,[status(thm)],[4233, 4232])).
% 2.28/1.83 tff(4235,plain,
% 2.28/1.83 (~c3_1(a692)),
% 2.28/1.83 inference(unit_resolution,[status(thm)],[4234, 227, 4228, 4227, 2046, 4226, 4225, 2022, 4224, 10, 4216])).
% 2.28/1.83 tff(4236,plain,
% 2.28/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a726) | c3_1(a726) | c2_1(a702) | c0_1(a692) | (~ndr1_0) | (~c2_1(a692)) | c3_1(a692) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a726)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a726) | c3_1(a726) | c2_1(a702) | c0_1(a692) | (~ndr1_0) | (~c2_1(a692)) | c3_1(a692) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a726)))),
% 2.28/1.83 inference(rewrite,[status(thm)],[])).
% 2.28/1.83 tff(4237,plain,
% 2.28/1.83 (((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a692) | c0_1(a692) | (~c2_1(a692)) | c3_1(a726) | c0_1(a726) | (~c1_1(a726))) <=> (c0_1(a726) | c3_1(a726) | c2_1(a702) | c0_1(a692) | (~ndr1_0) | (~c2_1(a692)) | c3_1(a692) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a726)))),
% 2.28/1.83 inference(rewrite,[status(thm)],[])).
% 2.28/1.83 tff(4238,plain,
% 2.28/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a692) | c0_1(a692) | (~c2_1(a692)) | c3_1(a726) | c0_1(a726) | (~c1_1(a726)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a726) | c3_1(a726) | c2_1(a702) | c0_1(a692) | (~ndr1_0) | (~c2_1(a692)) | c3_1(a692) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a726))))),
% 2.28/1.83 inference(monotonicity,[status(thm)],[4237])).
% 2.28/1.83 tff(4239,plain,
% 2.28/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a692) | c0_1(a692) | (~c2_1(a692)) | c3_1(a726) | c0_1(a726) | (~c1_1(a726)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a726) | c3_1(a726) | c2_1(a702) | c0_1(a692) | (~ndr1_0) | (~c2_1(a692)) | c3_1(a692) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a726)))),
% 2.28/1.83 inference(transitivity,[status(thm)],[4238, 4236])).
% 2.28/1.83 tff(4240,plain,
% 2.28/1.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a692) | c0_1(a692) | (~c2_1(a692)) | c3_1(a726) | c0_1(a726) | (~c1_1(a726)))),
% 2.28/1.83 inference(quant_inst,[status(thm)],[])).
% 2.28/1.83 tff(4241,plain,
% 2.28/1.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a726) | c3_1(a726) | c2_1(a702) | c0_1(a692) | (~ndr1_0) | (~c2_1(a692)) | c3_1(a692) | (~c3_1(a702)) | (~c0_1(a702)) | (~c1_1(a726))),
% 2.28/1.83 inference(modus_ponens,[status(thm)],[4240, 4239])).
% 2.28/1.83 tff(4242,plain,
% 2.28/1.83 ($false),
% 2.28/1.83 inference(unit_resolution,[status(thm)],[4241, 227, 2046, 3833, 3832, 4226, 2028, 2022, 3831, 4224, 174, 4235])).
% 2.28/1.83 tff(4243,plain,(~hskp13), inference(lemma,lemma(discharge,[]))).
% 2.28/1.83 tff(4244,plain,
% 2.28/1.83 (hskp7),
% 2.28/1.83 inference(unit_resolution,[status(thm)],[3321, 4243, 4215])).
% 2.28/1.83 tff(4245,plain,
% 2.28/1.83 (hskp20),
% 2.28/1.83 inference(unit_resolution,[status(thm)],[3313, 4244, 3977])).
% 2.28/1.83 tff(4246,plain,
% 2.28/1.83 (~c3_1(a754)),
% 2.28/1.83 inference(unit_resolution,[status(thm)],[668, 4245])).
% 2.28/1.83 tff(4247,plain,
% 2.28/1.83 (~c0_1(a754)),
% 2.28/1.83 inference(unit_resolution,[status(thm)],[595, 4245])).
% 2.28/1.83 tff(4248,plain,
% 2.28/1.83 (c2_1(a754)),
% 2.28/1.83 inference(unit_resolution,[status(thm)],[190, 4245])).
