TSTP Solution File: SYN501-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN501-1 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 23:55:59 EDT 2022
% Result : Unsatisfiable 1.47s 1.22s
% Output : Proof 1.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN501-1 : TPTP v8.1.0. Released v2.1.0.
% 0.06/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.35 % Computer : n022.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Mon Sep 5 04:43:09 EDT 2022
% 0.12/0.35 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 1.47/1.22 % SZS status Unsatisfiable
% 1.47/1.22 % SZS output start Proof
% 1.47/1.22 tff(c3_1_type, type, (
% 1.47/1.22 c3_1: $i > $o)).
% 1.47/1.22 tff(a108_type, type, (
% 1.47/1.22 a108: $i)).
% 1.47/1.22 tff(a129_type, type, (
% 1.47/1.22 a129: $i)).
% 1.47/1.22 tff(c2_1_type, type, (
% 1.47/1.22 c2_1: $i > $o)).
% 1.47/1.22 tff(c0_1_type, type, (
% 1.47/1.22 c0_1: $i > $o)).
% 1.47/1.22 tff(c1_1_type, type, (
% 1.47/1.22 c1_1: $i > $o)).
% 1.47/1.22 tff(ndr1_0_type, type, (
% 1.47/1.22 ndr1_0: $o)).
% 1.47/1.22 tff(hskp18_type, type, (
% 1.47/1.22 hskp18: $o)).
% 1.47/1.22 tff(a130_type, type, (
% 1.47/1.22 a130: $i)).
% 1.47/1.22 tff(a132_type, type, (
% 1.47/1.22 a132: $i)).
% 1.47/1.22 tff(hskp19_type, type, (
% 1.47/1.22 hskp19: $o)).
% 1.47/1.22 tff(hskp20_type, type, (
% 1.47/1.22 hskp20: $o)).
% 1.47/1.22 tff(hskp4_type, type, (
% 1.47/1.22 hskp4: $o)).
% 1.47/1.22 tff(hskp0_type, type, (
% 1.47/1.22 hskp0: $o)).
% 1.47/1.22 tff(a97_type, type, (
% 1.47/1.22 a97: $i)).
% 1.47/1.22 tff(a124_type, type, (
% 1.47/1.22 a124: $i)).
% 1.47/1.22 tff(hskp17_type, type, (
% 1.47/1.22 hskp17: $o)).
% 1.47/1.22 tff(a106_type, type, (
% 1.47/1.22 a106: $i)).
% 1.47/1.22 tff(hskp7_type, type, (
% 1.47/1.22 hskp7: $o)).
% 1.47/1.22 tff(a138_type, type, (
% 1.47/1.22 a138: $i)).
% 1.47/1.22 tff(a137_type, type, (
% 1.47/1.22 a137: $i)).
% 1.47/1.22 tff(hskp28_type, type, (
% 1.47/1.22 hskp28: $o)).
% 1.47/1.22 tff(a103_type, type, (
% 1.47/1.22 a103: $i)).
% 1.47/1.22 tff(a112_type, type, (
% 1.47/1.22 a112: $i)).
% 1.47/1.22 tff(hskp11_type, type, (
% 1.47/1.22 hskp11: $o)).
% 1.47/1.22 tff(hskp22_type, type, (
% 1.47/1.22 hskp22: $o)).
% 1.47/1.22 tff(a173_type, type, (
% 1.47/1.22 a173: $i)).
% 1.47/1.22 tff(a136_type, type, (
% 1.47/1.22 a136: $i)).
% 1.47/1.22 tff(hskp16_type, type, (
% 1.47/1.22 hskp16: $o)).
% 1.47/1.22 tff(a122_type, type, (
% 1.47/1.22 a122: $i)).
% 1.47/1.22 tff(hskp21_type, type, (
% 1.47/1.22 hskp21: $o)).
% 1.47/1.22 tff(hskp25_type, type, (
% 1.47/1.22 hskp25: $o)).
% 1.47/1.22 tff(a105_type, type, (
% 1.47/1.22 a105: $i)).
% 1.47/1.22 tff(hskp6_type, type, (
% 1.47/1.22 hskp6: $o)).
% 1.47/1.22 tff(hskp2_type, type, (
% 1.47/1.22 hskp2: $o)).
% 1.47/1.22 tff(a99_type, type, (
% 1.47/1.22 a99: $i)).
% 1.47/1.22 tff(a107_type, type, (
% 1.47/1.22 a107: $i)).
% 1.47/1.22 tff(hskp8_type, type, (
% 1.47/1.22 hskp8: $o)).
% 1.47/1.22 tff(a104_type, type, (
% 1.47/1.22 a104: $i)).
% 1.47/1.22 tff(hskp5_type, type, (
% 1.47/1.22 hskp5: $o)).
% 1.47/1.22 tff(hskp9_type, type, (
% 1.47/1.22 hskp9: $o)).
% 1.47/1.22 tff(a98_type, type, (
% 1.47/1.22 a98: $i)).
% 1.47/1.22 tff(hskp1_type, type, (
% 1.47/1.22 hskp1: $o)).
% 1.47/1.22 tff(a101_type, type, (
% 1.47/1.22 a101: $i)).
% 1.47/1.22 tff(hskp27_type, type, (
% 1.47/1.22 hskp27: $o)).
% 1.47/1.22 tff(a147_type, type, (
% 1.47/1.22 a147: $i)).
% 1.47/1.22 tff(hskp24_type, type, (
% 1.47/1.22 hskp24: $o)).
% 1.47/1.22 tff(1,plain,
% 1.47/1.22 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W))))),
% 1.47/1.22 inference(bind,[status(th)],[])).
% 1.47/1.22 tff(2,plain,
% 1.47/1.22 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 1.47/1.22 inference(quant_intro,[status(thm)],[1])).
% 1.47/1.22 tff(3,plain,
% 1.47/1.22 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 1.47/1.22 inference(rewrite,[status(thm)],[])).
% 1.47/1.22 tff(4,plain,
% 1.47/1.22 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_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)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c1_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c1_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))))),
% 1.47/1.22 inference(bind,[status(th)],[])).
% 1.47/1.22 tff(5,plain,
% 1.47/1.22 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c1_1(V)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 1.47/1.22 inference(quant_intro,[status(thm)],[4])).
% 1.47/1.22 tff(6,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c1_1(V)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause199')).
% 1.47/1.22 tff(7,plain,
% 1.47/1.22 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 1.47/1.22 inference(modus_ponens,[status(thm)],[6, 5])).
% 1.47/1.22 tff(8,plain,
% 1.47/1.22 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 1.47/1.22 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.47/1.22 tff(9,plain,(
% 1.47/1.22 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 1.47/1.22 inference(skolemize,[status(sab)],[8])).
% 1.47/1.22 tff(10,plain,
% 1.47/1.22 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 1.47/1.22 inference(modus_ponens,[status(thm)],[9, 2])).
% 1.47/1.22 tff(11,plain,
% 1.47/1.22 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W))))),
% 1.47/1.22 inference(bind,[status(th)],[])).
% 1.47/1.22 tff(12,plain,
% 1.47/1.22 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_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) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.47/1.22 inference(quant_intro,[status(thm)],[11])).
