TSTP Solution File: SYN499-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN499-1 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 23:55:58 EDT 2022
% Result : Unsatisfiable 1.31s 1.11s
% Output : Proof 1.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYN499-1 : TPTP v8.1.0. Released v2.1.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n018.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Sep 5 04:44:01 EDT 2022
% 0.12/0.34 % 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.
% 1.31/1.11 % SZS status Unsatisfiable
% 1.31/1.11 % SZS output start Proof
% 1.31/1.11 tff(c2_1_type, type, (
% 1.31/1.11 c2_1: $i > $o)).
% 1.31/1.11 tff(a142_type, type, (
% 1.31/1.11 a142: $i)).
% 1.31/1.11 tff(c0_1_type, type, (
% 1.31/1.11 c0_1: $i > $o)).
% 1.31/1.11 tff(c1_1_type, type, (
% 1.31/1.11 c1_1: $i > $o)).
% 1.31/1.11 tff(c3_1_type, type, (
% 1.31/1.11 c3_1: $i > $o)).
% 1.31/1.11 tff(ndr1_0_type, type, (
% 1.31/1.11 ndr1_0: $o)).
% 1.31/1.11 tff(a123_type, type, (
% 1.31/1.11 a123: $i)).
% 1.31/1.11 tff(hskp0_type, type, (
% 1.31/1.11 hskp0: $o)).
% 1.31/1.11 tff(a131_type, type, (
% 1.31/1.11 a131: $i)).
% 1.31/1.11 tff(hskp6_type, type, (
% 1.31/1.11 hskp6: $o)).
% 1.31/1.11 tff(hskp18_type, type, (
% 1.31/1.11 hskp18: $o)).
% 1.31/1.11 tff(a182_type, type, (
% 1.31/1.11 a182: $i)).
% 1.31/1.11 tff(a140_type, type, (
% 1.31/1.11 a140: $i)).
% 1.31/1.11 tff(hskp10_type, type, (
% 1.31/1.11 hskp10: $o)).
% 1.31/1.11 tff(a138_type, type, (
% 1.31/1.11 a138: $i)).
% 1.31/1.11 tff(hskp9_type, type, (
% 1.31/1.11 hskp9: $o)).
% 1.31/1.11 tff(a143_type, type, (
% 1.31/1.11 a143: $i)).
% 1.31/1.11 tff(a167_type, type, (
% 1.31/1.11 a167: $i)).
% 1.31/1.11 tff(hskp30_type, type, (
% 1.31/1.11 hskp30: $o)).
% 1.31/1.11 tff(a164_type, type, (
% 1.31/1.11 a164: $i)).
% 1.31/1.11 tff(hskp17_type, type, (
% 1.31/1.11 hskp17: $o)).
% 1.31/1.11 tff(hskp19_type, type, (
% 1.31/1.11 hskp19: $o)).
% 1.31/1.11 tff(a176_type, type, (
% 1.31/1.11 a176: $i)).
% 1.31/1.11 tff(hskp22_type, type, (
% 1.31/1.11 hskp22: $o)).
% 1.31/1.11 tff(a124_type, type, (
% 1.31/1.11 a124: $i)).
% 1.31/1.11 tff(hskp1_type, type, (
% 1.31/1.11 hskp1: $o)).
% 1.31/1.11 tff(hskp2_type, type, (
% 1.31/1.11 hskp2: $o)).
% 1.31/1.11 tff(a125_type, type, (
% 1.31/1.11 a125: $i)).
% 1.31/1.11 tff(a132_type, type, (
% 1.31/1.11 a132: $i)).
% 1.31/1.11 tff(hskp7_type, type, (
% 1.31/1.11 hskp7: $o)).
% 1.31/1.11 tff(a155_type, type, (
% 1.31/1.11 a155: $i)).
% 1.31/1.11 tff(a147_type, type, (
% 1.31/1.11 a147: $i)).
% 1.31/1.11 tff(hskp12_type, type, (
% 1.31/1.11 hskp12: $o)).
% 1.31/1.11 tff(hskp14_type, type, (
% 1.31/1.11 hskp14: $o)).
% 1.31/1.11 tff(a160_type, type, (
% 1.31/1.11 a160: $i)).
% 1.31/1.11 tff(a168_type, type, (
% 1.31/1.11 a168: $i)).
% 1.31/1.11 tff(hskp20_type, type, (
% 1.31/1.11 hskp20: $o)).
% 1.31/1.11 tff(a122_type, type, (
% 1.31/1.11 a122: $i)).
% 1.31/1.11 tff(hskp27_type, type, (
% 1.31/1.11 hskp27: $o)).
% 1.31/1.11 tff(hskp13_type, type, (
% 1.31/1.11 hskp13: $o)).
% 1.31/1.11 tff(a136_type, type, (
% 1.31/1.11 a136: $i)).
% 1.31/1.11 tff(hskp29_type, type, (
% 1.31/1.11 hskp29: $o)).
% 1.31/1.11 tff(a170_type, type, (
% 1.31/1.11 a170: $i)).
% 1.31/1.11 tff(hskp21_type, type, (
% 1.31/1.11 hskp21: $o)).
% 1.31/1.11 tff(hskp24_type, type, (
% 1.31/1.11 hskp24: $o)).
% 1.31/1.11 tff(a134_type, type, (
% 1.31/1.11 a134: $i)).
% 1.31/1.11 tff(hskp8_type, type, (
% 1.31/1.11 hskp8: $o)).
% 1.31/1.11 tff(a127_type, type, (
% 1.31/1.11 a127: $i)).
% 1.31/1.11 tff(hskp3_type, type, (
% 1.31/1.11 hskp3: $o)).
% 1.31/1.11 tff(a153_type, type, (
% 1.31/1.11 a153: $i)).
% 1.31/1.11 tff(hskp15_type, type, (
% 1.31/1.11 hskp15: $o)).
% 1.31/1.11 tff(a133_type, type, (
% 1.31/1.11 a133: $i)).
% 1.31/1.11 tff(hskp28_type, type, (
% 1.31/1.11 hskp28: $o)).
% 1.31/1.11 tff(1,plain,
% 1.31/1.11 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))))),
% 1.31/1.11 inference(bind,[status(th)],[])).
% 1.31/1.11 tff(2,plain,
% 1.31/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.31/1.11 inference(quant_intro,[status(thm)],[1])).
% 1.31/1.11 tff(3,plain,
% 1.31/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.31/1.11 inference(rewrite,[status(thm)],[])).
% 1.31/1.11 tff(4,plain,
% 1.31/1.11 (^[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))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_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) | (~c3_1(U)) | (~c1_1(U)) | (~c2_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))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))))),
% 1.31/1.11 inference(bind,[status(th)],[])).
% 1.31/1.11 tff(5,plain,
% 1.31/1.11 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c1_1(V)) | c0_1(W)) | c1_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)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.31/1.11 inference(quant_intro,[status(thm)],[4])).
% 1.31/1.11 tff(6,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c1_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause200')).
% 1.31/1.11 tff(7,plain,
% 1.31/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.31/1.11 inference(modus_ponens,[status(thm)],[6, 5])).
% 1.31/1.11 tff(8,plain,
% 1.31/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.31/1.11 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.31/1.11 tff(9,plain,(
% 1.31/1.11 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.31/1.11 inference(skolemize,[status(sab)],[8])).
% 1.31/1.11 tff(10,plain,
% 1.31/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.31/1.11 inference(modus_ponens,[status(thm)],[9, 2])).
% 1.31/1.11 tff(11,assumption,(~hskp0), introduced(assumption)).
% 1.31/1.11 tff(12,plain,
% 1.31/1.11 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 1.31/1.11 inference(bind,[status(th)],[])).
% 1.31/1.11 tff(13,plain,
% 1.31/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.31/1.11 inference(quant_intro,[status(thm)],[12])).
% 1.31/1.11 tff(14,plain,
% 1.31/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.31/1.11 inference(rewrite,[status(thm)],[])).
% 1.31/1.11 tff(15,plain,
% 1.31/1.11 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 1.31/1.11 inference(bind,[status(th)],[])).
% 1.31/1.11 tff(16,plain,
% 1.31/1.11 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.31/1.11 inference(quant_intro,[status(thm)],[15])).
% 1.31/1.11 tff(17,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause191')).
% 1.31/1.11 tff(18,plain,
% 1.31/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.31/1.11 inference(modus_ponens,[status(thm)],[17, 16])).
% 1.31/1.11 tff(19,plain,
% 1.31/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.31/1.11 inference(modus_ponens,[status(thm)],[18, 14])).
% 1.31/1.11 tff(20,plain,(
% 1.31/1.11 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.31/1.11 inference(skolemize,[status(sab)],[19])).
% 1.31/1.11 tff(21,plain,
% 1.31/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.31/1.11 inference(modus_ponens,[status(thm)],[20, 13])).
% 1.31/1.11 tff(22,assumption,(~hskp18), introduced(assumption)).
% 1.31/1.11 tff(23,plain,
% 1.31/1.11 (^[U: $i] : refl((hskp18 | hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp18 | hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 1.31/1.11 inference(bind,[status(th)],[])).
% 1.31/1.11 tff(24,plain,
% 1.31/1.11 (![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.31/1.11 inference(quant_intro,[status(thm)],[23])).
% 1.31/1.11 tff(25,plain,
% 1.31/1.11 (![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.31/1.11 inference(rewrite,[status(thm)],[])).
% 1.31/1.11 tff(26,plain,
% 1.31/1.11 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp10) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp10))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp10) | hskp18) <=> ((hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp18))), rewrite(((hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp18) <=> (hskp18 | hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp10) | hskp18) <=> (hskp18 | hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 1.31/1.11 inference(bind,[status(th)],[])).
% 1.31/1.11 tff(27,plain,
% 1.31/1.11 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp10) | hskp18) <=> ![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.31/1.11 inference(quant_intro,[status(thm)],[26])).
% 1.31/1.11 tff(28,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp10) | hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause153')).
% 1.31/1.11 tff(29,plain,
% 1.31/1.11 (![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.31/1.11 inference(modus_ponens,[status(thm)],[28, 27])).
% 1.31/1.11 tff(30,plain,
% 1.31/1.11 (![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.31/1.11 inference(modus_ponens,[status(thm)],[29, 25])).
% 1.31/1.11 tff(31,plain,(
% 1.31/1.11 ![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.31/1.11 inference(skolemize,[status(sab)],[30])).
% 1.31/1.11 tff(32,plain,
% 1.31/1.11 (![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.31/1.11 inference(modus_ponens,[status(thm)],[31, 24])).
% 1.31/1.11 tff(33,assumption,(~hskp9), introduced(assumption)).
% 1.31/1.11 tff(34,plain,
% 1.31/1.11 (^[U: $i] : refl((hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 1.31/1.11 inference(bind,[status(th)],[])).
% 1.31/1.11 tff(35,plain,
% 1.31/1.11 (![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.31/1.11 inference(quant_intro,[status(thm)],[34])).
% 1.31/1.11 tff(36,plain,
% 1.31/1.11 (![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.31/1.11 inference(rewrite,[status(thm)],[])).
% 1.31/1.11 tff(37,plain,
% 1.31/1.11 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp17) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp17))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp17) <=> (hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp17) <=> (hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp17) | hskp0) <=> ((hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp0))), rewrite(((hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp0) <=> (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp17) | hskp0) <=> (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 1.31/1.11 inference(bind,[status(th)],[])).
% 1.31/1.11 tff(38,plain,
% 1.31/1.11 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp17) | hskp0) <=> ![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.31/1.11 inference(quant_intro,[status(thm)],[37])).
% 1.31/1.11 tff(39,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp17) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause144')).
% 1.31/1.11 tff(40,plain,
% 1.31/1.11 (![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.31/1.11 inference(modus_ponens,[status(thm)],[39, 38])).
% 1.31/1.11 tff(41,plain,
% 1.31/1.11 (![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.31/1.11 inference(modus_ponens,[status(thm)],[40, 36])).
% 1.31/1.11 tff(42,plain,(
% 1.31/1.11 ![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.31/1.11 inference(skolemize,[status(sab)],[41])).
% 1.31/1.11 tff(43,plain,
% 1.31/1.11 (![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.31/1.11 inference(modus_ponens,[status(thm)],[42, 35])).
% 1.31/1.11 tff(44,plain,
% 1.31/1.11 (^[U: $i] : refl((hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))),
% 1.31/1.11 inference(bind,[status(th)],[])).
% 1.31/1.11 tff(45,plain,
% 1.31/1.11 (![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.31/1.11 inference(quant_intro,[status(thm)],[44])).
% 1.31/1.11 tff(46,plain,
% 1.31/1.11 (![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.31/1.11 inference(rewrite,[status(thm)],[])).
% 1.31/1.11 tff(47,plain,
% 1.31/1.11 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp19) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp19))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp19) <=> (hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp19) <=> (hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp19) | hskp17) <=> ((hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp17))), rewrite(((hskp19 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp17) <=> (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp19) | hskp17) <=> (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))))),
% 1.31/1.11 inference(bind,[status(th)],[])).
% 1.31/1.11 tff(48,plain,
% 1.31/1.11 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp19) | hskp17) <=> ![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.31/1.11 inference(quant_intro,[status(thm)],[47])).
% 1.31/1.11 tff(49,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp19) | hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause140')).
% 1.31/1.11 tff(50,plain,
% 1.31/1.11 (![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[49, 48])).
% 1.31/1.12 tff(51,plain,
% 1.31/1.12 (![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[50, 46])).
% 1.31/1.12 tff(52,plain,(
% 1.31/1.12 ![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.31/1.12 inference(skolemize,[status(sab)],[51])).
% 1.31/1.12 tff(53,plain,
% 1.31/1.12 (![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[52, 45])).
% 1.31/1.12 tff(54,assumption,(~hskp30), introduced(assumption)).
% 1.31/1.12 tff(55,plain,
% 1.31/1.12 ((hskp30 | hskp9 | hskp6) <=> (hskp30 | hskp9 | hskp6)),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(56,plain,
% 1.31/1.12 (((hskp30 | hskp9) | hskp6) <=> (hskp30 | hskp9 | hskp6)),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(57,axiom,((hskp30 | hskp9) | hskp6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause32')).
% 1.31/1.12 tff(58,plain,
% 1.31/1.12 (hskp30 | hskp9 | hskp6),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[57, 56])).
% 1.31/1.12 tff(59,plain,
% 1.31/1.12 (hskp30 | hskp9 | hskp6),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[58, 55])).
% 1.31/1.12 tff(60,plain,
% 1.31/1.12 (hskp30 | hskp9 | hskp6),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[59, 55])).
% 1.31/1.12 tff(61,plain,
% 1.31/1.12 (hskp30 | hskp9 | hskp6),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[60, 55])).
% 1.31/1.12 tff(62,plain,
% 1.31/1.12 (hskp30 | hskp9 | hskp6),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[61, 55])).
% 1.31/1.12 tff(63,plain,
% 1.31/1.12 (hskp30 | hskp9 | hskp6),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[62, 55])).
% 1.31/1.12 tff(64,plain,
% 1.31/1.12 (hskp30 | hskp9 | hskp6),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[63, 55])).
% 1.31/1.12 tff(65,plain,
% 1.31/1.12 (hskp30 | hskp9 | hskp6),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[64, 55])).
% 1.31/1.12 tff(66,plain,
% 1.31/1.12 (hskp6),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[65, 54, 33])).
% 1.31/1.12 tff(67,plain,
% 1.31/1.12 (((~hskp6) | (~c2_1(a131))) <=> ((~hskp6) | (~c2_1(a131)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(68,plain,
% 1.31/1.12 (((~c2_1(a131)) | (~hskp6)) <=> ((~hskp6) | (~c2_1(a131)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(69,axiom,((~c2_1(a131)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause120')).
% 1.31/1.12 tff(70,plain,
% 1.31/1.12 ((~hskp6) | (~c2_1(a131))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[69, 68])).
% 1.31/1.12 tff(71,plain,
% 1.31/1.12 ((~hskp6) | (~c2_1(a131))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[70, 67])).
% 1.31/1.12 tff(72,plain,
% 1.31/1.12 (~c2_1(a131)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[71, 66])).
% 1.31/1.12 tff(73,plain,
% 1.31/1.12 (((~hskp6) | (~c1_1(a131))) <=> ((~hskp6) | (~c1_1(a131)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(74,plain,
% 1.31/1.12 (((~c1_1(a131)) | (~hskp6)) <=> ((~hskp6) | (~c1_1(a131)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(75,axiom,((~c1_1(a131)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause119')).
% 1.31/1.12 tff(76,plain,
% 1.31/1.12 ((~hskp6) | (~c1_1(a131))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[75, 74])).
% 1.31/1.12 tff(77,plain,
% 1.31/1.12 ((~hskp6) | (~c1_1(a131))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[76, 73])).
% 1.31/1.12 tff(78,plain,
% 1.31/1.12 (~c1_1(a131)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[77, 66])).
% 1.31/1.12 tff(79,plain,
% 1.31/1.12 (((~hskp6) | (~c0_1(a131))) <=> ((~hskp6) | (~c0_1(a131)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(80,plain,
% 1.31/1.12 (((~c0_1(a131)) | (~hskp6)) <=> ((~hskp6) | (~c0_1(a131)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(81,axiom,((~c0_1(a131)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause118')).
% 1.31/1.12 tff(82,plain,
% 1.31/1.12 ((~hskp6) | (~c0_1(a131))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[81, 80])).
% 1.31/1.12 tff(83,plain,
% 1.31/1.12 ((~hskp6) | (~c0_1(a131))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[82, 79])).
% 1.31/1.12 tff(84,plain,
% 1.31/1.12 (~c0_1(a131)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[83, 66])).
% 1.31/1.12 tff(85,plain,
% 1.31/1.12 (^[U: $i] : refl((hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))),
% 1.31/1.12 inference(bind,[status(th)],[])).
% 1.31/1.12 tff(86,plain,
% 1.31/1.12 (![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.31/1.12 inference(quant_intro,[status(thm)],[85])).
% 1.31/1.12 tff(87,plain,
% 1.31/1.12 (![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(88,plain,
% 1.31/1.12 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp9) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp9))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp9) | hskp7) <=> ((hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp7))), rewrite(((hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp7) <=> (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp9) | hskp7) <=> (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))))),
% 1.31/1.12 inference(bind,[status(th)],[])).
% 1.31/1.12 tff(89,plain,
% 1.31/1.12 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp9) | hskp7) <=> ![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.31/1.12 inference(quant_intro,[status(thm)],[88])).
% 1.31/1.12 tff(90,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp9) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause133')).
% 1.31/1.12 tff(91,plain,
% 1.31/1.12 (![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[90, 89])).
% 1.31/1.12 tff(92,plain,
% 1.31/1.12 (![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[91, 87])).
% 1.31/1.12 tff(93,plain,(
% 1.31/1.12 ![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.31/1.12 inference(skolemize,[status(sab)],[92])).
% 1.31/1.12 tff(94,plain,
% 1.31/1.12 (![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[93, 86])).
% 1.31/1.12 tff(95,assumption,(~c2_1(a131)), introduced(assumption)).
% 1.31/1.12 tff(96,assumption,(~hskp7), introduced(assumption)).
% 1.31/1.12 tff(97,assumption,(~c0_1(a131)), introduced(assumption)).
% 1.31/1.12 tff(98,assumption,(~ndr1_0), introduced(assumption)).
% 1.31/1.12 tff(99,plain,
% 1.31/1.12 ((ndr1_0 | (~hskp6)) <=> (ndr1_0 | (~hskp6))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(100,plain,
% 1.31/1.12 (((~hskp6) | ndr1_0) <=> (ndr1_0 | (~hskp6))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(101,axiom,((~hskp6) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause25')).
% 1.31/1.12 tff(102,plain,
% 1.31/1.12 (ndr1_0 | (~hskp6)),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[101, 100])).
% 1.31/1.12 tff(103,plain,
% 1.31/1.12 (ndr1_0 | (~hskp6)),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[102, 99])).
% 1.31/1.12 tff(104,plain,
% 1.31/1.12 (~hskp6),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[103, 98])).
% 1.31/1.12 tff(105,plain,
% 1.31/1.12 (((~hskp30) | ndr1_0) <=> ((~hskp30) | ndr1_0)),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(106,axiom,((~hskp30) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause1')).
% 1.31/1.12 tff(107,plain,
% 1.31/1.12 ((~hskp30) | ndr1_0),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[106, 105])).
% 1.31/1.12 tff(108,plain,
% 1.31/1.12 ((~hskp30) | ndr1_0),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[107, 105])).
% 1.31/1.12 tff(109,plain,
% 1.31/1.12 ((~hskp30) | ndr1_0),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[108, 105])).
% 1.31/1.12 tff(110,plain,
% 1.31/1.12 ((~hskp30) | ndr1_0),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[109, 105])).
% 1.31/1.12 tff(111,plain,
% 1.31/1.12 ((~hskp30) | ndr1_0),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[110, 105])).
% 1.31/1.12 tff(112,plain,
% 1.31/1.12 ((~hskp30) | ndr1_0),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[111, 105])).
% 1.31/1.12 tff(113,plain,
% 1.31/1.12 ((~hskp30) | ndr1_0),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[112, 105])).
% 1.31/1.12 tff(114,plain,
% 1.31/1.12 ((~hskp30) | ndr1_0),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[113, 105])).
% 1.31/1.12 tff(115,plain,
% 1.31/1.12 (~hskp30),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[114, 98])).
% 1.31/1.12 tff(116,plain,
% 1.31/1.12 ((ndr1_0 | (~hskp9)) <=> (ndr1_0 | (~hskp9))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(117,plain,
% 1.31/1.12 (((~hskp9) | ndr1_0) <=> (ndr1_0 | (~hskp9))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(118,axiom,((~hskp9) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause22')).
% 1.31/1.12 tff(119,plain,
% 1.31/1.12 (ndr1_0 | (~hskp9)),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[118, 117])).
% 1.31/1.12 tff(120,plain,
% 1.31/1.12 (ndr1_0 | (~hskp9)),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[119, 116])).
% 1.31/1.12 tff(121,plain,
% 1.31/1.12 (~hskp9),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[120, 98])).
% 1.31/1.12 tff(122,plain,
% 1.31/1.12 ($false),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[65, 121, 115, 104])).
% 1.31/1.12 tff(123,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 1.31/1.12 tff(124,plain,
% 1.31/1.12 (((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | c0_1(a131) | c2_1(a131) | (~ndr1_0) | c3_1(a131))) <=> ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp9 | hskp7 | c0_1(a131) | c2_1(a131) | (~ndr1_0) | c3_1(a131))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(125,plain,
% 1.31/1.12 ((hskp9 | hskp7 | (~ndr1_0) | c2_1(a131) | c0_1(a131) | c3_1(a131)) <=> (hskp9 | hskp7 | c0_1(a131) | c2_1(a131) | (~ndr1_0) | c3_1(a131))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(126,plain,
% 1.31/1.12 (((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | (~ndr1_0) | c2_1(a131) | c0_1(a131) | c3_1(a131))) <=> ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | c0_1(a131) | c2_1(a131) | (~ndr1_0) | c3_1(a131)))),
% 1.31/1.12 inference(monotonicity,[status(thm)],[125])).
% 1.31/1.12 tff(127,plain,
% 1.31/1.12 (((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | (~ndr1_0) | c2_1(a131) | c0_1(a131) | c3_1(a131))) <=> ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp9 | hskp7 | c0_1(a131) | c2_1(a131) | (~ndr1_0) | c3_1(a131))),
% 1.31/1.12 inference(transitivity,[status(thm)],[126, 124])).
% 1.31/1.12 tff(128,plain,
% 1.31/1.12 ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | (~ndr1_0) | c2_1(a131) | c0_1(a131) | c3_1(a131))),
% 1.31/1.12 inference(quant_inst,[status(thm)],[])).
% 1.31/1.12 tff(129,plain,
% 1.31/1.12 ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp9 | hskp7 | c0_1(a131) | c2_1(a131) | (~ndr1_0) | c3_1(a131)),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[128, 127])).
% 1.31/1.12 tff(130,plain,
% 1.31/1.12 (hskp7 | c3_1(a131)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[129, 123, 33, 97, 95, 94])).
% 1.31/1.12 tff(131,plain,
% 1.31/1.12 (c3_1(a131)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[130, 96])).
% 1.31/1.12 tff(132,assumption,(~c1_1(a131)), introduced(assumption)).
% 1.31/1.12 tff(133,assumption,(c3_1(a131)), introduced(assumption)).
% 1.31/1.12 tff(134,assumption,(~hskp17), introduced(assumption)).
% 1.31/1.12 tff(135,plain,
% 1.31/1.12 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))))),
% 1.31/1.12 inference(bind,[status(th)],[])).
% 1.31/1.12 tff(136,plain,
% 1.31/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.31/1.12 inference(quant_intro,[status(thm)],[135])).
% 1.31/1.12 tff(137,plain,
% 1.31/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(138,plain,
% 1.31/1.12 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c3_1(W)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c3_1(W))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c3_1(W)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c3_1(W))))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))))),
% 1.31/1.12 inference(bind,[status(th)],[])).
% 1.31/1.12 tff(139,plain,
% 1.31/1.12 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.31/1.12 inference(quant_intro,[status(thm)],[138])).
% 1.31/1.12 tff(140,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause193')).
% 1.31/1.12 tff(141,plain,
% 1.31/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[140, 139])).
% 1.31/1.12 tff(142,plain,
% 1.31/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[141, 137])).
% 1.31/1.12 tff(143,plain,(
% 1.31/1.12 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.31/1.12 inference(skolemize,[status(sab)],[142])).
% 1.31/1.12 tff(144,plain,
% 1.31/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[143, 136])).
% 1.31/1.12 tff(145,assumption,(hskp12), introduced(assumption)).
% 1.31/1.12 tff(146,plain,
% 1.31/1.12 (((~hskp12) | (~c1_1(a142))) <=> ((~hskp12) | (~c1_1(a142)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(147,plain,
% 1.31/1.12 (((~c1_1(a142)) | (~hskp12)) <=> ((~hskp12) | (~c1_1(a142)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(148,axiom,((~c1_1(a142)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause107')).
% 1.31/1.12 tff(149,plain,
% 1.31/1.12 ((~hskp12) | (~c1_1(a142))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[148, 147])).
% 1.31/1.12 tff(150,plain,
% 1.31/1.12 ((~hskp12) | (~c1_1(a142))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[149, 146])).
% 1.31/1.12 tff(151,plain,
% 1.31/1.12 (~c1_1(a142)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[150, 145])).
% 1.31/1.12 tff(152,plain,
% 1.31/1.12 (((~hskp12) | c3_1(a142)) <=> ((~hskp12) | c3_1(a142))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(153,axiom,((~hskp12) | c3_1(a142)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause70')).
% 1.31/1.12 tff(154,plain,
% 1.31/1.12 ((~hskp12) | c3_1(a142)),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[153, 152])).
% 1.31/1.12 tff(155,plain,
% 1.31/1.12 ((~hskp12) | c3_1(a142)),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[154, 152])).
% 1.31/1.12 tff(156,plain,
% 1.31/1.12 ((~hskp12) | c3_1(a142)),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[155, 152])).
% 1.31/1.12 tff(157,plain,
% 1.31/1.12 ((~hskp12) | c3_1(a142)),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[156, 152])).
% 1.31/1.12 tff(158,plain,
% 1.31/1.12 ((~hskp12) | c3_1(a142)),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[157, 152])).
% 1.31/1.12 tff(159,plain,
% 1.31/1.12 ((~hskp12) | c3_1(a142)),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[158, 152])).
% 1.31/1.12 tff(160,plain,
% 1.31/1.12 ((~hskp12) | c3_1(a142)),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[159, 152])).
% 1.31/1.12 tff(161,plain,
% 1.31/1.12 ((~hskp12) | c3_1(a142)),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[160, 152])).
% 1.31/1.12 tff(162,plain,
% 1.31/1.12 (c3_1(a142)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[161, 145])).
% 1.31/1.12 tff(163,plain,
% 1.31/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a142) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c2_1(a142)) | (~c3_1(a142)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a142) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c2_1(a142)) | (~c3_1(a142)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(164,plain,
% 1.31/1.12 (((~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c2_1(a142)) | c2_1(a131) | c1_1(a131) | (~c3_1(a131)) | c1_1(a131) | c0_1(a131) | (~c3_1(a131))) <=> (c1_1(a142) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c2_1(a142)) | (~c3_1(a142)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(165,plain,
% 1.31/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c2_1(a142)) | c2_1(a131) | c1_1(a131) | (~c3_1(a131)) | c1_1(a131) | c0_1(a131) | (~c3_1(a131)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a142) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c2_1(a142)) | (~c3_1(a142))))),
% 1.31/1.12 inference(monotonicity,[status(thm)],[164])).
% 1.31/1.12 tff(166,plain,
% 1.31/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c2_1(a142)) | c2_1(a131) | c1_1(a131) | (~c3_1(a131)) | c1_1(a131) | c0_1(a131) | (~c3_1(a131)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a142) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c2_1(a142)) | (~c3_1(a142)))),
% 1.31/1.12 inference(transitivity,[status(thm)],[165, 163])).
% 1.31/1.12 tff(167,plain,
% 1.31/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c2_1(a142)) | c2_1(a131) | c1_1(a131) | (~c3_1(a131)) | c1_1(a131) | c0_1(a131) | (~c3_1(a131)))),
% 1.31/1.12 inference(quant_inst,[status(thm)],[])).
% 1.31/1.12 tff(168,plain,
% 1.31/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a142) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c2_1(a142)) | (~c3_1(a142))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[167, 166])).
% 1.31/1.12 tff(169,plain,
% 1.31/1.12 (~c2_1(a142)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[168, 123, 162, 151, 97, 132, 95, 144, 133])).
% 1.31/1.12 tff(170,plain,
% 1.31/1.12 (^[U: $i] : refl((hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 1.31/1.12 inference(bind,[status(th)],[])).
% 1.31/1.12 tff(171,plain,
% 1.31/1.12 (![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.31/1.12 inference(quant_intro,[status(thm)],[170])).
% 1.31/1.12 tff(172,plain,
% 1.31/1.12 (![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(173,plain,
% 1.31/1.12 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp0) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp0))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp0) | hskp7) <=> ((hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp7))), rewrite(((hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp7) <=> (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp0) | hskp7) <=> (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 1.31/1.12 inference(bind,[status(th)],[])).
% 1.31/1.12 tff(174,plain,
% 1.31/1.12 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp0) | hskp7) <=> ![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.31/1.12 inference(quant_intro,[status(thm)],[173])).
% 1.31/1.12 tff(175,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp0) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause149')).
% 1.31/1.12 tff(176,plain,
% 1.31/1.12 (![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[175, 174])).
% 1.31/1.12 tff(177,plain,
% 1.31/1.12 (![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[176, 172])).
% 1.31/1.12 tff(178,plain,(
% 1.31/1.12 ![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.31/1.12 inference(skolemize,[status(sab)],[177])).
% 1.31/1.12 tff(179,plain,
% 1.31/1.12 (![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[178, 171])).
% 1.31/1.12 tff(180,plain,
% 1.31/1.12 (((~hskp12) | c0_1(a142)) <=> ((~hskp12) | c0_1(a142))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(181,axiom,((~hskp12) | c0_1(a142)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause69')).
% 1.31/1.12 tff(182,plain,
% 1.31/1.12 ((~hskp12) | c0_1(a142)),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[181, 180])).
% 1.31/1.12 tff(183,plain,
% 1.31/1.12 ((~hskp12) | c0_1(a142)),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[182, 180])).
% 1.31/1.12 tff(184,plain,
% 1.31/1.12 ((~hskp12) | c0_1(a142)),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[183, 180])).
% 1.31/1.12 tff(185,plain,
% 1.31/1.12 ((~hskp12) | c0_1(a142)),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[184, 180])).
% 1.31/1.12 tff(186,plain,
% 1.31/1.12 ((~hskp12) | c0_1(a142)),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[185, 180])).
% 1.31/1.12 tff(187,plain,
% 1.31/1.12 ((~hskp12) | c0_1(a142)),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[186, 180])).
% 1.31/1.12 tff(188,plain,
% 1.31/1.12 ((~hskp12) | c0_1(a142)),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[187, 180])).
% 1.31/1.12 tff(189,plain,
% 1.31/1.12 ((~hskp12) | c0_1(a142)),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[188, 180])).
% 1.31/1.12 tff(190,plain,
% 1.31/1.12 (c0_1(a142)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[189, 145])).
% 1.31/1.12 tff(191,plain,
% 1.31/1.12 (((~![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp0 | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142)))) <=> ((~![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp7 | hskp0 | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(192,plain,
% 1.31/1.12 ((hskp7 | hskp0 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142))) <=> (hskp7 | hskp0 | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(193,plain,
% 1.31/1.12 (((~![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp0 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142)))) <=> ((~![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp0 | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142))))),
% 1.31/1.12 inference(monotonicity,[status(thm)],[192])).
% 1.31/1.12 tff(194,plain,
% 1.31/1.12 (((~![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp0 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142)))) <=> ((~![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp7 | hskp0 | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142)))),
% 1.31/1.12 inference(transitivity,[status(thm)],[193, 191])).
% 1.31/1.12 tff(195,plain,
% 1.31/1.12 ((~![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp0 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142)))),
% 1.31/1.12 inference(quant_inst,[status(thm)],[])).
% 1.31/1.12 tff(196,plain,
% 1.31/1.12 ((~![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp7 | hskp0 | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[195, 194])).
% 1.31/1.12 tff(197,plain,
% 1.31/1.12 (hskp0),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[196, 123, 96, 190, 162, 151, 179])).
% 1.31/1.12 tff(198,plain,
% 1.31/1.12 (((~hskp0) | (~c1_1(a123))) <=> ((~hskp0) | (~c1_1(a123)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(199,plain,
% 1.31/1.12 (((~c1_1(a123)) | (~hskp0)) <=> ((~hskp0) | (~c1_1(a123)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(200,axiom,((~c1_1(a123)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause130')).
% 1.31/1.12 tff(201,plain,
% 1.31/1.12 ((~hskp0) | (~c1_1(a123))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[200, 199])).
% 1.31/1.12 tff(202,plain,
% 1.31/1.12 ((~hskp0) | (~c1_1(a123))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[201, 198])).
% 1.31/1.12 tff(203,plain,
% 1.31/1.12 (~c1_1(a123)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[202, 197])).
% 1.31/1.12 tff(204,plain,
% 1.31/1.12 (((~hskp0) | c2_1(a123)) <=> ((~hskp0) | c2_1(a123))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(205,axiom,((~hskp0) | c2_1(a123)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause83')).
% 1.31/1.12 tff(206,plain,
% 1.31/1.12 ((~hskp0) | c2_1(a123)),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[205, 204])).
% 1.31/1.12 tff(207,plain,
% 1.31/1.12 ((~hskp0) | c2_1(a123)),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[206, 204])).
% 1.31/1.12 tff(208,plain,
% 1.31/1.12 ((~hskp0) | c2_1(a123)),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[207, 204])).
% 1.31/1.12 tff(209,plain,
% 1.31/1.12 ((~hskp0) | c2_1(a123)),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[208, 204])).
% 1.31/1.12 tff(210,plain,
% 1.31/1.12 ((~hskp0) | c2_1(a123)),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[209, 204])).
% 1.31/1.12 tff(211,plain,
% 1.31/1.12 ((~hskp0) | c2_1(a123)),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[210, 204])).
% 1.31/1.12 tff(212,plain,
% 1.31/1.12 ((~hskp0) | c2_1(a123)),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[211, 204])).
% 1.31/1.12 tff(213,plain,
% 1.31/1.12 ((~hskp0) | c2_1(a123)),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[212, 204])).
% 1.31/1.12 tff(214,plain,
% 1.31/1.12 (c2_1(a123)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[213, 197])).
% 1.31/1.12 tff(215,plain,
% 1.31/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a142) | c0_1(a131) | c1_1(a131) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c2_1(a123)) | (~c3_1(a131)) | c2_1(a142) | (~c3_1(a142)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a142) | c0_1(a131) | c1_1(a131) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c2_1(a123)) | (~c3_1(a131)) | c2_1(a142) | (~c3_1(a142)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(216,plain,
% 1.31/1.12 (((~ndr1_0) | c1_1(a123) | (~c3_1(a123)) | (~c2_1(a123)) | c2_1(a142) | c1_1(a142) | (~c3_1(a142)) | c1_1(a131) | c0_1(a131) | (~c3_1(a131))) <=> (c1_1(a142) | c0_1(a131) | c1_1(a131) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c2_1(a123)) | (~c3_1(a131)) | c2_1(a142) | (~c3_1(a142)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(217,plain,
% 1.31/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a123) | (~c3_1(a123)) | (~c2_1(a123)) | c2_1(a142) | c1_1(a142) | (~c3_1(a142)) | c1_1(a131) | c0_1(a131) | (~c3_1(a131)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a142) | c0_1(a131) | c1_1(a131) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c2_1(a123)) | (~c3_1(a131)) | c2_1(a142) | (~c3_1(a142))))),
% 1.31/1.12 inference(monotonicity,[status(thm)],[216])).
% 1.31/1.12 tff(218,plain,
% 1.31/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a123) | (~c3_1(a123)) | (~c2_1(a123)) | c2_1(a142) | c1_1(a142) | (~c3_1(a142)) | c1_1(a131) | c0_1(a131) | (~c3_1(a131)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a142) | c0_1(a131) | c1_1(a131) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c2_1(a123)) | (~c3_1(a131)) | c2_1(a142) | (~c3_1(a142)))),
% 1.31/1.13 inference(transitivity,[status(thm)],[217, 215])).
% 1.31/1.13 tff(219,plain,
% 1.31/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a123) | (~c3_1(a123)) | (~c2_1(a123)) | c2_1(a142) | c1_1(a142) | (~c3_1(a142)) | c1_1(a131) | c0_1(a131) | (~c3_1(a131)))),
% 1.31/1.13 inference(quant_inst,[status(thm)],[])).
% 1.31/1.13 tff(220,plain,
% 1.31/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a142) | c0_1(a131) | c1_1(a131) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c2_1(a123)) | (~c3_1(a131)) | c2_1(a142) | (~c3_1(a142))),
% 1.31/1.13 inference(modus_ponens,[status(thm)],[219, 218])).
% 1.31/1.13 tff(221,plain,
% 1.31/1.13 (~c3_1(a123)),
% 1.31/1.13 inference(unit_resolution,[status(thm)],[220, 123, 162, 214, 151, 97, 132, 203, 144, 133, 169])).
% 1.31/1.13 tff(222,plain,
% 1.31/1.13 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 1.31/1.13 inference(bind,[status(th)],[])).
% 1.31/1.13 tff(223,plain,
% 1.31/1.13 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.31/1.13 inference(quant_intro,[status(thm)],[222])).
% 1.31/1.13 tff(224,plain,
% 1.31/1.13 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.31/1.13 inference(rewrite,[status(thm)],[])).
% 1.31/1.13 tff(225,plain,
% 1.31/1.13 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | 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)) | 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)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c0_1(W))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c0_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 1.31/1.13 inference(bind,[status(th)],[])).
% 1.31/1.13 tff(226,plain,
% 1.31/1.13 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.31/1.13 inference(quant_intro,[status(thm)],[225])).
% 1.31/1.13 tff(227,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause189')).
% 1.31/1.13 tff(228,plain,
% 1.31/1.13 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.31/1.13 inference(modus_ponens,[status(thm)],[227, 226])).
% 1.31/1.13 tff(229,plain,
% 1.31/1.13 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.31/1.13 inference(modus_ponens,[status(thm)],[228, 224])).
% 1.31/1.13 tff(230,plain,(
% 1.31/1.13 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.31/1.13 inference(skolemize,[status(sab)],[229])).
% 1.31/1.13 tff(231,plain,
% 1.31/1.13 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.31/1.13 inference(modus_ponens,[status(thm)],[230, 223])).
% 1.31/1.13 tff(232,plain,
% 1.31/1.13 (((~hskp0) | (~c0_1(a123))) <=> ((~hskp0) | (~c0_1(a123)))),
% 1.31/1.13 inference(rewrite,[status(thm)],[])).
% 1.31/1.13 tff(233,plain,
% 1.31/1.13 (((~c0_1(a123)) | (~hskp0)) <=> ((~hskp0) | (~c0_1(a123)))),
% 1.31/1.13 inference(rewrite,[status(thm)],[])).
% 1.31/1.13 tff(234,axiom,((~c0_1(a123)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause129')).
% 1.31/1.13 tff(235,plain,
% 1.31/1.13 ((~hskp0) | (~c0_1(a123))),
% 1.31/1.13 inference(modus_ponens,[status(thm)],[234, 233])).
% 1.31/1.13 tff(236,plain,
% 1.31/1.13 ((~hskp0) | (~c0_1(a123))),
% 1.31/1.13 inference(modus_ponens,[status(thm)],[235, 232])).
% 1.31/1.13 tff(237,plain,
% 1.31/1.13 (~c0_1(a123)),
% 1.31/1.13 inference(unit_resolution,[status(thm)],[236, 197])).
% 1.31/1.13 tff(238,plain,
% 1.31/1.13 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | c1_1(a142) | (~ndr1_0) | c2_1(a142) | (~c0_1(a142)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp17 | c1_1(a142) | (~ndr1_0) | c2_1(a142) | (~c0_1(a142)))),
% 1.31/1.13 inference(rewrite,[status(thm)],[])).
% 1.31/1.13 tff(239,plain,
% 1.31/1.13 ((hskp19 | hskp17 | (~ndr1_0) | c2_1(a142) | c1_1(a142) | (~c0_1(a142))) <=> (hskp19 | hskp17 | c1_1(a142) | (~ndr1_0) | c2_1(a142) | (~c0_1(a142)))),
% 1.31/1.13 inference(rewrite,[status(thm)],[])).
% 1.31/1.13 tff(240,plain,
% 1.31/1.13 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c2_1(a142) | c1_1(a142) | (~c0_1(a142)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | c1_1(a142) | (~ndr1_0) | c2_1(a142) | (~c0_1(a142))))),
% 1.31/1.13 inference(monotonicity,[status(thm)],[239])).
% 1.31/1.13 tff(241,plain,
% 1.31/1.13 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c2_1(a142) | c1_1(a142) | (~c0_1(a142)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp17 | c1_1(a142) | (~ndr1_0) | c2_1(a142) | (~c0_1(a142)))),
% 1.31/1.13 inference(transitivity,[status(thm)],[240, 238])).
% 1.31/1.13 tff(242,plain,
% 1.31/1.13 ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c2_1(a142) | c1_1(a142) | (~c0_1(a142)))),
% 1.31/1.13 inference(quant_inst,[status(thm)],[])).
% 1.31/1.13 tff(243,plain,
% 1.31/1.13 ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp17 | c1_1(a142) | (~ndr1_0) | c2_1(a142) | (~c0_1(a142))),
% 1.31/1.13 inference(modus_ponens,[status(thm)],[242, 241])).
% 1.31/1.13 tff(244,plain,
% 1.31/1.13 (hskp19 | c2_1(a142)),
% 1.31/1.13 inference(unit_resolution,[status(thm)],[243, 123, 134, 190, 151, 53])).
% 1.31/1.13 tff(245,plain,
% 1.31/1.13 (hskp19),
% 1.31/1.13 inference(unit_resolution,[status(thm)],[244, 169])).
% 1.31/1.13 tff(246,plain,
% 1.31/1.13 (((~hskp19) | (~c2_1(a164))) <=> ((~hskp19) | (~c2_1(a164)))),
% 1.31/1.13 inference(rewrite,[status(thm)],[])).
% 1.31/1.13 tff(247,plain,
% 1.31/1.13 (((~c2_1(a164)) | (~hskp19)) <=> ((~hskp19) | (~c2_1(a164)))),
% 1.31/1.13 inference(rewrite,[status(thm)],[])).
% 1.31/1.13 tff(248,axiom,((~c2_1(a164)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause97')).
% 1.31/1.13 tff(249,plain,
% 1.31/1.13 ((~hskp19) | (~c2_1(a164))),
% 1.31/1.13 inference(modus_ponens,[status(thm)],[248, 247])).
% 1.31/1.13 tff(250,plain,
% 1.31/1.13 ((~hskp19) | (~c2_1(a164))),
% 1.31/1.13 inference(modus_ponens,[status(thm)],[249, 246])).
% 1.31/1.13 tff(251,plain,
% 1.31/1.13 (~c2_1(a164)),
% 1.31/1.13 inference(unit_resolution,[status(thm)],[250, 245])).
% 1.31/1.13 tff(252,plain,
% 1.31/1.13 (((~hskp19) | c3_1(a164)) <=> ((~hskp19) | c3_1(a164))),
% 1.31/1.13 inference(rewrite,[status(thm)],[])).
% 1.31/1.13 tff(253,axiom,((~hskp19) | c3_1(a164)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause59')).
% 1.31/1.13 tff(254,plain,
% 1.31/1.13 ((~hskp19) | c3_1(a164)),
% 1.31/1.13 inference(modus_ponens,[status(thm)],[253, 252])).
% 1.31/1.13 tff(255,plain,
% 1.31/1.13 ((~hskp19) | c3_1(a164)),
% 1.31/1.13 inference(modus_ponens,[status(thm)],[254, 252])).
% 1.31/1.13 tff(256,plain,
% 1.31/1.13 ((~hskp19) | c3_1(a164)),
% 1.31/1.13 inference(modus_ponens,[status(thm)],[255, 252])).
% 1.31/1.13 tff(257,plain,
% 1.31/1.13 ((~hskp19) | c3_1(a164)),
% 1.31/1.13 inference(modus_ponens,[status(thm)],[256, 252])).
% 1.31/1.13 tff(258,plain,
% 1.31/1.13 ((~hskp19) | c3_1(a164)),
% 1.31/1.13 inference(modus_ponens,[status(thm)],[257, 252])).
% 1.31/1.13 tff(259,plain,
% 1.31/1.13 ((~hskp19) | c3_1(a164)),
% 1.31/1.13 inference(modus_ponens,[status(thm)],[258, 252])).
% 1.31/1.13 tff(260,plain,
% 1.31/1.13 ((~hskp19) | c3_1(a164)),
% 1.31/1.13 inference(modus_ponens,[status(thm)],[259, 252])).
% 1.31/1.13 tff(261,plain,
% 1.31/1.13 ((~hskp19) | c3_1(a164)),
% 1.31/1.13 inference(modus_ponens,[status(thm)],[260, 252])).
% 1.31/1.13 tff(262,plain,
% 1.31/1.13 (c3_1(a164)),
% 1.31/1.13 inference(unit_resolution,[status(thm)],[261, 245])).
% 1.31/1.13 tff(263,plain,
% 1.31/1.13 (((~hskp19) | c1_1(a164)) <=> ((~hskp19) | c1_1(a164))),
% 1.31/1.13 inference(rewrite,[status(thm)],[])).
% 1.31/1.13 tff(264,axiom,((~hskp19) | c1_1(a164)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause58')).
% 1.31/1.13 tff(265,plain,
% 1.31/1.13 ((~hskp19) | c1_1(a164)),
% 1.31/1.13 inference(modus_ponens,[status(thm)],[264, 263])).
% 1.31/1.13 tff(266,plain,
% 1.31/1.13 ((~hskp19) | c1_1(a164)),
% 1.31/1.13 inference(modus_ponens,[status(thm)],[265, 263])).
% 1.31/1.13 tff(267,plain,
% 1.31/1.13 ((~hskp19) | c1_1(a164)),
% 1.31/1.13 inference(modus_ponens,[status(thm)],[266, 263])).
% 1.31/1.13 tff(268,plain,
% 1.31/1.13 ((~hskp19) | c1_1(a164)),
% 1.31/1.13 inference(modus_ponens,[status(thm)],[267, 263])).
% 1.31/1.13 tff(269,plain,
% 1.31/1.13 ((~hskp19) | c1_1(a164)),
% 1.31/1.13 inference(modus_ponens,[status(thm)],[268, 263])).
% 1.31/1.13 tff(270,plain,
% 1.31/1.13 ((~hskp19) | c1_1(a164)),
% 1.31/1.13 inference(modus_ponens,[status(thm)],[269, 263])).
% 1.31/1.13 tff(271,plain,
% 1.31/1.13 ((~hskp19) | c1_1(a164)),
% 1.31/1.13 inference(modus_ponens,[status(thm)],[270, 263])).
% 1.31/1.13 tff(272,plain,
% 1.31/1.13 ((~hskp19) | c1_1(a164)),
% 1.31/1.13 inference(modus_ponens,[status(thm)],[271, 263])).
% 1.31/1.13 tff(273,plain,
% 1.31/1.13 (c1_1(a164)),
% 1.31/1.13 inference(unit_resolution,[status(thm)],[272, 245])).
% 1.31/1.13 tff(274,plain,
% 1.31/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a164) | c0_1(a131) | c1_1(a131) | c2_1(a131) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | c3_1(a123) | (~c3_1(a164)) | (~c1_1(a164)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a164) | c0_1(a131) | c1_1(a131) | c2_1(a131) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | c3_1(a123) | (~c3_1(a164)) | (~c1_1(a164)))),
% 1.31/1.13 inference(rewrite,[status(thm)],[])).
% 1.31/1.13 tff(275,plain,
% 1.31/1.13 (((~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)) | c1_1(a123) | c0_1(a123) | c3_1(a123) | c2_1(a131) | c1_1(a131) | c0_1(a131)) <=> (c2_1(a164) | c0_1(a131) | c1_1(a131) | c2_1(a131) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | c3_1(a123) | (~c3_1(a164)) | (~c1_1(a164)))),
% 1.31/1.13 inference(rewrite,[status(thm)],[])).
% 1.31/1.13 tff(276,plain,
% 1.31/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)) | c1_1(a123) | c0_1(a123) | c3_1(a123) | c2_1(a131) | c1_1(a131) | c0_1(a131))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a164) | c0_1(a131) | c1_1(a131) | c2_1(a131) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | c3_1(a123) | (~c3_1(a164)) | (~c1_1(a164))))),
% 1.31/1.13 inference(monotonicity,[status(thm)],[275])).
% 1.31/1.13 tff(277,plain,
% 1.31/1.13 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)) | c1_1(a123) | c0_1(a123) | c3_1(a123) | c2_1(a131) | c1_1(a131) | c0_1(a131))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a164) | c0_1(a131) | c1_1(a131) | c2_1(a131) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | c3_1(a123) | (~c3_1(a164)) | (~c1_1(a164)))),
% 1.31/1.13 inference(transitivity,[status(thm)],[276, 274])).
% 1.31/1.13 tff(278,plain,
% 1.31/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)) | c1_1(a123) | c0_1(a123) | c3_1(a123) | c2_1(a131) | c1_1(a131) | c0_1(a131))),
% 1.31/1.13 inference(quant_inst,[status(thm)],[])).
% 1.31/1.13 tff(279,plain,
% 1.31/1.13 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a164) | c0_1(a131) | c1_1(a131) | c2_1(a131) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | c3_1(a123) | (~c3_1(a164)) | (~c1_1(a164))),
% 1.31/1.13 inference(modus_ponens,[status(thm)],[278, 277])).
% 1.31/1.13 tff(280,plain,
% 1.31/1.13 ($false),
% 1.31/1.13 inference(unit_resolution,[status(thm)],[279, 123, 273, 262, 251, 97, 132, 95, 237, 203, 231, 221])).
% 1.31/1.13 tff(281,plain,((~hskp12) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~c3_1(a131)) | hskp17 | hskp7), inference(lemma,lemma(discharge,[]))).
% 1.31/1.13 tff(282,plain,
% 1.31/1.13 (~hskp12),
% 1.31/1.13 inference(unit_resolution,[status(thm)],[281, 134, 132, 95, 133, 97, 96])).
% 1.31/1.13 tff(283,plain,
% 1.31/1.13 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.31/1.13 inference(bind,[status(th)],[])).
% 1.31/1.13 tff(284,plain,
% 1.31/1.13 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.31/1.13 inference(quant_intro,[status(thm)],[283])).
% 1.31/1.13 tff(285,plain,
% 1.31/1.13 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.31/1.13 inference(rewrite,[status(thm)],[])).
% 1.31/1.13 tff(286,plain,
% 1.31/1.13 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp12) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp12))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.31/1.13 inference(bind,[status(th)],[])).
% 1.31/1.13 tff(287,plain,
% 1.31/1.13 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.31/1.13 inference(quant_intro,[status(thm)],[286])).
% 1.31/1.13 tff(288,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause183')).
% 1.31/1.13 tff(289,plain,
% 1.31/1.13 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.31/1.13 inference(modus_ponens,[status(thm)],[288, 287])).
% 1.31/1.13 tff(290,plain,
% 1.31/1.13 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.31/1.13 inference(modus_ponens,[status(thm)],[289, 285])).
% 1.31/1.13 tff(291,plain,(
% 1.31/1.13 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.31/1.13 inference(skolemize,[status(sab)],[290])).
% 1.31/1.13 tff(292,plain,
% 1.31/1.13 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.31/1.13 inference(modus_ponens,[status(thm)],[291, 284])).
% 1.31/1.13 tff(293,plain,
% 1.31/1.13 (^[U: $i] : refl((hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))),
% 1.31/1.13 inference(bind,[status(th)],[])).
% 1.31/1.13 tff(294,plain,
% 1.31/1.13 (![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.31/1.13 inference(quant_intro,[status(thm)],[293])).
% 1.31/1.13 tff(295,plain,
% 1.31/1.13 (![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.31/1.13 inference(rewrite,[status(thm)],[])).
% 1.31/1.13 tff(296,plain,
% 1.31/1.13 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp14) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp14))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp14) | hskp7) <=> ((hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp7))), rewrite(((hskp14 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp7) <=> (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp14) | hskp7) <=> (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))))),
% 1.31/1.13 inference(bind,[status(th)],[])).
% 1.31/1.13 tff(297,plain,
% 1.31/1.13 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp14) | hskp7) <=> ![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.31/1.13 inference(quant_intro,[status(thm)],[296])).
% 1.31/1.13 tff(298,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp14) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause138')).
% 1.31/1.13 tff(299,plain,
% 1.31/1.13 (![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.31/1.13 inference(modus_ponens,[status(thm)],[298, 297])).
% 1.31/1.13 tff(300,plain,
% 1.31/1.13 (![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.31/1.13 inference(modus_ponens,[status(thm)],[299, 295])).
% 1.31/1.13 tff(301,plain,(
% 1.31/1.13 ![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.31/1.13 inference(skolemize,[status(sab)],[300])).
% 1.31/1.13 tff(302,plain,
% 1.31/1.13 (![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.31/1.13 inference(modus_ponens,[status(thm)],[301, 294])).
% 1.31/1.13 tff(303,plain,
% 1.31/1.13 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp14 | hskp7 | c0_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp14 | hskp7 | c0_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)))),
% 1.31/1.13 inference(rewrite,[status(thm)],[])).
% 1.31/1.13 tff(304,plain,
% 1.31/1.13 ((hskp14 | hskp7 | (~ndr1_0) | c2_1(a131) | c0_1(a131) | (~c3_1(a131))) <=> (hskp14 | hskp7 | c0_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)))),
% 1.31/1.13 inference(rewrite,[status(thm)],[])).
% 1.31/1.13 tff(305,plain,
% 1.31/1.13 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c2_1(a131) | c0_1(a131) | (~c3_1(a131)))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp14 | hskp7 | c0_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131))))),
% 1.31/1.13 inference(monotonicity,[status(thm)],[304])).
% 1.31/1.13 tff(306,plain,
% 1.31/1.13 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c2_1(a131) | c0_1(a131) | (~c3_1(a131)))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp14 | hskp7 | c0_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)))),
% 1.31/1.13 inference(transitivity,[status(thm)],[305, 303])).
% 1.31/1.13 tff(307,plain,
% 1.31/1.13 ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c2_1(a131) | c0_1(a131) | (~c3_1(a131)))),
% 1.31/1.13 inference(quant_inst,[status(thm)],[])).
% 1.31/1.13 tff(308,plain,
% 1.31/1.13 ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp14 | hskp7 | c0_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131))),
% 1.31/1.13 inference(modus_ponens,[status(thm)],[307, 306])).
% 1.31/1.13 tff(309,plain,
% 1.31/1.13 (hskp14 | hskp7 | (~c3_1(a131))),
% 1.31/1.13 inference(unit_resolution,[status(thm)],[308, 123, 97, 95, 302])).
% 1.31/1.13 tff(310,plain,
% 1.31/1.13 (hskp14),
% 1.31/1.13 inference(unit_resolution,[status(thm)],[309, 96, 133])).
% 1.31/1.13 tff(311,plain,
% 1.31/1.13 (((~hskp14) | (~c3_1(a147))) <=> ((~hskp14) | (~c3_1(a147)))),
% 1.31/1.13 inference(rewrite,[status(thm)],[])).
% 1.31/1.13 tff(312,plain,
% 1.31/1.13 (((~c3_1(a147)) | (~hskp14)) <=> ((~hskp14) | (~c3_1(a147)))),
% 1.31/1.13 inference(rewrite,[status(thm)],[])).
% 1.31/1.13 tff(313,axiom,((~c3_1(a147)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause105')).
% 1.31/1.13 tff(314,plain,
% 1.31/1.13 ((~hskp14) | (~c3_1(a147))),
% 1.31/1.13 inference(modus_ponens,[status(thm)],[313, 312])).
% 1.31/1.13 tff(315,plain,
% 1.31/1.13 ((~hskp14) | (~c3_1(a147))),
% 1.31/1.13 inference(modus_ponens,[status(thm)],[314, 311])).
% 1.31/1.13 tff(316,plain,
% 1.31/1.13 (~c3_1(a147)),
% 1.31/1.13 inference(unit_resolution,[status(thm)],[315, 310])).
% 1.31/1.13 tff(317,plain,
% 1.31/1.13 (((~hskp14) | c0_1(a147)) <=> ((~hskp14) | c0_1(a147))),
% 1.31/1.13 inference(rewrite,[status(thm)],[])).
% 1.31/1.13 tff(318,axiom,((~hskp14) | c0_1(a147)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause66')).
% 1.31/1.13 tff(319,plain,
% 1.31/1.13 ((~hskp14) | c0_1(a147)),
% 1.31/1.13 inference(modus_ponens,[status(thm)],[318, 317])).
% 1.31/1.13 tff(320,plain,
% 1.31/1.13 ((~hskp14) | c0_1(a147)),
% 1.31/1.13 inference(modus_ponens,[status(thm)],[319, 317])).
% 1.31/1.13 tff(321,plain,
% 1.31/1.13 ((~hskp14) | c0_1(a147)),
% 1.31/1.13 inference(modus_ponens,[status(thm)],[320, 317])).
% 1.31/1.13 tff(322,plain,
% 1.31/1.13 ((~hskp14) | c0_1(a147)),
% 1.31/1.13 inference(modus_ponens,[status(thm)],[321, 317])).
% 1.31/1.13 tff(323,plain,
% 1.31/1.13 ((~hskp14) | c0_1(a147)),
% 1.31/1.13 inference(modus_ponens,[status(thm)],[322, 317])).
% 1.31/1.13 tff(324,plain,
% 1.31/1.13 ((~hskp14) | c0_1(a147)),
% 1.31/1.13 inference(modus_ponens,[status(thm)],[323, 317])).
% 1.31/1.13 tff(325,plain,
% 1.31/1.13 ((~hskp14) | c0_1(a147)),
% 1.31/1.13 inference(modus_ponens,[status(thm)],[324, 317])).
% 1.31/1.13 tff(326,plain,
% 1.31/1.13 ((~hskp14) | c0_1(a147)),
% 1.31/1.13 inference(modus_ponens,[status(thm)],[325, 317])).
% 1.31/1.13 tff(327,plain,
% 1.31/1.13 (c0_1(a147)),
% 1.31/1.13 inference(unit_resolution,[status(thm)],[326, 310])).
% 1.31/1.13 tff(328,plain,
% 1.31/1.13 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c3_1(a147) | c0_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c2_1(a147)) | (~c0_1(a147)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c3_1(a147) | c0_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c2_1(a147)) | (~c0_1(a147)))),
% 1.31/1.13 inference(rewrite,[status(thm)],[])).
% 1.31/1.13 tff(329,plain,
% 1.31/1.13 ((hskp12 | (~ndr1_0) | c3_1(a147) | (~c0_1(a147)) | (~c2_1(a147)) | c2_1(a131) | c0_1(a131) | (~c3_1(a131))) <=> (hskp12 | c3_1(a147) | c0_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c2_1(a147)) | (~c0_1(a147)))),
% 1.31/1.13 inference(rewrite,[status(thm)],[])).
% 1.31/1.13 tff(330,plain,
% 1.31/1.13 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a147) | (~c0_1(a147)) | (~c2_1(a147)) | c2_1(a131) | c0_1(a131) | (~c3_1(a131)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c3_1(a147) | c0_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c2_1(a147)) | (~c0_1(a147))))),
% 1.31/1.13 inference(monotonicity,[status(thm)],[329])).
% 1.31/1.13 tff(331,plain,
% 1.31/1.13 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a147) | (~c0_1(a147)) | (~c2_1(a147)) | c2_1(a131) | c0_1(a131) | (~c3_1(a131)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c3_1(a147) | c0_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c2_1(a147)) | (~c0_1(a147)))),
% 1.31/1.13 inference(transitivity,[status(thm)],[330, 328])).
% 1.31/1.13 tff(332,plain,
% 1.31/1.13 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a147) | (~c0_1(a147)) | (~c2_1(a147)) | c2_1(a131) | c0_1(a131) | (~c3_1(a131)))),
% 1.31/1.13 inference(quant_inst,[status(thm)],[])).
% 1.31/1.13 tff(333,plain,
% 1.31/1.13 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c3_1(a147) | c0_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c2_1(a147)) | (~c0_1(a147))),
% 1.31/1.13 inference(modus_ponens,[status(thm)],[332, 331])).
% 1.31/1.13 tff(334,plain,
% 1.31/1.13 (hskp12 | (~c2_1(a147))),
% 1.31/1.13 inference(unit_resolution,[status(thm)],[333, 123, 327, 316, 97, 95, 292, 133])).
% 1.31/1.13 tff(335,plain,
% 1.31/1.13 (~c2_1(a147)),
% 1.31/1.13 inference(unit_resolution,[status(thm)],[334, 282])).
% 1.31/1.13 tff(336,plain,
% 1.31/1.13 (((~hskp14) | (~c1_1(a147))) <=> ((~hskp14) | (~c1_1(a147)))),
% 1.31/1.13 inference(rewrite,[status(thm)],[])).
% 1.31/1.13 tff(337,plain,
% 1.31/1.13 (((~c1_1(a147)) | (~hskp14)) <=> ((~hskp14) | (~c1_1(a147)))),
% 1.31/1.13 inference(rewrite,[status(thm)],[])).
% 1.31/1.13 tff(338,axiom,((~c1_1(a147)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause104')).
% 1.31/1.13 tff(339,plain,
% 1.31/1.13 ((~hskp14) | (~c1_1(a147))),
% 1.31/1.13 inference(modus_ponens,[status(thm)],[338, 337])).
% 1.31/1.13 tff(340,plain,
% 1.31/1.13 ((~hskp14) | (~c1_1(a147))),
% 1.31/1.13 inference(modus_ponens,[status(thm)],[339, 336])).
% 1.31/1.13 tff(341,plain,
% 1.31/1.13 (~c1_1(a147)),
% 1.31/1.13 inference(unit_resolution,[status(thm)],[340, 310])).
% 1.31/1.13 tff(342,plain,
% 1.31/1.13 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | c1_1(a147) | (~ndr1_0) | c2_1(a147) | (~c0_1(a147)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp17 | c1_1(a147) | (~ndr1_0) | c2_1(a147) | (~c0_1(a147)))),
% 1.31/1.13 inference(rewrite,[status(thm)],[])).
% 1.31/1.13 tff(343,plain,
% 1.31/1.13 ((hskp19 | hskp17 | (~ndr1_0) | c2_1(a147) | c1_1(a147) | (~c0_1(a147))) <=> (hskp19 | hskp17 | c1_1(a147) | (~ndr1_0) | c2_1(a147) | (~c0_1(a147)))),
% 1.31/1.13 inference(rewrite,[status(thm)],[])).
% 1.31/1.13 tff(344,plain,
% 1.31/1.13 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c2_1(a147) | c1_1(a147) | (~c0_1(a147)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | c1_1(a147) | (~ndr1_0) | c2_1(a147) | (~c0_1(a147))))),
% 1.31/1.13 inference(monotonicity,[status(thm)],[343])).
% 1.31/1.13 tff(345,plain,
% 1.31/1.13 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c2_1(a147) | c1_1(a147) | (~c0_1(a147)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp17 | c1_1(a147) | (~ndr1_0) | c2_1(a147) | (~c0_1(a147)))),
% 1.31/1.13 inference(transitivity,[status(thm)],[344, 342])).
% 1.31/1.13 tff(346,plain,
% 1.31/1.14 ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c2_1(a147) | c1_1(a147) | (~c0_1(a147)))),
% 1.31/1.14 inference(quant_inst,[status(thm)],[])).
% 1.31/1.14 tff(347,plain,
% 1.31/1.14 ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp17 | c1_1(a147) | (~ndr1_0) | c2_1(a147) | (~c0_1(a147))),
% 1.31/1.14 inference(modus_ponens,[status(thm)],[346, 345])).
% 1.31/1.14 tff(348,plain,
% 1.31/1.14 (hskp19 | hskp17 | c2_1(a147)),
% 1.31/1.14 inference(unit_resolution,[status(thm)],[347, 123, 327, 341, 53])).
% 1.31/1.14 tff(349,plain,
% 1.31/1.14 (hskp19),
% 1.31/1.14 inference(unit_resolution,[status(thm)],[348, 335, 134])).
% 1.31/1.14 tff(350,plain,
% 1.31/1.14 (~c2_1(a164)),
% 1.31/1.14 inference(unit_resolution,[status(thm)],[250, 349])).
% 1.31/1.14 tff(351,plain,
% 1.31/1.14 (c1_1(a164)),
% 1.31/1.14 inference(unit_resolution,[status(thm)],[272, 349])).
% 1.31/1.14 tff(352,plain,
% 1.31/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a164) | c3_1(a147) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | c2_1(a147) | (~c0_1(a147)) | c0_1(a164) | (~c1_1(a164)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a164) | c3_1(a147) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | c2_1(a147) | (~c0_1(a147)) | c0_1(a164) | (~c1_1(a164)))),
% 1.31/1.14 inference(rewrite,[status(thm)],[])).
% 1.31/1.14 tff(353,plain,
% 1.31/1.14 (((~ndr1_0) | c2_1(a147) | c3_1(a147) | (~c0_1(a147)) | c2_1(a164) | c0_1(a164) | (~c1_1(a164)) | c2_1(a131) | c1_1(a131) | c0_1(a131)) <=> (c2_1(a164) | c3_1(a147) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | c2_1(a147) | (~c0_1(a147)) | c0_1(a164) | (~c1_1(a164)))),
% 1.31/1.14 inference(rewrite,[status(thm)],[])).
% 1.31/1.14 tff(354,plain,
% 1.31/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a147) | c3_1(a147) | (~c0_1(a147)) | c2_1(a164) | c0_1(a164) | (~c1_1(a164)) | c2_1(a131) | c1_1(a131) | c0_1(a131))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a164) | c3_1(a147) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | c2_1(a147) | (~c0_1(a147)) | c0_1(a164) | (~c1_1(a164))))),
% 1.31/1.14 inference(monotonicity,[status(thm)],[353])).
% 1.31/1.14 tff(355,plain,
% 1.31/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a147) | c3_1(a147) | (~c0_1(a147)) | c2_1(a164) | c0_1(a164) | (~c1_1(a164)) | c2_1(a131) | c1_1(a131) | c0_1(a131))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a164) | c3_1(a147) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | c2_1(a147) | (~c0_1(a147)) | c0_1(a164) | (~c1_1(a164)))),
% 1.31/1.14 inference(transitivity,[status(thm)],[354, 352])).
% 1.31/1.14 tff(356,plain,
% 1.31/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a147) | c3_1(a147) | (~c0_1(a147)) | c2_1(a164) | c0_1(a164) | (~c1_1(a164)) | c2_1(a131) | c1_1(a131) | c0_1(a131))),
% 1.31/1.14 inference(quant_inst,[status(thm)],[])).
% 1.31/1.14 tff(357,plain,
% 1.31/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a164) | c3_1(a147) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | c2_1(a147) | (~c0_1(a147)) | c0_1(a164) | (~c1_1(a164))),
% 1.31/1.14 inference(modus_ponens,[status(thm)],[356, 355])).
% 1.31/1.14 tff(358,plain,
% 1.31/1.14 (c0_1(a164)),
% 1.31/1.14 inference(unit_resolution,[status(thm)],[357, 123, 351, 327, 350, 316, 97, 132, 95, 21, 335])).
% 1.31/1.14 tff(359,plain,
% 1.31/1.14 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.31/1.14 inference(bind,[status(th)],[])).
% 1.31/1.14 tff(360,plain,
% 1.31/1.14 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.31/1.14 inference(quant_intro,[status(thm)],[359])).
% 1.31/1.14 tff(361,plain,
% 1.31/1.14 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.31/1.14 inference(rewrite,[status(thm)],[])).
% 1.31/1.14 tff(362,plain,
% 1.31/1.14 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp7) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp7))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.31/1.14 inference(bind,[status(th)],[])).
% 1.31/1.14 tff(363,plain,
% 1.31/1.14 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.31/1.14 inference(quant_intro,[status(thm)],[362])).
% 1.31/1.14 tff(364,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause180')).
% 1.31/1.14 tff(365,plain,
% 1.31/1.14 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.31/1.14 inference(modus_ponens,[status(thm)],[364, 363])).
% 1.31/1.14 tff(366,plain,
% 1.31/1.14 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.31/1.14 inference(modus_ponens,[status(thm)],[365, 361])).
% 1.31/1.14 tff(367,plain,(
% 1.31/1.14 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.31/1.14 inference(skolemize,[status(sab)],[366])).
% 1.31/1.14 tff(368,plain,
% 1.31/1.14 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.31/1.14 inference(modus_ponens,[status(thm)],[367, 360])).
% 1.31/1.14 tff(369,plain,
% 1.31/1.14 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c2_1(a164) | c0_1(a131) | c1_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c0_1(a164)) | (~c1_1(a164)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c2_1(a164) | c0_1(a131) | c1_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c0_1(a164)) | (~c1_1(a164)))),
% 1.31/1.14 inference(rewrite,[status(thm)],[])).
% 1.31/1.14 tff(370,plain,
% 1.31/1.14 ((hskp7 | (~ndr1_0) | c2_1(a164) | (~c1_1(a164)) | (~c0_1(a164)) | c1_1(a131) | c0_1(a131) | (~c3_1(a131))) <=> (hskp7 | c2_1(a164) | c0_1(a131) | c1_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c0_1(a164)) | (~c1_1(a164)))),
% 1.31/1.14 inference(rewrite,[status(thm)],[])).
% 1.31/1.14 tff(371,plain,
% 1.31/1.14 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a164) | (~c1_1(a164)) | (~c0_1(a164)) | c1_1(a131) | c0_1(a131) | (~c3_1(a131)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c2_1(a164) | c0_1(a131) | c1_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c0_1(a164)) | (~c1_1(a164))))),
% 1.31/1.14 inference(monotonicity,[status(thm)],[370])).
% 1.31/1.14 tff(372,plain,
% 1.31/1.14 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a164) | (~c1_1(a164)) | (~c0_1(a164)) | c1_1(a131) | c0_1(a131) | (~c3_1(a131)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c2_1(a164) | c0_1(a131) | c1_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c0_1(a164)) | (~c1_1(a164)))),
% 1.38/1.14 inference(transitivity,[status(thm)],[371, 369])).
% 1.38/1.14 tff(373,plain,
% 1.38/1.14 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a164) | (~c1_1(a164)) | (~c0_1(a164)) | c1_1(a131) | c0_1(a131) | (~c3_1(a131)))),
% 1.38/1.14 inference(quant_inst,[status(thm)],[])).
% 1.38/1.14 tff(374,plain,
% 1.38/1.14 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c2_1(a164) | c0_1(a131) | c1_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c0_1(a164)) | (~c1_1(a164))),
% 1.38/1.14 inference(modus_ponens,[status(thm)],[373, 372])).
% 1.38/1.14 tff(375,plain,
% 1.38/1.14 ($false),
% 1.38/1.14 inference(unit_resolution,[status(thm)],[374, 123, 96, 351, 350, 97, 132, 368, 133, 358])).
% 1.38/1.14 tff(376,plain,(hskp17 | hskp7 | c0_1(a131) | c1_1(a131) | (~c3_1(a131)) | c2_1(a131)), inference(lemma,lemma(discharge,[]))).
% 1.38/1.14 tff(377,plain,
% 1.38/1.14 (hskp17),
% 1.38/1.14 inference(unit_resolution,[status(thm)],[376, 96, 97, 132, 131, 95])).
% 1.38/1.14 tff(378,plain,
% 1.38/1.14 (((~hskp17) | (~c2_1(a155))) <=> ((~hskp17) | (~c2_1(a155)))),
% 1.38/1.14 inference(rewrite,[status(thm)],[])).
% 1.38/1.14 tff(379,plain,
% 1.38/1.14 (((~c2_1(a155)) | (~hskp17)) <=> ((~hskp17) | (~c2_1(a155)))),
% 1.38/1.14 inference(rewrite,[status(thm)],[])).
% 1.38/1.14 tff(380,axiom,((~c2_1(a155)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause101')).
% 1.38/1.14 tff(381,plain,
% 1.38/1.14 ((~hskp17) | (~c2_1(a155))),
% 1.38/1.14 inference(modus_ponens,[status(thm)],[380, 379])).
% 1.38/1.14 tff(382,plain,
% 1.38/1.14 ((~hskp17) | (~c2_1(a155))),
% 1.38/1.14 inference(modus_ponens,[status(thm)],[381, 378])).
% 1.38/1.14 tff(383,plain,
% 1.38/1.14 (~c2_1(a155)),
% 1.38/1.14 inference(unit_resolution,[status(thm)],[382, 377])).
% 1.38/1.14 tff(384,plain,
% 1.38/1.14 (((~hskp17) | (~c0_1(a155))) <=> ((~hskp17) | (~c0_1(a155)))),
% 1.38/1.14 inference(rewrite,[status(thm)],[])).
% 1.38/1.14 tff(385,plain,
% 1.38/1.14 (((~c0_1(a155)) | (~hskp17)) <=> ((~hskp17) | (~c0_1(a155)))),
% 1.38/1.14 inference(rewrite,[status(thm)],[])).
% 1.38/1.14 tff(386,axiom,((~c0_1(a155)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause100')).
% 1.38/1.14 tff(387,plain,
% 1.38/1.14 ((~hskp17) | (~c0_1(a155))),
% 1.38/1.14 inference(modus_ponens,[status(thm)],[386, 385])).
% 1.38/1.14 tff(388,plain,
% 1.38/1.14 ((~hskp17) | (~c0_1(a155))),
% 1.38/1.14 inference(modus_ponens,[status(thm)],[387, 384])).
% 1.38/1.14 tff(389,plain,
% 1.38/1.14 (~c0_1(a155)),
% 1.38/1.14 inference(unit_resolution,[status(thm)],[388, 377])).
% 1.38/1.14 tff(390,plain,
% 1.38/1.14 (((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | c0_1(a155) | c2_1(a155) | (~ndr1_0) | c3_1(a155))) <=> ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp9 | hskp7 | c0_1(a155) | c2_1(a155) | (~ndr1_0) | c3_1(a155))),
% 1.38/1.14 inference(rewrite,[status(thm)],[])).
% 1.38/1.14 tff(391,plain,
% 1.38/1.14 ((hskp9 | hskp7 | (~ndr1_0) | c2_1(a155) | c0_1(a155) | c3_1(a155)) <=> (hskp9 | hskp7 | c0_1(a155) | c2_1(a155) | (~ndr1_0) | c3_1(a155))),
% 1.38/1.14 inference(rewrite,[status(thm)],[])).