% 2.28/1.83 tff(4249,plain,
% 2.28/1.83 (hskp8),
% 2.28/1.83 inference(unit_resolution,[status(thm)],[3733, 227, 2771, 2760, 4248, 4247, 4246, 1862, 3977])).
% 2.28/1.83 tff(4250,plain,
% 2.28/1.83 (~c0_1(a710)),
% 2.28/1.83 inference(unit_resolution,[status(thm)],[1875, 4249])).
% 2.28/1.83 tff(4251,plain,
% 2.28/1.83 (~c1_1(a754)),
% 2.28/1.83 inference(unit_resolution,[status(thm)],[1119, 227, 4248, 3833, 3832, 4247, 4246, 3831, 174])).
% 2.28/1.83 tff(4252,plain,
% 2.28/1.83 (hskp14),
% 2.28/1.83 inference(unit_resolution,[status(thm)],[3724, 227, 2802, 2760, 4248, 4246, 1614, 4251, 3977])).
% 2.28/1.83 tff(4253,plain,
% 2.28/1.83 (~c3_1(a730)),
% 2.28/1.83 inference(unit_resolution,[status(thm)],[486, 4252])).
% 2.28/1.83 tff(4254,plain,
% 2.28/1.83 (c3_1(a710)),
% 2.28/1.83 inference(unit_resolution,[status(thm)],[1886, 4249])).
% 2.28/1.83 tff(4255,plain,
% 2.28/1.83 (c2_1(a710)),
% 2.28/1.83 inference(unit_resolution,[status(thm)],[1958, 4249])).
% 2.28/1.83 tff(4256,plain,
% 2.28/1.83 (c1_1(a730)),
% 2.28/1.83 inference(unit_resolution,[status(thm)],[461, 4252])).
% 2.28/1.83 tff(4257,plain,
% 2.28/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a738) | c3_1(a730) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | (~c1_1(a730)) | c2_1(a730) | (~c2_1(a738)) | (~c3_1(a738)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a738) | c3_1(a730) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | (~c1_1(a730)) | c2_1(a730) | (~c2_1(a738)) | (~c3_1(a738)))),
% 2.28/1.83 inference(rewrite,[status(thm)],[])).
% 2.28/1.83 tff(4258,plain,
% 2.28/1.83 (((~ndr1_0) | c3_1(a730) | c2_1(a730) | (~c1_1(a730)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c0_1(a710) | (~c3_1(a710)) | (~c2_1(a710))) <=> (c1_1(a738) | c3_1(a730) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | (~c1_1(a730)) | c2_1(a730) | (~c2_1(a738)) | (~c3_1(a738)))),
% 2.28/1.83 inference(rewrite,[status(thm)],[])).
% 2.28/1.83 tff(4259,plain,
% 2.28/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a730) | c2_1(a730) | (~c1_1(a730)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c0_1(a710) | (~c3_1(a710)) | (~c2_1(a710)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a738) | c3_1(a730) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | (~c1_1(a730)) | c2_1(a730) | (~c2_1(a738)) | (~c3_1(a738))))),
% 2.28/1.83 inference(monotonicity,[status(thm)],[4258])).
% 2.28/1.83 tff(4260,plain,
% 2.28/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a730) | c2_1(a730) | (~c1_1(a730)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c0_1(a710) | (~c3_1(a710)) | (~c2_1(a710)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a738) | c3_1(a730) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | (~c1_1(a730)) | c2_1(a730) | (~c2_1(a738)) | (~c3_1(a738)))),
% 2.28/1.83 inference(transitivity,[status(thm)],[4259, 4257])).
% 2.28/1.83 tff(4261,plain,
% 2.28/1.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a730) | c2_1(a730) | (~c1_1(a730)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c0_1(a710) | (~c3_1(a710)) | (~c2_1(a710)))),
% 2.28/1.83 inference(quant_inst,[status(thm)],[])).
% 2.28/1.83 tff(4262,plain,
% 2.28/1.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a738) | c3_1(a730) | c0_1(a710) | (~ndr1_0) | (~c3_1(a710)) | (~c2_1(a710)) | (~c1_1(a730)) | c2_1(a730) | (~c2_1(a738)) | (~c3_1(a738))),
% 2.28/1.83 inference(modus_ponens,[status(thm)],[4261, 4260])).
% 2.28/1.83 tff(4263,plain,
% 2.28/1.83 (c2_1(a730)),
% 2.28/1.83 inference(unit_resolution,[status(thm)],[4262, 227, 4228, 4227, 4256, 4255, 4254, 4225, 4253, 4250, 10])).