% 1.47/1.22 tff(13,plain,
% 1.47/1.22 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_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) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.47/1.22 inference(rewrite,[status(thm)],[])).
% 1.47/1.22 tff(14,plain,
% 1.47/1.22 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c0_1(W)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c0_1(W))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c0_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c0_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c0_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c0_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c0_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c0_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c0_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_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) | (~c0_1(V)) | (~c0_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c0_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c0_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_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) | (~c0_1(V)) | (~c0_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))))),
% 1.47/1.22 inference(bind,[status(th)],[])).
% 1.47/1.22 tff(15,plain,
% 1.47/1.22 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.47/1.22 inference(quant_intro,[status(thm)],[14])).
% 1.47/1.22 tff(16,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause193')).
% 1.47/1.22 tff(17,plain,
% 1.47/1.22 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.47/1.22 inference(modus_ponens,[status(thm)],[16, 15])).
% 1.47/1.22 tff(18,plain,
% 1.47/1.22 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.47/1.22 inference(modus_ponens,[status(thm)],[17, 13])).
% 1.47/1.22 tff(19,plain,(
% 1.47/1.22 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.47/1.22 inference(skolemize,[status(sab)],[18])).
% 1.47/1.22 tff(20,plain,
% 1.47/1.22 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.47/1.22 inference(modus_ponens,[status(thm)],[19, 12])).
% 1.47/1.22 tff(21,plain,
% 1.47/1.22 (^[U: $i] : refl((hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))),
% 1.47/1.22 inference(bind,[status(th)],[])).
% 1.47/1.22 tff(22,plain,
% 1.47/1.22 (![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> ![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.47/1.22 inference(quant_intro,[status(thm)],[21])).
% 1.47/1.22 tff(23,plain,
% 1.47/1.22 (![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> ![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.47/1.22 inference(rewrite,[status(thm)],[])).
% 1.47/1.22 tff(24,plain,
% 1.47/1.22 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U)))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp18) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp18))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp18) <=> (hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp18) <=> (hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp18) | hskp19) <=> ((hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp19))), rewrite(((hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp19) <=> (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp18) | hskp19) <=> (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))))),
% 1.47/1.22 inference(bind,[status(th)],[])).
% 1.47/1.22 tff(25,plain,
% 1.47/1.22 (![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp18) | hskp19) <=> ![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.47/1.22 inference(quant_intro,[status(thm)],[24])).
% 1.47/1.22 tff(26,axiom,(![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp18) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause135')).
% 1.47/1.22 tff(27,plain,
% 1.47/1.22 (![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.47/1.22 inference(modus_ponens,[status(thm)],[26, 25])).
% 1.47/1.22 tff(28,plain,
% 1.47/1.22 (![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.47/1.22 inference(modus_ponens,[status(thm)],[27, 23])).
% 1.47/1.22 tff(29,plain,(
% 1.47/1.22 ![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.47/1.22 inference(skolemize,[status(sab)],[28])).
% 1.47/1.22 tff(30,plain,
% 1.47/1.22 (![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.47/1.22 inference(modus_ponens,[status(thm)],[29, 22])).
% 1.47/1.22 tff(31,assumption,(~c2_1(a97)), introduced(assumption)).
% 1.47/1.22 tff(32,plain,
% 1.47/1.22 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 1.47/1.22 inference(bind,[status(th)],[])).
% 1.47/1.22 tff(33,plain,
% 1.47/1.22 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.47/1.22 inference(quant_intro,[status(thm)],[32])).
% 1.47/1.22 tff(34,plain,
% 1.47/1.22 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.47/1.22 inference(rewrite,[status(thm)],[])).
% 1.47/1.22 tff(35,plain,
% 1.47/1.22 (^[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(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c0_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c0_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_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) | (~c0_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp4) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp4))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 1.47/1.22 inference(bind,[status(th)],[])).
% 1.47/1.22 tff(36,plain,
% 1.47/1.22 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.47/1.22 inference(quant_intro,[status(thm)],[35])).
% 1.47/1.22 tff(37,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause168')).
% 1.47/1.22 tff(38,plain,
% 1.47/1.22 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.47/1.22 inference(modus_ponens,[status(thm)],[37, 36])).
% 1.47/1.22 tff(39,plain,
% 1.47/1.22 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.47/1.22 inference(modus_ponens,[status(thm)],[38, 34])).
% 1.47/1.22 tff(40,plain,(
% 1.47/1.22 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.47/1.22 inference(skolemize,[status(sab)],[39])).
% 1.47/1.22 tff(41,plain,
% 1.47/1.22 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.47/1.22 inference(modus_ponens,[status(thm)],[40, 33])).
% 1.47/1.22 tff(42,plain,
% 1.47/1.22 (^[V: $i, U: $i] : refl((hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> (hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))),
% 1.47/1.22 inference(bind,[status(th)],[])).
% 1.47/1.22 tff(43,plain,
% 1.47/1.22 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.47/1.22 inference(quant_intro,[status(thm)],[42])).
% 1.47/1.22 tff(44,plain,
% 1.47/1.22 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.47/1.22 inference(rewrite,[status(thm)],[])).
% 1.47/1.22 tff(45,plain,
% 1.47/1.22 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V))), (((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V)))), ((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V))), ((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V)))), (((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), ((((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp17) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp17))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp17) <=> (hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))))),
% 1.47/1.23 inference(bind,[status(th)],[])).
% 1.47/1.23 tff(46,plain,
% 1.47/1.23 (![V: $i, U: $i] : ((((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp17) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.47/1.23 inference(quant_intro,[status(thm)],[45])).
% 1.47/1.23 tff(47,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause166')).
% 1.47/1.23 tff(48,plain,
% 1.47/1.23 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[47, 46])).
% 1.47/1.23 tff(49,plain,
% 1.47/1.23 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[48, 44])).
% 1.47/1.23 tff(50,plain,(
% 1.47/1.23 ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.47/1.23 inference(skolemize,[status(sab)],[49])).
% 1.47/1.23 tff(51,plain,
% 1.47/1.23 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[50, 43])).
% 1.47/1.23 tff(52,assumption,(~hskp18), introduced(assumption)).
% 1.47/1.23 tff(53,assumption,(~c3_1(a97)), introduced(assumption)).
% 1.47/1.23 tff(54,assumption,(~c0_1(a97)), introduced(assumption)).
% 1.47/1.23 tff(55,plain,
% 1.47/1.23 (((~hskp0) | c0_1(a97)) <=> ((~hskp0) | c0_1(a97))),
% 1.47/1.23 inference(rewrite,[status(thm)],[])).
% 1.47/1.23 tff(56,axiom,((~hskp0) | c0_1(a97)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause86')).
% 1.47/1.23 tff(57,plain,
% 1.47/1.23 ((~hskp0) | c0_1(a97)),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[56, 55])).
% 1.47/1.23 tff(58,plain,
% 1.47/1.23 ((~hskp0) | c0_1(a97)),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[57, 55])).
% 1.47/1.23 tff(59,plain,
% 1.47/1.23 ((~hskp0) | c0_1(a97)),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[58, 55])).
% 1.47/1.23 tff(60,plain,
% 1.47/1.23 ((~hskp0) | c0_1(a97)),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[59, 55])).