% 1.38/1.14 tff(392,plain,
% 1.38/1.14 (((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | (~ndr1_0) | c2_1(a155) | c0_1(a155) | c3_1(a155))) <=> ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | c0_1(a155) | c2_1(a155) | (~ndr1_0) | c3_1(a155)))),
% 1.38/1.14 inference(monotonicity,[status(thm)],[391])).
% 1.38/1.14 tff(393,plain,
% 1.38/1.14 (((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | (~ndr1_0) | c2_1(a155) | c0_1(a155) | c3_1(a155))) <=> ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp9 | hskp7 | c0_1(a155) | c2_1(a155) | (~ndr1_0) | c3_1(a155))),
% 1.38/1.14 inference(transitivity,[status(thm)],[392, 390])).
% 1.38/1.14 tff(394,plain,
% 1.38/1.14 ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | (~ndr1_0) | c2_1(a155) | c0_1(a155) | c3_1(a155))),
% 1.38/1.14 inference(quant_inst,[status(thm)],[])).
% 1.38/1.14 tff(395,plain,
% 1.38/1.14 ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp9 | hskp7 | c0_1(a155) | c2_1(a155) | (~ndr1_0) | c3_1(a155)),
% 1.38/1.14 inference(modus_ponens,[status(thm)],[394, 393])).
% 1.38/1.14 tff(396,plain,
% 1.38/1.14 (c3_1(a155)),
% 1.38/1.14 inference(unit_resolution,[status(thm)],[395, 123, 33, 96, 389, 383, 94])).
% 1.38/1.14 tff(397,plain,
% 1.38/1.14 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 1.38/1.14 inference(bind,[status(th)],[])).
% 1.38/1.14 tff(398,plain,
% 1.38/1.14 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.38/1.14 inference(quant_intro,[status(thm)],[397])).
% 1.38/1.14 tff(399,plain,
% 1.38/1.14 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.38/1.14 inference(rewrite,[status(thm)],[])).
% 1.38/1.14 tff(400,plain,
% 1.38/1.14 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(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))) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | (~c1_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | (~c1_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W)))), ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 1.38/1.14 inference(bind,[status(th)],[])).
% 1.38/1.14 tff(401,plain,
% 1.38/1.14 (![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.38/1.14 inference(quant_intro,[status(thm)],[400])).
% 1.38/1.14 tff(402,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause190')).
% 1.38/1.14 tff(403,plain,
% 1.38/1.14 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.38/1.14 inference(modus_ponens,[status(thm)],[402, 401])).
% 1.38/1.14 tff(404,plain,
% 1.38/1.14 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.38/1.14 inference(modus_ponens,[status(thm)],[403, 399])).
% 1.38/1.14 tff(405,plain,(
% 1.38/1.14 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.38/1.14 inference(skolemize,[status(sab)],[404])).
% 1.38/1.14 tff(406,plain,
% 1.38/1.14 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.38/1.14 inference(modus_ponens,[status(thm)],[405, 398])).
% 1.38/1.14 tff(407,plain,
% 1.38/1.14 (((~hskp17) | c1_1(a155)) <=> ((~hskp17) | c1_1(a155))),
% 1.38/1.14 inference(rewrite,[status(thm)],[])).
% 1.38/1.14 tff(408,axiom,((~hskp17) | c1_1(a155)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause61')).
% 1.38/1.14 tff(409,plain,
% 1.38/1.14 ((~hskp17) | c1_1(a155)),
% 1.38/1.14 inference(modus_ponens,[status(thm)],[408, 407])).
% 1.38/1.14 tff(410,plain,
% 1.38/1.14 ((~hskp17) | c1_1(a155)),
% 1.38/1.14 inference(modus_ponens,[status(thm)],[409, 407])).
% 1.38/1.14 tff(411,plain,
% 1.38/1.14 ((~hskp17) | c1_1(a155)),
% 1.38/1.14 inference(modus_ponens,[status(thm)],[410, 407])).
% 1.38/1.14 tff(412,plain,
% 1.38/1.14 ((~hskp17) | c1_1(a155)),
% 1.38/1.14 inference(modus_ponens,[status(thm)],[411, 407])).
% 1.38/1.14 tff(413,plain,
% 1.38/1.14 ((~hskp17) | c1_1(a155)),
% 1.38/1.14 inference(modus_ponens,[status(thm)],[412, 407])).
% 1.38/1.14 tff(414,plain,
% 1.38/1.14 ((~hskp17) | c1_1(a155)),
% 1.38/1.14 inference(modus_ponens,[status(thm)],[413, 407])).
% 1.38/1.14 tff(415,plain,
% 1.38/1.14 ((~hskp17) | c1_1(a155)),
% 1.38/1.14 inference(modus_ponens,[status(thm)],[414, 407])).
% 1.38/1.14 tff(416,plain,
% 1.38/1.14 ((~hskp17) | c1_1(a155)),
% 1.38/1.14 inference(modus_ponens,[status(thm)],[415, 407])).
% 1.38/1.14 tff(417,plain,
% 1.38/1.14 (c1_1(a155)),
% 1.38/1.14 inference(unit_resolution,[status(thm)],[416, 377])).
% 1.38/1.14 tff(418,plain,
% 1.38/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a155) | c2_1(a155) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a155)) | (~c1_1(a155)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a155) | c2_1(a155) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a155)) | (~c1_1(a155)))),
% 1.38/1.14 inference(rewrite,[status(thm)],[])).
% 1.38/1.14 tff(419,plain,
% 1.38/1.14 (((~ndr1_0) | c2_1(a155) | c0_1(a155) | (~c3_1(a155)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)) | c2_1(a131) | c1_1(a131) | c0_1(a131)) <=> (c0_1(a155) | c2_1(a155) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a155)) | (~c1_1(a155)))),
% 1.38/1.14 inference(rewrite,[status(thm)],[])).
% 1.38/1.14 tff(420,plain,
% 1.38/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a155) | c0_1(a155) | (~c3_1(a155)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)) | c2_1(a131) | c1_1(a131) | c0_1(a131))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a155) | c2_1(a155) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a155)) | (~c1_1(a155))))),
% 1.38/1.14 inference(monotonicity,[status(thm)],[419])).
% 1.38/1.14 tff(421,plain,
% 1.38/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a155) | c0_1(a155) | (~c3_1(a155)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)) | c2_1(a131) | c1_1(a131) | c0_1(a131))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a155) | c2_1(a155) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a155)) | (~c1_1(a155)))),
% 1.38/1.14 inference(transitivity,[status(thm)],[420, 418])).
% 1.38/1.14 tff(422,plain,
% 1.38/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a155) | c0_1(a155) | (~c3_1(a155)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)) | c2_1(a131) | c1_1(a131) | c0_1(a131))),
% 1.38/1.14 inference(quant_inst,[status(thm)],[])).
% 1.38/1.14 tff(423,plain,
% 1.38/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a155) | c2_1(a155) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a155)) | (~c1_1(a155))),
% 1.38/1.14 inference(modus_ponens,[status(thm)],[422, 421])).
% 1.38/1.14 tff(424,plain,
% 1.38/1.14 ($false),
% 1.38/1.14 inference(unit_resolution,[status(thm)],[423, 123, 417, 389, 383, 97, 132, 95, 406, 396])).
% 1.38/1.14 tff(425,plain,(hskp7 | c0_1(a131) | c1_1(a131) | c2_1(a131) | hskp9), inference(lemma,lemma(discharge,[]))).
% 1.38/1.14 tff(426,plain,
% 1.38/1.14 (hskp7),
% 1.38/1.14 inference(unit_resolution,[status(thm)],[425, 84, 78, 72, 33])).
% 1.38/1.14 tff(427,plain,
% 1.38/1.14 (((~hskp7) | (~c0_1(a132))) <=> ((~hskp7) | (~c0_1(a132)))),
% 1.38/1.14 inference(rewrite,[status(thm)],[])).
% 1.38/1.14 tff(428,plain,
% 1.38/1.14 (((~c0_1(a132)) | (~hskp7)) <=> ((~hskp7) | (~c0_1(a132)))),
% 1.38/1.14 inference(rewrite,[status(thm)],[])).
% 1.38/1.14 tff(429,axiom,((~c0_1(a132)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause116')).
% 1.38/1.14 tff(430,plain,
% 1.38/1.14 ((~hskp7) | (~c0_1(a132))),
% 1.38/1.14 inference(modus_ponens,[status(thm)],[429, 428])).
% 1.38/1.14 tff(431,plain,
% 1.38/1.14 ((~hskp7) | (~c0_1(a132))),
% 1.38/1.14 inference(modus_ponens,[status(thm)],[430, 427])).
% 1.38/1.14 tff(432,plain,
% 1.38/1.14 (~c0_1(a132)),
% 1.38/1.14 inference(unit_resolution,[status(thm)],[431, 426])).
% 1.38/1.14 tff(433,assumption,(~c0_1(a125)), introduced(assumption)).
% 1.38/1.14 tff(434,assumption,(~c0_1(a132)), introduced(assumption)).
% 1.38/1.14 tff(435,assumption,(~c3_1(a124)), introduced(assumption)).
% 1.38/1.14 tff(436,assumption,(~c2_1(a132)), introduced(assumption)).
% 1.38/1.14 tff(437,assumption,(~c3_1(a132)), introduced(assumption)).
% 1.38/1.14 tff(438,plain,
% 1.38/1.14 (((~hskp7) | c3_1(a132)) <=> ((~hskp7) | c3_1(a132))),
% 1.38/1.14 inference(rewrite,[status(thm)],[])).
% 1.38/1.14 tff(439,axiom,((~hskp7) | c3_1(a132)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause75')).
% 1.38/1.14 tff(440,plain,
% 1.38/1.14 ((~hskp7) | c3_1(a132)),
% 1.38/1.14 inference(modus_ponens,[status(thm)],[439, 438])).
% 1.38/1.14 tff(441,plain,
% 1.38/1.14 ((~hskp7) | c3_1(a132)),
% 1.38/1.14 inference(modus_ponens,[status(thm)],[440, 438])).
% 1.38/1.14 tff(442,plain,
% 1.38/1.14 ((~hskp7) | c3_1(a132)),
% 1.38/1.14 inference(modus_ponens,[status(thm)],[441, 438])).
% 1.38/1.14 tff(443,plain,
% 1.38/1.14 ((~hskp7) | c3_1(a132)),
% 1.38/1.14 inference(modus_ponens,[status(thm)],[442, 438])).
% 1.38/1.14 tff(444,plain,
% 1.38/1.14 ((~hskp7) | c3_1(a132)),
% 1.38/1.14 inference(modus_ponens,[status(thm)],[443, 438])).
% 1.38/1.14 tff(445,plain,
% 1.38/1.14 ((~hskp7) | c3_1(a132)),
% 1.38/1.14 inference(modus_ponens,[status(thm)],[444, 438])).
% 1.38/1.14 tff(446,plain,
% 1.38/1.14 ((~hskp7) | c3_1(a132)),
% 1.38/1.14 inference(modus_ponens,[status(thm)],[445, 438])).
% 1.38/1.14 tff(447,plain,
% 1.38/1.14 ((~hskp7) | c3_1(a132)),
% 1.38/1.14 inference(modus_ponens,[status(thm)],[446, 438])).
% 1.38/1.14 tff(448,plain,
% 1.38/1.14 (~hskp7),
% 1.38/1.14 inference(unit_resolution,[status(thm)],[447, 437])).
% 1.38/1.14 tff(449,plain,
% 1.38/1.14 (((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | c3_1(a132) | c0_1(a132) | c2_1(a132) | (~ndr1_0))) <=> ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp9 | hskp7 | c3_1(a132) | c0_1(a132) | c2_1(a132) | (~ndr1_0))),
% 1.38/1.14 inference(rewrite,[status(thm)],[])).
% 1.38/1.14 tff(450,plain,
% 1.38/1.14 ((hskp9 | hskp7 | (~ndr1_0) | c2_1(a132) | c0_1(a132) | c3_1(a132)) <=> (hskp9 | hskp7 | c3_1(a132) | c0_1(a132) | c2_1(a132) | (~ndr1_0))),
% 1.38/1.14 inference(rewrite,[status(thm)],[])).
% 1.38/1.14 tff(451,plain,
% 1.38/1.14 (((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | (~ndr1_0) | c2_1(a132) | c0_1(a132) | c3_1(a132))) <=> ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | c3_1(a132) | c0_1(a132) | c2_1(a132) | (~ndr1_0)))),
% 1.38/1.14 inference(monotonicity,[status(thm)],[450])).
% 1.38/1.14 tff(452,plain,
% 1.38/1.14 (((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | (~ndr1_0) | c2_1(a132) | c0_1(a132) | c3_1(a132))) <=> ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp9 | hskp7 | c3_1(a132) | c0_1(a132) | c2_1(a132) | (~ndr1_0))),
% 1.38/1.14 inference(transitivity,[status(thm)],[451, 449])).
% 1.38/1.14 tff(453,plain,
% 1.38/1.14 ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | (~ndr1_0) | c2_1(a132) | c0_1(a132) | c3_1(a132))),
% 1.38/1.14 inference(quant_inst,[status(thm)],[])).
% 1.38/1.14 tff(454,plain,
% 1.38/1.14 ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp9 | hskp7 | c3_1(a132) | c0_1(a132) | c2_1(a132) | (~ndr1_0)),
% 1.38/1.14 inference(modus_ponens,[status(thm)],[453, 452])).
% 1.38/1.14 tff(455,plain,
% 1.38/1.14 (hskp7 | c3_1(a132) | c0_1(a132)),
% 1.38/1.14 inference(unit_resolution,[status(thm)],[454, 123, 33, 436, 94])).
% 1.38/1.14 tff(456,plain,
% 1.38/1.14 ($false),
% 1.38/1.14 inference(unit_resolution,[status(thm)],[455, 448, 437, 434])).
% 1.38/1.14 tff(457,plain,(c3_1(a132) | c0_1(a132) | hskp9 | c2_1(a132)), inference(lemma,lemma(discharge,[]))).
% 1.38/1.14 tff(458,plain,
% 1.38/1.14 (c3_1(a132)),
% 1.38/1.14 inference(unit_resolution,[status(thm)],[457, 436, 33, 434])).
% 1.38/1.14 tff(459,plain,
% 1.38/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a132) | c2_1(a132) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a132) | c2_1(a132) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)))),
% 1.38/1.14 inference(rewrite,[status(thm)],[])).
% 1.38/1.14 tff(460,plain,
% 1.38/1.14 (((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132)) | c2_1(a131) | c1_1(a131) | c0_1(a131)) <=> (c0_1(a132) | c2_1(a132) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)))),
% 1.38/1.14 inference(rewrite,[status(thm)],[])).
% 1.38/1.14 tff(461,plain,
% 1.38/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132)) | c2_1(a131) | c1_1(a131) | c0_1(a131))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a132) | c2_1(a132) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132))))),
% 1.38/1.14 inference(monotonicity,[status(thm)],[460])).
% 1.38/1.14 tff(462,plain,
% 1.38/1.14 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132)) | c2_1(a131) | c1_1(a131) | c0_1(a131))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a132) | c2_1(a132) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)))),
% 1.38/1.14 inference(transitivity,[status(thm)],[461, 459])).
% 1.38/1.14 tff(463,plain,
% 1.38/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132)) | c2_1(a131) | c1_1(a131) | c0_1(a131))),
% 1.38/1.14 inference(quant_inst,[status(thm)],[])).
% 1.38/1.14 tff(464,plain,
% 1.38/1.14 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a132) | c2_1(a132) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132))),
% 1.38/1.14 inference(modus_ponens,[status(thm)],[463, 462])).
% 1.38/1.14 tff(465,plain,
% 1.38/1.14 (~c1_1(a132)),
% 1.38/1.14 inference(unit_resolution,[status(thm)],[464, 123, 458, 434, 436, 84, 78, 72, 406])).
% 1.38/1.14 tff(466,assumption,(~c1_1(a132)), introduced(assumption)).
% 1.38/1.14 tff(467,assumption,(hskp17), introduced(assumption)).
% 1.38/1.14 tff(468,plain,
% 1.38/1.14 (~c2_1(a155)),
% 1.38/1.14 inference(unit_resolution,[status(thm)],[382, 467])).
% 1.38/1.14 tff(469,plain,
% 1.38/1.14 (~c0_1(a155)),
% 1.38/1.14 inference(unit_resolution,[status(thm)],[388, 467])).
% 1.38/1.14 tff(470,assumption,(c3_1(a132)), introduced(assumption)).
% 1.38/1.14 tff(471,plain,
% 1.38/1.14 (c1_1(a155)),
% 1.38/1.14 inference(unit_resolution,[status(thm)],[416, 467])).
% 1.38/1.15 tff(472,plain,
% 1.38/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a155) | c2_1(a155) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a155)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a155) | c2_1(a155) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a155)))),
% 1.38/1.15 inference(rewrite,[status(thm)],[])).
% 1.38/1.15 tff(473,plain,
% 1.38/1.15 (((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)) | c2_1(a132) | c1_1(a132) | c0_1(a132)) <=> (c0_1(a155) | c2_1(a155) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a155)))),
% 1.38/1.15 inference(rewrite,[status(thm)],[])).
% 1.38/1.15 tff(474,plain,
% 1.38/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)) | c2_1(a132) | c1_1(a132) | c0_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a155) | c2_1(a155) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a155))))),
% 1.38/1.15 inference(monotonicity,[status(thm)],[473])).
% 1.38/1.15 tff(475,plain,
% 1.38/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)) | c2_1(a132) | c1_1(a132) | c0_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a155) | c2_1(a155) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a155)))),
% 1.38/1.15 inference(transitivity,[status(thm)],[474, 472])).
% 1.38/1.15 tff(476,plain,
% 1.38/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)) | c2_1(a132) | c1_1(a132) | c0_1(a132))),
% 1.38/1.15 inference(quant_inst,[status(thm)],[])).
% 1.38/1.15 tff(477,plain,
% 1.38/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a155) | c2_1(a155) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a155))),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[476, 475])).
% 1.38/1.15 tff(478,plain,
% 1.38/1.15 ($false),
% 1.38/1.15 inference(unit_resolution,[status(thm)],[477, 123, 471, 470, 469, 468, 434, 436, 406, 466])).
% 1.38/1.15 tff(479,plain,((~hskp17) | (~c3_1(a132)) | c0_1(a132) | c2_1(a132) | c1_1(a132)), inference(lemma,lemma(discharge,[]))).
% 1.38/1.15 tff(480,plain,
% 1.38/1.15 (~hskp17),
% 1.38/1.15 inference(unit_resolution,[status(thm)],[479, 465, 434, 436, 458])).
% 1.38/1.15 tff(481,plain,
% 1.38/1.15 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))))),
% 1.38/1.15 inference(bind,[status(th)],[])).
% 1.38/1.15 tff(482,plain,
% 1.38/1.15 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.38/1.15 inference(quant_intro,[status(thm)],[481])).
% 1.38/1.15 tff(483,plain,
% 1.38/1.15 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.38/1.15 inference(rewrite,[status(thm)],[])).
% 1.38/1.15 tff(484,plain,
% 1.38/1.15 (^[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))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_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) | (~c3_1(U)) | (~c0_1(U)) | (~c2_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))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))))),
% 1.38/1.15 inference(bind,[status(th)],[])).
% 1.38/1.15 tff(485,plain,
% 1.38/1.15 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.38/1.15 inference(quant_intro,[status(thm)],[484])).
% 1.38/1.15 tff(486,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause201')).
% 1.38/1.15 tff(487,plain,
% 1.38/1.15 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[486, 485])).
% 1.38/1.15 tff(488,plain,
% 1.38/1.15 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[487, 483])).
% 1.38/1.15 tff(489,plain,(
% 1.38/1.15 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.38/1.15 inference(skolemize,[status(sab)],[488])).
% 1.38/1.15 tff(490,plain,
% 1.38/1.15 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[489, 482])).
% 1.38/1.15 tff(491,assumption,(hskp0), introduced(assumption)).
% 1.38/1.15 tff(492,plain,
% 1.38/1.15 (~c1_1(a123)),
% 1.38/1.15 inference(unit_resolution,[status(thm)],[202, 491])).
% 1.38/1.15 tff(493,plain,
% 1.38/1.15 (~c0_1(a123)),
% 1.38/1.15 inference(unit_resolution,[status(thm)],[236, 491])).
% 1.38/1.15 tff(494,plain,
% 1.38/1.15 (c2_1(a123)),
% 1.38/1.15 inference(unit_resolution,[status(thm)],[213, 491])).
% 1.38/1.15 tff(495,plain,
% 1.38/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a132) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c2_1(a123)) | (~c3_1(a132)) | c1_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a132) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c2_1(a123)) | (~c3_1(a132)) | c1_1(a132))),
% 1.38/1.15 inference(rewrite,[status(thm)],[])).
% 1.38/1.15 tff(496,plain,
% 1.38/1.15 (((~ndr1_0) | c1_1(a123) | (~c3_1(a123)) | (~c2_1(a123)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)) | c1_1(a123) | c0_1(a123) | (~c3_1(a123))) <=> (c2_1(a132) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c2_1(a123)) | (~c3_1(a132)) | c1_1(a132))),
% 1.38/1.15 inference(rewrite,[status(thm)],[])).
% 1.38/1.15 tff(497,plain,
% 1.38/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a123) | (~c3_1(a123)) | (~c2_1(a123)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)) | c1_1(a123) | c0_1(a123) | (~c3_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a132) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c2_1(a123)) | (~c3_1(a132)) | c1_1(a132)))),
% 1.38/1.15 inference(monotonicity,[status(thm)],[496])).
% 1.38/1.15 tff(498,plain,
% 1.38/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a123) | (~c3_1(a123)) | (~c2_1(a123)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)) | c1_1(a123) | c0_1(a123) | (~c3_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a132) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c2_1(a123)) | (~c3_1(a132)) | c1_1(a132))),
% 1.38/1.15 inference(transitivity,[status(thm)],[497, 495])).
% 1.38/1.15 tff(499,plain,
% 1.38/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a123) | (~c3_1(a123)) | (~c2_1(a123)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)) | c1_1(a123) | c0_1(a123) | (~c3_1(a123)))),
% 1.38/1.15 inference(quant_inst,[status(thm)],[])).
% 1.38/1.15 tff(500,plain,
% 1.38/1.15 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a132) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c2_1(a123)) | (~c3_1(a132)) | c1_1(a132)),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[499, 498])).
% 1.38/1.15 tff(501,plain,
% 1.38/1.15 (~c3_1(a123)),
% 1.38/1.15 inference(unit_resolution,[status(thm)],[500, 123, 470, 494, 436, 493, 492, 144, 466])).
% 1.38/1.15 tff(502,plain,
% 1.38/1.15 (^[U: $i] : refl((hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))),
% 1.38/1.15 inference(bind,[status(th)],[])).
% 1.38/1.15 tff(503,plain,
% 1.38/1.15 (![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.38/1.15 inference(quant_intro,[status(thm)],[502])).
% 1.38/1.15 tff(504,plain,
% 1.38/1.15 (![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.38/1.15 inference(rewrite,[status(thm)],[])).
% 1.38/1.15 tff(505,plain,
% 1.38/1.15 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp30) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp30))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp30) <=> (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp30) <=> (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp30) | hskp20) <=> ((hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp20))), rewrite(((hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp20) <=> (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp30) | hskp20) <=> (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))))),
% 1.38/1.15 inference(bind,[status(th)],[])).
% 1.38/1.15 tff(506,plain,
% 1.38/1.15 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp30) | hskp20) <=> ![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.38/1.15 inference(quant_intro,[status(thm)],[505])).
% 1.38/1.15 tff(507,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp30) | hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause141')).
% 1.38/1.15 tff(508,plain,
% 1.38/1.15 (![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[507, 506])).
% 1.38/1.15 tff(509,plain,
% 1.38/1.15 (![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[508, 504])).
% 1.38/1.15 tff(510,plain,(
% 1.38/1.15 ![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.38/1.15 inference(skolemize,[status(sab)],[509])).
% 1.38/1.15 tff(511,plain,
% 1.38/1.15 (![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[510, 503])).
% 1.38/1.15 tff(512,plain,
% 1.38/1.15 (((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp30 | hskp20 | c1_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)))) <=> ((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp30 | hskp20 | c1_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)))),
% 1.38/1.15 inference(rewrite,[status(thm)],[])).
% 1.38/1.15 tff(513,plain,
% 1.38/1.15 ((hskp30 | hskp20 | (~ndr1_0) | c1_1(a123) | c3_1(a123) | (~c2_1(a123))) <=> (hskp30 | hskp20 | c1_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)))),
% 1.38/1.15 inference(rewrite,[status(thm)],[])).
% 1.38/1.15 tff(514,plain,
% 1.38/1.15 (((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp30 | hskp20 | (~ndr1_0) | c1_1(a123) | c3_1(a123) | (~c2_1(a123)))) <=> ((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp30 | hskp20 | c1_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123))))),
% 1.38/1.15 inference(monotonicity,[status(thm)],[513])).
% 1.38/1.15 tff(515,plain,
% 1.38/1.15 (((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp30 | hskp20 | (~ndr1_0) | c1_1(a123) | c3_1(a123) | (~c2_1(a123)))) <=> ((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp30 | hskp20 | c1_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)))),
% 1.38/1.15 inference(transitivity,[status(thm)],[514, 512])).
% 1.38/1.15 tff(516,plain,
% 1.38/1.15 ((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp30 | hskp20 | (~ndr1_0) | c1_1(a123) | c3_1(a123) | (~c2_1(a123)))),
% 1.38/1.15 inference(quant_inst,[status(thm)],[])).
% 1.38/1.15 tff(517,plain,
% 1.38/1.15 ((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp30 | hskp20 | c1_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123))),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[516, 515])).
% 1.38/1.15 tff(518,plain,
% 1.38/1.15 (hskp20 | c3_1(a123)),
% 1.38/1.15 inference(unit_resolution,[status(thm)],[517, 54, 123, 494, 492, 511])).
% 1.38/1.15 tff(519,plain,
% 1.38/1.15 (hskp20),
% 1.38/1.15 inference(unit_resolution,[status(thm)],[518, 501])).
% 1.38/1.15 tff(520,plain,
% 1.38/1.15 (((~hskp20) | (~c3_1(a168))) <=> ((~hskp20) | (~c3_1(a168)))),
% 1.38/1.15 inference(rewrite,[status(thm)],[])).
% 1.38/1.15 tff(521,plain,
% 1.38/1.15 (((~c3_1(a168)) | (~hskp20)) <=> ((~hskp20) | (~c3_1(a168)))),
% 1.38/1.15 inference(rewrite,[status(thm)],[])).
% 1.38/1.15 tff(522,axiom,((~c3_1(a168)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause96')).
% 1.38/1.15 tff(523,plain,
% 1.38/1.15 ((~hskp20) | (~c3_1(a168))),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[522, 521])).
% 1.38/1.15 tff(524,plain,
% 1.38/1.15 ((~hskp20) | (~c3_1(a168))),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[523, 520])).
% 1.38/1.15 tff(525,plain,
% 1.38/1.15 (~c3_1(a168)),
% 1.38/1.15 inference(unit_resolution,[status(thm)],[524, 519])).
% 1.38/1.15 tff(526,plain,
% 1.38/1.15 (((~hskp20) | (~c0_1(a168))) <=> ((~hskp20) | (~c0_1(a168)))),
% 1.38/1.15 inference(rewrite,[status(thm)],[])).
% 1.38/1.15 tff(527,plain,
% 1.38/1.15 (((~c0_1(a168)) | (~hskp20)) <=> ((~hskp20) | (~c0_1(a168)))),
% 1.38/1.15 inference(rewrite,[status(thm)],[])).
% 1.38/1.15 tff(528,axiom,((~c0_1(a168)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause95')).
% 1.38/1.15 tff(529,plain,
% 1.38/1.15 ((~hskp20) | (~c0_1(a168))),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[528, 527])).
% 1.38/1.15 tff(530,plain,
% 1.38/1.15 ((~hskp20) | (~c0_1(a168))),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[529, 526])).
% 1.38/1.15 tff(531,plain,
% 1.38/1.15 (~c0_1(a168)),
% 1.38/1.15 inference(unit_resolution,[status(thm)],[530, 519])).
% 1.38/1.15 tff(532,plain,
% 1.38/1.15 (((~hskp20) | c1_1(a168)) <=> ((~hskp20) | c1_1(a168))),
% 1.38/1.15 inference(rewrite,[status(thm)],[])).
% 1.38/1.15 tff(533,axiom,((~hskp20) | c1_1(a168)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause57')).
% 1.38/1.15 tff(534,plain,
% 1.38/1.15 ((~hskp20) | c1_1(a168)),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[533, 532])).
% 1.38/1.15 tff(535,plain,
% 1.38/1.15 ((~hskp20) | c1_1(a168)),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[534, 532])).
% 1.38/1.15 tff(536,plain,
% 1.38/1.15 ((~hskp20) | c1_1(a168)),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[535, 532])).
% 1.38/1.15 tff(537,plain,
% 1.38/1.15 ((~hskp20) | c1_1(a168)),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[536, 532])).
% 1.38/1.15 tff(538,plain,
% 1.38/1.15 ((~hskp20) | c1_1(a168)),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[537, 532])).
% 1.38/1.15 tff(539,plain,
% 1.38/1.15 ((~hskp20) | c1_1(a168)),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[538, 532])).
% 1.38/1.15 tff(540,plain,
% 1.38/1.15 ((~hskp20) | c1_1(a168)),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[539, 532])).
% 1.38/1.15 tff(541,plain,
% 1.38/1.15 ((~hskp20) | c1_1(a168)),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[540, 532])).
% 1.38/1.15 tff(542,plain,
% 1.38/1.15 (c1_1(a168)),
% 1.38/1.15 inference(unit_resolution,[status(thm)],[541, 519])).
% 1.38/1.15 tff(543,plain,
% 1.38/1.15 (^[V: $i, U: $i] : refl((hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 1.38/1.15 inference(bind,[status(th)],[])).
% 1.38/1.15 tff(544,plain,
% 1.38/1.15 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.38/1.15 inference(quant_intro,[status(thm)],[543])).
% 1.38/1.15 tff(545,plain,
% 1.38/1.15 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.38/1.15 inference(rewrite,[status(thm)],[])).
% 1.38/1.15 tff(546,plain,
% 1.38/1.15 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp27) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp27))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 1.38/1.15 inference(bind,[status(th)],[])).
% 1.38/1.15 tff(547,plain,
% 1.38/1.15 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp27) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.38/1.15 inference(quant_intro,[status(thm)],[546])).
% 1.38/1.15 tff(548,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause168')).
% 1.38/1.15 tff(549,plain,
% 1.38/1.15 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[548, 547])).
% 1.38/1.15 tff(550,plain,
% 1.38/1.15 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[549, 545])).
% 1.38/1.15 tff(551,plain,(
% 1.38/1.15 ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.38/1.15 inference(skolemize,[status(sab)],[550])).
% 1.38/1.15 tff(552,plain,
% 1.38/1.15 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[551, 544])).
% 1.38/1.15 tff(553,plain,
% 1.38/1.15 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | c0_1(a132) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | c1_1(a132))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp27 | c0_1(a132) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | c1_1(a132))),
% 1.38/1.15 inference(rewrite,[status(thm)],[])).
% 1.38/1.15 tff(554,plain,
% 1.38/1.15 ((hskp27 | (~ndr1_0) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)) | c2_1(a132) | c1_1(a132) | c0_1(a132)) <=> (hskp27 | c0_1(a132) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | c1_1(a132))),
% 1.38/1.15 inference(rewrite,[status(thm)],[])).
% 1.38/1.15 tff(555,plain,
% 1.38/1.15 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)) | c2_1(a132) | c1_1(a132) | c0_1(a132))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | c0_1(a132) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | c1_1(a132)))),
% 1.38/1.15 inference(monotonicity,[status(thm)],[554])).
% 1.38/1.15 tff(556,plain,
% 1.38/1.15 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)) | c2_1(a132) | c1_1(a132) | c0_1(a132))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp27 | c0_1(a132) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | c1_1(a132))),
% 1.38/1.15 inference(transitivity,[status(thm)],[555, 553])).
% 1.38/1.15 tff(557,plain,
% 1.38/1.15 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)) | c2_1(a132) | c1_1(a132) | c0_1(a132))),
% 1.38/1.15 inference(quant_inst,[status(thm)],[])).
% 1.38/1.15 tff(558,plain,
% 1.38/1.15 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp27 | c0_1(a132) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | c1_1(a132)),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[557, 556])).
% 1.38/1.15 tff(559,plain,
% 1.38/1.15 (hskp27 | c3_1(a123)),
% 1.38/1.15 inference(unit_resolution,[status(thm)],[558, 123, 494, 434, 436, 493, 552, 466])).
% 1.38/1.15 tff(560,plain,
% 1.38/1.15 (hskp27),
% 1.38/1.15 inference(unit_resolution,[status(thm)],[559, 501])).
% 1.38/1.15 tff(561,plain,
% 1.38/1.15 (((~hskp27) | c3_1(a122)) <=> ((~hskp27) | c3_1(a122))),
% 1.38/1.15 inference(rewrite,[status(thm)],[])).
% 1.38/1.15 tff(562,axiom,((~hskp27) | c3_1(a122)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause49')).
% 1.38/1.15 tff(563,plain,
% 1.38/1.15 ((~hskp27) | c3_1(a122)),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[562, 561])).
% 1.38/1.15 tff(564,plain,
% 1.38/1.15 ((~hskp27) | c3_1(a122)),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[563, 561])).
% 1.38/1.15 tff(565,plain,
% 1.38/1.15 ((~hskp27) | c3_1(a122)),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[564, 561])).
% 1.38/1.15 tff(566,plain,
% 1.38/1.15 ((~hskp27) | c3_1(a122)),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[565, 561])).
% 1.38/1.15 tff(567,plain,
% 1.38/1.15 ((~hskp27) | c3_1(a122)),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[566, 561])).
% 1.38/1.15 tff(568,plain,
% 1.38/1.15 ((~hskp27) | c3_1(a122)),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[567, 561])).
% 1.38/1.15 tff(569,plain,
% 1.38/1.15 ((~hskp27) | c3_1(a122)),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[568, 561])).
% 1.38/1.15 tff(570,plain,
% 1.38/1.15 ((~hskp27) | c3_1(a122)),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[569, 561])).
% 1.38/1.15 tff(571,plain,
% 1.38/1.15 (c3_1(a122)),
% 1.38/1.15 inference(unit_resolution,[status(thm)],[570, 560])).
% 1.38/1.15 tff(572,plain,
% 1.38/1.15 (((~hskp27) | c2_1(a122)) <=> ((~hskp27) | c2_1(a122))),
% 1.38/1.15 inference(rewrite,[status(thm)],[])).
% 1.38/1.15 tff(573,axiom,((~hskp27) | c2_1(a122)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause48')).
% 1.38/1.15 tff(574,plain,
% 1.38/1.15 ((~hskp27) | c2_1(a122)),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[573, 572])).
% 1.38/1.15 tff(575,plain,
% 1.38/1.15 ((~hskp27) | c2_1(a122)),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[574, 572])).
% 1.38/1.15 tff(576,plain,
% 1.38/1.15 ((~hskp27) | c2_1(a122)),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[575, 572])).
% 1.38/1.15 tff(577,plain,
% 1.38/1.15 ((~hskp27) | c2_1(a122)),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[576, 572])).
% 1.38/1.15 tff(578,plain,
% 1.38/1.15 ((~hskp27) | c2_1(a122)),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[577, 572])).
% 1.38/1.15 tff(579,plain,
% 1.38/1.15 ((~hskp27) | c2_1(a122)),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[578, 572])).
% 1.38/1.15 tff(580,plain,
% 1.38/1.15 ((~hskp27) | c2_1(a122)),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[579, 572])).
% 1.38/1.15 tff(581,plain,
% 1.38/1.15 ((~hskp27) | c2_1(a122)),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[580, 572])).
% 1.38/1.15 tff(582,plain,
% 1.38/1.15 (c2_1(a122)),
% 1.38/1.15 inference(unit_resolution,[status(thm)],[581, 560])).
% 1.38/1.15 tff(583,plain,
% 1.38/1.15 (((~hskp27) | c0_1(a122)) <=> ((~hskp27) | c0_1(a122))),
% 1.38/1.15 inference(rewrite,[status(thm)],[])).
% 1.38/1.15 tff(584,axiom,((~hskp27) | c0_1(a122)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause47')).
% 1.38/1.15 tff(585,plain,
% 1.38/1.15 ((~hskp27) | c0_1(a122)),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[584, 583])).
% 1.38/1.15 tff(586,plain,
% 1.38/1.15 ((~hskp27) | c0_1(a122)),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[585, 583])).
% 1.38/1.15 tff(587,plain,
% 1.38/1.15 ((~hskp27) | c0_1(a122)),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[586, 583])).
% 1.38/1.15 tff(588,plain,
% 1.38/1.15 ((~hskp27) | c0_1(a122)),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[587, 583])).
% 1.38/1.15 tff(589,plain,
% 1.38/1.15 ((~hskp27) | c0_1(a122)),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[588, 583])).
% 1.38/1.15 tff(590,plain,
% 1.38/1.15 ((~hskp27) | c0_1(a122)),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[589, 583])).
% 1.38/1.15 tff(591,plain,
% 1.38/1.15 ((~hskp27) | c0_1(a122)),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[590, 583])).
% 1.38/1.15 tff(592,plain,
% 1.38/1.15 ((~hskp27) | c0_1(a122)),
% 1.38/1.15 inference(modus_ponens,[status(thm)],[591, 583])).
% 1.38/1.15 tff(593,plain,
% 1.38/1.15 (c0_1(a122)),
% 1.38/1.15 inference(unit_resolution,[status(thm)],[592, 560])).
% 1.38/1.15 tff(594,plain,
% 1.38/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a168) | c3_1(a168) | (~ndr1_0) | (~c1_1(a168)) | (~c2_1(a168)) | (~c3_1(a122)) | (~c0_1(a122)) | (~c2_1(a122)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a168) | c3_1(a168) | (~ndr1_0) | (~c1_1(a168)) | (~c2_1(a168)) | (~c3_1(a122)) | (~c0_1(a122)) | (~c2_1(a122)))),
% 1.38/1.15 inference(rewrite,[status(thm)],[])).
% 1.38/1.15 tff(595,plain,
% 1.38/1.15 (((~ndr1_0) | (~c3_1(a122)) | (~c0_1(a122)) | (~c2_1(a122)) | c3_1(a168) | (~c2_1(a168)) | (~c1_1(a168)) | c0_1(a168) | c3_1(a168) | (~c1_1(a168))) <=> (c0_1(a168) | c3_1(a168) | (~ndr1_0) | (~c1_1(a168)) | (~c2_1(a168)) | (~c3_1(a122)) | (~c0_1(a122)) | (~c2_1(a122)))),
% 1.38/1.15 inference(rewrite,[status(thm)],[])).
% 1.38/1.15 tff(596,plain,
% 1.38/1.15 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a122)) | (~c0_1(a122)) | (~c2_1(a122)) | c3_1(a168) | (~c2_1(a168)) | (~c1_1(a168)) | c0_1(a168) | c3_1(a168) | (~c1_1(a168)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a168) | c3_1(a168) | (~ndr1_0) | (~c1_1(a168)) | (~c2_1(a168)) | (~c3_1(a122)) | (~c0_1(a122)) | (~c2_1(a122))))),
% 1.38/1.16 inference(monotonicity,[status(thm)],[595])).
% 1.38/1.16 tff(597,plain,
% 1.38/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a122)) | (~c0_1(a122)) | (~c2_1(a122)) | c3_1(a168) | (~c2_1(a168)) | (~c1_1(a168)) | c0_1(a168) | c3_1(a168) | (~c1_1(a168)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a168) | c3_1(a168) | (~ndr1_0) | (~c1_1(a168)) | (~c2_1(a168)) | (~c3_1(a122)) | (~c0_1(a122)) | (~c2_1(a122)))),
% 1.38/1.16 inference(transitivity,[status(thm)],[596, 594])).
% 1.38/1.16 tff(598,plain,
% 1.38/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a122)) | (~c0_1(a122)) | (~c2_1(a122)) | c3_1(a168) | (~c2_1(a168)) | (~c1_1(a168)) | c0_1(a168) | c3_1(a168) | (~c1_1(a168)))),
% 1.38/1.16 inference(quant_inst,[status(thm)],[])).
% 1.38/1.16 tff(599,plain,
% 1.38/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a168) | c3_1(a168) | (~ndr1_0) | (~c1_1(a168)) | (~c2_1(a168)) | (~c3_1(a122)) | (~c0_1(a122)) | (~c2_1(a122))),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[598, 597])).
% 1.38/1.16 tff(600,plain,
% 1.38/1.16 (~c2_1(a168)),
% 1.38/1.16 inference(unit_resolution,[status(thm)],[599, 123, 593, 582, 571, 542, 531, 525, 490])).
% 1.38/1.16 tff(601,plain,
% 1.38/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a168) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a168)) | c2_1(a168))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a168) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a168)) | c2_1(a168))),
% 1.38/1.16 inference(rewrite,[status(thm)],[])).
% 1.38/1.16 tff(602,plain,
% 1.38/1.16 (((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a168) | c0_1(a168) | (~c1_1(a168)) | c2_1(a132) | c1_1(a132) | c0_1(a132)) <=> (c0_1(a168) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a168)) | c2_1(a168))),
% 1.38/1.16 inference(rewrite,[status(thm)],[])).
% 1.38/1.16 tff(603,plain,
% 1.38/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a168) | c0_1(a168) | (~c1_1(a168)) | c2_1(a132) | c1_1(a132) | c0_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a168) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a168)) | c2_1(a168)))),
% 1.38/1.16 inference(monotonicity,[status(thm)],[602])).
% 1.38/1.16 tff(604,plain,
% 1.38/1.16 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a168) | c0_1(a168) | (~c1_1(a168)) | c2_1(a132) | c1_1(a132) | c0_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a168) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a168)) | c2_1(a168))),
% 1.38/1.16 inference(transitivity,[status(thm)],[603, 601])).
% 1.38/1.16 tff(605,plain,
% 1.38/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a168) | c0_1(a168) | (~c1_1(a168)) | c2_1(a132) | c1_1(a132) | c0_1(a132))),
% 1.38/1.16 inference(quant_inst,[status(thm)],[])).
% 1.38/1.16 tff(606,plain,
% 1.38/1.16 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a168) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a168)) | c2_1(a168)),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[605, 604])).
% 1.38/1.16 tff(607,plain,
% 1.38/1.16 ($false),
% 1.38/1.16 inference(unit_resolution,[status(thm)],[606, 123, 542, 470, 531, 434, 436, 406, 466, 600])).
% 1.38/1.16 tff(608,plain,((~hskp0) | (~c3_1(a132)) | c0_1(a132) | c2_1(a132) | c1_1(a132) | hskp30), inference(lemma,lemma(discharge,[]))).
% 1.38/1.16 tff(609,plain,
% 1.38/1.16 (~hskp0),
% 1.38/1.16 inference(unit_resolution,[status(thm)],[608, 465, 434, 436, 458, 54])).
% 1.38/1.16 tff(610,assumption,(~hskp22), introduced(assumption)).
% 1.38/1.16 tff(611,assumption,(hskp1), introduced(assumption)).
% 1.38/1.16 tff(612,plain,
% 1.38/1.16 (((~hskp1) | c1_1(a124)) <=> ((~hskp1) | c1_1(a124))),
% 1.38/1.16 inference(rewrite,[status(thm)],[])).
% 1.38/1.16 tff(613,axiom,((~hskp1) | c1_1(a124)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause81')).
% 1.38/1.16 tff(614,plain,
% 1.38/1.16 ((~hskp1) | c1_1(a124)),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[613, 612])).
% 1.38/1.16 tff(615,plain,
% 1.38/1.16 ((~hskp1) | c1_1(a124)),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[614, 612])).
% 1.38/1.16 tff(616,plain,
% 1.38/1.16 ((~hskp1) | c1_1(a124)),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[615, 612])).
% 1.38/1.16 tff(617,plain,
% 1.38/1.16 ((~hskp1) | c1_1(a124)),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[616, 612])).
% 1.38/1.16 tff(618,plain,
% 1.38/1.16 ((~hskp1) | c1_1(a124)),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[617, 612])).
% 1.38/1.16 tff(619,plain,
% 1.38/1.16 ((~hskp1) | c1_1(a124)),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[618, 612])).
% 1.38/1.16 tff(620,plain,
% 1.38/1.16 ((~hskp1) | c1_1(a124)),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[619, 612])).
% 1.38/1.16 tff(621,plain,
% 1.38/1.16 ((~hskp1) | c1_1(a124)),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[620, 612])).
% 1.38/1.16 tff(622,plain,
% 1.38/1.16 (c1_1(a124)),
% 1.38/1.16 inference(unit_resolution,[status(thm)],[621, 611])).
% 1.38/1.16 tff(623,plain,
% 1.38/1.16 (((~hskp1) | c2_1(a124)) <=> ((~hskp1) | c2_1(a124))),
% 1.38/1.16 inference(rewrite,[status(thm)],[])).
% 1.38/1.16 tff(624,axiom,((~hskp1) | c2_1(a124)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause82')).
% 1.38/1.16 tff(625,plain,
% 1.38/1.16 ((~hskp1) | c2_1(a124)),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[624, 623])).
% 1.38/1.16 tff(626,plain,
% 1.38/1.16 ((~hskp1) | c2_1(a124)),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[625, 623])).
% 1.38/1.16 tff(627,plain,
% 1.38/1.16 ((~hskp1) | c2_1(a124)),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[626, 623])).
% 1.38/1.16 tff(628,plain,
% 1.38/1.16 ((~hskp1) | c2_1(a124)),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[627, 623])).
% 1.38/1.16 tff(629,plain,
% 1.38/1.16 ((~hskp1) | c2_1(a124)),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[628, 623])).
% 1.38/1.16 tff(630,plain,
% 1.38/1.16 ((~hskp1) | c2_1(a124)),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[629, 623])).
% 1.38/1.16 tff(631,plain,
% 1.38/1.16 ((~hskp1) | c2_1(a124)),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[630, 623])).
% 1.38/1.16 tff(632,plain,
% 1.38/1.16 ((~hskp1) | c2_1(a124)),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[631, 623])).
% 1.38/1.16 tff(633,plain,
% 1.38/1.16 (c2_1(a124)),
% 1.38/1.16 inference(unit_resolution,[status(thm)],[632, 611])).
% 1.38/1.16 tff(634,plain,
% 1.38/1.16 (^[U: $i] : refl((hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))))),
% 1.38/1.16 inference(bind,[status(th)],[])).
% 1.38/1.16 tff(635,plain,
% 1.38/1.16 (![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.38/1.16 inference(quant_intro,[status(thm)],[634])).
% 1.38/1.16 tff(636,plain,
% 1.38/1.16 (![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.38/1.16 inference(rewrite,[status(thm)],[])).
% 1.38/1.16 tff(637,plain,
% 1.38/1.16 (^[U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp22) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp22))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp22) <=> (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp22) <=> (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))))),
% 1.38/1.16 inference(bind,[status(th)],[])).
% 1.38/1.16 tff(638,plain,
% 1.38/1.16 (![U: $i] : (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp22) <=> ![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.38/1.16 inference(quant_intro,[status(thm)],[637])).
% 1.38/1.16 tff(639,axiom,(![U: $i] : (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause143')).
% 1.38/1.16 tff(640,plain,
% 1.38/1.16 (![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[639, 638])).
% 1.38/1.16 tff(641,plain,
% 1.38/1.16 (![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[640, 636])).
% 1.38/1.16 tff(642,plain,(
% 1.38/1.16 ![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.38/1.16 inference(skolemize,[status(sab)],[641])).
% 1.38/1.16 tff(643,plain,
% 1.38/1.16 (![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[642, 635])).
% 1.38/1.16 tff(644,plain,
% 1.38/1.16 (((~![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp22 | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c1_1(a124)))) <=> ((~![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp22 | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c1_1(a124)))),
% 1.38/1.16 inference(rewrite,[status(thm)],[])).
% 1.38/1.16 tff(645,plain,
% 1.38/1.16 ((hskp22 | (~ndr1_0) | c3_1(a124) | (~c1_1(a124)) | (~c2_1(a124))) <=> (hskp22 | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c1_1(a124)))),
% 1.38/1.16 inference(rewrite,[status(thm)],[])).
% 1.38/1.16 tff(646,plain,
% 1.38/1.16 (((~![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp22 | (~ndr1_0) | c3_1(a124) | (~c1_1(a124)) | (~c2_1(a124)))) <=> ((~![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp22 | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c1_1(a124))))),
% 1.38/1.16 inference(monotonicity,[status(thm)],[645])).
% 1.38/1.16 tff(647,plain,
% 1.38/1.16 (((~![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp22 | (~ndr1_0) | c3_1(a124) | (~c1_1(a124)) | (~c2_1(a124)))) <=> ((~![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp22 | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c1_1(a124)))),
% 1.38/1.16 inference(transitivity,[status(thm)],[646, 644])).
% 1.38/1.16 tff(648,plain,
% 1.38/1.16 ((~![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp22 | (~ndr1_0) | c3_1(a124) | (~c1_1(a124)) | (~c2_1(a124)))),
% 1.38/1.16 inference(quant_inst,[status(thm)],[])).
% 1.38/1.16 tff(649,plain,
% 1.38/1.16 ((~![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp22 | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c1_1(a124))),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[648, 647])).
% 1.38/1.16 tff(650,plain,
% 1.38/1.16 (hskp22 | (~c2_1(a124)) | (~c1_1(a124))),
% 1.38/1.16 inference(unit_resolution,[status(thm)],[649, 123, 435, 643])).
% 1.38/1.16 tff(651,plain,
% 1.38/1.16 ($false),
% 1.38/1.16 inference(unit_resolution,[status(thm)],[650, 633, 622, 610])).
% 1.38/1.16 tff(652,plain,((~hskp1) | hskp22 | c3_1(a124)), inference(lemma,lemma(discharge,[]))).
% 1.38/1.16 tff(653,plain,
% 1.38/1.16 (~hskp1),
% 1.38/1.16 inference(unit_resolution,[status(thm)],[652, 610, 435])).
% 1.38/1.16 tff(654,plain,
% 1.38/1.16 (^[U: $i] : refl((hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))),
% 1.38/1.16 inference(bind,[status(th)],[])).
% 1.38/1.16 tff(655,plain,
% 1.38/1.16 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.38/1.16 inference(quant_intro,[status(thm)],[654])).
% 1.38/1.16 tff(656,plain,
% 1.38/1.16 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.38/1.16 inference(rewrite,[status(thm)],[])).
% 1.38/1.16 tff(657,plain,
% 1.38/1.16 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp2) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp2))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp2) | hskp1) <=> ((hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1))), rewrite(((hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1) <=> (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp2) | hskp1) <=> (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))))),
% 1.38/1.16 inference(bind,[status(th)],[])).
% 1.38/1.16 tff(658,plain,
% 1.38/1.16 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp2) | hskp1) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.38/1.16 inference(quant_intro,[status(thm)],[657])).
% 1.38/1.16 tff(659,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp2) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause131')).
% 1.38/1.16 tff(660,plain,
% 1.38/1.16 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[659, 658])).
% 1.38/1.16 tff(661,plain,
% 1.38/1.16 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[660, 656])).
% 1.38/1.16 tff(662,plain,(
% 1.38/1.16 ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.38/1.16 inference(skolemize,[status(sab)],[661])).
% 1.38/1.16 tff(663,plain,
% 1.38/1.16 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[662, 655])).
% 1.38/1.16 tff(664,plain,
% 1.38/1.16 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0))),
% 1.38/1.16 inference(rewrite,[status(thm)],[])).
% 1.38/1.16 tff(665,plain,
% 1.38/1.16 ((hskp2 | hskp1 | (~ndr1_0) | c2_1(a131) | c1_1(a131) | c0_1(a131)) <=> (hskp2 | hskp1 | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0))),
% 1.38/1.16 inference(rewrite,[status(thm)],[])).
% 1.38/1.16 tff(666,plain,
% 1.38/1.16 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a131) | c1_1(a131) | c0_1(a131))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0)))),
% 1.38/1.16 inference(monotonicity,[status(thm)],[665])).
% 1.38/1.16 tff(667,plain,
% 1.38/1.16 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a131) | c1_1(a131) | c0_1(a131))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0))),
% 1.38/1.16 inference(transitivity,[status(thm)],[666, 664])).
% 1.38/1.16 tff(668,plain,
% 1.38/1.16 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a131) | c1_1(a131) | c0_1(a131))),
% 1.38/1.16 inference(quant_inst,[status(thm)],[])).
% 1.38/1.16 tff(669,plain,
% 1.38/1.16 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0)),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[668, 667])).
% 1.38/1.16 tff(670,plain,
% 1.38/1.16 (hskp2 | hskp1),
% 1.38/1.16 inference(unit_resolution,[status(thm)],[669, 123, 97, 132, 95, 663])).
% 1.38/1.16 tff(671,plain,
% 1.38/1.16 (hskp2),
% 1.38/1.16 inference(unit_resolution,[status(thm)],[670, 653])).
% 1.38/1.16 tff(672,plain,
% 1.38/1.16 (((~hskp2) | c1_1(a125)) <=> ((~hskp2) | c1_1(a125))),
% 1.38/1.16 inference(rewrite,[status(thm)],[])).
% 1.38/1.16 tff(673,axiom,((~hskp2) | c1_1(a125)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause79')).
% 1.38/1.16 tff(674,plain,
% 1.38/1.16 ((~hskp2) | c1_1(a125)),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[673, 672])).
% 1.38/1.16 tff(675,plain,
% 1.38/1.16 ((~hskp2) | c1_1(a125)),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[674, 672])).
% 1.38/1.16 tff(676,plain,
% 1.38/1.16 ((~hskp2) | c1_1(a125)),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[675, 672])).
% 1.38/1.16 tff(677,plain,
% 1.38/1.16 ((~hskp2) | c1_1(a125)),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[676, 672])).
% 1.38/1.16 tff(678,plain,
% 1.38/1.16 ((~hskp2) | c1_1(a125)),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[677, 672])).
% 1.38/1.16 tff(679,plain,
% 1.38/1.16 ((~hskp2) | c1_1(a125)),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[678, 672])).
% 1.38/1.16 tff(680,plain,
% 1.38/1.16 ((~hskp2) | c1_1(a125)),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[679, 672])).
% 1.38/1.16 tff(681,plain,
% 1.38/1.16 ((~hskp2) | c1_1(a125)),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[680, 672])).
% 1.38/1.16 tff(682,plain,
% 1.38/1.16 (c1_1(a125)),
% 1.38/1.16 inference(unit_resolution,[status(thm)],[681, 671])).
% 1.38/1.16 tff(683,plain,
% 1.38/1.16 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp0 | c0_1(a125) | (~ndr1_0) | (~c1_1(a125)) | (~c3_1(a125)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp0 | c0_1(a125) | (~ndr1_0) | (~c1_1(a125)) | (~c3_1(a125)))),
% 1.38/1.16 inference(rewrite,[status(thm)],[])).
% 1.38/1.16 tff(684,plain,
% 1.38/1.16 ((hskp17 | hskp0 | (~ndr1_0) | c0_1(a125) | (~c3_1(a125)) | (~c1_1(a125))) <=> (hskp17 | hskp0 | c0_1(a125) | (~ndr1_0) | (~c1_1(a125)) | (~c3_1(a125)))),
% 1.38/1.16 inference(rewrite,[status(thm)],[])).
% 1.38/1.16 tff(685,plain,
% 1.38/1.16 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a125) | (~c3_1(a125)) | (~c1_1(a125)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp0 | c0_1(a125) | (~ndr1_0) | (~c1_1(a125)) | (~c3_1(a125))))),
% 1.38/1.16 inference(monotonicity,[status(thm)],[684])).
% 1.38/1.16 tff(686,plain,
% 1.38/1.16 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a125) | (~c3_1(a125)) | (~c1_1(a125)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp0 | c0_1(a125) | (~ndr1_0) | (~c1_1(a125)) | (~c3_1(a125)))),
% 1.38/1.16 inference(transitivity,[status(thm)],[685, 683])).
% 1.38/1.16 tff(687,plain,
% 1.38/1.16 ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a125) | (~c3_1(a125)) | (~c1_1(a125)))),
% 1.38/1.16 inference(quant_inst,[status(thm)],[])).
% 1.38/1.16 tff(688,plain,
% 1.38/1.16 ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp0 | c0_1(a125) | (~ndr1_0) | (~c1_1(a125)) | (~c3_1(a125))),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[687, 686])).
% 1.38/1.16 tff(689,plain,
% 1.38/1.16 (hskp17 | hskp0 | (~c1_1(a125)) | (~c3_1(a125))),
% 1.38/1.16 inference(unit_resolution,[status(thm)],[688, 123, 433, 43])).
% 1.38/1.16 tff(690,plain,
% 1.38/1.16 (~c3_1(a125)),
% 1.38/1.16 inference(unit_resolution,[status(thm)],[689, 682, 134, 11])).
% 1.38/1.16 tff(691,plain,
% 1.38/1.16 (((~hskp2) | c2_1(a125)) <=> ((~hskp2) | c2_1(a125))),
% 1.38/1.16 inference(rewrite,[status(thm)],[])).
% 1.38/1.16 tff(692,axiom,((~hskp2) | c2_1(a125)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause80')).
% 1.38/1.16 tff(693,plain,
% 1.38/1.16 ((~hskp2) | c2_1(a125)),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[692, 691])).
% 1.38/1.16 tff(694,plain,
% 1.38/1.16 ((~hskp2) | c2_1(a125)),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[693, 691])).
% 1.38/1.16 tff(695,plain,
% 1.38/1.16 ((~hskp2) | c2_1(a125)),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[694, 691])).
% 1.38/1.16 tff(696,plain,
% 1.38/1.16 ((~hskp2) | c2_1(a125)),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[695, 691])).
% 1.38/1.16 tff(697,plain,
% 1.38/1.16 ((~hskp2) | c2_1(a125)),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[696, 691])).
% 1.38/1.16 tff(698,plain,
% 1.38/1.16 ((~hskp2) | c2_1(a125)),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[697, 691])).
% 1.38/1.16 tff(699,plain,
% 1.38/1.16 ((~hskp2) | c2_1(a125)),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[698, 691])).
% 1.38/1.16 tff(700,plain,
% 1.38/1.16 ((~hskp2) | c2_1(a125)),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[699, 691])).
% 1.38/1.16 tff(701,plain,
% 1.38/1.16 (c2_1(a125)),
% 1.38/1.16 inference(unit_resolution,[status(thm)],[700, 671])).
% 1.38/1.16 tff(702,plain,
% 1.38/1.16 (((~![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp22 | (~ndr1_0) | (~c1_1(a125)) | (~c2_1(a125)) | c3_1(a125))) <=> ((~![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp22 | (~ndr1_0) | (~c1_1(a125)) | (~c2_1(a125)) | c3_1(a125))),
% 1.38/1.16 inference(rewrite,[status(thm)],[])).
% 1.38/1.16 tff(703,plain,
% 1.38/1.16 ((hskp22 | (~ndr1_0) | c3_1(a125) | (~c1_1(a125)) | (~c2_1(a125))) <=> (hskp22 | (~ndr1_0) | (~c1_1(a125)) | (~c2_1(a125)) | c3_1(a125))),
% 1.38/1.16 inference(rewrite,[status(thm)],[])).
% 1.38/1.16 tff(704,plain,
% 1.38/1.16 (((~![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp22 | (~ndr1_0) | c3_1(a125) | (~c1_1(a125)) | (~c2_1(a125)))) <=> ((~![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp22 | (~ndr1_0) | (~c1_1(a125)) | (~c2_1(a125)) | c3_1(a125)))),
% 1.38/1.16 inference(monotonicity,[status(thm)],[703])).
% 1.38/1.16 tff(705,plain,
% 1.38/1.16 (((~![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp22 | (~ndr1_0) | c3_1(a125) | (~c1_1(a125)) | (~c2_1(a125)))) <=> ((~![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp22 | (~ndr1_0) | (~c1_1(a125)) | (~c2_1(a125)) | c3_1(a125))),
% 1.38/1.16 inference(transitivity,[status(thm)],[704, 702])).
% 1.38/1.16 tff(706,plain,
% 1.38/1.16 ((~![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp22 | (~ndr1_0) | c3_1(a125) | (~c1_1(a125)) | (~c2_1(a125)))),
% 1.38/1.16 inference(quant_inst,[status(thm)],[])).
% 1.38/1.16 tff(707,plain,
% 1.38/1.16 ((~![U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp22 | (~ndr1_0) | (~c1_1(a125)) | (~c2_1(a125)) | c3_1(a125)),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[706, 705])).
% 1.38/1.16 tff(708,plain,
% 1.38/1.16 ($false),
% 1.38/1.16 inference(unit_resolution,[status(thm)],[707, 123, 610, 682, 701, 643, 690])).
% 1.38/1.16 tff(709,plain,(hskp22 | hskp17 | hskp0 | c0_1(a125) | c0_1(a131) | c1_1(a131) | c2_1(a131) | c3_1(a124)), inference(lemma,lemma(discharge,[]))).
% 1.38/1.16 tff(710,plain,
% 1.38/1.16 (hskp22),
% 1.38/1.16 inference(unit_resolution,[status(thm)],[709, 609, 480, 433, 84, 78, 72, 435])).
% 1.38/1.16 tff(711,plain,
% 1.38/1.16 (((~hskp22) | (~c2_1(a176))) <=> ((~hskp22) | (~c2_1(a176)))),
% 1.38/1.16 inference(rewrite,[status(thm)],[])).
% 1.38/1.16 tff(712,plain,
% 1.38/1.16 (((~c2_1(a176)) | (~hskp22)) <=> ((~hskp22) | (~c2_1(a176)))),
% 1.38/1.16 inference(rewrite,[status(thm)],[])).
% 1.38/1.16 tff(713,axiom,((~c2_1(a176)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause93')).
% 1.38/1.16 tff(714,plain,
% 1.38/1.16 ((~hskp22) | (~c2_1(a176))),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[713, 712])).
% 1.38/1.16 tff(715,plain,
% 1.38/1.16 ((~hskp22) | (~c2_1(a176))),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[714, 711])).
% 1.38/1.16 tff(716,plain,
% 1.38/1.16 (~c2_1(a176)),
% 1.38/1.16 inference(unit_resolution,[status(thm)],[715, 710])).
% 1.38/1.16 tff(717,plain,
% 1.38/1.16 (((~hskp22) | (~c1_1(a176))) <=> ((~hskp22) | (~c1_1(a176)))),
% 1.38/1.16 inference(rewrite,[status(thm)],[])).
% 1.38/1.16 tff(718,plain,
% 1.38/1.16 (((~c1_1(a176)) | (~hskp22)) <=> ((~hskp22) | (~c1_1(a176)))),
% 1.38/1.16 inference(rewrite,[status(thm)],[])).
% 1.38/1.16 tff(719,axiom,((~c1_1(a176)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause92')).
% 1.38/1.16 tff(720,plain,
% 1.38/1.16 ((~hskp22) | (~c1_1(a176))),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[719, 718])).
% 1.38/1.16 tff(721,plain,
% 1.38/1.16 ((~hskp22) | (~c1_1(a176))),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[720, 717])).
% 1.38/1.16 tff(722,plain,
% 1.38/1.16 (~c1_1(a176)),
% 1.38/1.16 inference(unit_resolution,[status(thm)],[721, 710])).
% 1.38/1.16 tff(723,plain,
% 1.38/1.16 (((~hskp22) | c0_1(a176)) <=> ((~hskp22) | c0_1(a176))),
% 1.41/1.16 inference(rewrite,[status(thm)],[])).
% 1.41/1.16 tff(724,axiom,((~hskp22) | c0_1(a176)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause54')).
% 1.41/1.16 tff(725,plain,
% 1.41/1.16 ((~hskp22) | c0_1(a176)),
% 1.41/1.16 inference(modus_ponens,[status(thm)],[724, 723])).
% 1.41/1.16 tff(726,plain,
% 1.41/1.16 ((~hskp22) | c0_1(a176)),
% 1.41/1.16 inference(modus_ponens,[status(thm)],[725, 723])).
% 1.41/1.16 tff(727,plain,
% 1.41/1.16 ((~hskp22) | c0_1(a176)),
% 1.41/1.16 inference(modus_ponens,[status(thm)],[726, 723])).
% 1.41/1.16 tff(728,plain,
% 1.41/1.16 ((~hskp22) | c0_1(a176)),
% 1.41/1.16 inference(modus_ponens,[status(thm)],[727, 723])).
% 1.41/1.16 tff(729,plain,
% 1.41/1.16 ((~hskp22) | c0_1(a176)),
% 1.41/1.16 inference(modus_ponens,[status(thm)],[728, 723])).
% 1.41/1.16 tff(730,plain,
% 1.41/1.16 ((~hskp22) | c0_1(a176)),
% 1.41/1.16 inference(modus_ponens,[status(thm)],[729, 723])).
% 1.41/1.16 tff(731,plain,
% 1.41/1.16 ((~hskp22) | c0_1(a176)),
% 1.41/1.16 inference(modus_ponens,[status(thm)],[730, 723])).
% 1.41/1.16 tff(732,plain,
% 1.41/1.16 ((~hskp22) | c0_1(a176)),
% 1.41/1.16 inference(modus_ponens,[status(thm)],[731, 723])).
% 1.41/1.16 tff(733,plain,
% 1.41/1.16 (c0_1(a176)),
% 1.41/1.16 inference(unit_resolution,[status(thm)],[732, 710])).
% 1.41/1.16 tff(734,plain,
% 1.41/1.16 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | c1_1(a176) | c2_1(a176) | (~ndr1_0) | (~c0_1(a176)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp17 | c1_1(a176) | c2_1(a176) | (~ndr1_0) | (~c0_1(a176)))),
% 1.41/1.16 inference(rewrite,[status(thm)],[])).
% 1.41/1.16 tff(735,plain,
% 1.41/1.16 ((hskp19 | hskp17 | (~ndr1_0) | c2_1(a176) | c1_1(a176) | (~c0_1(a176))) <=> (hskp19 | hskp17 | c1_1(a176) | c2_1(a176) | (~ndr1_0) | (~c0_1(a176)))),
% 1.41/1.16 inference(rewrite,[status(thm)],[])).
% 1.41/1.16 tff(736,plain,
% 1.41/1.16 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c2_1(a176) | c1_1(a176) | (~c0_1(a176)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | c1_1(a176) | c2_1(a176) | (~ndr1_0) | (~c0_1(a176))))),
% 1.41/1.16 inference(monotonicity,[status(thm)],[735])).
% 1.41/1.16 tff(737,plain,
% 1.41/1.16 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c2_1(a176) | c1_1(a176) | (~c0_1(a176)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp17 | c1_1(a176) | c2_1(a176) | (~ndr1_0) | (~c0_1(a176)))),
% 1.41/1.16 inference(transitivity,[status(thm)],[736, 734])).
% 1.41/1.16 tff(738,plain,
% 1.41/1.16 ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c2_1(a176) | c1_1(a176) | (~c0_1(a176)))),
% 1.41/1.16 inference(quant_inst,[status(thm)],[])).
% 1.41/1.16 tff(739,plain,
% 1.41/1.16 ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp17 | c1_1(a176) | c2_1(a176) | (~ndr1_0) | (~c0_1(a176))),
% 1.41/1.16 inference(modus_ponens,[status(thm)],[738, 737])).
% 1.41/1.16 tff(740,plain,
% 1.41/1.16 (hskp19),
% 1.41/1.16 inference(unit_resolution,[status(thm)],[739, 123, 480, 733, 722, 716, 53])).
% 1.41/1.16 tff(741,plain,
% 1.41/1.16 (c3_1(a164)),
% 1.41/1.16 inference(unit_resolution,[status(thm)],[261, 740])).
% 1.41/1.16 tff(742,plain,
% 1.41/1.16 (c1_1(a164)),
% 1.41/1.16 inference(unit_resolution,[status(thm)],[272, 740])).
% 1.41/1.16 tff(743,plain,
% 1.41/1.16 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | (~c3_1(a164)) | c0_1(a164) | (~c1_1(a164)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp0 | (~ndr1_0) | (~c3_1(a164)) | c0_1(a164) | (~c1_1(a164)))),
% 1.41/1.16 inference(rewrite,[status(thm)],[])).
% 1.41/1.16 tff(744,plain,
% 1.41/1.16 ((hskp17 | hskp0 | (~ndr1_0) | c0_1(a164) | (~c3_1(a164)) | (~c1_1(a164))) <=> (hskp17 | hskp0 | (~ndr1_0) | (~c3_1(a164)) | c0_1(a164) | (~c1_1(a164)))),
% 1.41/1.16 inference(rewrite,[status(thm)],[])).
% 1.41/1.16 tff(745,plain,
% 1.41/1.16 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a164) | (~c3_1(a164)) | (~c1_1(a164)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | (~c3_1(a164)) | c0_1(a164) | (~c1_1(a164))))),
% 1.41/1.16 inference(monotonicity,[status(thm)],[744])).
% 1.41/1.17 tff(746,plain,
% 1.41/1.17 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a164) | (~c3_1(a164)) | (~c1_1(a164)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp0 | (~ndr1_0) | (~c3_1(a164)) | c0_1(a164) | (~c1_1(a164)))),
% 1.41/1.17 inference(transitivity,[status(thm)],[745, 743])).
% 1.41/1.17 tff(747,plain,
% 1.41/1.17 ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a164) | (~c3_1(a164)) | (~c1_1(a164)))),
% 1.41/1.17 inference(quant_inst,[status(thm)],[])).
% 1.41/1.17 tff(748,plain,
% 1.41/1.17 ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp0 | (~ndr1_0) | (~c3_1(a164)) | c0_1(a164) | (~c1_1(a164))),
% 1.41/1.17 inference(modus_ponens,[status(thm)],[747, 746])).
% 1.41/1.17 tff(749,plain,
% 1.41/1.17 (c0_1(a164)),
% 1.41/1.17 inference(unit_resolution,[status(thm)],[748, 123, 480, 609, 742, 741, 43])).
% 1.41/1.17 tff(750,plain,
% 1.41/1.17 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W))))),
% 1.41/1.17 inference(bind,[status(th)],[])).
% 1.41/1.17 tff(751,plain,
% 1.41/1.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.41/1.17 inference(quant_intro,[status(thm)],[750])).
% 1.41/1.17 tff(752,plain,
% 1.41/1.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.41/1.17 inference(rewrite,[status(thm)],[])).
% 1.41/1.17 tff(753,plain,
% 1.41/1.17 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c2_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))))),
% 1.41/1.17 inference(bind,[status(th)],[])).
% 1.41/1.17 tff(754,plain,
% 1.41/1.17 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(V)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.41/1.17 inference(quant_intro,[status(thm)],[753])).
% 1.41/1.17 tff(755,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(V)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause204')).
% 1.41/1.17 tff(756,plain,
% 1.41/1.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.41/1.17 inference(modus_ponens,[status(thm)],[755, 754])).
% 1.41/1.17 tff(757,plain,
% 1.41/1.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.41/1.17 inference(modus_ponens,[status(thm)],[756, 752])).
% 1.41/1.17 tff(758,plain,(
% 1.41/1.17 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.41/1.17 inference(skolemize,[status(sab)],[757])).
% 1.41/1.17 tff(759,plain,
% 1.41/1.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.41/1.17 inference(modus_ponens,[status(thm)],[758, 751])).
% 1.41/1.17 tff(760,plain,
% 1.41/1.17 (^[U: $i] : refl((hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 1.41/1.17 inference(bind,[status(th)],[])).
% 1.41/1.17 tff(761,plain,
% 1.41/1.17 (![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.41/1.17 inference(quant_intro,[status(thm)],[760])).
% 1.41/1.17 tff(762,plain,
% 1.41/1.17 (![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.41/1.17 inference(rewrite,[status(thm)],[])).
% 1.41/1.17 tff(763,plain,
% 1.41/1.17 (^[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)) | hskp17) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp17))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp17) | hskp13) <=> ((hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp13))), rewrite(((hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp13) <=> (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp17) | hskp13) <=> (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 1.41/1.17 inference(bind,[status(th)],[])).
% 1.41/1.17 tff(764,plain,
% 1.41/1.17 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp17) | hskp13) <=> ![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.41/1.17 inference(quant_intro,[status(thm)],[763])).
% 1.41/1.17 tff(765,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp17) | hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause156')).
% 1.41/1.17 tff(766,plain,
% 1.41/1.17 (![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.41/1.17 inference(modus_ponens,[status(thm)],[765, 764])).
% 1.41/1.17 tff(767,plain,
% 1.41/1.17 (![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.41/1.17 inference(modus_ponens,[status(thm)],[766, 762])).
% 1.41/1.17 tff(768,plain,(
% 1.41/1.17 ![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.41/1.17 inference(skolemize,[status(sab)],[767])).
% 1.41/1.17 tff(769,plain,
% 1.41/1.17 (![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.41/1.17 inference(modus_ponens,[status(thm)],[768, 761])).
% 1.41/1.17 tff(770,plain,
% 1.41/1.17 (~c2_1(a164)),
% 1.41/1.17 inference(unit_resolution,[status(thm)],[250, 740])).
% 1.41/1.17 tff(771,plain,
% 1.41/1.17 (((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164)))) <=> ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp13 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164)))),
% 1.41/1.17 inference(rewrite,[status(thm)],[])).
% 1.41/1.17 tff(772,plain,
% 1.41/1.17 ((hskp17 | hskp13 | (~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164))) <=> (hskp17 | hskp13 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164)))),
% 1.41/1.17 inference(rewrite,[status(thm)],[])).
% 1.41/1.17 tff(773,plain,
% 1.41/1.17 (((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | (~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)))) <=> ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164))))),
% 1.41/1.17 inference(monotonicity,[status(thm)],[772])).
% 1.41/1.17 tff(774,plain,
% 1.41/1.17 (((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | (~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)))) <=> ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp13 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164)))),
% 1.41/1.17 inference(transitivity,[status(thm)],[773, 771])).
% 1.41/1.17 tff(775,plain,
% 1.41/1.17 ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | (~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)))),
% 1.41/1.17 inference(quant_inst,[status(thm)],[])).
% 1.41/1.17 tff(776,plain,
% 1.41/1.17 ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp13 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164))),
% 1.41/1.17 inference(modus_ponens,[status(thm)],[775, 774])).
% 1.41/1.17 tff(777,plain,
% 1.41/1.17 (hskp13),
% 1.41/1.17 inference(unit_resolution,[status(thm)],[776, 123, 480, 742, 741, 770, 769])).
% 1.41/1.17 tff(778,plain,
% 1.41/1.17 (((~hskp13) | (~c1_1(a143))) <=> ((~hskp13) | (~c1_1(a143)))),
% 1.41/1.17 inference(rewrite,[status(thm)],[])).
% 1.41/1.17 tff(779,plain,
% 1.41/1.17 (((~c1_1(a143)) | (~hskp13)) <=> ((~hskp13) | (~c1_1(a143)))),
% 1.41/1.17 inference(rewrite,[status(thm)],[])).
% 1.41/1.17 tff(780,axiom,((~c1_1(a143)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause106')).
% 1.41/1.17 tff(781,plain,
% 1.41/1.17 ((~hskp13) | (~c1_1(a143))),
% 1.41/1.17 inference(modus_ponens,[status(thm)],[780, 779])).
% 1.41/1.17 tff(782,plain,
% 1.41/1.17 ((~hskp13) | (~c1_1(a143))),
% 1.41/1.17 inference(modus_ponens,[status(thm)],[781, 778])).
% 1.41/1.17 tff(783,plain,
% 1.41/1.17 (~c1_1(a143)),
% 1.41/1.17 inference(unit_resolution,[status(thm)],[782, 777])).
% 1.41/1.17 tff(784,assumption,(hskp2), introduced(assumption)).
% 1.41/1.17 tff(785,plain,
% 1.41/1.17 (c1_1(a125)),
% 1.41/1.17 inference(unit_resolution,[status(thm)],[681, 784])).
% 1.41/1.17 tff(786,plain,
% 1.41/1.17 (~c3_1(a125)),
% 1.41/1.17 inference(unit_resolution,[status(thm)],[689, 785, 134, 11])).