% 2.28/1.83 tff(4264,plain,
% 2.28/1.83 (~c3_1(a708)),
% 2.28/1.83 inference(unit_resolution,[status(thm)],[3141, 4244])).
% 2.28/1.83 tff(4265,plain,
% 2.28/1.83 (c1_1(a708)),
% 2.28/1.83 inference(unit_resolution,[status(thm)],[3163, 4244])).
% 2.28/1.83 tff(4266,plain,
% 2.28/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a754) | c3_1(a754) | c3_1(a708) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | c0_1(a708) | (~c1_1(a708)) | (~c2_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a754) | c3_1(a754) | c3_1(a708) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | c0_1(a708) | (~c1_1(a708)) | (~c2_1(a754)))),
% 2.28/1.83 inference(rewrite,[status(thm)],[])).
% 2.28/1.83 tff(4267,plain,
% 2.28/1.83 (((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a708) | c0_1(a708) | (~c1_1(a708))) <=> (c0_1(a754) | c3_1(a754) | c3_1(a708) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | c0_1(a708) | (~c1_1(a708)) | (~c2_1(a754)))),
% 2.28/1.83 inference(rewrite,[status(thm)],[])).
% 2.28/1.83 tff(4268,plain,
% 2.28/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a708) | c0_1(a708) | (~c1_1(a708)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a754) | c3_1(a754) | c3_1(a708) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | c0_1(a708) | (~c1_1(a708)) | (~c2_1(a754))))),
% 2.28/1.83 inference(monotonicity,[status(thm)],[4267])).
% 2.28/1.83 tff(4269,plain,
% 2.28/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a708) | c0_1(a708) | (~c1_1(a708)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a754) | c3_1(a754) | c3_1(a708) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | c0_1(a708) | (~c1_1(a708)) | (~c2_1(a754)))),
% 2.28/1.83 inference(transitivity,[status(thm)],[4268, 4266])).
% 2.28/1.83 tff(4270,plain,
% 2.28/1.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a702) | (~c3_1(a702)) | (~c0_1(a702)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)) | c3_1(a708) | c0_1(a708) | (~c1_1(a708)))),
% 2.28/1.83 inference(quant_inst,[status(thm)],[])).
% 2.28/1.83 tff(4271,plain,
% 2.28/1.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a754) | c3_1(a754) | c3_1(a708) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c0_1(a702)) | c0_1(a708) | (~c1_1(a708)) | (~c2_1(a754))),
% 2.28/1.83 inference(modus_ponens,[status(thm)],[4270, 4269])).
% 2.28/1.83 tff(4272,plain,
% 2.28/1.83 (c0_1(a708)),
% 2.28/1.83 inference(unit_resolution,[status(thm)],[4271, 227, 4248, 4265, 3833, 3832, 4247, 4246, 4264, 3831, 174])).
% 2.28/1.83 tff(4273,plain,
% 2.28/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c1_1(a738) | c3_1(a708) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | c1_1(a702) | (~c0_1(a708)) | (~c1_1(a708)) | (~c2_1(a738)) | (~c3_1(a738)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c1_1(a738) | c3_1(a708) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | c1_1(a702) | (~c0_1(a708)) | (~c1_1(a708)) | (~c2_1(a738)) | (~c3_1(a738)))),
% 2.28/1.83 inference(rewrite,[status(thm)],[])).
% 2.28/1.83 tff(4274,plain,
% 2.28/1.83 (((~ndr1_0) | c3_1(a708) | (~c0_1(a708)) | (~c1_1(a708)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c2_1(a702) | (~c3_1(a702)) | c1_1(a702)) <=> (c1_1(a738) | c3_1(a708) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | c1_1(a702) | (~c0_1(a708)) | (~c1_1(a708)) | (~c2_1(a738)) | (~c3_1(a738)))),
% 2.28/1.83 inference(rewrite,[status(thm)],[])).
% 2.28/1.83 tff(4275,plain,
% 2.28/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a708) | (~c0_1(a708)) | (~c1_1(a708)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c2_1(a702) | (~c3_1(a702)) | c1_1(a702))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c1_1(a738) | c3_1(a708) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | c1_1(a702) | (~c0_1(a708)) | (~c1_1(a708)) | (~c2_1(a738)) | (~c3_1(a738))))),
% 2.28/1.83 inference(monotonicity,[status(thm)],[4274])).