% 1.47/1.23 tff(61,plain,
% 1.47/1.23 ((~hskp0) | c0_1(a97)),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[60, 55])).
% 1.47/1.23 tff(62,plain,
% 1.47/1.23 ((~hskp0) | c0_1(a97)),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[61, 55])).
% 1.47/1.23 tff(63,plain,
% 1.47/1.23 ((~hskp0) | c0_1(a97)),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[62, 55])).
% 1.47/1.23 tff(64,plain,
% 1.47/1.23 ((~hskp0) | c0_1(a97)),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[63, 55])).
% 1.47/1.23 tff(65,plain,
% 1.47/1.23 (~hskp0),
% 1.47/1.23 inference(unit_resolution,[status(thm)],[64, 54])).
% 1.47/1.23 tff(66,plain,
% 1.47/1.23 (^[U: $i] : refl((hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))))),
% 1.47/1.23 inference(bind,[status(th)],[])).
% 1.47/1.23 tff(67,plain,
% 1.47/1.23 (![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.47/1.23 inference(quant_intro,[status(thm)],[66])).
% 1.47/1.23 tff(68,plain,
% 1.47/1.23 (![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.47/1.23 inference(rewrite,[status(thm)],[])).
% 1.47/1.23 tff(69,plain,
% 1.47/1.23 (^[U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp0) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp0))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))))),
% 1.47/1.23 inference(bind,[status(th)],[])).
% 1.47/1.23 tff(70,plain,
% 1.47/1.23 (![U: $i] : (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp0) <=> ![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.47/1.23 inference(quant_intro,[status(thm)],[69])).
% 1.47/1.23 tff(71,axiom,(![U: $i] : (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause149')).
% 1.47/1.23 tff(72,plain,
% 1.47/1.23 (![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[71, 70])).
% 1.47/1.23 tff(73,plain,
% 1.47/1.23 (![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[72, 68])).
% 1.47/1.23 tff(74,plain,(
% 1.47/1.23 ![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.47/1.23 inference(skolemize,[status(sab)],[73])).
% 1.47/1.23 tff(75,plain,
% 1.47/1.23 (![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[74, 67])).
% 1.47/1.23 tff(76,assumption,(hskp4), introduced(assumption)).
% 1.47/1.23 tff(77,plain,
% 1.47/1.23 (((~hskp4) | (~c3_1(a103))) <=> ((~hskp4) | (~c3_1(a103)))),
% 1.47/1.23 inference(rewrite,[status(thm)],[])).
% 1.47/1.23 tff(78,plain,
% 1.47/1.23 (((~c3_1(a103)) | (~hskp4)) <=> ((~hskp4) | (~c3_1(a103)))),
% 1.47/1.23 inference(rewrite,[status(thm)],[])).
% 1.47/1.23 tff(79,axiom,((~c3_1(a103)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause125')).
% 1.47/1.23 tff(80,plain,
% 1.47/1.23 ((~hskp4) | (~c3_1(a103))),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[79, 78])).
% 1.47/1.23 tff(81,plain,
% 1.47/1.23 ((~hskp4) | (~c3_1(a103))),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[80, 77])).
% 1.47/1.23 tff(82,plain,
% 1.47/1.23 (~c3_1(a103)),
% 1.47/1.23 inference(unit_resolution,[status(thm)],[81, 76])).
% 1.47/1.23 tff(83,plain,
% 1.47/1.23 (((~hskp4) | c0_1(a103)) <=> ((~hskp4) | c0_1(a103))),
% 1.47/1.23 inference(rewrite,[status(thm)],[])).
% 1.47/1.23 tff(84,axiom,((~hskp4) | c0_1(a103)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause80')).
% 1.47/1.23 tff(85,plain,
% 1.47/1.23 ((~hskp4) | c0_1(a103)),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[84, 83])).
% 1.47/1.23 tff(86,plain,
% 1.47/1.23 ((~hskp4) | c0_1(a103)),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[85, 83])).
% 1.47/1.23 tff(87,plain,
% 1.47/1.23 ((~hskp4) | c0_1(a103)),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[86, 83])).
% 1.47/1.23 tff(88,plain,
% 1.47/1.23 ((~hskp4) | c0_1(a103)),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[87, 83])).
% 1.47/1.23 tff(89,plain,
% 1.47/1.23 ((~hskp4) | c0_1(a103)),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[88, 83])).
% 1.47/1.23 tff(90,plain,
% 1.47/1.23 ((~hskp4) | c0_1(a103)),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[89, 83])).
% 1.47/1.23 tff(91,plain,
% 1.47/1.23 ((~hskp4) | c0_1(a103)),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[90, 83])).
% 1.47/1.23 tff(92,plain,
% 1.47/1.23 ((~hskp4) | c0_1(a103)),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[91, 83])).
% 1.47/1.23 tff(93,plain,
% 1.47/1.23 (c0_1(a103)),
% 1.47/1.23 inference(unit_resolution,[status(thm)],[92, 76])).
% 1.47/1.23 tff(94,assumption,(~hskp0), introduced(assumption)).
% 1.47/1.23 tff(95,assumption,(~ndr1_0), introduced(assumption)).
% 1.47/1.23 tff(96,plain,
% 1.47/1.23 ((ndr1_0 | (~hskp4)) <=> (ndr1_0 | (~hskp4))),
% 1.47/1.23 inference(rewrite,[status(thm)],[])).
% 1.47/1.23 tff(97,plain,
% 1.47/1.23 (((~hskp4) | ndr1_0) <=> (ndr1_0 | (~hskp4))),
% 1.47/1.23 inference(rewrite,[status(thm)],[])).
% 1.47/1.23 tff(98,axiom,((~hskp4) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause27')).
% 1.47/1.23 tff(99,plain,
% 1.47/1.23 (ndr1_0 | (~hskp4)),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[98, 97])).
% 1.47/1.23 tff(100,plain,
% 1.47/1.23 (ndr1_0 | (~hskp4)),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[99, 96])).
% 1.47/1.23 tff(101,plain,
% 1.47/1.23 (~hskp4),
% 1.47/1.23 inference(unit_resolution,[status(thm)],[100, 95])).
% 1.47/1.23 tff(102,plain,
% 1.47/1.23 ((ndr1_0 | (~hskp28)) <=> (ndr1_0 | (~hskp28))),
% 1.47/1.23 inference(rewrite,[status(thm)],[])).
% 1.47/1.23 tff(103,plain,
% 1.47/1.23 (((~hskp28) | ndr1_0) <=> (ndr1_0 | (~hskp28))),
% 1.47/1.23 inference(rewrite,[status(thm)],[])).
% 1.47/1.23 tff(104,axiom,((~hskp28) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause3')).
% 1.47/1.23 tff(105,plain,
% 1.47/1.23 (ndr1_0 | (~hskp28)),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[104, 103])).
% 1.47/1.23 tff(106,plain,
% 1.47/1.23 (ndr1_0 | (~hskp28)),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[105, 102])).
% 1.47/1.23 tff(107,plain,
% 1.47/1.23 (~hskp28),
% 1.47/1.23 inference(unit_resolution,[status(thm)],[106, 95])).