% 1.41/1.17 tff(787,plain,
% 1.41/1.17 (c2_1(a125)),
% 1.41/1.17 inference(unit_resolution,[status(thm)],[700, 784])).
% 1.41/1.17 tff(788,assumption,(~c1_1(a176)), introduced(assumption)).
% 1.41/1.17 tff(789,plain,
% 1.41/1.17 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))))),
% 1.41/1.17 inference(bind,[status(th)],[])).
% 1.41/1.17 tff(790,plain,
% 1.41/1.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.41/1.17 inference(quant_intro,[status(thm)],[789])).
% 1.41/1.17 tff(791,plain,
% 1.41/1.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.41/1.17 inference(rewrite,[status(thm)],[])).
% 1.41/1.17 tff(792,plain,
% 1.41/1.17 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))))),
% 1.41/1.17 inference(bind,[status(th)],[])).
% 1.41/1.17 tff(793,plain,
% 1.41/1.17 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.41/1.17 inference(quant_intro,[status(thm)],[792])).
% 1.41/1.17 tff(794,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause195')).
% 1.41/1.17 tff(795,plain,
% 1.41/1.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.41/1.17 inference(modus_ponens,[status(thm)],[794, 793])).
% 1.41/1.17 tff(796,plain,
% 1.41/1.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.41/1.17 inference(modus_ponens,[status(thm)],[795, 791])).
% 1.41/1.17 tff(797,plain,(
% 1.41/1.17 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.41/1.17 inference(skolemize,[status(sab)],[796])).
% 1.41/1.17 tff(798,plain,
% 1.41/1.17 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.41/1.17 inference(modus_ponens,[status(thm)],[797, 790])).
% 1.41/1.17 tff(799,assumption,(~c2_1(a176)), introduced(assumption)).
% 1.41/1.17 tff(800,plain,
% 1.41/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a176) | c2_1(a176) | c0_1(a132) | c2_1(a132) | c0_1(a125) | (~ndr1_0) | (~c1_1(a125)) | (~c2_1(a125)) | (~c3_1(a132)) | (~c0_1(a176)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a176) | c2_1(a176) | c0_1(a132) | c2_1(a132) | c0_1(a125) | (~ndr1_0) | (~c1_1(a125)) | (~c2_1(a125)) | (~c3_1(a132)) | (~c0_1(a176)))),
% 1.41/1.17 inference(rewrite,[status(thm)],[])).
% 1.41/1.17 tff(801,plain,
% 1.41/1.17 (((~ndr1_0) | c2_1(a176) | c1_1(a176) | (~c0_1(a176)) | c0_1(a125) | (~c2_1(a125)) | (~c1_1(a125)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132))) <=> (c1_1(a176) | c2_1(a176) | c0_1(a132) | c2_1(a132) | c0_1(a125) | (~ndr1_0) | (~c1_1(a125)) | (~c2_1(a125)) | (~c3_1(a132)) | (~c0_1(a176)))),
% 1.41/1.17 inference(rewrite,[status(thm)],[])).
% 1.41/1.17 tff(802,plain,
% 1.41/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a176) | c1_1(a176) | (~c0_1(a176)) | c0_1(a125) | (~c2_1(a125)) | (~c1_1(a125)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a176) | c2_1(a176) | c0_1(a132) | c2_1(a132) | c0_1(a125) | (~ndr1_0) | (~c1_1(a125)) | (~c2_1(a125)) | (~c3_1(a132)) | (~c0_1(a176))))),
% 1.41/1.17 inference(monotonicity,[status(thm)],[801])).
% 1.41/1.17 tff(803,plain,
% 1.41/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a176) | c1_1(a176) | (~c0_1(a176)) | c0_1(a125) | (~c2_1(a125)) | (~c1_1(a125)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a176) | c2_1(a176) | c0_1(a132) | c2_1(a132) | c0_1(a125) | (~ndr1_0) | (~c1_1(a125)) | (~c2_1(a125)) | (~c3_1(a132)) | (~c0_1(a176)))),
% 1.41/1.17 inference(transitivity,[status(thm)],[802, 800])).
% 1.41/1.17 tff(804,plain,
% 1.41/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a176) | c1_1(a176) | (~c0_1(a176)) | c0_1(a125) | (~c2_1(a125)) | (~c1_1(a125)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)))),
% 1.41/1.17 inference(quant_inst,[status(thm)],[])).
% 1.41/1.17 tff(805,plain,
% 1.41/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a176) | c2_1(a176) | c0_1(a132) | c2_1(a132) | c0_1(a125) | (~ndr1_0) | (~c1_1(a125)) | (~c2_1(a125)) | (~c3_1(a132)) | (~c0_1(a176))),
% 1.41/1.17 inference(modus_ponens,[status(thm)],[804, 803])).
% 1.41/1.17 tff(806,plain,
% 1.41/1.17 (c1_1(a176) | (~c1_1(a125)) | (~c2_1(a125)) | (~c3_1(a132)) | (~c0_1(a176))),
% 1.41/1.17 inference(unit_resolution,[status(thm)],[805, 123, 799, 434, 436, 433, 798])).
% 1.41/1.17 tff(807,plain,
% 1.41/1.17 (~c0_1(a176)),
% 1.41/1.17 inference(unit_resolution,[status(thm)],[806, 785, 470, 787, 788])).
% 1.41/1.17 tff(808,plain,
% 1.41/1.17 (~hskp22),
% 1.41/1.17 inference(unit_resolution,[status(thm)],[732, 807])).
% 1.41/1.17 tff(809,plain,
% 1.41/1.17 ($false),
% 1.41/1.17 inference(unit_resolution,[status(thm)],[707, 123, 808, 785, 787, 643, 786])).
% 1.41/1.17 tff(810,plain,((~hskp2) | hskp17 | hskp0 | c0_1(a125) | (~c3_1(a132)) | c1_1(a176) | c2_1(a176) | c0_1(a132) | c2_1(a132)), inference(lemma,lemma(discharge,[]))).
% 1.41/1.17 tff(811,plain,
% 1.41/1.17 (~hskp2),
% 1.41/1.17 inference(unit_resolution,[status(thm)],[810, 716, 609, 433, 458, 480, 722, 434, 436])).
% 1.41/1.17 tff(812,plain,
% 1.41/1.17 (hskp2 | hskp1),
% 1.41/1.17 inference(unit_resolution,[status(thm)],[669, 123, 84, 78, 72, 663])).
% 1.41/1.17 tff(813,plain,
% 1.41/1.17 (hskp1),
% 1.41/1.17 inference(unit_resolution,[status(thm)],[812, 811])).
% 1.41/1.17 tff(814,plain,
% 1.41/1.17 (c2_1(a124)),
% 1.41/1.17 inference(unit_resolution,[status(thm)],[632, 813])).
% 1.41/1.17 tff(815,plain,
% 1.41/1.17 (c1_1(a124)),
% 1.41/1.17 inference(unit_resolution,[status(thm)],[621, 813])).
% 1.41/1.17 tff(816,plain,
% 1.41/1.17 (((~hskp13) | c3_1(a143)) <=> ((~hskp13) | c3_1(a143))),
% 1.41/1.17 inference(rewrite,[status(thm)],[])).
% 1.41/1.17 tff(817,axiom,((~hskp13) | c3_1(a143)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause68')).
% 1.41/1.17 tff(818,plain,
% 1.41/1.17 ((~hskp13) | c3_1(a143)),
% 1.41/1.17 inference(modus_ponens,[status(thm)],[817, 816])).
% 1.41/1.17 tff(819,plain,
% 1.41/1.17 ((~hskp13) | c3_1(a143)),
% 1.41/1.17 inference(modus_ponens,[status(thm)],[818, 816])).
% 1.41/1.17 tff(820,plain,
% 1.41/1.17 ((~hskp13) | c3_1(a143)),
% 1.41/1.17 inference(modus_ponens,[status(thm)],[819, 816])).
% 1.41/1.17 tff(821,plain,
% 1.41/1.17 ((~hskp13) | c3_1(a143)),
% 1.41/1.17 inference(modus_ponens,[status(thm)],[820, 816])).
% 1.41/1.17 tff(822,plain,
% 1.41/1.17 ((~hskp13) | c3_1(a143)),
% 1.41/1.17 inference(modus_ponens,[status(thm)],[821, 816])).
% 1.41/1.17 tff(823,plain,
% 1.41/1.17 ((~hskp13) | c3_1(a143)),
% 1.41/1.17 inference(modus_ponens,[status(thm)],[822, 816])).
% 1.41/1.17 tff(824,plain,
% 1.41/1.17 ((~hskp13) | c3_1(a143)),
% 1.41/1.17 inference(modus_ponens,[status(thm)],[823, 816])).
% 1.41/1.17 tff(825,plain,
% 1.41/1.17 ((~hskp13) | c3_1(a143)),
% 1.41/1.17 inference(modus_ponens,[status(thm)],[824, 816])).
% 1.41/1.17 tff(826,plain,
% 1.41/1.17 (c3_1(a143)),
% 1.41/1.17 inference(unit_resolution,[status(thm)],[825, 777])).
% 1.41/1.17 tff(827,plain,
% 1.41/1.17 (((~hskp13) | c2_1(a143)) <=> ((~hskp13) | c2_1(a143))),
% 1.41/1.17 inference(rewrite,[status(thm)],[])).
% 1.41/1.17 tff(828,axiom,((~hskp13) | c2_1(a143)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause67')).
% 1.41/1.17 tff(829,plain,
% 1.41/1.17 ((~hskp13) | c2_1(a143)),
% 1.41/1.17 inference(modus_ponens,[status(thm)],[828, 827])).
% 1.41/1.17 tff(830,plain,
% 1.41/1.17 ((~hskp13) | c2_1(a143)),
% 1.41/1.17 inference(modus_ponens,[status(thm)],[829, 827])).
% 1.41/1.17 tff(831,plain,
% 1.41/1.17 ((~hskp13) | c2_1(a143)),
% 1.41/1.17 inference(modus_ponens,[status(thm)],[830, 827])).
% 1.41/1.17 tff(832,plain,
% 1.41/1.17 ((~hskp13) | c2_1(a143)),
% 1.41/1.17 inference(modus_ponens,[status(thm)],[831, 827])).
% 1.41/1.17 tff(833,plain,
% 1.41/1.17 ((~hskp13) | c2_1(a143)),
% 1.41/1.17 inference(modus_ponens,[status(thm)],[832, 827])).
% 1.41/1.17 tff(834,plain,
% 1.41/1.17 ((~hskp13) | c2_1(a143)),
% 1.41/1.17 inference(modus_ponens,[status(thm)],[833, 827])).
% 1.41/1.17 tff(835,plain,
% 1.41/1.17 ((~hskp13) | c2_1(a143)),
% 1.41/1.17 inference(modus_ponens,[status(thm)],[834, 827])).
% 1.41/1.17 tff(836,plain,
% 1.41/1.17 ((~hskp13) | c2_1(a143)),
% 1.41/1.17 inference(modus_ponens,[status(thm)],[835, 827])).
% 1.41/1.17 tff(837,plain,
% 1.41/1.17 (c2_1(a143)),
% 1.41/1.17 inference(unit_resolution,[status(thm)],[836, 777])).
% 1.41/1.17 tff(838,plain,
% 1.41/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a143) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c1_1(a124)) | (~c2_1(a143)) | (~c3_1(a143)) | (~c3_1(a164)) | (~c0_1(a164)) | (~c1_1(a164)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a143) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c1_1(a124)) | (~c2_1(a143)) | (~c3_1(a143)) | (~c3_1(a164)) | (~c0_1(a164)) | (~c1_1(a164)))),
% 1.41/1.17 inference(rewrite,[status(thm)],[])).
% 1.41/1.17 tff(839,plain,
% 1.41/1.17 (((~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164)) | (~c0_1(a164)) | c3_1(a124) | (~c2_1(a124)) | (~c1_1(a124)) | c1_1(a143) | (~c3_1(a143)) | (~c2_1(a143))) <=> (c1_1(a143) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c1_1(a124)) | (~c2_1(a143)) | (~c3_1(a143)) | (~c3_1(a164)) | (~c0_1(a164)) | (~c1_1(a164)))),
% 1.41/1.17 inference(rewrite,[status(thm)],[])).
% 1.41/1.17 tff(840,plain,
% 1.41/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164)) | (~c0_1(a164)) | c3_1(a124) | (~c2_1(a124)) | (~c1_1(a124)) | c1_1(a143) | (~c3_1(a143)) | (~c2_1(a143)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a143) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c1_1(a124)) | (~c2_1(a143)) | (~c3_1(a143)) | (~c3_1(a164)) | (~c0_1(a164)) | (~c1_1(a164))))),
% 1.41/1.17 inference(monotonicity,[status(thm)],[839])).
% 1.41/1.17 tff(841,plain,
% 1.41/1.17 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164)) | (~c0_1(a164)) | c3_1(a124) | (~c2_1(a124)) | (~c1_1(a124)) | c1_1(a143) | (~c3_1(a143)) | (~c2_1(a143)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a143) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c1_1(a124)) | (~c2_1(a143)) | (~c3_1(a143)) | (~c3_1(a164)) | (~c0_1(a164)) | (~c1_1(a164)))),
% 1.41/1.17 inference(transitivity,[status(thm)],[840, 838])).
% 1.41/1.17 tff(842,plain,
% 1.41/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164)) | (~c0_1(a164)) | c3_1(a124) | (~c2_1(a124)) | (~c1_1(a124)) | c1_1(a143) | (~c3_1(a143)) | (~c2_1(a143)))),
% 1.41/1.17 inference(quant_inst,[status(thm)],[])).
% 1.41/1.17 tff(843,plain,
% 1.41/1.17 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a143) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c1_1(a124)) | (~c2_1(a143)) | (~c3_1(a143)) | (~c3_1(a164)) | (~c0_1(a164)) | (~c1_1(a164))),
% 1.41/1.17 inference(modus_ponens,[status(thm)],[842, 841])).
% 1.41/1.17 tff(844,plain,
% 1.41/1.17 ($false),
% 1.41/1.17 inference(unit_resolution,[status(thm)],[843, 123, 742, 741, 837, 826, 815, 814, 783, 435, 759, 749])).
% 1.41/1.17 tff(845,plain,(c2_1(a132) | c3_1(a124) | c0_1(a125) | c0_1(a132) | hskp30 | hskp9), inference(lemma,lemma(discharge,[]))).
% 1.41/1.17 tff(846,plain,
% 1.41/1.17 (c2_1(a132)),
% 1.41/1.17 inference(unit_resolution,[status(thm)],[845, 434, 433, 435, 54, 33])).
% 1.41/1.17 tff(847,assumption,(c2_1(a132)), introduced(assumption)).
% 1.41/1.17 tff(848,plain,
% 1.41/1.17 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | c3_1(a132) | c0_1(a132) | (~c2_1(a132)) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp27 | c3_1(a132) | c0_1(a132) | (~c2_1(a132)) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0))),
% 1.41/1.17 inference(rewrite,[status(thm)],[])).
% 1.41/1.17 tff(849,plain,
% 1.41/1.17 ((hskp27 | (~ndr1_0) | c0_1(a132) | c3_1(a132) | (~c2_1(a132)) | c2_1(a131) | c1_1(a131) | c0_1(a131)) <=> (hskp27 | c3_1(a132) | c0_1(a132) | (~c2_1(a132)) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0))),
% 1.41/1.17 inference(rewrite,[status(thm)],[])).
% 1.41/1.17 tff(850,plain,
% 1.41/1.17 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a132) | c3_1(a132) | (~c2_1(a132)) | c2_1(a131) | c1_1(a131) | c0_1(a131))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | c3_1(a132) | c0_1(a132) | (~c2_1(a132)) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0)))),
% 1.41/1.17 inference(monotonicity,[status(thm)],[849])).
% 1.41/1.17 tff(851,plain,
% 1.41/1.17 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a132) | c3_1(a132) | (~c2_1(a132)) | c2_1(a131) | c1_1(a131) | c0_1(a131))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp27 | c3_1(a132) | c0_1(a132) | (~c2_1(a132)) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0))),
% 1.41/1.18 inference(transitivity,[status(thm)],[850, 848])).
% 1.41/1.18 tff(852,plain,
% 1.41/1.18 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a132) | c3_1(a132) | (~c2_1(a132)) | c2_1(a131) | c1_1(a131) | c0_1(a131))),
% 1.41/1.18 inference(quant_inst,[status(thm)],[])).
% 1.41/1.18 tff(853,plain,
% 1.41/1.18 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp27 | c3_1(a132) | c0_1(a132) | (~c2_1(a132)) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0)),
% 1.41/1.18 inference(modus_ponens,[status(thm)],[852, 851])).
% 1.41/1.18 tff(854,plain,
% 1.41/1.18 (hskp27 | c3_1(a132) | (~c2_1(a132))),
% 1.41/1.18 inference(unit_resolution,[status(thm)],[853, 123, 434, 84, 78, 72, 552])).
% 1.41/1.18 tff(855,plain,
% 1.41/1.18 (hskp27),
% 1.41/1.18 inference(unit_resolution,[status(thm)],[854, 437, 847])).
% 1.41/1.18 tff(856,plain,
% 1.41/1.18 (c3_1(a122)),
% 1.41/1.18 inference(unit_resolution,[status(thm)],[570, 855])).
% 1.41/1.18 tff(857,plain,
% 1.41/1.18 (c2_1(a122)),
% 1.41/1.18 inference(unit_resolution,[status(thm)],[581, 855])).
% 1.41/1.18 tff(858,plain,
% 1.41/1.18 (c0_1(a122)),
% 1.41/1.18 inference(unit_resolution,[status(thm)],[592, 855])).
% 1.41/1.18 tff(859,plain,
% 1.41/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c3_1(a132) | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c1_1(a132)) | (~c3_1(a122)) | (~c0_1(a122)) | (~c2_1(a122)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c3_1(a132) | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c1_1(a132)) | (~c3_1(a122)) | (~c0_1(a122)) | (~c2_1(a122)))),
% 1.41/1.18 inference(rewrite,[status(thm)],[])).
% 1.41/1.18 tff(860,plain,
% 1.41/1.18 (((~ndr1_0) | (~c3_1(a122)) | (~c0_1(a122)) | (~c2_1(a122)) | c3_1(a132) | (~c2_1(a132)) | (~c1_1(a132)) | c0_1(a132) | c3_1(a132) | (~c1_1(a132))) <=> (c3_1(a132) | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c1_1(a132)) | (~c3_1(a122)) | (~c0_1(a122)) | (~c2_1(a122)))),
% 1.41/1.18 inference(rewrite,[status(thm)],[])).
% 1.41/1.18 tff(861,plain,
% 1.41/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a122)) | (~c0_1(a122)) | (~c2_1(a122)) | c3_1(a132) | (~c2_1(a132)) | (~c1_1(a132)) | c0_1(a132) | c3_1(a132) | (~c1_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c3_1(a132) | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c1_1(a132)) | (~c3_1(a122)) | (~c0_1(a122)) | (~c2_1(a122))))),
% 1.41/1.18 inference(monotonicity,[status(thm)],[860])).
% 1.41/1.18 tff(862,plain,
% 1.41/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a122)) | (~c0_1(a122)) | (~c2_1(a122)) | c3_1(a132) | (~c2_1(a132)) | (~c1_1(a132)) | c0_1(a132) | c3_1(a132) | (~c1_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c3_1(a132) | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c1_1(a132)) | (~c3_1(a122)) | (~c0_1(a122)) | (~c2_1(a122)))),
% 1.41/1.18 inference(transitivity,[status(thm)],[861, 859])).
% 1.41/1.18 tff(863,plain,
% 1.41/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a122)) | (~c0_1(a122)) | (~c2_1(a122)) | c3_1(a132) | (~c2_1(a132)) | (~c1_1(a132)) | c0_1(a132) | c3_1(a132) | (~c1_1(a132)))),
% 1.41/1.18 inference(quant_inst,[status(thm)],[])).
% 1.41/1.18 tff(864,plain,
% 1.41/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c3_1(a132) | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c1_1(a132)) | (~c3_1(a122)) | (~c0_1(a122)) | (~c2_1(a122))),
% 1.41/1.18 inference(modus_ponens,[status(thm)],[863, 862])).
% 1.41/1.18 tff(865,plain,
% 1.41/1.18 (~c1_1(a132)),
% 1.41/1.18 inference(unit_resolution,[status(thm)],[864, 123, 858, 857, 856, 437, 434, 847, 490])).
% 1.41/1.18 tff(866,plain,
% 1.41/1.18 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))))),
% 1.41/1.18 inference(bind,[status(th)],[])).
% 1.41/1.18 tff(867,plain,
% 1.41/1.18 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_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) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 1.41/1.18 inference(quant_intro,[status(thm)],[866])).
% 1.41/1.18 tff(868,plain,
% 1.41/1.18 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_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) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 1.41/1.18 inference(rewrite,[status(thm)],[])).
% 1.41/1.18 tff(869,plain,
% 1.41/1.18 (^[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) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(W)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(W))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))))),
% 1.41/1.18 inference(bind,[status(th)],[])).
% 1.41/1.18 tff(870,plain,
% 1.41/1.18 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 1.41/1.18 inference(quant_intro,[status(thm)],[869])).
% 1.41/1.18 tff(871,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause199')).
% 1.41/1.18 tff(872,plain,
% 1.41/1.18 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 1.41/1.18 inference(modus_ponens,[status(thm)],[871, 870])).
% 1.41/1.18 tff(873,plain,
% 1.41/1.18 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 1.41/1.18 inference(modus_ponens,[status(thm)],[872, 868])).
% 1.41/1.18 tff(874,plain,(
% 1.41/1.18 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 1.41/1.18 inference(skolemize,[status(sab)],[873])).
% 1.41/1.18 tff(875,plain,
% 1.41/1.18 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 1.41/1.18 inference(modus_ponens,[status(thm)],[874, 867])).
% 1.41/1.18 tff(876,plain,
% 1.41/1.18 (((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp30 | hskp20 | c3_1(a132) | (~c2_1(a132)) | (~ndr1_0) | c1_1(a132))) <=> ((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp30 | hskp20 | c3_1(a132) | (~c2_1(a132)) | (~ndr1_0) | c1_1(a132))),
% 1.41/1.18 inference(rewrite,[status(thm)],[])).
% 1.41/1.18 tff(877,plain,
% 1.41/1.18 ((hskp30 | hskp20 | (~ndr1_0) | c1_1(a132) | c3_1(a132) | (~c2_1(a132))) <=> (hskp30 | hskp20 | c3_1(a132) | (~c2_1(a132)) | (~ndr1_0) | c1_1(a132))),
% 1.41/1.18 inference(rewrite,[status(thm)],[])).
% 1.41/1.18 tff(878,plain,
% 1.41/1.18 (((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp30 | hskp20 | (~ndr1_0) | c1_1(a132) | c3_1(a132) | (~c2_1(a132)))) <=> ((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp30 | hskp20 | c3_1(a132) | (~c2_1(a132)) | (~ndr1_0) | c1_1(a132)))),
% 1.41/1.18 inference(monotonicity,[status(thm)],[877])).
% 1.41/1.18 tff(879,plain,
% 1.41/1.18 (((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp30 | hskp20 | (~ndr1_0) | c1_1(a132) | c3_1(a132) | (~c2_1(a132)))) <=> ((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp30 | hskp20 | c3_1(a132) | (~c2_1(a132)) | (~ndr1_0) | c1_1(a132))),
% 1.41/1.18 inference(transitivity,[status(thm)],[878, 876])).
% 1.41/1.18 tff(880,plain,
% 1.41/1.18 ((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp30 | hskp20 | (~ndr1_0) | c1_1(a132) | c3_1(a132) | (~c2_1(a132)))),
% 1.41/1.18 inference(quant_inst,[status(thm)],[])).
% 1.41/1.18 tff(881,plain,
% 1.41/1.18 ((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp30 | hskp20 | c3_1(a132) | (~c2_1(a132)) | (~ndr1_0) | c1_1(a132)),
% 1.41/1.18 inference(modus_ponens,[status(thm)],[880, 879])).
% 1.41/1.18 tff(882,plain,
% 1.41/1.18 (hskp20 | c3_1(a132) | c1_1(a132)),
% 1.41/1.18 inference(unit_resolution,[status(thm)],[881, 54, 123, 847, 511])).
% 1.41/1.18 tff(883,plain,
% 1.41/1.18 (hskp20),
% 1.41/1.18 inference(unit_resolution,[status(thm)],[882, 865, 437])).
% 1.41/1.18 tff(884,plain,
% 1.41/1.18 (~c3_1(a168)),
% 1.41/1.18 inference(unit_resolution,[status(thm)],[524, 883])).
% 1.41/1.18 tff(885,plain,
% 1.41/1.18 (~c0_1(a168)),
% 1.41/1.18 inference(unit_resolution,[status(thm)],[530, 883])).
% 1.41/1.18 tff(886,plain,
% 1.41/1.18 (c1_1(a168)),
% 1.41/1.18 inference(unit_resolution,[status(thm)],[541, 883])).
% 1.41/1.18 tff(887,plain,
% 1.41/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c3_1(a132) | c0_1(a168) | c3_1(a168) | (~c2_1(a132)) | (~ndr1_0) | c1_1(a132) | (~c1_1(a168)) | (~c2_1(a168)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c3_1(a132) | c0_1(a168) | c3_1(a168) | (~c2_1(a132)) | (~ndr1_0) | c1_1(a132) | (~c1_1(a168)) | (~c2_1(a168)))),
% 1.41/1.18 inference(rewrite,[status(thm)],[])).
% 1.41/1.18 tff(888,plain,
% 1.41/1.18 (((~ndr1_0) | c3_1(a168) | (~c1_1(a168)) | (~c2_1(a168)) | c1_1(a132) | c3_1(a132) | (~c2_1(a132)) | c0_1(a168) | (~c1_1(a168)) | (~c2_1(a168))) <=> (c3_1(a132) | c0_1(a168) | c3_1(a168) | (~c2_1(a132)) | (~ndr1_0) | c1_1(a132) | (~c1_1(a168)) | (~c2_1(a168)))),
% 1.41/1.18 inference(rewrite,[status(thm)],[])).
% 1.41/1.18 tff(889,plain,
% 1.41/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a168) | (~c1_1(a168)) | (~c2_1(a168)) | c1_1(a132) | c3_1(a132) | (~c2_1(a132)) | c0_1(a168) | (~c1_1(a168)) | (~c2_1(a168)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c3_1(a132) | c0_1(a168) | c3_1(a168) | (~c2_1(a132)) | (~ndr1_0) | c1_1(a132) | (~c1_1(a168)) | (~c2_1(a168))))),
% 1.41/1.18 inference(monotonicity,[status(thm)],[888])).
% 1.41/1.18 tff(890,plain,
% 1.41/1.18 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a168) | (~c1_1(a168)) | (~c2_1(a168)) | c1_1(a132) | c3_1(a132) | (~c2_1(a132)) | c0_1(a168) | (~c1_1(a168)) | (~c2_1(a168)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c3_1(a132) | c0_1(a168) | c3_1(a168) | (~c2_1(a132)) | (~ndr1_0) | c1_1(a132) | (~c1_1(a168)) | (~c2_1(a168)))),
% 1.41/1.18 inference(transitivity,[status(thm)],[889, 887])).
% 1.41/1.18 tff(891,plain,
% 1.41/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a168) | (~c1_1(a168)) | (~c2_1(a168)) | c1_1(a132) | c3_1(a132) | (~c2_1(a132)) | c0_1(a168) | (~c1_1(a168)) | (~c2_1(a168)))),
% 1.41/1.18 inference(quant_inst,[status(thm)],[])).
% 1.41/1.18 tff(892,plain,
% 1.41/1.18 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c3_1(a132) | c0_1(a168) | c3_1(a168) | (~c2_1(a132)) | (~ndr1_0) | c1_1(a132) | (~c1_1(a168)) | (~c2_1(a168))),
% 1.41/1.18 inference(modus_ponens,[status(thm)],[891, 890])).
% 1.41/1.18 tff(893,plain,
% 1.41/1.18 (~c2_1(a168)),
% 1.41/1.18 inference(unit_resolution,[status(thm)],[892, 123, 886, 437, 885, 884, 847, 875, 865])).
% 1.41/1.18 tff(894,plain,
% 1.41/1.18 (((~hskp7) | (~c2_1(a132))) <=> ((~hskp7) | (~c2_1(a132)))),
% 1.41/1.18 inference(rewrite,[status(thm)],[])).
% 1.41/1.18 tff(895,plain,
% 1.41/1.18 (((~c2_1(a132)) | (~hskp7)) <=> ((~hskp7) | (~c2_1(a132)))),
% 1.41/1.18 inference(rewrite,[status(thm)],[])).
% 1.41/1.18 tff(896,axiom,((~c2_1(a132)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause117')).
% 1.41/1.18 tff(897,plain,
% 1.41/1.18 ((~hskp7) | (~c2_1(a132))),
% 1.41/1.18 inference(modus_ponens,[status(thm)],[896, 895])).
% 1.41/1.18 tff(898,plain,
% 1.41/1.18 ((~hskp7) | (~c2_1(a132))),
% 1.41/1.18 inference(modus_ponens,[status(thm)],[897, 894])).
% 1.41/1.18 tff(899,plain,
% 1.41/1.18 (~hskp7),
% 1.41/1.18 inference(unit_resolution,[status(thm)],[898, 847])).
% 1.41/1.18 tff(900,plain,
% 1.41/1.18 (((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | c0_1(a168) | c3_1(a168) | (~ndr1_0) | c2_1(a168))) <=> ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp9 | hskp7 | c0_1(a168) | c3_1(a168) | (~ndr1_0) | c2_1(a168))),
% 1.41/1.18 inference(rewrite,[status(thm)],[])).
% 1.41/1.18 tff(901,plain,
% 1.41/1.18 ((hskp9 | hskp7 | (~ndr1_0) | c2_1(a168) | c0_1(a168) | c3_1(a168)) <=> (hskp9 | hskp7 | c0_1(a168) | c3_1(a168) | (~ndr1_0) | c2_1(a168))),
% 1.41/1.18 inference(rewrite,[status(thm)],[])).
% 1.41/1.18 tff(902,plain,
% 1.41/1.18 (((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | (~ndr1_0) | c2_1(a168) | c0_1(a168) | c3_1(a168))) <=> ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | c0_1(a168) | c3_1(a168) | (~ndr1_0) | c2_1(a168)))),
% 1.41/1.18 inference(monotonicity,[status(thm)],[901])).
% 1.41/1.18 tff(903,plain,
% 1.41/1.18 (((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | (~ndr1_0) | c2_1(a168) | c0_1(a168) | c3_1(a168))) <=> ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp9 | hskp7 | c0_1(a168) | c3_1(a168) | (~ndr1_0) | c2_1(a168))),
% 1.41/1.18 inference(transitivity,[status(thm)],[902, 900])).
% 1.41/1.18 tff(904,plain,
% 1.41/1.18 ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | (~ndr1_0) | c2_1(a168) | c0_1(a168) | c3_1(a168))),
% 1.41/1.18 inference(quant_inst,[status(thm)],[])).
% 1.41/1.18 tff(905,plain,
% 1.41/1.18 ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp9 | hskp7 | c0_1(a168) | c3_1(a168) | (~ndr1_0) | c2_1(a168)),
% 1.41/1.18 inference(modus_ponens,[status(thm)],[904, 903])).
% 1.41/1.18 tff(906,plain,
% 1.41/1.18 ($false),
% 1.41/1.18 inference(unit_resolution,[status(thm)],[905, 123, 33, 899, 885, 884, 94, 893])).
% 1.41/1.18 tff(907,plain,(c3_1(a132) | hskp9 | (~c2_1(a132)) | hskp30 | c0_1(a132)), inference(lemma,lemma(discharge,[]))).
% 1.41/1.18 tff(908,plain,
% 1.41/1.18 (c3_1(a132)),
% 1.41/1.18 inference(unit_resolution,[status(thm)],[907, 846, 33, 54, 434])).
% 1.41/1.18 tff(909,plain,
% 1.41/1.18 (~hskp7),
% 1.41/1.18 inference(unit_resolution,[status(thm)],[898, 846])).
% 1.41/1.18 tff(910,plain,
% 1.41/1.18 (^[U: $i] : refl((hskp29 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp29 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))),
% 1.41/1.18 inference(bind,[status(th)],[])).
% 1.41/1.18 tff(911,plain,
% 1.41/1.18 (![U: $i] : (hskp29 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp29 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.41/1.18 inference(quant_intro,[status(thm)],[910])).
% 1.41/1.18 tff(912,plain,
% 1.41/1.18 (![U: $i] : (hskp29 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp29 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.41/1.18 inference(rewrite,[status(thm)],[])).
% 1.41/1.18 tff(913,plain,
% 1.41/1.18 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp29) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp29))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp29) <=> (hskp29 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp29) <=> (hskp29 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp29) | hskp7) <=> ((hskp29 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp7))), rewrite(((hskp29 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp7) <=> (hskp29 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp29) | hskp7) <=> (hskp29 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))))),
% 1.41/1.18 inference(bind,[status(th)],[])).
% 1.41/1.18 tff(914,plain,
% 1.41/1.18 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp29) | hskp7) <=> ![U: $i] : (hskp29 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.41/1.18 inference(quant_intro,[status(thm)],[913])).
% 1.41/1.18 tff(915,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp29) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause145')).
% 1.41/1.18 tff(916,plain,
% 1.41/1.18 (![U: $i] : (hskp29 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.41/1.18 inference(modus_ponens,[status(thm)],[915, 914])).
% 1.41/1.18 tff(917,plain,
% 1.41/1.18 (![U: $i] : (hskp29 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.41/1.18 inference(modus_ponens,[status(thm)],[916, 912])).
% 1.41/1.18 tff(918,plain,(
% 1.41/1.18 ![U: $i] : (hskp29 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.41/1.18 inference(skolemize,[status(sab)],[917])).
% 1.41/1.18 tff(919,plain,
% 1.41/1.18 (![U: $i] : (hskp29 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.41/1.18 inference(modus_ponens,[status(thm)],[918, 911])).
% 1.41/1.18 tff(920,plain,
% 1.41/1.18 (((~![U: $i] : (hskp29 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp29 | hskp7 | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c3_1(a132)))) <=> ((~![U: $i] : (hskp29 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp29 | hskp7 | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c3_1(a132)))),
% 1.41/1.18 inference(rewrite,[status(thm)],[])).
% 1.41/1.18 tff(921,plain,
% 1.41/1.18 ((hskp29 | hskp7 | (~ndr1_0) | c0_1(a132) | (~c3_1(a132)) | (~c2_1(a132))) <=> (hskp29 | hskp7 | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c3_1(a132)))),
% 1.41/1.18 inference(rewrite,[status(thm)],[])).
% 1.41/1.18 tff(922,plain,
% 1.41/1.18 (((~![U: $i] : (hskp29 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp29 | hskp7 | (~ndr1_0) | c0_1(a132) | (~c3_1(a132)) | (~c2_1(a132)))) <=> ((~![U: $i] : (hskp29 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp29 | hskp7 | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c3_1(a132))))),
% 1.41/1.18 inference(monotonicity,[status(thm)],[921])).
% 1.41/1.18 tff(923,plain,
% 1.41/1.18 (((~![U: $i] : (hskp29 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp29 | hskp7 | (~ndr1_0) | c0_1(a132) | (~c3_1(a132)) | (~c2_1(a132)))) <=> ((~![U: $i] : (hskp29 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp29 | hskp7 | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c3_1(a132)))),
% 1.41/1.18 inference(transitivity,[status(thm)],[922, 920])).
% 1.41/1.18 tff(924,plain,
% 1.41/1.18 ((~![U: $i] : (hskp29 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp29 | hskp7 | (~ndr1_0) | c0_1(a132) | (~c3_1(a132)) | (~c2_1(a132)))),
% 1.41/1.18 inference(quant_inst,[status(thm)],[])).
% 1.41/1.18 tff(925,plain,
% 1.41/1.18 ((~![U: $i] : (hskp29 | hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp29 | hskp7 | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c3_1(a132))),
% 1.41/1.18 inference(modus_ponens,[status(thm)],[924, 923])).
% 1.41/1.18 tff(926,plain,
% 1.41/1.18 (hskp29 | hskp7 | (~c2_1(a132)) | (~c3_1(a132))),
% 1.41/1.18 inference(unit_resolution,[status(thm)],[925, 123, 434, 919])).
% 1.41/1.18 tff(927,plain,
% 1.41/1.18 (hskp29),
% 1.41/1.18 inference(unit_resolution,[status(thm)],[926, 908, 909, 846])).
% 1.41/1.18 tff(928,plain,
% 1.41/1.18 (((~hskp29) | c2_1(a136)) <=> ((~hskp29) | c2_1(a136))),
% 1.41/1.18 inference(rewrite,[status(thm)],[])).
% 1.41/1.18 tff(929,axiom,((~hskp29) | c2_1(a136)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause43')).
% 1.41/1.18 tff(930,plain,
% 1.41/1.18 ((~hskp29) | c2_1(a136)),
% 1.41/1.18 inference(modus_ponens,[status(thm)],[929, 928])).
% 1.41/1.18 tff(931,plain,
% 1.41/1.18 ((~hskp29) | c2_1(a136)),
% 1.41/1.18 inference(modus_ponens,[status(thm)],[930, 928])).
% 1.41/1.18 tff(932,plain,
% 1.41/1.18 ((~hskp29) | c2_1(a136)),
% 1.41/1.18 inference(modus_ponens,[status(thm)],[931, 928])).
% 1.41/1.18 tff(933,plain,
% 1.41/1.18 ((~hskp29) | c2_1(a136)),
% 1.41/1.18 inference(modus_ponens,[status(thm)],[932, 928])).
% 1.41/1.18 tff(934,plain,
% 1.41/1.18 ((~hskp29) | c2_1(a136)),
% 1.41/1.18 inference(modus_ponens,[status(thm)],[933, 928])).
% 1.41/1.18 tff(935,plain,
% 1.41/1.18 ((~hskp29) | c2_1(a136)),
% 1.41/1.18 inference(modus_ponens,[status(thm)],[934, 928])).
% 1.41/1.18 tff(936,plain,
% 1.41/1.18 ((~hskp29) | c2_1(a136)),
% 1.41/1.18 inference(modus_ponens,[status(thm)],[935, 928])).
% 1.41/1.18 tff(937,plain,
% 1.41/1.18 ((~hskp29) | c2_1(a136)),
% 1.41/1.18 inference(modus_ponens,[status(thm)],[936, 928])).
% 1.41/1.18 tff(938,plain,
% 1.41/1.18 (c2_1(a136)),
% 1.41/1.18 inference(unit_resolution,[status(thm)],[937, 927])).
% 1.41/1.18 tff(939,plain,
% 1.41/1.18 (((~hskp29) | c1_1(a136)) <=> ((~hskp29) | c1_1(a136))),
% 1.41/1.18 inference(rewrite,[status(thm)],[])).
% 1.41/1.18 tff(940,axiom,((~hskp29) | c1_1(a136)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause42')).
% 1.41/1.18 tff(941,plain,
% 1.41/1.18 ((~hskp29) | c1_1(a136)),
% 1.41/1.18 inference(modus_ponens,[status(thm)],[940, 939])).
% 1.41/1.18 tff(942,plain,
% 1.41/1.18 ((~hskp29) | c1_1(a136)),
% 1.41/1.18 inference(modus_ponens,[status(thm)],[941, 939])).
% 1.41/1.18 tff(943,plain,
% 1.41/1.18 ((~hskp29) | c1_1(a136)),
% 1.41/1.18 inference(modus_ponens,[status(thm)],[942, 939])).
% 1.41/1.18 tff(944,plain,
% 1.41/1.18 ((~hskp29) | c1_1(a136)),
% 1.41/1.18 inference(modus_ponens,[status(thm)],[943, 939])).
% 1.41/1.18 tff(945,plain,
% 1.41/1.18 ((~hskp29) | c1_1(a136)),
% 1.41/1.18 inference(modus_ponens,[status(thm)],[944, 939])).
% 1.41/1.18 tff(946,plain,
% 1.41/1.18 ((~hskp29) | c1_1(a136)),
% 1.41/1.18 inference(modus_ponens,[status(thm)],[945, 939])).
% 1.41/1.18 tff(947,plain,
% 1.41/1.18 ((~hskp29) | c1_1(a136)),
% 1.41/1.18 inference(modus_ponens,[status(thm)],[946, 939])).
% 1.41/1.18 tff(948,plain,
% 1.41/1.18 ((~hskp29) | c1_1(a136)),
% 1.41/1.18 inference(modus_ponens,[status(thm)],[947, 939])).
% 1.41/1.18 tff(949,plain,
% 1.41/1.18 (c1_1(a136)),
% 1.41/1.18 inference(unit_resolution,[status(thm)],[948, 927])).
% 1.41/1.18 tff(950,plain,
% 1.41/1.18 (((~hskp29) | c0_1(a136)) <=> ((~hskp29) | c0_1(a136))),
% 1.41/1.18 inference(rewrite,[status(thm)],[])).
% 1.41/1.18 tff(951,axiom,((~hskp29) | c0_1(a136)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause41')).
% 1.41/1.18 tff(952,plain,
% 1.41/1.18 ((~hskp29) | c0_1(a136)),
% 1.41/1.18 inference(modus_ponens,[status(thm)],[951, 950])).
% 1.41/1.18 tff(953,plain,
% 1.41/1.18 ((~hskp29) | c0_1(a136)),
% 1.41/1.18 inference(modus_ponens,[status(thm)],[952, 950])).
% 1.41/1.18 tff(954,plain,
% 1.41/1.18 ((~hskp29) | c0_1(a136)),
% 1.41/1.18 inference(modus_ponens,[status(thm)],[953, 950])).
% 1.41/1.18 tff(955,plain,
% 1.41/1.18 ((~hskp29) | c0_1(a136)),
% 1.41/1.18 inference(modus_ponens,[status(thm)],[954, 950])).
% 1.41/1.18 tff(956,plain,
% 1.41/1.18 ((~hskp29) | c0_1(a136)),
% 1.41/1.18 inference(modus_ponens,[status(thm)],[955, 950])).
% 1.41/1.18 tff(957,plain,
% 1.41/1.18 ((~hskp29) | c0_1(a136)),
% 1.41/1.18 inference(modus_ponens,[status(thm)],[956, 950])).
% 1.41/1.18 tff(958,plain,
% 1.41/1.18 ((~hskp29) | c0_1(a136)),
% 1.41/1.18 inference(modus_ponens,[status(thm)],[957, 950])).
% 1.41/1.18 tff(959,plain,
% 1.41/1.18 ((~hskp29) | c0_1(a136)),
% 1.41/1.18 inference(modus_ponens,[status(thm)],[958, 950])).
% 1.41/1.18 tff(960,plain,
% 1.41/1.18 (c0_1(a136)),
% 1.41/1.18 inference(unit_resolution,[status(thm)],[959, 927])).
% 1.41/1.18 tff(961,plain,
% 1.41/1.18 (hskp7 | c3_1(a131)),
% 1.41/1.18 inference(unit_resolution,[status(thm)],[129, 123, 33, 84, 72, 94])).
% 1.41/1.18 tff(962,plain,
% 1.41/1.18 (c3_1(a131)),
% 1.41/1.18 inference(unit_resolution,[status(thm)],[961, 909])).
% 1.41/1.18 tff(963,plain,
% 1.41/1.18 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))))),
% 1.41/1.18 inference(bind,[status(th)],[])).
% 1.41/1.18 tff(964,plain,
% 1.41/1.18 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.41/1.18 inference(quant_intro,[status(thm)],[963])).
% 1.41/1.18 tff(965,plain,
% 1.41/1.18 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.41/1.18 inference(rewrite,[status(thm)],[])).
% 1.41/1.18 tff(966,plain,
% 1.41/1.18 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c1_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))))),
% 1.41/1.19 inference(bind,[status(th)],[])).
% 1.41/1.19 tff(967,plain,
% 1.41/1.19 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.41/1.19 inference(quant_intro,[status(thm)],[966])).
% 1.41/1.19 tff(968,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause198')).
% 1.41/1.19 tff(969,plain,
% 1.41/1.19 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.41/1.19 inference(modus_ponens,[status(thm)],[968, 967])).
% 1.41/1.19 tff(970,plain,
% 1.41/1.19 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.41/1.19 inference(modus_ponens,[status(thm)],[969, 965])).
% 1.41/1.19 tff(971,plain,(
% 1.41/1.19 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.41/1.19 inference(skolemize,[status(sab)],[970])).
% 1.41/1.19 tff(972,plain,
% 1.41/1.19 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.41/1.19 inference(modus_ponens,[status(thm)],[971, 964])).
% 1.41/1.19 tff(973,assumption,(c2_1(a136)), introduced(assumption)).
% 1.41/1.19 tff(974,assumption,(c1_1(a136)), introduced(assumption)).
% 1.41/1.19 tff(975,assumption,(c0_1(a136)), introduced(assumption)).
% 1.41/1.19 tff(976,plain,
% 1.41/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c1_1(a131) | c2_1(a131) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)) | (~c3_1(a131)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a131) | c2_1(a131) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)) | (~c3_1(a131)))),
% 1.41/1.19 inference(rewrite,[status(thm)],[])).
% 1.41/1.19 tff(977,plain,
% 1.41/1.19 (((~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)) | c2_1(a131) | c1_1(a131) | (~c3_1(a131)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123))) <=> (c1_1(a131) | c2_1(a131) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)) | (~c3_1(a131)))),
% 1.41/1.19 inference(rewrite,[status(thm)],[])).
% 1.41/1.19 tff(978,plain,
% 1.41/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)) | c2_1(a131) | c1_1(a131) | (~c3_1(a131)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c1_1(a131) | c2_1(a131) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)) | (~c3_1(a131))))),
% 1.41/1.19 inference(monotonicity,[status(thm)],[977])).
% 1.41/1.19 tff(979,plain,
% 1.41/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)) | c2_1(a131) | c1_1(a131) | (~c3_1(a131)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a131) | c2_1(a131) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)) | (~c3_1(a131)))),
% 1.41/1.19 inference(transitivity,[status(thm)],[978, 976])).
% 1.41/1.19 tff(980,plain,
% 1.41/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)) | c2_1(a131) | c1_1(a131) | (~c3_1(a131)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)))),
% 1.41/1.19 inference(quant_inst,[status(thm)],[])).
% 1.41/1.19 tff(981,plain,
% 1.41/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a131) | c2_1(a131) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)) | (~c3_1(a131))),
% 1.41/1.19 inference(modus_ponens,[status(thm)],[980, 979])).
% 1.41/1.19 tff(982,plain,
% 1.41/1.19 (c3_1(a123)),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[981, 123, 975, 974, 973, 494, 132, 95, 493, 972, 133])).
% 1.41/1.19 tff(983,plain,
% 1.41/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a131) | c2_1(a131) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c2_1(a123)) | (~c3_1(a131)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a131) | c2_1(a131) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c2_1(a123)) | (~c3_1(a131)))),
% 1.41/1.19 inference(rewrite,[status(thm)],[])).
% 1.41/1.19 tff(984,plain,
% 1.41/1.19 (((~ndr1_0) | c1_1(a123) | (~c3_1(a123)) | (~c2_1(a123)) | c2_1(a131) | c1_1(a131) | (~c3_1(a131)) | c1_1(a123) | c0_1(a123) | (~c3_1(a123))) <=> (c1_1(a131) | c2_1(a131) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c2_1(a123)) | (~c3_1(a131)))),
% 1.41/1.19 inference(rewrite,[status(thm)],[])).
% 1.41/1.19 tff(985,plain,
% 1.41/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a123) | (~c3_1(a123)) | (~c2_1(a123)) | c2_1(a131) | c1_1(a131) | (~c3_1(a131)) | c1_1(a123) | c0_1(a123) | (~c3_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a131) | c2_1(a131) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c2_1(a123)) | (~c3_1(a131))))),
% 1.41/1.19 inference(monotonicity,[status(thm)],[984])).
% 1.41/1.19 tff(986,plain,
% 1.41/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a123) | (~c3_1(a123)) | (~c2_1(a123)) | c2_1(a131) | c1_1(a131) | (~c3_1(a131)) | c1_1(a123) | c0_1(a123) | (~c3_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a131) | c2_1(a131) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c2_1(a123)) | (~c3_1(a131)))),
% 1.41/1.19 inference(transitivity,[status(thm)],[985, 983])).
% 1.41/1.19 tff(987,plain,
% 1.41/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a123) | (~c3_1(a123)) | (~c2_1(a123)) | c2_1(a131) | c1_1(a131) | (~c3_1(a131)) | c1_1(a123) | c0_1(a123) | (~c3_1(a123)))),
% 1.41/1.19 inference(quant_inst,[status(thm)],[])).
% 1.41/1.19 tff(988,plain,
% 1.41/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a131) | c2_1(a131) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c2_1(a123)) | (~c3_1(a131))),
% 1.41/1.19 inference(modus_ponens,[status(thm)],[987, 986])).
% 1.41/1.19 tff(989,plain,
% 1.41/1.19 ($false),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[988, 123, 494, 132, 95, 493, 492, 144, 133, 982])).
% 1.41/1.19 tff(990,plain,((~hskp0) | c1_1(a131) | c2_1(a131) | (~c3_1(a131)) | (~c0_1(a136)) | (~c1_1(a136)) | (~c2_1(a136))), inference(lemma,lemma(discharge,[]))).
% 1.41/1.19 tff(991,plain,
% 1.41/1.19 (~hskp0),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[990, 962, 72, 78, 960, 949, 938])).
% 1.41/1.19 tff(992,plain,
% 1.41/1.19 (^[U: $i] : refl((hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))),
% 1.41/1.19 inference(bind,[status(th)],[])).
% 1.41/1.19 tff(993,plain,
% 1.41/1.19 (![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.41/1.19 inference(quant_intro,[status(thm)],[992])).
% 1.41/1.19 tff(994,plain,
% 1.41/1.19 (![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.41/1.19 inference(rewrite,[status(thm)],[])).
% 1.41/1.19 tff(995,plain,
% 1.41/1.19 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp0) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp0))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp0) | hskp18) <=> ((hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp18))), rewrite(((hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp18) <=> (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp0) | hskp18) <=> (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))))),
% 1.41/1.19 inference(bind,[status(th)],[])).
% 1.41/1.19 tff(996,plain,
% 1.41/1.19 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp0) | hskp18) <=> ![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.41/1.19 inference(quant_intro,[status(thm)],[995])).
% 1.41/1.19 tff(997,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp0) | hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause146')).
% 1.41/1.19 tff(998,plain,
% 1.41/1.19 (![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.41/1.19 inference(modus_ponens,[status(thm)],[997, 996])).
% 1.41/1.19 tff(999,plain,
% 1.41/1.19 (![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.41/1.19 inference(modus_ponens,[status(thm)],[998, 994])).
% 1.41/1.19 tff(1000,plain,(
% 1.41/1.19 ![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.41/1.19 inference(skolemize,[status(sab)],[999])).
% 1.41/1.19 tff(1001,plain,
% 1.41/1.19 (![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.41/1.19 inference(modus_ponens,[status(thm)],[1000, 993])).
% 1.41/1.19 tff(1002,plain,
% 1.41/1.19 (((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp18 | hskp0 | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c3_1(a132)))) <=> ((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp18 | hskp0 | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c3_1(a132)))),
% 1.41/1.19 inference(rewrite,[status(thm)],[])).
% 1.41/1.19 tff(1003,plain,
% 1.41/1.19 ((hskp18 | hskp0 | (~ndr1_0) | c0_1(a132) | (~c3_1(a132)) | (~c2_1(a132))) <=> (hskp18 | hskp0 | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c3_1(a132)))),
% 1.41/1.19 inference(rewrite,[status(thm)],[])).
% 1.41/1.19 tff(1004,plain,
% 1.41/1.19 (((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp18 | hskp0 | (~ndr1_0) | c0_1(a132) | (~c3_1(a132)) | (~c2_1(a132)))) <=> ((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp18 | hskp0 | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c3_1(a132))))),
% 1.41/1.19 inference(monotonicity,[status(thm)],[1003])).
% 1.41/1.19 tff(1005,plain,
% 1.41/1.19 (((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp18 | hskp0 | (~ndr1_0) | c0_1(a132) | (~c3_1(a132)) | (~c2_1(a132)))) <=> ((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp18 | hskp0 | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c3_1(a132)))),
% 1.41/1.19 inference(transitivity,[status(thm)],[1004, 1002])).
% 1.41/1.19 tff(1006,plain,
% 1.41/1.19 ((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp18 | hskp0 | (~ndr1_0) | c0_1(a132) | (~c3_1(a132)) | (~c2_1(a132)))),
% 1.41/1.19 inference(quant_inst,[status(thm)],[])).
% 1.41/1.19 tff(1007,plain,
% 1.41/1.19 ((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp18 | hskp0 | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c3_1(a132))),
% 1.41/1.19 inference(modus_ponens,[status(thm)],[1006, 1005])).
% 1.41/1.19 tff(1008,plain,
% 1.41/1.19 (hskp18 | hskp0 | (~c2_1(a132)) | (~c3_1(a132))),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[1007, 123, 434, 1001])).
% 1.41/1.19 tff(1009,plain,
% 1.41/1.19 (hskp18),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[1008, 991, 846, 908])).
% 1.41/1.19 tff(1010,plain,
% 1.41/1.19 (((~hskp18) | (~c1_1(a160))) <=> ((~hskp18) | (~c1_1(a160)))),
% 1.41/1.19 inference(rewrite,[status(thm)],[])).
% 1.41/1.19 tff(1011,plain,
% 1.41/1.19 (((~c1_1(a160)) | (~hskp18)) <=> ((~hskp18) | (~c1_1(a160)))),
% 1.41/1.19 inference(rewrite,[status(thm)],[])).
% 1.41/1.19 tff(1012,axiom,((~c1_1(a160)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause98')).
% 1.41/1.19 tff(1013,plain,
% 1.41/1.19 ((~hskp18) | (~c1_1(a160))),
% 1.41/1.19 inference(modus_ponens,[status(thm)],[1012, 1011])).
% 1.41/1.19 tff(1014,plain,
% 1.41/1.19 ((~hskp18) | (~c1_1(a160))),
% 1.41/1.19 inference(modus_ponens,[status(thm)],[1013, 1010])).
% 1.41/1.19 tff(1015,plain,
% 1.41/1.19 (~c1_1(a160)),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[1014, 1009])).
% 1.41/1.19 tff(1016,plain,
% 1.41/1.19 (((~hskp18) | c3_1(a160)) <=> ((~hskp18) | c3_1(a160))),
% 1.41/1.19 inference(rewrite,[status(thm)],[])).
% 1.41/1.19 tff(1017,axiom,((~hskp18) | c3_1(a160)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause60')).
% 1.41/1.19 tff(1018,plain,
% 1.41/1.19 ((~hskp18) | c3_1(a160)),
% 1.41/1.19 inference(modus_ponens,[status(thm)],[1017, 1016])).
% 1.41/1.19 tff(1019,plain,
% 1.41/1.19 ((~hskp18) | c3_1(a160)),
% 1.41/1.19 inference(modus_ponens,[status(thm)],[1018, 1016])).
% 1.41/1.19 tff(1020,plain,
% 1.41/1.19 ((~hskp18) | c3_1(a160)),
% 1.41/1.19 inference(modus_ponens,[status(thm)],[1019, 1016])).
% 1.41/1.19 tff(1021,plain,
% 1.41/1.19 ((~hskp18) | c3_1(a160)),
% 1.41/1.19 inference(modus_ponens,[status(thm)],[1020, 1016])).
% 1.41/1.19 tff(1022,plain,
% 1.41/1.19 ((~hskp18) | c3_1(a160)),
% 1.41/1.19 inference(modus_ponens,[status(thm)],[1021, 1016])).
% 1.41/1.19 tff(1023,plain,
% 1.41/1.19 ((~hskp18) | c3_1(a160)),
% 1.41/1.19 inference(modus_ponens,[status(thm)],[1022, 1016])).
% 1.41/1.19 tff(1024,plain,
% 1.41/1.19 ((~hskp18) | c3_1(a160)),
% 1.41/1.19 inference(modus_ponens,[status(thm)],[1023, 1016])).
% 1.41/1.19 tff(1025,plain,
% 1.41/1.19 ((~hskp18) | c3_1(a160)),
% 1.41/1.19 inference(modus_ponens,[status(thm)],[1024, 1016])).
% 1.41/1.19 tff(1026,plain,
% 1.41/1.19 (c3_1(a160)),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[1025, 1009])).
% 1.41/1.19 tff(1027,plain,
% 1.41/1.19 (((~![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp0 | c1_1(a160) | (~ndr1_0) | (~c3_1(a160)) | (~c0_1(a160)))) <=> ((~![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp7 | hskp0 | c1_1(a160) | (~ndr1_0) | (~c3_1(a160)) | (~c0_1(a160)))),
% 1.41/1.19 inference(rewrite,[status(thm)],[])).
% 1.41/1.19 tff(1028,plain,
% 1.41/1.19 ((hskp7 | hskp0 | (~ndr1_0) | c1_1(a160) | (~c3_1(a160)) | (~c0_1(a160))) <=> (hskp7 | hskp0 | c1_1(a160) | (~ndr1_0) | (~c3_1(a160)) | (~c0_1(a160)))),
% 1.41/1.19 inference(rewrite,[status(thm)],[])).
% 1.41/1.19 tff(1029,plain,
% 1.41/1.19 (((~![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp0 | (~ndr1_0) | c1_1(a160) | (~c3_1(a160)) | (~c0_1(a160)))) <=> ((~![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp0 | c1_1(a160) | (~ndr1_0) | (~c3_1(a160)) | (~c0_1(a160))))),
% 1.41/1.19 inference(monotonicity,[status(thm)],[1028])).
% 1.41/1.19 tff(1030,plain,
% 1.41/1.19 (((~![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp0 | (~ndr1_0) | c1_1(a160) | (~c3_1(a160)) | (~c0_1(a160)))) <=> ((~![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp7 | hskp0 | c1_1(a160) | (~ndr1_0) | (~c3_1(a160)) | (~c0_1(a160)))),
% 1.41/1.19 inference(transitivity,[status(thm)],[1029, 1027])).
% 1.41/1.19 tff(1031,plain,
% 1.41/1.19 ((~![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp0 | (~ndr1_0) | c1_1(a160) | (~c3_1(a160)) | (~c0_1(a160)))),
% 1.41/1.19 inference(quant_inst,[status(thm)],[])).
% 1.41/1.19 tff(1032,plain,
% 1.41/1.19 ((~![U: $i] : (hskp7 | hskp0 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp7 | hskp0 | c1_1(a160) | (~ndr1_0) | (~c3_1(a160)) | (~c0_1(a160))),
% 1.41/1.19 inference(modus_ponens,[status(thm)],[1031, 1030])).
% 1.41/1.19 tff(1033,plain,
% 1.41/1.19 (~c0_1(a160)),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[1032, 123, 909, 991, 1026, 1015, 179])).
% 1.41/1.19 tff(1034,plain,
% 1.41/1.19 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp0 | c0_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp0 | c0_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)))),
% 1.41/1.19 inference(rewrite,[status(thm)],[])).
% 1.41/1.19 tff(1035,plain,
% 1.41/1.19 ((hskp17 | hskp0 | (~ndr1_0) | c0_1(a132) | (~c3_1(a132)) | (~c1_1(a132))) <=> (hskp17 | hskp0 | c0_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)))),
% 1.41/1.19 inference(rewrite,[status(thm)],[])).
% 1.41/1.19 tff(1036,plain,
% 1.41/1.19 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a132) | (~c3_1(a132)) | (~c1_1(a132)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp0 | c0_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132))))),
% 1.41/1.19 inference(monotonicity,[status(thm)],[1035])).
% 1.41/1.19 tff(1037,plain,
% 1.41/1.19 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a132) | (~c3_1(a132)) | (~c1_1(a132)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp0 | c0_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)))),
% 1.41/1.19 inference(transitivity,[status(thm)],[1036, 1034])).
% 1.41/1.19 tff(1038,plain,
% 1.41/1.19 ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a132) | (~c3_1(a132)) | (~c1_1(a132)))),
% 1.41/1.19 inference(quant_inst,[status(thm)],[])).
% 1.41/1.19 tff(1039,plain,
% 1.41/1.19 ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp0 | c0_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132))),
% 1.41/1.19 inference(modus_ponens,[status(thm)],[1038, 1037])).
% 1.41/1.19 tff(1040,plain,
% 1.41/1.19 (hskp17 | hskp0 | (~c3_1(a132)) | (~c1_1(a132))),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[1039, 123, 434, 43])).
% 1.41/1.19 tff(1041,plain,
% 1.41/1.19 (~c1_1(a132)),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[1040, 11, 470, 134])).
% 1.41/1.19 tff(1042,plain,
% 1.41/1.19 (hskp18),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[1008, 11, 847, 470])).
% 1.41/1.19 tff(1043,plain,
% 1.41/1.19 (((~hskp18) | (~c2_1(a160))) <=> ((~hskp18) | (~c2_1(a160)))),
% 1.41/1.19 inference(rewrite,[status(thm)],[])).
% 1.41/1.19 tff(1044,plain,
% 1.41/1.19 (((~c2_1(a160)) | (~hskp18)) <=> ((~hskp18) | (~c2_1(a160)))),
% 1.41/1.19 inference(rewrite,[status(thm)],[])).
% 1.41/1.19 tff(1045,axiom,((~c2_1(a160)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause99')).
% 1.41/1.19 tff(1046,plain,
% 1.41/1.19 ((~hskp18) | (~c2_1(a160))),
% 1.41/1.19 inference(modus_ponens,[status(thm)],[1045, 1044])).
% 1.41/1.19 tff(1047,plain,
% 1.41/1.19 ((~hskp18) | (~c2_1(a160))),
% 1.41/1.19 inference(modus_ponens,[status(thm)],[1046, 1043])).
% 1.41/1.19 tff(1048,plain,
% 1.41/1.19 (~c2_1(a160)),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[1047, 1042])).
% 1.41/1.19 tff(1049,plain,
% 1.41/1.19 (~c1_1(a160)),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[1014, 1042])).
% 1.41/1.19 tff(1050,plain,
% 1.41/1.19 (c3_1(a160)),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[1025, 1042])).
% 1.41/1.19 tff(1051,plain,
% 1.41/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a160) | c2_1(a160) | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c3_1(a160)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a160) | c2_1(a160) | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c3_1(a160)))),
% 1.41/1.19 inference(rewrite,[status(thm)],[])).
% 1.41/1.19 tff(1052,plain,
% 1.41/1.19 (((~ndr1_0) | c1_1(a132) | (~c3_1(a132)) | (~c2_1(a132)) | c2_1(a160) | c1_1(a160) | (~c3_1(a160)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132))) <=> (c1_1(a160) | c2_1(a160) | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c3_1(a160)))),
% 1.41/1.19 inference(rewrite,[status(thm)],[])).
% 1.41/1.19 tff(1053,plain,
% 1.41/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a132) | (~c3_1(a132)) | (~c2_1(a132)) | c2_1(a160) | c1_1(a160) | (~c3_1(a160)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a160) | c2_1(a160) | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c3_1(a160))))),
% 1.41/1.19 inference(monotonicity,[status(thm)],[1052])).
% 1.41/1.19 tff(1054,plain,
% 1.41/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a132) | (~c3_1(a132)) | (~c2_1(a132)) | c2_1(a160) | c1_1(a160) | (~c3_1(a160)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a160) | c2_1(a160) | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c3_1(a160)))),
% 1.41/1.19 inference(transitivity,[status(thm)],[1053, 1051])).
% 1.41/1.19 tff(1055,plain,
% 1.41/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a132) | (~c3_1(a132)) | (~c2_1(a132)) | c2_1(a160) | c1_1(a160) | (~c3_1(a160)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))),
% 1.41/1.19 inference(quant_inst,[status(thm)],[])).
% 1.41/1.19 tff(1056,plain,
% 1.41/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a160) | c2_1(a160) | c0_1(a132) | (~c2_1(a132)) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c3_1(a160))),
% 1.41/1.19 inference(modus_ponens,[status(thm)],[1055, 1054])).
% 1.41/1.19 tff(1057,plain,
% 1.41/1.19 ($false),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[1056, 123, 1050, 470, 1049, 1048, 434, 847, 144, 1041])).
% 1.41/1.19 tff(1058,plain,(hskp0 | (~c3_1(a132)) | c0_1(a132) | (~c2_1(a132)) | hskp17), inference(lemma,lemma(discharge,[]))).
% 1.41/1.19 tff(1059,plain,
% 1.41/1.19 (hskp17),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[1058, 991, 434, 846, 908])).
% 1.41/1.19 tff(1060,plain,
% 1.41/1.19 (~c2_1(a155)),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[382, 1059])).
% 1.41/1.19 tff(1061,plain,
% 1.41/1.19 (~c0_1(a155)),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[388, 1059])).
% 1.41/1.19 tff(1062,plain,
% 1.41/1.19 (~c2_1(a160)),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[1047, 1009])).
% 1.41/1.19 tff(1063,plain,
% 1.41/1.19 (c1_1(a155)),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[416, 1059])).
% 1.41/1.19 tff(1064,plain,
% 1.41/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a160) | c2_1(a160) | c0_1(a155) | c2_1(a155) | (~ndr1_0) | (~c1_1(a155)) | (~c3_1(a160)) | c0_1(a160))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a160) | c2_1(a160) | c0_1(a155) | c2_1(a155) | (~ndr1_0) | (~c1_1(a155)) | (~c3_1(a160)) | c0_1(a160))),
% 1.41/1.19 inference(rewrite,[status(thm)],[])).
% 1.41/1.19 tff(1065,plain,
% 1.41/1.19 (((~ndr1_0) | c2_1(a160) | c0_1(a160) | (~c3_1(a160)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)) | c2_1(a160) | c1_1(a160) | c0_1(a160)) <=> (c1_1(a160) | c2_1(a160) | c0_1(a155) | c2_1(a155) | (~ndr1_0) | (~c1_1(a155)) | (~c3_1(a160)) | c0_1(a160))),
% 1.41/1.19 inference(rewrite,[status(thm)],[])).
% 1.41/1.19 tff(1066,plain,
% 1.41/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a160) | c0_1(a160) | (~c3_1(a160)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)) | c2_1(a160) | c1_1(a160) | c0_1(a160))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a160) | c2_1(a160) | c0_1(a155) | c2_1(a155) | (~ndr1_0) | (~c1_1(a155)) | (~c3_1(a160)) | c0_1(a160)))),
% 1.41/1.19 inference(monotonicity,[status(thm)],[1065])).
% 1.41/1.19 tff(1067,plain,
% 1.41/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a160) | c0_1(a160) | (~c3_1(a160)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)) | c2_1(a160) | c1_1(a160) | c0_1(a160))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a160) | c2_1(a160) | c0_1(a155) | c2_1(a155) | (~ndr1_0) | (~c1_1(a155)) | (~c3_1(a160)) | c0_1(a160))),
% 1.41/1.19 inference(transitivity,[status(thm)],[1066, 1064])).
% 1.41/1.19 tff(1068,plain,
% 1.41/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a160) | c0_1(a160) | (~c3_1(a160)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)) | c2_1(a160) | c1_1(a160) | c0_1(a160))),
% 1.41/1.19 inference(quant_inst,[status(thm)],[])).
% 1.41/1.19 tff(1069,plain,
% 1.41/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a160) | c2_1(a160) | c0_1(a155) | c2_1(a155) | (~ndr1_0) | (~c1_1(a155)) | (~c3_1(a160)) | c0_1(a160)),
% 1.41/1.19 inference(modus_ponens,[status(thm)],[1068, 1067])).
% 1.41/1.19 tff(1070,plain,
% 1.41/1.19 ($false),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[1069, 123, 1026, 1063, 1015, 1062, 1061, 1060, 406, 1033])).
% 1.41/1.19 tff(1071,plain,(c0_1(a132) | hskp9 | hskp30 | c0_1(a125) | c3_1(a124)), inference(lemma,lemma(discharge,[]))).
% 1.41/1.19 tff(1072,plain,
% 1.41/1.19 (c3_1(a124)),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[1071, 433, 54, 33, 432])).
% 1.41/1.19 tff(1073,plain,
% 1.41/1.19 (((~hskp1) | (~c3_1(a124))) <=> ((~hskp1) | (~c3_1(a124)))),
% 1.41/1.19 inference(rewrite,[status(thm)],[])).
% 1.41/1.19 tff(1074,plain,
% 1.41/1.19 (((~c3_1(a124)) | (~hskp1)) <=> ((~hskp1) | (~c3_1(a124)))),
% 1.41/1.19 inference(rewrite,[status(thm)],[])).
% 1.41/1.19 tff(1075,axiom,((~c3_1(a124)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause128')).
% 1.41/1.19 tff(1076,plain,
% 1.41/1.19 ((~hskp1) | (~c3_1(a124))),
% 1.41/1.19 inference(modus_ponens,[status(thm)],[1075, 1074])).
% 1.41/1.19 tff(1077,plain,
% 1.41/1.19 ((~hskp1) | (~c3_1(a124))),
% 1.41/1.19 inference(modus_ponens,[status(thm)],[1076, 1073])).
% 1.41/1.19 tff(1078,plain,
% 1.41/1.19 (~hskp1),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[1077, 1072])).
% 1.41/1.19 tff(1079,plain,
% 1.41/1.19 (hskp2),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[812, 1078])).
% 1.41/1.19 tff(1080,plain,
% 1.41/1.19 (c3_1(a132)),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[447, 426])).
% 1.41/1.19 tff(1081,plain,
% 1.41/1.19 (~c2_1(a132)),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[898, 426])).
% 1.41/1.19 tff(1082,plain,
% 1.41/1.19 (~c1_1(a132)),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[464, 123, 1080, 432, 1081, 84, 78, 72, 406])).
% 1.41/1.19 tff(1083,plain,
% 1.41/1.19 (~hskp17),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[479, 1082, 432, 1081, 1080])).
% 1.41/1.19 tff(1084,plain,
% 1.41/1.19 (~hskp0),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[608, 1082, 432, 1081, 1080, 54])).
% 1.41/1.19 tff(1085,plain,
% 1.41/1.19 (c1_1(a125)),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[681, 1079])).
% 1.41/1.19 tff(1086,plain,
% 1.41/1.19 (~c3_1(a125)),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[688, 123, 1083, 1084, 1085, 433, 43])).
% 1.41/1.19 tff(1087,plain,
% 1.41/1.19 (c2_1(a125)),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[700, 1079])).
% 1.41/1.19 tff(1088,plain,
% 1.41/1.19 (hskp22),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[707, 123, 1085, 1087, 643, 1086])).
% 1.41/1.19 tff(1089,plain,
% 1.41/1.19 (~c1_1(a176)),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[721, 1088])).
% 1.41/1.19 tff(1090,plain,
% 1.41/1.19 (~c2_1(a176)),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[715, 1088])).
% 1.41/1.19 tff(1091,plain,
% 1.41/1.19 ($false),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[810, 1090, 1089, 1081, 1084, 1080, 1083, 433, 432, 1079])).
% 1.41/1.19 tff(1092,plain,(c0_1(a125) | hskp30 | hskp9), inference(lemma,lemma(discharge,[]))).
% 1.41/1.19 tff(1093,plain,
% 1.41/1.19 (c0_1(a125)),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[1092, 54, 33])).
% 1.41/1.19 tff(1094,plain,
% 1.41/1.19 (((~hskp2) | (~c0_1(a125))) <=> ((~hskp2) | (~c0_1(a125)))),
% 1.41/1.19 inference(rewrite,[status(thm)],[])).
% 1.41/1.19 tff(1095,plain,
% 1.41/1.19 (((~c0_1(a125)) | (~hskp2)) <=> ((~hskp2) | (~c0_1(a125)))),
% 1.41/1.19 inference(rewrite,[status(thm)],[])).
% 1.41/1.19 tff(1096,axiom,((~c0_1(a125)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause127')).
% 1.41/1.19 tff(1097,plain,
% 1.41/1.19 ((~hskp2) | (~c0_1(a125))),
% 1.41/1.19 inference(modus_ponens,[status(thm)],[1096, 1095])).
% 1.41/1.19 tff(1098,plain,
% 1.41/1.19 ((~hskp2) | (~c0_1(a125))),
% 1.41/1.19 inference(modus_ponens,[status(thm)],[1097, 1094])).
% 1.41/1.19 tff(1099,plain,
% 1.41/1.19 (~hskp2),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[1098, 1093])).
% 1.41/1.19 tff(1100,plain,
% 1.41/1.19 (hskp1),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[812, 1099])).
% 1.41/1.19 tff(1101,plain,
% 1.41/1.19 (~c3_1(a124)),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[1077, 1100])).
% 1.41/1.19 tff(1102,plain,
% 1.41/1.19 (hskp22),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[652, 1100, 1101])).
% 1.41/1.19 tff(1103,plain,
% 1.41/1.19 (~c2_1(a176)),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[715, 1102])).
% 1.41/1.19 tff(1104,plain,
% 1.41/1.19 (~c1_1(a176)),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[721, 1102])).
% 1.41/1.19 tff(1105,plain,
% 1.41/1.19 (c0_1(a176)),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[732, 1102])).
% 1.41/1.19 tff(1106,plain,
% 1.41/1.19 (hskp19),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[739, 123, 1083, 1105, 1104, 1103, 53])).
% 1.41/1.19 tff(1107,plain,
% 1.41/1.19 (c3_1(a164)),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[261, 1106])).
% 1.41/1.19 tff(1108,plain,
% 1.41/1.19 (c1_1(a164)),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[272, 1106])).
% 1.41/1.19 tff(1109,plain,
% 1.41/1.19 (c0_1(a164)),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[748, 123, 1083, 1084, 1108, 1107, 43])).
% 1.41/1.19 tff(1110,plain,
% 1.41/1.19 (~c2_1(a164)),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[250, 1106])).
% 1.41/1.19 tff(1111,plain,
% 1.41/1.19 (hskp13),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[776, 123, 1083, 1108, 1107, 1110, 769])).
% 1.41/1.19 tff(1112,plain,
% 1.41/1.19 (~c1_1(a143)),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[782, 1111])).
% 1.41/1.19 tff(1113,plain,
% 1.41/1.19 (c2_1(a124)),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[632, 1100])).
% 1.41/1.19 tff(1114,plain,
% 1.41/1.19 (c1_1(a124)),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[621, 1100])).
% 1.41/1.19 tff(1115,plain,
% 1.41/1.19 (c3_1(a143)),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[825, 1111])).
% 1.41/1.19 tff(1116,plain,
% 1.41/1.19 (c2_1(a143)),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[836, 1111])).
% 1.41/1.19 tff(1117,plain,
% 1.41/1.19 ($false),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[843, 123, 1108, 1107, 1116, 1115, 1114, 1113, 1112, 1101, 759, 1109])).
% 1.41/1.19 tff(1118,plain,(hskp30 | hskp9), inference(lemma,lemma(discharge,[]))).
% 1.41/1.19 tff(1119,plain,
% 1.41/1.19 (hskp30),
% 1.41/1.19 inference(unit_resolution,[status(thm)],[1118, 33])).
% 1.41/1.19 tff(1120,plain,
% 1.41/1.19 (((~hskp30) | c0_1(a167)) <=> ((~hskp30) | c0_1(a167))),
% 1.41/1.19 inference(rewrite,[status(thm)],[])).
% 1.41/1.19 tff(1121,axiom,((~hskp30) | c0_1(a167)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause38')).
% 1.41/1.19 tff(1122,plain,
% 1.41/1.19 ((~hskp30) | c0_1(a167)),
% 1.41/1.19 inference(modus_ponens,[status(thm)],[1121, 1120])).
% 1.41/1.19 tff(1123,plain,
% 1.41/1.19 ((~hskp30) | c0_1(a167)),
% 1.41/1.19 inference(modus_ponens,[status(thm)],[1122, 1120])).
% 1.41/1.19 tff(1124,plain,
% 1.41/1.19 ((~hskp30) | c0_1(a167)),
% 1.41/1.19 inference(modus_ponens,[status(thm)],[1123, 1120])).