% 2.28/1.83 tff(4276,plain,
% 2.28/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a708) | (~c0_1(a708)) | (~c1_1(a708)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c2_1(a702) | (~c3_1(a702)) | c1_1(a702))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c1_1(a738) | c3_1(a708) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | c1_1(a702) | (~c0_1(a708)) | (~c1_1(a708)) | (~c2_1(a738)) | (~c3_1(a738)))),
% 2.28/1.83 inference(transitivity,[status(thm)],[4275, 4273])).
% 2.28/1.83 tff(4277,plain,
% 2.28/1.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a708) | (~c0_1(a708)) | (~c1_1(a708)) | c1_1(a738) | (~c2_1(a738)) | (~c3_1(a738)) | c2_1(a702) | (~c3_1(a702)) | c1_1(a702))),
% 2.28/1.83 inference(quant_inst,[status(thm)],[])).
% 2.28/1.83 tff(4278,plain,
% 2.28/1.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c1_1(a738) | c3_1(a708) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | c1_1(a702) | (~c0_1(a708)) | (~c1_1(a708)) | (~c2_1(a738)) | (~c3_1(a738))),
% 2.28/1.83 inference(modus_ponens,[status(thm)],[4277, 4276])).
% 2.28/1.83 tff(4279,plain,
% 2.28/1.83 (c1_1(a702) | (~c0_1(a708))),
% 2.28/1.83 inference(unit_resolution,[status(thm)],[4278, 227, 4228, 4227, 4265, 3832, 4225, 4264, 3831, 3116])).
% 2.28/1.83 tff(4280,plain,
% 2.28/1.83 (c1_1(a702)),
% 2.28/1.83 inference(unit_resolution,[status(thm)],[4279, 4272])).
% 2.28/1.83 tff(4281,plain,
% 2.28/1.83 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c3_1(a708) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c1_1(a702)) | (~c0_1(a708)) | (~c1_1(a708)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c3_1(a708) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c1_1(a702)) | (~c0_1(a708)) | (~c1_1(a708)))),
% 2.28/1.83 inference(rewrite,[status(thm)],[])).
% 2.28/1.83 tff(4282,plain,
% 2.28/1.83 ((hskp17 | (~ndr1_0) | c3_1(a708) | (~c0_1(a708)) | (~c1_1(a708)) | c2_1(a702) | (~c3_1(a702)) | (~c1_1(a702))) <=> (hskp17 | c3_1(a708) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c1_1(a702)) | (~c0_1(a708)) | (~c1_1(a708)))),
% 2.28/1.83 inference(rewrite,[status(thm)],[])).
% 2.28/1.83 tff(4283,plain,
% 2.28/1.83 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a708) | (~c0_1(a708)) | (~c1_1(a708)) | c2_1(a702) | (~c3_1(a702)) | (~c1_1(a702)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c3_1(a708) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c1_1(a702)) | (~c0_1(a708)) | (~c1_1(a708))))),
% 2.28/1.83 inference(monotonicity,[status(thm)],[4282])).
% 2.28/1.83 tff(4284,plain,
% 2.28/1.83 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a708) | (~c0_1(a708)) | (~c1_1(a708)) | c2_1(a702) | (~c3_1(a702)) | (~c1_1(a702)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c3_1(a708) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c1_1(a702)) | (~c0_1(a708)) | (~c1_1(a708)))),
% 2.28/1.83 inference(transitivity,[status(thm)],[4283, 4281])).
% 2.28/1.83 tff(4285,plain,
% 2.28/1.83 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a708) | (~c0_1(a708)) | (~c1_1(a708)) | c2_1(a702) | (~c3_1(a702)) | (~c1_1(a702)))),
% 2.28/1.83 inference(quant_inst,[status(thm)],[])).
% 2.28/1.83 tff(4286,plain,
% 2.28/1.83 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c3_1(a708) | c2_1(a702) | (~ndr1_0) | (~c3_1(a702)) | (~c1_1(a702)) | (~c0_1(a708)) | (~c1_1(a708))),
% 2.28/1.83 inference(modus_ponens,[status(thm)],[4285, 4284])).