% 1.47/1.23 tff(108,plain,
% 1.47/1.23 ((ndr1_0 | (~hskp22)) <=> (ndr1_0 | (~hskp22))),
% 1.47/1.23 inference(rewrite,[status(thm)],[])).
% 1.47/1.23 tff(109,plain,
% 1.47/1.23 (((~hskp22) | ndr1_0) <=> (ndr1_0 | (~hskp22))),
% 1.47/1.23 inference(rewrite,[status(thm)],[])).
% 1.47/1.23 tff(110,axiom,((~hskp22) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause9')).
% 1.47/1.23 tff(111,plain,
% 1.47/1.23 (ndr1_0 | (~hskp22)),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[110, 109])).
% 1.47/1.23 tff(112,plain,
% 1.47/1.23 (ndr1_0 | (~hskp22)),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[111, 108])).
% 1.47/1.23 tff(113,plain,
% 1.47/1.23 (~hskp22),
% 1.47/1.23 inference(unit_resolution,[status(thm)],[112, 95])).
% 1.47/1.23 tff(114,plain,
% 1.47/1.23 ((hskp28 | hskp22 | hskp4) <=> (hskp28 | hskp22 | hskp4)),
% 1.47/1.23 inference(rewrite,[status(thm)],[])).
% 1.47/1.23 tff(115,plain,
% 1.47/1.23 (((hskp28 | hskp4) | hskp22) <=> (hskp28 | hskp22 | hskp4)),
% 1.47/1.23 inference(rewrite,[status(thm)],[])).
% 1.47/1.23 tff(116,axiom,((hskp28 | hskp4) | hskp22), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause32')).
% 1.47/1.23 tff(117,plain,
% 1.47/1.23 (hskp28 | hskp22 | hskp4),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[116, 115])).
% 1.47/1.23 tff(118,plain,
% 1.47/1.23 (hskp28 | hskp22 | hskp4),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[117, 114])).
% 1.47/1.23 tff(119,plain,
% 1.47/1.23 (hskp28 | hskp22 | hskp4),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[118, 114])).
% 1.47/1.23 tff(120,plain,
% 1.47/1.23 (hskp28 | hskp22 | hskp4),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[119, 114])).
% 1.47/1.23 tff(121,plain,
% 1.47/1.23 (hskp28 | hskp22 | hskp4),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[120, 114])).
% 1.47/1.23 tff(122,plain,
% 1.47/1.23 (hskp28 | hskp22 | hskp4),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[121, 114])).
% 1.47/1.23 tff(123,plain,
% 1.47/1.23 (hskp28 | hskp22 | hskp4),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[122, 114])).
% 1.47/1.23 tff(124,plain,
% 1.47/1.23 (hskp28 | hskp22 | hskp4),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[123, 114])).
% 1.47/1.23 tff(125,plain,
% 1.47/1.23 ($false),
% 1.47/1.23 inference(unit_resolution,[status(thm)],[124, 113, 107, 101])).
% 1.47/1.23 tff(126,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 1.47/1.23 tff(127,plain,
% 1.47/1.23 (((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp0 | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | (~c1_1(a103)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp0 | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | (~c1_1(a103)))),
% 1.47/1.23 inference(rewrite,[status(thm)],[])).
% 1.47/1.23 tff(128,plain,
% 1.47/1.23 ((hskp0 | (~ndr1_0) | c3_1(a103) | (~c0_1(a103)) | (~c1_1(a103))) <=> (hskp0 | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | (~c1_1(a103)))),
% 1.47/1.23 inference(rewrite,[status(thm)],[])).
% 1.47/1.23 tff(129,plain,
% 1.47/1.23 (((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp0 | (~ndr1_0) | c3_1(a103) | (~c0_1(a103)) | (~c1_1(a103)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp0 | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | (~c1_1(a103))))),
% 1.47/1.23 inference(monotonicity,[status(thm)],[128])).
% 1.47/1.23 tff(130,plain,
% 1.47/1.23 (((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp0 | (~ndr1_0) | c3_1(a103) | (~c0_1(a103)) | (~c1_1(a103)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp0 | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | (~c1_1(a103)))),
% 1.47/1.23 inference(transitivity,[status(thm)],[129, 127])).
% 1.47/1.23 tff(131,plain,
% 1.47/1.23 ((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp0 | (~ndr1_0) | c3_1(a103) | (~c0_1(a103)) | (~c1_1(a103)))),
% 1.47/1.23 inference(quant_inst,[status(thm)],[])).
% 1.47/1.23 tff(132,plain,
% 1.47/1.23 ((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp0 | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | (~c1_1(a103))),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[131, 130])).
% 1.47/1.23 tff(133,plain,
% 1.47/1.23 (~c1_1(a103)),
% 1.47/1.23 inference(unit_resolution,[status(thm)],[132, 126, 94, 93, 82, 75])).
% 1.47/1.23 tff(134,plain,
% 1.47/1.23 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))))),
% 1.47/1.23 inference(bind,[status(th)],[])).
% 1.47/1.23 tff(135,plain,
% 1.47/1.23 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 1.47/1.23 inference(quant_intro,[status(thm)],[134])).
% 1.47/1.23 tff(136,plain,
% 1.47/1.23 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 1.47/1.23 inference(rewrite,[status(thm)],[])).
% 1.47/1.23 tff(137,plain,
% 1.47/1.23 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c1_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c1_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_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) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))))),
% 1.47/1.23 inference(bind,[status(th)],[])).
% 1.47/1.23 tff(138,plain,
% 1.47/1.23 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 1.47/1.23 inference(quant_intro,[status(thm)],[137])).
% 1.47/1.23 tff(139,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause196')).
% 1.47/1.23 tff(140,plain,
% 1.47/1.23 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[139, 138])).
% 1.47/1.23 tff(141,plain,
% 1.47/1.23 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[140, 136])).
% 1.47/1.23 tff(142,plain,(
% 1.47/1.23 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 1.47/1.23 inference(skolemize,[status(sab)],[141])).
% 1.47/1.23 tff(143,plain,
% 1.47/1.23 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[142, 135])).
% 1.47/1.23 tff(144,assumption,(~hskp22), introduced(assumption)).
% 1.47/1.23 tff(145,assumption,(~hskp28), introduced(assumption)).
% 1.47/1.23 tff(146,plain,
% 1.47/1.23 (hskp4),
% 1.47/1.23 inference(unit_resolution,[status(thm)],[124, 145, 144])).
% 1.47/1.23 tff(147,plain,
% 1.47/1.23 (~c3_1(a103)),
% 1.47/1.23 inference(unit_resolution,[status(thm)],[81, 146])).
% 1.47/1.23 tff(148,plain,
% 1.47/1.23 (((~hskp4) | c2_1(a103)) <=> ((~hskp4) | c2_1(a103))),
% 1.47/1.23 inference(rewrite,[status(thm)],[])).
% 1.47/1.23 tff(149,axiom,((~hskp4) | c2_1(a103)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause81')).
% 1.47/1.23 tff(150,plain,
% 1.47/1.23 ((~hskp4) | c2_1(a103)),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[149, 148])).
% 1.47/1.23 tff(151,plain,
% 1.47/1.23 ((~hskp4) | c2_1(a103)),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[150, 148])).