% 1.41/1.19 tff(1125,plain,
% 1.41/1.19 ((~hskp30) | c0_1(a167)),
% 1.41/1.19 inference(modus_ponens,[status(thm)],[1124, 1120])).
% 1.41/1.19 tff(1126,plain,
% 1.41/1.19 ((~hskp30) | c0_1(a167)),
% 1.41/1.19 inference(modus_ponens,[status(thm)],[1125, 1120])).
% 1.41/1.19 tff(1127,plain,
% 1.41/1.19 ((~hskp30) | c0_1(a167)),
% 1.41/1.19 inference(modus_ponens,[status(thm)],[1126, 1120])).
% 1.41/1.20 tff(1128,plain,
% 1.41/1.20 ((~hskp30) | c0_1(a167)),
% 1.41/1.20 inference(modus_ponens,[status(thm)],[1127, 1120])).
% 1.41/1.20 tff(1129,plain,
% 1.41/1.20 ((~hskp30) | c0_1(a167)),
% 1.41/1.20 inference(modus_ponens,[status(thm)],[1128, 1120])).
% 1.41/1.20 tff(1130,plain,
% 1.41/1.20 (c0_1(a167)),
% 1.41/1.20 inference(unit_resolution,[status(thm)],[1129, 1119])).
% 1.41/1.20 tff(1131,plain,
% 1.41/1.20 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) <=> (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))))),
% 1.41/1.20 inference(bind,[status(th)],[])).
% 1.41/1.20 tff(1132,plain,
% 1.41/1.20 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.41/1.20 inference(quant_intro,[status(thm)],[1131])).
% 1.41/1.20 tff(1133,plain,
% 1.41/1.20 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.41/1.20 inference(rewrite,[status(thm)],[])).
% 1.41/1.20 tff(1134,plain,
% 1.41/1.20 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp9) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) | hskp9))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))))),
% 1.41/1.20 inference(bind,[status(th)],[])).
% 1.41/1.20 tff(1135,plain,
% 1.41/1.20 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.41/1.20 inference(quant_intro,[status(thm)],[1134])).
% 1.41/1.20 tff(1136,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause184')).
% 1.41/1.20 tff(1137,plain,
% 1.41/1.20 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.41/1.20 inference(modus_ponens,[status(thm)],[1136, 1135])).
% 1.41/1.20 tff(1138,plain,
% 1.41/1.20 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.41/1.20 inference(modus_ponens,[status(thm)],[1137, 1133])).
% 1.41/1.20 tff(1139,plain,(
% 1.41/1.20 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.41/1.20 inference(skolemize,[status(sab)],[1138])).
% 1.41/1.20 tff(1140,plain,
% 1.41/1.20 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.41/1.20 inference(modus_ponens,[status(thm)],[1139, 1132])).
% 1.41/1.20 tff(1141,plain,
% 1.41/1.20 (^[U: $i] : refl((hskp21 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp21 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 1.41/1.20 inference(bind,[status(th)],[])).
% 1.41/1.20 tff(1142,plain,
% 1.41/1.20 (![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.41/1.20 inference(quant_intro,[status(thm)],[1141])).
% 1.41/1.20 tff(1143,plain,
% 1.41/1.20 (![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.41/1.20 inference(rewrite,[status(thm)],[])).
% 1.41/1.20 tff(1144,plain,
% 1.41/1.20 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp21) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp21))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp21) <=> (hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp21) <=> (hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp21) | hskp6) <=> ((hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp6))), rewrite(((hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp6) <=> (hskp21 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp21) | hskp6) <=> (hskp21 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 1.41/1.20 inference(bind,[status(th)],[])).
% 1.41/1.20 tff(1145,plain,
% 1.41/1.20 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp21) | hskp6) <=> ![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.41/1.20 inference(quant_intro,[status(thm)],[1144])).
% 1.41/1.20 tff(1146,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp21) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause147')).
% 1.41/1.20 tff(1147,plain,
% 1.41/1.20 (![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.41/1.20 inference(modus_ponens,[status(thm)],[1146, 1145])).
% 1.41/1.20 tff(1148,plain,
% 1.41/1.20 (![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.41/1.20 inference(modus_ponens,[status(thm)],[1147, 1143])).
% 1.41/1.20 tff(1149,plain,(
% 1.41/1.20 ![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.41/1.20 inference(skolemize,[status(sab)],[1148])).
% 1.41/1.20 tff(1150,plain,
% 1.41/1.20 (![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.41/1.20 inference(modus_ponens,[status(thm)],[1149, 1142])).
% 1.41/1.20 tff(1151,plain,
% 1.41/1.20 (^[V: $i, U: $i] : refl((hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 1.41/1.20 inference(bind,[status(th)],[])).
% 1.41/1.20 tff(1152,plain,
% 1.41/1.20 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.41/1.20 inference(quant_intro,[status(thm)],[1151])).
% 1.41/1.20 tff(1153,plain,
% 1.41/1.20 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.41/1.20 inference(rewrite,[status(thm)],[])).
% 1.41/1.20 tff(1154,plain,
% 1.41/1.20 (^[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))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp13) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp13))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp13) <=> (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 1.41/1.20 inference(bind,[status(th)],[])).
% 1.41/1.20 tff(1155,plain,
% 1.41/1.20 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp13) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.41/1.20 inference(quant_intro,[status(thm)],[1154])).
% 1.41/1.20 tff(1156,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause174')).
% 1.41/1.20 tff(1157,plain,
% 1.41/1.20 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.41/1.20 inference(modus_ponens,[status(thm)],[1156, 1155])).
% 1.41/1.20 tff(1158,plain,
% 1.41/1.20 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.41/1.20 inference(modus_ponens,[status(thm)],[1157, 1153])).
% 1.41/1.20 tff(1159,plain,(
% 1.41/1.20 ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.41/1.20 inference(skolemize,[status(sab)],[1158])).
% 1.41/1.20 tff(1160,plain,
% 1.41/1.20 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.41/1.20 inference(modus_ponens,[status(thm)],[1159, 1152])).
% 1.41/1.20 tff(1161,plain,
% 1.41/1.20 (hskp7),
% 1.41/1.20 inference(unit_resolution,[status(thm)],[425, 97, 132, 95, 33])).
% 1.41/1.20 tff(1162,plain,
% 1.41/1.20 (~c2_1(a132)),
% 1.41/1.20 inference(unit_resolution,[status(thm)],[898, 1161])).
% 1.41/1.20 tff(1163,plain,
% 1.41/1.20 (~c0_1(a132)),
% 1.41/1.20 inference(unit_resolution,[status(thm)],[431, 1161])).
% 1.41/1.20 tff(1164,plain,
% 1.41/1.20 (c3_1(a132)),
% 1.41/1.20 inference(unit_resolution,[status(thm)],[447, 1161])).
% 1.41/1.20 tff(1165,plain,
% 1.41/1.20 (~c1_1(a132)),
% 1.41/1.20 inference(unit_resolution,[status(thm)],[464, 123, 1164, 1163, 1162, 97, 132, 95, 406])).
% 1.41/1.20 tff(1166,plain,
% 1.41/1.20 (((~hskp30) | c3_1(a167)) <=> ((~hskp30) | c3_1(a167))),
% 1.41/1.20 inference(rewrite,[status(thm)],[])).
% 1.41/1.20 tff(1167,axiom,((~hskp30) | c3_1(a167)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause40')).
% 1.41/1.20 tff(1168,plain,
% 1.41/1.20 ((~hskp30) | c3_1(a167)),
% 1.41/1.20 inference(modus_ponens,[status(thm)],[1167, 1166])).
% 1.41/1.20 tff(1169,plain,
% 1.41/1.20 ((~hskp30) | c3_1(a167)),
% 1.41/1.20 inference(modus_ponens,[status(thm)],[1168, 1166])).
% 1.41/1.20 tff(1170,plain,
% 1.41/1.20 ((~hskp30) | c3_1(a167)),
% 1.41/1.20 inference(modus_ponens,[status(thm)],[1169, 1166])).
% 1.41/1.20 tff(1171,plain,
% 1.41/1.20 ((~hskp30) | c3_1(a167)),
% 1.41/1.20 inference(modus_ponens,[status(thm)],[1170, 1166])).
% 1.41/1.20 tff(1172,plain,
% 1.41/1.20 ((~hskp30) | c3_1(a167)),
% 1.41/1.20 inference(modus_ponens,[status(thm)],[1171, 1166])).
% 1.41/1.20 tff(1173,plain,
% 1.41/1.20 ((~hskp30) | c3_1(a167)),
% 1.41/1.20 inference(modus_ponens,[status(thm)],[1172, 1166])).
% 1.41/1.20 tff(1174,plain,
% 1.41/1.20 ((~hskp30) | c3_1(a167)),
% 1.41/1.20 inference(modus_ponens,[status(thm)],[1173, 1166])).
% 1.41/1.20 tff(1175,plain,
% 1.41/1.20 ((~hskp30) | c3_1(a167)),
% 1.41/1.20 inference(modus_ponens,[status(thm)],[1174, 1166])).
% 1.41/1.20 tff(1176,plain,
% 1.41/1.20 (c3_1(a167)),
% 1.41/1.20 inference(unit_resolution,[status(thm)],[1175, 1119])).
% 1.41/1.20 tff(1177,plain,
% 1.41/1.20 (((~hskp30) | c1_1(a167)) <=> ((~hskp30) | c1_1(a167))),
% 1.41/1.20 inference(rewrite,[status(thm)],[])).
% 1.41/1.20 tff(1178,axiom,((~hskp30) | c1_1(a167)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause39')).
% 1.41/1.20 tff(1179,plain,
% 1.41/1.20 ((~hskp30) | c1_1(a167)),
% 1.41/1.20 inference(modus_ponens,[status(thm)],[1178, 1177])).
% 1.41/1.20 tff(1180,plain,
% 1.41/1.20 ((~hskp30) | c1_1(a167)),
% 1.41/1.20 inference(modus_ponens,[status(thm)],[1179, 1177])).
% 1.41/1.20 tff(1181,plain,
% 1.41/1.20 ((~hskp30) | c1_1(a167)),
% 1.41/1.20 inference(modus_ponens,[status(thm)],[1180, 1177])).
% 1.41/1.20 tff(1182,plain,
% 1.41/1.20 ((~hskp30) | c1_1(a167)),
% 1.41/1.20 inference(modus_ponens,[status(thm)],[1181, 1177])).
% 1.41/1.20 tff(1183,plain,
% 1.41/1.20 ((~hskp30) | c1_1(a167)),
% 1.41/1.20 inference(modus_ponens,[status(thm)],[1182, 1177])).
% 1.41/1.20 tff(1184,plain,
% 1.41/1.20 ((~hskp30) | c1_1(a167)),
% 1.41/1.20 inference(modus_ponens,[status(thm)],[1183, 1177])).
% 1.41/1.20 tff(1185,plain,
% 1.41/1.20 ((~hskp30) | c1_1(a167)),
% 1.41/1.20 inference(modus_ponens,[status(thm)],[1184, 1177])).
% 1.41/1.20 tff(1186,plain,
% 1.41/1.20 ((~hskp30) | c1_1(a167)),
% 1.41/1.20 inference(modus_ponens,[status(thm)],[1185, 1177])).
% 1.41/1.20 tff(1187,plain,
% 1.41/1.20 (c1_1(a167)),
% 1.41/1.20 inference(unit_resolution,[status(thm)],[1186, 1119])).
% 1.41/1.20 tff(1188,plain,
% 1.41/1.20 (~hskp17),
% 1.41/1.20 inference(unit_resolution,[status(thm)],[479, 1165, 1163, 1162, 1164])).
% 1.41/1.20 tff(1189,assumption,(~hskp2), introduced(assumption)).
% 1.41/1.20 tff(1190,plain,
% 1.41/1.20 (hskp2 | hskp1 | c0_1(a131) | c1_1(a131)),
% 1.41/1.20 inference(unit_resolution,[status(thm)],[669, 123, 95, 663])).
% 1.41/1.20 tff(1191,plain,
% 1.41/1.20 (hskp1),
% 1.41/1.20 inference(unit_resolution,[status(thm)],[1190, 1189, 97, 132])).
% 1.41/1.20 tff(1192,plain,
% 1.41/1.20 (~c3_1(a124)),
% 1.41/1.20 inference(unit_resolution,[status(thm)],[1077, 1191])).
% 1.41/1.20 tff(1193,plain,
% 1.41/1.20 (^[U: $i] : refl((hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 1.41/1.20 inference(bind,[status(th)],[])).
% 1.41/1.20 tff(1194,plain,
% 1.41/1.20 (![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.41/1.20 inference(quant_intro,[status(thm)],[1193])).
% 1.41/1.20 tff(1195,plain,
% 1.41/1.20 (![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.41/1.20 inference(rewrite,[status(thm)],[])).
% 1.41/1.20 tff(1196,plain,
% 1.41/1.20 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp2) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp2))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp2) <=> (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp2) <=> (hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp2) | hskp19) <=> ((hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp19))), rewrite(((hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp19) <=> (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp2) | hskp19) <=> (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 1.41/1.20 inference(bind,[status(th)],[])).
% 1.41/1.20 tff(1197,plain,
% 1.41/1.20 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp2) | hskp19) <=> ![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.41/1.20 inference(quant_intro,[status(thm)],[1196])).
% 1.41/1.20 tff(1198,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp2) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause165')).
% 1.41/1.20 tff(1199,plain,
% 1.41/1.20 (![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.41/1.20 inference(modus_ponens,[status(thm)],[1198, 1197])).
% 1.41/1.20 tff(1200,plain,
% 1.41/1.20 (![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.41/1.20 inference(modus_ponens,[status(thm)],[1199, 1195])).
% 1.41/1.20 tff(1201,plain,(
% 1.41/1.20 ![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.41/1.20 inference(skolemize,[status(sab)],[1200])).
% 1.41/1.20 tff(1202,plain,
% 1.41/1.20 (![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.41/1.20 inference(modus_ponens,[status(thm)],[1201, 1194])).
% 1.41/1.20 tff(1203,assumption,(c3_1(a167)), introduced(assumption)).
% 1.41/1.20 tff(1204,assumption,(c1_1(a167)), introduced(assumption)).
% 1.41/1.20 tff(1205,assumption,(c0_1(a167)), introduced(assumption)).
% 1.41/1.20 tff(1206,plain,
% 1.41/1.20 (((~![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c0_1(a167)))) <=> ((~![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp19 | hskp2 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c0_1(a167)))),
% 1.41/1.20 inference(rewrite,[status(thm)],[])).
% 1.41/1.20 tff(1207,plain,
% 1.41/1.20 ((~![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c0_1(a167)))),
% 1.41/1.20 inference(quant_inst,[status(thm)],[])).
% 1.41/1.20 tff(1208,plain,
% 1.41/1.20 ((~![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp19 | hskp2 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c0_1(a167))),
% 1.41/1.20 inference(modus_ponens,[status(thm)],[1207, 1206])).
% 1.41/1.20 tff(1209,plain,
% 1.41/1.20 (hskp19 | hskp2),
% 1.41/1.20 inference(unit_resolution,[status(thm)],[1208, 123, 1205, 1204, 1203, 1202])).
% 1.41/1.20 tff(1210,plain,
% 1.41/1.20 (hskp19),
% 1.41/1.20 inference(unit_resolution,[status(thm)],[1209, 1189])).
% 1.41/1.20 tff(1211,plain,
% 1.41/1.20 (~c2_1(a164)),
% 1.41/1.20 inference(unit_resolution,[status(thm)],[250, 1210])).
% 1.41/1.20 tff(1212,plain,
% 1.41/1.20 (c3_1(a164)),
% 1.41/1.20 inference(unit_resolution,[status(thm)],[261, 1210])).
% 1.41/1.20 tff(1213,plain,
% 1.41/1.20 (c1_1(a164)),
% 1.41/1.20 inference(unit_resolution,[status(thm)],[272, 1210])).
% 1.41/1.20 tff(1214,plain,
% 1.41/1.20 (hskp13),
% 1.41/1.20 inference(unit_resolution,[status(thm)],[776, 123, 134, 1213, 1212, 1211, 769])).
% 1.41/1.20 tff(1215,plain,
% 1.41/1.20 (~c1_1(a143)),
% 1.41/1.20 inference(unit_resolution,[status(thm)],[782, 1214])).
% 1.41/1.20 tff(1216,plain,
% 1.41/1.20 (c2_1(a124)),
% 1.41/1.20 inference(unit_resolution,[status(thm)],[632, 1191])).
% 1.41/1.20 tff(1217,plain,
% 1.41/1.20 (c1_1(a124)),
% 1.41/1.20 inference(unit_resolution,[status(thm)],[621, 1191])).
% 1.41/1.20 tff(1218,plain,
% 1.41/1.20 (c3_1(a143)),
% 1.41/1.20 inference(unit_resolution,[status(thm)],[825, 1214])).
% 1.41/1.20 tff(1219,plain,
% 1.41/1.20 (c2_1(a143)),
% 1.41/1.20 inference(unit_resolution,[status(thm)],[836, 1214])).
% 1.41/1.20 tff(1220,plain,
% 1.41/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a143) | c3_1(a124) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a124)) | (~c1_1(a124)) | (~c2_1(a143)) | (~c3_1(a143)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a143) | c3_1(a124) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a124)) | (~c1_1(a124)) | (~c2_1(a143)) | (~c3_1(a143)))),
% 1.41/1.20 inference(rewrite,[status(thm)],[])).
% 1.41/1.20 tff(1221,plain,
% 1.41/1.20 (((~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c0_1(a167)) | c3_1(a124) | (~c2_1(a124)) | (~c1_1(a124)) | c1_1(a143) | (~c3_1(a143)) | (~c2_1(a143))) <=> (c1_1(a143) | c3_1(a124) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a124)) | (~c1_1(a124)) | (~c2_1(a143)) | (~c3_1(a143)))),
% 1.41/1.20 inference(rewrite,[status(thm)],[])).
% 1.41/1.20 tff(1222,plain,
% 1.41/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c0_1(a167)) | c3_1(a124) | (~c2_1(a124)) | (~c1_1(a124)) | c1_1(a143) | (~c3_1(a143)) | (~c2_1(a143)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a143) | c3_1(a124) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a124)) | (~c1_1(a124)) | (~c2_1(a143)) | (~c3_1(a143))))),
% 1.41/1.20 inference(monotonicity,[status(thm)],[1221])).
% 1.41/1.20 tff(1223,plain,
% 1.41/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c0_1(a167)) | c3_1(a124) | (~c2_1(a124)) | (~c1_1(a124)) | c1_1(a143) | (~c3_1(a143)) | (~c2_1(a143)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a143) | c3_1(a124) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a124)) | (~c1_1(a124)) | (~c2_1(a143)) | (~c3_1(a143)))),
% 1.41/1.20 inference(transitivity,[status(thm)],[1222, 1220])).
% 1.41/1.20 tff(1224,plain,
% 1.41/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c0_1(a167)) | c3_1(a124) | (~c2_1(a124)) | (~c1_1(a124)) | c1_1(a143) | (~c3_1(a143)) | (~c2_1(a143)))),
% 1.41/1.20 inference(quant_inst,[status(thm)],[])).
% 1.41/1.20 tff(1225,plain,
% 1.41/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a143) | c3_1(a124) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a124)) | (~c1_1(a124)) | (~c2_1(a143)) | (~c3_1(a143))),
% 1.41/1.20 inference(modus_ponens,[status(thm)],[1224, 1223])).
% 1.41/1.20 tff(1226,plain,
% 1.41/1.20 ($false),
% 1.41/1.20 inference(unit_resolution,[status(thm)],[1225, 123, 1205, 1204, 1203, 1219, 1218, 1217, 1216, 1215, 1192, 759])).
% 1.41/1.20 tff(1227,plain,(hskp2 | (~c0_1(a167)) | (~c1_1(a167)) | (~c3_1(a167)) | hskp17 | c0_1(a131) | c1_1(a131) | c2_1(a131)), inference(lemma,lemma(discharge,[]))).
% 1.41/1.20 tff(1228,plain,
% 1.41/1.20 (hskp2),
% 1.41/1.20 inference(unit_resolution,[status(thm)],[1227, 1188, 1187, 1176, 1130, 97, 132, 95])).
% 1.41/1.20 tff(1229,plain,
% 1.41/1.20 (~c0_1(a125)),
% 1.41/1.20 inference(unit_resolution,[status(thm)],[1098, 1228])).
% 1.41/1.20 tff(1230,plain,
% 1.41/1.20 (~hskp17),
% 1.41/1.20 inference(unit_resolution,[status(thm)],[479, 466, 434, 436, 470])).
% 1.41/1.20 tff(1231,plain,
% 1.41/1.20 ((~c1_1(a125)) | (~c3_1(a125))),
% 1.41/1.20 inference(unit_resolution,[status(thm)],[688, 123, 1230, 11, 433, 43])).
% 1.41/1.20 tff(1232,plain,
% 1.41/1.20 (~c3_1(a125)),
% 1.41/1.20 inference(unit_resolution,[status(thm)],[1231, 785])).
% 1.41/1.20 tff(1233,plain,
% 1.41/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a132) | c0_1(a125) | (~ndr1_0) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | (~c2_1(a125)) | c3_1(a125) | (~c3_1(a132)) | c1_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a132) | c0_1(a125) | (~ndr1_0) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | (~c2_1(a125)) | c3_1(a125) | (~c3_1(a132)) | c1_1(a132))),
% 1.41/1.20 inference(rewrite,[status(thm)],[])).
% 1.41/1.20 tff(1234,plain,
% 1.41/1.20 (((~ndr1_0) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)) | c0_1(a125) | c3_1(a125) | (~c2_1(a125))) <=> (c2_1(a132) | c0_1(a125) | (~ndr1_0) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | (~c2_1(a125)) | c3_1(a125) | (~c3_1(a132)) | c1_1(a132))),
% 1.41/1.20 inference(rewrite,[status(thm)],[])).
% 1.41/1.20 tff(1235,plain,
% 1.41/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)) | c0_1(a125) | c3_1(a125) | (~c2_1(a125)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a132) | c0_1(a125) | (~ndr1_0) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | (~c2_1(a125)) | c3_1(a125) | (~c3_1(a132)) | c1_1(a132)))),
% 1.41/1.20 inference(monotonicity,[status(thm)],[1234])).
% 1.41/1.20 tff(1236,plain,
% 1.41/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)) | c0_1(a125) | c3_1(a125) | (~c2_1(a125)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a132) | c0_1(a125) | (~ndr1_0) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | (~c2_1(a125)) | c3_1(a125) | (~c3_1(a132)) | c1_1(a132))),
% 1.41/1.20 inference(transitivity,[status(thm)],[1235, 1233])).
% 1.41/1.20 tff(1237,plain,
% 1.41/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)) | c0_1(a125) | c3_1(a125) | (~c2_1(a125)))),
% 1.41/1.20 inference(quant_inst,[status(thm)],[])).
% 1.41/1.20 tff(1238,plain,
% 1.41/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a132) | c0_1(a125) | (~ndr1_0) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | (~c2_1(a125)) | c3_1(a125) | (~c3_1(a132)) | c1_1(a132)),
% 1.41/1.20 inference(modus_ponens,[status(thm)],[1237, 1236])).
% 1.41/1.20 tff(1239,plain,
% 1.41/1.20 ((~c2_1(a167)) | (~c2_1(a125)) | c3_1(a125)),
% 1.41/1.20 inference(unit_resolution,[status(thm)],[1238, 123, 1130, 1187, 470, 436, 433, 972, 466])).
% 1.41/1.20 tff(1240,plain,
% 1.41/1.20 (~c2_1(a167)),
% 1.41/1.20 inference(unit_resolution,[status(thm)],[1239, 787, 1232])).
% 1.41/1.20 tff(1241,plain,
% 1.41/1.20 (^[U: $i] : refl((hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 1.41/1.20 inference(bind,[status(th)],[])).
% 1.41/1.20 tff(1242,plain,
% 1.41/1.20 (![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.41/1.20 inference(quant_intro,[status(thm)],[1241])).
% 1.41/1.20 tff(1243,plain,
% 1.41/1.20 (![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.41/1.20 inference(rewrite,[status(thm)],[])).
% 1.41/1.20 tff(1244,plain,
% 1.41/1.20 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp9) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp9))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp9) | hskp22) <=> ((hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp22))), rewrite(((hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp22) <=> (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp9) | hskp22) <=> (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 1.41/1.20 inference(bind,[status(th)],[])).
% 1.41/1.20 tff(1245,plain,
% 1.41/1.20 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp9) | hskp22) <=> ![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.41/1.20 inference(quant_intro,[status(thm)],[1244])).
% 1.41/1.20 tff(1246,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp9) | hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause152')).
% 1.41/1.20 tff(1247,plain,
% 1.41/1.20 (![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.41/1.20 inference(modus_ponens,[status(thm)],[1246, 1245])).
% 1.41/1.20 tff(1248,plain,
% 1.41/1.20 (![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.41/1.20 inference(modus_ponens,[status(thm)],[1247, 1243])).
% 1.41/1.20 tff(1249,plain,(
% 1.41/1.20 ![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.41/1.20 inference(skolemize,[status(sab)],[1248])).
% 1.41/1.20 tff(1250,plain,
% 1.41/1.20 (![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.41/1.20 inference(modus_ponens,[status(thm)],[1249, 1242])).
% 1.41/1.20 tff(1251,plain,
% 1.41/1.20 (((~![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp9 | (~ndr1_0) | (~c1_1(a167)) | c2_1(a167) | (~c0_1(a167)))) <=> ((~![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp22 | hskp9 | (~ndr1_0) | (~c1_1(a167)) | c2_1(a167) | (~c0_1(a167)))),
% 1.41/1.20 inference(rewrite,[status(thm)],[])).
% 1.41/1.20 tff(1252,plain,
% 1.41/1.20 ((hskp22 | hskp9 | (~ndr1_0) | c2_1(a167) | (~c1_1(a167)) | (~c0_1(a167))) <=> (hskp22 | hskp9 | (~ndr1_0) | (~c1_1(a167)) | c2_1(a167) | (~c0_1(a167)))),
% 1.41/1.20 inference(rewrite,[status(thm)],[])).
% 1.41/1.20 tff(1253,plain,
% 1.41/1.20 (((~![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp9 | (~ndr1_0) | c2_1(a167) | (~c1_1(a167)) | (~c0_1(a167)))) <=> ((~![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp9 | (~ndr1_0) | (~c1_1(a167)) | c2_1(a167) | (~c0_1(a167))))),
% 1.41/1.21 inference(monotonicity,[status(thm)],[1252])).
% 1.41/1.21 tff(1254,plain,
% 1.41/1.21 (((~![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp9 | (~ndr1_0) | c2_1(a167) | (~c1_1(a167)) | (~c0_1(a167)))) <=> ((~![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp22 | hskp9 | (~ndr1_0) | (~c1_1(a167)) | c2_1(a167) | (~c0_1(a167)))),
% 1.41/1.21 inference(transitivity,[status(thm)],[1253, 1251])).
% 1.41/1.21 tff(1255,plain,
% 1.41/1.21 ((~![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp9 | (~ndr1_0) | c2_1(a167) | (~c1_1(a167)) | (~c0_1(a167)))),
% 1.41/1.21 inference(quant_inst,[status(thm)],[])).
% 1.41/1.21 tff(1256,plain,
% 1.41/1.21 ((~![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp22 | hskp9 | (~ndr1_0) | (~c1_1(a167)) | c2_1(a167) | (~c0_1(a167))),
% 1.41/1.21 inference(modus_ponens,[status(thm)],[1255, 1254])).
% 1.41/1.21 tff(1257,plain,
% 1.41/1.21 (hskp22 | c2_1(a167)),
% 1.41/1.21 inference(unit_resolution,[status(thm)],[1256, 123, 33, 1130, 1187, 1250])).
% 1.41/1.21 tff(1258,plain,
% 1.41/1.21 (hskp22),
% 1.41/1.21 inference(unit_resolution,[status(thm)],[1257, 1240])).
% 1.41/1.21 tff(1259,plain,
% 1.41/1.21 (~c1_1(a176)),
% 1.41/1.21 inference(unit_resolution,[status(thm)],[721, 1258])).
% 1.41/1.21 tff(1260,plain,
% 1.41/1.21 (~c2_1(a176)),
% 1.41/1.21 inference(unit_resolution,[status(thm)],[715, 1258])).
% 1.41/1.21 tff(1261,plain,
% 1.41/1.21 ($false),
% 1.41/1.21 inference(unit_resolution,[status(thm)],[810, 1260, 1259, 436, 11, 470, 1230, 433, 434, 784])).
% 1.41/1.21 tff(1262,plain,((~hskp2) | c2_1(a132) | hskp0 | (~c3_1(a132)) | c0_1(a125) | c0_1(a132) | hskp9 | c1_1(a132)), inference(lemma,lemma(discharge,[]))).
% 1.41/1.21 tff(1263,plain,
% 1.41/1.21 (hskp0),
% 1.41/1.21 inference(unit_resolution,[status(thm)],[1262, 1229, 1228, 1164, 1162, 1163, 33, 1165])).
% 1.41/1.21 tff(1264,plain,
% 1.41/1.21 (~c1_1(a123)),
% 1.41/1.21 inference(unit_resolution,[status(thm)],[202, 1263])).
% 1.41/1.21 tff(1265,plain,
% 1.41/1.21 (~c0_1(a123)),
% 1.41/1.21 inference(unit_resolution,[status(thm)],[236, 1263])).
% 1.41/1.21 tff(1266,plain,
% 1.41/1.21 (c2_1(a123)),
% 1.41/1.21 inference(unit_resolution,[status(thm)],[213, 1263])).
% 1.41/1.21 tff(1267,plain,
% 1.41/1.21 (~c3_1(a123)),
% 1.41/1.21 inference(unit_resolution,[status(thm)],[500, 123, 1164, 1266, 1162, 1265, 1264, 144, 1165])).
% 1.41/1.21 tff(1268,plain,
% 1.41/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a132) | c0_1(a123) | (~ndr1_0) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132)) | c1_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132)) | c1_1(a132))),
% 1.41/1.21 inference(rewrite,[status(thm)],[])).
% 1.41/1.21 tff(1269,plain,
% 1.41/1.21 (((~ndr1_0) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123))) <=> (c2_1(a132) | c0_1(a123) | (~ndr1_0) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132)) | c1_1(a132))),
% 1.41/1.21 inference(rewrite,[status(thm)],[])).
% 1.41/1.21 tff(1270,plain,
% 1.41/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a132) | c0_1(a123) | (~ndr1_0) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132)) | c1_1(a132)))),
% 1.41/1.21 inference(monotonicity,[status(thm)],[1269])).
% 1.41/1.21 tff(1271,plain,
% 1.41/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132)) | c1_1(a132))),
% 1.41/1.21 inference(transitivity,[status(thm)],[1270, 1268])).
% 1.41/1.21 tff(1272,plain,
% 1.41/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)))),
% 1.41/1.21 inference(quant_inst,[status(thm)],[])).
% 1.41/1.21 tff(1273,plain,
% 1.41/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | (~c1_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132)) | c1_1(a132)),
% 1.41/1.21 inference(modus_ponens,[status(thm)],[1272, 1271])).
% 1.41/1.21 tff(1274,plain,
% 1.41/1.21 (~c2_1(a167)),
% 1.41/1.21 inference(unit_resolution,[status(thm)],[1273, 123, 1130, 1187, 1164, 1266, 1162, 1265, 972, 1165, 1267])).
% 1.41/1.21 tff(1275,plain,
% 1.41/1.21 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))))),
% 1.41/1.21 inference(bind,[status(th)],[])).
% 1.41/1.21 tff(1276,plain,
% 1.41/1.21 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.41/1.21 inference(quant_intro,[status(thm)],[1275])).
% 1.41/1.21 tff(1277,plain,
% 1.41/1.21 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.41/1.21 inference(rewrite,[status(thm)],[])).
% 1.41/1.21 tff(1278,plain,
% 1.41/1.21 (^[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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(W)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(W))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | 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(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))))),
% 1.41/1.21 inference(bind,[status(th)],[])).
% 1.41/1.21 tff(1279,plain,
% 1.41/1.21 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.41/1.21 inference(quant_intro,[status(thm)],[1278])).
% 1.41/1.21 tff(1280,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause197')).
% 1.41/1.21 tff(1281,plain,
% 1.41/1.21 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.41/1.21 inference(modus_ponens,[status(thm)],[1280, 1279])).
% 1.41/1.21 tff(1282,plain,
% 1.41/1.21 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.41/1.21 inference(modus_ponens,[status(thm)],[1281, 1277])).
% 1.41/1.21 tff(1283,plain,(
% 1.41/1.21 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.41/1.21 inference(skolemize,[status(sab)],[1282])).
% 1.41/1.21 tff(1284,plain,
% 1.41/1.21 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.41/1.21 inference(modus_ponens,[status(thm)],[1283, 1276])).
% 1.41/1.21 tff(1285,plain,
% 1.41/1.21 (^[U: $i] : refl((hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 1.41/1.21 inference(bind,[status(th)],[])).
% 1.41/1.21 tff(1286,plain,
% 1.41/1.21 (![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.41/1.21 inference(quant_intro,[status(thm)],[1285])).
% 1.41/1.21 tff(1287,plain,
% 1.41/1.21 (![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.41/1.21 inference(rewrite,[status(thm)],[])).
% 1.41/1.21 tff(1288,plain,
% 1.41/1.21 (^[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)) | hskp17) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp17))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp17) | hskp24) <=> ((hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp24))), rewrite(((hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp24) <=> (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp17) | hskp24) <=> (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 1.41/1.21 inference(bind,[status(th)],[])).
% 1.41/1.21 tff(1289,plain,
% 1.41/1.21 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp17) | hskp24) <=> ![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.41/1.21 inference(quant_intro,[status(thm)],[1288])).
% 1.41/1.21 tff(1290,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp17) | hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause157')).
% 1.41/1.21 tff(1291,plain,
% 1.41/1.21 (![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.41/1.21 inference(modus_ponens,[status(thm)],[1290, 1289])).
% 1.41/1.21 tff(1292,plain,
% 1.41/1.21 (![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.41/1.21 inference(modus_ponens,[status(thm)],[1291, 1287])).
% 1.41/1.21 tff(1293,plain,(
% 1.41/1.21 ![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.41/1.21 inference(skolemize,[status(sab)],[1292])).
% 1.41/1.21 tff(1294,plain,
% 1.41/1.21 (![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.41/1.21 inference(modus_ponens,[status(thm)],[1293, 1286])).
% 1.41/1.21 tff(1295,plain,
% 1.41/1.21 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | c2_1(a167))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp17 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | c2_1(a167))),
% 1.41/1.21 inference(rewrite,[status(thm)],[])).
% 1.41/1.21 tff(1296,plain,
% 1.41/1.21 ((hskp24 | hskp17 | (~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c1_1(a167))) <=> (hskp24 | hskp17 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | c2_1(a167))),
% 1.41/1.21 inference(rewrite,[status(thm)],[])).
% 1.41/1.21 tff(1297,plain,
% 1.41/1.21 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c1_1(a167)))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | c2_1(a167)))),
% 1.41/1.21 inference(monotonicity,[status(thm)],[1296])).
% 1.41/1.21 tff(1298,plain,
% 1.41/1.21 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c1_1(a167)))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp17 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | c2_1(a167))),
% 1.41/1.21 inference(transitivity,[status(thm)],[1297, 1295])).
% 1.41/1.21 tff(1299,plain,
% 1.41/1.21 ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c1_1(a167)))),
% 1.41/1.21 inference(quant_inst,[status(thm)],[])).
% 1.41/1.21 tff(1300,plain,
% 1.41/1.21 ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp17 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | c2_1(a167)),
% 1.41/1.21 inference(modus_ponens,[status(thm)],[1299, 1298])).
% 1.41/1.21 tff(1301,plain,
% 1.41/1.21 (hskp24 | hskp17 | c2_1(a167)),
% 1.41/1.21 inference(unit_resolution,[status(thm)],[1300, 123, 1187, 1176, 1294])).
% 1.41/1.21 tff(1302,plain,
% 1.41/1.21 (hskp24),
% 1.41/1.21 inference(unit_resolution,[status(thm)],[1301, 1274, 1188])).
% 1.41/1.21 tff(1303,plain,
% 1.41/1.21 (((~hskp24) | (~c3_1(a182))) <=> ((~hskp24) | (~c3_1(a182)))),
% 1.41/1.21 inference(rewrite,[status(thm)],[])).
% 1.41/1.21 tff(1304,plain,
% 1.41/1.21 (((~c3_1(a182)) | (~hskp24)) <=> ((~hskp24) | (~c3_1(a182)))),
% 1.41/1.21 inference(rewrite,[status(thm)],[])).
% 1.41/1.21 tff(1305,axiom,((~c3_1(a182)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause89')).
% 1.41/1.21 tff(1306,plain,
% 1.41/1.21 ((~hskp24) | (~c3_1(a182))),
% 1.41/1.21 inference(modus_ponens,[status(thm)],[1305, 1304])).
% 1.41/1.21 tff(1307,plain,
% 1.41/1.21 ((~hskp24) | (~c3_1(a182))),
% 1.41/1.21 inference(modus_ponens,[status(thm)],[1306, 1303])).
% 1.41/1.21 tff(1308,plain,
% 1.41/1.21 (~c3_1(a182)),
% 1.41/1.21 inference(unit_resolution,[status(thm)],[1307, 1302])).
% 1.41/1.21 tff(1309,plain,
% 1.41/1.21 (((~hskp24) | (~c2_1(a182))) <=> ((~hskp24) | (~c2_1(a182)))),
% 1.41/1.21 inference(rewrite,[status(thm)],[])).
% 1.41/1.21 tff(1310,plain,
% 1.41/1.21 (((~c2_1(a182)) | (~hskp24)) <=> ((~hskp24) | (~c2_1(a182)))),
% 1.41/1.21 inference(rewrite,[status(thm)],[])).
% 1.41/1.21 tff(1311,axiom,((~c2_1(a182)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause88')).
% 1.41/1.21 tff(1312,plain,
% 1.41/1.21 ((~hskp24) | (~c2_1(a182))),
% 1.41/1.21 inference(modus_ponens,[status(thm)],[1311, 1310])).
% 1.41/1.21 tff(1313,plain,
% 1.41/1.21 ((~hskp24) | (~c2_1(a182))),
% 1.41/1.21 inference(modus_ponens,[status(thm)],[1312, 1309])).
% 1.41/1.21 tff(1314,plain,
% 1.41/1.21 (~c2_1(a182)),
% 1.41/1.21 inference(unit_resolution,[status(thm)],[1313, 1302])).
% 1.41/1.21 tff(1315,plain,
% 1.41/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a182) | c3_1(a182) | c2_1(a132) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a182)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a182) | c3_1(a182) | c2_1(a132) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a182)))),
% 1.41/1.21 inference(rewrite,[status(thm)],[])).
% 1.41/1.21 tff(1316,plain,
% 1.41/1.21 (((~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c0_1(a167)) | c2_1(a182) | c3_1(a182) | (~c1_1(a182)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132))) <=> (c2_1(a182) | c3_1(a182) | c2_1(a132) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a182)))),
% 1.41/1.21 inference(rewrite,[status(thm)],[])).
% 1.41/1.21 tff(1317,plain,
% 1.41/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c0_1(a167)) | c2_1(a182) | c3_1(a182) | (~c1_1(a182)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a182) | c3_1(a182) | c2_1(a132) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a182))))),
% 1.41/1.21 inference(monotonicity,[status(thm)],[1316])).
% 1.41/1.21 tff(1318,plain,
% 1.41/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c0_1(a167)) | c2_1(a182) | c3_1(a182) | (~c1_1(a182)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a182) | c3_1(a182) | c2_1(a132) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a182)))),
% 1.41/1.21 inference(transitivity,[status(thm)],[1317, 1315])).
% 1.41/1.21 tff(1319,plain,
% 1.41/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c0_1(a167)) | c2_1(a182) | c3_1(a182) | (~c1_1(a182)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)))),
% 1.41/1.21 inference(quant_inst,[status(thm)],[])).
% 1.41/1.21 tff(1320,plain,
% 1.41/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a182) | c3_1(a182) | c2_1(a132) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a182))),
% 1.41/1.21 inference(modus_ponens,[status(thm)],[1319, 1318])).
% 1.41/1.21 tff(1321,plain,
% 1.41/1.21 (~c1_1(a182)),
% 1.41/1.21 inference(unit_resolution,[status(thm)],[1320, 123, 1130, 1176, 1164, 1314, 1308, 1162, 1284, 1165, 1274])).
% 1.41/1.21 tff(1322,plain,
% 1.41/1.21 (((~hskp24) | (~c0_1(a182))) <=> ((~hskp24) | (~c0_1(a182)))),
% 1.41/1.21 inference(rewrite,[status(thm)],[])).
% 1.41/1.21 tff(1323,plain,
% 1.41/1.21 (((~c0_1(a182)) | (~hskp24)) <=> ((~hskp24) | (~c0_1(a182)))),
% 1.41/1.21 inference(rewrite,[status(thm)],[])).
% 1.41/1.21 tff(1324,axiom,((~c0_1(a182)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause87')).
% 1.41/1.21 tff(1325,plain,
% 1.41/1.21 ((~hskp24) | (~c0_1(a182))),
% 1.41/1.21 inference(modus_ponens,[status(thm)],[1324, 1323])).
% 1.41/1.21 tff(1326,plain,
% 1.41/1.21 ((~hskp24) | (~c0_1(a182))),
% 1.41/1.21 inference(modus_ponens,[status(thm)],[1325, 1322])).
% 1.41/1.21 tff(1327,plain,
% 1.41/1.21 (~c0_1(a182)),
% 1.41/1.21 inference(unit_resolution,[status(thm)],[1326, 1302])).
% 1.41/1.21 tff(1328,plain,
% 1.41/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a182) | c2_1(a182) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | c2_1(a167) | c3_1(a123) | c1_1(a182))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a182) | c2_1(a182) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | c2_1(a167) | c3_1(a123) | c1_1(a182))),
% 1.41/1.21 inference(rewrite,[status(thm)],[])).
% 1.41/1.21 tff(1329,plain,
% 1.41/1.21 (((~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c1_1(a167)) | c1_1(a123) | c0_1(a123) | c3_1(a123) | c2_1(a182) | c1_1(a182) | c0_1(a182)) <=> (c0_1(a182) | c2_1(a182) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | c2_1(a167) | c3_1(a123) | c1_1(a182))),
% 1.41/1.21 inference(rewrite,[status(thm)],[])).
% 1.41/1.21 tff(1330,plain,
% 1.41/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c1_1(a167)) | c1_1(a123) | c0_1(a123) | c3_1(a123) | c2_1(a182) | c1_1(a182) | c0_1(a182))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a182) | c2_1(a182) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | c2_1(a167) | c3_1(a123) | c1_1(a182)))),
% 1.41/1.21 inference(monotonicity,[status(thm)],[1329])).
% 1.41/1.21 tff(1331,plain,
% 1.41/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c1_1(a167)) | c1_1(a123) | c0_1(a123) | c3_1(a123) | c2_1(a182) | c1_1(a182) | c0_1(a182))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a182) | c2_1(a182) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | c2_1(a167) | c3_1(a123) | c1_1(a182))),
% 1.41/1.21 inference(transitivity,[status(thm)],[1330, 1328])).
% 1.41/1.21 tff(1332,plain,
% 1.41/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c1_1(a167)) | c1_1(a123) | c0_1(a123) | c3_1(a123) | c2_1(a182) | c1_1(a182) | c0_1(a182))),
% 1.41/1.21 inference(quant_inst,[status(thm)],[])).
% 1.41/1.21 tff(1333,plain,
% 1.41/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a182) | c2_1(a182) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | c2_1(a167) | c3_1(a123) | c1_1(a182)),
% 1.41/1.21 inference(modus_ponens,[status(thm)],[1332, 1331])).
% 1.41/1.21 tff(1334,plain,
% 1.41/1.21 ($false),
% 1.41/1.21 inference(unit_resolution,[status(thm)],[1333, 123, 1187, 1176, 1327, 1314, 1265, 1264, 231, 1274, 1267, 1321])).
% 1.41/1.21 tff(1335,plain,(c0_1(a131) | hskp9 | c1_1(a131) | c2_1(a131)), inference(lemma,lemma(discharge,[]))).
% 1.41/1.21 tff(1336,plain,
% 1.41/1.21 (c0_1(a131)),
% 1.41/1.21 inference(unit_resolution,[status(thm)],[1335, 132, 33, 95])).
% 1.41/1.21 tff(1337,plain,
% 1.41/1.21 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.41/1.21 inference(bind,[status(th)],[])).
% 1.41/1.21 tff(1338,plain,
% 1.41/1.21 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.41/1.21 inference(quant_intro,[status(thm)],[1337])).
% 1.41/1.21 tff(1339,plain,
% 1.41/1.21 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.41/1.21 inference(rewrite,[status(thm)],[])).
% 1.41/1.21 tff(1340,plain,
% 1.41/1.21 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp6) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp6))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp6) <=> (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.41/1.21 inference(bind,[status(th)],[])).
% 1.41/1.21 tff(1341,plain,
% 1.41/1.21 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.41/1.21 inference(quant_intro,[status(thm)],[1340])).
% 1.41/1.21 tff(1342,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause179')).
% 1.41/1.21 tff(1343,plain,
% 1.41/1.21 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.41/1.21 inference(modus_ponens,[status(thm)],[1342, 1341])).
% 1.41/1.21 tff(1344,plain,
% 1.41/1.21 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.41/1.21 inference(modus_ponens,[status(thm)],[1343, 1339])).
% 1.41/1.21 tff(1345,plain,(
% 1.41/1.21 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.41/1.21 inference(skolemize,[status(sab)],[1344])).
% 1.41/1.21 tff(1346,plain,
% 1.41/1.21 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.41/1.21 inference(modus_ponens,[status(thm)],[1345, 1338])).
% 1.41/1.21 tff(1347,plain,
% 1.41/1.21 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp17 | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0))),
% 1.41/1.21 inference(rewrite,[status(thm)],[])).
% 1.41/1.21 tff(1348,plain,
% 1.41/1.21 ((hskp19 | hskp17 | (~ndr1_0) | c2_1(a131) | c1_1(a131) | (~c0_1(a131))) <=> (hskp19 | hskp17 | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0))),
% 1.41/1.21 inference(rewrite,[status(thm)],[])).
% 1.41/1.21 tff(1349,plain,
% 1.41/1.21 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c2_1(a131) | c1_1(a131) | (~c0_1(a131)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0)))),
% 1.41/1.21 inference(monotonicity,[status(thm)],[1348])).
% 1.41/1.21 tff(1350,plain,
% 1.41/1.21 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c2_1(a131) | c1_1(a131) | (~c0_1(a131)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp17 | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0))),
% 1.41/1.21 inference(transitivity,[status(thm)],[1349, 1347])).
% 1.41/1.21 tff(1351,plain,
% 1.41/1.21 ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c2_1(a131) | c1_1(a131) | (~c0_1(a131)))),
% 1.41/1.21 inference(quant_inst,[status(thm)],[])).
% 1.41/1.21 tff(1352,plain,
% 1.41/1.21 ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp17 | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0)),
% 1.41/1.21 inference(modus_ponens,[status(thm)],[1351, 1350])).
% 1.41/1.21 tff(1353,plain,
% 1.41/1.21 (hskp19 | hskp17 | (~c0_1(a131)) | c1_1(a131)),
% 1.41/1.21 inference(unit_resolution,[status(thm)],[1352, 123, 95, 53])).
% 1.41/1.21 tff(1354,plain,
% 1.41/1.21 (hskp19),
% 1.41/1.21 inference(unit_resolution,[status(thm)],[1353, 134, 1336, 132])).
% 1.41/1.21 tff(1355,plain,
% 1.41/1.21 (~c2_1(a164)),
% 1.41/1.21 inference(unit_resolution,[status(thm)],[250, 1354])).
% 1.41/1.21 tff(1356,plain,
% 1.41/1.21 (c3_1(a164)),
% 1.41/1.21 inference(unit_resolution,[status(thm)],[261, 1354])).
% 1.41/1.22 tff(1357,plain,
% 1.41/1.22 (c1_1(a164)),
% 1.41/1.22 inference(unit_resolution,[status(thm)],[272, 1354])).
% 1.41/1.22 tff(1358,plain,
% 1.41/1.22 (hskp13),
% 1.41/1.22 inference(unit_resolution,[status(thm)],[776, 123, 134, 1357, 1356, 1355, 769])).
% 1.41/1.22 tff(1359,plain,
% 1.41/1.22 (~c1_1(a143)),
% 1.41/1.22 inference(unit_resolution,[status(thm)],[782, 1358])).
% 1.41/1.22 tff(1360,plain,
% 1.41/1.22 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164)))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp17 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164)))),
% 1.41/1.22 inference(rewrite,[status(thm)],[])).
% 1.41/1.22 tff(1361,plain,
% 1.41/1.22 ((hskp24 | hskp17 | (~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164))) <=> (hskp24 | hskp17 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164)))),
% 1.41/1.22 inference(rewrite,[status(thm)],[])).
% 1.41/1.22 tff(1362,plain,
% 1.41/1.22 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164))))),
% 1.41/1.22 inference(monotonicity,[status(thm)],[1361])).
% 1.41/1.22 tff(1363,plain,
% 1.41/1.22 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp17 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164)))),
% 1.41/1.22 inference(transitivity,[status(thm)],[1362, 1360])).
% 1.41/1.22 tff(1364,plain,
% 1.41/1.22 ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)))),
% 1.41/1.22 inference(quant_inst,[status(thm)],[])).
% 1.41/1.22 tff(1365,plain,
% 1.41/1.22 ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp17 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164))),
% 1.41/1.22 inference(modus_ponens,[status(thm)],[1364, 1363])).
% 1.41/1.22 tff(1366,plain,
% 1.41/1.22 (hskp24),
% 1.41/1.22 inference(unit_resolution,[status(thm)],[1365, 123, 134, 1357, 1356, 1355, 1294])).
% 1.41/1.22 tff(1367,plain,
% 1.41/1.22 (~c3_1(a182)),
% 1.41/1.22 inference(unit_resolution,[status(thm)],[1307, 1366])).
% 1.41/1.22 tff(1368,plain,
% 1.41/1.22 (~c2_1(a182)),
% 1.41/1.22 inference(unit_resolution,[status(thm)],[1313, 1366])).
% 1.41/1.22 tff(1369,plain,
% 1.41/1.22 (~c0_1(a182)),
% 1.41/1.22 inference(unit_resolution,[status(thm)],[1326, 1366])).
% 1.41/1.22 tff(1370,plain,
% 1.41/1.22 (((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | c0_1(a182) | c2_1(a182) | c3_1(a182) | (~ndr1_0))) <=> ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp9 | hskp7 | c0_1(a182) | c2_1(a182) | c3_1(a182) | (~ndr1_0))),
% 1.41/1.22 inference(rewrite,[status(thm)],[])).
% 1.41/1.22 tff(1371,plain,
% 1.41/1.22 ((hskp9 | hskp7 | (~ndr1_0) | c2_1(a182) | c0_1(a182) | c3_1(a182)) <=> (hskp9 | hskp7 | c0_1(a182) | c2_1(a182) | c3_1(a182) | (~ndr1_0))),
% 1.41/1.22 inference(rewrite,[status(thm)],[])).
% 1.41/1.22 tff(1372,plain,
% 1.41/1.22 (((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | (~ndr1_0) | c2_1(a182) | c0_1(a182) | c3_1(a182))) <=> ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | c0_1(a182) | c2_1(a182) | c3_1(a182) | (~ndr1_0)))),
% 1.41/1.22 inference(monotonicity,[status(thm)],[1371])).
% 1.41/1.22 tff(1373,plain,
% 1.41/1.22 (((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | (~ndr1_0) | c2_1(a182) | c0_1(a182) | c3_1(a182))) <=> ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp9 | hskp7 | c0_1(a182) | c2_1(a182) | c3_1(a182) | (~ndr1_0))),
% 1.41/1.22 inference(transitivity,[status(thm)],[1372, 1370])).
% 1.41/1.22 tff(1374,plain,
% 1.41/1.22 ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp9 | hskp7 | (~ndr1_0) | c2_1(a182) | c0_1(a182) | c3_1(a182))),
% 1.41/1.22 inference(quant_inst,[status(thm)],[])).
% 1.41/1.22 tff(1375,plain,
% 1.41/1.22 ((~![U: $i] : (hskp9 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp9 | hskp7 | c0_1(a182) | c2_1(a182) | c3_1(a182) | (~ndr1_0)),
% 1.41/1.22 inference(modus_ponens,[status(thm)],[1374, 1373])).
% 1.41/1.22 tff(1376,plain,
% 1.41/1.22 (hskp7),
% 1.41/1.22 inference(unit_resolution,[status(thm)],[1375, 123, 33, 1369, 1368, 1367, 94])).
% 1.41/1.22 tff(1377,plain,
% 1.41/1.22 (~c2_1(a132)),
% 1.41/1.22 inference(unit_resolution,[status(thm)],[898, 1376])).
% 1.41/1.22 tff(1378,plain,
% 1.41/1.22 (c3_1(a132)),
% 1.41/1.22 inference(unit_resolution,[status(thm)],[447, 1376])).
% 1.41/1.22 tff(1379,plain,
% 1.41/1.22 (c3_1(a143)),
% 1.41/1.22 inference(unit_resolution,[status(thm)],[825, 1358])).
% 1.41/1.22 tff(1380,plain,
% 1.41/1.22 (~hskp6),
% 1.41/1.22 inference(unit_resolution,[status(thm)],[83, 1336])).
% 1.41/1.22 tff(1381,plain,
% 1.41/1.22 (c2_1(a143)),
% 1.41/1.22 inference(unit_resolution,[status(thm)],[836, 1358])).
% 1.41/1.22 tff(1382,assumption,(~c1_1(a143)), introduced(assumption)).
% 1.41/1.22 tff(1383,assumption,(c3_1(a143)), introduced(assumption)).
% 1.41/1.22 tff(1384,assumption,(c2_1(a143)), introduced(assumption)).
% 1.41/1.22 tff(1385,plain,
% 1.41/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a143) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c2_1(a143)) | (~c3_1(a143)) | c0_1(a143))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a143) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c2_1(a143)) | (~c3_1(a143)) | c0_1(a143))),
% 1.41/1.22 inference(rewrite,[status(thm)],[])).
% 1.41/1.22 tff(1386,plain,
% 1.41/1.22 (((~ndr1_0) | c1_1(a143) | (~c3_1(a143)) | (~c2_1(a143)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)) | c1_1(a143) | c0_1(a143) | (~c3_1(a143))) <=> (c1_1(a143) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c2_1(a143)) | (~c3_1(a143)) | c0_1(a143))),
% 1.41/1.22 inference(rewrite,[status(thm)],[])).
% 1.41/1.22 tff(1387,plain,
% 1.41/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a143) | (~c3_1(a143)) | (~c2_1(a143)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)) | c1_1(a143) | c0_1(a143) | (~c3_1(a143)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a143) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c2_1(a143)) | (~c3_1(a143)) | c0_1(a143)))),
% 1.41/1.22 inference(monotonicity,[status(thm)],[1386])).
% 1.41/1.22 tff(1388,plain,
% 1.41/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a143) | (~c3_1(a143)) | (~c2_1(a143)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)) | c1_1(a143) | c0_1(a143) | (~c3_1(a143)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a143) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c2_1(a143)) | (~c3_1(a143)) | c0_1(a143))),
% 1.41/1.22 inference(transitivity,[status(thm)],[1387, 1385])).
% 1.41/1.22 tff(1389,plain,
% 1.41/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a143) | (~c3_1(a143)) | (~c2_1(a143)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)) | c1_1(a143) | c0_1(a143) | (~c3_1(a143)))),
% 1.41/1.22 inference(quant_inst,[status(thm)],[])).
% 1.41/1.22 tff(1390,plain,
% 1.41/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a143) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c2_1(a143)) | (~c3_1(a143)) | c0_1(a143)),
% 1.41/1.22 inference(modus_ponens,[status(thm)],[1389, 1388])).
% 1.41/1.22 tff(1391,plain,
% 1.41/1.22 (c1_1(a132) | c0_1(a143)),
% 1.41/1.22 inference(unit_resolution,[status(thm)],[1390, 123, 1384, 1383, 470, 1382, 436, 144])).
% 1.41/1.22 tff(1392,plain,
% 1.41/1.22 (c0_1(a143)),
% 1.41/1.22 inference(unit_resolution,[status(thm)],[1391, 466])).
% 1.41/1.22 tff(1393,plain,
% 1.41/1.22 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))),
% 1.41/1.22 inference(bind,[status(th)],[])).
% 1.41/1.22 tff(1394,plain,
% 1.41/1.22 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.41/1.22 inference(quant_intro,[status(thm)],[1393])).
% 1.41/1.22 tff(1395,plain,
% 1.41/1.22 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.41/1.22 inference(rewrite,[status(thm)],[])).
% 1.41/1.22 tff(1396,plain,
% 1.41/1.22 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) | hskp6) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp6))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp6) <=> (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))))),
% 1.41/1.22 inference(bind,[status(th)],[])).
% 1.41/1.22 tff(1397,plain,
% 1.41/1.22 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.41/1.22 inference(quant_intro,[status(thm)],[1396])).
% 1.41/1.22 tff(1398,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause187')).
% 1.41/1.22 tff(1399,plain,
% 1.41/1.22 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.41/1.22 inference(modus_ponens,[status(thm)],[1398, 1397])).
% 1.41/1.22 tff(1400,plain,
% 1.41/1.22 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.41/1.22 inference(modus_ponens,[status(thm)],[1399, 1395])).
% 1.41/1.22 tff(1401,plain,(
% 1.41/1.22 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.41/1.22 inference(skolemize,[status(sab)],[1400])).
% 1.41/1.22 tff(1402,plain,
% 1.41/1.22 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.41/1.22 inference(modus_ponens,[status(thm)],[1401, 1394])).
% 1.41/1.22 tff(1403,assumption,(~hskp6), introduced(assumption)).
% 1.41/1.22 tff(1404,plain,
% 1.41/1.22 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp6 | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c2_1(a143)) | (~c3_1(a143)) | (~c0_1(a143)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c2_1(a143)) | (~c3_1(a143)) | (~c0_1(a143)))),
% 1.41/1.22 inference(rewrite,[status(thm)],[])).
% 1.41/1.22 tff(1405,plain,
% 1.41/1.22 ((hskp6 | (~ndr1_0) | (~c3_1(a143)) | (~c0_1(a143)) | (~c2_1(a143)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132))) <=> (hskp6 | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c2_1(a143)) | (~c3_1(a143)) | (~c0_1(a143)))),
% 1.41/1.22 inference(rewrite,[status(thm)],[])).
% 1.41/1.22 tff(1406,plain,
% 1.41/1.22 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c3_1(a143)) | (~c0_1(a143)) | (~c2_1(a143)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp6 | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c2_1(a143)) | (~c3_1(a143)) | (~c0_1(a143))))),
% 1.41/1.22 inference(monotonicity,[status(thm)],[1405])).
% 1.41/1.22 tff(1407,plain,
% 1.41/1.22 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c3_1(a143)) | (~c0_1(a143)) | (~c2_1(a143)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c2_1(a143)) | (~c3_1(a143)) | (~c0_1(a143)))),
% 1.41/1.22 inference(transitivity,[status(thm)],[1406, 1404])).
% 1.41/1.22 tff(1408,plain,
% 1.41/1.22 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c3_1(a143)) | (~c0_1(a143)) | (~c2_1(a143)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)))),
% 1.41/1.22 inference(quant_inst,[status(thm)],[])).
% 1.41/1.22 tff(1409,plain,
% 1.41/1.22 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c2_1(a143)) | (~c3_1(a143)) | (~c0_1(a143))),
% 1.41/1.22 inference(modus_ponens,[status(thm)],[1408, 1407])).
% 1.41/1.22 tff(1410,plain,
% 1.41/1.22 (c1_1(a132) | (~c0_1(a143))),
% 1.41/1.22 inference(unit_resolution,[status(thm)],[1409, 123, 1403, 1384, 1383, 470, 436, 1402])).
% 1.41/1.22 tff(1411,plain,
% 1.41/1.22 ($false),
% 1.41/1.22 inference(unit_resolution,[status(thm)],[1410, 1392, 466])).
% 1.41/1.22 tff(1412,plain,(c1_1(a132) | hskp6 | (~c2_1(a143)) | (~c3_1(a143)) | (~c3_1(a132)) | c2_1(a132) | c1_1(a143)), inference(lemma,lemma(discharge,[]))).
% 1.41/1.22 tff(1413,plain,
% 1.41/1.22 (c1_1(a132)),
% 1.41/1.22 inference(unit_resolution,[status(thm)],[1412, 1381, 1380, 1379, 1378, 1377, 1359])).
% 1.41/1.22 tff(1414,plain,
% 1.41/1.22 (~c0_1(a132)),
% 1.41/1.22 inference(unit_resolution,[status(thm)],[431, 1376])).
% 1.41/1.22 tff(1415,plain,
% 1.41/1.22 (hskp0 | (~c1_1(a132))),
% 1.41/1.22 inference(unit_resolution,[status(thm)],[1039, 123, 134, 1378, 1414, 43])).
% 1.41/1.22 tff(1416,plain,
% 1.41/1.22 (hskp0),
% 1.41/1.22 inference(unit_resolution,[status(thm)],[1415, 1413])).
% 1.41/1.22 tff(1417,plain,
% 1.41/1.22 (~c1_1(a123)),
% 1.41/1.22 inference(unit_resolution,[status(thm)],[202, 1416])).
% 1.46/1.22 tff(1418,plain,
% 1.46/1.22 (~c0_1(a123)),
% 1.46/1.22 inference(unit_resolution,[status(thm)],[236, 1416])).
% 1.46/1.22 tff(1419,plain,
% 1.46/1.22 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))))),
% 1.46/1.22 inference(bind,[status(th)],[])).
% 1.46/1.22 tff(1420,plain,
% 1.46/1.22 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.46/1.22 inference(quant_intro,[status(thm)],[1419])).
% 1.46/1.22 tff(1421,plain,
% 1.46/1.22 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.46/1.22 inference(rewrite,[status(thm)],[])).
% 1.46/1.22 tff(1422,plain,
% 1.46/1.22 (^[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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_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) | (~c3_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))))),
% 1.46/1.22 inference(bind,[status(th)],[])).
% 1.46/1.22 tff(1423,plain,
% 1.46/1.22 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.46/1.22 inference(quant_intro,[status(thm)],[1422])).
% 1.46/1.22 tff(1424,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause194')).
% 1.46/1.22 tff(1425,plain,
% 1.46/1.22 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.46/1.22 inference(modus_ponens,[status(thm)],[1424, 1423])).
% 1.46/1.22 tff(1426,plain,
% 1.46/1.22 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.46/1.22 inference(modus_ponens,[status(thm)],[1425, 1421])).
% 1.46/1.22 tff(1427,plain,(
% 1.46/1.22 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.46/1.22 inference(skolemize,[status(sab)],[1426])).
% 1.46/1.22 tff(1428,plain,
% 1.46/1.22 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.46/1.22 inference(modus_ponens,[status(thm)],[1427, 1420])).
% 1.46/1.22 tff(1429,plain,
% 1.46/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a164) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | (~c3_1(a164)) | (~c0_1(a164)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a164) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | (~c3_1(a164)) | (~c0_1(a164)))),
% 1.46/1.22 inference(rewrite,[status(thm)],[])).
% 1.46/1.22 tff(1430,plain,
% 1.46/1.22 (((~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c0_1(a164)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132))) <=> (c2_1(a164) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | (~c3_1(a164)) | (~c0_1(a164)))),
% 1.46/1.22 inference(rewrite,[status(thm)],[])).
% 1.46/1.22 tff(1431,plain,
% 1.46/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c0_1(a164)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a164) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | (~c3_1(a164)) | (~c0_1(a164))))),
% 1.46/1.22 inference(monotonicity,[status(thm)],[1430])).
% 1.46/1.22 tff(1432,plain,
% 1.46/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c0_1(a164)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a164) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | (~c3_1(a164)) | (~c0_1(a164)))),
% 1.46/1.22 inference(transitivity,[status(thm)],[1431, 1429])).
% 1.46/1.22 tff(1433,plain,
% 1.46/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c0_1(a164)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132)))),
% 1.46/1.22 inference(quant_inst,[status(thm)],[])).
% 1.46/1.22 tff(1434,plain,
% 1.46/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a164) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | (~c3_1(a164)) | (~c0_1(a164))),
% 1.46/1.22 inference(modus_ponens,[status(thm)],[1433, 1432])).
% 1.46/1.22 tff(1435,plain,
% 1.46/1.22 ((~c1_1(a132)) | (~c0_1(a164))),
% 1.46/1.22 inference(unit_resolution,[status(thm)],[1434, 123, 1356, 1378, 1355, 1414, 1377, 1428])).
% 1.46/1.22 tff(1436,plain,
% 1.46/1.22 (~c0_1(a164)),
% 1.46/1.22 inference(unit_resolution,[status(thm)],[1435, 1413])).
% 1.46/1.22 tff(1437,plain,
% 1.46/1.22 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 1.46/1.22 inference(bind,[status(th)],[])).
% 1.46/1.22 tff(1438,plain,
% 1.46/1.22 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.46/1.22 inference(quant_intro,[status(thm)],[1437])).
% 1.46/1.22 tff(1439,plain,
% 1.46/1.22 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.46/1.22 inference(rewrite,[status(thm)],[])).
% 1.46/1.22 tff(1440,plain,
% 1.46/1.22 (^[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))) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | (~c1_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | (~c1_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp12) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp12))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 1.46/1.23 inference(bind,[status(th)],[])).
% 1.46/1.23 tff(1441,plain,
% 1.46/1.23 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.46/1.23 inference(quant_intro,[status(thm)],[1440])).
% 1.46/1.23 tff(1442,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause173')).
% 1.46/1.23 tff(1443,plain,
% 1.46/1.23 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.46/1.23 inference(modus_ponens,[status(thm)],[1442, 1441])).
% 1.46/1.23 tff(1444,plain,
% 1.46/1.23 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.46/1.23 inference(modus_ponens,[status(thm)],[1443, 1439])).
% 1.46/1.23 tff(1445,plain,(
% 1.46/1.23 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.46/1.23 inference(skolemize,[status(sab)],[1444])).
% 1.46/1.23 tff(1446,plain,
% 1.46/1.23 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.46/1.23 inference(modus_ponens,[status(thm)],[1445, 1438])).
% 1.46/1.23 tff(1447,plain,
% 1.46/1.23 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c2_1(a164) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c1_1(a132)) | (~c3_1(a164)) | c0_1(a164))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a164) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c1_1(a132)) | (~c3_1(a164)) | c0_1(a164))),
% 1.46/1.23 inference(rewrite,[status(thm)],[])).
% 1.46/1.23 tff(1448,plain,
% 1.46/1.23 ((hskp12 | (~ndr1_0) | c2_1(a164) | c0_1(a164) | (~c3_1(a164)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132))) <=> (hskp12 | c2_1(a164) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c1_1(a132)) | (~c3_1(a164)) | c0_1(a164))),
% 1.46/1.23 inference(rewrite,[status(thm)],[])).
% 1.46/1.23 tff(1449,plain,
% 1.46/1.23 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a164) | c0_1(a164) | (~c3_1(a164)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c2_1(a164) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c1_1(a132)) | (~c3_1(a164)) | c0_1(a164)))),
% 1.46/1.23 inference(monotonicity,[status(thm)],[1448])).
% 1.46/1.23 tff(1450,plain,
% 1.46/1.23 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a164) | c0_1(a164) | (~c3_1(a164)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a164) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c1_1(a132)) | (~c3_1(a164)) | c0_1(a164))),
% 1.46/1.23 inference(transitivity,[status(thm)],[1449, 1447])).
% 1.46/1.23 tff(1451,plain,
% 1.46/1.23 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a164) | c0_1(a164) | (~c3_1(a164)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132)))),
% 1.46/1.23 inference(quant_inst,[status(thm)],[])).
% 1.46/1.23 tff(1452,plain,
% 1.46/1.23 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a164) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c1_1(a132)) | (~c3_1(a164)) | c0_1(a164)),
% 1.46/1.23 inference(modus_ponens,[status(thm)],[1451, 1450])).
% 1.46/1.23 tff(1453,plain,
% 1.46/1.23 (hskp12 | (~c1_1(a132)) | c0_1(a164)),
% 1.46/1.23 inference(unit_resolution,[status(thm)],[1452, 123, 1356, 1355, 1414, 1377, 1446])).
% 1.46/1.23 tff(1454,plain,
% 1.46/1.23 (hskp12),
% 1.46/1.23 inference(unit_resolution,[status(thm)],[1453, 1413, 1436])).
% 1.46/1.23 tff(1455,plain,
% 1.46/1.23 (~c1_1(a142)),
% 1.46/1.23 inference(unit_resolution,[status(thm)],[150, 1454])).
% 1.46/1.23 tff(1456,plain,
% 1.46/1.23 (c3_1(a142)),
% 1.46/1.23 inference(unit_resolution,[status(thm)],[161, 1454])).
% 1.46/1.23 tff(1457,plain,
% 1.46/1.23 (c0_1(a142)),
% 1.46/1.23 inference(unit_resolution,[status(thm)],[189, 1454])).
% 1.46/1.23 tff(1458,plain,
% 1.46/1.23 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c1_1(a142) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c3_1(a142)) | (~c0_1(a142)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c1_1(a142) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c3_1(a142)) | (~c0_1(a142)))),
% 1.46/1.23 inference(rewrite,[status(thm)],[])).
% 1.46/1.23 tff(1459,plain,
% 1.46/1.23 ((hskp6 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142)) | c1_1(a123) | c0_1(a123) | (~c3_1(a123))) <=> (hskp6 | c1_1(a142) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c3_1(a142)) | (~c0_1(a142)))),
% 1.46/1.23 inference(rewrite,[status(thm)],[])).
% 1.46/1.23 tff(1460,plain,
% 1.46/1.23 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142)) | c1_1(a123) | c0_1(a123) | (~c3_1(a123)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c1_1(a142) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c3_1(a142)) | (~c0_1(a142))))),
% 1.46/1.23 inference(monotonicity,[status(thm)],[1459])).
% 1.46/1.23 tff(1461,plain,
% 1.46/1.23 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142)) | c1_1(a123) | c0_1(a123) | (~c3_1(a123)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c1_1(a142) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c3_1(a142)) | (~c0_1(a142)))),
% 1.46/1.23 inference(transitivity,[status(thm)],[1460, 1458])).
% 1.46/1.23 tff(1462,plain,
% 1.46/1.23 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142)) | c1_1(a123) | c0_1(a123) | (~c3_1(a123)))),
% 1.46/1.23 inference(quant_inst,[status(thm)],[])).
% 1.46/1.23 tff(1463,plain,
% 1.46/1.23 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c1_1(a142) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c3_1(a142)) | (~c0_1(a142))),
% 1.46/1.23 inference(modus_ponens,[status(thm)],[1462, 1461])).
% 1.46/1.23 tff(1464,plain,
% 1.46/1.23 (~c3_1(a123)),
% 1.46/1.23 inference(unit_resolution,[status(thm)],[1463, 123, 1380, 1457, 1456, 1455, 1418, 1417, 1346])).
% 1.46/1.23 tff(1465,plain,
% 1.46/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a182) | c2_1(a182) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | c1_1(a182))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a182) | c2_1(a182) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | c1_1(a182))),
% 1.46/1.23 inference(rewrite,[status(thm)],[])).
% 1.46/1.23 tff(1466,plain,
% 1.46/1.23 (((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132)) | c2_1(a182) | c1_1(a182) | c0_1(a182)) <=> (c0_1(a182) | c2_1(a182) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | c1_1(a182))),
% 1.46/1.23 inference(rewrite,[status(thm)],[])).
% 1.46/1.23 tff(1467,plain,
% 1.46/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132)) | c2_1(a182) | c1_1(a182) | c0_1(a182))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a182) | c2_1(a182) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | c1_1(a182)))),
% 1.46/1.23 inference(monotonicity,[status(thm)],[1466])).
% 1.46/1.23 tff(1468,plain,
% 1.46/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132)) | c2_1(a182) | c1_1(a182) | c0_1(a182))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a182) | c2_1(a182) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | c1_1(a182))),
% 1.46/1.23 inference(transitivity,[status(thm)],[1467, 1465])).
% 1.46/1.23 tff(1469,plain,
% 1.46/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132)) | c2_1(a182) | c1_1(a182) | c0_1(a182))),
% 1.46/1.23 inference(quant_inst,[status(thm)],[])).
% 1.46/1.23 tff(1470,plain,
% 1.46/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a182) | c2_1(a182) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | c1_1(a182)),
% 1.46/1.23 inference(modus_ponens,[status(thm)],[1469, 1468])).
% 1.46/1.23 tff(1471,plain,
% 1.46/1.23 ((~c1_1(a132)) | c1_1(a182)),
% 1.46/1.23 inference(unit_resolution,[status(thm)],[1470, 123, 1378, 1369, 1368, 1414, 1377, 406])).
% 1.46/1.23 tff(1472,plain,
% 1.46/1.23 (c1_1(a182)),
% 1.46/1.23 inference(unit_resolution,[status(thm)],[1471, 1413])).
% 1.46/1.23 tff(1473,plain,
% 1.46/1.23 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))))),
% 1.46/1.23 inference(bind,[status(th)],[])).
% 1.46/1.23 tff(1474,plain,
% 1.46/1.23 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.46/1.23 inference(quant_intro,[status(thm)],[1473])).
% 1.46/1.23 tff(1475,plain,
% 1.46/1.23 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.46/1.23 inference(rewrite,[status(thm)],[])).
% 1.46/1.23 tff(1476,plain,
% 1.46/1.23 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(W)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(W))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c2_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c2_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c2_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))))),
% 1.46/1.23 inference(bind,[status(th)],[])).
% 1.46/1.23 tff(1477,plain,
% 1.46/1.23 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_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)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.46/1.23 inference(quant_intro,[status(thm)],[1476])).
% 1.46/1.23 tff(1478,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause196')).
% 1.46/1.23 tff(1479,plain,
% 1.46/1.23 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.46/1.23 inference(modus_ponens,[status(thm)],[1478, 1477])).
% 1.46/1.23 tff(1480,plain,
% 1.46/1.23 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.46/1.23 inference(modus_ponens,[status(thm)],[1479, 1475])).
% 1.46/1.23 tff(1481,plain,(
% 1.46/1.23 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.46/1.23 inference(skolemize,[status(sab)],[1480])).
% 1.46/1.23 tff(1482,plain,
% 1.46/1.23 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.46/1.23 inference(modus_ponens,[status(thm)],[1481, 1474])).
% 1.46/1.23 tff(1483,plain,
% 1.46/1.23 (c2_1(a123)),
% 1.46/1.23 inference(unit_resolution,[status(thm)],[213, 1416])).
% 1.46/1.23 tff(1484,plain,
% 1.46/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a182) | c3_1(a182) | c2_1(a164) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a164)) | (~c1_1(a164)) | (~c1_1(a182)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a182) | c3_1(a182) | c2_1(a164) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a164)) | (~c1_1(a164)) | (~c1_1(a182)))),
% 1.46/1.23 inference(rewrite,[status(thm)],[])).
% 1.46/1.23 tff(1485,plain,
% 1.46/1.23 (((~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)) | c2_1(a182) | c3_1(a182) | (~c1_1(a182)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123))) <=> (c2_1(a182) | c3_1(a182) | c2_1(a164) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a164)) | (~c1_1(a164)) | (~c1_1(a182)))),
% 1.46/1.23 inference(rewrite,[status(thm)],[])).
% 1.46/1.23 tff(1486,plain,
% 1.46/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)) | c2_1(a182) | c3_1(a182) | (~c1_1(a182)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a182) | c3_1(a182) | c2_1(a164) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a164)) | (~c1_1(a164)) | (~c1_1(a182))))),
% 1.46/1.23 inference(monotonicity,[status(thm)],[1485])).