% 2.28/1.83 tff(4287,plain,
% 2.28/1.83 (hskp17 | (~c1_1(a702))),
% 2.28/1.83 inference(unit_resolution,[status(thm)],[4286, 227, 4265, 3832, 4264, 3831, 3236, 4272])).
% 2.28/1.83 tff(4288,plain,
% 2.28/1.83 (hskp17),
% 2.28/1.83 inference(unit_resolution,[status(thm)],[4287, 4280])).
% 2.28/1.83 tff(4289,plain,
% 2.28/1.83 (~c3_1(a744)),
% 2.28/1.83 inference(unit_resolution,[status(thm)],[3248, 4288])).
% 2.28/1.83 tff(4290,plain,
% 2.28/1.83 (~c2_1(a744)),
% 2.28/1.83 inference(unit_resolution,[status(thm)],[3268, 4288])).
% 2.28/1.83 tff(4291,plain,
% 2.28/1.83 (~c1_1(a744)),
% 2.28/1.83 inference(unit_resolution,[status(thm)],[3254, 4288])).
% 2.28/1.83 tff(4292,plain,
% 2.28/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a754) | c3_1(a754) | c1_1(a744) | c2_1(a744) | c3_1(a744) | (~ndr1_0) | (~c0_1(a744)) | (~c2_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a754) | c3_1(a754) | c1_1(a744) | c2_1(a744) | c3_1(a744) | (~ndr1_0) | (~c0_1(a744)) | (~c2_1(a754)))),
% 2.28/1.83 inference(rewrite,[status(thm)],[])).
% 2.28/1.83 tff(4293,plain,
% 2.28/1.83 (((~ndr1_0) | c3_1(a744) | c2_1(a744) | (~c0_1(a744)) | c1_1(a744) | c2_1(a744) | (~c0_1(a744)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754))) <=> (c0_1(a754) | c3_1(a754) | c1_1(a744) | c2_1(a744) | c3_1(a744) | (~ndr1_0) | (~c0_1(a744)) | (~c2_1(a754)))),
% 2.28/1.83 inference(rewrite,[status(thm)],[])).
% 2.28/1.83 tff(4294,plain,
% 2.28/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a744) | c2_1(a744) | (~c0_1(a744)) | c1_1(a744) | c2_1(a744) | (~c0_1(a744)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a754) | c3_1(a754) | c1_1(a744) | c2_1(a744) | c3_1(a744) | (~ndr1_0) | (~c0_1(a744)) | (~c2_1(a754))))),
% 2.28/1.83 inference(monotonicity,[status(thm)],[4293])).
% 2.28/1.83 tff(4295,plain,
% 2.28/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a744) | c2_1(a744) | (~c0_1(a744)) | c1_1(a744) | c2_1(a744) | (~c0_1(a744)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a754) | c3_1(a754) | c1_1(a744) | c2_1(a744) | c3_1(a744) | (~ndr1_0) | (~c0_1(a744)) | (~c2_1(a754)))),
% 2.28/1.83 inference(transitivity,[status(thm)],[4294, 4292])).
% 2.28/1.83 tff(4296,plain,
% 2.28/1.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a744) | c2_1(a744) | (~c0_1(a744)) | c1_1(a744) | c2_1(a744) | (~c0_1(a744)) | c3_1(a754) | c0_1(a754) | (~c2_1(a754)))),
% 2.28/1.83 inference(quant_inst,[status(thm)],[])).
% 2.28/1.83 tff(4297,plain,
% 2.28/1.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a754) | c3_1(a754) | c1_1(a744) | c2_1(a744) | c3_1(a744) | (~ndr1_0) | (~c0_1(a744)) | (~c2_1(a754))),
% 2.28/1.83 inference(modus_ponens,[status(thm)],[4296, 4295])).
% 2.28/1.83 tff(4298,plain,
% 2.28/1.83 (~c0_1(a744)),
% 2.28/1.83 inference(unit_resolution,[status(thm)],[4297, 227, 4248, 4247, 4246, 4291, 4290, 4289, 2445])).
% 2.28/1.83 tff(4299,plain,
% 2.28/1.83 (c2_1(a708)),
% 2.28/1.83 inference(unit_resolution,[status(thm)],[3152, 4244])).