% 1.47/1.23 tff(152,plain,
% 1.47/1.23 ((~hskp4) | c2_1(a103)),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[151, 148])).
% 1.47/1.23 tff(153,plain,
% 1.47/1.23 ((~hskp4) | c2_1(a103)),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[152, 148])).
% 1.47/1.23 tff(154,plain,
% 1.47/1.23 ((~hskp4) | c2_1(a103)),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[153, 148])).
% 1.47/1.23 tff(155,plain,
% 1.47/1.23 ((~hskp4) | c2_1(a103)),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[154, 148])).
% 1.47/1.23 tff(156,plain,
% 1.47/1.23 ((~hskp4) | c2_1(a103)),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[155, 148])).
% 1.47/1.23 tff(157,plain,
% 1.47/1.23 ((~hskp4) | c2_1(a103)),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[156, 148])).
% 1.47/1.23 tff(158,plain,
% 1.47/1.23 (c2_1(a103)),
% 1.47/1.23 inference(unit_resolution,[status(thm)],[157, 146])).
% 1.47/1.23 tff(159,plain,
% 1.47/1.23 (c0_1(a103)),
% 1.47/1.23 inference(unit_resolution,[status(thm)],[92, 146])).
% 1.47/1.23 tff(160,assumption,(~c3_1(a103)), introduced(assumption)).
% 1.47/1.23 tff(161,assumption,(c0_1(a103)), introduced(assumption)).
% 1.47/1.23 tff(162,plain,
% 1.47/1.23 (hskp0 | (~c1_1(a103))),
% 1.47/1.23 inference(unit_resolution,[status(thm)],[132, 126, 161, 160, 75])).
% 1.47/1.23 tff(163,plain,
% 1.47/1.23 (~c1_1(a103)),
% 1.47/1.23 inference(unit_resolution,[status(thm)],[162, 94])).
% 1.47/1.23 tff(164,plain,
% 1.47/1.23 (^[U: $i] : refl((hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))),
% 1.47/1.23 inference(bind,[status(th)],[])).
% 1.47/1.23 tff(165,plain,
% 1.47/1.23 (![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.47/1.23 inference(quant_intro,[status(thm)],[164])).
% 1.47/1.23 tff(166,plain,
% 1.47/1.23 (![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.47/1.23 inference(rewrite,[status(thm)],[])).
% 1.47/1.23 tff(167,plain,
% 1.47/1.23 (^[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)) | 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)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp22) <=> (hskp22 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp22) | hskp21) <=> ((hskp22 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp21))), rewrite(((hskp22 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp21) <=> (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp22) | hskp21) <=> (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))))),
% 1.47/1.23 inference(bind,[status(th)],[])).
% 1.47/1.23 tff(168,plain,
% 1.47/1.23 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp22) | hskp21) <=> ![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.47/1.23 inference(quant_intro,[status(thm)],[167])).
% 1.47/1.23 tff(169,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp22) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause144')).
% 1.47/1.23 tff(170,plain,
% 1.47/1.23 (![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[169, 168])).
% 1.47/1.23 tff(171,plain,
% 1.47/1.23 (![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[170, 166])).
% 1.47/1.23 tff(172,plain,(
% 1.47/1.23 ![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.47/1.23 inference(skolemize,[status(sab)],[171])).
% 1.47/1.23 tff(173,plain,
% 1.47/1.23 (![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[172, 165])).
% 1.47/1.23 tff(174,assumption,(c2_1(a103)), introduced(assumption)).
% 1.47/1.23 tff(175,plain,
% 1.47/1.23 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | c1_1(a103))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp22 | hskp21 | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | c1_1(a103))),
% 1.47/1.23 inference(rewrite,[status(thm)],[])).
% 1.47/1.23 tff(176,plain,
% 1.47/1.23 ((hskp22 | hskp21 | (~ndr1_0) | c1_1(a103) | c3_1(a103) | (~c2_1(a103))) <=> (hskp22 | hskp21 | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | c1_1(a103))),
% 1.47/1.23 inference(rewrite,[status(thm)],[])).
% 1.47/1.23 tff(177,plain,
% 1.47/1.23 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c1_1(a103) | c3_1(a103) | (~c2_1(a103)))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | c1_1(a103)))),
% 1.47/1.23 inference(monotonicity,[status(thm)],[176])).
% 1.47/1.23 tff(178,plain,
% 1.47/1.23 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c1_1(a103) | c3_1(a103) | (~c2_1(a103)))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp22 | hskp21 | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | c1_1(a103))),
% 1.47/1.23 inference(transitivity,[status(thm)],[177, 175])).
% 1.47/1.23 tff(179,plain,
% 1.47/1.23 ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c1_1(a103) | c3_1(a103) | (~c2_1(a103)))),
% 1.47/1.23 inference(quant_inst,[status(thm)],[])).
% 1.47/1.23 tff(180,plain,
% 1.47/1.23 ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp22 | hskp21 | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | c1_1(a103)),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[179, 178])).
% 1.47/1.23 tff(181,plain,
% 1.47/1.23 (hskp21 | c1_1(a103)),
% 1.47/1.23 inference(unit_resolution,[status(thm)],[180, 126, 144, 174, 160, 173])).
% 1.47/1.23 tff(182,plain,
% 1.47/1.23 (hskp21),
% 1.47/1.23 inference(unit_resolution,[status(thm)],[181, 163])).
% 1.47/1.23 tff(183,plain,
% 1.47/1.23 (((~hskp21) | (~c2_1(a136))) <=> ((~hskp21) | (~c2_1(a136)))),
% 1.47/1.23 inference(rewrite,[status(thm)],[])).
% 1.47/1.23 tff(184,plain,
% 1.47/1.23 (((~c2_1(a136)) | (~hskp21)) <=> ((~hskp21) | (~c2_1(a136)))),
% 1.47/1.23 inference(rewrite,[status(thm)],[])).
% 1.47/1.23 tff(185,axiom,((~c2_1(a136)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause96')).
% 1.47/1.23 tff(186,plain,
% 1.47/1.23 ((~hskp21) | (~c2_1(a136))),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[185, 184])).
% 1.47/1.23 tff(187,plain,
% 1.47/1.23 ((~hskp21) | (~c2_1(a136))),
% 1.47/1.23 inference(modus_ponens,[status(thm)],[186, 183])).
% 1.47/1.23 tff(188,plain,
% 1.47/1.23 (~c2_1(a136)),
% 1.47/1.23 inference(unit_resolution,[status(thm)],[187, 182])).
% 1.47/1.23 tff(189,plain,
% 1.47/1.23 (((~hskp21) | (~c1_1(a136))) <=> ((~hskp21) | (~c1_1(a136)))),
% 1.47/1.23 inference(rewrite,[status(thm)],[])).
% 1.47/1.23 tff(190,plain,
% 1.47/1.24 (((~c1_1(a136)) | (~hskp21)) <=> ((~hskp21) | (~c1_1(a136)))),
% 1.47/1.24 inference(rewrite,[status(thm)],[])).
% 1.47/1.24 tff(191,axiom,((~c1_1(a136)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause95')).