% 1.46/1.23 tff(1487,plain,
% 1.46/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)) | c2_1(a182) | c3_1(a182) | (~c1_1(a182)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a182) | c3_1(a182) | c2_1(a164) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a164)) | (~c1_1(a164)) | (~c1_1(a182)))),
% 1.46/1.23 inference(transitivity,[status(thm)],[1486, 1484])).
% 1.46/1.23 tff(1488,plain,
% 1.46/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)) | c2_1(a182) | c3_1(a182) | (~c1_1(a182)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)))),
% 1.46/1.23 inference(quant_inst,[status(thm)],[])).
% 1.46/1.23 tff(1489,plain,
% 1.46/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a182) | c3_1(a182) | c2_1(a164) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a164)) | (~c1_1(a164)) | (~c1_1(a182))),
% 1.46/1.23 inference(modus_ponens,[status(thm)],[1488, 1487])).
% 1.46/1.23 tff(1490,plain,
% 1.46/1.23 ($false),
% 1.46/1.23 inference(unit_resolution,[status(thm)],[1489, 123, 1357, 1356, 1483, 1368, 1367, 1355, 1418, 1482, 1472, 1464])).
% 1.46/1.23 tff(1491,plain,(hskp17 | hskp9 | c1_1(a131) | c2_1(a131)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.23 tff(1492,plain,
% 1.46/1.23 (hskp17),
% 1.46/1.23 inference(unit_resolution,[status(thm)],[1491, 132, 33, 95])).
% 1.46/1.23 tff(1493,plain,
% 1.46/1.23 (~c2_1(a155)),
% 1.46/1.23 inference(unit_resolution,[status(thm)],[382, 1492])).
% 1.46/1.23 tff(1494,plain,
% 1.46/1.23 (~c0_1(a155)),
% 1.46/1.23 inference(unit_resolution,[status(thm)],[388, 1492])).
% 1.46/1.23 tff(1495,plain,
% 1.46/1.23 (c1_1(a155)),
% 1.46/1.23 inference(unit_resolution,[status(thm)],[416, 1492])).
% 1.46/1.23 tff(1496,plain,
% 1.46/1.23 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp13 | c0_1(a155) | c2_1(a155) | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c1_1(a155)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp13 | c0_1(a155) | c2_1(a155) | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c1_1(a155)))),
% 1.46/1.23 inference(rewrite,[status(thm)],[])).
% 1.46/1.23 tff(1497,plain,
% 1.46/1.23 ((hskp13 | (~ndr1_0) | c2_1(a131) | c1_1(a131) | (~c0_1(a131)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155))) <=> (hskp13 | c0_1(a155) | c2_1(a155) | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c1_1(a155)))),
% 1.46/1.23 inference(rewrite,[status(thm)],[])).
% 1.46/1.23 tff(1498,plain,
% 1.46/1.23 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | c2_1(a131) | c1_1(a131) | (~c0_1(a131)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp13 | c0_1(a155) | c2_1(a155) | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c1_1(a155))))),
% 1.46/1.23 inference(monotonicity,[status(thm)],[1497])).
% 1.46/1.23 tff(1499,plain,
% 1.46/1.23 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | c2_1(a131) | c1_1(a131) | (~c0_1(a131)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp13 | c0_1(a155) | c2_1(a155) | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c1_1(a155)))),
% 1.46/1.23 inference(transitivity,[status(thm)],[1498, 1496])).
% 1.46/1.23 tff(1500,plain,
% 1.46/1.23 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp13 | (~ndr1_0) | c2_1(a131) | c1_1(a131) | (~c0_1(a131)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)))),
% 1.46/1.23 inference(quant_inst,[status(thm)],[])).
% 1.46/1.23 tff(1501,plain,
% 1.46/1.23 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp13 | c0_1(a155) | c2_1(a155) | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c1_1(a155))),
% 1.46/1.23 inference(modus_ponens,[status(thm)],[1500, 1499])).
% 1.46/1.23 tff(1502,plain,
% 1.46/1.23 (hskp13),
% 1.46/1.23 inference(unit_resolution,[status(thm)],[1501, 123, 1495, 1494, 1493, 1336, 132, 95, 1160])).
% 1.46/1.23 tff(1503,plain,
% 1.46/1.23 (~c1_1(a143)),
% 1.46/1.23 inference(unit_resolution,[status(thm)],[782, 1502])).
% 1.46/1.23 tff(1504,assumption,(~c2_1(a155)), introduced(assumption)).
% 1.46/1.23 tff(1505,assumption,(~c0_1(a155)), introduced(assumption)).
% 1.46/1.23 tff(1506,plain,
% 1.46/1.23 (hskp7 | c3_1(a155)),
% 1.46/1.23 inference(unit_resolution,[status(thm)],[395, 123, 33, 1505, 1504, 94])).
% 1.46/1.23 tff(1507,plain,
% 1.46/1.23 (c3_1(a155)),
% 1.46/1.23 inference(unit_resolution,[status(thm)],[1506, 96])).
% 1.46/1.23 tff(1508,assumption,(c1_1(a155)), introduced(assumption)).
% 1.46/1.23 tff(1509,plain,
% 1.46/1.23 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a155) | c2_1(a155) | (~ndr1_0) | (~c3_1(a155)) | (~c1_1(a155)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a155) | c2_1(a155) | (~ndr1_0) | (~c3_1(a155)) | (~c1_1(a155)))),
% 1.46/1.23 inference(rewrite,[status(thm)],[])).
% 1.46/1.23 tff(1510,plain,
% 1.46/1.23 ((hskp12 | (~ndr1_0) | c2_1(a155) | c0_1(a155) | (~c3_1(a155)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155))) <=> (hskp12 | c0_1(a155) | c2_1(a155) | (~ndr1_0) | (~c3_1(a155)) | (~c1_1(a155)))),
% 1.46/1.23 inference(rewrite,[status(thm)],[])).
% 1.46/1.23 tff(1511,plain,
% 1.46/1.23 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a155) | c0_1(a155) | (~c3_1(a155)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a155) | c2_1(a155) | (~ndr1_0) | (~c3_1(a155)) | (~c1_1(a155))))),
% 1.46/1.23 inference(monotonicity,[status(thm)],[1510])).
% 1.46/1.23 tff(1512,plain,
% 1.46/1.23 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a155) | c0_1(a155) | (~c3_1(a155)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a155) | c2_1(a155) | (~ndr1_0) | (~c3_1(a155)) | (~c1_1(a155)))),
% 1.46/1.23 inference(transitivity,[status(thm)],[1511, 1509])).
% 1.46/1.23 tff(1513,plain,
% 1.46/1.23 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a155) | c0_1(a155) | (~c3_1(a155)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)))),
% 1.46/1.23 inference(quant_inst,[status(thm)],[])).
% 1.46/1.23 tff(1514,plain,
% 1.46/1.23 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a155) | c2_1(a155) | (~ndr1_0) | (~c3_1(a155)) | (~c1_1(a155))),
% 1.46/1.23 inference(modus_ponens,[status(thm)],[1513, 1512])).
% 1.46/1.23 tff(1515,plain,
% 1.46/1.23 (hskp12 | (~c3_1(a155))),
% 1.46/1.23 inference(unit_resolution,[status(thm)],[1514, 123, 1508, 1505, 1504, 1446])).
% 1.46/1.23 tff(1516,plain,
% 1.46/1.23 (hskp12),
% 1.46/1.23 inference(unit_resolution,[status(thm)],[1515, 1507])).
% 1.46/1.23 tff(1517,plain,
% 1.46/1.23 (~c1_1(a142)),
% 1.46/1.23 inference(unit_resolution,[status(thm)],[150, 1516])).
% 1.46/1.23 tff(1518,plain,
% 1.46/1.23 (c3_1(a142)),
% 1.46/1.23 inference(unit_resolution,[status(thm)],[161, 1516])).
% 1.46/1.23 tff(1519,plain,
% 1.46/1.23 (c0_1(a142)),
% 1.46/1.23 inference(unit_resolution,[status(thm)],[189, 1516])).
% 1.46/1.23 tff(1520,plain,
% 1.46/1.23 (hskp0),
% 1.46/1.23 inference(unit_resolution,[status(thm)],[196, 123, 96, 1519, 1518, 1517, 179])).
% 1.46/1.23 tff(1521,plain,
% 1.46/1.23 (~c1_1(a123)),
% 1.46/1.23 inference(unit_resolution,[status(thm)],[202, 1520])).
% 1.46/1.23 tff(1522,plain,
% 1.46/1.23 (~c0_1(a123)),
% 1.46/1.23 inference(unit_resolution,[status(thm)],[236, 1520])).
% 1.46/1.23 tff(1523,plain,
% 1.46/1.23 (((~![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp6 | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142)))) <=> ((~![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp6 | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142)))),
% 1.46/1.23 inference(rewrite,[status(thm)],[])).
% 1.46/1.23 tff(1524,plain,
% 1.46/1.23 ((hskp21 | hskp6 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142))) <=> (hskp21 | hskp6 | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142)))),
% 1.46/1.23 inference(rewrite,[status(thm)],[])).
% 1.46/1.23 tff(1525,plain,
% 1.46/1.23 (((~![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp6 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142)))) <=> ((~![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp6 | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142))))),
% 1.46/1.23 inference(monotonicity,[status(thm)],[1524])).
% 1.46/1.23 tff(1526,plain,
% 1.46/1.23 (((~![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp6 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142)))) <=> ((~![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp6 | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142)))),
% 1.46/1.23 inference(transitivity,[status(thm)],[1525, 1523])).
% 1.46/1.23 tff(1527,plain,
% 1.46/1.23 ((~![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp6 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142)))),
% 1.46/1.23 inference(quant_inst,[status(thm)],[])).
% 1.46/1.23 tff(1528,plain,
% 1.46/1.23 ((~![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp6 | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142))),
% 1.46/1.23 inference(modus_ponens,[status(thm)],[1527, 1526])).
% 1.46/1.23 tff(1529,plain,
% 1.46/1.23 (hskp21),
% 1.46/1.23 inference(unit_resolution,[status(thm)],[1528, 123, 1403, 1519, 1518, 1517, 1150])).
% 1.46/1.23 tff(1530,plain,
% 1.46/1.23 (((~hskp21) | (~c1_1(a170))) <=> ((~hskp21) | (~c1_1(a170)))),
% 1.46/1.23 inference(rewrite,[status(thm)],[])).
% 1.46/1.23 tff(1531,plain,
% 1.46/1.23 (((~c1_1(a170)) | (~hskp21)) <=> ((~hskp21) | (~c1_1(a170)))),
% 1.46/1.23 inference(rewrite,[status(thm)],[])).
% 1.46/1.23 tff(1532,axiom,((~c1_1(a170)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause94')).
% 1.46/1.23 tff(1533,plain,
% 1.46/1.23 ((~hskp21) | (~c1_1(a170))),
% 1.46/1.23 inference(modus_ponens,[status(thm)],[1532, 1531])).
% 1.46/1.23 tff(1534,plain,
% 1.46/1.23 ((~hskp21) | (~c1_1(a170))),
% 1.46/1.23 inference(modus_ponens,[status(thm)],[1533, 1530])).
% 1.46/1.23 tff(1535,plain,
% 1.46/1.23 (~c1_1(a170)),
% 1.46/1.23 inference(unit_resolution,[status(thm)],[1534, 1529])).
% 1.46/1.23 tff(1536,plain,
% 1.46/1.23 (c2_1(a123)),
% 1.46/1.23 inference(unit_resolution,[status(thm)],[213, 1520])).
% 1.46/1.23 tff(1537,plain,
% 1.46/1.23 (((~hskp21) | c2_1(a170)) <=> ((~hskp21) | c2_1(a170))),
% 1.46/1.23 inference(rewrite,[status(thm)],[])).
% 1.46/1.23 tff(1538,axiom,((~hskp21) | c2_1(a170)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause56')).
% 1.46/1.23 tff(1539,plain,
% 1.46/1.23 ((~hskp21) | c2_1(a170)),
% 1.46/1.23 inference(modus_ponens,[status(thm)],[1538, 1537])).
% 1.46/1.23 tff(1540,plain,
% 1.46/1.23 ((~hskp21) | c2_1(a170)),
% 1.46/1.23 inference(modus_ponens,[status(thm)],[1539, 1537])).
% 1.46/1.23 tff(1541,plain,
% 1.46/1.23 ((~hskp21) | c2_1(a170)),
% 1.46/1.23 inference(modus_ponens,[status(thm)],[1540, 1537])).
% 1.46/1.23 tff(1542,plain,
% 1.46/1.23 ((~hskp21) | c2_1(a170)),
% 1.46/1.23 inference(modus_ponens,[status(thm)],[1541, 1537])).
% 1.46/1.23 tff(1543,plain,
% 1.46/1.23 ((~hskp21) | c2_1(a170)),
% 1.46/1.23 inference(modus_ponens,[status(thm)],[1542, 1537])).
% 1.46/1.23 tff(1544,plain,
% 1.46/1.23 ((~hskp21) | c2_1(a170)),
% 1.46/1.23 inference(modus_ponens,[status(thm)],[1543, 1537])).
% 1.46/1.23 tff(1545,plain,
% 1.46/1.23 ((~hskp21) | c2_1(a170)),
% 1.46/1.23 inference(modus_ponens,[status(thm)],[1544, 1537])).
% 1.46/1.23 tff(1546,plain,
% 1.46/1.23 ((~hskp21) | c2_1(a170)),
% 1.46/1.23 inference(modus_ponens,[status(thm)],[1545, 1537])).
% 1.46/1.23 tff(1547,plain,
% 1.46/1.23 (c2_1(a170)),
% 1.46/1.23 inference(unit_resolution,[status(thm)],[1546, 1529])).
% 1.46/1.23 tff(1548,plain,
% 1.46/1.23 (((~hskp21) | c0_1(a170)) <=> ((~hskp21) | c0_1(a170))),
% 1.46/1.23 inference(rewrite,[status(thm)],[])).
% 1.46/1.23 tff(1549,axiom,((~hskp21) | c0_1(a170)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause55')).
% 1.46/1.23 tff(1550,plain,
% 1.46/1.23 ((~hskp21) | c0_1(a170)),
% 1.46/1.23 inference(modus_ponens,[status(thm)],[1549, 1548])).
% 1.46/1.23 tff(1551,plain,
% 1.46/1.23 ((~hskp21) | c0_1(a170)),
% 1.46/1.23 inference(modus_ponens,[status(thm)],[1550, 1548])).
% 1.46/1.23 tff(1552,plain,
% 1.46/1.23 ((~hskp21) | c0_1(a170)),
% 1.46/1.23 inference(modus_ponens,[status(thm)],[1551, 1548])).
% 1.46/1.23 tff(1553,plain,
% 1.46/1.23 ((~hskp21) | c0_1(a170)),
% 1.46/1.23 inference(modus_ponens,[status(thm)],[1552, 1548])).
% 1.46/1.23 tff(1554,plain,
% 1.46/1.23 ((~hskp21) | c0_1(a170)),
% 1.46/1.23 inference(modus_ponens,[status(thm)],[1553, 1548])).
% 1.46/1.23 tff(1555,plain,
% 1.46/1.23 ((~hskp21) | c0_1(a170)),
% 1.46/1.23 inference(modus_ponens,[status(thm)],[1554, 1548])).
% 1.46/1.23 tff(1556,plain,
% 1.46/1.23 ((~hskp21) | c0_1(a170)),
% 1.46/1.23 inference(modus_ponens,[status(thm)],[1555, 1548])).
% 1.46/1.23 tff(1557,plain,
% 1.46/1.23 ((~hskp21) | c0_1(a170)),
% 1.46/1.23 inference(modus_ponens,[status(thm)],[1556, 1548])).
% 1.46/1.23 tff(1558,plain,
% 1.46/1.23 (c0_1(a170)),
% 1.46/1.23 inference(unit_resolution,[status(thm)],[1557, 1529])).
% 1.46/1.23 tff(1559,plain,
% 1.46/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a170) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | (~c2_1(a123)) | (~c2_1(a170)) | (~c0_1(a170)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a170) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | (~c2_1(a123)) | (~c2_1(a170)) | (~c0_1(a170)))),
% 1.46/1.24 inference(rewrite,[status(thm)],[])).
% 1.46/1.24 tff(1560,plain,
% 1.46/1.24 (((~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | c1_1(a170) | (~c2_1(a170)) | (~c0_1(a170)) | c1_1(a123) | c0_1(a123) | (~c2_1(a123))) <=> (c1_1(a170) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | (~c2_1(a123)) | (~c2_1(a170)) | (~c0_1(a170)))),
% 1.46/1.24 inference(rewrite,[status(thm)],[])).
% 1.46/1.24 tff(1561,plain,
% 1.46/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | c1_1(a170) | (~c2_1(a170)) | (~c0_1(a170)) | c1_1(a123) | c0_1(a123) | (~c2_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a170) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | (~c2_1(a123)) | (~c2_1(a170)) | (~c0_1(a170))))),
% 1.46/1.24 inference(monotonicity,[status(thm)],[1560])).
% 1.46/1.24 tff(1562,plain,
% 1.46/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | c1_1(a170) | (~c2_1(a170)) | (~c0_1(a170)) | c1_1(a123) | c0_1(a123) | (~c2_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a170) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | (~c2_1(a123)) | (~c2_1(a170)) | (~c0_1(a170)))),
% 1.46/1.24 inference(transitivity,[status(thm)],[1561, 1559])).
% 1.46/1.24 tff(1563,plain,
% 1.46/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | c1_1(a170) | (~c2_1(a170)) | (~c0_1(a170)) | c1_1(a123) | c0_1(a123) | (~c2_1(a123)))),
% 1.46/1.24 inference(quant_inst,[status(thm)],[])).
% 1.46/1.24 tff(1564,plain,
% 1.46/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a170) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | (~c2_1(a123)) | (~c2_1(a170)) | (~c0_1(a170))),
% 1.46/1.24 inference(modus_ponens,[status(thm)],[1563, 1562])).
% 1.46/1.24 tff(1565,plain,
% 1.46/1.24 (~c2_1(a167)),
% 1.46/1.24 inference(unit_resolution,[status(thm)],[1564, 123, 1187, 1176, 1558, 1547, 1536, 1535, 1522, 1521, 10])).
% 1.46/1.24 tff(1566,plain,
% 1.46/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a155) | c2_1(a155) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a155)) | (~c1_1(a155)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a155) | c2_1(a155) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a155)) | (~c1_1(a155)))),
% 1.46/1.24 inference(rewrite,[status(thm)],[])).
% 1.46/1.24 tff(1567,plain,
% 1.46/1.24 (((~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c0_1(a167)) | c2_1(a155) | c0_1(a155) | (~c3_1(a155)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155))) <=> (c0_1(a155) | c2_1(a155) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a155)) | (~c1_1(a155)))),
% 1.46/1.24 inference(rewrite,[status(thm)],[])).
% 1.46/1.24 tff(1568,plain,
% 1.46/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c0_1(a167)) | c2_1(a155) | c0_1(a155) | (~c3_1(a155)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a155) | c2_1(a155) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a155)) | (~c1_1(a155))))),
% 1.46/1.24 inference(monotonicity,[status(thm)],[1567])).
% 1.46/1.24 tff(1569,plain,
% 1.46/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c0_1(a167)) | c2_1(a155) | c0_1(a155) | (~c3_1(a155)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a155) | c2_1(a155) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a155)) | (~c1_1(a155)))),
% 1.46/1.24 inference(transitivity,[status(thm)],[1568, 1566])).
% 1.46/1.24 tff(1570,plain,
% 1.46/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c0_1(a167)) | c2_1(a155) | c0_1(a155) | (~c3_1(a155)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)))),
% 1.46/1.24 inference(quant_inst,[status(thm)],[])).
% 1.46/1.24 tff(1571,plain,
% 1.46/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a155) | c2_1(a155) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a155)) | (~c1_1(a155))),
% 1.46/1.24 inference(modus_ponens,[status(thm)],[1570, 1569])).
% 1.46/1.24 tff(1572,plain,
% 1.46/1.24 ($false),
% 1.46/1.24 inference(unit_resolution,[status(thm)],[1571, 123, 1130, 1176, 1508, 1505, 1504, 1428, 1565, 1507])).
% 1.46/1.24 tff(1573,plain,(hskp7 | (~c1_1(a155)) | c0_1(a155) | c2_1(a155) | hskp6 | hskp9), inference(lemma,lemma(discharge,[]))).
% 1.46/1.24 tff(1574,plain,
% 1.46/1.24 (hskp7),
% 1.46/1.24 inference(unit_resolution,[status(thm)],[1573, 1495, 1494, 1493, 1380, 33])).
% 1.46/1.24 tff(1575,plain,
% 1.46/1.24 (~c2_1(a132)),
% 1.46/1.24 inference(unit_resolution,[status(thm)],[898, 1574])).
% 1.46/1.24 tff(1576,plain,
% 1.46/1.24 (c2_1(a143)),
% 1.46/1.24 inference(unit_resolution,[status(thm)],[836, 1502])).
% 1.46/1.24 tff(1577,plain,
% 1.46/1.24 (c3_1(a143)),
% 1.46/1.24 inference(unit_resolution,[status(thm)],[825, 1502])).
% 1.46/1.24 tff(1578,plain,
% 1.46/1.24 (c3_1(a132)),
% 1.46/1.24 inference(unit_resolution,[status(thm)],[447, 1574])).
% 1.46/1.24 tff(1579,plain,
% 1.46/1.24 (c1_1(a132)),
% 1.46/1.24 inference(unit_resolution,[status(thm)],[1412, 1578, 1380, 1577, 1576, 1575, 1503])).
% 1.46/1.24 tff(1580,plain,
% 1.46/1.24 (~c0_1(a132)),
% 1.46/1.24 inference(unit_resolution,[status(thm)],[431, 1574])).
% 1.46/1.24 tff(1581,plain,
% 1.46/1.24 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)))),
% 1.46/1.24 inference(rewrite,[status(thm)],[])).
% 1.46/1.24 tff(1582,plain,
% 1.46/1.24 ((hskp12 | (~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132))) <=> (hskp12 | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)))),
% 1.46/1.24 inference(rewrite,[status(thm)],[])).
% 1.46/1.24 tff(1583,plain,
% 1.46/1.24 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132))))),
% 1.46/1.24 inference(monotonicity,[status(thm)],[1582])).
% 1.46/1.24 tff(1584,plain,
% 1.46/1.24 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)))),
% 1.46/1.24 inference(transitivity,[status(thm)],[1583, 1581])).
% 1.46/1.24 tff(1585,plain,
% 1.46/1.24 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132)))),
% 1.46/1.24 inference(quant_inst,[status(thm)],[])).
% 1.46/1.24 tff(1586,plain,
% 1.46/1.24 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132))),
% 1.46/1.24 inference(modus_ponens,[status(thm)],[1585, 1584])).
% 1.46/1.24 tff(1587,plain,
% 1.46/1.24 (hskp12),
% 1.46/1.24 inference(unit_resolution,[status(thm)],[1586, 123, 1578, 1580, 1575, 1446, 1579])).
% 1.46/1.24 tff(1588,plain,
% 1.46/1.24 (~c1_1(a142)),
% 1.46/1.24 inference(unit_resolution,[status(thm)],[150, 1587])).
% 1.46/1.24 tff(1589,plain,
% 1.46/1.24 (c3_1(a142)),
% 1.46/1.24 inference(unit_resolution,[status(thm)],[161, 1587])).
% 1.46/1.24 tff(1590,plain,
% 1.46/1.24 (c0_1(a142)),
% 1.46/1.24 inference(unit_resolution,[status(thm)],[189, 1587])).
% 1.46/1.24 tff(1591,plain,
% 1.46/1.24 (hskp21),
% 1.46/1.24 inference(unit_resolution,[status(thm)],[1528, 123, 1380, 1590, 1589, 1588, 1150])).
% 1.46/1.24 tff(1592,plain,
% 1.46/1.24 (~c1_1(a170)),
% 1.46/1.24 inference(unit_resolution,[status(thm)],[1534, 1591])).
% 1.46/1.24 tff(1593,plain,
% 1.46/1.24 (c2_1(a170)),
% 1.46/1.24 inference(unit_resolution,[status(thm)],[1546, 1591])).
% 1.46/1.24 tff(1594,plain,
% 1.46/1.24 (c0_1(a170)),
% 1.46/1.24 inference(unit_resolution,[status(thm)],[1557, 1591])).
% 1.46/1.24 tff(1595,assumption,(c2_1(a167)), introduced(assumption)).
% 1.46/1.24 tff(1596,plain,
% 1.46/1.24 (^[U: $i] : refl((hskp9 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) <=> (hskp9 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))),
% 1.46/1.24 inference(bind,[status(th)],[])).
% 1.46/1.24 tff(1597,plain,
% 1.46/1.24 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 1.46/1.24 inference(quant_intro,[status(thm)],[1596])).
% 1.46/1.24 tff(1598,plain,
% 1.46/1.24 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 1.46/1.24 inference(rewrite,[status(thm)],[])).
% 1.46/1.24 tff(1599,plain,
% 1.46/1.24 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp9) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | hskp9))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | hskp9) <=> (hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp9) <=> (hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp9) | hskp8) <=> ((hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | hskp8))), rewrite(((hskp9 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | hskp8) <=> (hskp9 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp9) | hskp8) <=> (hskp9 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))))),
% 1.46/1.24 inference(bind,[status(th)],[])).
% 1.46/1.24 tff(1600,plain,
% 1.46/1.24 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp9) | hskp8) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 1.46/1.24 inference(quant_intro,[status(thm)],[1599])).
% 1.46/1.24 tff(1601,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp9) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause166')).
% 1.46/1.24 tff(1602,plain,
% 1.46/1.24 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 1.46/1.24 inference(modus_ponens,[status(thm)],[1601, 1600])).
% 1.46/1.24 tff(1603,plain,
% 1.46/1.24 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 1.46/1.24 inference(modus_ponens,[status(thm)],[1602, 1598])).
% 1.46/1.24 tff(1604,plain,(
% 1.46/1.24 ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 1.46/1.24 inference(skolemize,[status(sab)],[1603])).
% 1.46/1.24 tff(1605,plain,
% 1.46/1.24 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 1.46/1.24 inference(modus_ponens,[status(thm)],[1604, 1597])).
% 1.46/1.24 tff(1606,plain,
% 1.46/1.24 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp9 | hskp8 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)))),
% 1.46/1.24 inference(rewrite,[status(thm)],[])).
% 1.46/1.24 tff(1607,plain,
% 1.46/1.24 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)))),
% 1.46/1.24 inference(quant_inst,[status(thm)],[])).
% 1.46/1.24 tff(1608,plain,
% 1.46/1.24 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp9 | hskp8 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167))),
% 1.46/1.24 inference(modus_ponens,[status(thm)],[1607, 1606])).
% 1.46/1.24 tff(1609,plain,
% 1.46/1.24 (hskp8 | (~c2_1(a167))),
% 1.46/1.24 inference(unit_resolution,[status(thm)],[1608, 123, 33, 1187, 1176, 1605])).
% 1.46/1.24 tff(1610,plain,
% 1.46/1.24 (hskp8),
% 1.46/1.24 inference(unit_resolution,[status(thm)],[1609, 1595])).
% 1.46/1.24 tff(1611,plain,
% 1.46/1.24 (((~hskp8) | (~c3_1(a134))) <=> ((~hskp8) | (~c3_1(a134)))),
% 1.46/1.24 inference(rewrite,[status(thm)],[])).
% 1.46/1.24 tff(1612,plain,
% 1.46/1.24 (((~c3_1(a134)) | (~hskp8)) <=> ((~hskp8) | (~c3_1(a134)))),
% 1.46/1.24 inference(rewrite,[status(thm)],[])).
% 1.46/1.24 tff(1613,axiom,((~c3_1(a134)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause115')).
% 1.46/1.24 tff(1614,plain,
% 1.46/1.24 ((~hskp8) | (~c3_1(a134))),
% 1.46/1.24 inference(modus_ponens,[status(thm)],[1613, 1612])).
% 1.46/1.24 tff(1615,plain,
% 1.46/1.24 ((~hskp8) | (~c3_1(a134))),
% 1.46/1.24 inference(modus_ponens,[status(thm)],[1614, 1611])).
% 1.46/1.24 tff(1616,plain,
% 1.46/1.24 (~c3_1(a134)),
% 1.46/1.24 inference(unit_resolution,[status(thm)],[1615, 1610])).
% 1.46/1.24 tff(1617,plain,
% 1.46/1.24 (((~hskp8) | (~c0_1(a134))) <=> ((~hskp8) | (~c0_1(a134)))),
% 1.46/1.24 inference(rewrite,[status(thm)],[])).
% 1.46/1.24 tff(1618,plain,
% 1.46/1.24 (((~c0_1(a134)) | (~hskp8)) <=> ((~hskp8) | (~c0_1(a134)))),
% 1.46/1.24 inference(rewrite,[status(thm)],[])).
% 1.46/1.24 tff(1619,axiom,((~c0_1(a134)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause114')).
% 1.46/1.24 tff(1620,plain,
% 1.46/1.24 ((~hskp8) | (~c0_1(a134))),
% 1.46/1.24 inference(modus_ponens,[status(thm)],[1619, 1618])).
% 1.46/1.24 tff(1621,plain,
% 1.46/1.24 ((~hskp8) | (~c0_1(a134))),
% 1.46/1.24 inference(modus_ponens,[status(thm)],[1620, 1617])).
% 1.46/1.24 tff(1622,plain,
% 1.46/1.24 (~c0_1(a134)),
% 1.46/1.24 inference(unit_resolution,[status(thm)],[1621, 1610])).
% 1.46/1.24 tff(1623,plain,
% 1.46/1.24 (((~hskp8) | c2_1(a134)) <=> ((~hskp8) | c2_1(a134))),
% 1.46/1.24 inference(rewrite,[status(thm)],[])).
% 1.46/1.24 tff(1624,axiom,((~hskp8) | c2_1(a134)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause74')).
% 1.46/1.24 tff(1625,plain,
% 1.46/1.24 ((~hskp8) | c2_1(a134)),
% 1.46/1.24 inference(modus_ponens,[status(thm)],[1624, 1623])).
% 1.46/1.24 tff(1626,plain,
% 1.46/1.24 ((~hskp8) | c2_1(a134)),
% 1.46/1.24 inference(modus_ponens,[status(thm)],[1625, 1623])).
% 1.46/1.24 tff(1627,plain,
% 1.46/1.24 ((~hskp8) | c2_1(a134)),
% 1.46/1.24 inference(modus_ponens,[status(thm)],[1626, 1623])).
% 1.46/1.24 tff(1628,plain,
% 1.46/1.24 ((~hskp8) | c2_1(a134)),
% 1.46/1.24 inference(modus_ponens,[status(thm)],[1627, 1623])).
% 1.46/1.24 tff(1629,plain,
% 1.46/1.24 ((~hskp8) | c2_1(a134)),
% 1.46/1.24 inference(modus_ponens,[status(thm)],[1628, 1623])).
% 1.46/1.24 tff(1630,plain,
% 1.46/1.24 ((~hskp8) | c2_1(a134)),
% 1.46/1.24 inference(modus_ponens,[status(thm)],[1629, 1623])).
% 1.46/1.24 tff(1631,plain,
% 1.46/1.24 ((~hskp8) | c2_1(a134)),
% 1.46/1.24 inference(modus_ponens,[status(thm)],[1630, 1623])).
% 1.46/1.24 tff(1632,plain,
% 1.46/1.24 ((~hskp8) | c2_1(a134)),
% 1.46/1.24 inference(modus_ponens,[status(thm)],[1631, 1623])).
% 1.46/1.24 tff(1633,plain,
% 1.46/1.24 (c2_1(a134)),
% 1.46/1.24 inference(unit_resolution,[status(thm)],[1632, 1610])).
% 1.46/1.24 tff(1634,plain,
% 1.46/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a134) | c3_1(a134) | (~ndr1_0) | (~c3_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | (~c1_1(a134)) | (~c2_1(a134)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a134) | c3_1(a134) | (~ndr1_0) | (~c3_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | (~c1_1(a134)) | (~c2_1(a134)))),
% 1.46/1.24 inference(rewrite,[status(thm)],[])).
% 1.46/1.24 tff(1635,plain,
% 1.46/1.24 (((~ndr1_0) | (~c3_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | c3_1(a134) | (~c2_1(a134)) | (~c1_1(a134)) | c0_1(a134) | c3_1(a134) | (~c1_1(a134))) <=> (c0_1(a134) | c3_1(a134) | (~ndr1_0) | (~c3_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | (~c1_1(a134)) | (~c2_1(a134)))),
% 1.46/1.24 inference(rewrite,[status(thm)],[])).
% 1.46/1.24 tff(1636,plain,
% 1.46/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | c3_1(a134) | (~c2_1(a134)) | (~c1_1(a134)) | c0_1(a134) | c3_1(a134) | (~c1_1(a134)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a134) | c3_1(a134) | (~ndr1_0) | (~c3_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | (~c1_1(a134)) | (~c2_1(a134))))),
% 1.46/1.24 inference(monotonicity,[status(thm)],[1635])).
% 1.46/1.24 tff(1637,plain,
% 1.46/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | c3_1(a134) | (~c2_1(a134)) | (~c1_1(a134)) | c0_1(a134) | c3_1(a134) | (~c1_1(a134)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a134) | c3_1(a134) | (~ndr1_0) | (~c3_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | (~c1_1(a134)) | (~c2_1(a134)))),
% 1.46/1.24 inference(transitivity,[status(thm)],[1636, 1634])).
% 1.46/1.24 tff(1638,plain,
% 1.46/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | c3_1(a134) | (~c2_1(a134)) | (~c1_1(a134)) | c0_1(a134) | c3_1(a134) | (~c1_1(a134)))),
% 1.46/1.24 inference(quant_inst,[status(thm)],[])).
% 1.46/1.24 tff(1639,plain,
% 1.46/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a134) | c3_1(a134) | (~ndr1_0) | (~c3_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | (~c1_1(a134)) | (~c2_1(a134))),
% 1.46/1.24 inference(modus_ponens,[status(thm)],[1638, 1637])).
% 1.46/1.24 tff(1640,plain,
% 1.46/1.24 (~c1_1(a134)),
% 1.46/1.24 inference(unit_resolution,[status(thm)],[1639, 123, 1130, 1176, 1633, 1622, 1616, 490, 1595])).
% 1.46/1.24 tff(1641,assumption,(~c1_1(a170)), introduced(assumption)).
% 1.46/1.24 tff(1642,assumption,(c2_1(a170)), introduced(assumption)).
% 1.46/1.24 tff(1643,assumption,(c0_1(a170)), introduced(assumption)).
% 1.46/1.24 tff(1644,plain,
% 1.46/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a170) | c0_1(a134) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | c1_1(a134) | (~c2_1(a134)) | (~c2_1(a170)) | (~c0_1(a170)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a170) | c0_1(a134) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | c1_1(a134) | (~c2_1(a134)) | (~c2_1(a170)) | (~c0_1(a170)))),
% 1.46/1.24 inference(rewrite,[status(thm)],[])).
% 1.46/1.24 tff(1645,plain,
% 1.46/1.24 (((~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | c1_1(a170) | (~c2_1(a170)) | (~c0_1(a170)) | c1_1(a134) | c0_1(a134) | (~c2_1(a134))) <=> (c1_1(a170) | c0_1(a134) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | c1_1(a134) | (~c2_1(a134)) | (~c2_1(a170)) | (~c0_1(a170)))),
% 1.46/1.24 inference(rewrite,[status(thm)],[])).
% 1.46/1.24 tff(1646,plain,
% 1.46/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | c1_1(a170) | (~c2_1(a170)) | (~c0_1(a170)) | c1_1(a134) | c0_1(a134) | (~c2_1(a134)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a170) | c0_1(a134) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | c1_1(a134) | (~c2_1(a134)) | (~c2_1(a170)) | (~c0_1(a170))))),
% 1.46/1.24 inference(monotonicity,[status(thm)],[1645])).
% 1.46/1.24 tff(1647,plain,
% 1.46/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | c1_1(a170) | (~c2_1(a170)) | (~c0_1(a170)) | c1_1(a134) | c0_1(a134) | (~c2_1(a134)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a170) | c0_1(a134) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | c1_1(a134) | (~c2_1(a134)) | (~c2_1(a170)) | (~c0_1(a170)))),
% 1.46/1.24 inference(transitivity,[status(thm)],[1646, 1644])).
% 1.46/1.24 tff(1648,plain,
% 1.46/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | c1_1(a170) | (~c2_1(a170)) | (~c0_1(a170)) | c1_1(a134) | c0_1(a134) | (~c2_1(a134)))),
% 1.46/1.24 inference(quant_inst,[status(thm)],[])).
% 1.46/1.24 tff(1649,plain,
% 1.46/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a170) | c0_1(a134) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | c1_1(a134) | (~c2_1(a134)) | (~c2_1(a170)) | (~c0_1(a170))),
% 1.46/1.24 inference(modus_ponens,[status(thm)],[1648, 1647])).
% 1.46/1.24 tff(1650,plain,
% 1.46/1.24 ($false),
% 1.46/1.24 inference(unit_resolution,[status(thm)],[1649, 123, 1187, 1176, 1643, 1642, 1633, 1641, 1622, 10, 1595, 1640])).
% 1.46/1.24 tff(1651,plain,((~c2_1(a167)) | (~c0_1(a170)) | (~c2_1(a170)) | c1_1(a170) | hskp9), inference(lemma,lemma(discharge,[]))).
% 1.46/1.24 tff(1652,plain,
% 1.46/1.24 (~c2_1(a167)),
% 1.46/1.24 inference(unit_resolution,[status(thm)],[1651, 1594, 1593, 1592, 33])).
% 1.46/1.24 tff(1653,plain,
% 1.46/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a155) | c2_1(a155) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a132)) | (~c1_1(a155)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a155) | c2_1(a155) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a132)) | (~c1_1(a155)))),
% 1.46/1.24 inference(rewrite,[status(thm)],[])).
% 1.46/1.24 tff(1654,plain,
% 1.46/1.24 (((~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c0_1(a167)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155))) <=> (c0_1(a155) | c2_1(a155) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a132)) | (~c1_1(a155)))),
% 1.46/1.24 inference(rewrite,[status(thm)],[])).
% 1.46/1.24 tff(1655,plain,
% 1.46/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c0_1(a167)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a155) | c2_1(a155) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a132)) | (~c1_1(a155))))),
% 1.46/1.24 inference(monotonicity,[status(thm)],[1654])).
% 1.46/1.24 tff(1656,plain,
% 1.46/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c0_1(a167)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a155) | c2_1(a155) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a132)) | (~c1_1(a155)))),
% 1.46/1.24 inference(transitivity,[status(thm)],[1655, 1653])).
% 1.46/1.24 tff(1657,plain,
% 1.46/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c0_1(a167)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)))),
% 1.46/1.24 inference(quant_inst,[status(thm)],[])).
% 1.46/1.24 tff(1658,plain,
% 1.46/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a155) | c2_1(a155) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a132)) | (~c1_1(a155))),
% 1.46/1.24 inference(modus_ponens,[status(thm)],[1657, 1656])).
% 1.46/1.24 tff(1659,plain,
% 1.46/1.24 ($false),
% 1.46/1.24 inference(unit_resolution,[status(thm)],[1658, 123, 1130, 1176, 1495, 1578, 1494, 1493, 1580, 1575, 1428, 1652])).
% 1.46/1.24 tff(1660,plain,(c1_1(a131) | hskp9 | c2_1(a131)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.24 tff(1661,plain,
% 1.46/1.24 (c1_1(a131)),
% 1.46/1.24 inference(unit_resolution,[status(thm)],[1660, 95, 33])).
% 1.46/1.24 tff(1662,plain,
% 1.46/1.24 (~hskp6),
% 1.46/1.24 inference(unit_resolution,[status(thm)],[77, 1661])).
% 1.46/1.24 tff(1663,plain,
% 1.46/1.24 (hskp7),
% 1.46/1.24 inference(unit_resolution,[status(thm)],[1573, 469, 471, 468, 1403, 33])).
% 1.46/1.24 tff(1664,plain,
% 1.46/1.24 (~c2_1(a132)),
% 1.46/1.24 inference(unit_resolution,[status(thm)],[898, 1663])).
% 1.46/1.24 tff(1665,plain,
% 1.46/1.24 (~c0_1(a132)),
% 1.46/1.24 inference(unit_resolution,[status(thm)],[431, 1663])).
% 1.46/1.24 tff(1666,plain,
% 1.46/1.24 (c3_1(a132)),
% 1.46/1.24 inference(unit_resolution,[status(thm)],[447, 1663])).
% 1.46/1.24 tff(1667,plain,
% 1.46/1.24 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a155) | c2_1(a155) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a155)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a155) | c2_1(a155) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a155)))),
% 1.46/1.24 inference(rewrite,[status(thm)],[])).
% 1.46/1.24 tff(1668,plain,
% 1.46/1.24 ((hskp12 | (~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155))) <=> (hskp12 | c0_1(a155) | c2_1(a155) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a155)))),
% 1.46/1.24 inference(rewrite,[status(thm)],[])).
% 1.46/1.24 tff(1669,plain,
% 1.46/1.24 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c0_1(a155) | c2_1(a155) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a155))))),
% 1.46/1.24 inference(monotonicity,[status(thm)],[1668])).
% 1.46/1.24 tff(1670,plain,
% 1.46/1.24 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a155) | c2_1(a155) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a155)))),
% 1.46/1.25 inference(transitivity,[status(thm)],[1669, 1667])).
% 1.46/1.25 tff(1671,plain,
% 1.46/1.25 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)))),
% 1.46/1.25 inference(quant_inst,[status(thm)],[])).
% 1.46/1.25 tff(1672,plain,
% 1.46/1.25 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c0_1(a155) | c2_1(a155) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a155))),
% 1.46/1.25 inference(modus_ponens,[status(thm)],[1671, 1670])).
% 1.46/1.25 tff(1673,plain,
% 1.46/1.25 (hskp12),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[1672, 123, 471, 1666, 469, 468, 1665, 1664, 1446])).
% 1.46/1.25 tff(1674,plain,
% 1.46/1.25 (~c1_1(a142)),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[150, 1673])).
% 1.46/1.25 tff(1675,plain,
% 1.46/1.25 (c3_1(a142)),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[161, 1673])).
% 1.46/1.25 tff(1676,plain,
% 1.46/1.25 (c0_1(a142)),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[189, 1673])).
% 1.46/1.25 tff(1677,plain,
% 1.46/1.25 (hskp21),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[1528, 123, 1403, 1676, 1675, 1674, 1150])).
% 1.46/1.25 tff(1678,plain,
% 1.46/1.25 (~c1_1(a170)),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[1534, 1677])).
% 1.46/1.25 tff(1679,plain,
% 1.46/1.25 (c2_1(a170)),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[1546, 1677])).
% 1.46/1.25 tff(1680,plain,
% 1.46/1.25 (c0_1(a170)),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[1557, 1677])).
% 1.46/1.25 tff(1681,plain,
% 1.46/1.25 (~c2_1(a167)),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[1651, 1680, 1679, 1678, 33])).
% 1.46/1.25 tff(1682,plain,
% 1.46/1.25 ($false),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[1658, 123, 1130, 1176, 471, 1666, 469, 468, 1665, 1664, 1428, 1681])).
% 1.46/1.25 tff(1683,plain,((~hskp17) | hskp9 | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.46/1.25 tff(1684,plain,
% 1.46/1.25 (~hskp17),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[1683, 1662, 33])).
% 1.46/1.25 tff(1685,plain,
% 1.46/1.25 (hskp7 | c0_1(a131) | c3_1(a131)),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[129, 123, 33, 95, 94])).
% 1.46/1.25 tff(1686,plain,
% 1.46/1.25 (c3_1(a131)),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[1685, 96, 97])).
% 1.46/1.25 tff(1687,plain,
% 1.46/1.25 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp17 | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)))),
% 1.46/1.25 inference(rewrite,[status(thm)],[])).
% 1.46/1.25 tff(1688,plain,
% 1.46/1.25 ((hskp24 | hskp17 | (~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131))) <=> (hskp24 | hskp17 | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)))),
% 1.46/1.25 inference(rewrite,[status(thm)],[])).
% 1.46/1.25 tff(1689,plain,
% 1.46/1.25 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131)))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131))))),
% 1.46/1.25 inference(monotonicity,[status(thm)],[1688])).
% 1.46/1.25 tff(1690,plain,
% 1.46/1.25 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131)))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp17 | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)))),
% 1.46/1.25 inference(transitivity,[status(thm)],[1689, 1687])).
% 1.46/1.25 tff(1691,plain,
% 1.46/1.25 ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131)))),
% 1.46/1.25 inference(quant_inst,[status(thm)],[])).
% 1.46/1.25 tff(1692,plain,
% 1.46/1.25 ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp17 | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131))),
% 1.46/1.25 inference(modus_ponens,[status(thm)],[1691, 1690])).
% 1.46/1.25 tff(1693,plain,
% 1.46/1.25 (hskp24 | hskp17 | (~c1_1(a131)) | (~c3_1(a131))),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[1692, 123, 95, 1294])).
% 1.46/1.25 tff(1694,plain,
% 1.46/1.25 (hskp24),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[1693, 1686, 1661, 134])).
% 1.46/1.25 tff(1695,plain,
% 1.46/1.25 (~c3_1(a182)),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[1307, 1694])).
% 1.46/1.25 tff(1696,plain,
% 1.46/1.25 (~c2_1(a182)),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[1313, 1694])).
% 1.46/1.25 tff(1697,plain,
% 1.46/1.25 (~c0_1(a182)),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[1326, 1694])).
% 1.46/1.25 tff(1698,plain,
% 1.46/1.25 ($false),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[1375, 123, 33, 96, 1697, 1696, 1695, 94])).
% 1.46/1.25 tff(1699,plain,(hskp7 | hskp9 | hskp17 | c2_1(a131) | c0_1(a131)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.25 tff(1700,plain,
% 1.46/1.25 (hskp7),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[1699, 134, 33, 95, 97])).
% 1.46/1.25 tff(1701,plain,
% 1.46/1.25 (~c2_1(a132)),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[898, 1700])).
% 1.46/1.25 tff(1702,plain,
% 1.46/1.25 (~c0_1(a132)),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[431, 1700])).
% 1.46/1.25 tff(1703,plain,
% 1.46/1.25 (c3_1(a132)),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[447, 1700])).
% 1.46/1.25 tff(1704,plain,
% 1.46/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a132) | c2_1(a132) | c0_1(a131) | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a132) | c2_1(a132) | c0_1(a131) | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132))),
% 1.46/1.25 inference(rewrite,[status(thm)],[])).
% 1.46/1.25 tff(1705,plain,
% 1.46/1.25 (((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a131) | c0_1(a131) | (~c1_1(a131)) | c2_1(a132) | c1_1(a132) | c0_1(a132)) <=> (c0_1(a132) | c2_1(a132) | c0_1(a131) | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132))),
% 1.46/1.25 inference(rewrite,[status(thm)],[])).
% 1.46/1.25 tff(1706,plain,
% 1.46/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a131) | c0_1(a131) | (~c1_1(a131)) | c2_1(a132) | c1_1(a132) | c0_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a132) | c2_1(a132) | c0_1(a131) | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132)))),
% 1.46/1.25 inference(monotonicity,[status(thm)],[1705])).
% 1.46/1.25 tff(1707,plain,
% 1.46/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a131) | c0_1(a131) | (~c1_1(a131)) | c2_1(a132) | c1_1(a132) | c0_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a132) | c2_1(a132) | c0_1(a131) | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132))),
% 1.46/1.25 inference(transitivity,[status(thm)],[1706, 1704])).
% 1.46/1.25 tff(1708,plain,
% 1.46/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a131) | c0_1(a131) | (~c1_1(a131)) | c2_1(a132) | c1_1(a132) | c0_1(a132))),
% 1.46/1.25 inference(quant_inst,[status(thm)],[])).
% 1.46/1.25 tff(1709,plain,
% 1.46/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a132) | c2_1(a132) | c0_1(a131) | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132)),
% 1.46/1.25 inference(modus_ponens,[status(thm)],[1708, 1707])).
% 1.46/1.25 tff(1710,plain,
% 1.46/1.25 (c1_1(a132)),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[1709, 123, 1703, 1702, 1701, 97, 1661, 95, 406])).
% 1.46/1.25 tff(1711,plain,
% 1.46/1.25 (hskp0 | (~c1_1(a132))),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[1039, 123, 134, 1703, 1702, 43])).
% 1.46/1.25 tff(1712,plain,
% 1.46/1.25 (hskp0),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[1711, 1710])).
% 1.46/1.25 tff(1713,plain,
% 1.46/1.25 (~c1_1(a123)),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[202, 1712])).
% 1.46/1.25 tff(1714,plain,
% 1.46/1.25 (~c0_1(a123)),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[236, 1712])).
% 1.46/1.25 tff(1715,plain,
% 1.46/1.25 (hskp12),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[1586, 123, 1703, 1702, 1701, 1446, 1710])).
% 1.46/1.25 tff(1716,plain,
% 1.46/1.25 (~c1_1(a142)),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[150, 1715])).
% 1.46/1.25 tff(1717,plain,
% 1.46/1.25 (c3_1(a142)),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[161, 1715])).
% 1.46/1.25 tff(1718,plain,
% 1.46/1.25 (c0_1(a142)),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[189, 1715])).
% 1.46/1.25 tff(1719,plain,
% 1.46/1.25 (~c3_1(a123)),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[1463, 123, 1662, 1718, 1717, 1716, 1714, 1713, 1346])).
% 1.46/1.25 tff(1720,plain,
% 1.46/1.25 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp17 | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)))),
% 1.46/1.25 inference(rewrite,[status(thm)],[])).
% 1.46/1.25 tff(1721,plain,
% 1.46/1.25 ((hskp24 | hskp17 | (~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132))) <=> (hskp24 | hskp17 | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)))),
% 1.46/1.25 inference(rewrite,[status(thm)],[])).
% 1.46/1.25 tff(1722,plain,
% 1.46/1.25 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132)))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132))))),
% 1.46/1.25 inference(monotonicity,[status(thm)],[1721])).
% 1.46/1.25 tff(1723,plain,
% 1.46/1.25 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132)))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp17 | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)))),
% 1.46/1.25 inference(transitivity,[status(thm)],[1722, 1720])).
% 1.46/1.25 tff(1724,plain,
% 1.46/1.25 ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132)))),
% 1.46/1.25 inference(quant_inst,[status(thm)],[])).
% 1.46/1.25 tff(1725,plain,
% 1.46/1.25 ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp17 | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132))),
% 1.46/1.25 inference(modus_ponens,[status(thm)],[1724, 1723])).
% 1.46/1.25 tff(1726,plain,
% 1.46/1.25 (hskp24 | (~c1_1(a132))),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[1725, 123, 134, 1703, 1701, 1294])).
% 1.46/1.25 tff(1727,plain,
% 1.46/1.25 (hskp24),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[1726, 1710])).
% 1.46/1.25 tff(1728,plain,
% 1.46/1.25 (~c2_1(a182)),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[1313, 1727])).
% 1.46/1.25 tff(1729,plain,
% 1.46/1.25 (~c0_1(a182)),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[1326, 1727])).
% 1.46/1.25 tff(1730,plain,
% 1.46/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a182) | c2_1(a182) | c2_1(a132) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | c3_1(a123) | (~c3_1(a132)) | (~c1_1(a132)) | c1_1(a182))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a182) | c2_1(a182) | c2_1(a132) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | c3_1(a123) | (~c3_1(a132)) | (~c1_1(a132)) | c1_1(a182))),
% 1.46/1.25 inference(rewrite,[status(thm)],[])).
% 1.46/1.25 tff(1731,plain,
% 1.46/1.25 (((~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132)) | c1_1(a123) | c0_1(a123) | c3_1(a123) | c2_1(a182) | c1_1(a182) | c0_1(a182)) <=> (c0_1(a182) | c2_1(a182) | c2_1(a132) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | c3_1(a123) | (~c3_1(a132)) | (~c1_1(a132)) | c1_1(a182))),
% 1.46/1.25 inference(rewrite,[status(thm)],[])).
% 1.46/1.25 tff(1732,plain,
% 1.46/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132)) | c1_1(a123) | c0_1(a123) | c3_1(a123) | c2_1(a182) | c1_1(a182) | c0_1(a182))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a182) | c2_1(a182) | c2_1(a132) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | c3_1(a123) | (~c3_1(a132)) | (~c1_1(a132)) | c1_1(a182)))),
% 1.46/1.25 inference(monotonicity,[status(thm)],[1731])).
% 1.46/1.25 tff(1733,plain,
% 1.46/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132)) | c1_1(a123) | c0_1(a123) | c3_1(a123) | c2_1(a182) | c1_1(a182) | c0_1(a182))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a182) | c2_1(a182) | c2_1(a132) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | c3_1(a123) | (~c3_1(a132)) | (~c1_1(a132)) | c1_1(a182))),
% 1.46/1.25 inference(transitivity,[status(thm)],[1732, 1730])).
% 1.46/1.25 tff(1734,plain,
% 1.46/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132)) | c1_1(a123) | c0_1(a123) | c3_1(a123) | c2_1(a182) | c1_1(a182) | c0_1(a182))),
% 1.46/1.25 inference(quant_inst,[status(thm)],[])).
% 1.46/1.25 tff(1735,plain,
% 1.46/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a182) | c2_1(a182) | c2_1(a132) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | c3_1(a123) | (~c3_1(a132)) | (~c1_1(a132)) | c1_1(a182)),
% 1.46/1.25 inference(modus_ponens,[status(thm)],[1734, 1733])).
% 1.46/1.25 tff(1736,plain,
% 1.46/1.25 (c1_1(a182)),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[1735, 123, 1703, 1729, 1728, 1701, 1714, 1713, 231, 1710, 1719])).
% 1.46/1.25 tff(1737,plain,
% 1.46/1.25 (~c3_1(a182)),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[1307, 1727])).
% 1.46/1.25 tff(1738,plain,
% 1.46/1.25 (c2_1(a123)),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[213, 1712])).
% 1.46/1.25 tff(1739,plain,
% 1.46/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a182) | c3_1(a182) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132)) | (~c1_1(a132)) | (~c1_1(a182)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a182) | c3_1(a182) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132)) | (~c1_1(a132)) | (~c1_1(a182)))),
% 1.46/1.25 inference(rewrite,[status(thm)],[])).
% 1.46/1.25 tff(1740,plain,
% 1.46/1.25 (((~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132)) | c2_1(a182) | c3_1(a182) | (~c1_1(a182)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123))) <=> (c2_1(a182) | c3_1(a182) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132)) | (~c1_1(a132)) | (~c1_1(a182)))),
% 1.46/1.25 inference(rewrite,[status(thm)],[])).
% 1.46/1.25 tff(1741,plain,
% 1.46/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132)) | c2_1(a182) | c3_1(a182) | (~c1_1(a182)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a182) | c3_1(a182) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132)) | (~c1_1(a132)) | (~c1_1(a182))))),
% 1.46/1.25 inference(monotonicity,[status(thm)],[1740])).
% 1.46/1.25 tff(1742,plain,
% 1.46/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132)) | c2_1(a182) | c3_1(a182) | (~c1_1(a182)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a182) | c3_1(a182) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132)) | (~c1_1(a132)) | (~c1_1(a182)))),
% 1.46/1.25 inference(transitivity,[status(thm)],[1741, 1739])).
% 1.46/1.25 tff(1743,plain,
% 1.46/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132)) | c2_1(a182) | c3_1(a182) | (~c1_1(a182)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)))),
% 1.46/1.25 inference(quant_inst,[status(thm)],[])).
% 1.46/1.25 tff(1744,plain,
% 1.46/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a182) | c3_1(a182) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132)) | (~c1_1(a132)) | (~c1_1(a182))),
% 1.46/1.25 inference(modus_ponens,[status(thm)],[1743, 1742])).
% 1.46/1.25 tff(1745,plain,
% 1.46/1.25 ($false),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[1744, 123, 1703, 1738, 1728, 1737, 1701, 1714, 1482, 1710, 1719, 1736])).
% 1.46/1.25 tff(1746,plain,(hskp17 | c0_1(a131) | c2_1(a131) | hskp9), inference(lemma,lemma(discharge,[]))).
% 1.46/1.25 tff(1747,plain,
% 1.46/1.25 (c0_1(a131)),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[1746, 1684, 95, 33])).
% 1.46/1.25 tff(1748,plain,
% 1.46/1.25 (((~![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp9 | (~c0_1(a131)) | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0))) <=> ((~![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp22 | hskp9 | (~c0_1(a131)) | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0))),
% 1.46/1.25 inference(rewrite,[status(thm)],[])).
% 1.46/1.25 tff(1749,plain,
% 1.46/1.25 ((hskp22 | hskp9 | (~ndr1_0) | c2_1(a131) | (~c1_1(a131)) | (~c0_1(a131))) <=> (hskp22 | hskp9 | (~c0_1(a131)) | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0))),
% 1.46/1.25 inference(rewrite,[status(thm)],[])).
% 1.46/1.25 tff(1750,plain,
% 1.46/1.25 (((~![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp9 | (~ndr1_0) | c2_1(a131) | (~c1_1(a131)) | (~c0_1(a131)))) <=> ((~![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp9 | (~c0_1(a131)) | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0)))),
% 1.46/1.25 inference(monotonicity,[status(thm)],[1749])).
% 1.46/1.25 tff(1751,plain,
% 1.46/1.25 (((~![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp9 | (~ndr1_0) | c2_1(a131) | (~c1_1(a131)) | (~c0_1(a131)))) <=> ((~![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp22 | hskp9 | (~c0_1(a131)) | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0))),
% 1.46/1.25 inference(transitivity,[status(thm)],[1750, 1748])).
% 1.46/1.25 tff(1752,plain,
% 1.46/1.25 ((~![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp9 | (~ndr1_0) | c2_1(a131) | (~c1_1(a131)) | (~c0_1(a131)))),
% 1.46/1.25 inference(quant_inst,[status(thm)],[])).
% 1.46/1.25 tff(1753,plain,
% 1.46/1.25 ((~![U: $i] : (hskp22 | hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp22 | hskp9 | (~c0_1(a131)) | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0)),
% 1.46/1.25 inference(modus_ponens,[status(thm)],[1752, 1751])).
% 1.46/1.25 tff(1754,plain,
% 1.46/1.25 (hskp22 | (~c0_1(a131)) | (~c1_1(a131))),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[1753, 123, 33, 95, 1250])).
% 1.46/1.25 tff(1755,plain,
% 1.46/1.25 (hskp22),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[1754, 1747, 1661])).
% 1.46/1.25 tff(1756,plain,
% 1.46/1.25 (~c2_1(a176)),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[715, 1755])).
% 1.46/1.25 tff(1757,plain,
% 1.46/1.25 (~c1_1(a176)),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[721, 1755])).
% 1.46/1.25 tff(1758,plain,
% 1.46/1.25 (c0_1(a176)),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[732, 1755])).
% 1.46/1.25 tff(1759,plain,
% 1.46/1.25 (hskp19),
% 1.46/1.25 inference(unit_resolution,[status(thm)],[739, 123, 1684, 1758, 1757, 1756, 53])).
% 1.46/1.25 tff(1760,plain,
% 1.49/1.25 (~c2_1(a164)),
% 1.49/1.25 inference(unit_resolution,[status(thm)],[250, 1759])).
% 1.49/1.25 tff(1761,plain,
% 1.49/1.25 (c3_1(a164)),
% 1.49/1.25 inference(unit_resolution,[status(thm)],[261, 1759])).
% 1.49/1.25 tff(1762,plain,
% 1.49/1.25 (c1_1(a164)),
% 1.49/1.25 inference(unit_resolution,[status(thm)],[272, 1759])).
% 1.49/1.25 tff(1763,plain,
% 1.49/1.25 (hskp13),
% 1.49/1.25 inference(unit_resolution,[status(thm)],[776, 123, 1684, 1762, 1761, 1760, 769])).
% 1.49/1.25 tff(1764,plain,
% 1.49/1.25 (~c1_1(a143)),
% 1.49/1.25 inference(unit_resolution,[status(thm)],[782, 1763])).
% 1.49/1.25 tff(1765,plain,
% 1.49/1.25 (hskp24),
% 1.49/1.25 inference(unit_resolution,[status(thm)],[1365, 123, 1684, 1762, 1761, 1760, 1294])).
% 1.49/1.25 tff(1766,plain,
% 1.49/1.25 (~c3_1(a182)),
% 1.49/1.25 inference(unit_resolution,[status(thm)],[1307, 1765])).
% 1.49/1.25 tff(1767,plain,
% 1.49/1.25 (~c2_1(a182)),
% 1.49/1.25 inference(unit_resolution,[status(thm)],[1313, 1765])).
% 1.49/1.25 tff(1768,plain,
% 1.49/1.25 (~c0_1(a182)),
% 1.49/1.25 inference(unit_resolution,[status(thm)],[1326, 1765])).
% 1.49/1.25 tff(1769,plain,
% 1.49/1.25 (hskp7),
% 1.49/1.25 inference(unit_resolution,[status(thm)],[1375, 123, 33, 1768, 1767, 1766, 94])).
% 1.49/1.25 tff(1770,plain,
% 1.49/1.25 (~c2_1(a132)),
% 1.49/1.25 inference(unit_resolution,[status(thm)],[898, 1769])).
% 1.49/1.25 tff(1771,plain,
% 1.49/1.25 (c2_1(a143)),
% 1.49/1.25 inference(unit_resolution,[status(thm)],[836, 1763])).
% 1.49/1.25 tff(1772,plain,
% 1.49/1.25 (c3_1(a143)),
% 1.49/1.25 inference(unit_resolution,[status(thm)],[825, 1763])).
% 1.49/1.25 tff(1773,plain,
% 1.49/1.25 (c3_1(a132)),
% 1.49/1.25 inference(unit_resolution,[status(thm)],[447, 1769])).
% 1.49/1.25 tff(1774,plain,
% 1.49/1.25 (c1_1(a132)),
% 1.49/1.25 inference(unit_resolution,[status(thm)],[1412, 1773, 1662, 1772, 1771, 1770, 1764])).
% 1.49/1.25 tff(1775,plain,
% 1.49/1.25 (~c0_1(a132)),
% 1.49/1.25 inference(unit_resolution,[status(thm)],[431, 1769])).
% 1.49/1.25 tff(1776,plain,
% 1.49/1.25 (~c0_1(a164)),
% 1.49/1.25 inference(unit_resolution,[status(thm)],[1434, 123, 1761, 1773, 1760, 1775, 1770, 1428, 1774])).
% 1.49/1.25 tff(1777,assumption,(~c0_1(a164)), introduced(assumption)).
% 1.49/1.25 tff(1778,assumption,(~c2_1(a167)), introduced(assumption)).
% 1.49/1.25 tff(1779,assumption,(~c2_1(a164)), introduced(assumption)).
% 1.49/1.25 tff(1780,assumption,(c3_1(a164)), introduced(assumption)).
% 1.49/1.25 tff(1781,assumption,(c1_1(a164)), introduced(assumption)).
% 1.49/1.25 tff(1782,plain,
% 1.49/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a164) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a164)) | c0_1(a164) | (~c1_1(a164)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a164) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a164)) | c0_1(a164) | (~c1_1(a164)))),
% 1.49/1.25 inference(rewrite,[status(thm)],[])).
% 1.49/1.25 tff(1783,plain,
% 1.49/1.25 (((~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c0_1(a167)) | c2_1(a164) | c0_1(a164) | (~c3_1(a164)) | c2_1(a164) | c0_1(a164) | (~c1_1(a164))) <=> (c2_1(a164) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a164)) | c0_1(a164) | (~c1_1(a164)))),
% 1.49/1.25 inference(rewrite,[status(thm)],[])).
% 1.49/1.25 tff(1784,plain,
% 1.49/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c0_1(a167)) | c2_1(a164) | c0_1(a164) | (~c3_1(a164)) | c2_1(a164) | c0_1(a164) | (~c1_1(a164)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a164) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a164)) | c0_1(a164) | (~c1_1(a164))))),
% 1.49/1.25 inference(monotonicity,[status(thm)],[1783])).
% 1.49/1.25 tff(1785,plain,
% 1.49/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c0_1(a167)) | c2_1(a164) | c0_1(a164) | (~c3_1(a164)) | c2_1(a164) | c0_1(a164) | (~c1_1(a164)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a164) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a164)) | c0_1(a164) | (~c1_1(a164)))),
% 1.49/1.25 inference(transitivity,[status(thm)],[1784, 1782])).
% 1.49/1.25 tff(1786,plain,
% 1.49/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c0_1(a167)) | c2_1(a164) | c0_1(a164) | (~c3_1(a164)) | c2_1(a164) | c0_1(a164) | (~c1_1(a164)))),
% 1.49/1.25 inference(quant_inst,[status(thm)],[])).
% 1.49/1.25 tff(1787,plain,
% 1.49/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a164) | (~ndr1_0) | (~c3_1(a167)) | c2_1(a167) | (~c0_1(a167)) | (~c3_1(a164)) | c0_1(a164) | (~c1_1(a164))),
% 1.49/1.25 inference(modus_ponens,[status(thm)],[1786, 1785])).
% 1.49/1.25 tff(1788,plain,
% 1.49/1.25 ($false),
% 1.49/1.25 inference(unit_resolution,[status(thm)],[1787, 123, 1205, 1203, 1781, 1780, 1779, 1428, 1778, 1777])).
% 1.49/1.25 tff(1789,plain,(c2_1(a167) | (~c0_1(a167)) | (~c3_1(a167)) | (~c1_1(a164)) | (~c3_1(a164)) | c2_1(a164) | c0_1(a164)), inference(lemma,lemma(discharge,[]))).
% 1.49/1.25 tff(1790,plain,
% 1.49/1.25 (c2_1(a167)),
% 1.49/1.25 inference(unit_resolution,[status(thm)],[1789, 1776, 1176, 1762, 1761, 1760, 1130])).
% 1.49/1.25 tff(1791,plain,
% 1.49/1.25 (hskp0),
% 1.49/1.25 inference(unit_resolution,[status(thm)],[1039, 123, 1684, 1773, 1775, 43, 1774])).
% 1.49/1.25 tff(1792,plain,
% 1.49/1.25 (~c1_1(a123)),
% 1.49/1.25 inference(unit_resolution,[status(thm)],[202, 1791])).
% 1.49/1.25 tff(1793,plain,
% 1.49/1.25 (~c0_1(a123)),
% 1.49/1.25 inference(unit_resolution,[status(thm)],[236, 1791])).
% 1.49/1.25 tff(1794,plain,
% 1.49/1.25 (c2_1(a123)),
% 1.49/1.25 inference(unit_resolution,[status(thm)],[213, 1791])).
% 1.49/1.25 tff(1795,plain,
% 1.49/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a143) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | (~c2_1(a123)) | (~c2_1(a143)) | (~c0_1(a143)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a143) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | (~c2_1(a123)) | (~c2_1(a143)) | (~c0_1(a143)))),
% 1.49/1.25 inference(rewrite,[status(thm)],[])).
% 1.49/1.25 tff(1796,plain,
% 1.49/1.25 (((~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | c1_1(a143) | (~c2_1(a143)) | (~c0_1(a143)) | c1_1(a123) | c0_1(a123) | (~c2_1(a123))) <=> (c1_1(a143) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | (~c2_1(a123)) | (~c2_1(a143)) | (~c0_1(a143)))),
% 1.49/1.25 inference(rewrite,[status(thm)],[])).
% 1.49/1.25 tff(1797,plain,
% 1.49/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | c1_1(a143) | (~c2_1(a143)) | (~c0_1(a143)) | c1_1(a123) | c0_1(a123) | (~c2_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a143) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | (~c2_1(a123)) | (~c2_1(a143)) | (~c0_1(a143))))),
% 1.49/1.25 inference(monotonicity,[status(thm)],[1796])).
% 1.49/1.25 tff(1798,plain,
% 1.49/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | c1_1(a143) | (~c2_1(a143)) | (~c0_1(a143)) | c1_1(a123) | c0_1(a123) | (~c2_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a143) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | (~c2_1(a123)) | (~c2_1(a143)) | (~c0_1(a143)))),
% 1.49/1.25 inference(transitivity,[status(thm)],[1797, 1795])).
% 1.49/1.25 tff(1799,plain,
% 1.49/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | c1_1(a143) | (~c2_1(a143)) | (~c0_1(a143)) | c1_1(a123) | c0_1(a123) | (~c2_1(a123)))),
% 1.49/1.26 inference(quant_inst,[status(thm)],[])).
% 1.49/1.26 tff(1800,plain,
% 1.49/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a143) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c2_1(a167)) | (~c2_1(a123)) | (~c2_1(a143)) | (~c0_1(a143))),
% 1.49/1.26 inference(modus_ponens,[status(thm)],[1799, 1798])).
% 1.49/1.26 tff(1801,plain,
% 1.49/1.26 (~c0_1(a143)),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[1800, 123, 1187, 1176, 1771, 1794, 1764, 1793, 1792, 10, 1790])).
% 1.49/1.26 tff(1802,plain,
% 1.49/1.26 (hskp12),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[1452, 123, 1761, 1760, 1775, 1770, 1446, 1774, 1776])).
% 1.49/1.26 tff(1803,plain,
% 1.49/1.26 (~c1_1(a142)),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[150, 1802])).
% 1.49/1.26 tff(1804,plain,
% 1.49/1.26 (c3_1(a142)),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[161, 1802])).
% 1.49/1.26 tff(1805,plain,
% 1.49/1.26 (c0_1(a142)),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[189, 1802])).
% 1.49/1.26 tff(1806,plain,
% 1.49/1.26 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c1_1(a143) | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142)) | (~c3_1(a143)) | c0_1(a143))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c1_1(a143) | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142)) | (~c3_1(a143)) | c0_1(a143))),
% 1.49/1.26 inference(rewrite,[status(thm)],[])).
% 1.49/1.26 tff(1807,plain,
% 1.49/1.26 ((hskp6 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142)) | c1_1(a143) | c0_1(a143) | (~c3_1(a143))) <=> (hskp6 | c1_1(a143) | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142)) | (~c3_1(a143)) | c0_1(a143))),
% 1.49/1.26 inference(rewrite,[status(thm)],[])).
% 1.49/1.26 tff(1808,plain,
% 1.49/1.26 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142)) | c1_1(a143) | c0_1(a143) | (~c3_1(a143)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c1_1(a143) | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142)) | (~c3_1(a143)) | c0_1(a143)))),
% 1.49/1.26 inference(monotonicity,[status(thm)],[1807])).
% 1.49/1.26 tff(1809,plain,
% 1.49/1.26 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142)) | c1_1(a143) | c0_1(a143) | (~c3_1(a143)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c1_1(a143) | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142)) | (~c3_1(a143)) | c0_1(a143))),
% 1.49/1.26 inference(transitivity,[status(thm)],[1808, 1806])).
% 1.49/1.26 tff(1810,plain,
% 1.49/1.26 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142)) | c1_1(a143) | c0_1(a143) | (~c3_1(a143)))),
% 1.49/1.26 inference(quant_inst,[status(thm)],[])).
% 1.49/1.26 tff(1811,plain,
% 1.49/1.26 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c1_1(a143) | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142)) | (~c3_1(a143)) | c0_1(a143)),
% 1.49/1.26 inference(modus_ponens,[status(thm)],[1810, 1809])).
% 1.49/1.26 tff(1812,plain,
% 1.49/1.26 ($false),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[1811, 123, 1662, 1772, 1805, 1804, 1764, 1803, 1346, 1801])).
% 1.49/1.26 tff(1813,plain,(c2_1(a131) | hskp9), inference(lemma,lemma(discharge,[]))).
% 1.49/1.26 tff(1814,plain,
% 1.49/1.26 (c2_1(a131)),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[1813, 33])).
% 1.49/1.26 tff(1815,plain,
% 1.49/1.26 (~hskp6),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[71, 1814])).
% 1.49/1.26 tff(1816,plain,
% 1.49/1.26 (~hskp17),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[1683, 1815, 33])).
% 1.49/1.26 tff(1817,assumption,(~hskp19), introduced(assumption)).
% 1.49/1.26 tff(1818,assumption,(hskp22), introduced(assumption)).
% 1.49/1.26 tff(1819,plain,
% 1.49/1.26 (~c2_1(a176)),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[715, 1818])).
% 1.49/1.26 tff(1820,plain,
% 1.49/1.26 (~c1_1(a176)),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[721, 1818])).
% 1.49/1.26 tff(1821,plain,
% 1.49/1.26 (c0_1(a176)),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[732, 1818])).
% 1.49/1.26 tff(1822,plain,
% 1.49/1.26 ($false),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[739, 123, 1817, 134, 1821, 1820, 1819, 53])).
% 1.49/1.26 tff(1823,plain,((~hskp22) | hskp19 | hskp17), inference(lemma,lemma(discharge,[]))).
% 1.49/1.26 tff(1824,plain,
% 1.49/1.26 (~hskp22),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[1823, 1817, 1816])).
% 1.49/1.26 tff(1825,plain,
% 1.49/1.26 (^[U: $i] : refl((hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 1.49/1.26 inference(bind,[status(th)],[])).
% 1.49/1.26 tff(1826,plain,
% 1.49/1.26 (![U: $i] : (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.49/1.26 inference(quant_intro,[status(thm)],[1825])).
% 1.49/1.26 tff(1827,plain,
% 1.49/1.26 (![U: $i] : (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.49/1.26 inference(rewrite,[status(thm)],[])).
% 1.49/1.26 tff(1828,plain,
% 1.49/1.26 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp22))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp22) <=> (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) <=> (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) | hskp10) <=> ((hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp10))), rewrite(((hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp10) <=> (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) | hskp10) <=> (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 1.49/1.26 inference(bind,[status(th)],[])).
% 1.49/1.26 tff(1829,plain,
% 1.49/1.26 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) | hskp10) <=> ![U: $i] : (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.49/1.26 inference(quant_intro,[status(thm)],[1828])).
% 1.49/1.26 tff(1830,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause164')).
% 1.49/1.26 tff(1831,plain,
% 1.49/1.26 (![U: $i] : (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.49/1.26 inference(modus_ponens,[status(thm)],[1830, 1829])).
% 1.49/1.26 tff(1832,plain,
% 1.49/1.26 (![U: $i] : (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.49/1.26 inference(modus_ponens,[status(thm)],[1831, 1827])).
% 1.49/1.26 tff(1833,plain,(
% 1.49/1.26 ![U: $i] : (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.49/1.26 inference(skolemize,[status(sab)],[1832])).
% 1.49/1.26 tff(1834,plain,
% 1.49/1.26 (![U: $i] : (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.49/1.26 inference(modus_ponens,[status(thm)],[1833, 1826])).
% 1.49/1.26 tff(1835,plain,
% 1.49/1.26 (((~![U: $i] : (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c0_1(a167)))) <=> ((~![U: $i] : (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp22 | hskp10 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c0_1(a167)))),
% 1.49/1.26 inference(rewrite,[status(thm)],[])).
% 1.49/1.26 tff(1836,plain,
% 1.49/1.26 ((~![U: $i] : (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c0_1(a167)))),
% 1.49/1.26 inference(quant_inst,[status(thm)],[])).
% 1.49/1.26 tff(1837,plain,
% 1.49/1.26 ((~![U: $i] : (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp22 | hskp10 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | (~c0_1(a167))),
% 1.49/1.26 inference(modus_ponens,[status(thm)],[1836, 1835])).
% 1.49/1.26 tff(1838,plain,
% 1.49/1.26 (hskp22 | hskp10),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[1837, 123, 1130, 1187, 1176, 1834])).
% 1.49/1.26 tff(1839,plain,
% 1.49/1.26 (hskp10),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[1838, 1824])).
% 1.49/1.26 tff(1840,plain,
% 1.49/1.26 (((~hskp10) | (~c3_1(a140))) <=> ((~hskp10) | (~c3_1(a140)))),
% 1.49/1.26 inference(rewrite,[status(thm)],[])).
% 1.49/1.26 tff(1841,plain,
% 1.49/1.26 (((~c3_1(a140)) | (~hskp10)) <=> ((~hskp10) | (~c3_1(a140)))),
% 1.49/1.26 inference(rewrite,[status(thm)],[])).
% 1.49/1.26 tff(1842,axiom,((~c3_1(a140)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause112')).