% 2.28/1.83 tff(4300,plain,
% 2.28/1.83 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | c3_1(a708) | (~ndr1_0) | (~c3_1(a695)) | (~c1_1(a695)) | (~c2_1(a695)) | (~c0_1(a708)) | (~c2_1(a708)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp3 | c3_1(a708) | (~ndr1_0) | (~c3_1(a695)) | (~c1_1(a695)) | (~c2_1(a695)) | (~c0_1(a708)) | (~c2_1(a708)))),
% 2.28/1.83 inference(rewrite,[status(thm)],[])).
% 2.28/1.83 tff(4301,plain,
% 2.28/1.83 ((hskp3 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c1_1(a695)) | c3_1(a708) | (~c2_1(a708)) | (~c0_1(a708))) <=> (hskp3 | c3_1(a708) | (~ndr1_0) | (~c3_1(a695)) | (~c1_1(a695)) | (~c2_1(a695)) | (~c0_1(a708)) | (~c2_1(a708)))),
% 2.28/1.83 inference(rewrite,[status(thm)],[])).
% 2.28/1.83 tff(4302,plain,
% 2.28/1.83 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c1_1(a695)) | c3_1(a708) | (~c2_1(a708)) | (~c0_1(a708)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | c3_1(a708) | (~ndr1_0) | (~c3_1(a695)) | (~c1_1(a695)) | (~c2_1(a695)) | (~c0_1(a708)) | (~c2_1(a708))))),
% 2.28/1.83 inference(monotonicity,[status(thm)],[4301])).
% 2.28/1.83 tff(4303,plain,
% 2.28/1.83 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c1_1(a695)) | c3_1(a708) | (~c2_1(a708)) | (~c0_1(a708)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp3 | c3_1(a708) | (~ndr1_0) | (~c3_1(a695)) | (~c1_1(a695)) | (~c2_1(a695)) | (~c0_1(a708)) | (~c2_1(a708)))),
% 2.28/1.83 inference(transitivity,[status(thm)],[4302, 4300])).
% 2.28/1.83 tff(4304,plain,
% 2.28/1.83 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c1_1(a695)) | c3_1(a708) | (~c2_1(a708)) | (~c0_1(a708)))),
% 2.28/1.83 inference(quant_inst,[status(thm)],[])).
% 2.28/1.83 tff(4305,plain,
% 2.28/1.83 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp3 | c3_1(a708) | (~ndr1_0) | (~c3_1(a695)) | (~c1_1(a695)) | (~c2_1(a695)) | (~c0_1(a708)) | (~c2_1(a708))),
% 2.28/1.83 inference(modus_ponens,[status(thm)],[4304, 4303])).
% 2.28/1.83 tff(4306,plain,
% 2.28/1.83 (hskp3),
% 2.28/1.83 inference(unit_resolution,[status(thm)],[4305, 227, 2771, 2760, 4299, 4264, 2234, 3977, 4272])).
% 2.28/1.83 tff(4307,plain,
% 2.28/1.83 (~c3_1(a697)),
% 2.28/1.83 inference(unit_resolution,[status(thm)],[1355, 4306])).
% 2.28/1.83 tff(4308,plain,
% 2.28/1.83 (c0_1(a697)),
% 2.28/1.83 inference(unit_resolution,[status(thm)],[508, 4306])).
% 2.28/1.83 tff(4309,plain,
% 2.28/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a744) | c3_1(a744) | c3_1(a697) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c0_1(a697)) | (~c1_1(a697)) | c0_1(a744))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a744) | c3_1(a744) | c3_1(a697) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c0_1(a697)) | (~c1_1(a697)) | c0_1(a744))),
% 2.28/1.83 inference(rewrite,[status(thm)],[])).
% 2.28/1.83 tff(4310,plain,
% 2.28/1.83 (((~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c3_1(a744) | c2_1(a744) | c0_1(a744)) <=> (c2_1(a744) | c3_1(a744) | c3_1(a697) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c0_1(a697)) | (~c1_1(a697)) | c0_1(a744))),
% 2.28/1.83 inference(rewrite,[status(thm)],[])).
% 2.28/1.83 tff(4311,plain,
% 2.28/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c3_1(a744) | c2_1(a744) | c0_1(a744))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c2_1(a744) | c3_1(a744) | c3_1(a697) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c0_1(a697)) | (~c1_1(a697)) | c0_1(a744)))),
% 2.29/1.84 inference(monotonicity,[status(thm)],[4310])).