% 1.47/1.24 tff(192,plain,
% 1.47/1.24 ((~hskp21) | (~c1_1(a136))),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[191, 190])).
% 1.47/1.24 tff(193,plain,
% 1.47/1.24 ((~hskp21) | (~c1_1(a136))),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[192, 189])).
% 1.47/1.24 tff(194,plain,
% 1.47/1.24 (~c1_1(a136)),
% 1.47/1.24 inference(unit_resolution,[status(thm)],[193, 182])).
% 1.47/1.24 tff(195,plain,
% 1.47/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a136) | c2_1(a136) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c0_1(a136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a136) | c2_1(a136) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c0_1(a136)))),
% 1.47/1.24 inference(rewrite,[status(thm)],[])).
% 1.47/1.24 tff(196,plain,
% 1.47/1.24 (((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c2_1(a136) | c1_1(a136) | (~c0_1(a136))) <=> (c1_1(a136) | c2_1(a136) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c0_1(a136)))),
% 1.47/1.24 inference(rewrite,[status(thm)],[])).
% 1.47/1.24 tff(197,plain,
% 1.47/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c2_1(a136) | c1_1(a136) | (~c0_1(a136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a136) | c2_1(a136) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c0_1(a136))))),
% 1.47/1.24 inference(monotonicity,[status(thm)],[196])).
% 1.47/1.24 tff(198,plain,
% 1.47/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c2_1(a136) | c1_1(a136) | (~c0_1(a136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a136) | c2_1(a136) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c0_1(a136)))),
% 1.47/1.24 inference(transitivity,[status(thm)],[197, 195])).
% 1.47/1.24 tff(199,plain,
% 1.47/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c2_1(a136) | c1_1(a136) | (~c0_1(a136)))),
% 1.47/1.24 inference(quant_inst,[status(thm)],[])).
% 1.47/1.24 tff(200,plain,
% 1.47/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a136) | c2_1(a136) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c0_1(a136))),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[199, 198])).
% 1.47/1.24 tff(201,plain,
% 1.47/1.24 (~c0_1(a136)),
% 1.47/1.24 inference(unit_resolution,[status(thm)],[200, 126, 161, 174, 194, 188, 160, 143, 163])).
% 1.47/1.24 tff(202,plain,
% 1.47/1.24 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 1.47/1.24 inference(bind,[status(th)],[])).
% 1.47/1.24 tff(203,plain,
% 1.47/1.24 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.47/1.24 inference(quant_intro,[status(thm)],[202])).
% 1.47/1.24 tff(204,plain,
% 1.47/1.24 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.47/1.24 inference(rewrite,[status(thm)],[])).
% 1.47/1.24 tff(205,plain,
% 1.47/1.24 (^[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)) | 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)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_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) | c1_1(V) | c0_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 1.47/1.24 inference(bind,[status(th)],[])).
% 1.47/1.24 tff(206,plain,
% 1.47/1.24 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.47/1.24 inference(quant_intro,[status(thm)],[205])).
% 1.47/1.24 tff(207,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause161')).
% 1.47/1.24 tff(208,plain,
% 1.47/1.24 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[207, 206])).
% 1.47/1.24 tff(209,plain,
% 1.47/1.24 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[208, 204])).
% 1.47/1.24 tff(210,plain,(
% 1.47/1.24 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.47/1.24 inference(skolemize,[status(sab)],[209])).
% 1.47/1.24 tff(211,plain,
% 1.47/1.24 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[210, 203])).
% 1.47/1.24 tff(212,plain,
% 1.47/1.24 (((~hskp21) | c3_1(a136)) <=> ((~hskp21) | c3_1(a136))),
% 1.47/1.24 inference(rewrite,[status(thm)],[])).
% 1.47/1.24 tff(213,axiom,((~hskp21) | c3_1(a136)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause59')).
% 1.47/1.24 tff(214,plain,
% 1.47/1.24 ((~hskp21) | c3_1(a136)),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[213, 212])).
% 1.47/1.24 tff(215,plain,
% 1.47/1.24 ((~hskp21) | c3_1(a136)),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[214, 212])).
% 1.47/1.24 tff(216,plain,
% 1.47/1.24 ((~hskp21) | c3_1(a136)),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[215, 212])).
% 1.47/1.24 tff(217,plain,
% 1.47/1.24 ((~hskp21) | c3_1(a136)),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[216, 212])).
% 1.47/1.24 tff(218,plain,
% 1.47/1.24 ((~hskp21) | c3_1(a136)),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[217, 212])).
% 1.47/1.24 tff(219,plain,
% 1.47/1.24 ((~hskp21) | c3_1(a136)),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[218, 212])).
% 1.47/1.24 tff(220,plain,
% 1.47/1.24 ((~hskp21) | c3_1(a136)),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[219, 212])).
% 1.47/1.24 tff(221,plain,
% 1.47/1.24 ((~hskp21) | c3_1(a136)),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[220, 212])).
% 1.47/1.24 tff(222,plain,
% 1.47/1.24 (c3_1(a136)),
% 1.47/1.24 inference(unit_resolution,[status(thm)],[221, 182])).
% 1.47/1.24 tff(223,plain,
% 1.47/1.24 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a136) | c2_1(a136) | (~ndr1_0) | c0_1(a136) | (~c3_1(a136)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a136) | c2_1(a136) | (~ndr1_0) | c0_1(a136) | (~c3_1(a136)))),
% 1.47/1.24 inference(rewrite,[status(thm)],[])).
% 1.47/1.24 tff(224,plain,
% 1.47/1.24 ((hskp0 | (~ndr1_0) | c2_1(a136) | c0_1(a136) | (~c3_1(a136)) | c2_1(a136) | c1_1(a136) | c0_1(a136)) <=> (hskp0 | c1_1(a136) | c2_1(a136) | (~ndr1_0) | c0_1(a136) | (~c3_1(a136)))),
% 1.47/1.24 inference(rewrite,[status(thm)],[])).
% 1.47/1.24 tff(225,plain,
% 1.47/1.24 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a136) | c0_1(a136) | (~c3_1(a136)) | c2_1(a136) | c1_1(a136) | c0_1(a136))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a136) | c2_1(a136) | (~ndr1_0) | c0_1(a136) | (~c3_1(a136))))),
% 1.47/1.24 inference(monotonicity,[status(thm)],[224])).
% 1.47/1.24 tff(226,plain,
% 1.47/1.24 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a136) | c0_1(a136) | (~c3_1(a136)) | c2_1(a136) | c1_1(a136) | c0_1(a136))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a136) | c2_1(a136) | (~ndr1_0) | c0_1(a136) | (~c3_1(a136)))),
% 1.47/1.24 inference(transitivity,[status(thm)],[225, 223])).
% 1.47/1.24 tff(227,plain,
% 1.47/1.24 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a136) | c0_1(a136) | (~c3_1(a136)) | c2_1(a136) | c1_1(a136) | c0_1(a136))),
% 1.47/1.24 inference(quant_inst,[status(thm)],[])).
% 1.47/1.24 tff(228,plain,
% 1.47/1.24 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a136) | c2_1(a136) | (~ndr1_0) | c0_1(a136) | (~c3_1(a136))),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[227, 226])).