% 1.49/1.26 tff(1843,plain,
% 1.49/1.26 ((~hskp10) | (~c3_1(a140))),
% 1.49/1.26 inference(modus_ponens,[status(thm)],[1842, 1841])).
% 1.49/1.26 tff(1844,plain,
% 1.49/1.26 ((~hskp10) | (~c3_1(a140))),
% 1.49/1.26 inference(modus_ponens,[status(thm)],[1843, 1840])).
% 1.49/1.26 tff(1845,plain,
% 1.49/1.26 (~c3_1(a140)),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[1844, 1839])).
% 1.49/1.26 tff(1846,plain,
% 1.49/1.26 (((~hskp10) | (~c2_1(a140))) <=> ((~hskp10) | (~c2_1(a140)))),
% 1.49/1.26 inference(rewrite,[status(thm)],[])).
% 1.49/1.26 tff(1847,plain,
% 1.49/1.26 (((~c2_1(a140)) | (~hskp10)) <=> ((~hskp10) | (~c2_1(a140)))),
% 1.49/1.26 inference(rewrite,[status(thm)],[])).
% 1.49/1.26 tff(1848,axiom,((~c2_1(a140)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause111')).
% 1.49/1.26 tff(1849,plain,
% 1.49/1.26 ((~hskp10) | (~c2_1(a140))),
% 1.49/1.26 inference(modus_ponens,[status(thm)],[1848, 1847])).
% 1.49/1.26 tff(1850,plain,
% 1.49/1.26 ((~hskp10) | (~c2_1(a140))),
% 1.49/1.26 inference(modus_ponens,[status(thm)],[1849, 1846])).
% 1.49/1.26 tff(1851,plain,
% 1.49/1.26 (~c2_1(a140)),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[1850, 1839])).
% 1.49/1.26 tff(1852,plain,
% 1.49/1.26 (((~hskp10) | c0_1(a140)) <=> ((~hskp10) | c0_1(a140))),
% 1.49/1.26 inference(rewrite,[status(thm)],[])).
% 1.49/1.26 tff(1853,axiom,((~hskp10) | c0_1(a140)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause71')).
% 1.49/1.26 tff(1854,plain,
% 1.49/1.26 ((~hskp10) | c0_1(a140)),
% 1.49/1.26 inference(modus_ponens,[status(thm)],[1853, 1852])).
% 1.49/1.26 tff(1855,plain,
% 1.49/1.26 ((~hskp10) | c0_1(a140)),
% 1.49/1.26 inference(modus_ponens,[status(thm)],[1854, 1852])).
% 1.49/1.26 tff(1856,plain,
% 1.49/1.26 ((~hskp10) | c0_1(a140)),
% 1.49/1.26 inference(modus_ponens,[status(thm)],[1855, 1852])).
% 1.49/1.26 tff(1857,plain,
% 1.49/1.26 ((~hskp10) | c0_1(a140)),
% 1.49/1.26 inference(modus_ponens,[status(thm)],[1856, 1852])).
% 1.49/1.26 tff(1858,plain,
% 1.49/1.26 ((~hskp10) | c0_1(a140)),
% 1.49/1.26 inference(modus_ponens,[status(thm)],[1857, 1852])).
% 1.49/1.26 tff(1859,plain,
% 1.49/1.26 ((~hskp10) | c0_1(a140)),
% 1.49/1.26 inference(modus_ponens,[status(thm)],[1858, 1852])).
% 1.49/1.26 tff(1860,plain,
% 1.49/1.26 ((~hskp10) | c0_1(a140)),
% 1.49/1.26 inference(modus_ponens,[status(thm)],[1859, 1852])).
% 1.49/1.26 tff(1861,plain,
% 1.49/1.26 ((~hskp10) | c0_1(a140)),
% 1.49/1.26 inference(modus_ponens,[status(thm)],[1860, 1852])).
% 1.49/1.26 tff(1862,plain,
% 1.49/1.26 (c0_1(a140)),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[1861, 1839])).
% 1.49/1.26 tff(1863,plain,
% 1.49/1.26 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c2_1(a140) | c3_1(a140) | (~ndr1_0) | (~c1_1(a140)) | (~c0_1(a140)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c2_1(a140) | c3_1(a140) | (~ndr1_0) | (~c1_1(a140)) | (~c0_1(a140)))),
% 1.49/1.26 inference(rewrite,[status(thm)],[])).
% 1.49/1.26 tff(1864,plain,
% 1.49/1.26 ((hskp9 | (~ndr1_0) | c3_1(a140) | (~c1_1(a140)) | (~c0_1(a140)) | c2_1(a140) | c3_1(a140) | (~c1_1(a140))) <=> (hskp9 | c2_1(a140) | c3_1(a140) | (~ndr1_0) | (~c1_1(a140)) | (~c0_1(a140)))),
% 1.49/1.26 inference(rewrite,[status(thm)],[])).
% 1.49/1.26 tff(1865,plain,
% 1.49/1.26 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a140) | (~c1_1(a140)) | (~c0_1(a140)) | c2_1(a140) | c3_1(a140) | (~c1_1(a140)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | c2_1(a140) | c3_1(a140) | (~ndr1_0) | (~c1_1(a140)) | (~c0_1(a140))))),
% 1.49/1.26 inference(monotonicity,[status(thm)],[1864])).
% 1.49/1.26 tff(1866,plain,
% 1.49/1.26 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a140) | (~c1_1(a140)) | (~c0_1(a140)) | c2_1(a140) | c3_1(a140) | (~c1_1(a140)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c2_1(a140) | c3_1(a140) | (~ndr1_0) | (~c1_1(a140)) | (~c0_1(a140)))),
% 1.49/1.26 inference(transitivity,[status(thm)],[1865, 1863])).
% 1.49/1.26 tff(1867,plain,
% 1.49/1.26 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a140) | (~c1_1(a140)) | (~c0_1(a140)) | c2_1(a140) | c3_1(a140) | (~c1_1(a140)))),
% 1.49/1.26 inference(quant_inst,[status(thm)],[])).
% 1.49/1.26 tff(1868,plain,
% 1.49/1.26 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp9 | c2_1(a140) | c3_1(a140) | (~ndr1_0) | (~c1_1(a140)) | (~c0_1(a140))),
% 1.49/1.26 inference(modus_ponens,[status(thm)],[1867, 1866])).
% 1.49/1.26 tff(1869,plain,
% 1.49/1.26 (~c1_1(a140)),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[1868, 123, 33, 1862, 1851, 1845, 1140])).
% 1.49/1.26 tff(1870,plain,
% 1.49/1.26 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | c2_1(a140) | (~ndr1_0) | c1_1(a140) | (~c0_1(a140)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp17 | c2_1(a140) | (~ndr1_0) | c1_1(a140) | (~c0_1(a140)))),
% 1.49/1.26 inference(rewrite,[status(thm)],[])).
% 1.49/1.26 tff(1871,plain,
% 1.49/1.26 ((hskp19 | hskp17 | (~ndr1_0) | c2_1(a140) | c1_1(a140) | (~c0_1(a140))) <=> (hskp19 | hskp17 | c2_1(a140) | (~ndr1_0) | c1_1(a140) | (~c0_1(a140)))),
% 1.49/1.26 inference(rewrite,[status(thm)],[])).
% 1.49/1.26 tff(1872,plain,
% 1.49/1.26 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c2_1(a140) | c1_1(a140) | (~c0_1(a140)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | c2_1(a140) | (~ndr1_0) | c1_1(a140) | (~c0_1(a140))))),
% 1.49/1.26 inference(monotonicity,[status(thm)],[1871])).
% 1.49/1.26 tff(1873,plain,
% 1.49/1.26 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c2_1(a140) | c1_1(a140) | (~c0_1(a140)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp17 | c2_1(a140) | (~ndr1_0) | c1_1(a140) | (~c0_1(a140)))),
% 1.49/1.26 inference(transitivity,[status(thm)],[1872, 1870])).
% 1.49/1.26 tff(1874,plain,
% 1.49/1.26 ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c2_1(a140) | c1_1(a140) | (~c0_1(a140)))),
% 1.49/1.26 inference(quant_inst,[status(thm)],[])).
% 1.49/1.26 tff(1875,plain,
% 1.49/1.26 ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp19 | hskp17 | c2_1(a140) | (~ndr1_0) | c1_1(a140) | (~c0_1(a140))),
% 1.49/1.26 inference(modus_ponens,[status(thm)],[1874, 1873])).
% 1.49/1.26 tff(1876,plain,
% 1.49/1.26 ($false),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[1875, 123, 1817, 1816, 1862, 1851, 53, 1869])).
% 1.49/1.26 tff(1877,plain,(hskp19 | hskp9), inference(lemma,lemma(discharge,[]))).
% 1.49/1.26 tff(1878,plain,
% 1.49/1.26 (hskp19),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[1877, 33])).
% 1.49/1.26 tff(1879,plain,
% 1.49/1.26 (~c2_1(a164)),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[250, 1878])).
% 1.49/1.26 tff(1880,plain,
% 1.49/1.26 (c3_1(a164)),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[261, 1878])).
% 1.49/1.26 tff(1881,plain,
% 1.49/1.26 (c1_1(a164)),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[272, 1878])).
% 1.49/1.26 tff(1882,assumption,(hskp19), introduced(assumption)).
% 1.49/1.26 tff(1883,plain,
% 1.49/1.26 (~c2_1(a164)),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[250, 1882])).
% 1.49/1.26 tff(1884,plain,
% 1.49/1.26 (c3_1(a164)),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[261, 1882])).
% 1.49/1.26 tff(1885,plain,
% 1.49/1.26 (c1_1(a164)),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[272, 1882])).
% 1.49/1.26 tff(1886,assumption,(~hskp24), introduced(assumption)).
% 1.49/1.26 tff(1887,plain,
% 1.49/1.26 ($false),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[1365, 123, 1886, 134, 1885, 1884, 1883, 1294])).
% 1.49/1.26 tff(1888,plain,((~hskp19) | hskp24 | hskp17), inference(lemma,lemma(discharge,[]))).
% 1.49/1.26 tff(1889,plain,
% 1.49/1.26 (hskp24),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[1888, 1878, 1816])).
% 1.49/1.26 tff(1890,assumption,(hskp24), introduced(assumption)).
% 1.49/1.26 tff(1891,plain,
% 1.49/1.26 (~c3_1(a182)),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[1307, 1890])).
% 1.49/1.26 tff(1892,plain,
% 1.49/1.26 (~c2_1(a182)),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[1313, 1890])).
% 1.49/1.26 tff(1893,plain,
% 1.49/1.26 (~c0_1(a182)),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[1326, 1890])).
% 1.49/1.26 tff(1894,plain,
% 1.49/1.26 ($false),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[1375, 123, 33, 96, 1893, 1892, 1891, 94])).
% 1.49/1.26 tff(1895,plain,((~hskp24) | hskp9 | hskp7), inference(lemma,lemma(discharge,[]))).
% 1.49/1.26 tff(1896,plain,
% 1.49/1.26 (hskp7),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[1895, 1889, 33])).
% 1.49/1.26 tff(1897,plain,
% 1.49/1.26 (~c2_1(a132)),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[898, 1896])).
% 1.49/1.26 tff(1898,plain,
% 1.49/1.26 (c3_1(a132)),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[447, 1896])).
% 1.49/1.26 tff(1899,plain,
% 1.49/1.26 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp6 | c2_1(a132) | (~ndr1_0) | (~c3_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | (~c3_1(a132)) | c1_1(a132))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a132) | (~ndr1_0) | (~c3_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | (~c3_1(a132)) | c1_1(a132))),
% 1.49/1.26 inference(rewrite,[status(thm)],[])).
% 1.49/1.26 tff(1900,plain,
% 1.49/1.26 ((hskp6 | (~ndr1_0) | (~c3_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132))) <=> (hskp6 | c2_1(a132) | (~ndr1_0) | (~c3_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | (~c3_1(a132)) | c1_1(a132))),
% 1.49/1.26 inference(rewrite,[status(thm)],[])).
% 1.49/1.26 tff(1901,plain,
% 1.49/1.26 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c3_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp6 | c2_1(a132) | (~ndr1_0) | (~c3_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | (~c3_1(a132)) | c1_1(a132)))),
% 1.49/1.26 inference(monotonicity,[status(thm)],[1900])).
% 1.49/1.26 tff(1902,plain,
% 1.49/1.26 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c3_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a132) | (~ndr1_0) | (~c3_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | (~c3_1(a132)) | c1_1(a132))),
% 1.49/1.26 inference(transitivity,[status(thm)],[1901, 1899])).
% 1.49/1.26 tff(1903,plain,
% 1.49/1.26 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c3_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)))),
% 1.49/1.26 inference(quant_inst,[status(thm)],[])).
% 1.49/1.26 tff(1904,plain,
% 1.49/1.26 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a132) | (~ndr1_0) | (~c3_1(a167)) | (~c0_1(a167)) | (~c2_1(a167)) | (~c3_1(a132)) | c1_1(a132)),
% 1.49/1.26 inference(modus_ponens,[status(thm)],[1903, 1902])).
% 1.49/1.26 tff(1905,plain,
% 1.49/1.26 ((~c2_1(a167)) | (~c3_1(a132)) | c1_1(a132)),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[1904, 123, 1403, 1205, 1203, 436, 1402])).
% 1.49/1.26 tff(1906,plain,
% 1.49/1.26 (~c2_1(a167)),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[1905, 466, 470])).
% 1.49/1.26 tff(1907,plain,
% 1.49/1.26 (((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | c2_1(a167))) <=> ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp13 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | c2_1(a167))),
% 1.49/1.26 inference(rewrite,[status(thm)],[])).
% 1.49/1.26 tff(1908,plain,
% 1.49/1.26 ((hskp17 | hskp13 | (~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c1_1(a167))) <=> (hskp17 | hskp13 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | c2_1(a167))),
% 1.49/1.26 inference(rewrite,[status(thm)],[])).
% 1.49/1.26 tff(1909,plain,
% 1.49/1.26 (((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | (~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c1_1(a167)))) <=> ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | c2_1(a167)))),
% 1.49/1.26 inference(monotonicity,[status(thm)],[1908])).
% 1.49/1.26 tff(1910,plain,
% 1.49/1.26 (((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | (~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c1_1(a167)))) <=> ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp13 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | c2_1(a167))),
% 1.49/1.26 inference(transitivity,[status(thm)],[1909, 1907])).
% 1.49/1.26 tff(1911,plain,
% 1.49/1.26 ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | (~ndr1_0) | c2_1(a167) | (~c3_1(a167)) | (~c1_1(a167)))),
% 1.49/1.26 inference(quant_inst,[status(thm)],[])).
% 1.49/1.26 tff(1912,plain,
% 1.49/1.26 ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp13 | (~ndr1_0) | (~c3_1(a167)) | (~c1_1(a167)) | c2_1(a167)),
% 1.49/1.26 inference(modus_ponens,[status(thm)],[1911, 1910])).
% 1.49/1.26 tff(1913,plain,
% 1.49/1.26 (hskp17 | hskp13 | c2_1(a167)),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[1912, 123, 1204, 1203, 769])).
% 1.49/1.26 tff(1914,plain,
% 1.49/1.26 (hskp13),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[1913, 1906, 134])).
% 1.49/1.26 tff(1915,plain,
% 1.49/1.26 (~c1_1(a143)),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[782, 1914])).
% 1.49/1.26 tff(1916,plain,
% 1.49/1.26 (c2_1(a143)),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[836, 1914])).
% 1.49/1.26 tff(1917,plain,
% 1.49/1.26 (c3_1(a143)),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[825, 1914])).
% 1.49/1.26 tff(1918,plain,
% 1.49/1.26 ($false),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[1412, 1917, 1916, 1403, 470, 466, 436, 1915])).
% 1.49/1.26 tff(1919,plain,(c1_1(a132) | hskp6 | (~c3_1(a132)) | c2_1(a132) | hskp17 | (~c1_1(a167)) | (~c3_1(a167)) | (~c0_1(a167))), inference(lemma,lemma(discharge,[]))).
% 1.49/1.26 tff(1920,plain,
% 1.49/1.26 (c1_1(a132)),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[1919, 1898, 1815, 1897, 1816, 1187, 1176, 1130])).
% 1.49/1.26 tff(1921,plain,
% 1.49/1.26 (~c0_1(a132)),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[431, 1896])).
% 1.49/1.26 tff(1922,plain,
% 1.49/1.26 (~c0_1(a164)),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[1434, 123, 1880, 1898, 1879, 1921, 1897, 1428, 1920])).
% 1.49/1.26 tff(1923,plain,
% 1.49/1.26 (c2_1(a167)),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[1789, 1922, 1176, 1881, 1880, 1879, 1130])).
% 1.49/1.26 tff(1924,plain,
% 1.49/1.26 (hskp0),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[1039, 123, 1816, 1898, 1921, 43, 1920])).
% 1.49/1.26 tff(1925,plain,
% 1.49/1.26 (~c1_1(a123)),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[202, 1924])).
% 1.49/1.26 tff(1926,plain,
% 1.49/1.26 (~c0_1(a123)),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[236, 1924])).
% 1.49/1.26 tff(1927,plain,
% 1.49/1.26 (hskp13),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[776, 123, 1816, 1881, 1880, 1879, 769])).
% 1.49/1.26 tff(1928,plain,
% 1.49/1.26 (~c1_1(a143)),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[782, 1927])).
% 1.49/1.26 tff(1929,plain,
% 1.49/1.26 (c2_1(a123)),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[213, 1924])).
% 1.49/1.26 tff(1930,plain,
% 1.49/1.26 (c2_1(a143)),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[836, 1927])).
% 1.49/1.26 tff(1931,plain,
% 1.49/1.26 (~c0_1(a143)),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[1800, 123, 1187, 1176, 1930, 1929, 1928, 1926, 1925, 10, 1923])).
% 1.49/1.26 tff(1932,plain,
% 1.49/1.26 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | c0_1(a164) | (~c1_1(a164)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | c0_1(a164) | (~c1_1(a164)))),
% 1.49/1.26 inference(rewrite,[status(thm)],[])).
% 1.49/1.26 tff(1933,plain,
% 1.49/1.26 ((hskp12 | (~ndr1_0) | c2_1(a164) | c0_1(a164) | (~c3_1(a164)) | c2_1(a164) | c0_1(a164) | (~c1_1(a164))) <=> (hskp12 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | c0_1(a164) | (~c1_1(a164)))),
% 1.49/1.26 inference(rewrite,[status(thm)],[])).
% 1.49/1.26 tff(1934,plain,
% 1.49/1.26 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a164) | c0_1(a164) | (~c3_1(a164)) | c2_1(a164) | c0_1(a164) | (~c1_1(a164)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | c0_1(a164) | (~c1_1(a164))))),
% 1.49/1.26 inference(monotonicity,[status(thm)],[1933])).
% 1.49/1.26 tff(1935,plain,
% 1.49/1.26 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a164) | c0_1(a164) | (~c3_1(a164)) | c2_1(a164) | c0_1(a164) | (~c1_1(a164)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | c0_1(a164) | (~c1_1(a164)))),
% 1.49/1.26 inference(transitivity,[status(thm)],[1934, 1932])).
% 1.49/1.26 tff(1936,plain,
% 1.49/1.26 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | c2_1(a164) | c0_1(a164) | (~c3_1(a164)) | c2_1(a164) | c0_1(a164) | (~c1_1(a164)))),
% 1.49/1.26 inference(quant_inst,[status(thm)],[])).
% 1.49/1.26 tff(1937,plain,
% 1.49/1.26 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | c0_1(a164) | (~c1_1(a164))),
% 1.49/1.26 inference(modus_ponens,[status(thm)],[1936, 1935])).
% 1.49/1.26 tff(1938,plain,
% 1.49/1.26 (hskp12),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[1937, 123, 1881, 1880, 1879, 1446, 1922])).
% 1.49/1.26 tff(1939,plain,
% 1.49/1.26 (~c1_1(a142)),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[150, 1938])).
% 1.49/1.26 tff(1940,plain,
% 1.49/1.26 (c3_1(a142)),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[161, 1938])).
% 1.49/1.26 tff(1941,plain,
% 1.49/1.26 (c0_1(a142)),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[189, 1938])).
% 1.49/1.26 tff(1942,plain,
% 1.49/1.26 (c3_1(a143)),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[825, 1927])).
% 1.49/1.26 tff(1943,plain,
% 1.49/1.26 ($false),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[1811, 123, 1815, 1942, 1941, 1940, 1928, 1939, 1346, 1931])).
% 1.49/1.26 tff(1944,plain,(hskp9), inference(lemma,lemma(discharge,[]))).
% 1.49/1.26 tff(1945,plain,
% 1.49/1.26 (((~hskp9) | (~c2_1(a138))) <=> ((~hskp9) | (~c2_1(a138)))),
% 1.49/1.26 inference(rewrite,[status(thm)],[])).
% 1.49/1.26 tff(1946,plain,
% 1.49/1.26 (((~c2_1(a138)) | (~hskp9)) <=> ((~hskp9) | (~c2_1(a138)))),
% 1.49/1.26 inference(rewrite,[status(thm)],[])).
% 1.49/1.26 tff(1947,axiom,((~c2_1(a138)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause113')).
% 1.49/1.26 tff(1948,plain,
% 1.49/1.26 ((~hskp9) | (~c2_1(a138))),
% 1.49/1.26 inference(modus_ponens,[status(thm)],[1947, 1946])).
% 1.49/1.26 tff(1949,plain,
% 1.49/1.26 ((~hskp9) | (~c2_1(a138))),
% 1.49/1.26 inference(modus_ponens,[status(thm)],[1948, 1945])).
% 1.49/1.26 tff(1950,plain,
% 1.49/1.26 (~c2_1(a138)),
% 1.49/1.26 inference(unit_resolution,[status(thm)],[1949, 1944])).
% 1.49/1.26 tff(1951,plain,
% 1.49/1.26 (((~hskp9) | c1_1(a138)) <=> ((~hskp9) | c1_1(a138))),
% 1.49/1.26 inference(rewrite,[status(thm)],[])).
% 1.49/1.26 tff(1952,axiom,((~hskp9) | c1_1(a138)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause73')).
% 1.49/1.26 tff(1953,plain,
% 1.49/1.26 ((~hskp9) | c1_1(a138)),
% 1.49/1.26 inference(modus_ponens,[status(thm)],[1952, 1951])).
% 1.49/1.26 tff(1954,plain,
% 1.49/1.26 ((~hskp9) | c1_1(a138)),
% 1.49/1.26 inference(modus_ponens,[status(thm)],[1953, 1951])).
% 1.49/1.26 tff(1955,plain,
% 1.49/1.26 ((~hskp9) | c1_1(a138)),
% 1.49/1.26 inference(modus_ponens,[status(thm)],[1954, 1951])).
% 1.49/1.26 tff(1956,plain,
% 1.49/1.26 ((~hskp9) | c1_1(a138)),
% 1.49/1.27 inference(modus_ponens,[status(thm)],[1955, 1951])).
% 1.49/1.27 tff(1957,plain,
% 1.49/1.27 ((~hskp9) | c1_1(a138)),
% 1.49/1.27 inference(modus_ponens,[status(thm)],[1956, 1951])).
% 1.49/1.27 tff(1958,plain,
% 1.49/1.27 ((~hskp9) | c1_1(a138)),
% 1.49/1.27 inference(modus_ponens,[status(thm)],[1957, 1951])).
% 1.49/1.27 tff(1959,plain,
% 1.49/1.27 ((~hskp9) | c1_1(a138)),
% 1.49/1.27 inference(modus_ponens,[status(thm)],[1958, 1951])).
% 1.49/1.27 tff(1960,plain,
% 1.49/1.27 ((~hskp9) | c1_1(a138)),
% 1.49/1.27 inference(modus_ponens,[status(thm)],[1959, 1951])).
% 1.49/1.27 tff(1961,plain,
% 1.49/1.27 (c1_1(a138)),
% 1.49/1.27 inference(unit_resolution,[status(thm)],[1960, 1944])).
% 1.49/1.27 tff(1962,plain,
% 1.49/1.27 (((~hskp9) | c0_1(a138)) <=> ((~hskp9) | c0_1(a138))),
% 1.49/1.27 inference(rewrite,[status(thm)],[])).
% 1.49/1.27 tff(1963,axiom,((~hskp9) | c0_1(a138)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause72')).
% 1.49/1.27 tff(1964,plain,
% 1.49/1.27 ((~hskp9) | c0_1(a138)),
% 1.49/1.27 inference(modus_ponens,[status(thm)],[1963, 1962])).
% 1.49/1.27 tff(1965,plain,
% 1.49/1.27 ((~hskp9) | c0_1(a138)),
% 1.49/1.27 inference(modus_ponens,[status(thm)],[1964, 1962])).
% 1.49/1.27 tff(1966,plain,
% 1.49/1.27 ((~hskp9) | c0_1(a138)),
% 1.49/1.27 inference(modus_ponens,[status(thm)],[1965, 1962])).
% 1.49/1.27 tff(1967,plain,
% 1.49/1.27 ((~hskp9) | c0_1(a138)),
% 1.49/1.27 inference(modus_ponens,[status(thm)],[1966, 1962])).
% 1.49/1.27 tff(1968,plain,
% 1.49/1.27 ((~hskp9) | c0_1(a138)),
% 1.49/1.27 inference(modus_ponens,[status(thm)],[1967, 1962])).
% 1.49/1.27 tff(1969,plain,
% 1.49/1.27 ((~hskp9) | c0_1(a138)),
% 1.49/1.27 inference(modus_ponens,[status(thm)],[1968, 1962])).
% 1.49/1.27 tff(1970,plain,
% 1.49/1.27 ((~hskp9) | c0_1(a138)),
% 1.49/1.27 inference(modus_ponens,[status(thm)],[1969, 1962])).
% 1.49/1.27 tff(1971,plain,
% 1.49/1.27 ((~hskp9) | c0_1(a138)),
% 1.49/1.27 inference(modus_ponens,[status(thm)],[1970, 1962])).
% 1.49/1.27 tff(1972,plain,
% 1.49/1.27 (c0_1(a138)),
% 1.49/1.27 inference(unit_resolution,[status(thm)],[1971, 1944])).
% 1.49/1.27 tff(1973,plain,
% 1.49/1.27 (((~![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp18 | hskp10 | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138)))) <=> ((~![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp18 | hskp10 | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138)))),
% 1.49/1.27 inference(rewrite,[status(thm)],[])).
% 1.49/1.27 tff(1974,plain,
% 1.49/1.27 ((hskp18 | hskp10 | (~ndr1_0) | c2_1(a138) | (~c1_1(a138)) | (~c0_1(a138))) <=> (hskp18 | hskp10 | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138)))),
% 1.49/1.27 inference(rewrite,[status(thm)],[])).
% 1.49/1.27 tff(1975,plain,
% 1.49/1.27 (((~![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp18 | hskp10 | (~ndr1_0) | c2_1(a138) | (~c1_1(a138)) | (~c0_1(a138)))) <=> ((~![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp18 | hskp10 | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138))))),
% 1.49/1.27 inference(monotonicity,[status(thm)],[1974])).
% 1.49/1.27 tff(1976,plain,
% 1.49/1.27 (((~![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp18 | hskp10 | (~ndr1_0) | c2_1(a138) | (~c1_1(a138)) | (~c0_1(a138)))) <=> ((~![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp18 | hskp10 | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138)))),
% 1.49/1.27 inference(transitivity,[status(thm)],[1975, 1973])).
% 1.49/1.27 tff(1977,plain,
% 1.49/1.27 ((~![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp18 | hskp10 | (~ndr1_0) | c2_1(a138) | (~c1_1(a138)) | (~c0_1(a138)))),
% 1.49/1.27 inference(quant_inst,[status(thm)],[])).
% 1.49/1.27 tff(1978,plain,
% 1.49/1.27 ((~![U: $i] : (hskp18 | hskp10 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp18 | hskp10 | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138))),
% 1.49/1.27 inference(modus_ponens,[status(thm)],[1977, 1976])).
% 1.49/1.27 tff(1979,plain,
% 1.49/1.27 (hskp18 | hskp10),
% 1.49/1.27 inference(unit_resolution,[status(thm)],[1978, 123, 1972, 1961, 1950, 32])).
% 1.49/1.27 tff(1980,plain,
% 1.49/1.27 (hskp10),
% 1.49/1.27 inference(unit_resolution,[status(thm)],[1979, 22])).
% 1.49/1.27 tff(1981,plain,
% 1.49/1.27 (~c3_1(a140)),
% 1.49/1.27 inference(unit_resolution,[status(thm)],[1844, 1980])).
% 1.49/1.27 tff(1982,plain,
% 1.49/1.27 (~c2_1(a140)),
% 1.49/1.27 inference(unit_resolution,[status(thm)],[1850, 1980])).
% 1.49/1.27 tff(1983,plain,
% 1.49/1.27 (^[U: $i] : refl((hskp22 | hskp7 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp22 | hskp7 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))),
% 1.49/1.27 inference(bind,[status(th)],[])).
% 1.49/1.27 tff(1984,plain,
% 1.49/1.27 (![U: $i] : (hskp22 | hskp7 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp22 | hskp7 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.49/1.27 inference(quant_intro,[status(thm)],[1983])).
% 1.49/1.27 tff(1985,plain,
% 1.49/1.27 (![U: $i] : (hskp22 | hskp7 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp22 | hskp7 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.49/1.27 inference(rewrite,[status(thm)],[])).
% 1.49/1.27 tff(1986,plain,
% 1.49/1.27 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp22) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp22))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp22) <=> (hskp22 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp22) <=> (hskp22 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp22) | hskp7) <=> ((hskp22 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp7))), rewrite(((hskp22 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp7) <=> (hskp22 | hskp7 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp22) | hskp7) <=> (hskp22 | hskp7 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))))),
% 1.49/1.27 inference(bind,[status(th)],[])).
% 1.49/1.27 tff(1987,plain,
% 1.49/1.27 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp22) | hskp7) <=> ![U: $i] : (hskp22 | hskp7 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.49/1.27 inference(quant_intro,[status(thm)],[1986])).
% 1.49/1.27 tff(1988,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp22) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause150')).
% 1.49/1.27 tff(1989,plain,
% 1.49/1.27 (![U: $i] : (hskp22 | hskp7 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.49/1.27 inference(modus_ponens,[status(thm)],[1988, 1987])).
% 1.49/1.27 tff(1990,plain,
% 1.49/1.27 (![U: $i] : (hskp22 | hskp7 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.49/1.27 inference(modus_ponens,[status(thm)],[1989, 1985])).
% 1.49/1.27 tff(1991,plain,(
% 1.49/1.27 ![U: $i] : (hskp22 | hskp7 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.49/1.27 inference(skolemize,[status(sab)],[1990])).
% 1.49/1.27 tff(1992,plain,
% 1.49/1.27 (![U: $i] : (hskp22 | hskp7 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.49/1.27 inference(modus_ponens,[status(thm)],[1991, 1984])).
% 1.49/1.27 tff(1993,plain,
% 1.49/1.27 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 1.49/1.27 inference(bind,[status(th)],[])).
% 1.49/1.27 tff(1994,plain,
% 1.49/1.27 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.49/1.27 inference(quant_intro,[status(thm)],[1993])).
% 1.49/1.27 tff(1995,plain,
% 1.49/1.27 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.49/1.27 inference(rewrite,[status(thm)],[])).
% 1.49/1.27 tff(1996,plain,
% 1.49/1.27 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp7) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp7))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 1.49/1.27 inference(bind,[status(th)],[])).
% 1.49/1.27 tff(1997,plain,
% 1.49/1.27 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.49/1.27 inference(quant_intro,[status(thm)],[1996])).
% 1.49/1.27 tff(1998,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause188')).
% 1.49/1.27 tff(1999,plain,
% 1.49/1.27 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.49/1.27 inference(modus_ponens,[status(thm)],[1998, 1997])).
% 1.49/1.27 tff(2000,plain,
% 1.49/1.27 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.49/1.27 inference(modus_ponens,[status(thm)],[1999, 1995])).
% 1.49/1.27 tff(2001,plain,(
% 1.49/1.27 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.49/1.27 inference(skolemize,[status(sab)],[2000])).
% 1.49/1.27 tff(2002,plain,
% 1.49/1.27 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.49/1.27 inference(modus_ponens,[status(thm)],[2001, 1994])).
% 1.49/1.27 tff(2003,assumption,(hskp13), introduced(assumption)).
% 1.49/1.27 tff(2004,plain,
% 1.49/1.27 (~c1_1(a143)),
% 1.49/1.27 inference(unit_resolution,[status(thm)],[782, 2003])).
% 1.49/1.27 tff(2005,plain,
% 1.49/1.27 (c3_1(a143)),
% 1.49/1.27 inference(unit_resolution,[status(thm)],[825, 2003])).
% 1.49/1.27 tff(2006,plain,
% 1.49/1.27 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp7 | c1_1(a143) | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138)) | (~c3_1(a143)) | (~c0_1(a143)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a143) | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138)) | (~c3_1(a143)) | (~c0_1(a143)))),
% 1.49/1.27 inference(rewrite,[status(thm)],[])).
% 1.49/1.27 tff(2007,plain,
% 1.49/1.27 ((hskp7 | (~ndr1_0) | c2_1(a138) | (~c1_1(a138)) | (~c0_1(a138)) | c1_1(a143) | (~c3_1(a143)) | (~c0_1(a143))) <=> (hskp7 | c1_1(a143) | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138)) | (~c3_1(a143)) | (~c0_1(a143)))),
% 1.49/1.27 inference(rewrite,[status(thm)],[])).
% 1.49/1.27 tff(2008,plain,
% 1.49/1.27 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a138) | (~c1_1(a138)) | (~c0_1(a138)) | c1_1(a143) | (~c3_1(a143)) | (~c0_1(a143)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp7 | c1_1(a143) | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138)) | (~c3_1(a143)) | (~c0_1(a143))))),
% 1.49/1.27 inference(monotonicity,[status(thm)],[2007])).
% 1.49/1.27 tff(2009,plain,
% 1.49/1.27 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a138) | (~c1_1(a138)) | (~c0_1(a138)) | c1_1(a143) | (~c3_1(a143)) | (~c0_1(a143)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a143) | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138)) | (~c3_1(a143)) | (~c0_1(a143)))),
% 1.49/1.27 inference(transitivity,[status(thm)],[2008, 2006])).
% 1.49/1.27 tff(2010,plain,
% 1.49/1.27 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a138) | (~c1_1(a138)) | (~c0_1(a138)) | c1_1(a143) | (~c3_1(a143)) | (~c0_1(a143)))),
% 1.49/1.27 inference(quant_inst,[status(thm)],[])).
% 1.49/1.27 tff(2011,plain,
% 1.49/1.27 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a143) | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138)) | (~c3_1(a143)) | (~c0_1(a143))),
% 1.49/1.27 inference(modus_ponens,[status(thm)],[2010, 2009])).
% 1.49/1.27 tff(2012,plain,
% 1.49/1.27 (~c0_1(a143)),
% 1.49/1.27 inference(unit_resolution,[status(thm)],[2011, 123, 96, 2005, 1972, 1961, 2004, 1950, 2002])).
% 1.49/1.27 tff(2013,plain,
% 1.49/1.27 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a143) | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138)) | (~c3_1(a143)) | c0_1(a143))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a143) | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138)) | (~c3_1(a143)) | c0_1(a143))),
% 1.49/1.27 inference(rewrite,[status(thm)],[])).
% 1.49/1.27 tff(2014,plain,
% 1.49/1.27 ((hskp7 | (~ndr1_0) | c2_1(a138) | (~c1_1(a138)) | (~c0_1(a138)) | c1_1(a143) | c0_1(a143) | (~c3_1(a143))) <=> (hskp7 | c1_1(a143) | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138)) | (~c3_1(a143)) | c0_1(a143))),
% 1.49/1.27 inference(rewrite,[status(thm)],[])).
% 1.49/1.27 tff(2015,plain,
% 1.49/1.27 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a138) | (~c1_1(a138)) | (~c0_1(a138)) | c1_1(a143) | c0_1(a143) | (~c3_1(a143)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a143) | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138)) | (~c3_1(a143)) | c0_1(a143)))),
% 1.49/1.27 inference(monotonicity,[status(thm)],[2014])).
% 1.49/1.27 tff(2016,plain,
% 1.49/1.27 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a138) | (~c1_1(a138)) | (~c0_1(a138)) | c1_1(a143) | c0_1(a143) | (~c3_1(a143)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a143) | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138)) | (~c3_1(a143)) | c0_1(a143))),
% 1.49/1.27 inference(transitivity,[status(thm)],[2015, 2013])).
% 1.49/1.27 tff(2017,plain,
% 1.49/1.27 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a138) | (~c1_1(a138)) | (~c0_1(a138)) | c1_1(a143) | c0_1(a143) | (~c3_1(a143)))),
% 1.49/1.27 inference(quant_inst,[status(thm)],[])).
% 1.49/1.27 tff(2018,plain,
% 1.49/1.27 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a143) | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138)) | (~c3_1(a143)) | c0_1(a143)),
% 1.49/1.27 inference(modus_ponens,[status(thm)],[2017, 2016])).
% 1.49/1.27 tff(2019,plain,
% 1.49/1.27 ($false),
% 1.49/1.27 inference(unit_resolution,[status(thm)],[2018, 123, 96, 2005, 1972, 1961, 2004, 1950, 368, 2012])).
% 1.49/1.27 tff(2020,plain,((~hskp13) | hskp7), inference(lemma,lemma(discharge,[]))).
% 1.49/1.27 tff(2021,plain,
% 1.49/1.27 (~hskp13),
% 1.49/1.27 inference(unit_resolution,[status(thm)],[2020, 96])).
% 1.49/1.27 tff(2022,assumption,(~hskp13), introduced(assumption)).
% 1.49/1.27 tff(2023,plain,
% 1.49/1.27 ($false),
% 1.49/1.27 inference(unit_resolution,[status(thm)],[776, 123, 134, 2022, 1885, 1884, 1883, 769])).
% 1.49/1.27 tff(2024,plain,((~hskp19) | hskp17 | hskp13), inference(lemma,lemma(discharge,[]))).
% 1.49/1.27 tff(2025,plain,
% 1.49/1.27 (~hskp19),
% 1.49/1.27 inference(unit_resolution,[status(thm)],[2024, 2021, 134])).
% 1.49/1.27 tff(2026,plain,
% 1.49/1.27 ((hskp19 | hskp13 | hskp12) <=> (hskp19 | hskp13 | hskp12)),
% 1.49/1.27 inference(rewrite,[status(thm)],[])).
% 1.49/1.27 tff(2027,plain,
% 1.49/1.27 (((hskp12 | hskp19) | hskp13) <=> (hskp19 | hskp13 | hskp12)),
% 1.49/1.27 inference(rewrite,[status(thm)],[])).
% 1.49/1.27 tff(2028,axiom,((hskp12 | hskp19) | hskp13), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause36')).
% 1.49/1.27 tff(2029,plain,
% 1.49/1.27 (hskp19 | hskp13 | hskp12),
% 1.49/1.27 inference(modus_ponens,[status(thm)],[2028, 2027])).
% 1.49/1.27 tff(2030,plain,
% 1.49/1.27 (hskp19 | hskp13 | hskp12),
% 1.49/1.27 inference(modus_ponens,[status(thm)],[2029, 2026])).
% 1.49/1.27 tff(2031,plain,
% 1.49/1.27 (hskp19 | hskp13 | hskp12),
% 1.49/1.27 inference(modus_ponens,[status(thm)],[2030, 2026])).
% 1.49/1.27 tff(2032,plain,
% 1.49/1.27 (hskp19 | hskp13 | hskp12),
% 1.49/1.27 inference(modus_ponens,[status(thm)],[2031, 2026])).
% 1.49/1.27 tff(2033,plain,
% 1.49/1.27 (hskp19 | hskp13 | hskp12),
% 1.49/1.27 inference(modus_ponens,[status(thm)],[2032, 2026])).
% 1.49/1.27 tff(2034,plain,
% 1.49/1.27 (hskp19 | hskp13 | hskp12),
% 1.49/1.27 inference(modus_ponens,[status(thm)],[2033, 2026])).
% 1.49/1.27 tff(2035,plain,
% 1.49/1.27 (hskp19 | hskp13 | hskp12),
% 1.49/1.27 inference(modus_ponens,[status(thm)],[2034, 2026])).
% 1.49/1.27 tff(2036,plain,
% 1.49/1.27 (hskp19 | hskp13 | hskp12),
% 1.49/1.27 inference(modus_ponens,[status(thm)],[2035, 2026])).
% 1.49/1.27 tff(2037,plain,
% 1.49/1.27 (hskp12),
% 1.49/1.27 inference(unit_resolution,[status(thm)],[2036, 2025, 2021])).
% 1.49/1.27 tff(2038,plain,
% 1.49/1.27 (~c1_1(a142)),
% 1.49/1.27 inference(unit_resolution,[status(thm)],[150, 2037])).
% 1.49/1.27 tff(2039,plain,
% 1.49/1.27 (c3_1(a142)),
% 1.49/1.27 inference(unit_resolution,[status(thm)],[161, 2037])).
% 1.49/1.27 tff(2040,plain,
% 1.49/1.27 (~hskp22),
% 1.49/1.27 inference(unit_resolution,[status(thm)],[1823, 2025, 134])).
% 1.49/1.27 tff(2041,plain,
% 1.49/1.27 (((~![U: $i] : (hskp22 | hskp7 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp22 | hskp7 | c1_1(a142) | (~ndr1_0) | (~c2_1(a142)) | (~c3_1(a142)))) <=> ((~![U: $i] : (hskp22 | hskp7 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp22 | hskp7 | c1_1(a142) | (~ndr1_0) | (~c2_1(a142)) | (~c3_1(a142)))),
% 1.49/1.27 inference(rewrite,[status(thm)],[])).
% 1.49/1.27 tff(2042,plain,
% 1.49/1.27 ((hskp22 | hskp7 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c2_1(a142))) <=> (hskp22 | hskp7 | c1_1(a142) | (~ndr1_0) | (~c2_1(a142)) | (~c3_1(a142)))),
% 1.49/1.27 inference(rewrite,[status(thm)],[])).
% 1.49/1.27 tff(2043,plain,
% 1.49/1.27 (((~![U: $i] : (hskp22 | hskp7 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp22 | hskp7 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c2_1(a142)))) <=> ((~![U: $i] : (hskp22 | hskp7 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp22 | hskp7 | c1_1(a142) | (~ndr1_0) | (~c2_1(a142)) | (~c3_1(a142))))),
% 1.49/1.27 inference(monotonicity,[status(thm)],[2042])).
% 1.49/1.27 tff(2044,plain,
% 1.49/1.27 (((~![U: $i] : (hskp22 | hskp7 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp22 | hskp7 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c2_1(a142)))) <=> ((~![U: $i] : (hskp22 | hskp7 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp22 | hskp7 | c1_1(a142) | (~ndr1_0) | (~c2_1(a142)) | (~c3_1(a142)))),
% 1.49/1.27 inference(transitivity,[status(thm)],[2043, 2041])).
% 1.49/1.27 tff(2045,plain,
% 1.49/1.27 ((~![U: $i] : (hskp22 | hskp7 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp22 | hskp7 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c2_1(a142)))),
% 1.49/1.27 inference(quant_inst,[status(thm)],[])).
% 1.49/1.27 tff(2046,plain,
% 1.49/1.27 ((~![U: $i] : (hskp22 | hskp7 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp22 | hskp7 | c1_1(a142) | (~ndr1_0) | (~c2_1(a142)) | (~c3_1(a142))),
% 1.49/1.27 inference(modus_ponens,[status(thm)],[2045, 2044])).
% 1.49/1.27 tff(2047,plain,
% 1.49/1.27 (~c2_1(a142)),
% 1.49/1.27 inference(unit_resolution,[status(thm)],[2046, 123, 2040, 96, 2039, 2038, 1992])).
% 1.49/1.27 tff(2048,plain,
% 1.49/1.27 (c0_1(a142)),
% 1.49/1.27 inference(unit_resolution,[status(thm)],[189, 2037])).
% 1.49/1.27 tff(2049,plain,
% 1.49/1.27 ($false),
% 1.49/1.27 inference(unit_resolution,[status(thm)],[243, 123, 2025, 134, 2048, 2038, 53, 2047])).
% 1.49/1.27 tff(2050,plain,(hskp7 | hskp17), inference(lemma,lemma(discharge,[]))).
% 1.49/1.27 tff(2051,plain,
% 1.49/1.27 (hskp7),
% 1.49/1.27 inference(unit_resolution,[status(thm)],[2050, 134])).
% 1.49/1.27 tff(2052,plain,
% 1.49/1.27 (c3_1(a132)),
% 1.49/1.27 inference(unit_resolution,[status(thm)],[447, 2051])).
% 1.49/1.27 tff(2053,plain,
% 1.49/1.27 (~c2_1(a132)),
% 1.49/1.27 inference(unit_resolution,[status(thm)],[898, 2051])).
% 1.49/1.27 tff(2054,plain,
% 1.49/1.27 (~c0_1(a132)),
% 1.49/1.27 inference(unit_resolution,[status(thm)],[431, 2051])).
% 1.49/1.27 tff(2055,assumption,(c1_1(a131)), introduced(assumption)).
% 1.49/1.27 tff(2056,plain,
% 1.49/1.27 (hskp0 | (~c1_1(a132))),
% 1.49/1.27 inference(unit_resolution,[status(thm)],[1039, 123, 134, 2052, 2054, 43])).
% 1.49/1.27 tff(2057,plain,
% 1.49/1.27 (~c1_1(a132)),
% 1.49/1.27 inference(unit_resolution,[status(thm)],[2056, 11])).
% 1.49/1.27 tff(2058,plain,
% 1.49/1.27 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 1.49/1.27 inference(bind,[status(th)],[])).
% 1.49/1.27 tff(2059,plain,
% 1.49/1.27 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.49/1.27 inference(quant_intro,[status(thm)],[2058])).
% 1.49/1.27 tff(2060,plain,
% 1.49/1.27 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.49/1.27 inference(rewrite,[status(thm)],[])).
% 1.49/1.27 tff(2061,plain,
% 1.49/1.27 (^[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(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | 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)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 1.49/1.27 inference(bind,[status(th)],[])).
% 1.49/1.27 tff(2062,plain,
% 1.49/1.27 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.49/1.27 inference(quant_intro,[status(thm)],[2061])).
% 1.49/1.27 tff(2063,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause169')).
% 1.49/1.27 tff(2064,plain,
% 1.49/1.27 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.49/1.27 inference(modus_ponens,[status(thm)],[2063, 2062])).
% 1.49/1.27 tff(2065,plain,
% 1.49/1.27 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.49/1.27 inference(modus_ponens,[status(thm)],[2064, 2060])).
% 1.49/1.27 tff(2066,plain,(
% 1.49/1.27 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.49/1.27 inference(skolemize,[status(sab)],[2065])).
% 1.49/1.27 tff(2067,plain,
% 1.49/1.27 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.49/1.27 inference(modus_ponens,[status(thm)],[2066, 2059])).
% 1.49/1.27 tff(2068,plain,
% 1.49/1.27 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a132) | c2_1(a132) | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | c3_1(a131) | c1_1(a132))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a132) | c2_1(a132) | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | c3_1(a131) | c1_1(a132))),
% 1.49/1.27 inference(rewrite,[status(thm)],[])).
% 1.49/1.27 tff(2069,plain,
% 1.49/1.27 ((hskp0 | (~ndr1_0) | c2_1(a131) | c3_1(a131) | (~c1_1(a131)) | c2_1(a132) | c1_1(a132) | c0_1(a132)) <=> (hskp0 | c0_1(a132) | c2_1(a132) | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | c3_1(a131) | c1_1(a132))),
% 1.49/1.27 inference(rewrite,[status(thm)],[])).
% 1.49/1.27 tff(2070,plain,
% 1.49/1.27 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a131) | c3_1(a131) | (~c1_1(a131)) | c2_1(a132) | c1_1(a132) | c0_1(a132))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a132) | c2_1(a132) | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | c3_1(a131) | c1_1(a132)))),
% 1.49/1.27 inference(monotonicity,[status(thm)],[2069])).
% 1.49/1.27 tff(2071,plain,
% 1.49/1.27 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a131) | c3_1(a131) | (~c1_1(a131)) | c2_1(a132) | c1_1(a132) | c0_1(a132))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a132) | c2_1(a132) | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | c3_1(a131) | c1_1(a132))),
% 1.49/1.27 inference(transitivity,[status(thm)],[2070, 2068])).
% 1.49/1.27 tff(2072,plain,
% 1.49/1.27 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a131) | c3_1(a131) | (~c1_1(a131)) | c2_1(a132) | c1_1(a132) | c0_1(a132))),
% 1.49/1.27 inference(quant_inst,[status(thm)],[])).
% 1.49/1.27 tff(2073,plain,
% 1.49/1.27 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a132) | c2_1(a132) | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | c3_1(a131) | c1_1(a132)),
% 1.49/1.27 inference(modus_ponens,[status(thm)],[2072, 2071])).
% 1.49/1.27 tff(2074,plain,
% 1.49/1.27 (hskp0 | (~c1_1(a131)) | c3_1(a131) | c1_1(a132)),
% 1.49/1.27 inference(unit_resolution,[status(thm)],[2073, 123, 2054, 2053, 95, 2067])).
% 1.49/1.27 tff(2075,plain,
% 1.49/1.27 (c3_1(a131)),
% 1.49/1.27 inference(unit_resolution,[status(thm)],[2074, 11, 2055, 2057])).
% 1.49/1.27 tff(2076,plain,
% 1.49/1.27 (((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)))) <=> ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp13 | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)))),
% 1.49/1.27 inference(rewrite,[status(thm)],[])).
% 1.49/1.27 tff(2077,plain,
% 1.49/1.27 ((hskp17 | hskp13 | (~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131))) <=> (hskp17 | hskp13 | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)))),
% 1.49/1.27 inference(rewrite,[status(thm)],[])).
% 1.49/1.27 tff(2078,plain,
% 1.49/1.27 (((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | (~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131)))) <=> ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131))))),
% 1.49/1.27 inference(monotonicity,[status(thm)],[2077])).
% 1.49/1.27 tff(2079,plain,
% 1.49/1.27 (((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | (~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131)))) <=> ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp13 | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)))),
% 1.49/1.27 inference(transitivity,[status(thm)],[2078, 2076])).
% 1.49/1.27 tff(2080,plain,
% 1.49/1.27 ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | (~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131)))),
% 1.49/1.27 inference(quant_inst,[status(thm)],[])).
% 1.49/1.27 tff(2081,plain,
% 1.49/1.27 ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp13 | (~c1_1(a131)) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131))),
% 1.49/1.27 inference(modus_ponens,[status(thm)],[2080, 2079])).
% 1.49/1.27 tff(2082,plain,
% 1.49/1.27 (hskp13 | (~c1_1(a131)) | (~c3_1(a131))),
% 1.49/1.27 inference(unit_resolution,[status(thm)],[2081, 123, 134, 95, 769])).
% 1.49/1.27 tff(2083,plain,
% 1.49/1.27 (hskp13),
% 1.49/1.27 inference(unit_resolution,[status(thm)],[2082, 2075, 2055])).
% 1.49/1.27 tff(2084,plain,
% 1.49/1.27 (c2_1(a143)),
% 1.49/1.27 inference(unit_resolution,[status(thm)],[836, 2083])).
% 1.49/1.27 tff(2085,plain,
% 1.49/1.27 (~hskp6),
% 1.49/1.27 inference(unit_resolution,[status(thm)],[77, 2055])).
% 1.49/1.27 tff(2086,plain,
% 1.49/1.27 (c3_1(a143)),
% 1.49/1.27 inference(unit_resolution,[status(thm)],[825, 2083])).
% 1.49/1.27 tff(2087,plain,
% 1.49/1.27 (~c1_1(a143)),
% 1.49/1.27 inference(unit_resolution,[status(thm)],[782, 2083])).
% 1.49/1.27 tff(2088,plain,
% 1.49/1.27 ($false),
% 1.49/1.27 inference(unit_resolution,[status(thm)],[1412, 2087, 2086, 2052, 2085, 2057, 2053, 2084])).
% 1.49/1.27 tff(2089,plain,(hskp0 | (~c1_1(a131)) | hskp17 | c2_1(a131)), inference(lemma,lemma(discharge,[]))).
% 1.49/1.27 tff(2090,plain,
% 1.49/1.27 (hskp0),
% 1.49/1.27 inference(unit_resolution,[status(thm)],[2089, 2055, 134, 95])).
% 1.49/1.27 tff(2091,plain,
% 1.49/1.27 (c2_1(a123)),
% 1.49/1.27 inference(unit_resolution,[status(thm)],[213, 2090])).
% 1.49/1.27 tff(2092,plain,
% 1.49/1.27 (~c1_1(a123)),
% 1.49/1.27 inference(unit_resolution,[status(thm)],[202, 2090])).
% 1.49/1.27 tff(2093,plain,
% 1.49/1.27 (~c0_1(a123)),
% 1.49/1.27 inference(unit_resolution,[status(thm)],[236, 2090])).
% 1.49/1.27 tff(2094,assumption,(c1_1(a132)), introduced(assumption)).
% 1.49/1.27 tff(2095,plain,
% 1.49/1.27 (hskp12 | (~c1_1(a132))),
% 1.49/1.27 inference(unit_resolution,[status(thm)],[1586, 123, 2052, 2054, 2053, 1446])).
% 1.49/1.28 tff(2096,plain,
% 1.49/1.28 (hskp12),
% 1.49/1.28 inference(unit_resolution,[status(thm)],[2095, 2094])).
% 1.49/1.28 tff(2097,plain,
% 1.49/1.28 (~c1_1(a142)),
% 1.49/1.28 inference(unit_resolution,[status(thm)],[150, 2096])).
% 1.49/1.28 tff(2098,plain,
% 1.49/1.28 (((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)))) <=> ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp13 | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)))),
% 1.49/1.28 inference(rewrite,[status(thm)],[])).
% 1.49/1.28 tff(2099,plain,
% 1.49/1.28 ((hskp17 | hskp13 | (~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132))) <=> (hskp17 | hskp13 | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)))),
% 1.49/1.28 inference(rewrite,[status(thm)],[])).
% 1.49/1.28 tff(2100,plain,
% 1.49/1.28 (((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | (~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132)))) <=> ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132))))),
% 1.49/1.28 inference(monotonicity,[status(thm)],[2099])).
% 1.49/1.28 tff(2101,plain,
% 1.49/1.28 (((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | (~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132)))) <=> ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp13 | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)))),
% 1.49/1.28 inference(transitivity,[status(thm)],[2100, 2098])).
% 1.49/1.28 tff(2102,plain,
% 1.49/1.28 ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | (~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132)))),
% 1.49/1.28 inference(quant_inst,[status(thm)],[])).
% 1.49/1.28 tff(2103,plain,
% 1.49/1.28 ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp13 | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132))),
% 1.49/1.28 inference(modus_ponens,[status(thm)],[2102, 2101])).
% 1.49/1.28 tff(2104,plain,
% 1.49/1.28 (hskp13 | (~c1_1(a132))),
% 1.49/1.28 inference(unit_resolution,[status(thm)],[2103, 123, 134, 2052, 2053, 769])).
% 1.49/1.28 tff(2105,plain,
% 1.49/1.28 (hskp13),
% 1.49/1.28 inference(unit_resolution,[status(thm)],[2104, 2094])).
% 1.49/1.28 tff(2106,plain,
% 1.49/1.28 (~c1_1(a143)),
% 1.49/1.28 inference(unit_resolution,[status(thm)],[782, 2105])).
% 1.49/1.28 tff(2107,plain,
% 1.49/1.28 (c3_1(a142)),
% 1.49/1.28 inference(unit_resolution,[status(thm)],[161, 2096])).
% 1.49/1.28 tff(2108,plain,
% 1.49/1.28 (c0_1(a142)),
% 1.49/1.28 inference(unit_resolution,[status(thm)],[189, 2096])).
% 1.49/1.28 tff(2109,plain,
% 1.49/1.28 (c3_1(a143)),
% 1.49/1.28 inference(unit_resolution,[status(thm)],[825, 2105])).
% 1.49/1.28 tff(2110,plain,
% 1.49/1.28 (c0_1(a143)),
% 1.49/1.28 inference(unit_resolution,[status(thm)],[1811, 123, 1403, 2109, 2108, 2107, 2106, 2097, 1346])).
% 1.49/1.28 tff(2111,plain,
% 1.49/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a138) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | (~c3_1(a138)) | (~c0_1(a138)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a138) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | (~c3_1(a138)) | (~c0_1(a138)))),
% 1.49/1.28 inference(rewrite,[status(thm)],[])).
% 1.49/1.28 tff(2112,plain,
% 1.49/1.28 (((~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132))) <=> (c2_1(a138) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | (~c3_1(a138)) | (~c0_1(a138)))),
% 1.49/1.28 inference(rewrite,[status(thm)],[])).
% 1.49/1.28 tff(2113,plain,
% 1.49/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a138) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | (~c3_1(a138)) | (~c0_1(a138))))),
% 1.49/1.28 inference(monotonicity,[status(thm)],[2112])).
% 1.49/1.28 tff(2114,plain,
% 1.49/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a138) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | (~c3_1(a138)) | (~c0_1(a138)))),
% 1.49/1.28 inference(transitivity,[status(thm)],[2113, 2111])).
% 1.49/1.28 tff(2115,plain,
% 1.49/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a132) | c0_1(a132) | (~c1_1(a132)))),
% 1.49/1.28 inference(quant_inst,[status(thm)],[])).
% 1.49/1.28 tff(2116,plain,
% 1.49/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a138) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | (~c3_1(a138)) | (~c0_1(a138))),
% 1.49/1.28 inference(modus_ponens,[status(thm)],[2115, 2114])).
% 1.49/1.28 tff(2117,plain,
% 1.49/1.28 ((~c1_1(a132)) | (~c3_1(a138))),
% 1.49/1.28 inference(unit_resolution,[status(thm)],[2116, 123, 1972, 2052, 1950, 2054, 2053, 1428])).
% 1.49/1.28 tff(2118,plain,
% 1.49/1.28 (~c3_1(a138)),
% 1.49/1.28 inference(unit_resolution,[status(thm)],[2117, 2094])).
% 1.49/1.28 tff(2119,assumption,(~c0_1(a123)), introduced(assumption)).
% 1.49/1.28 tff(2120,assumption,(c2_1(a123)), introduced(assumption)).
% 1.49/1.28 tff(2121,plain,
% 1.49/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a138) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132)) | (~c1_1(a132)) | c3_1(a138) | (~c1_1(a138)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a138) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132)) | (~c1_1(a132)) | c3_1(a138) | (~c1_1(a138)))),
% 1.49/1.28 inference(rewrite,[status(thm)],[])).
% 1.49/1.28 tff(2122,plain,
% 1.49/1.28 (((~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132)) | c2_1(a138) | c3_1(a138) | (~c1_1(a138)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123))) <=> (c2_1(a138) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132)) | (~c1_1(a132)) | c3_1(a138) | (~c1_1(a138)))),
% 1.49/1.28 inference(rewrite,[status(thm)],[])).
% 1.49/1.28 tff(2123,plain,
% 1.49/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132)) | c2_1(a138) | c3_1(a138) | (~c1_1(a138)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a138) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132)) | (~c1_1(a132)) | c3_1(a138) | (~c1_1(a138))))),
% 1.49/1.28 inference(monotonicity,[status(thm)],[2122])).
% 1.49/1.28 tff(2124,plain,
% 1.49/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132)) | c2_1(a138) | c3_1(a138) | (~c1_1(a138)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a138) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132)) | (~c1_1(a132)) | c3_1(a138) | (~c1_1(a138)))),
% 1.49/1.28 inference(transitivity,[status(thm)],[2123, 2121])).
% 1.49/1.28 tff(2125,plain,
% 1.49/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132)) | c2_1(a138) | c3_1(a138) | (~c1_1(a138)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)))),
% 1.49/1.28 inference(quant_inst,[status(thm)],[])).
% 1.49/1.28 tff(2126,plain,
% 1.49/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a138) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132)) | (~c1_1(a132)) | c3_1(a138) | (~c1_1(a138))),
% 1.49/1.28 inference(modus_ponens,[status(thm)],[2125, 2124])).
% 1.49/1.28 tff(2127,plain,
% 1.49/1.28 (c3_1(a123) | (~c1_1(a132)) | c3_1(a138)),
% 1.49/1.28 inference(unit_resolution,[status(thm)],[2126, 123, 1961, 2052, 2120, 1950, 2053, 2119, 1482])).
% 1.49/1.28 tff(2128,plain,
% 1.49/1.28 (c3_1(a123)),
% 1.49/1.28 inference(unit_resolution,[status(thm)],[2127, 2118, 2094])).
% 1.49/1.28 tff(2129,assumption,(~c1_1(a123)), introduced(assumption)).
% 1.49/1.28 tff(2130,plain,
% 1.49/1.28 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c1_1(a143) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c3_1(a143)) | (~c0_1(a143)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c1_1(a143) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c3_1(a143)) | (~c0_1(a143)))),
% 1.49/1.28 inference(rewrite,[status(thm)],[])).
% 1.49/1.28 tff(2131,plain,
% 1.49/1.28 ((hskp6 | (~ndr1_0) | c1_1(a143) | (~c3_1(a143)) | (~c0_1(a143)) | c1_1(a123) | c0_1(a123) | (~c3_1(a123))) <=> (hskp6 | c1_1(a143) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c3_1(a143)) | (~c0_1(a143)))),
% 1.49/1.28 inference(rewrite,[status(thm)],[])).
% 1.49/1.28 tff(2132,plain,
% 1.49/1.28 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a143) | (~c3_1(a143)) | (~c0_1(a143)) | c1_1(a123) | c0_1(a123) | (~c3_1(a123)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c1_1(a143) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c3_1(a143)) | (~c0_1(a143))))),
% 1.49/1.28 inference(monotonicity,[status(thm)],[2131])).
% 1.49/1.28 tff(2133,plain,
% 1.49/1.28 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a143) | (~c3_1(a143)) | (~c0_1(a143)) | c1_1(a123) | c0_1(a123) | (~c3_1(a123)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c1_1(a143) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c3_1(a143)) | (~c0_1(a143)))),
% 1.49/1.28 inference(transitivity,[status(thm)],[2132, 2130])).
% 1.49/1.28 tff(2134,plain,
% 1.49/1.28 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a143) | (~c3_1(a143)) | (~c0_1(a143)) | c1_1(a123) | c0_1(a123) | (~c3_1(a123)))),
% 1.49/1.28 inference(quant_inst,[status(thm)],[])).
% 1.49/1.28 tff(2135,plain,
% 1.49/1.28 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c1_1(a143) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c3_1(a143)) | (~c0_1(a143))),
% 1.49/1.28 inference(modus_ponens,[status(thm)],[2134, 2133])).
% 1.49/1.28 tff(2136,plain,
% 1.49/1.28 ($false),
% 1.49/1.28 inference(unit_resolution,[status(thm)],[2135, 123, 1403, 2109, 2106, 2119, 2129, 1346, 2128, 2110])).
% 1.49/1.28 tff(2137,plain,((~c1_1(a132)) | hskp6 | c0_1(a123) | c1_1(a123) | (~c2_1(a123)) | hskp17), inference(lemma,lemma(discharge,[]))).
% 1.49/1.28 tff(2138,plain,
% 1.49/1.28 (~c1_1(a132)),
% 1.49/1.28 inference(unit_resolution,[status(thm)],[2137, 2085, 2093, 2092, 2091, 134])).
% 1.49/1.28 tff(2139,plain,
% 1.49/1.28 (hskp30),
% 1.49/1.28 inference(unit_resolution,[status(thm)],[608, 2138, 2054, 2053, 2052, 2090])).
% 1.49/1.28 tff(2140,plain,
% 1.49/1.28 (c0_1(a167)),
% 1.49/1.28 inference(unit_resolution,[status(thm)],[1129, 2139])).
% 1.49/1.28 tff(2141,plain,
% 1.49/1.28 (c1_1(a167)),
% 1.49/1.28 inference(unit_resolution,[status(thm)],[1186, 2139])).
% 1.49/1.28 tff(2142,plain,
% 1.49/1.28 (c3_1(a167)),
% 1.49/1.28 inference(unit_resolution,[status(thm)],[1175, 2139])).
% 1.49/1.28 tff(2143,plain,
% 1.49/1.28 ($false),
% 1.49/1.28 inference(unit_resolution,[status(thm)],[1919, 2142, 2141, 2052, 2053, 134, 2085, 2138, 2140])).
% 1.49/1.28 tff(2144,plain,((~c1_1(a131)) | hskp17 | c2_1(a131)), inference(lemma,lemma(discharge,[]))).
% 1.49/1.28 tff(2145,plain,
% 1.49/1.28 (~c1_1(a131)),
% 1.49/1.28 inference(unit_resolution,[status(thm)],[2144, 95, 134])).
% 1.49/1.28 tff(2146,plain,
% 1.49/1.28 (hskp19 | (~c0_1(a131)) | c1_1(a131)),
% 1.49/1.28 inference(unit_resolution,[status(thm)],[1352, 123, 134, 95, 53])).
% 1.49/1.28 tff(2147,plain,
% 1.49/1.28 (~c0_1(a131)),
% 1.49/1.28 inference(unit_resolution,[status(thm)],[2146, 132, 1817])).
% 1.49/1.28 tff(2148,plain,
% 1.49/1.28 (c0_1(a131) | c1_1(a131) | (~c1_1(a132))),
% 1.49/1.28 inference(unit_resolution,[status(thm)],[464, 123, 2052, 2054, 2053, 95, 406])).
% 1.49/1.28 tff(2149,plain,
% 1.49/1.28 (~c1_1(a132)),
% 1.49/1.28 inference(unit_resolution,[status(thm)],[2148, 2147, 132])).
% 1.49/1.28 tff(2150,plain,
% 1.49/1.28 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c2_1(a138) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | c1_1(a132) | c3_1(a138) | (~c1_1(a138)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c2_1(a138) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | c1_1(a132) | c3_1(a138) | (~c1_1(a138)))),
% 1.49/1.28 inference(rewrite,[status(thm)],[])).
% 1.49/1.28 tff(2151,plain,
% 1.49/1.28 ((hskp0 | (~ndr1_0) | c2_1(a138) | c3_1(a138) | (~c1_1(a138)) | c2_1(a132) | c1_1(a132) | c0_1(a132)) <=> (hskp0 | c2_1(a138) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | c1_1(a132) | c3_1(a138) | (~c1_1(a138)))),
% 1.49/1.28 inference(rewrite,[status(thm)],[])).
% 1.49/1.28 tff(2152,plain,
% 1.49/1.28 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a138) | c3_1(a138) | (~c1_1(a138)) | c2_1(a132) | c1_1(a132) | c0_1(a132))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c2_1(a138) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | c1_1(a132) | c3_1(a138) | (~c1_1(a138))))),
% 1.49/1.28 inference(monotonicity,[status(thm)],[2151])).
% 1.49/1.28 tff(2153,plain,
% 1.49/1.28 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a138) | c3_1(a138) | (~c1_1(a138)) | c2_1(a132) | c1_1(a132) | c0_1(a132))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c2_1(a138) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | c1_1(a132) | c3_1(a138) | (~c1_1(a138)))),
% 1.49/1.28 inference(transitivity,[status(thm)],[2152, 2150])).
% 1.49/1.28 tff(2154,plain,
% 1.49/1.28 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a138) | c3_1(a138) | (~c1_1(a138)) | c2_1(a132) | c1_1(a132) | c0_1(a132))),
% 1.49/1.28 inference(quant_inst,[status(thm)],[])).
% 1.49/1.28 tff(2155,plain,
% 1.49/1.28 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c2_1(a138) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | c1_1(a132) | c3_1(a138) | (~c1_1(a138))),
% 1.49/1.28 inference(modus_ponens,[status(thm)],[2154, 2153])).
% 1.49/1.28 tff(2156,plain,
% 1.49/1.28 (hskp0 | c1_1(a132) | c3_1(a138)),
% 1.49/1.28 inference(unit_resolution,[status(thm)],[2155, 123, 1961, 1950, 2054, 2053, 2067])).
% 1.49/1.28 tff(2157,plain,
% 1.49/1.28 (c3_1(a138)),
% 1.49/1.28 inference(unit_resolution,[status(thm)],[2156, 11, 2149])).
% 1.49/1.28 tff(2158,plain,
% 1.49/1.28 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | c2_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c1_1(a138)))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp17 | c2_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c1_1(a138)))),
% 1.49/1.28 inference(rewrite,[status(thm)],[])).
% 1.49/1.28 tff(2159,plain,
% 1.49/1.28 ((hskp24 | hskp17 | (~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138))) <=> (hskp24 | hskp17 | c2_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c1_1(a138)))),
% 1.49/1.28 inference(rewrite,[status(thm)],[])).
% 1.49/1.28 tff(2160,plain,
% 1.49/1.28 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138)))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | c2_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c1_1(a138))))),
% 1.49/1.28 inference(monotonicity,[status(thm)],[2159])).
% 1.49/1.28 tff(2161,plain,
% 1.49/1.28 (((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138)))) <=> ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp17 | c2_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c1_1(a138)))),
% 1.49/1.28 inference(transitivity,[status(thm)],[2160, 2158])).
% 1.49/1.28 tff(2162,plain,
% 1.49/1.28 ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp17 | (~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138)))),
% 1.49/1.28 inference(quant_inst,[status(thm)],[])).
% 1.49/1.28 tff(2163,plain,
% 1.49/1.28 ((~![U: $i] : (hskp24 | hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp17 | c2_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c1_1(a138))),
% 1.49/1.28 inference(modus_ponens,[status(thm)],[2162, 2161])).
% 1.49/1.28 tff(2164,plain,
% 1.49/1.28 (hskp24 | hskp17 | (~c3_1(a138))),
% 1.49/1.28 inference(unit_resolution,[status(thm)],[2163, 123, 1961, 1950, 1294])).
% 1.49/1.28 tff(2165,plain,
% 1.49/1.28 (hskp24),
% 1.49/1.28 inference(unit_resolution,[status(thm)],[2164, 2157, 134])).
% 1.49/1.28 tff(2166,plain,
% 1.49/1.28 (~c3_1(a182)),
% 1.49/1.28 inference(unit_resolution,[status(thm)],[1307, 2165])).
% 1.49/1.28 tff(2167,plain,
% 1.49/1.28 (~c2_1(a182)),
% 1.49/1.28 inference(unit_resolution,[status(thm)],[1313, 2165])).
% 1.49/1.28 tff(2168,plain,
% 1.49/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a182) | c3_1(a182) | c2_1(a138) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c3_1(a138)) | (~c0_1(a138)) | (~c1_1(a182)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a182) | c3_1(a182) | c2_1(a138) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c3_1(a138)) | (~c0_1(a138)) | (~c1_1(a182)))),
% 1.49/1.28 inference(rewrite,[status(thm)],[])).
% 1.49/1.28 tff(2169,plain,
% 1.49/1.28 (((~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a182) | c3_1(a182) | (~c1_1(a182)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132))) <=> (c2_1(a182) | c3_1(a182) | c2_1(a138) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c3_1(a138)) | (~c0_1(a138)) | (~c1_1(a182)))),
% 1.49/1.28 inference(rewrite,[status(thm)],[])).
% 1.49/1.28 tff(2170,plain,
% 1.49/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a182) | c3_1(a182) | (~c1_1(a182)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a182) | c3_1(a182) | c2_1(a138) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c3_1(a138)) | (~c0_1(a138)) | (~c1_1(a182))))),
% 1.49/1.28 inference(monotonicity,[status(thm)],[2169])).
% 1.49/1.28 tff(2171,plain,
% 1.49/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a182) | c3_1(a182) | (~c1_1(a182)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a182) | c3_1(a182) | c2_1(a138) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c3_1(a138)) | (~c0_1(a138)) | (~c1_1(a182)))),
% 1.49/1.28 inference(transitivity,[status(thm)],[2170, 2168])).
% 1.49/1.28 tff(2172,plain,
% 1.49/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a182) | c3_1(a182) | (~c1_1(a182)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)))),
% 1.49/1.28 inference(quant_inst,[status(thm)],[])).
% 1.49/1.28 tff(2173,plain,
% 1.49/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a182) | c3_1(a182) | c2_1(a138) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c3_1(a138)) | (~c0_1(a138)) | (~c1_1(a182))),
% 1.49/1.28 inference(modus_ponens,[status(thm)],[2172, 2171])).
% 1.49/1.28 tff(2174,plain,
% 1.49/1.28 (~c1_1(a182)),
% 1.49/1.28 inference(unit_resolution,[status(thm)],[2173, 123, 1972, 2052, 2167, 2166, 1950, 2053, 1284, 2149, 2157])).
% 1.49/1.28 tff(2175,plain,
% 1.49/1.28 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 1.49/1.28 inference(bind,[status(th)],[])).
% 1.49/1.28 tff(2176,plain,
% 1.49/1.28 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.49/1.28 inference(quant_intro,[status(thm)],[2175])).
% 1.49/1.28 tff(2177,plain,
% 1.49/1.28 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.49/1.28 inference(rewrite,[status(thm)],[])).
% 1.49/1.28 tff(2178,plain,
% 1.49/1.28 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | 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)) | (~c1_1(U))) | (~ndr1_0)) | 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)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp1))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 1.49/1.28 inference(bind,[status(th)],[])).
% 1.49/1.28 tff(2179,plain,
% 1.49/1.28 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.49/1.28 inference(quant_intro,[status(thm)],[2178])).
% 1.49/1.28 tff(2180,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause171')).
% 1.49/1.28 tff(2181,plain,
% 1.49/1.28 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.49/1.28 inference(modus_ponens,[status(thm)],[2180, 2179])).
% 1.49/1.28 tff(2182,plain,
% 1.49/1.28 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.49/1.28 inference(modus_ponens,[status(thm)],[2181, 2177])).
% 1.49/1.28 tff(2183,plain,(
% 1.49/1.28 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.49/1.28 inference(skolemize,[status(sab)],[2182])).
% 1.49/1.28 tff(2184,plain,
% 1.49/1.28 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.49/1.28 inference(modus_ponens,[status(thm)],[2183, 2176])).
% 1.49/1.28 tff(2185,plain,
% 1.49/1.28 (~hskp22),
% 1.49/1.28 inference(unit_resolution,[status(thm)],[1823, 1817, 134])).
% 1.49/1.28 tff(2186,plain,
% 1.49/1.28 (((~![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | (~c1_1(a138)))) <=> ((~![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp19 | hskp2 | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | (~c1_1(a138)))),
% 1.49/1.28 inference(rewrite,[status(thm)],[])).
% 1.49/1.28 tff(2187,plain,
% 1.49/1.28 ((hskp19 | hskp2 | (~ndr1_0) | (~c3_1(a138)) | (~c1_1(a138)) | (~c0_1(a138))) <=> (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | (~c1_1(a138)))),
% 1.49/1.28 inference(rewrite,[status(thm)],[])).
% 1.49/1.28 tff(2188,plain,
% 1.49/1.28 (((~![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(a138)) | (~c1_1(a138)) | (~c0_1(a138)))) <=> ((~![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | (~c1_1(a138))))),
% 1.49/1.28 inference(monotonicity,[status(thm)],[2187])).
% 1.49/1.28 tff(2189,plain,
% 1.49/1.28 (((~![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(a138)) | (~c1_1(a138)) | (~c0_1(a138)))) <=> ((~![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp19 | hskp2 | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | (~c1_1(a138)))),
% 1.49/1.28 inference(transitivity,[status(thm)],[2188, 2186])).
% 1.49/1.28 tff(2190,plain,
% 1.49/1.28 ((~![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(a138)) | (~c1_1(a138)) | (~c0_1(a138)))),
% 1.49/1.28 inference(quant_inst,[status(thm)],[])).
% 1.49/1.28 tff(2191,plain,
% 1.49/1.28 ((~![U: $i] : (hskp19 | hskp2 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp19 | hskp2 | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | (~c1_1(a138))),
% 1.49/1.28 inference(modus_ponens,[status(thm)],[2190, 2189])).