% 2.29/1.84 tff(4312,plain,
% 2.29/1.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c3_1(a744) | c2_1(a744) | c0_1(a744))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a744) | c3_1(a744) | c3_1(a697) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c0_1(a697)) | (~c1_1(a697)) | c0_1(a744))),
% 2.29/1.84 inference(transitivity,[status(thm)],[4311, 4309])).
% 2.29/1.84 tff(4313,plain,
% 2.29/1.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a695)) | (~c3_1(a695)) | (~c0_1(a695)) | c3_1(a697) | (~c1_1(a697)) | (~c0_1(a697)) | c3_1(a744) | c2_1(a744) | c0_1(a744))),
% 2.29/1.84 inference(quant_inst,[status(thm)],[])).
% 2.29/1.84 tff(4314,plain,
% 2.29/1.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c2_1(a744) | c3_1(a744) | c3_1(a697) | (~ndr1_0) | (~c0_1(a695)) | (~c3_1(a695)) | (~c2_1(a695)) | (~c0_1(a697)) | (~c1_1(a697)) | c0_1(a744)),
% 2.29/1.84 inference(modus_ponens,[status(thm)],[4313, 4312])).
% 2.29/1.84 tff(4315,plain,
% 2.29/1.84 (~c1_1(a697)),
% 2.29/1.84 inference(unit_resolution,[status(thm)],[4314, 227, 2802, 2760, 4308, 4290, 4289, 4307, 1777, 4298, 3977])).
% 2.29/1.84 tff(4316,plain,
% 2.29/1.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | (c0_1(a754) | c3_1(a730) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c1_1(a730)) | (~c2_1(a730)) | c1_1(a754) | (~c2_1(a754)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c0_1(a754) | c3_1(a730) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c1_1(a730)) | (~c2_1(a730)) | c1_1(a754) | (~c2_1(a754)))),
% 2.29/1.84 inference(rewrite,[status(thm)],[])).
% 2.29/1.84 tff(4317,plain,
% 2.29/1.84 (((~ndr1_0) | c3_1(a730) | (~c2_1(a730)) | (~c1_1(a730)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a754) | (~c2_1(a754)) | c1_1(a754)) <=> (c0_1(a754) | c3_1(a730) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c1_1(a730)) | (~c2_1(a730)) | c1_1(a754) | (~c2_1(a754)))),
% 2.29/1.84 inference(rewrite,[status(thm)],[])).
% 2.29/1.84 tff(4318,plain,
% 2.29/1.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a730) | (~c2_1(a730)) | (~c1_1(a730)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a754) | (~c2_1(a754)) | c1_1(a754))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | (c0_1(a754) | c3_1(a730) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c1_1(a730)) | (~c2_1(a730)) | c1_1(a754) | (~c2_1(a754))))),
% 2.29/1.84 inference(monotonicity,[status(thm)],[4317])).
% 2.29/1.84 tff(4319,plain,
% 2.29/1.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a730) | (~c2_1(a730)) | (~c1_1(a730)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a754) | (~c2_1(a754)) | c1_1(a754))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c0_1(a754) | c3_1(a730) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c1_1(a730)) | (~c2_1(a730)) | c1_1(a754) | (~c2_1(a754)))),
% 2.29/1.84 inference(transitivity,[status(thm)],[4318, 4316])).
% 2.29/1.84 tff(4320,plain,
% 2.29/1.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | ((~ndr1_0) | c3_1(a730) | (~c2_1(a730)) | (~c1_1(a730)) | c3_1(a697) | c1_1(a697) | (~c0_1(a697)) | c0_1(a754) | (~c2_1(a754)) | c1_1(a754))),
% 2.29/1.84 inference(quant_inst,[status(thm)],[])).
% 2.29/1.84 tff(4321,plain,
% 2.29/1.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c1_1(W))) | c0_1(a754) | c3_1(a730) | c3_1(a697) | (~ndr1_0) | (~c0_1(a697)) | c1_1(a697) | (~c1_1(a730)) | (~c2_1(a730)) | c1_1(a754) | (~c2_1(a754))),
% 2.29/1.84 inference(modus_ponens,[status(thm)],[4320, 4319])).
% 2.29/1.84 tff(4322,plain,
% 2.29/1.84 ($false),
% 2.29/1.84 inference(unit_resolution,[status(thm)],[4321, 227, 4248, 4256, 4308, 4247, 4253, 4307, 566, 4251, 4315, 4263])).
% 2.29/1.84 % SZS output end Proof
%------------------------------------------------------------------------------