% 1.47/1.24 tff(229,plain,
% 1.47/1.24 ($false),
% 1.47/1.24 inference(unit_resolution,[status(thm)],[228, 126, 94, 222, 194, 188, 211, 201])).
% 1.47/1.24 tff(230,plain,(hskp0 | (~c0_1(a103)) | (~c2_1(a103)) | c3_1(a103) | hskp22), inference(lemma,lemma(discharge,[]))).
% 1.47/1.24 tff(231,plain,
% 1.47/1.24 (hskp0),
% 1.47/1.24 inference(unit_resolution,[status(thm)],[230, 159, 158, 147, 144])).
% 1.47/1.24 tff(232,plain,
% 1.47/1.24 (((~hskp0) | (~c3_1(a97))) <=> ((~hskp0) | (~c3_1(a97)))),
% 1.47/1.24 inference(rewrite,[status(thm)],[])).
% 1.47/1.24 tff(233,plain,
% 1.47/1.24 (((~c3_1(a97)) | (~hskp0)) <=> ((~hskp0) | (~c3_1(a97)))),
% 1.47/1.24 inference(rewrite,[status(thm)],[])).
% 1.47/1.24 tff(234,axiom,((~c3_1(a97)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause132')).
% 1.47/1.24 tff(235,plain,
% 1.47/1.24 ((~hskp0) | (~c3_1(a97))),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[234, 233])).
% 1.47/1.24 tff(236,plain,
% 1.47/1.24 ((~hskp0) | (~c3_1(a97))),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[235, 232])).
% 1.47/1.24 tff(237,plain,
% 1.47/1.24 (~c3_1(a97)),
% 1.47/1.24 inference(unit_resolution,[status(thm)],[236, 231])).
% 1.47/1.24 tff(238,plain,
% 1.47/1.24 (((~hskp0) | (~c2_1(a97))) <=> ((~hskp0) | (~c2_1(a97)))),
% 1.47/1.24 inference(rewrite,[status(thm)],[])).
% 1.47/1.24 tff(239,plain,
% 1.47/1.24 (((~c2_1(a97)) | (~hskp0)) <=> ((~hskp0) | (~c2_1(a97)))),
% 1.47/1.24 inference(rewrite,[status(thm)],[])).
% 1.47/1.24 tff(240,axiom,((~c2_1(a97)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause131')).
% 1.47/1.24 tff(241,plain,
% 1.47/1.24 ((~hskp0) | (~c2_1(a97))),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[240, 239])).
% 1.47/1.24 tff(242,plain,
% 1.47/1.24 ((~hskp0) | (~c2_1(a97))),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[241, 238])).
% 1.47/1.24 tff(243,plain,
% 1.47/1.24 (~c2_1(a97)),
% 1.47/1.24 inference(unit_resolution,[status(thm)],[242, 231])).
% 1.47/1.24 tff(244,plain,
% 1.47/1.24 (c0_1(a97)),
% 1.47/1.24 inference(unit_resolution,[status(thm)],[64, 231])).
% 1.47/1.24 tff(245,assumption,(~c1_1(a97)), introduced(assumption)).
% 1.47/1.24 tff(246,assumption,(c0_1(a97)), introduced(assumption)).
% 1.47/1.24 tff(247,assumption,(hskp19), introduced(assumption)).
% 1.47/1.24 tff(248,plain,
% 1.47/1.24 (((~hskp19) | (~c2_1(a130))) <=> ((~hskp19) | (~c2_1(a130)))),
% 1.47/1.24 inference(rewrite,[status(thm)],[])).
% 1.47/1.24 tff(249,plain,
% 1.47/1.24 (((~c2_1(a130)) | (~hskp19)) <=> ((~hskp19) | (~c2_1(a130)))),
% 1.47/1.24 inference(rewrite,[status(thm)],[])).
% 1.47/1.24 tff(250,axiom,((~c2_1(a130)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause100')).
% 1.47/1.24 tff(251,plain,
% 1.47/1.24 ((~hskp19) | (~c2_1(a130))),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[250, 249])).
% 1.47/1.24 tff(252,plain,
% 1.47/1.24 ((~hskp19) | (~c2_1(a130))),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[251, 248])).
% 1.47/1.24 tff(253,plain,
% 1.47/1.24 (~c2_1(a130)),
% 1.47/1.24 inference(unit_resolution,[status(thm)],[252, 247])).
% 1.47/1.24 tff(254,plain,
% 1.47/1.24 (((~hskp19) | c3_1(a130)) <=> ((~hskp19) | c3_1(a130))),
% 1.47/1.24 inference(rewrite,[status(thm)],[])).
% 1.47/1.24 tff(255,axiom,((~hskp19) | c3_1(a130)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause61')).
% 1.47/1.24 tff(256,plain,
% 1.47/1.24 ((~hskp19) | c3_1(a130)),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[255, 254])).
% 1.47/1.24 tff(257,plain,
% 1.47/1.24 ((~hskp19) | c3_1(a130)),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[256, 254])).
% 1.47/1.24 tff(258,plain,
% 1.47/1.24 ((~hskp19) | c3_1(a130)),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[257, 254])).
% 1.47/1.24 tff(259,plain,
% 1.47/1.24 ((~hskp19) | c3_1(a130)),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[258, 254])).
% 1.47/1.24 tff(260,plain,
% 1.47/1.24 ((~hskp19) | c3_1(a130)),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[259, 254])).
% 1.47/1.24 tff(261,plain,
% 1.47/1.24 ((~hskp19) | c3_1(a130)),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[260, 254])).
% 1.47/1.24 tff(262,plain,
% 1.47/1.24 ((~hskp19) | c3_1(a130)),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[261, 254])).
% 1.47/1.24 tff(263,plain,
% 1.47/1.24 ((~hskp19) | c3_1(a130)),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[262, 254])).
% 1.47/1.24 tff(264,plain,
% 1.47/1.24 (c3_1(a130)),
% 1.47/1.24 inference(unit_resolution,[status(thm)],[263, 247])).
% 1.47/1.24 tff(265,plain,
% 1.47/1.24 (((~hskp19) | c1_1(a130)) <=> ((~hskp19) | c1_1(a130))),
% 1.47/1.24 inference(rewrite,[status(thm)],[])).
% 1.47/1.24 tff(266,axiom,((~hskp19) | c1_1(a130)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause60')).
% 1.47/1.24 tff(267,plain,
% 1.47/1.24 ((~hskp19) | c1_1(a130)),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[266, 265])).
% 1.47/1.24 tff(268,plain,
% 1.47/1.24 ((~hskp19) | c1_1(a130)),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[267, 265])).
% 1.47/1.24 tff(269,plain,
% 1.47/1.24 ((~hskp19) | c1_1(a130)),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[268, 265])).
% 1.47/1.24 tff(270,plain,
% 1.47/1.24 ((~hskp19) | c1_1(a130)),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[269, 265])).
% 1.47/1.24 tff(271,plain,
% 1.47/1.24 ((~hskp19) | c1_1(a130)),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[270, 265])).
% 1.47/1.24 tff(272,plain,
% 1.47/1.24 ((~hskp19) | c1_1(a130)),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[271, 265])).