% 1.49/1.28 tff(2192,plain,
% 1.49/1.28 (hskp19 | hskp2 | (~c3_1(a138))),
% 1.49/1.28 inference(unit_resolution,[status(thm)],[2191, 123, 1972, 1961, 1202])).
% 1.49/1.28 tff(2193,plain,
% 1.49/1.28 (hskp2),
% 1.49/1.28 inference(unit_resolution,[status(thm)],[2192, 2157, 1817])).
% 1.49/1.28 tff(2194,plain,
% 1.49/1.28 (~c0_1(a125)),
% 1.49/1.28 inference(unit_resolution,[status(thm)],[1098, 2193])).
% 1.49/1.28 tff(2195,plain,
% 1.49/1.28 (c3_1(a124)),
% 1.49/1.28 inference(unit_resolution,[status(thm)],[709, 2194, 134, 2185, 2147, 132, 95, 11])).
% 1.49/1.28 tff(2196,plain,
% 1.49/1.28 (~hskp1),
% 1.49/1.28 inference(unit_resolution,[status(thm)],[1077, 2195])).
% 1.49/1.28 tff(2197,plain,
% 1.49/1.28 (^[U: $i] : refl((hskp3 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp3 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 1.49/1.28 inference(bind,[status(th)],[])).
% 1.49/1.29 tff(2198,plain,
% 1.49/1.29 (![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.49/1.29 inference(quant_intro,[status(thm)],[2197])).
% 1.49/1.29 tff(2199,plain,
% 1.49/1.29 (![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.49/1.29 inference(rewrite,[status(thm)],[])).
% 1.49/1.29 tff(2200,plain,
% 1.49/1.29 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp1))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) | hskp3) <=> ((hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp3))), rewrite(((hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp3) <=> (hskp3 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) | hskp3) <=> (hskp3 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 1.49/1.29 inference(bind,[status(th)],[])).
% 1.49/1.29 tff(2201,plain,
% 1.49/1.29 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) | hskp3) <=> ![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.49/1.29 inference(quant_intro,[status(thm)],[2200])).
% 1.49/1.29 tff(2202,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause154')).
% 1.49/1.29 tff(2203,plain,
% 1.49/1.29 (![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.49/1.29 inference(modus_ponens,[status(thm)],[2202, 2201])).
% 1.49/1.29 tff(2204,plain,
% 1.49/1.29 (![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.49/1.29 inference(modus_ponens,[status(thm)],[2203, 2199])).
% 1.49/1.29 tff(2205,plain,(
% 1.49/1.29 ![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.49/1.29 inference(skolemize,[status(sab)],[2204])).
% 1.49/1.29 tff(2206,plain,
% 1.49/1.29 (![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.49/1.29 inference(modus_ponens,[status(thm)],[2205, 2198])).
% 1.49/1.29 tff(2207,plain,
% 1.49/1.29 (((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp3 | hskp1 | c2_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)))) <=> ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp3 | hskp1 | c2_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)))),
% 1.49/1.29 inference(rewrite,[status(thm)],[])).
% 1.49/1.29 tff(2208,plain,
% 1.49/1.29 ((hskp3 | hskp1 | (~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c0_1(a138))) <=> (hskp3 | hskp1 | c2_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)))),
% 1.49/1.29 inference(rewrite,[status(thm)],[])).
% 1.49/1.29 tff(2209,plain,
% 1.49/1.29 (((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp3 | hskp1 | (~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c0_1(a138)))) <=> ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp3 | hskp1 | c2_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138))))),
% 1.49/1.29 inference(monotonicity,[status(thm)],[2208])).
% 1.49/1.29 tff(2210,plain,
% 1.49/1.29 (((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp3 | hskp1 | (~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c0_1(a138)))) <=> ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp3 | hskp1 | c2_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)))),
% 1.49/1.29 inference(transitivity,[status(thm)],[2209, 2207])).
% 1.49/1.29 tff(2211,plain,
% 1.49/1.29 ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp3 | hskp1 | (~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c0_1(a138)))),
% 1.49/1.29 inference(quant_inst,[status(thm)],[])).
% 1.49/1.29 tff(2212,plain,
% 1.49/1.29 ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp3 | hskp1 | c2_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138))),
% 1.49/1.29 inference(modus_ponens,[status(thm)],[2211, 2210])).
% 1.49/1.29 tff(2213,plain,
% 1.49/1.29 (hskp3 | hskp1 | (~c3_1(a138))),
% 1.49/1.29 inference(unit_resolution,[status(thm)],[2212, 123, 1972, 1950, 2206])).
% 1.49/1.29 tff(2214,plain,
% 1.49/1.29 (hskp3),
% 1.49/1.29 inference(unit_resolution,[status(thm)],[2213, 2196, 2157])).
% 1.49/1.29 tff(2215,plain,
% 1.49/1.29 (((~hskp3) | (~c3_1(a127))) <=> ((~hskp3) | (~c3_1(a127)))),
% 1.49/1.29 inference(rewrite,[status(thm)],[])).
% 1.49/1.29 tff(2216,plain,
% 1.49/1.29 (((~c3_1(a127)) | (~hskp3)) <=> ((~hskp3) | (~c3_1(a127)))),
% 1.49/1.29 inference(rewrite,[status(thm)],[])).
% 1.49/1.29 tff(2217,axiom,((~c3_1(a127)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause126')).
% 1.49/1.29 tff(2218,plain,
% 1.49/1.29 ((~hskp3) | (~c3_1(a127))),
% 1.49/1.29 inference(modus_ponens,[status(thm)],[2217, 2216])).
% 1.49/1.29 tff(2219,plain,
% 1.49/1.29 ((~hskp3) | (~c3_1(a127))),
% 1.49/1.29 inference(modus_ponens,[status(thm)],[2218, 2215])).
% 1.49/1.29 tff(2220,plain,
% 1.49/1.29 (~c3_1(a127)),
% 1.49/1.29 inference(unit_resolution,[status(thm)],[2219, 2214])).
% 1.49/1.29 tff(2221,plain,
% 1.49/1.29 (((~hskp3) | c1_1(a127)) <=> ((~hskp3) | c1_1(a127))),
% 1.49/1.29 inference(rewrite,[status(thm)],[])).
% 1.49/1.29 tff(2222,axiom,((~hskp3) | c1_1(a127)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause78')).
% 1.49/1.29 tff(2223,plain,
% 1.49/1.29 ((~hskp3) | c1_1(a127)),
% 1.49/1.29 inference(modus_ponens,[status(thm)],[2222, 2221])).
% 1.49/1.29 tff(2224,plain,
% 1.49/1.29 ((~hskp3) | c1_1(a127)),
% 1.49/1.29 inference(modus_ponens,[status(thm)],[2223, 2221])).
% 1.49/1.29 tff(2225,plain,
% 1.49/1.29 ((~hskp3) | c1_1(a127)),
% 1.49/1.29 inference(modus_ponens,[status(thm)],[2224, 2221])).
% 1.49/1.29 tff(2226,plain,
% 1.49/1.29 ((~hskp3) | c1_1(a127)),
% 1.49/1.29 inference(modus_ponens,[status(thm)],[2225, 2221])).
% 1.49/1.29 tff(2227,plain,
% 1.49/1.29 ((~hskp3) | c1_1(a127)),
% 1.49/1.29 inference(modus_ponens,[status(thm)],[2226, 2221])).
% 1.49/1.29 tff(2228,plain,
% 1.49/1.29 ((~hskp3) | c1_1(a127)),
% 1.49/1.29 inference(modus_ponens,[status(thm)],[2227, 2221])).
% 1.49/1.29 tff(2229,plain,
% 1.49/1.29 ((~hskp3) | c1_1(a127)),
% 1.49/1.29 inference(modus_ponens,[status(thm)],[2228, 2221])).
% 1.49/1.29 tff(2230,plain,
% 1.49/1.29 ((~hskp3) | c1_1(a127)),
% 1.49/1.29 inference(modus_ponens,[status(thm)],[2229, 2221])).
% 1.49/1.29 tff(2231,plain,
% 1.49/1.29 (c1_1(a127)),
% 1.49/1.29 inference(unit_resolution,[status(thm)],[2230, 2214])).
% 1.49/1.29 tff(2232,plain,
% 1.49/1.29 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a132) | c2_1(a132) | c3_1(a127) | (~ndr1_0) | (~c1_1(a127)) | (~c0_1(a127)) | c1_1(a132))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a132) | c2_1(a132) | c3_1(a127) | (~ndr1_0) | (~c1_1(a127)) | (~c0_1(a127)) | c1_1(a132))),
% 1.49/1.29 inference(rewrite,[status(thm)],[])).
% 1.49/1.29 tff(2233,plain,
% 1.49/1.29 ((hskp1 | (~ndr1_0) | c3_1(a127) | (~c1_1(a127)) | (~c0_1(a127)) | c2_1(a132) | c1_1(a132) | c0_1(a132)) <=> (hskp1 | c0_1(a132) | c2_1(a132) | c3_1(a127) | (~ndr1_0) | (~c1_1(a127)) | (~c0_1(a127)) | c1_1(a132))),
% 1.49/1.29 inference(rewrite,[status(thm)],[])).
% 1.49/1.29 tff(2234,plain,
% 1.49/1.29 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a127) | (~c1_1(a127)) | (~c0_1(a127)) | c2_1(a132) | c1_1(a132) | c0_1(a132))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a132) | c2_1(a132) | c3_1(a127) | (~ndr1_0) | (~c1_1(a127)) | (~c0_1(a127)) | c1_1(a132)))),
% 1.49/1.29 inference(monotonicity,[status(thm)],[2233])).
% 1.49/1.29 tff(2235,plain,
% 1.49/1.29 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a127) | (~c1_1(a127)) | (~c0_1(a127)) | c2_1(a132) | c1_1(a132) | c0_1(a132))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a132) | c2_1(a132) | c3_1(a127) | (~ndr1_0) | (~c1_1(a127)) | (~c0_1(a127)) | c1_1(a132))),
% 1.49/1.29 inference(transitivity,[status(thm)],[2234, 2232])).
% 1.49/1.29 tff(2236,plain,
% 1.49/1.29 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c3_1(a127) | (~c1_1(a127)) | (~c0_1(a127)) | c2_1(a132) | c1_1(a132) | c0_1(a132))),
% 1.49/1.29 inference(quant_inst,[status(thm)],[])).
% 1.49/1.29 tff(2237,plain,
% 1.49/1.29 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a132) | c2_1(a132) | c3_1(a127) | (~ndr1_0) | (~c1_1(a127)) | (~c0_1(a127)) | c1_1(a132)),
% 1.49/1.29 inference(modus_ponens,[status(thm)],[2236, 2235])).
% 1.49/1.29 tff(2238,plain,
% 1.49/1.29 (~c0_1(a127)),
% 1.49/1.29 inference(unit_resolution,[status(thm)],[2237, 123, 2196, 2231, 2054, 2053, 2220, 2184, 2149])).
% 1.49/1.29 tff(2239,plain,
% 1.49/1.29 (((~hskp3) | (~c2_1(a127))) <=> ((~hskp3) | (~c2_1(a127)))),
% 1.49/1.29 inference(rewrite,[status(thm)],[])).
% 1.49/1.29 tff(2240,plain,
% 1.49/1.29 (((~c2_1(a127)) | (~hskp3)) <=> ((~hskp3) | (~c2_1(a127)))),
% 1.49/1.29 inference(rewrite,[status(thm)],[])).
% 1.49/1.29 tff(2241,axiom,((~c2_1(a127)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause125')).
% 1.49/1.29 tff(2242,plain,
% 1.49/1.29 ((~hskp3) | (~c2_1(a127))),
% 1.49/1.29 inference(modus_ponens,[status(thm)],[2241, 2240])).
% 1.49/1.29 tff(2243,plain,
% 1.49/1.29 ((~hskp3) | (~c2_1(a127))),
% 1.49/1.29 inference(modus_ponens,[status(thm)],[2242, 2239])).
% 1.49/1.29 tff(2244,plain,
% 1.49/1.29 (~c2_1(a127)),
% 1.49/1.29 inference(unit_resolution,[status(thm)],[2243, 2214])).
% 1.49/1.29 tff(2245,plain,
% 1.49/1.29 (((~![U: $i] : (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | (~c1_1(a138)))) <=> ((~![U: $i] : (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp22 | hskp10 | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | (~c1_1(a138)))),
% 1.49/1.29 inference(rewrite,[status(thm)],[])).
% 1.49/1.29 tff(2246,plain,
% 1.49/1.29 ((hskp22 | hskp10 | (~ndr1_0) | (~c3_1(a138)) | (~c1_1(a138)) | (~c0_1(a138))) <=> (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | (~c1_1(a138)))),
% 1.49/1.29 inference(rewrite,[status(thm)],[])).
% 1.49/1.29 tff(2247,plain,
% 1.49/1.29 (((~![U: $i] : (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(a138)) | (~c1_1(a138)) | (~c0_1(a138)))) <=> ((~![U: $i] : (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | (~c1_1(a138))))),
% 1.49/1.29 inference(monotonicity,[status(thm)],[2246])).
% 1.49/1.29 tff(2248,plain,
% 1.49/1.29 (((~![U: $i] : (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(a138)) | (~c1_1(a138)) | (~c0_1(a138)))) <=> ((~![U: $i] : (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp22 | hskp10 | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | (~c1_1(a138)))),
% 1.49/1.29 inference(transitivity,[status(thm)],[2247, 2245])).
% 1.49/1.29 tff(2249,plain,
% 1.49/1.29 ((~![U: $i] : (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(a138)) | (~c1_1(a138)) | (~c0_1(a138)))),
% 1.49/1.29 inference(quant_inst,[status(thm)],[])).
% 1.49/1.29 tff(2250,plain,
% 1.49/1.29 ((~![U: $i] : (hskp22 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp22 | hskp10 | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | (~c1_1(a138))),
% 1.49/1.29 inference(modus_ponens,[status(thm)],[2249, 2248])).
% 1.49/1.29 tff(2251,plain,
% 1.49/1.29 (hskp22 | hskp10 | (~c3_1(a138))),
% 1.49/1.29 inference(unit_resolution,[status(thm)],[2250, 123, 1972, 1961, 1834])).
% 1.49/1.29 tff(2252,plain,
% 1.49/1.29 (hskp10),
% 1.49/1.29 inference(unit_resolution,[status(thm)],[2251, 2157, 2185])).
% 1.49/1.29 tff(2253,plain,
% 1.49/1.29 (~c3_1(a140)),
% 1.49/1.29 inference(unit_resolution,[status(thm)],[1844, 2252])).
% 1.49/1.29 tff(2254,plain,
% 1.49/1.29 (~c2_1(a140)),
% 1.49/1.29 inference(unit_resolution,[status(thm)],[1850, 2252])).
% 1.49/1.29 tff(2255,plain,
% 1.49/1.29 (~c0_1(a182)),
% 1.49/1.29 inference(unit_resolution,[status(thm)],[1326, 2165])).
% 1.49/1.29 tff(2256,plain,
% 1.49/1.29 (c0_1(a140)),
% 1.49/1.29 inference(unit_resolution,[status(thm)],[1861, 2252])).
% 1.49/1.29 tff(2257,plain,
% 1.49/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a182) | c2_1(a182) | c2_1(a140) | c3_1(a140) | c2_1(a127) | (~ndr1_0) | (~c1_1(a127)) | c0_1(a127) | (~c0_1(a140)) | c1_1(a182))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a182) | c2_1(a182) | c2_1(a140) | c3_1(a140) | c2_1(a127) | (~ndr1_0) | (~c1_1(a127)) | c0_1(a127) | (~c0_1(a140)) | c1_1(a182))),
% 1.49/1.29 inference(rewrite,[status(thm)],[])).
% 1.49/1.29 tff(2258,plain,
% 1.49/1.29 (((~ndr1_0) | c2_1(a140) | c3_1(a140) | (~c0_1(a140)) | c2_1(a127) | c0_1(a127) | (~c1_1(a127)) | c2_1(a182) | c1_1(a182) | c0_1(a182)) <=> (c0_1(a182) | c2_1(a182) | c2_1(a140) | c3_1(a140) | c2_1(a127) | (~ndr1_0) | (~c1_1(a127)) | c0_1(a127) | (~c0_1(a140)) | c1_1(a182))),
% 1.49/1.29 inference(rewrite,[status(thm)],[])).
% 1.49/1.29 tff(2259,plain,
% 1.49/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a140) | c3_1(a140) | (~c0_1(a140)) | c2_1(a127) | c0_1(a127) | (~c1_1(a127)) | c2_1(a182) | c1_1(a182) | c0_1(a182))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a182) | c2_1(a182) | c2_1(a140) | c3_1(a140) | c2_1(a127) | (~ndr1_0) | (~c1_1(a127)) | c0_1(a127) | (~c0_1(a140)) | c1_1(a182)))),
% 1.49/1.29 inference(monotonicity,[status(thm)],[2258])).
% 1.49/1.29 tff(2260,plain,
% 1.49/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a140) | c3_1(a140) | (~c0_1(a140)) | c2_1(a127) | c0_1(a127) | (~c1_1(a127)) | c2_1(a182) | c1_1(a182) | c0_1(a182))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a182) | c2_1(a182) | c2_1(a140) | c3_1(a140) | c2_1(a127) | (~ndr1_0) | (~c1_1(a127)) | c0_1(a127) | (~c0_1(a140)) | c1_1(a182))),
% 1.49/1.29 inference(transitivity,[status(thm)],[2259, 2257])).
% 1.49/1.29 tff(2261,plain,
% 1.49/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a140) | c3_1(a140) | (~c0_1(a140)) | c2_1(a127) | c0_1(a127) | (~c1_1(a127)) | c2_1(a182) | c1_1(a182) | c0_1(a182))),
% 1.49/1.29 inference(quant_inst,[status(thm)],[])).
% 1.49/1.29 tff(2262,plain,
% 1.49/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a182) | c2_1(a182) | c2_1(a140) | c3_1(a140) | c2_1(a127) | (~ndr1_0) | (~c1_1(a127)) | c0_1(a127) | (~c0_1(a140)) | c1_1(a182)),
% 1.49/1.29 inference(modus_ponens,[status(thm)],[2261, 2260])).
% 1.49/1.29 tff(2263,plain,
% 1.49/1.29 ($false),
% 1.49/1.29 inference(unit_resolution,[status(thm)],[2262, 123, 2256, 2231, 2255, 2167, 2254, 2253, 2244, 21, 2238, 2174])).
% 1.49/1.29 tff(2264,plain,(hskp0 | hskp17 | c1_1(a131) | c2_1(a131) | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.49/1.29 tff(2265,plain,
% 1.49/1.29 (hskp0),
% 1.49/1.29 inference(unit_resolution,[status(thm)],[2264, 132, 134, 95, 1817])).
% 1.49/1.29 tff(2266,plain,
% 1.49/1.29 (hskp30),
% 1.49/1.29 inference(unit_resolution,[status(thm)],[608, 2265, 2054, 2053, 2052, 2149])).
% 1.49/1.29 tff(2267,plain,
% 1.49/1.29 (c0_1(a167)),
% 1.49/1.29 inference(unit_resolution,[status(thm)],[1129, 2266])).
% 1.49/1.29 tff(2268,plain,
% 1.49/1.29 (c3_1(a167)),
% 1.49/1.29 inference(unit_resolution,[status(thm)],[1175, 2266])).
% 1.49/1.29 tff(2269,plain,
% 1.49/1.29 (c1_1(a167)),
% 1.49/1.29 inference(unit_resolution,[status(thm)],[1186, 2266])).
% 1.49/1.29 tff(2270,plain,
% 1.49/1.29 (hskp2),
% 1.49/1.29 inference(unit_resolution,[status(thm)],[1227, 2269, 95, 2268, 2267, 132, 134, 2147])).
% 1.49/1.29 tff(2271,plain,
% 1.49/1.29 (c2_1(a125)),
% 1.49/1.29 inference(unit_resolution,[status(thm)],[700, 2270])).
% 1.49/1.29 tff(2272,plain,
% 1.49/1.29 (c1_1(a125)),
% 1.49/1.29 inference(unit_resolution,[status(thm)],[681, 2270])).
% 1.49/1.29 tff(2273,plain,
% 1.49/1.29 (c3_1(a125)),
% 1.49/1.29 inference(unit_resolution,[status(thm)],[707, 123, 2185, 2272, 2271, 643])).
% 1.49/1.29 tff(2274,plain,
% 1.49/1.29 (~c1_1(a123)),
% 1.49/1.29 inference(unit_resolution,[status(thm)],[202, 2265])).
% 1.49/1.29 tff(2275,plain,
% 1.49/1.29 (~c0_1(a123)),
% 1.49/1.29 inference(unit_resolution,[status(thm)],[236, 2265])).
% 1.49/1.29 tff(2276,plain,
% 1.49/1.29 (c2_1(a123)),
% 1.49/1.29 inference(unit_resolution,[status(thm)],[213, 2265])).
% 1.49/1.29 tff(2277,plain,
% 1.49/1.29 (~c3_1(a123)),
% 1.49/1.29 inference(unit_resolution,[status(thm)],[500, 123, 2052, 2276, 2053, 2275, 2274, 144, 2149])).
% 1.49/1.29 tff(2278,plain,
% 1.49/1.29 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.49/1.29 inference(bind,[status(th)],[])).
% 1.49/1.29 tff(2279,plain,
% 1.49/1.29 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.49/1.29 inference(quant_intro,[status(thm)],[2278])).
% 1.49/1.29 tff(2280,plain,
% 1.49/1.29 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.49/1.29 inference(rewrite,[status(thm)],[])).
% 1.49/1.29 tff(2281,plain,
% 1.49/1.29 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~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))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp14) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp14))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp14) <=> (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.49/1.29 inference(bind,[status(th)],[])).
% 1.49/1.29 tff(2282,plain,
% 1.49/1.29 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.49/1.29 inference(quant_intro,[status(thm)],[2281])).
% 1.49/1.29 tff(2283,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause175')).
% 1.49/1.29 tff(2284,plain,
% 1.49/1.29 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.49/1.29 inference(modus_ponens,[status(thm)],[2283, 2282])).
% 1.49/1.29 tff(2285,plain,
% 1.49/1.29 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.49/1.29 inference(modus_ponens,[status(thm)],[2284, 2280])).
% 1.49/1.29 tff(2286,plain,(
% 1.49/1.29 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.49/1.29 inference(skolemize,[status(sab)],[2285])).
% 1.49/1.29 tff(2287,plain,
% 1.49/1.29 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.49/1.29 inference(modus_ponens,[status(thm)],[2286, 2279])).
% 1.49/1.29 tff(2288,plain,
% 1.49/1.29 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp14 | c0_1(a132) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp14 | c0_1(a132) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132)))),
% 1.49/1.29 inference(rewrite,[status(thm)],[])).
% 1.49/1.29 tff(2289,plain,
% 1.49/1.29 ((hskp14 | (~ndr1_0) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132))) <=> (hskp14 | c0_1(a132) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132)))),
% 1.49/1.29 inference(rewrite,[status(thm)],[])).
% 1.49/1.29 tff(2290,plain,
% 1.49/1.29 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp14 | c0_1(a132) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132))))),
% 1.49/1.29 inference(monotonicity,[status(thm)],[2289])).
% 1.49/1.29 tff(2291,plain,
% 1.49/1.29 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp14 | c0_1(a132) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132)))),
% 1.49/1.29 inference(transitivity,[status(thm)],[2290, 2288])).
% 1.49/1.29 tff(2292,plain,
% 1.49/1.29 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)))),
% 1.49/1.29 inference(quant_inst,[status(thm)],[])).
% 1.49/1.29 tff(2293,plain,
% 1.49/1.29 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp14 | c0_1(a132) | c2_1(a132) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | (~c3_1(a132))),
% 1.49/1.29 inference(modus_ponens,[status(thm)],[2292, 2291])).
% 1.49/1.29 tff(2294,plain,
% 1.49/1.29 (hskp14 | c3_1(a123)),
% 1.49/1.29 inference(unit_resolution,[status(thm)],[2293, 123, 2052, 2276, 2054, 2053, 2275, 2287])).
% 1.49/1.29 tff(2295,plain,
% 1.49/1.29 (hskp14),
% 1.49/1.29 inference(unit_resolution,[status(thm)],[2294, 2277])).
% 1.49/1.29 tff(2296,plain,
% 1.49/1.29 (~c1_1(a147)),
% 1.49/1.29 inference(unit_resolution,[status(thm)],[340, 2295])).
% 1.49/1.29 tff(2297,plain,
% 1.49/1.29 (c0_1(a147)),
% 1.49/1.29 inference(unit_resolution,[status(thm)],[326, 2295])).
% 1.49/1.29 tff(2298,plain,
% 1.49/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a147) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c2_1(a123)) | (~c1_1(a125)) | (~c2_1(a125)) | (~c3_1(a125)) | (~c2_1(a147)) | (~c0_1(a147)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a147) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c2_1(a123)) | (~c1_1(a125)) | (~c2_1(a125)) | (~c3_1(a125)) | (~c2_1(a147)) | (~c0_1(a147)))),
% 1.49/1.29 inference(rewrite,[status(thm)],[])).
% 1.49/1.29 tff(2299,plain,
% 1.49/1.29 (((~ndr1_0) | (~c3_1(a125)) | (~c1_1(a125)) | (~c2_1(a125)) | c1_1(a147) | (~c2_1(a147)) | (~c0_1(a147)) | c1_1(a123) | c0_1(a123) | (~c2_1(a123))) <=> (c1_1(a147) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c2_1(a123)) | (~c1_1(a125)) | (~c2_1(a125)) | (~c3_1(a125)) | (~c2_1(a147)) | (~c0_1(a147)))),
% 1.49/1.29 inference(rewrite,[status(thm)],[])).
% 1.49/1.29 tff(2300,plain,
% 1.49/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a125)) | (~c1_1(a125)) | (~c2_1(a125)) | c1_1(a147) | (~c2_1(a147)) | (~c0_1(a147)) | c1_1(a123) | c0_1(a123) | (~c2_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a147) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c2_1(a123)) | (~c1_1(a125)) | (~c2_1(a125)) | (~c3_1(a125)) | (~c2_1(a147)) | (~c0_1(a147))))),
% 1.49/1.29 inference(monotonicity,[status(thm)],[2299])).
% 1.49/1.29 tff(2301,plain,
% 1.49/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a125)) | (~c1_1(a125)) | (~c2_1(a125)) | c1_1(a147) | (~c2_1(a147)) | (~c0_1(a147)) | c1_1(a123) | c0_1(a123) | (~c2_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a147) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c2_1(a123)) | (~c1_1(a125)) | (~c2_1(a125)) | (~c3_1(a125)) | (~c2_1(a147)) | (~c0_1(a147)))),
% 1.49/1.29 inference(transitivity,[status(thm)],[2300, 2298])).
% 1.49/1.29 tff(2302,plain,
% 1.49/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a125)) | (~c1_1(a125)) | (~c2_1(a125)) | c1_1(a147) | (~c2_1(a147)) | (~c0_1(a147)) | c1_1(a123) | c0_1(a123) | (~c2_1(a123)))),
% 1.49/1.29 inference(quant_inst,[status(thm)],[])).
% 1.49/1.29 tff(2303,plain,
% 1.49/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a147) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c2_1(a123)) | (~c1_1(a125)) | (~c2_1(a125)) | (~c3_1(a125)) | (~c2_1(a147)) | (~c0_1(a147))),
% 1.49/1.29 inference(modus_ponens,[status(thm)],[2302, 2301])).
% 1.49/1.29 tff(2304,plain,
% 1.49/1.29 (~c2_1(a147)),
% 1.49/1.29 inference(unit_resolution,[status(thm)],[2303, 123, 2297, 2272, 2271, 2276, 2296, 2275, 2274, 10, 2273])).
% 1.49/1.29 tff(2305,plain,
% 1.49/1.29 ($false),
% 1.49/1.29 inference(unit_resolution,[status(thm)],[347, 123, 1817, 134, 2297, 2296, 53, 2304])).
% 1.49/1.29 tff(2306,plain,(c1_1(a131) | hskp19 | hskp17 | c2_1(a131)), inference(lemma,lemma(discharge,[]))).
% 1.49/1.29 tff(2307,plain,
% 1.49/1.29 (hskp19),
% 1.49/1.29 inference(unit_resolution,[status(thm)],[2306, 2145, 134, 95])).
% 1.49/1.29 tff(2308,plain,
% 1.49/1.29 (hskp13),
% 1.49/1.29 inference(unit_resolution,[status(thm)],[2024, 2307, 134])).
% 1.49/1.29 tff(2309,plain,
% 1.49/1.29 (~c1_1(a143)),
% 1.49/1.29 inference(unit_resolution,[status(thm)],[782, 2308])).
% 1.49/1.29 tff(2310,plain,
% 1.49/1.29 (c3_1(a143)),
% 1.49/1.29 inference(unit_resolution,[status(thm)],[825, 2308])).
% 1.49/1.29 tff(2311,plain,
% 1.49/1.29 (c2_1(a143)),
% 1.49/1.29 inference(unit_resolution,[status(thm)],[836, 2308])).
% 1.49/1.29 tff(2312,plain,
% 1.49/1.29 (~c2_1(a164)),
% 1.49/1.29 inference(unit_resolution,[status(thm)],[250, 2307])).
% 1.49/1.29 tff(2313,plain,
% 1.49/1.29 (hskp24),
% 1.49/1.29 inference(unit_resolution,[status(thm)],[1888, 2307, 134])).
% 1.49/1.30 tff(2314,plain,
% 1.49/1.30 (~c2_1(a182)),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[1313, 2313])).
% 1.49/1.30 tff(2315,plain,
% 1.49/1.30 (~c0_1(a182)),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[1326, 2313])).
% 1.49/1.30 tff(2316,plain,
% 1.49/1.30 (c3_1(a164)),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[261, 2307])).
% 1.49/1.30 tff(2317,plain,
% 1.49/1.30 (c1_1(a164)),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[272, 2307])).
% 1.49/1.30 tff(2318,assumption,(~c2_1(a182)), introduced(assumption)).
% 1.49/1.30 tff(2319,assumption,(~c0_1(a182)), introduced(assumption)).
% 1.49/1.30 tff(2320,plain,
% 1.49/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a182) | c2_1(a182) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a182)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a182) | c2_1(a182) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a182)))),
% 1.49/1.30 inference(rewrite,[status(thm)],[])).
% 1.49/1.30 tff(2321,plain,
% 1.49/1.30 (((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a182) | c0_1(a182) | (~c1_1(a182)) | c2_1(a132) | c1_1(a132) | c0_1(a132)) <=> (c0_1(a182) | c2_1(a182) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a182)))),
% 1.49/1.30 inference(rewrite,[status(thm)],[])).
% 1.49/1.30 tff(2322,plain,
% 1.49/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a182) | c0_1(a182) | (~c1_1(a182)) | c2_1(a132) | c1_1(a132) | c0_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a182) | c2_1(a182) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a182))))),
% 1.49/1.30 inference(monotonicity,[status(thm)],[2321])).
% 1.49/1.30 tff(2323,plain,
% 1.49/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a182) | c0_1(a182) | (~c1_1(a182)) | c2_1(a132) | c1_1(a132) | c0_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a182) | c2_1(a182) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a182)))),
% 1.49/1.30 inference(transitivity,[status(thm)],[2322, 2320])).
% 1.49/1.30 tff(2324,plain,
% 1.49/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a182) | c0_1(a182) | (~c1_1(a182)) | c2_1(a132) | c1_1(a132) | c0_1(a132))),
% 1.49/1.30 inference(quant_inst,[status(thm)],[])).
% 1.49/1.30 tff(2325,plain,
% 1.49/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a182) | c2_1(a182) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | c1_1(a132) | (~c1_1(a182))),
% 1.49/1.30 inference(modus_ponens,[status(thm)],[2324, 2323])).
% 1.49/1.30 tff(2326,plain,
% 1.49/1.30 (c1_1(a132) | (~c1_1(a182))),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[2325, 123, 470, 2319, 2318, 434, 436, 406])).
% 1.49/1.30 tff(2327,plain,
% 1.49/1.30 (~c1_1(a182)),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[2326, 466])).
% 1.49/1.30 tff(2328,plain,
% 1.49/1.30 (hskp6),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[1412, 466, 470, 1383, 1382, 436, 1384])).
% 1.49/1.30 tff(2329,plain,
% 1.49/1.30 (~c0_1(a131)),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[83, 2328])).
% 1.49/1.30 tff(2330,plain,
% 1.49/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a143) | c2_1(a132) | c0_1(a131) | c1_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c3_1(a132)) | c1_1(a132) | (~c2_1(a143)) | (~c3_1(a143)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a143) | c2_1(a132) | c0_1(a131) | c1_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c3_1(a132)) | c1_1(a132) | (~c2_1(a143)) | (~c3_1(a143)))),
% 1.49/1.30 inference(rewrite,[status(thm)],[])).
% 1.49/1.30 tff(2331,plain,
% 1.49/1.30 (((~ndr1_0) | c1_1(a143) | (~c3_1(a143)) | (~c2_1(a143)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)) | c1_1(a131) | c0_1(a131) | (~c3_1(a131))) <=> (c1_1(a143) | c2_1(a132) | c0_1(a131) | c1_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c3_1(a132)) | c1_1(a132) | (~c2_1(a143)) | (~c3_1(a143)))),
% 1.49/1.30 inference(rewrite,[status(thm)],[])).
% 1.49/1.30 tff(2332,plain,
% 1.49/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a143) | (~c3_1(a143)) | (~c2_1(a143)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)) | c1_1(a131) | c0_1(a131) | (~c3_1(a131)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a143) | c2_1(a132) | c0_1(a131) | c1_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c3_1(a132)) | c1_1(a132) | (~c2_1(a143)) | (~c3_1(a143))))),
% 1.49/1.30 inference(monotonicity,[status(thm)],[2331])).
% 1.49/1.30 tff(2333,plain,
% 1.49/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a143) | (~c3_1(a143)) | (~c2_1(a143)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)) | c1_1(a131) | c0_1(a131) | (~c3_1(a131)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a143) | c2_1(a132) | c0_1(a131) | c1_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c3_1(a132)) | c1_1(a132) | (~c2_1(a143)) | (~c3_1(a143)))),
% 1.49/1.30 inference(transitivity,[status(thm)],[2332, 2330])).
% 1.49/1.30 tff(2334,plain,
% 1.49/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a143) | (~c3_1(a143)) | (~c2_1(a143)) | c2_1(a132) | c1_1(a132) | (~c3_1(a132)) | c1_1(a131) | c0_1(a131) | (~c3_1(a131)))),
% 1.49/1.30 inference(quant_inst,[status(thm)],[])).
% 1.49/1.30 tff(2335,plain,
% 1.49/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a143) | c2_1(a132) | c0_1(a131) | c1_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c3_1(a132)) | c1_1(a132) | (~c2_1(a143)) | (~c3_1(a143))),
% 1.49/1.30 inference(modus_ponens,[status(thm)],[2334, 2333])).
% 1.49/1.30 tff(2336,plain,
% 1.49/1.30 (c0_1(a131) | (~c3_1(a131)) | c1_1(a132)),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[2335, 123, 1384, 1383, 470, 1382, 436, 132, 144])).
% 1.49/1.30 tff(2337,plain,
% 1.49/1.30 (~c3_1(a131)),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[2336, 2329, 466])).
% 1.49/1.30 tff(2338,plain,
% 1.49/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a182) | c2_1(a182) | c2_1(a164) | c0_1(a131) | c1_1(a131) | (~ndr1_0) | c3_1(a131) | (~c3_1(a164)) | (~c1_1(a164)) | c1_1(a182))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a182) | c2_1(a182) | c2_1(a164) | c0_1(a131) | c1_1(a131) | (~ndr1_0) | c3_1(a131) | (~c3_1(a164)) | (~c1_1(a164)) | c1_1(a182))),
% 1.49/1.30 inference(rewrite,[status(thm)],[])).
% 1.49/1.30 tff(2339,plain,
% 1.49/1.30 (((~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)) | c1_1(a131) | c0_1(a131) | c3_1(a131) | c2_1(a182) | c1_1(a182) | c0_1(a182)) <=> (c0_1(a182) | c2_1(a182) | c2_1(a164) | c0_1(a131) | c1_1(a131) | (~ndr1_0) | c3_1(a131) | (~c3_1(a164)) | (~c1_1(a164)) | c1_1(a182))),
% 1.49/1.30 inference(rewrite,[status(thm)],[])).
% 1.49/1.30 tff(2340,plain,
% 1.49/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)) | c1_1(a131) | c0_1(a131) | c3_1(a131) | c2_1(a182) | c1_1(a182) | c0_1(a182))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a182) | c2_1(a182) | c2_1(a164) | c0_1(a131) | c1_1(a131) | (~ndr1_0) | c3_1(a131) | (~c3_1(a164)) | (~c1_1(a164)) | c1_1(a182)))),
% 1.49/1.30 inference(monotonicity,[status(thm)],[2339])).
% 1.49/1.30 tff(2341,plain,
% 1.49/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)) | c1_1(a131) | c0_1(a131) | c3_1(a131) | c2_1(a182) | c1_1(a182) | c0_1(a182))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a182) | c2_1(a182) | c2_1(a164) | c0_1(a131) | c1_1(a131) | (~ndr1_0) | c3_1(a131) | (~c3_1(a164)) | (~c1_1(a164)) | c1_1(a182))),
% 1.49/1.30 inference(transitivity,[status(thm)],[2340, 2338])).
% 1.49/1.30 tff(2342,plain,
% 1.49/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)) | c1_1(a131) | c0_1(a131) | c3_1(a131) | c2_1(a182) | c1_1(a182) | c0_1(a182))),
% 1.49/1.30 inference(quant_inst,[status(thm)],[])).
% 1.49/1.30 tff(2343,plain,
% 1.49/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c3_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a182) | c2_1(a182) | c2_1(a164) | c0_1(a131) | c1_1(a131) | (~ndr1_0) | c3_1(a131) | (~c3_1(a164)) | (~c1_1(a164)) | c1_1(a182)),
% 1.49/1.30 inference(modus_ponens,[status(thm)],[2342, 2341])).
% 1.49/1.30 tff(2344,plain,
% 1.49/1.30 (c0_1(a131) | c3_1(a131) | c1_1(a182)),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[2343, 123, 1781, 1780, 2319, 2318, 1779, 132, 231])).
% 1.49/1.30 tff(2345,plain,
% 1.49/1.30 ($false),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[2344, 2337, 2329, 2327])).
% 1.49/1.30 tff(2346,plain,(c1_1(a132) | (~c1_1(a164)) | (~c3_1(a164)) | c0_1(a182) | c2_1(a182) | c2_1(a164) | c1_1(a131) | (~c2_1(a143)) | (~c3_1(a143)) | (~c3_1(a132)) | c1_1(a143) | c2_1(a132) | c0_1(a132)), inference(lemma,lemma(discharge,[]))).
% 1.49/1.30 tff(2347,plain,
% 1.49/1.30 (c1_1(a132)),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[2346, 2317, 2316, 2315, 2314, 2312, 2145, 2311, 2310, 2052, 2309, 2053, 2054])).
% 1.49/1.30 tff(2348,plain,
% 1.49/1.30 (hskp0),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[2056, 2347])).
% 1.49/1.30 tff(2349,plain,
% 1.49/1.30 (c2_1(a123)),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[213, 2348])).
% 1.49/1.30 tff(2350,plain,
% 1.49/1.30 (~c1_1(a123)),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[202, 2348])).
% 1.49/1.30 tff(2351,plain,
% 1.49/1.30 (~c0_1(a123)),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[236, 2348])).
% 1.49/1.30 tff(2352,plain,
% 1.49/1.30 (c0_1(a131)),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[2148, 2347, 2145])).
% 1.49/1.30 tff(2353,plain,
% 1.49/1.30 (~hskp6),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[83, 2352])).
% 1.49/1.30 tff(2354,plain,
% 1.49/1.30 ($false),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[2137, 2353, 2351, 2347, 2350, 2349, 134])).
% 1.49/1.30 tff(2355,plain,(c2_1(a131) | hskp17), inference(lemma,lemma(discharge,[]))).
% 1.49/1.30 tff(2356,plain,
% 1.49/1.30 (c2_1(a131)),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[2355, 134])).
% 1.49/1.30 tff(2357,plain,
% 1.49/1.30 (~hskp6),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[71, 2356])).
% 1.49/1.30 tff(2358,plain,
% 1.49/1.30 (~c1_1(a132)),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[2137, 493, 2357, 492, 494, 134])).
% 1.49/1.30 tff(2359,plain,
% 1.49/1.30 (hskp30),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[608, 2358, 2054, 2053, 2052, 491])).
% 1.49/1.30 tff(2360,plain,
% 1.49/1.30 (c0_1(a167)),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[1129, 2359])).
% 1.49/1.30 tff(2361,plain,
% 1.49/1.30 (c1_1(a167)),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[1186, 2359])).
% 1.49/1.30 tff(2362,plain,
% 1.49/1.30 (c3_1(a167)),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[1175, 2359])).
% 1.49/1.30 tff(2363,plain,
% 1.49/1.30 ($false),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[1919, 2362, 2361, 2052, 2053, 134, 2357, 2358, 2360])).
% 1.49/1.30 tff(2364,plain,((~hskp0) | hskp17), inference(lemma,lemma(discharge,[]))).
% 1.49/1.30 tff(2365,plain,
% 1.49/1.30 (~hskp0),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[2364, 134])).
% 1.49/1.30 tff(2366,plain,
% 1.49/1.30 (~c1_1(a132)),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[2056, 2365])).
% 1.49/1.30 tff(2367,plain,
% 1.49/1.30 (c3_1(a138)),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[2156, 2365, 2366])).
% 1.49/1.30 tff(2368,plain,
% 1.49/1.30 (((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | c2_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c1_1(a138)))) <=> ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp13 | c2_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c1_1(a138)))),
% 1.49/1.30 inference(rewrite,[status(thm)],[])).
% 1.49/1.30 tff(2369,plain,
% 1.49/1.30 ((hskp17 | hskp13 | (~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138))) <=> (hskp17 | hskp13 | c2_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c1_1(a138)))),
% 1.49/1.30 inference(rewrite,[status(thm)],[])).
% 1.49/1.30 tff(2370,plain,
% 1.49/1.30 (((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | (~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138)))) <=> ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | c2_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c1_1(a138))))),
% 1.49/1.30 inference(monotonicity,[status(thm)],[2369])).
% 1.49/1.30 tff(2371,plain,
% 1.49/1.30 (((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | (~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138)))) <=> ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp13 | c2_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c1_1(a138)))),
% 1.49/1.30 inference(transitivity,[status(thm)],[2370, 2368])).
% 1.49/1.30 tff(2372,plain,
% 1.49/1.30 ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp13 | (~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138)))),
% 1.49/1.30 inference(quant_inst,[status(thm)],[])).
% 1.49/1.30 tff(2373,plain,
% 1.49/1.30 ((~![U: $i] : (hskp17 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp13 | c2_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c1_1(a138))),
% 1.49/1.30 inference(modus_ponens,[status(thm)],[2372, 2371])).
% 1.49/1.30 tff(2374,plain,
% 1.49/1.30 (hskp17 | hskp13 | (~c3_1(a138))),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[2373, 123, 1961, 1950, 769])).
% 1.49/1.30 tff(2375,plain,
% 1.49/1.30 (hskp13),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[2374, 2367, 134])).
% 1.49/1.30 tff(2376,plain,
% 1.49/1.30 (c2_1(a143)),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[836, 2375])).
% 1.49/1.30 tff(2377,plain,
% 1.49/1.30 (c3_1(a143)),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[825, 2375])).
% 1.49/1.30 tff(2378,plain,
% 1.49/1.30 (~c1_1(a143)),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[782, 2375])).
% 1.49/1.30 tff(2379,plain,
% 1.49/1.30 ($false),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[1412, 2378, 2377, 2052, 2357, 2366, 2053, 2376])).
% 1.49/1.30 tff(2380,plain,(hskp17), inference(lemma,lemma(discharge,[]))).
% 1.49/1.30 tff(2381,plain,
% 1.49/1.30 (~c2_1(a155)),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[382, 2380])).
% 1.49/1.30 tff(2382,plain,
% 1.49/1.30 (~c0_1(a155)),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[388, 2380])).
% 1.49/1.30 tff(2383,plain,
% 1.49/1.30 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp7 | c1_1(a142) | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138)) | (~c3_1(a142)) | (~c0_1(a142)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a142) | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138)) | (~c3_1(a142)) | (~c0_1(a142)))),
% 1.49/1.30 inference(rewrite,[status(thm)],[])).
% 1.49/1.30 tff(2384,plain,
% 1.49/1.30 ((hskp7 | (~ndr1_0) | c2_1(a138) | (~c1_1(a138)) | (~c0_1(a138)) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142))) <=> (hskp7 | c1_1(a142) | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138)) | (~c3_1(a142)) | (~c0_1(a142)))),
% 1.49/1.30 inference(rewrite,[status(thm)],[])).
% 1.49/1.30 tff(2385,plain,
% 1.49/1.30 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a138) | (~c1_1(a138)) | (~c0_1(a138)) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp7 | c1_1(a142) | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138)) | (~c3_1(a142)) | (~c0_1(a142))))),
% 1.49/1.30 inference(monotonicity,[status(thm)],[2384])).
% 1.49/1.30 tff(2386,plain,
% 1.49/1.30 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a138) | (~c1_1(a138)) | (~c0_1(a138)) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a142) | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138)) | (~c3_1(a142)) | (~c0_1(a142)))),
% 1.49/1.30 inference(transitivity,[status(thm)],[2385, 2383])).
% 1.49/1.30 tff(2387,plain,
% 1.49/1.30 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a138) | (~c1_1(a138)) | (~c0_1(a138)) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142)))),
% 1.49/1.30 inference(quant_inst,[status(thm)],[])).
% 1.49/1.30 tff(2388,plain,
% 1.49/1.30 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a142) | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c1_1(a138)) | (~c3_1(a142)) | (~c0_1(a142))),
% 1.49/1.30 inference(modus_ponens,[status(thm)],[2387, 2386])).
% 1.49/1.30 tff(2389,plain,
% 1.49/1.30 ($false),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[2388, 123, 96, 190, 162, 1972, 1961, 151, 1950, 2002])).
% 1.49/1.30 tff(2390,plain,((~hskp12) | hskp7), inference(lemma,lemma(discharge,[]))).
% 1.49/1.30 tff(2391,plain,
% 1.49/1.30 (~hskp12),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[2390, 96])).
% 1.49/1.30 tff(2392,plain,
% 1.49/1.30 (c1_1(a155)),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[416, 2380])).
% 1.49/1.30 tff(2393,plain,
% 1.49/1.30 (hskp12 | (~c3_1(a155))),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[1514, 123, 2392, 2382, 2381, 1446])).
% 1.49/1.30 tff(2394,plain,
% 1.49/1.30 (~c3_1(a155)),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[2393, 2391])).
% 1.49/1.30 tff(2395,plain,
% 1.49/1.30 (hskp19),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[2036, 2391, 2021])).
% 1.49/1.30 tff(2396,plain,
% 1.49/1.30 (~c2_1(a164)),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[250, 2395])).
% 1.49/1.30 tff(2397,plain,
% 1.49/1.30 (c3_1(a164)),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[261, 2395])).
% 1.49/1.30 tff(2398,plain,
% 1.49/1.30 (c1_1(a164)),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[272, 2395])).
% 1.49/1.30 tff(2399,plain,
% 1.49/1.30 (c0_1(a164)),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[1937, 123, 2391, 2398, 2397, 2396, 1446])).
% 1.49/1.30 tff(2400,assumption,(hskp18), introduced(assumption)).
% 1.49/1.30 tff(2401,plain,
% 1.49/1.30 (~c1_1(a160)),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[1014, 2400])).
% 1.49/1.30 tff(2402,plain,
% 1.49/1.30 (c3_1(a160)),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[1025, 2400])).
% 1.49/1.30 tff(2403,plain,
% 1.49/1.30 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp7 | c2_1(a164) | c1_1(a160) | (~ndr1_0) | (~c3_1(a160)) | (~c0_1(a160)) | (~c0_1(a164)) | (~c1_1(a164)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp7 | c2_1(a164) | c1_1(a160) | (~ndr1_0) | (~c3_1(a160)) | (~c0_1(a160)) | (~c0_1(a164)) | (~c1_1(a164)))),
% 1.49/1.30 inference(rewrite,[status(thm)],[])).
% 1.49/1.30 tff(2404,plain,
% 1.49/1.30 ((hskp7 | (~ndr1_0) | c2_1(a164) | (~c1_1(a164)) | (~c0_1(a164)) | c1_1(a160) | (~c3_1(a160)) | (~c0_1(a160))) <=> (hskp7 | c2_1(a164) | c1_1(a160) | (~ndr1_0) | (~c3_1(a160)) | (~c0_1(a160)) | (~c0_1(a164)) | (~c1_1(a164)))),
% 1.49/1.30 inference(rewrite,[status(thm)],[])).
% 1.49/1.30 tff(2405,plain,
% 1.49/1.30 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a164) | (~c1_1(a164)) | (~c0_1(a164)) | c1_1(a160) | (~c3_1(a160)) | (~c0_1(a160)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp7 | c2_1(a164) | c1_1(a160) | (~ndr1_0) | (~c3_1(a160)) | (~c0_1(a160)) | (~c0_1(a164)) | (~c1_1(a164))))),
% 1.49/1.30 inference(monotonicity,[status(thm)],[2404])).
% 1.49/1.30 tff(2406,plain,
% 1.49/1.30 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a164) | (~c1_1(a164)) | (~c0_1(a164)) | c1_1(a160) | (~c3_1(a160)) | (~c0_1(a160)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp7 | c2_1(a164) | c1_1(a160) | (~ndr1_0) | (~c3_1(a160)) | (~c0_1(a160)) | (~c0_1(a164)) | (~c1_1(a164)))),
% 1.49/1.30 inference(transitivity,[status(thm)],[2405, 2403])).
% 1.49/1.30 tff(2407,plain,
% 1.49/1.30 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a164) | (~c1_1(a164)) | (~c0_1(a164)) | c1_1(a160) | (~c3_1(a160)) | (~c0_1(a160)))),
% 1.49/1.30 inference(quant_inst,[status(thm)],[])).
% 1.49/1.30 tff(2408,plain,
% 1.49/1.30 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp7 | c2_1(a164) | c1_1(a160) | (~ndr1_0) | (~c3_1(a160)) | (~c0_1(a160)) | (~c0_1(a164)) | (~c1_1(a164))),
% 1.49/1.30 inference(modus_ponens,[status(thm)],[2407, 2406])).
% 1.49/1.30 tff(2409,plain,
% 1.49/1.30 (~c0_1(a160)),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[2408, 123, 96, 2398, 2402, 2396, 2401, 2002, 2399])).
% 1.49/1.30 tff(2410,plain,
% 1.49/1.30 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c2_1(a164) | c1_1(a160) | (~ndr1_0) | (~c3_1(a160)) | c0_1(a160) | (~c0_1(a164)) | (~c1_1(a164)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c2_1(a164) | c1_1(a160) | (~ndr1_0) | (~c3_1(a160)) | c0_1(a160) | (~c0_1(a164)) | (~c1_1(a164)))),
% 1.49/1.30 inference(rewrite,[status(thm)],[])).
% 1.49/1.30 tff(2411,plain,
% 1.49/1.30 ((hskp7 | (~ndr1_0) | c2_1(a164) | (~c1_1(a164)) | (~c0_1(a164)) | c1_1(a160) | c0_1(a160) | (~c3_1(a160))) <=> (hskp7 | c2_1(a164) | c1_1(a160) | (~ndr1_0) | (~c3_1(a160)) | c0_1(a160) | (~c0_1(a164)) | (~c1_1(a164)))),
% 1.49/1.30 inference(rewrite,[status(thm)],[])).
% 1.49/1.30 tff(2412,plain,
% 1.49/1.30 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a164) | (~c1_1(a164)) | (~c0_1(a164)) | c1_1(a160) | c0_1(a160) | (~c3_1(a160)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c2_1(a164) | c1_1(a160) | (~ndr1_0) | (~c3_1(a160)) | c0_1(a160) | (~c0_1(a164)) | (~c1_1(a164))))),
% 1.49/1.30 inference(monotonicity,[status(thm)],[2411])).
% 1.49/1.30 tff(2413,plain,
% 1.49/1.30 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a164) | (~c1_1(a164)) | (~c0_1(a164)) | c1_1(a160) | c0_1(a160) | (~c3_1(a160)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c2_1(a164) | c1_1(a160) | (~ndr1_0) | (~c3_1(a160)) | c0_1(a160) | (~c0_1(a164)) | (~c1_1(a164)))),
% 1.49/1.30 inference(transitivity,[status(thm)],[2412, 2410])).
% 1.49/1.30 tff(2414,plain,
% 1.49/1.30 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a164) | (~c1_1(a164)) | (~c0_1(a164)) | c1_1(a160) | c0_1(a160) | (~c3_1(a160)))),
% 1.49/1.30 inference(quant_inst,[status(thm)],[])).
% 1.49/1.30 tff(2415,plain,
% 1.49/1.30 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c2_1(a164) | c1_1(a160) | (~ndr1_0) | (~c3_1(a160)) | c0_1(a160) | (~c0_1(a164)) | (~c1_1(a164))),
% 1.49/1.30 inference(modus_ponens,[status(thm)],[2414, 2413])).
% 1.49/1.30 tff(2416,plain,
% 1.49/1.30 ($false),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[2415, 123, 96, 2398, 2402, 2396, 2401, 368, 2399, 2409])).
% 1.49/1.30 tff(2417,plain,((~hskp18) | hskp7), inference(lemma,lemma(discharge,[]))).
% 1.49/1.30 tff(2418,plain,
% 1.49/1.30 (~hskp18),
% 1.49/1.30 inference(unit_resolution,[status(thm)],[2417, 96])).
% 1.49/1.30 tff(2419,plain,
% 1.49/1.30 (^[U: $i] : refl((hskp15 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp15 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 1.49/1.30 inference(bind,[status(th)],[])).
% 1.49/1.30 tff(2420,plain,
% 1.49/1.30 (![U: $i] : (hskp15 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp15 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.49/1.30 inference(quant_intro,[status(thm)],[2419])).
% 1.49/1.30 tff(2421,plain,
% 1.49/1.30 (![U: $i] : (hskp15 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp15 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.49/1.30 inference(rewrite,[status(thm)],[])).
% 1.49/1.30 tff(2422,plain,
% 1.49/1.30 (^[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)) | hskp15) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp15))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) | hskp13) <=> ((hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp13))), rewrite(((hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp13) <=> (hskp15 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) | hskp13) <=> (hskp15 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 1.49/1.30 inference(bind,[status(th)],[])).
% 1.49/1.30 tff(2423,plain,
% 1.49/1.30 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) | hskp13) <=> ![U: $i] : (hskp15 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.49/1.30 inference(quant_intro,[status(thm)],[2422])).
% 1.49/1.30 tff(2424,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) | hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause158')).
% 1.49/1.30 tff(2425,plain,
% 1.49/1.30 (![U: $i] : (hskp15 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.49/1.30 inference(modus_ponens,[status(thm)],[2424, 2423])).
% 1.49/1.30 tff(2426,plain,
% 1.49/1.30 (![U: $i] : (hskp15 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.49/1.30 inference(modus_ponens,[status(thm)],[2425, 2421])).
% 1.49/1.30 tff(2427,plain,(
% 1.49/1.30 ![U: $i] : (hskp15 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.49/1.30 inference(skolemize,[status(sab)],[2426])).
% 1.49/1.30 tff(2428,plain,
% 1.49/1.30 (![U: $i] : (hskp15 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.49/1.30 inference(modus_ponens,[status(thm)],[2427, 2420])).
% 1.49/1.30 tff(2429,plain,
% 1.49/1.30 (((~![U: $i] : (hskp15 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp15 | hskp13 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164)))) <=> ((~![U: $i] : (hskp15 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp15 | hskp13 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164)))),
% 1.49/1.30 inference(rewrite,[status(thm)],[])).
% 1.49/1.30 tff(2430,plain,
% 1.49/1.30 ((hskp15 | hskp13 | (~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164))) <=> (hskp15 | hskp13 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164)))),
% 1.49/1.30 inference(rewrite,[status(thm)],[])).
% 1.49/1.30 tff(2431,plain,
% 1.49/1.30 (((~![U: $i] : (hskp15 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp15 | hskp13 | (~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)))) <=> ((~![U: $i] : (hskp15 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp15 | hskp13 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164))))),
% 1.49/1.30 inference(monotonicity,[status(thm)],[2430])).
% 1.49/1.30 tff(2432,plain,
% 1.49/1.30 (((~![U: $i] : (hskp15 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp15 | hskp13 | (~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)))) <=> ((~![U: $i] : (hskp15 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp15 | hskp13 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164)))),
% 1.49/1.31 inference(transitivity,[status(thm)],[2431, 2429])).
% 1.49/1.31 tff(2433,plain,
% 1.49/1.31 ((~![U: $i] : (hskp15 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp15 | hskp13 | (~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)))),
% 1.49/1.31 inference(quant_inst,[status(thm)],[])).
% 1.49/1.31 tff(2434,plain,
% 1.49/1.31 ((~![U: $i] : (hskp15 | hskp13 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp15 | hskp13 | c2_1(a164) | (~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164))),
% 1.49/1.31 inference(modus_ponens,[status(thm)],[2433, 2432])).
% 1.49/1.31 tff(2435,plain,
% 1.49/1.31 (hskp15),
% 1.49/1.31 inference(unit_resolution,[status(thm)],[2434, 123, 2021, 2398, 2397, 2396, 2428])).
% 1.49/1.31 tff(2436,plain,
% 1.49/1.31 (((~hskp15) | (~c0_1(a153))) <=> ((~hskp15) | (~c0_1(a153)))),
% 1.49/1.31 inference(rewrite,[status(thm)],[])).
% 1.49/1.31 tff(2437,plain,
% 1.49/1.31 (((~c0_1(a153)) | (~hskp15)) <=> ((~hskp15) | (~c0_1(a153)))),
% 1.49/1.31 inference(rewrite,[status(thm)],[])).
% 1.49/1.31 tff(2438,axiom,((~c0_1(a153)) | (~hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause103')).
% 1.49/1.31 tff(2439,plain,
% 1.49/1.31 ((~hskp15) | (~c0_1(a153))),
% 1.49/1.31 inference(modus_ponens,[status(thm)],[2438, 2437])).
% 1.49/1.31 tff(2440,plain,
% 1.49/1.31 ((~hskp15) | (~c0_1(a153))),
% 1.49/1.31 inference(modus_ponens,[status(thm)],[2439, 2436])).
% 1.49/1.31 tff(2441,plain,
% 1.49/1.31 (~c0_1(a153)),
% 1.49/1.31 inference(unit_resolution,[status(thm)],[2440, 2435])).
% 1.49/1.31 tff(2442,plain,
% 1.49/1.31 (((~hskp15) | c3_1(a153)) <=> ((~hskp15) | c3_1(a153))),
% 1.49/1.31 inference(rewrite,[status(thm)],[])).
% 1.49/1.31 tff(2443,axiom,((~hskp15) | c3_1(a153)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause65')).
% 1.49/1.31 tff(2444,plain,
% 1.49/1.31 ((~hskp15) | c3_1(a153)),
% 1.49/1.31 inference(modus_ponens,[status(thm)],[2443, 2442])).
% 1.49/1.31 tff(2445,plain,
% 1.49/1.31 ((~hskp15) | c3_1(a153)),
% 1.49/1.31 inference(modus_ponens,[status(thm)],[2444, 2442])).
% 1.49/1.31 tff(2446,plain,
% 1.49/1.31 ((~hskp15) | c3_1(a153)),
% 1.49/1.31 inference(modus_ponens,[status(thm)],[2445, 2442])).
% 1.49/1.31 tff(2447,plain,
% 1.49/1.31 ((~hskp15) | c3_1(a153)),
% 1.49/1.31 inference(modus_ponens,[status(thm)],[2446, 2442])).
% 1.49/1.31 tff(2448,plain,
% 1.49/1.31 ((~hskp15) | c3_1(a153)),
% 1.49/1.31 inference(modus_ponens,[status(thm)],[2447, 2442])).
% 1.49/1.31 tff(2449,plain,
% 1.49/1.31 ((~hskp15) | c3_1(a153)),
% 1.49/1.31 inference(modus_ponens,[status(thm)],[2448, 2442])).
% 1.49/1.31 tff(2450,plain,
% 1.49/1.31 ((~hskp15) | c3_1(a153)),
% 1.49/1.31 inference(modus_ponens,[status(thm)],[2449, 2442])).
% 1.49/1.31 tff(2451,plain,
% 1.49/1.31 ((~hskp15) | c3_1(a153)),
% 1.49/1.31 inference(modus_ponens,[status(thm)],[2450, 2442])).
% 1.49/1.31 tff(2452,plain,
% 1.49/1.31 (c3_1(a153)),
% 1.49/1.31 inference(unit_resolution,[status(thm)],[2451, 2435])).
% 1.49/1.31 tff(2453,plain,
% 1.49/1.31 (((~hskp15) | c2_1(a153)) <=> ((~hskp15) | c2_1(a153))),
% 1.49/1.31 inference(rewrite,[status(thm)],[])).
% 1.49/1.31 tff(2454,axiom,((~hskp15) | c2_1(a153)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause64')).
% 1.49/1.31 tff(2455,plain,
% 1.49/1.31 ((~hskp15) | c2_1(a153)),
% 1.49/1.31 inference(modus_ponens,[status(thm)],[2454, 2453])).
% 1.49/1.31 tff(2456,plain,
% 1.49/1.31 ((~hskp15) | c2_1(a153)),
% 1.49/1.31 inference(modus_ponens,[status(thm)],[2455, 2453])).
% 1.49/1.31 tff(2457,plain,
% 1.49/1.31 ((~hskp15) | c2_1(a153)),
% 1.49/1.31 inference(modus_ponens,[status(thm)],[2456, 2453])).
% 1.49/1.31 tff(2458,plain,
% 1.49/1.31 ((~hskp15) | c2_1(a153)),
% 1.49/1.31 inference(modus_ponens,[status(thm)],[2457, 2453])).
% 1.49/1.31 tff(2459,plain,
% 1.49/1.31 ((~hskp15) | c2_1(a153)),
% 1.49/1.31 inference(modus_ponens,[status(thm)],[2458, 2453])).
% 1.49/1.31 tff(2460,plain,
% 1.49/1.31 ((~hskp15) | c2_1(a153)),
% 1.49/1.31 inference(modus_ponens,[status(thm)],[2459, 2453])).
% 1.49/1.31 tff(2461,plain,
% 1.49/1.31 ((~hskp15) | c2_1(a153)),
% 1.49/1.31 inference(modus_ponens,[status(thm)],[2460, 2453])).
% 1.49/1.31 tff(2462,plain,
% 1.49/1.31 ((~hskp15) | c2_1(a153)),
% 1.49/1.31 inference(modus_ponens,[status(thm)],[2461, 2453])).
% 1.49/1.31 tff(2463,plain,
% 1.49/1.31 (c2_1(a153)),
% 1.49/1.31 inference(unit_resolution,[status(thm)],[2462, 2435])).
% 1.49/1.31 tff(2464,plain,
% 1.49/1.31 (((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp18 | hskp0 | c0_1(a153) | (~ndr1_0) | (~c2_1(a153)) | (~c3_1(a153)))) <=> ((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp18 | hskp0 | c0_1(a153) | (~ndr1_0) | (~c2_1(a153)) | (~c3_1(a153)))),
% 1.49/1.31 inference(rewrite,[status(thm)],[])).
% 1.49/1.31 tff(2465,plain,
% 1.49/1.31 ((hskp18 | hskp0 | (~ndr1_0) | c0_1(a153) | (~c3_1(a153)) | (~c2_1(a153))) <=> (hskp18 | hskp0 | c0_1(a153) | (~ndr1_0) | (~c2_1(a153)) | (~c3_1(a153)))),
% 1.49/1.31 inference(rewrite,[status(thm)],[])).
% 1.49/1.31 tff(2466,plain,
% 1.49/1.31 (((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp18 | hskp0 | (~ndr1_0) | c0_1(a153) | (~c3_1(a153)) | (~c2_1(a153)))) <=> ((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp18 | hskp0 | c0_1(a153) | (~ndr1_0) | (~c2_1(a153)) | (~c3_1(a153))))),
% 1.49/1.31 inference(monotonicity,[status(thm)],[2465])).
% 1.49/1.31 tff(2467,plain,
% 1.49/1.31 (((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp18 | hskp0 | (~ndr1_0) | c0_1(a153) | (~c3_1(a153)) | (~c2_1(a153)))) <=> ((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp18 | hskp0 | c0_1(a153) | (~ndr1_0) | (~c2_1(a153)) | (~c3_1(a153)))),
% 1.49/1.31 inference(transitivity,[status(thm)],[2466, 2464])).
% 1.49/1.31 tff(2468,plain,
% 1.49/1.31 ((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp18 | hskp0 | (~ndr1_0) | c0_1(a153) | (~c3_1(a153)) | (~c2_1(a153)))),
% 1.49/1.31 inference(quant_inst,[status(thm)],[])).
% 1.49/1.31 tff(2469,plain,
% 1.49/1.31 ((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp18 | hskp0 | c0_1(a153) | (~ndr1_0) | (~c2_1(a153)) | (~c3_1(a153))),
% 1.49/1.31 inference(modus_ponens,[status(thm)],[2468, 2467])).
% 1.49/1.31 tff(2470,plain,
% 1.49/1.31 (hskp18 | hskp0),
% 1.49/1.31 inference(unit_resolution,[status(thm)],[2469, 123, 2463, 2452, 2441, 1001])).
% 1.49/1.31 tff(2471,plain,
% 1.49/1.31 (hskp0),
% 1.49/1.31 inference(unit_resolution,[status(thm)],[2470, 2418])).
% 1.49/1.31 tff(2472,plain,
% 1.49/1.31 (~c0_1(a123)),
% 1.49/1.31 inference(unit_resolution,[status(thm)],[236, 2471])).
% 1.49/1.31 tff(2473,plain,
% 1.49/1.31 (c2_1(a123)),
% 1.49/1.31 inference(unit_resolution,[status(thm)],[213, 2471])).
% 1.49/1.31 tff(2474,plain,
% 1.49/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a164) | c2_1(a155) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | c3_1(a155) | (~c1_1(a155)) | (~c3_1(a164)) | (~c1_1(a164)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a164) | c2_1(a155) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | c3_1(a155) | (~c1_1(a155)) | (~c3_1(a164)) | (~c1_1(a164)))),
% 1.49/1.31 inference(rewrite,[status(thm)],[])).
% 1.49/1.31 tff(2475,plain,
% 1.49/1.31 (((~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)) | c2_1(a155) | c3_1(a155) | (~c1_1(a155)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123))) <=> (c2_1(a164) | c2_1(a155) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | c3_1(a155) | (~c1_1(a155)) | (~c3_1(a164)) | (~c1_1(a164)))),
% 1.49/1.31 inference(rewrite,[status(thm)],[])).
% 1.49/1.31 tff(2476,plain,
% 1.49/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)) | c2_1(a155) | c3_1(a155) | (~c1_1(a155)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a164) | c2_1(a155) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | c3_1(a155) | (~c1_1(a155)) | (~c3_1(a164)) | (~c1_1(a164))))),
% 1.49/1.31 inference(monotonicity,[status(thm)],[2475])).
% 1.49/1.31 tff(2477,plain,
% 1.49/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)) | c2_1(a155) | c3_1(a155) | (~c1_1(a155)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a164) | c2_1(a155) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | c3_1(a155) | (~c1_1(a155)) | (~c3_1(a164)) | (~c1_1(a164)))),
% 1.49/1.31 inference(transitivity,[status(thm)],[2476, 2474])).
% 1.49/1.31 tff(2478,plain,
% 1.49/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a164) | (~c3_1(a164)) | (~c1_1(a164)) | c2_1(a155) | c3_1(a155) | (~c1_1(a155)) | c0_1(a123) | c3_1(a123) | (~c2_1(a123)))),
% 1.49/1.31 inference(quant_inst,[status(thm)],[])).
% 1.49/1.31 tff(2479,plain,
% 1.49/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a164) | c2_1(a155) | c0_1(a123) | (~ndr1_0) | c3_1(a123) | (~c2_1(a123)) | c3_1(a155) | (~c1_1(a155)) | (~c3_1(a164)) | (~c1_1(a164))),
% 1.49/1.31 inference(modus_ponens,[status(thm)],[2478, 2477])).
% 1.49/1.31 tff(2480,plain,
% 1.49/1.31 (c3_1(a123)),
% 1.49/1.31 inference(unit_resolution,[status(thm)],[2479, 123, 2398, 2397, 2392, 2473, 2396, 2381, 2472, 1482, 2394])).
% 1.49/1.31 tff(2481,plain,
% 1.49/1.31 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))))),
% 1.49/1.31 inference(bind,[status(th)],[])).
% 1.49/1.31 tff(2482,plain,
% 1.49/1.31 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.49/1.31 inference(quant_intro,[status(thm)],[2481])).
% 1.49/1.31 tff(2483,plain,
% 1.49/1.31 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.49/1.31 inference(rewrite,[status(thm)],[])).
% 1.49/1.31 tff(2484,plain,
% 1.49/1.31 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))))),
% 1.49/1.31 inference(bind,[status(th)],[])).
% 1.49/1.31 tff(2485,plain,
% 1.49/1.31 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.49/1.31 inference(quant_intro,[status(thm)],[2484])).
% 1.49/1.31 tff(2486,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause202')).
% 1.49/1.31 tff(2487,plain,
% 1.49/1.31 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.49/1.31 inference(modus_ponens,[status(thm)],[2486, 2485])).
% 1.49/1.31 tff(2488,plain,
% 1.49/1.31 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.49/1.31 inference(modus_ponens,[status(thm)],[2487, 2483])).
% 1.49/1.31 tff(2489,plain,(
% 1.49/1.31 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.49/1.31 inference(skolemize,[status(sab)],[2488])).
% 1.49/1.31 tff(2490,plain,
% 1.49/1.31 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.49/1.31 inference(modus_ponens,[status(thm)],[2489, 2482])).
% 1.49/1.31 tff(2491,plain,
% 1.49/1.31 (hskp10),
% 1.49/1.31 inference(unit_resolution,[status(thm)],[1979, 2418])).
% 1.49/1.31 tff(2492,plain,
% 1.49/1.31 (~c2_1(a140)),
% 1.49/1.31 inference(unit_resolution,[status(thm)],[1850, 2491])).
% 1.49/1.31 tff(2493,plain,
% 1.49/1.31 (c0_1(a140)),
% 1.49/1.31 inference(unit_resolution,[status(thm)],[1861, 2491])).
% 1.49/1.31 tff(2494,plain,
% 1.49/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a153) | c2_1(a140) | (~ndr1_0) | c1_1(a140) | (~c0_1(a140)) | (~c2_1(a153)) | (~c3_1(a153)) | (~c3_1(a164)) | (~c0_1(a164)) | (~c1_1(a164)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a153) | c2_1(a140) | (~ndr1_0) | c1_1(a140) | (~c0_1(a140)) | (~c2_1(a153)) | (~c3_1(a153)) | (~c3_1(a164)) | (~c0_1(a164)) | (~c1_1(a164)))),
% 1.49/1.31 inference(rewrite,[status(thm)],[])).
% 1.49/1.31 tff(2495,plain,
% 1.49/1.31 (((~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164)) | (~c0_1(a164)) | c2_1(a140) | c1_1(a140) | (~c0_1(a140)) | c0_1(a153) | (~c3_1(a153)) | (~c2_1(a153))) <=> (c0_1(a153) | c2_1(a140) | (~ndr1_0) | c1_1(a140) | (~c0_1(a140)) | (~c2_1(a153)) | (~c3_1(a153)) | (~c3_1(a164)) | (~c0_1(a164)) | (~c1_1(a164)))),
% 1.49/1.31 inference(rewrite,[status(thm)],[])).
% 1.49/1.31 tff(2496,plain,
% 1.49/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164)) | (~c0_1(a164)) | c2_1(a140) | c1_1(a140) | (~c0_1(a140)) | c0_1(a153) | (~c3_1(a153)) | (~c2_1(a153)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a153) | c2_1(a140) | (~ndr1_0) | c1_1(a140) | (~c0_1(a140)) | (~c2_1(a153)) | (~c3_1(a153)) | (~c3_1(a164)) | (~c0_1(a164)) | (~c1_1(a164))))),
% 1.49/1.31 inference(monotonicity,[status(thm)],[2495])).
% 1.49/1.31 tff(2497,plain,
% 1.49/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164)) | (~c0_1(a164)) | c2_1(a140) | c1_1(a140) | (~c0_1(a140)) | c0_1(a153) | (~c3_1(a153)) | (~c2_1(a153)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a153) | c2_1(a140) | (~ndr1_0) | c1_1(a140) | (~c0_1(a140)) | (~c2_1(a153)) | (~c3_1(a153)) | (~c3_1(a164)) | (~c0_1(a164)) | (~c1_1(a164)))),
% 1.49/1.31 inference(transitivity,[status(thm)],[2496, 2494])).
% 1.49/1.31 tff(2498,plain,
% 1.49/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a164)) | (~c1_1(a164)) | (~c0_1(a164)) | c2_1(a140) | c1_1(a140) | (~c0_1(a140)) | c0_1(a153) | (~c3_1(a153)) | (~c2_1(a153)))),
% 1.49/1.31 inference(quant_inst,[status(thm)],[])).
% 1.49/1.31 tff(2499,plain,
% 1.49/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a153) | c2_1(a140) | (~ndr1_0) | c1_1(a140) | (~c0_1(a140)) | (~c2_1(a153)) | (~c3_1(a153)) | (~c3_1(a164)) | (~c0_1(a164)) | (~c1_1(a164))),
% 1.49/1.31 inference(modus_ponens,[status(thm)],[2498, 2497])).
% 1.49/1.31 tff(2500,plain,
% 1.49/1.31 (c1_1(a140)),
% 1.49/1.31 inference(unit_resolution,[status(thm)],[2499, 123, 2398, 2397, 2463, 2452, 2493, 2441, 2492, 2490, 2399])).
% 1.49/1.31 tff(2501,plain,
% 1.49/1.31 (~c1_1(a123)),
% 1.49/1.31 inference(unit_resolution,[status(thm)],[202, 2471])).
% 1.49/1.31 tff(2502,plain,
% 1.49/1.31 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c2_1(a140) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c1_1(a140)) | (~c0_1(a140)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c2_1(a140) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c1_1(a140)) | (~c0_1(a140)))),
% 1.49/1.31 inference(rewrite,[status(thm)],[])).
% 1.49/1.31 tff(2503,plain,
% 1.49/1.31 ((hskp7 | (~ndr1_0) | c2_1(a140) | (~c1_1(a140)) | (~c0_1(a140)) | c1_1(a123) | c0_1(a123) | (~c3_1(a123))) <=> (hskp7 | c2_1(a140) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c1_1(a140)) | (~c0_1(a140)))),
% 1.49/1.31 inference(rewrite,[status(thm)],[])).
% 1.49/1.31 tff(2504,plain,
% 1.49/1.31 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a140) | (~c1_1(a140)) | (~c0_1(a140)) | c1_1(a123) | c0_1(a123) | (~c3_1(a123)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c2_1(a140) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c1_1(a140)) | (~c0_1(a140))))),
% 1.49/1.31 inference(monotonicity,[status(thm)],[2503])).
% 1.49/1.31 tff(2505,plain,
% 1.49/1.31 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a140) | (~c1_1(a140)) | (~c0_1(a140)) | c1_1(a123) | c0_1(a123) | (~c3_1(a123)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c2_1(a140) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c1_1(a140)) | (~c0_1(a140)))),
% 1.49/1.31 inference(transitivity,[status(thm)],[2504, 2502])).
% 1.49/1.31 tff(2506,plain,
% 1.49/1.31 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a140) | (~c1_1(a140)) | (~c0_1(a140)) | c1_1(a123) | c0_1(a123) | (~c3_1(a123)))),
% 1.49/1.31 inference(quant_inst,[status(thm)],[])).
% 1.49/1.31 tff(2507,plain,
% 1.49/1.31 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c2_1(a140) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c3_1(a123)) | (~c1_1(a140)) | (~c0_1(a140))),
% 1.49/1.31 inference(modus_ponens,[status(thm)],[2506, 2505])).
% 1.49/1.31 tff(2508,plain,
% 1.49/1.31 ($false),
% 1.49/1.31 inference(unit_resolution,[status(thm)],[2507, 123, 96, 2493, 2492, 2472, 2501, 368, 2500, 2480])).
% 1.49/1.31 tff(2509,plain,(hskp7), inference(lemma,lemma(discharge,[]))).
% 1.49/1.31 tff(2510,plain,
% 1.49/1.31 (~c0_1(a132)),
% 1.49/1.31 inference(unit_resolution,[status(thm)],[431, 2509])).
% 1.49/1.31 tff(2511,plain,
% 1.49/1.31 (~c2_1(a132)),
% 1.49/1.31 inference(unit_resolution,[status(thm)],[898, 2509])).
% 1.49/1.31 tff(2512,plain,
% 1.49/1.31 (c3_1(a132)),
% 1.49/1.31 inference(unit_resolution,[status(thm)],[447, 2509])).
% 1.49/1.31 tff(2513,plain,
% 1.49/1.31 ((~c3_1(a132)) | c0_1(a132) | c2_1(a132) | c1_1(a132)),
% 1.49/1.31 inference(unit_resolution,[status(thm)],[479, 2380])).
% 1.49/1.31 tff(2514,plain,
% 1.49/1.31 (c1_1(a132)),
% 1.49/1.31 inference(unit_resolution,[status(thm)],[2513, 2512, 2511, 2510])).
% 1.49/1.31 tff(2515,plain,
% 1.49/1.31 (~c3_1(a138)),
% 1.49/1.31 inference(unit_resolution,[status(thm)],[2116, 123, 1972, 2512, 1950, 2510, 2511, 1428, 2514])).
% 1.49/1.31 tff(2516,assumption,(hskp15), introduced(assumption)).
% 1.49/1.31 tff(2517,plain,
% 1.49/1.31 (~c0_1(a153)),
% 1.49/1.31 inference(unit_resolution,[status(thm)],[2440, 2516])).
% 1.49/1.31 tff(2518,plain,
% 1.49/1.31 (c3_1(a153)),
% 1.49/1.31 inference(unit_resolution,[status(thm)],[2451, 2516])).
% 1.49/1.31 tff(2519,plain,
% 1.49/1.31 (c2_1(a153)),
% 1.49/1.31 inference(unit_resolution,[status(thm)],[2462, 2516])).
% 1.49/1.31 tff(2520,plain,
% 1.49/1.31 ($false),
% 1.49/1.31 inference(unit_resolution,[status(thm)],[2469, 123, 22, 11, 2519, 2518, 2517, 1001])).
% 1.49/1.31 tff(2521,plain,((~hskp15) | hskp18 | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.49/1.31 tff(2522,plain,
% 1.49/1.31 (~hskp15),
% 1.49/1.31 inference(unit_resolution,[status(thm)],[2521, 22, 11])).
% 1.49/1.31 tff(2523,plain,
% 1.49/1.31 (^[U: $i] : refl((hskp24 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp24 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))),
% 1.49/1.31 inference(bind,[status(th)],[])).
% 1.49/1.31 tff(2524,plain,
% 1.49/1.31 (![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.49/1.31 inference(quant_intro,[status(thm)],[2523])).
% 1.49/1.31 tff(2525,plain,
% 1.49/1.31 (![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.49/1.31 inference(rewrite,[status(thm)],[])).
% 1.49/1.31 tff(2526,plain,
% 1.49/1.31 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp15) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp15))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp15) | hskp24) <=> ((hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp24))), rewrite(((hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp24) <=> (hskp24 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp15) | hskp24) <=> (hskp24 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))))),
% 1.49/1.31 inference(bind,[status(th)],[])).
% 1.49/1.31 tff(2527,plain,
% 1.49/1.31 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp15) | hskp24) <=> ![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.49/1.31 inference(quant_intro,[status(thm)],[2526])).
% 1.49/1.31 tff(2528,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp15) | hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause142')).
% 1.49/1.31 tff(2529,plain,
% 1.49/1.31 (![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.49/1.31 inference(modus_ponens,[status(thm)],[2528, 2527])).
% 1.49/1.31 tff(2530,plain,
% 1.49/1.31 (![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.49/1.31 inference(modus_ponens,[status(thm)],[2529, 2525])).
% 1.49/1.31 tff(2531,plain,(
% 1.49/1.31 ![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.49/1.31 inference(skolemize,[status(sab)],[2530])).
% 1.49/1.31 tff(2532,plain,
% 1.49/1.31 (![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.49/1.31 inference(modus_ponens,[status(thm)],[2531, 2524])).
% 1.49/1.31 tff(2533,plain,
% 1.49/1.31 (((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp24 | hskp15 | c2_1(a138) | (~ndr1_0) | c3_1(a138) | (~c1_1(a138)))) <=> ((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp24 | hskp15 | c2_1(a138) | (~ndr1_0) | c3_1(a138) | (~c1_1(a138)))),
% 1.49/1.31 inference(rewrite,[status(thm)],[])).
% 1.49/1.31 tff(2534,plain,
% 1.49/1.31 ((hskp24 | hskp15 | (~ndr1_0) | c2_1(a138) | c3_1(a138) | (~c1_1(a138))) <=> (hskp24 | hskp15 | c2_1(a138) | (~ndr1_0) | c3_1(a138) | (~c1_1(a138)))),
% 1.49/1.31 inference(rewrite,[status(thm)],[])).
% 1.49/1.31 tff(2535,plain,
% 1.49/1.31 (((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp24 | hskp15 | (~ndr1_0) | c2_1(a138) | c3_1(a138) | (~c1_1(a138)))) <=> ((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp24 | hskp15 | c2_1(a138) | (~ndr1_0) | c3_1(a138) | (~c1_1(a138))))),
% 1.49/1.31 inference(monotonicity,[status(thm)],[2534])).
% 1.49/1.31 tff(2536,plain,
% 1.49/1.31 (((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp24 | hskp15 | (~ndr1_0) | c2_1(a138) | c3_1(a138) | (~c1_1(a138)))) <=> ((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp24 | hskp15 | c2_1(a138) | (~ndr1_0) | c3_1(a138) | (~c1_1(a138)))),
% 1.49/1.31 inference(transitivity,[status(thm)],[2535, 2533])).
% 1.49/1.31 tff(2537,plain,
% 1.49/1.31 ((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp24 | hskp15 | (~ndr1_0) | c2_1(a138) | c3_1(a138) | (~c1_1(a138)))),
% 1.49/1.31 inference(quant_inst,[status(thm)],[])).
% 1.49/1.31 tff(2538,plain,
% 1.49/1.31 ((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp24 | hskp15 | c2_1(a138) | (~ndr1_0) | c3_1(a138) | (~c1_1(a138))),
% 1.49/1.32 inference(modus_ponens,[status(thm)],[2537, 2536])).
% 1.49/1.32 tff(2539,plain,
% 1.49/1.32 (hskp24 | hskp15 | c3_1(a138)),
% 1.49/1.32 inference(unit_resolution,[status(thm)],[2538, 123, 1961, 1950, 2532])).
% 1.49/1.32 tff(2540,plain,
% 1.49/1.32 (hskp24),
% 1.49/1.32 inference(unit_resolution,[status(thm)],[2539, 2522, 2515])).
% 1.49/1.32 tff(2541,plain,
% 1.49/1.32 (~c2_1(a182)),
% 1.49/1.32 inference(unit_resolution,[status(thm)],[1313, 2540])).
% 1.49/1.32 tff(2542,plain,
% 1.49/1.32 (~c0_1(a182)),
% 1.49/1.32 inference(unit_resolution,[status(thm)],[1326, 2540])).
% 1.49/1.32 tff(2543,plain,
% 1.49/1.32 (c0_1(a140)),
% 1.49/1.32 inference(unit_resolution,[status(thm)],[1861, 1980])).
% 1.49/1.32 tff(2544,plain,
% 1.49/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a182) | c2_1(a182) | c0_1(a155) | c2_1(a155) | c2_1(a140) | c3_1(a140) | (~ndr1_0) | (~c0_1(a140)) | (~c1_1(a155)) | c1_1(a182))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a182) | c2_1(a182) | c0_1(a155) | c2_1(a155) | c2_1(a140) | c3_1(a140) | (~ndr1_0) | (~c0_1(a140)) | (~c1_1(a155)) | c1_1(a182))),
% 1.49/1.32 inference(rewrite,[status(thm)],[])).
% 1.49/1.32 tff(2545,plain,
% 1.49/1.32 (((~ndr1_0) | c2_1(a140) | c3_1(a140) | (~c0_1(a140)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)) | c2_1(a182) | c1_1(a182) | c0_1(a182)) <=> (c0_1(a182) | c2_1(a182) | c0_1(a155) | c2_1(a155) | c2_1(a140) | c3_1(a140) | (~ndr1_0) | (~c0_1(a140)) | (~c1_1(a155)) | c1_1(a182))),
% 1.49/1.32 inference(rewrite,[status(thm)],[])).
% 1.49/1.32 tff(2546,plain,
% 1.49/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a140) | c3_1(a140) | (~c0_1(a140)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)) | c2_1(a182) | c1_1(a182) | c0_1(a182))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a182) | c2_1(a182) | c0_1(a155) | c2_1(a155) | c2_1(a140) | c3_1(a140) | (~ndr1_0) | (~c0_1(a140)) | (~c1_1(a155)) | c1_1(a182)))),
% 1.49/1.32 inference(monotonicity,[status(thm)],[2545])).
% 1.49/1.32 tff(2547,plain,
% 1.49/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a140) | c3_1(a140) | (~c0_1(a140)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)) | c2_1(a182) | c1_1(a182) | c0_1(a182))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a182) | c2_1(a182) | c0_1(a155) | c2_1(a155) | c2_1(a140) | c3_1(a140) | (~ndr1_0) | (~c0_1(a140)) | (~c1_1(a155)) | c1_1(a182))),
% 1.49/1.32 inference(transitivity,[status(thm)],[2546, 2544])).
% 1.49/1.32 tff(2548,plain,
% 1.49/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a140) | c3_1(a140) | (~c0_1(a140)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)) | c2_1(a182) | c1_1(a182) | c0_1(a182))),
% 1.49/1.32 inference(quant_inst,[status(thm)],[])).
% 1.49/1.32 tff(2549,plain,
% 1.49/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a182) | c2_1(a182) | c0_1(a155) | c2_1(a155) | c2_1(a140) | c3_1(a140) | (~ndr1_0) | (~c0_1(a140)) | (~c1_1(a155)) | c1_1(a182)),
% 1.49/1.32 inference(modus_ponens,[status(thm)],[2548, 2547])).
% 1.49/1.32 tff(2550,plain,
% 1.49/1.32 (c1_1(a182)),
% 1.49/1.32 inference(unit_resolution,[status(thm)],[2549, 123, 2392, 2543, 2542, 2541, 2382, 2381, 1982, 1981, 21])).
% 1.49/1.32 tff(2551,plain,
% 1.49/1.32 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp28 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 1.49/1.32 inference(bind,[status(th)],[])).
% 1.49/1.32 tff(2552,plain,
% 1.49/1.32 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.49/1.32 inference(quant_intro,[status(thm)],[2551])).
% 1.49/1.32 tff(2553,plain,
% 1.49/1.32 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.49/1.32 inference(rewrite,[status(thm)],[])).
% 1.49/1.32 tff(2554,plain,
% 1.49/1.32 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp28) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp28))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp28) <=> (hskp28 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 1.49/1.32 inference(bind,[status(th)],[])).
% 1.49/1.32 tff(2555,plain,
% 1.49/1.32 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.49/1.32 inference(quant_intro,[status(thm)],[2554])).
% 1.49/1.32 tff(2556,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause182')).
% 1.49/1.32 tff(2557,plain,
% 1.49/1.32 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.49/1.32 inference(modus_ponens,[status(thm)],[2556, 2555])).
% 1.49/1.32 tff(2558,plain,
% 1.49/1.32 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.49/1.32 inference(modus_ponens,[status(thm)],[2557, 2553])).
% 1.49/1.32 tff(2559,plain,(
% 1.49/1.32 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.49/1.32 inference(skolemize,[status(sab)],[2558])).
% 1.49/1.32 tff(2560,plain,
% 1.49/1.32 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.49/1.32 inference(modus_ponens,[status(thm)],[2559, 2552])).
% 1.49/1.32 tff(2561,plain,
% 1.49/1.32 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | c0_1(a155) | c2_1(a155) | (~ndr1_0) | c3_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | (~c1_1(a155)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp28 | c0_1(a155) | c2_1(a155) | (~ndr1_0) | c3_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | (~c1_1(a155)))),
% 1.49/1.32 inference(rewrite,[status(thm)],[])).
% 1.49/1.32 tff(2562,plain,
% 1.49/1.32 ((hskp28 | (~ndr1_0) | c3_1(a138) | (~c1_1(a138)) | (~c0_1(a138)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155))) <=> (hskp28 | c0_1(a155) | c2_1(a155) | (~ndr1_0) | c3_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | (~c1_1(a155)))),
% 1.49/1.32 inference(rewrite,[status(thm)],[])).
% 1.49/1.32 tff(2563,plain,
% 1.49/1.32 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a138) | (~c1_1(a138)) | (~c0_1(a138)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | c0_1(a155) | c2_1(a155) | (~ndr1_0) | c3_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | (~c1_1(a155))))),
% 1.49/1.32 inference(monotonicity,[status(thm)],[2562])).
% 1.49/1.32 tff(2564,plain,
% 1.49/1.32 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a138) | (~c1_1(a138)) | (~c0_1(a138)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp28 | c0_1(a155) | c2_1(a155) | (~ndr1_0) | c3_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | (~c1_1(a155)))),
% 1.49/1.32 inference(transitivity,[status(thm)],[2563, 2561])).
% 1.49/1.32 tff(2565,plain,
% 1.49/1.32 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | c3_1(a138) | (~c1_1(a138)) | (~c0_1(a138)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)))),
% 1.49/1.32 inference(quant_inst,[status(thm)],[])).
% 1.49/1.32 tff(2566,plain,
% 1.49/1.32 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp28 | c0_1(a155) | c2_1(a155) | (~ndr1_0) | c3_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | (~c1_1(a155))),
% 1.49/1.32 inference(modus_ponens,[status(thm)],[2565, 2564])).
% 1.49/1.32 tff(2567,plain,
% 1.49/1.32 (hskp28),
% 1.49/1.32 inference(unit_resolution,[status(thm)],[2566, 123, 2392, 1972, 1961, 2382, 2381, 2560, 2515])).
% 1.49/1.32 tff(2568,plain,
% 1.49/1.32 (((~hskp28) | c3_1(a133)) <=> ((~hskp28) | c3_1(a133))),
% 1.49/1.32 inference(rewrite,[status(thm)],[])).
% 1.49/1.32 tff(2569,axiom,((~hskp28) | c3_1(a133)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause46')).
% 1.49/1.32 tff(2570,plain,
% 1.49/1.32 ((~hskp28) | c3_1(a133)),
% 1.49/1.32 inference(modus_ponens,[status(thm)],[2569, 2568])).
% 1.49/1.32 tff(2571,plain,
% 1.49/1.32 ((~hskp28) | c3_1(a133)),
% 1.49/1.32 inference(modus_ponens,[status(thm)],[2570, 2568])).
% 1.49/1.32 tff(2572,plain,
% 1.49/1.32 ((~hskp28) | c3_1(a133)),
% 1.49/1.32 inference(modus_ponens,[status(thm)],[2571, 2568])).
% 1.49/1.32 tff(2573,plain,
% 1.49/1.32 ((~hskp28) | c3_1(a133)),
% 1.49/1.32 inference(modus_ponens,[status(thm)],[2572, 2568])).
% 1.49/1.32 tff(2574,plain,
% 1.49/1.32 ((~hskp28) | c3_1(a133)),
% 1.49/1.32 inference(modus_ponens,[status(thm)],[2573, 2568])).
% 1.49/1.32 tff(2575,plain,
% 1.49/1.32 ((~hskp28) | c3_1(a133)),
% 1.49/1.32 inference(modus_ponens,[status(thm)],[2574, 2568])).
% 1.49/1.32 tff(2576,plain,
% 1.49/1.32 ((~hskp28) | c3_1(a133)),
% 1.49/1.32 inference(modus_ponens,[status(thm)],[2575, 2568])).
% 1.49/1.32 tff(2577,plain,
% 1.49/1.32 ((~hskp28) | c3_1(a133)),
% 1.49/1.32 inference(modus_ponens,[status(thm)],[2576, 2568])).
% 1.49/1.32 tff(2578,plain,
% 1.49/1.32 (c3_1(a133)),
% 1.49/1.32 inference(unit_resolution,[status(thm)],[2577, 2567])).
% 1.49/1.32 tff(2579,plain,
% 1.49/1.32 (((~hskp28) | c2_1(a133)) <=> ((~hskp28) | c2_1(a133))),
% 1.49/1.32 inference(rewrite,[status(thm)],[])).
% 1.49/1.32 tff(2580,axiom,((~hskp28) | c2_1(a133)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause45')).
% 1.49/1.32 tff(2581,plain,
% 1.49/1.32 ((~hskp28) | c2_1(a133)),
% 1.49/1.32 inference(modus_ponens,[status(thm)],[2580, 2579])).
% 1.49/1.32 tff(2582,plain,
% 1.49/1.32 ((~hskp28) | c2_1(a133)),
% 1.49/1.32 inference(modus_ponens,[status(thm)],[2581, 2579])).
% 1.49/1.32 tff(2583,plain,
% 1.49/1.32 ((~hskp28) | c2_1(a133)),
% 1.49/1.32 inference(modus_ponens,[status(thm)],[2582, 2579])).
% 1.49/1.32 tff(2584,plain,
% 1.49/1.32 ((~hskp28) | c2_1(a133)),
% 1.49/1.32 inference(modus_ponens,[status(thm)],[2583, 2579])).
% 1.49/1.32 tff(2585,plain,
% 1.49/1.32 ((~hskp28) | c2_1(a133)),
% 1.49/1.32 inference(modus_ponens,[status(thm)],[2584, 2579])).
% 1.49/1.32 tff(2586,plain,
% 1.49/1.32 ((~hskp28) | c2_1(a133)),
% 1.49/1.32 inference(modus_ponens,[status(thm)],[2585, 2579])).
% 1.49/1.32 tff(2587,plain,
% 1.49/1.32 ((~hskp28) | c2_1(a133)),
% 1.49/1.32 inference(modus_ponens,[status(thm)],[2586, 2579])).
% 1.49/1.32 tff(2588,plain,
% 1.49/1.32 ((~hskp28) | c2_1(a133)),
% 1.49/1.32 inference(modus_ponens,[status(thm)],[2587, 2579])).
% 1.49/1.32 tff(2589,plain,
% 1.49/1.32 (c2_1(a133)),
% 1.49/1.32 inference(unit_resolution,[status(thm)],[2588, 2567])).
% 1.49/1.32 tff(2590,plain,
% 1.49/1.32 (((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp18 | hskp0 | (~ndr1_0) | c0_1(a133) | (~c2_1(a133)) | (~c3_1(a133)))) <=> ((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp18 | hskp0 | (~ndr1_0) | c0_1(a133) | (~c2_1(a133)) | (~c3_1(a133)))),
% 1.49/1.32 inference(rewrite,[status(thm)],[])).
% 1.49/1.32 tff(2591,plain,
% 1.49/1.32 ((hskp18 | hskp0 | (~ndr1_0) | c0_1(a133) | (~c3_1(a133)) | (~c2_1(a133))) <=> (hskp18 | hskp0 | (~ndr1_0) | c0_1(a133) | (~c2_1(a133)) | (~c3_1(a133)))),
% 1.49/1.32 inference(rewrite,[status(thm)],[])).
% 1.49/1.32 tff(2592,plain,
% 1.49/1.32 (((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp18 | hskp0 | (~ndr1_0) | c0_1(a133) | (~c3_1(a133)) | (~c2_1(a133)))) <=> ((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp18 | hskp0 | (~ndr1_0) | c0_1(a133) | (~c2_1(a133)) | (~c3_1(a133))))),
% 1.49/1.32 inference(monotonicity,[status(thm)],[2591])).
% 1.49/1.32 tff(2593,plain,
% 1.49/1.32 (((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp18 | hskp0 | (~ndr1_0) | c0_1(a133) | (~c3_1(a133)) | (~c2_1(a133)))) <=> ((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp18 | hskp0 | (~ndr1_0) | c0_1(a133) | (~c2_1(a133)) | (~c3_1(a133)))),
% 1.49/1.32 inference(transitivity,[status(thm)],[2592, 2590])).
% 1.49/1.32 tff(2594,plain,
% 1.49/1.32 ((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp18 | hskp0 | (~ndr1_0) | c0_1(a133) | (~c3_1(a133)) | (~c2_1(a133)))),
% 1.49/1.32 inference(quant_inst,[status(thm)],[])).
% 1.49/1.32 tff(2595,plain,
% 1.49/1.32 ((~![U: $i] : (hskp18 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp18 | hskp0 | (~ndr1_0) | c0_1(a133) | (~c2_1(a133)) | (~c3_1(a133))),
% 1.49/1.32 inference(modus_ponens,[status(thm)],[2594, 2593])).
% 1.49/1.32 tff(2596,plain,
% 1.49/1.32 (hskp18 | hskp0 | c0_1(a133)),
% 1.49/1.32 inference(unit_resolution,[status(thm)],[2595, 123, 2589, 2578, 1001])).
% 1.49/1.32 tff(2597,plain,
% 1.49/1.32 (c0_1(a133)),
% 1.49/1.32 inference(unit_resolution,[status(thm)],[2596, 22, 11])).
% 1.49/1.32 tff(2598,plain,
% 1.49/1.32 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))),
% 1.49/1.32 inference(bind,[status(th)],[])).
% 1.49/1.32 tff(2599,plain,
% 1.49/1.32 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.49/1.32 inference(quant_intro,[status(thm)],[2598])).
% 1.49/1.32 tff(2600,plain,
% 1.49/1.32 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.49/1.32 inference(rewrite,[status(thm)],[])).
% 1.49/1.32 tff(2601,plain,
% 1.49/1.32 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp8) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp8))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))))),
% 1.49/1.32 inference(bind,[status(th)],[])).
% 1.49/1.32 tff(2602,plain,
% 1.49/1.32 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.49/1.32 inference(quant_intro,[status(thm)],[2601])).
% 1.49/1.32 tff(2603,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause181')).
% 1.49/1.32 tff(2604,plain,
% 1.49/1.32 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.49/1.32 inference(modus_ponens,[status(thm)],[2603, 2602])).
% 1.49/1.32 tff(2605,plain,
% 1.49/1.32 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.49/1.32 inference(modus_ponens,[status(thm)],[2604, 2600])).
% 1.49/1.32 tff(2606,plain,(
% 1.49/1.32 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.49/1.32 inference(skolemize,[status(sab)],[2605])).
% 1.49/1.32 tff(2607,plain,
% 1.49/1.32 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.49/1.32 inference(modus_ponens,[status(thm)],[2606, 2599])).
% 1.49/1.32 tff(2608,plain,
% 1.49/1.32 (~c3_1(a182)),
% 1.49/1.32 inference(unit_resolution,[status(thm)],[1307, 2540])).
% 1.49/1.32 tff(2609,plain,
% 1.49/1.32 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c0_1(a182) | c2_1(a182) | c3_1(a182) | (~ndr1_0) | (~c0_1(a133)) | (~c2_1(a133)) | (~c3_1(a133)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a182) | c2_1(a182) | c3_1(a182) | (~ndr1_0) | (~c0_1(a133)) | (~c2_1(a133)) | (~c3_1(a133)))),
% 1.49/1.32 inference(rewrite,[status(thm)],[])).
% 1.49/1.32 tff(2610,plain,
% 1.49/1.32 ((hskp8 | (~ndr1_0) | (~c3_1(a133)) | (~c0_1(a133)) | (~c2_1(a133)) | c2_1(a182) | c0_1(a182) | c3_1(a182)) <=> (hskp8 | c0_1(a182) | c2_1(a182) | c3_1(a182) | (~ndr1_0) | (~c0_1(a133)) | (~c2_1(a133)) | (~c3_1(a133)))),
% 1.49/1.32 inference(rewrite,[status(thm)],[])).
% 1.49/1.32 tff(2611,plain,
% 1.49/1.32 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | (~c3_1(a133)) | (~c0_1(a133)) | (~c2_1(a133)) | c2_1(a182) | c0_1(a182) | c3_1(a182))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c0_1(a182) | c2_1(a182) | c3_1(a182) | (~ndr1_0) | (~c0_1(a133)) | (~c2_1(a133)) | (~c3_1(a133))))),
% 1.49/1.32 inference(monotonicity,[status(thm)],[2610])).
% 1.49/1.32 tff(2612,plain,
% 1.49/1.32 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | (~c3_1(a133)) | (~c0_1(a133)) | (~c2_1(a133)) | c2_1(a182) | c0_1(a182) | c3_1(a182))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a182) | c2_1(a182) | c3_1(a182) | (~ndr1_0) | (~c0_1(a133)) | (~c2_1(a133)) | (~c3_1(a133)))),
% 1.49/1.32 inference(transitivity,[status(thm)],[2611, 2609])).
% 1.49/1.32 tff(2613,plain,
% 1.49/1.32 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | (~c3_1(a133)) | (~c0_1(a133)) | (~c2_1(a133)) | c2_1(a182) | c0_1(a182) | c3_1(a182))),
% 1.49/1.32 inference(quant_inst,[status(thm)],[])).
% 1.49/1.32 tff(2614,plain,
% 1.49/1.32 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a182) | c2_1(a182) | c3_1(a182) | (~ndr1_0) | (~c0_1(a133)) | (~c2_1(a133)) | (~c3_1(a133))),
% 1.49/1.32 inference(modus_ponens,[status(thm)],[2613, 2612])).
% 1.49/1.32 tff(2615,plain,
% 1.49/1.32 (hskp8),
% 1.49/1.32 inference(unit_resolution,[status(thm)],[2614, 123, 2589, 2578, 2542, 2541, 2608, 2607, 2597])).
% 1.49/1.32 tff(2616,plain,
% 1.49/1.32 (~c3_1(a134)),
% 1.49/1.32 inference(unit_resolution,[status(thm)],[1615, 2615])).
% 1.49/1.32 tff(2617,plain,
% 1.49/1.32 (~c0_1(a134)),
% 1.49/1.32 inference(unit_resolution,[status(thm)],[1621, 2615])).
% 1.49/1.32 tff(2618,plain,
% 1.49/1.32 (c2_1(a134)),
% 1.49/1.32 inference(unit_resolution,[status(thm)],[1632, 2615])).
% 1.49/1.32 tff(2619,plain,
% 1.49/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a182) | c3_1(a182) | c0_1(a134) | c3_1(a134) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | (~c2_1(a134)) | (~c1_1(a182)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a182) | c3_1(a182) | c0_1(a134) | c3_1(a134) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | (~c2_1(a134)) | (~c1_1(a182)))),
% 1.49/1.32 inference(rewrite,[status(thm)],[])).
% 1.49/1.32 tff(2620,plain,
% 1.49/1.32 (((~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132)) | c2_1(a182) | c3_1(a182) | (~c1_1(a182)) | c0_1(a134) | c3_1(a134) | (~c2_1(a134))) <=> (c2_1(a182) | c3_1(a182) | c0_1(a134) | c3_1(a134) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | (~c2_1(a134)) | (~c1_1(a182)))),
% 1.49/1.32 inference(rewrite,[status(thm)],[])).
% 1.49/1.32 tff(2621,plain,
% 1.49/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132)) | c2_1(a182) | c3_1(a182) | (~c1_1(a182)) | c0_1(a134) | c3_1(a134) | (~c2_1(a134)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a182) | c3_1(a182) | c0_1(a134) | c3_1(a134) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | (~c2_1(a134)) | (~c1_1(a182))))),
% 1.49/1.32 inference(monotonicity,[status(thm)],[2620])).
% 1.49/1.32 tff(2622,plain,
% 1.49/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132)) | c2_1(a182) | c3_1(a182) | (~c1_1(a182)) | c0_1(a134) | c3_1(a134) | (~c2_1(a134)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a182) | c3_1(a182) | c0_1(a134) | c3_1(a134) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | (~c2_1(a134)) | (~c1_1(a182)))),
% 1.49/1.32 inference(transitivity,[status(thm)],[2621, 2619])).
% 1.49/1.32 tff(2623,plain,
% 1.49/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a132) | (~c3_1(a132)) | (~c1_1(a132)) | c2_1(a182) | c3_1(a182) | (~c1_1(a182)) | c0_1(a134) | c3_1(a134) | (~c2_1(a134)))),
% 1.49/1.32 inference(quant_inst,[status(thm)],[])).
% 1.49/1.32 tff(2624,plain,
% 1.49/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a182) | c3_1(a182) | c0_1(a134) | c3_1(a134) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a132)) | (~c2_1(a134)) | (~c1_1(a182))),
% 1.49/1.32 inference(modus_ponens,[status(thm)],[2623, 2622])).
% 1.49/1.32 tff(2625,plain,
% 1.49/1.32 ($false),
% 1.49/1.32 inference(unit_resolution,[status(thm)],[2624, 123, 2618, 2512, 2541, 2608, 2617, 2616, 2511, 1482, 2514, 2550])).
% 1.49/1.32 tff(2626,plain,(hskp18 | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.49/1.32 tff(2627,plain,
% 1.49/1.32 (hskp18),
% 1.49/1.32 inference(unit_resolution,[status(thm)],[2626, 11])).
% 1.49/1.32 tff(2628,plain,
% 1.49/1.32 (hskp12),
% 1.49/1.32 inference(unit_resolution,[status(thm)],[1586, 123, 2512, 2510, 2511, 1446, 2514])).
% 1.49/1.32 tff(2629,plain,
% 1.49/1.32 (~c1_1(a142)),
% 1.49/1.32 inference(unit_resolution,[status(thm)],[150, 2628])).
% 1.49/1.32 tff(2630,plain,
% 1.49/1.32 (c3_1(a142)),
% 1.49/1.32 inference(unit_resolution,[status(thm)],[161, 2628])).
% 1.49/1.32 tff(2631,plain,
% 1.49/1.32 (c0_1(a142)),
% 1.49/1.32 inference(unit_resolution,[status(thm)],[189, 2628])).
% 1.49/1.32 tff(2632,plain,
% 1.49/1.32 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c1_1(a160) | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142)) | (~c3_1(a160)) | c0_1(a160))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c1_1(a160) | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142)) | (~c3_1(a160)) | c0_1(a160))),
% 1.49/1.32 inference(rewrite,[status(thm)],[])).
% 1.49/1.32 tff(2633,plain,
% 1.49/1.32 ((hskp6 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142)) | c1_1(a160) | c0_1(a160) | (~c3_1(a160))) <=> (hskp6 | c1_1(a160) | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142)) | (~c3_1(a160)) | c0_1(a160))),
% 1.49/1.32 inference(rewrite,[status(thm)],[])).
% 1.49/1.32 tff(2634,plain,
% 1.49/1.32 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142)) | c1_1(a160) | c0_1(a160) | (~c3_1(a160)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c1_1(a160) | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142)) | (~c3_1(a160)) | c0_1(a160)))),
% 1.49/1.32 inference(monotonicity,[status(thm)],[2633])).
% 1.49/1.32 tff(2635,plain,
% 1.49/1.32 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142)) | c1_1(a160) | c0_1(a160) | (~c3_1(a160)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c1_1(a160) | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142)) | (~c3_1(a160)) | c0_1(a160))),
% 1.49/1.32 inference(transitivity,[status(thm)],[2634, 2632])).
% 1.49/1.32 tff(2636,plain,
% 1.49/1.32 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a142) | (~c3_1(a142)) | (~c0_1(a142)) | c1_1(a160) | c0_1(a160) | (~c3_1(a160)))),
% 1.49/1.32 inference(quant_inst,[status(thm)],[])).
% 1.49/1.32 tff(2637,plain,
% 1.49/1.32 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c1_1(a160) | c1_1(a142) | (~ndr1_0) | (~c3_1(a142)) | (~c0_1(a142)) | (~c3_1(a160)) | c0_1(a160)),
% 1.49/1.32 inference(modus_ponens,[status(thm)],[2636, 2635])).
% 1.49/1.32 tff(2638,plain,
% 1.49/1.32 (c0_1(a160)),
% 1.49/1.32 inference(unit_resolution,[status(thm)],[2637, 123, 1403, 2402, 2631, 2630, 2401, 2629, 1346])).
% 1.49/1.32 tff(2639,plain,
% 1.49/1.32 (~c2_1(a160)),
% 1.49/1.32 inference(unit_resolution,[status(thm)],[1047, 2400])).
% 1.49/1.32 tff(2640,plain,
% 1.49/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a160) | c2_1(a160) | c2_1(a138) | (~ndr1_0) | c3_1(a138) | (~c1_1(a138)) | (~c3_1(a160)) | (~c0_1(a160)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a160) | c2_1(a160) | c2_1(a138) | (~ndr1_0) | c3_1(a138) | (~c1_1(a138)) | (~c3_1(a160)) | (~c0_1(a160)))),
% 1.49/1.32 inference(rewrite,[status(thm)],[])).
% 1.49/1.32 tff(2641,plain,
% 1.49/1.32 (((~ndr1_0) | c2_1(a160) | (~c3_1(a160)) | (~c0_1(a160)) | c2_1(a138) | c3_1(a138) | (~c1_1(a138)) | c2_1(a160) | c1_1(a160) | (~c3_1(a160))) <=> (c1_1(a160) | c2_1(a160) | c2_1(a138) | (~ndr1_0) | c3_1(a138) | (~c1_1(a138)) | (~c3_1(a160)) | (~c0_1(a160)))),
% 1.49/1.32 inference(rewrite,[status(thm)],[])).
% 1.49/1.32 tff(2642,plain,
% 1.49/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a160) | (~c3_1(a160)) | (~c0_1(a160)) | c2_1(a138) | c3_1(a138) | (~c1_1(a138)) | c2_1(a160) | c1_1(a160) | (~c3_1(a160)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a160) | c2_1(a160) | c2_1(a138) | (~ndr1_0) | c3_1(a138) | (~c1_1(a138)) | (~c3_1(a160)) | (~c0_1(a160))))),
% 1.49/1.32 inference(monotonicity,[status(thm)],[2641])).
% 1.49/1.32 tff(2643,plain,
% 1.49/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a160) | (~c3_1(a160)) | (~c0_1(a160)) | c2_1(a138) | c3_1(a138) | (~c1_1(a138)) | c2_1(a160) | c1_1(a160) | (~c3_1(a160)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a160) | c2_1(a160) | c2_1(a138) | (~ndr1_0) | c3_1(a138) | (~c1_1(a138)) | (~c3_1(a160)) | (~c0_1(a160)))),
% 1.49/1.32 inference(transitivity,[status(thm)],[2642, 2640])).
% 1.49/1.32 tff(2644,plain,
% 1.49/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a160) | (~c3_1(a160)) | (~c0_1(a160)) | c2_1(a138) | c3_1(a138) | (~c1_1(a138)) | c2_1(a160) | c1_1(a160) | (~c3_1(a160)))),
% 1.49/1.32 inference(quant_inst,[status(thm)],[])).
% 1.49/1.32 tff(2645,plain,
% 1.49/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a160) | c2_1(a160) | c2_1(a138) | (~ndr1_0) | c3_1(a138) | (~c1_1(a138)) | (~c3_1(a160)) | (~c0_1(a160))),
% 1.49/1.32 inference(modus_ponens,[status(thm)],[2644, 2643])).
% 1.49/1.32 tff(2646,plain,
% 1.49/1.32 ($false),
% 1.49/1.32 inference(unit_resolution,[status(thm)],[2645, 123, 2402, 1961, 2401, 2639, 1950, 1284, 2515, 2638])).
% 1.49/1.32 tff(2647,plain,((~hskp18) | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.49/1.32 tff(2648,plain,
% 1.49/1.32 (hskp6),
% 1.49/1.32 inference(unit_resolution,[status(thm)],[2647, 2627])).
% 1.49/1.32 tff(2649,plain,
% 1.49/1.32 (~c1_1(a131)),
% 1.49/1.32 inference(unit_resolution,[status(thm)],[77, 2648])).
% 1.49/1.32 tff(2650,plain,
% 1.49/1.32 (~c2_1(a131)),
% 1.49/1.32 inference(unit_resolution,[status(thm)],[71, 2648])).
% 1.49/1.32 tff(2651,plain,
% 1.49/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a155) | c2_1(a155) | c2_1(a138) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | c3_1(a138) | (~c0_1(a138)) | (~c1_1(a155)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a155) | c2_1(a155) | c2_1(a138) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | c3_1(a138) | (~c0_1(a138)) | (~c1_1(a155)))),
% 1.49/1.33 inference(rewrite,[status(thm)],[])).
% 1.49/1.33 tff(2652,plain,
% 1.49/1.33 (((~ndr1_0) | c2_1(a138) | c3_1(a138) | (~c0_1(a138)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)) | c2_1(a131) | c1_1(a131) | c0_1(a131)) <=> (c0_1(a155) | c2_1(a155) | c2_1(a138) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | c3_1(a138) | (~c0_1(a138)) | (~c1_1(a155)))),
% 1.49/1.33 inference(rewrite,[status(thm)],[])).
% 1.49/1.33 tff(2653,plain,
% 1.49/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a138) | c3_1(a138) | (~c0_1(a138)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)) | c2_1(a131) | c1_1(a131) | c0_1(a131))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a155) | c2_1(a155) | c2_1(a138) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | c3_1(a138) | (~c0_1(a138)) | (~c1_1(a155))))),
% 1.49/1.33 inference(monotonicity,[status(thm)],[2652])).
% 1.49/1.33 tff(2654,plain,
% 1.49/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a138) | c3_1(a138) | (~c0_1(a138)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)) | c2_1(a131) | c1_1(a131) | c0_1(a131))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a155) | c2_1(a155) | c2_1(a138) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | c3_1(a138) | (~c0_1(a138)) | (~c1_1(a155)))),
% 1.49/1.33 inference(transitivity,[status(thm)],[2653, 2651])).
% 1.49/1.33 tff(2655,plain,
% 1.49/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a138) | c3_1(a138) | (~c0_1(a138)) | c2_1(a155) | c0_1(a155) | (~c1_1(a155)) | c2_1(a131) | c1_1(a131) | c0_1(a131))),
% 1.49/1.33 inference(quant_inst,[status(thm)],[])).
% 1.49/1.33 tff(2656,plain,
% 1.49/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a155) | c2_1(a155) | c2_1(a138) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | c3_1(a138) | (~c0_1(a138)) | (~c1_1(a155))),
% 1.49/1.33 inference(modus_ponens,[status(thm)],[2655, 2654])).
% 1.49/1.33 tff(2657,plain,
% 1.49/1.33 (c0_1(a131) | c1_1(a131)),
% 1.49/1.33 inference(unit_resolution,[status(thm)],[2656, 123, 2392, 1972, 2382, 2381, 1950, 95, 21, 2515])).
% 1.49/1.33 tff(2658,plain,
% 1.49/1.33 (c0_1(a131)),
% 1.49/1.33 inference(unit_resolution,[status(thm)],[2657, 132])).
% 1.49/1.33 tff(2659,plain,
% 1.49/1.33 (((~hskp28) | c1_1(a133)) <=> ((~hskp28) | c1_1(a133))),
% 1.49/1.33 inference(rewrite,[status(thm)],[])).
% 1.49/1.33 tff(2660,axiom,((~hskp28) | c1_1(a133)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause44')).
% 1.49/1.33 tff(2661,plain,
% 1.49/1.33 ((~hskp28) | c1_1(a133)),
% 1.49/1.33 inference(modus_ponens,[status(thm)],[2660, 2659])).
% 1.49/1.33 tff(2662,plain,
% 1.49/1.33 ((~hskp28) | c1_1(a133)),
% 1.49/1.33 inference(modus_ponens,[status(thm)],[2661, 2659])).
% 1.49/1.33 tff(2663,plain,
% 1.49/1.33 ((~hskp28) | c1_1(a133)),
% 1.49/1.33 inference(modus_ponens,[status(thm)],[2662, 2659])).
% 1.49/1.33 tff(2664,plain,
% 1.49/1.33 ((~hskp28) | c1_1(a133)),
% 1.49/1.33 inference(modus_ponens,[status(thm)],[2663, 2659])).
% 1.49/1.33 tff(2665,plain,
% 1.49/1.33 ((~hskp28) | c1_1(a133)),
% 1.49/1.33 inference(modus_ponens,[status(thm)],[2664, 2659])).
% 1.49/1.33 tff(2666,plain,
% 1.49/1.33 ((~hskp28) | c1_1(a133)),
% 1.49/1.33 inference(modus_ponens,[status(thm)],[2665, 2659])).
% 1.49/1.33 tff(2667,plain,
% 1.49/1.33 ((~hskp28) | c1_1(a133)),
% 1.49/1.33 inference(modus_ponens,[status(thm)],[2666, 2659])).
% 1.49/1.33 tff(2668,plain,
% 1.49/1.33 ((~hskp28) | c1_1(a133)),
% 1.49/1.33 inference(modus_ponens,[status(thm)],[2667, 2659])).
% 1.57/1.33 tff(2669,plain,
% 1.57/1.33 (c1_1(a133)),
% 1.57/1.33 inference(unit_resolution,[status(thm)],[2668, 2567])).
% 1.57/1.33 tff(2670,plain,
% 1.57/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a153) | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c0_1(a133)) | (~c1_1(a133)) | (~c3_1(a133)) | (~c2_1(a153)) | (~c3_1(a153)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a153) | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c0_1(a133)) | (~c1_1(a133)) | (~c3_1(a133)) | (~c2_1(a153)) | (~c3_1(a153)))),
% 1.57/1.33 inference(rewrite,[status(thm)],[])).
% 1.57/1.33 tff(2671,plain,
% 1.57/1.33 (((~ndr1_0) | (~c3_1(a133)) | (~c1_1(a133)) | (~c0_1(a133)) | c2_1(a131) | c1_1(a131) | (~c0_1(a131)) | c0_1(a153) | (~c3_1(a153)) | (~c2_1(a153))) <=> (c0_1(a153) | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c0_1(a133)) | (~c1_1(a133)) | (~c3_1(a133)) | (~c2_1(a153)) | (~c3_1(a153)))),
% 1.57/1.33 inference(rewrite,[status(thm)],[])).
% 1.57/1.33 tff(2672,plain,
% 1.57/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a133)) | (~c1_1(a133)) | (~c0_1(a133)) | c2_1(a131) | c1_1(a131) | (~c0_1(a131)) | c0_1(a153) | (~c3_1(a153)) | (~c2_1(a153)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a153) | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c0_1(a133)) | (~c1_1(a133)) | (~c3_1(a133)) | (~c2_1(a153)) | (~c3_1(a153))))),
% 1.57/1.33 inference(monotonicity,[status(thm)],[2671])).
% 1.57/1.33 tff(2673,plain,
% 1.57/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a133)) | (~c1_1(a133)) | (~c0_1(a133)) | c2_1(a131) | c1_1(a131) | (~c0_1(a131)) | c0_1(a153) | (~c3_1(a153)) | (~c2_1(a153)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a153) | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c0_1(a133)) | (~c1_1(a133)) | (~c3_1(a133)) | (~c2_1(a153)) | (~c3_1(a153)))),
% 1.57/1.33 inference(transitivity,[status(thm)],[2672, 2670])).
% 1.57/1.33 tff(2674,plain,
% 1.57/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a133)) | (~c1_1(a133)) | (~c0_1(a133)) | c2_1(a131) | c1_1(a131) | (~c0_1(a131)) | c0_1(a153) | (~c3_1(a153)) | (~c2_1(a153)))),
% 1.57/1.33 inference(quant_inst,[status(thm)],[])).
% 1.57/1.33 tff(2675,plain,
% 1.57/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a153) | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c0_1(a133)) | (~c1_1(a133)) | (~c3_1(a133)) | (~c2_1(a153)) | (~c3_1(a153))),
% 1.57/1.33 inference(modus_ponens,[status(thm)],[2674, 2673])).
% 1.57/1.33 tff(2676,plain,
% 1.57/1.33 (~c0_1(a133)),
% 1.57/1.33 inference(unit_resolution,[status(thm)],[2675, 123, 2669, 2578, 2519, 2518, 2517, 2658, 132, 95, 2490])).
% 1.57/1.33 tff(2677,plain,
% 1.57/1.33 (hskp18),
% 1.57/1.33 inference(unit_resolution,[status(thm)],[2469, 123, 11, 2519, 2518, 2517, 1001])).
% 1.57/1.33 tff(2678,plain,
% 1.57/1.33 (~c2_1(a160)),
% 1.57/1.33 inference(unit_resolution,[status(thm)],[1047, 2677])).
% 1.57/1.33 tff(2679,plain,
% 1.57/1.33 (~c1_1(a160)),
% 1.57/1.33 inference(unit_resolution,[status(thm)],[1014, 2677])).
% 1.57/1.33 tff(2680,plain,
% 1.57/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a160) | c2_1(a160) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a133)) | c0_1(a133) | (~c2_1(a133)) | (~c0_1(a160)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a160) | c2_1(a160) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a133)) | c0_1(a133) | (~c2_1(a133)) | (~c0_1(a160)))),
% 1.57/1.33 inference(rewrite,[status(thm)],[])).
% 1.57/1.33 tff(2681,plain,
% 1.57/1.33 (((~ndr1_0) | c2_1(a160) | c1_1(a160) | (~c0_1(a160)) | c0_1(a133) | (~c2_1(a133)) | (~c1_1(a133)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132))) <=> (c1_1(a160) | c2_1(a160) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a133)) | c0_1(a133) | (~c2_1(a133)) | (~c0_1(a160)))),
% 1.57/1.33 inference(rewrite,[status(thm)],[])).
% 1.57/1.33 tff(2682,plain,
% 1.57/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a160) | c1_1(a160) | (~c0_1(a160)) | c0_1(a133) | (~c2_1(a133)) | (~c1_1(a133)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a160) | c2_1(a160) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a133)) | c0_1(a133) | (~c2_1(a133)) | (~c0_1(a160))))),
% 1.57/1.33 inference(monotonicity,[status(thm)],[2681])).
% 1.57/1.33 tff(2683,plain,
% 1.57/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a160) | c1_1(a160) | (~c0_1(a160)) | c0_1(a133) | (~c2_1(a133)) | (~c1_1(a133)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a160) | c2_1(a160) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a133)) | c0_1(a133) | (~c2_1(a133)) | (~c0_1(a160)))),
% 1.57/1.33 inference(transitivity,[status(thm)],[2682, 2680])).
% 1.57/1.33 tff(2684,plain,
% 1.57/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a160) | c1_1(a160) | (~c0_1(a160)) | c0_1(a133) | (~c2_1(a133)) | (~c1_1(a133)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)))),
% 1.57/1.33 inference(quant_inst,[status(thm)],[])).
% 1.57/1.33 tff(2685,plain,
% 1.57/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a160) | c2_1(a160) | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c1_1(a133)) | c0_1(a133) | (~c2_1(a133)) | (~c0_1(a160))),
% 1.57/1.33 inference(modus_ponens,[status(thm)],[2684, 2683])).
% 1.57/1.33 tff(2686,plain,
% 1.57/1.33 (~c0_1(a160)),
% 1.57/1.33 inference(unit_resolution,[status(thm)],[2685, 123, 2669, 2589, 2512, 2679, 2678, 2510, 2511, 798, 2676])).
% 1.57/1.33 tff(2687,plain,
% 1.57/1.33 (c3_1(a160)),
% 1.57/1.33 inference(unit_resolution,[status(thm)],[1025, 2677])).
% 1.57/1.33 tff(2688,plain,
% 1.57/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a160) | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c1_1(a133)) | c0_1(a133) | (~c2_1(a133)) | (~c3_1(a160)) | c0_1(a160))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a160) | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c1_1(a133)) | c0_1(a133) | (~c2_1(a133)) | (~c3_1(a160)) | c0_1(a160))),
% 1.57/1.33 inference(rewrite,[status(thm)],[])).
% 1.57/1.33 tff(2689,plain,
% 1.57/1.33 (((~ndr1_0) | c2_1(a131) | c1_1(a131) | (~c0_1(a131)) | c0_1(a133) | (~c2_1(a133)) | (~c1_1(a133)) | c2_1(a160) | c0_1(a160) | (~c3_1(a160))) <=> (c2_1(a160) | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c1_1(a133)) | c0_1(a133) | (~c2_1(a133)) | (~c3_1(a160)) | c0_1(a160))),
% 1.57/1.33 inference(rewrite,[status(thm)],[])).
% 1.57/1.33 tff(2690,plain,
% 1.57/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a131) | c1_1(a131) | (~c0_1(a131)) | c0_1(a133) | (~c2_1(a133)) | (~c1_1(a133)) | c2_1(a160) | c0_1(a160) | (~c3_1(a160)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a160) | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c1_1(a133)) | c0_1(a133) | (~c2_1(a133)) | (~c3_1(a160)) | c0_1(a160)))),
% 1.57/1.33 inference(monotonicity,[status(thm)],[2689])).
% 1.57/1.33 tff(2691,plain,
% 1.57/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a131) | c1_1(a131) | (~c0_1(a131)) | c0_1(a133) | (~c2_1(a133)) | (~c1_1(a133)) | c2_1(a160) | c0_1(a160) | (~c3_1(a160)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a160) | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c1_1(a133)) | c0_1(a133) | (~c2_1(a133)) | (~c3_1(a160)) | c0_1(a160))),
% 1.57/1.33 inference(transitivity,[status(thm)],[2690, 2688])).
% 1.57/1.33 tff(2692,plain,
% 1.57/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a131) | c1_1(a131) | (~c0_1(a131)) | c0_1(a133) | (~c2_1(a133)) | (~c1_1(a133)) | c2_1(a160) | c0_1(a160) | (~c3_1(a160)))),
% 1.57/1.33 inference(quant_inst,[status(thm)],[])).
% 1.57/1.33 tff(2693,plain,
% 1.57/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a160) | (~c0_1(a131)) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | (~c1_1(a133)) | c0_1(a133) | (~c2_1(a133)) | (~c3_1(a160)) | c0_1(a160)),
% 1.57/1.33 inference(modus_ponens,[status(thm)],[2692, 2691])).
% 1.57/1.33 tff(2694,plain,
% 1.57/1.33 ($false),
% 1.57/1.33 inference(unit_resolution,[status(thm)],[2693, 123, 2669, 2589, 2687, 2678, 2658, 132, 95, 798, 2676, 2686])).
% 1.57/1.33 tff(2695,plain,((~hskp15) | c1_1(a131) | c2_1(a131) | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.57/1.33 tff(2696,plain,
% 1.57/1.33 (~hskp15),
% 1.57/1.33 inference(unit_resolution,[status(thm)],[2695, 132, 95, 11])).
% 1.57/1.33 tff(2697,plain,
% 1.57/1.33 (^[U: $i] : refl((hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))),
% 1.57/1.33 inference(bind,[status(th)],[])).
% 1.57/1.33 tff(2698,plain,
% 1.57/1.33 (![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.57/1.33 inference(quant_intro,[status(thm)],[2697])).
% 1.57/1.33 tff(2699,plain,
% 1.57/1.33 (![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.57/1.33 inference(rewrite,[status(thm)],[])).
% 1.57/1.33 tff(2700,plain,
% 1.57/1.33 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp10) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp10))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp10) | hskp15) <=> ((hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp15))), rewrite(((hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp15) <=> (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp10) | hskp15) <=> (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))))),
% 1.57/1.33 inference(bind,[status(th)],[])).
% 1.57/1.33 tff(2701,plain,
% 1.57/1.33 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp10) | hskp15) <=> ![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.57/1.33 inference(quant_intro,[status(thm)],[2700])).
% 1.57/1.33 tff(2702,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp10) | hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause139')).
% 1.57/1.33 tff(2703,plain,
% 1.57/1.33 (![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.57/1.33 inference(modus_ponens,[status(thm)],[2702, 2701])).
% 1.57/1.33 tff(2704,plain,
% 1.57/1.33 (![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.57/1.33 inference(modus_ponens,[status(thm)],[2703, 2699])).
% 1.57/1.33 tff(2705,plain,(
% 1.57/1.33 ![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.57/1.33 inference(skolemize,[status(sab)],[2704])).
% 1.57/1.33 tff(2706,plain,
% 1.57/1.33 (![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.57/1.33 inference(modus_ponens,[status(thm)],[2705, 2698])).
% 1.57/1.33 tff(2707,plain,
% 1.57/1.33 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp15 | hskp10 | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp15 | hskp10 | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)))),
% 1.57/1.33 inference(rewrite,[status(thm)],[])).
% 1.57/1.33 tff(2708,plain,
% 1.57/1.33 ((hskp15 | hskp10 | (~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132))) <=> (hskp15 | hskp10 | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)))),
% 1.57/1.33 inference(rewrite,[status(thm)],[])).
% 1.57/1.33 tff(2709,plain,
% 1.57/1.33 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp15 | hskp10 | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132))))),
% 1.57/1.33 inference(monotonicity,[status(thm)],[2708])).
% 1.57/1.33 tff(2710,plain,
% 1.57/1.33 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp15 | hskp10 | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132)))),
% 1.57/1.33 inference(transitivity,[status(thm)],[2709, 2707])).
% 1.57/1.33 tff(2711,plain,
% 1.57/1.33 ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)))),
% 1.57/1.33 inference(quant_inst,[status(thm)],[])).
% 1.57/1.33 tff(2712,plain,
% 1.57/1.33 ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp15 | hskp10 | c0_1(a132) | c2_1(a132) | (~ndr1_0) | (~c3_1(a132))),
% 1.57/1.33 inference(modus_ponens,[status(thm)],[2711, 2710])).
% 1.57/1.33 tff(2713,plain,
% 1.57/1.33 (hskp15 | hskp10),
% 1.57/1.33 inference(unit_resolution,[status(thm)],[2712, 123, 2512, 2510, 2511, 2706])).
% 1.57/1.33 tff(2714,plain,
% 1.57/1.33 (hskp10),
% 1.57/1.33 inference(unit_resolution,[status(thm)],[2713, 2696])).
% 1.57/1.33 tff(2715,plain,
% 1.57/1.33 (~c3_1(a140)),
% 1.57/1.33 inference(unit_resolution,[status(thm)],[1844, 2714])).
% 1.57/1.33 tff(2716,plain,
% 1.57/1.33 (~c2_1(a140)),
% 1.57/1.33 inference(unit_resolution,[status(thm)],[1850, 2714])).
% 1.57/1.33 tff(2717,plain,
% 1.57/1.33 (hskp24),
% 1.57/1.33 inference(unit_resolution,[status(thm)],[2539, 2696, 2515])).
% 1.57/1.33 tff(2718,plain,
% 1.57/1.33 (~c2_1(a182)),
% 1.57/1.33 inference(unit_resolution,[status(thm)],[1313, 2717])).
% 1.57/1.33 tff(2719,plain,
% 1.57/1.33 (~c0_1(a182)),
% 1.57/1.33 inference(unit_resolution,[status(thm)],[1326, 2717])).
% 1.57/1.33 tff(2720,plain,
% 1.57/1.33 (c0_1(a140)),
% 1.57/1.33 inference(unit_resolution,[status(thm)],[1861, 2714])).
% 1.57/1.33 tff(2721,plain,
% 1.57/1.33 (c1_1(a182)),
% 1.57/1.33 inference(unit_resolution,[status(thm)],[2549, 123, 2392, 2720, 2719, 2718, 2382, 2381, 2716, 2715, 21])).
% 1.57/1.33 tff(2722,plain,
% 1.57/1.33 ((~c0_1(a131)) | c1_1(a131)),
% 1.57/1.33 inference(unit_resolution,[status(thm)],[1501, 123, 2022, 2392, 2382, 2381, 95, 1160])).
% 1.57/1.33 tff(2723,plain,
% 1.57/1.33 (~c0_1(a131)),
% 1.57/1.33 inference(unit_resolution,[status(thm)],[2722, 132])).
% 1.57/1.33 tff(2724,plain,
% 1.57/1.33 (c0_1(a131) | c1_1(a131) | (~c3_1(a155))),
% 1.57/1.33 inference(unit_resolution,[status(thm)],[423, 123, 2392, 2382, 2381, 95, 406])).
% 1.57/1.33 tff(2725,plain,
% 1.57/1.33 (~c3_1(a155)),
% 1.57/1.33 inference(unit_resolution,[status(thm)],[2724, 2723, 132])).
% 1.57/1.33 tff(2726,plain,
% 1.57/1.33 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c2_1(a155) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | c3_1(a155) | (~c1_1(a155)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c2_1(a155) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | c3_1(a155) | (~c1_1(a155)))),
% 1.57/1.33 inference(rewrite,[status(thm)],[])).
% 1.57/1.33 tff(2727,plain,
% 1.57/1.33 ((hskp0 | (~ndr1_0) | c2_1(a155) | c3_1(a155) | (~c1_1(a155)) | c2_1(a131) | c1_1(a131) | c0_1(a131)) <=> (hskp0 | c2_1(a155) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | c3_1(a155) | (~c1_1(a155)))),
% 1.57/1.33 inference(rewrite,[status(thm)],[])).
% 1.57/1.33 tff(2728,plain,
% 1.57/1.33 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a155) | c3_1(a155) | (~c1_1(a155)) | c2_1(a131) | c1_1(a131) | c0_1(a131))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c2_1(a155) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | c3_1(a155) | (~c1_1(a155))))),
% 1.57/1.33 inference(monotonicity,[status(thm)],[2727])).
% 1.57/1.33 tff(2729,plain,
% 1.57/1.33 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a155) | c3_1(a155) | (~c1_1(a155)) | c2_1(a131) | c1_1(a131) | c0_1(a131))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c2_1(a155) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | c3_1(a155) | (~c1_1(a155)))),
% 1.57/1.33 inference(transitivity,[status(thm)],[2728, 2726])).
% 1.57/1.33 tff(2730,plain,
% 1.57/1.33 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a155) | c3_1(a155) | (~c1_1(a155)) | c2_1(a131) | c1_1(a131) | c0_1(a131))),
% 1.57/1.33 inference(quant_inst,[status(thm)],[])).
% 1.57/1.33 tff(2731,plain,
% 1.57/1.33 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c2_1(a155) | c0_1(a131) | c1_1(a131) | c2_1(a131) | (~ndr1_0) | c3_1(a155) | (~c1_1(a155))),
% 1.57/1.33 inference(modus_ponens,[status(thm)],[2730, 2729])).
% 1.57/1.33 tff(2732,plain,
% 1.57/1.33 (hskp0 | c0_1(a131) | c1_1(a131) | c3_1(a155)),
% 1.57/1.33 inference(unit_resolution,[status(thm)],[2731, 123, 2392, 2381, 95, 2067])).
% 1.57/1.33 tff(2733,plain,
% 1.57/1.33 ($false),
% 1.57/1.33 inference(unit_resolution,[status(thm)],[2732, 2725, 2723, 11, 132])).
% 1.57/1.33 tff(2734,plain,(c1_1(a131) | hskp0 | c2_1(a131) | hskp13), inference(lemma,lemma(discharge,[]))).
% 1.57/1.33 tff(2735,plain,
% 1.57/1.33 (hskp13),
% 1.57/1.33 inference(unit_resolution,[status(thm)],[2734, 132, 11, 95])).
% 1.57/1.33 tff(2736,plain,
% 1.57/1.33 (~c1_1(a143)),
% 1.57/1.33 inference(unit_resolution,[status(thm)],[782, 2735])).
% 1.57/1.33 tff(2737,plain,
% 1.57/1.33 (~hskp6),
% 1.57/1.33 inference(unit_resolution,[status(thm)],[83, 2658])).
% 1.57/1.33 tff(2738,plain,
% 1.57/1.33 (hskp21 | hskp6),
% 1.57/1.33 inference(unit_resolution,[status(thm)],[1528, 123, 2631, 2630, 2629, 1150])).
% 1.57/1.33 tff(2739,plain,
% 1.57/1.33 (hskp21),
% 1.57/1.33 inference(unit_resolution,[status(thm)],[2738, 2737])).
% 1.57/1.33 tff(2740,plain,
% 1.57/1.33 (~c1_1(a170)),
% 1.57/1.33 inference(unit_resolution,[status(thm)],[1534, 2739])).
% 1.57/1.33 tff(2741,plain,
% 1.57/1.33 (c2_1(a143)),
% 1.57/1.33 inference(unit_resolution,[status(thm)],[836, 2735])).
% 1.57/1.33 tff(2742,plain,
% 1.57/1.33 (c2_1(a170)),
% 1.57/1.33 inference(unit_resolution,[status(thm)],[1546, 2739])).
% 1.57/1.33 tff(2743,plain,
% 1.57/1.33 (c0_1(a170)),
% 1.57/1.33 inference(unit_resolution,[status(thm)],[1557, 2739])).
% 1.57/1.33 tff(2744,plain,
% 1.57/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a170) | c1_1(a143) | (~ndr1_0) | (~c1_1(a133)) | (~c2_1(a133)) | (~c3_1(a133)) | (~c2_1(a143)) | c0_1(a143) | (~c2_1(a170)) | (~c0_1(a170)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a170) | c1_1(a143) | (~ndr1_0) | (~c1_1(a133)) | (~c2_1(a133)) | (~c3_1(a133)) | (~c2_1(a143)) | c0_1(a143) | (~c2_1(a170)) | (~c0_1(a170)))),
% 1.57/1.33 inference(rewrite,[status(thm)],[])).
% 1.57/1.33 tff(2745,plain,
% 1.57/1.33 (((~ndr1_0) | (~c3_1(a133)) | (~c1_1(a133)) | (~c2_1(a133)) | c1_1(a170) | (~c2_1(a170)) | (~c0_1(a170)) | c1_1(a143) | c0_1(a143) | (~c2_1(a143))) <=> (c1_1(a170) | c1_1(a143) | (~ndr1_0) | (~c1_1(a133)) | (~c2_1(a133)) | (~c3_1(a133)) | (~c2_1(a143)) | c0_1(a143) | (~c2_1(a170)) | (~c0_1(a170)))),
% 1.57/1.33 inference(rewrite,[status(thm)],[])).
% 1.57/1.33 tff(2746,plain,
% 1.57/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a133)) | (~c1_1(a133)) | (~c2_1(a133)) | c1_1(a170) | (~c2_1(a170)) | (~c0_1(a170)) | c1_1(a143) | c0_1(a143) | (~c2_1(a143)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a170) | c1_1(a143) | (~ndr1_0) | (~c1_1(a133)) | (~c2_1(a133)) | (~c3_1(a133)) | (~c2_1(a143)) | c0_1(a143) | (~c2_1(a170)) | (~c0_1(a170))))),
% 1.57/1.33 inference(monotonicity,[status(thm)],[2745])).
% 1.57/1.33 tff(2747,plain,
% 1.57/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a133)) | (~c1_1(a133)) | (~c2_1(a133)) | c1_1(a170) | (~c2_1(a170)) | (~c0_1(a170)) | c1_1(a143) | c0_1(a143) | (~c2_1(a143)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a170) | c1_1(a143) | (~ndr1_0) | (~c1_1(a133)) | (~c2_1(a133)) | (~c3_1(a133)) | (~c2_1(a143)) | c0_1(a143) | (~c2_1(a170)) | (~c0_1(a170)))),
% 1.57/1.34 inference(transitivity,[status(thm)],[2746, 2744])).
% 1.57/1.34 tff(2748,plain,
% 1.57/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a133)) | (~c1_1(a133)) | (~c2_1(a133)) | c1_1(a170) | (~c2_1(a170)) | (~c0_1(a170)) | c1_1(a143) | c0_1(a143) | (~c2_1(a143)))),
% 1.57/1.34 inference(quant_inst,[status(thm)],[])).
% 1.57/1.34 tff(2749,plain,
% 1.57/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a170) | c1_1(a143) | (~ndr1_0) | (~c1_1(a133)) | (~c2_1(a133)) | (~c3_1(a133)) | (~c2_1(a143)) | c0_1(a143) | (~c2_1(a170)) | (~c0_1(a170))),
% 1.57/1.34 inference(modus_ponens,[status(thm)],[2748, 2747])).
% 1.57/1.34 tff(2750,plain,
% 1.57/1.34 (c0_1(a143)),
% 1.57/1.34 inference(unit_resolution,[status(thm)],[2749, 123, 2669, 2589, 2578, 2743, 2742, 2741, 2740, 2736, 10])).
% 1.57/1.34 tff(2751,plain,
% 1.57/1.34 (~c3_1(a182)),
% 1.57/1.34 inference(unit_resolution,[status(thm)],[1307, 2717])).
% 1.57/1.34 tff(2752,plain,
% 1.57/1.34 (c3_1(a143)),
% 1.57/1.34 inference(unit_resolution,[status(thm)],[825, 2735])).
% 1.57/1.34 tff(2753,plain,
% 1.57/1.34 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c0_1(a182) | c2_1(a182) | c3_1(a182) | (~ndr1_0) | (~c2_1(a143)) | (~c3_1(a143)) | (~c0_1(a143)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a182) | c2_1(a182) | c3_1(a182) | (~ndr1_0) | (~c2_1(a143)) | (~c3_1(a143)) | (~c0_1(a143)))),
% 1.57/1.34 inference(rewrite,[status(thm)],[])).
% 1.57/1.34 tff(2754,plain,
% 1.57/1.34 ((hskp8 | (~ndr1_0) | (~c3_1(a143)) | (~c0_1(a143)) | (~c2_1(a143)) | c2_1(a182) | c0_1(a182) | c3_1(a182)) <=> (hskp8 | c0_1(a182) | c2_1(a182) | c3_1(a182) | (~ndr1_0) | (~c2_1(a143)) | (~c3_1(a143)) | (~c0_1(a143)))),
% 1.57/1.34 inference(rewrite,[status(thm)],[])).
% 1.57/1.34 tff(2755,plain,
% 1.57/1.34 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | (~c3_1(a143)) | (~c0_1(a143)) | (~c2_1(a143)) | c2_1(a182) | c0_1(a182) | c3_1(a182))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c0_1(a182) | c2_1(a182) | c3_1(a182) | (~ndr1_0) | (~c2_1(a143)) | (~c3_1(a143)) | (~c0_1(a143))))),
% 1.57/1.34 inference(monotonicity,[status(thm)],[2754])).
% 1.57/1.34 tff(2756,plain,
% 1.57/1.34 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | (~c3_1(a143)) | (~c0_1(a143)) | (~c2_1(a143)) | c2_1(a182) | c0_1(a182) | c3_1(a182))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a182) | c2_1(a182) | c3_1(a182) | (~ndr1_0) | (~c2_1(a143)) | (~c3_1(a143)) | (~c0_1(a143)))),
% 1.57/1.34 inference(transitivity,[status(thm)],[2755, 2753])).
% 1.57/1.34 tff(2757,plain,
% 1.57/1.34 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | (~c3_1(a143)) | (~c0_1(a143)) | (~c2_1(a143)) | c2_1(a182) | c0_1(a182) | c3_1(a182))),
% 1.57/1.34 inference(quant_inst,[status(thm)],[])).
% 1.57/1.34 tff(2758,plain,
% 1.57/1.34 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a182) | c2_1(a182) | c3_1(a182) | (~ndr1_0) | (~c2_1(a143)) | (~c3_1(a143)) | (~c0_1(a143))),
% 1.57/1.34 inference(modus_ponens,[status(thm)],[2757, 2756])).
% 1.57/1.34 tff(2759,plain,
% 1.57/1.34 (hskp8),
% 1.57/1.34 inference(unit_resolution,[status(thm)],[2758, 123, 2741, 2752, 2719, 2718, 2751, 2607, 2750])).
% 1.57/1.34 tff(2760,plain,
% 1.57/1.34 (~c3_1(a134)),
% 1.57/1.34 inference(unit_resolution,[status(thm)],[1615, 2759])).
% 1.57/1.34 tff(2761,plain,
% 1.57/1.34 (~c0_1(a134)),
% 1.57/1.34 inference(unit_resolution,[status(thm)],[1621, 2759])).
% 1.57/1.34 tff(2762,plain,
% 1.57/1.34 (c2_1(a134)),
% 1.57/1.34 inference(unit_resolution,[status(thm)],[1632, 2759])).
% 1.57/1.34 tff(2763,plain,
% 1.57/1.34 ($false),
% 1.57/1.34 inference(unit_resolution,[status(thm)],[2624, 123, 2762, 2512, 2718, 2751, 2761, 2760, 2511, 1482, 2514, 2721])).
% 1.57/1.34 tff(2764,plain,(c1_1(a131) | c2_1(a131) | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.57/1.34 tff(2765,plain,
% 1.57/1.34 ($false),
% 1.57/1.34 inference(unit_resolution,[status(thm)],[2764, 2650, 2649, 11])).
% 1.57/1.34 tff(2766,plain,(hskp0), inference(lemma,lemma(discharge,[]))).
% 1.57/1.34 tff(2767,plain,
% 1.57/1.34 (~c1_1(a123)),
% 1.57/1.34 inference(unit_resolution,[status(thm)],[202, 2766])).
% 1.57/1.34 tff(2768,plain,
% 1.57/1.34 (~c0_1(a123)),
% 1.57/1.34 inference(unit_resolution,[status(thm)],[236, 2766])).
% 1.57/1.34 tff(2769,plain,
% 1.57/1.34 (c2_1(a123)),
% 1.57/1.34 inference(unit_resolution,[status(thm)],[213, 2766])).
% 1.57/1.34 tff(2770,plain,
% 1.57/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a142) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c2_1(a123)) | (~c1_1(a133)) | (~c2_1(a133)) | (~c3_1(a133)) | (~c2_1(a142)) | (~c0_1(a142)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a142) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c2_1(a123)) | (~c1_1(a133)) | (~c2_1(a133)) | (~c3_1(a133)) | (~c2_1(a142)) | (~c0_1(a142)))),
% 1.57/1.34 inference(rewrite,[status(thm)],[])).
% 1.57/1.34 tff(2771,plain,
% 1.57/1.34 (((~ndr1_0) | (~c3_1(a133)) | (~c1_1(a133)) | (~c2_1(a133)) | c1_1(a142) | (~c2_1(a142)) | (~c0_1(a142)) | c1_1(a123) | c0_1(a123) | (~c2_1(a123))) <=> (c1_1(a142) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c2_1(a123)) | (~c1_1(a133)) | (~c2_1(a133)) | (~c3_1(a133)) | (~c2_1(a142)) | (~c0_1(a142)))),
% 1.57/1.34 inference(rewrite,[status(thm)],[])).
% 1.57/1.34 tff(2772,plain,
% 1.57/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a133)) | (~c1_1(a133)) | (~c2_1(a133)) | c1_1(a142) | (~c2_1(a142)) | (~c0_1(a142)) | c1_1(a123) | c0_1(a123) | (~c2_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a142) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c2_1(a123)) | (~c1_1(a133)) | (~c2_1(a133)) | (~c3_1(a133)) | (~c2_1(a142)) | (~c0_1(a142))))),
% 1.57/1.34 inference(monotonicity,[status(thm)],[2771])).
% 1.57/1.34 tff(2773,plain,
% 1.57/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a133)) | (~c1_1(a133)) | (~c2_1(a133)) | c1_1(a142) | (~c2_1(a142)) | (~c0_1(a142)) | c1_1(a123) | c0_1(a123) | (~c2_1(a123)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a142) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c2_1(a123)) | (~c1_1(a133)) | (~c2_1(a133)) | (~c3_1(a133)) | (~c2_1(a142)) | (~c0_1(a142)))),
% 1.57/1.34 inference(transitivity,[status(thm)],[2772, 2770])).
% 1.57/1.34 tff(2774,plain,
% 1.57/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a133)) | (~c1_1(a133)) | (~c2_1(a133)) | c1_1(a142) | (~c2_1(a142)) | (~c0_1(a142)) | c1_1(a123) | c0_1(a123) | (~c2_1(a123)))),
% 1.57/1.34 inference(quant_inst,[status(thm)],[])).
% 1.57/1.34 tff(2775,plain,
% 1.57/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a142) | c0_1(a123) | c1_1(a123) | (~ndr1_0) | (~c2_1(a123)) | (~c1_1(a133)) | (~c2_1(a133)) | (~c3_1(a133)) | (~c2_1(a142)) | (~c0_1(a142))),
% 1.57/1.34 inference(modus_ponens,[status(thm)],[2774, 2773])).
% 1.57/1.34 tff(2776,plain,
% 1.57/1.34 (~c2_1(a142)),
% 1.57/1.34 inference(unit_resolution,[status(thm)],[2775, 123, 2669, 2589, 2578, 2631, 2769, 2629, 2768, 2767, 10])).
% 1.57/1.34 tff(2777,plain,
% 1.57/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a142) | c2_1(a138) | (~ndr1_0) | c3_1(a138) | (~c1_1(a138)) | c2_1(a142) | (~c3_1(a142)) | (~c0_1(a142)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a142) | c2_1(a138) | (~ndr1_0) | c3_1(a138) | (~c1_1(a138)) | c2_1(a142) | (~c3_1(a142)) | (~c0_1(a142)))),
% 1.57/1.34 inference(rewrite,[status(thm)],[])).
% 1.57/1.34 tff(2778,plain,
% 1.57/1.34 (((~ndr1_0) | c2_1(a142) | (~c3_1(a142)) | (~c0_1(a142)) | c2_1(a138) | c3_1(a138) | (~c1_1(a138)) | c2_1(a142) | c1_1(a142) | (~c3_1(a142))) <=> (c1_1(a142) | c2_1(a138) | (~ndr1_0) | c3_1(a138) | (~c1_1(a138)) | c2_1(a142) | (~c3_1(a142)) | (~c0_1(a142)))),
% 1.57/1.34 inference(rewrite,[status(thm)],[])).
% 1.57/1.34 tff(2779,plain,
% 1.57/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a142) | (~c3_1(a142)) | (~c0_1(a142)) | c2_1(a138) | c3_1(a138) | (~c1_1(a138)) | c2_1(a142) | c1_1(a142) | (~c3_1(a142)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a142) | c2_1(a138) | (~ndr1_0) | c3_1(a138) | (~c1_1(a138)) | c2_1(a142) | (~c3_1(a142)) | (~c0_1(a142))))),
% 1.57/1.34 inference(monotonicity,[status(thm)],[2778])).
% 1.57/1.34 tff(2780,plain,
% 1.57/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a142) | (~c3_1(a142)) | (~c0_1(a142)) | c2_1(a138) | c3_1(a138) | (~c1_1(a138)) | c2_1(a142) | c1_1(a142) | (~c3_1(a142)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a142) | c2_1(a138) | (~ndr1_0) | c3_1(a138) | (~c1_1(a138)) | c2_1(a142) | (~c3_1(a142)) | (~c0_1(a142)))),
% 1.57/1.34 inference(transitivity,[status(thm)],[2779, 2777])).
% 1.57/1.34 tff(2781,plain,
% 1.57/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a142) | (~c3_1(a142)) | (~c0_1(a142)) | c2_1(a138) | c3_1(a138) | (~c1_1(a138)) | c2_1(a142) | c1_1(a142) | (~c3_1(a142)))),
% 1.57/1.34 inference(quant_inst,[status(thm)],[])).
% 1.57/1.34 tff(2782,plain,
% 1.57/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a142) | c2_1(a138) | (~ndr1_0) | c3_1(a138) | (~c1_1(a138)) | c2_1(a142) | (~c3_1(a142)) | (~c0_1(a142))),
% 1.57/1.34 inference(modus_ponens,[status(thm)],[2781, 2780])).
% 1.57/1.34 tff(2783,plain,
% 1.57/1.34 ($false),
% 1.57/1.34 inference(unit_resolution,[status(thm)],[2782, 123, 2631, 2630, 1961, 2629, 1950, 1284, 2515, 2776])).
% 1.57/1.34 % SZS output end Proof
%------------------------------------------------------------------------------