% 1.47/1.24 tff(273,plain,
% 1.47/1.24 ((~hskp19) | c1_1(a130)),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[272, 265])).
% 1.47/1.24 tff(274,plain,
% 1.47/1.24 ((~hskp19) | c1_1(a130)),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[273, 265])).
% 1.47/1.24 tff(275,plain,
% 1.47/1.24 (c1_1(a130)),
% 1.47/1.24 inference(unit_resolution,[status(thm)],[274, 247])).
% 1.47/1.24 tff(276,plain,
% 1.47/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a130) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | c1_1(a97) | (~c3_1(a130)) | (~c1_1(a130)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a130) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | c1_1(a97) | (~c3_1(a130)) | (~c1_1(a130)))),
% 1.47/1.24 inference(rewrite,[status(thm)],[])).
% 1.47/1.24 tff(277,plain,
% 1.47/1.24 (((~ndr1_0) | c2_1(a130) | (~c3_1(a130)) | (~c1_1(a130)) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)) | c1_1(a97) | c3_1(a97) | (~c0_1(a97))) <=> (c2_1(a130) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | c1_1(a97) | (~c3_1(a130)) | (~c1_1(a130)))),
% 1.47/1.24 inference(rewrite,[status(thm)],[])).
% 1.47/1.24 tff(278,plain,
% 1.47/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a130) | (~c3_1(a130)) | (~c1_1(a130)) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)) | c1_1(a97) | c3_1(a97) | (~c0_1(a97)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a130) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | c1_1(a97) | (~c3_1(a130)) | (~c1_1(a130))))),
% 1.47/1.24 inference(monotonicity,[status(thm)],[277])).
% 1.47/1.24 tff(279,plain,
% 1.47/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a130) | (~c3_1(a130)) | (~c1_1(a130)) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)) | c1_1(a97) | c3_1(a97) | (~c0_1(a97)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a130) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | c1_1(a97) | (~c3_1(a130)) | (~c1_1(a130)))),
% 1.47/1.24 inference(transitivity,[status(thm)],[278, 276])).
% 1.47/1.24 tff(280,plain,
% 1.47/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a130) | (~c3_1(a130)) | (~c1_1(a130)) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)) | c1_1(a97) | c3_1(a97) | (~c0_1(a97)))),
% 1.47/1.24 inference(quant_inst,[status(thm)],[])).
% 1.47/1.24 tff(281,plain,
% 1.47/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a130) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | c1_1(a97) | (~c3_1(a130)) | (~c1_1(a130))),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[280, 279])).
% 1.47/1.24 tff(282,plain,
% 1.47/1.24 ($false),
% 1.47/1.24 inference(unit_resolution,[status(thm)],[281, 126, 275, 264, 246, 253, 31, 53, 20, 245])).
% 1.47/1.24 tff(283,plain,((~hskp19) | (~c0_1(a97)) | c2_1(a97) | c3_1(a97) | c1_1(a97)), inference(lemma,lemma(discharge,[]))).
% 1.47/1.24 tff(284,plain,
% 1.47/1.24 (~hskp19),
% 1.47/1.24 inference(unit_resolution,[status(thm)],[283, 245, 31, 53, 246])).
% 1.47/1.24 tff(285,plain,
% 1.47/1.24 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp18 | c2_1(a97) | c3_1(a97) | (~ndr1_0) | c1_1(a97))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp19 | hskp18 | c2_1(a97) | c3_1(a97) | (~ndr1_0) | c1_1(a97))),
% 1.47/1.24 inference(rewrite,[status(thm)],[])).
% 1.47/1.24 tff(286,plain,
% 1.47/1.24 ((hskp19 | hskp18 | (~ndr1_0) | c2_1(a97) | c1_1(a97) | c3_1(a97)) <=> (hskp19 | hskp18 | c2_1(a97) | c3_1(a97) | (~ndr1_0) | c1_1(a97))),
% 1.47/1.24 inference(rewrite,[status(thm)],[])).
% 1.47/1.24 tff(287,plain,
% 1.47/1.24 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a97) | c1_1(a97) | c3_1(a97))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp18 | c2_1(a97) | c3_1(a97) | (~ndr1_0) | c1_1(a97)))),
% 1.47/1.24 inference(monotonicity,[status(thm)],[286])).
% 1.47/1.24 tff(288,plain,
% 1.47/1.24 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a97) | c1_1(a97) | c3_1(a97))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp19 | hskp18 | c2_1(a97) | c3_1(a97) | (~ndr1_0) | c1_1(a97))),
% 1.47/1.24 inference(transitivity,[status(thm)],[287, 285])).
% 1.47/1.24 tff(289,plain,
% 1.47/1.24 ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a97) | c1_1(a97) | c3_1(a97))),
% 1.47/1.24 inference(quant_inst,[status(thm)],[])).
% 1.47/1.24 tff(290,plain,
% 1.47/1.24 ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp19 | hskp18 | c2_1(a97) | c3_1(a97) | (~ndr1_0) | c1_1(a97)),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[289, 288])).
% 1.47/1.24 tff(291,plain,
% 1.47/1.24 (hskp19 | hskp18 | c1_1(a97)),
% 1.47/1.24 inference(unit_resolution,[status(thm)],[290, 126, 31, 53, 30])).
% 1.47/1.24 tff(292,plain,
% 1.47/1.24 (hskp18),
% 1.47/1.24 inference(unit_resolution,[status(thm)],[291, 284, 245])).
% 1.47/1.24 tff(293,plain,
% 1.47/1.24 (((~hskp18) | (~c1_1(a129))) <=> ((~hskp18) | (~c1_1(a129)))),
% 1.47/1.24 inference(rewrite,[status(thm)],[])).
% 1.47/1.24 tff(294,plain,
% 1.47/1.24 (((~c1_1(a129)) | (~hskp18)) <=> ((~hskp18) | (~c1_1(a129)))),
% 1.47/1.24 inference(rewrite,[status(thm)],[])).
% 1.47/1.24 tff(295,axiom,((~c1_1(a129)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause101')).
% 1.47/1.24 tff(296,plain,
% 1.47/1.24 ((~hskp18) | (~c1_1(a129))),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[295, 294])).
% 1.47/1.24 tff(297,plain,
% 1.47/1.24 ((~hskp18) | (~c1_1(a129))),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[296, 293])).
% 1.47/1.24 tff(298,plain,
% 1.47/1.24 (~c1_1(a129)),
% 1.47/1.24 inference(unit_resolution,[status(thm)],[297, 292])).
% 1.47/1.24 tff(299,plain,
% 1.47/1.24 (((~hskp18) | c2_1(a129)) <=> ((~hskp18) | c2_1(a129))),
% 1.47/1.24 inference(rewrite,[status(thm)],[])).
% 1.47/1.24 tff(300,axiom,((~hskp18) | c2_1(a129)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause63')).
% 1.47/1.24 tff(301,plain,
% 1.47/1.24 ((~hskp18) | c2_1(a129)),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[300, 299])).
% 1.47/1.24 tff(302,plain,
% 1.47/1.24 ((~hskp18) | c2_1(a129)),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[301, 299])).
% 1.47/1.24 tff(303,plain,
% 1.47/1.24 ((~hskp18) | c2_1(a129)),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[302, 299])).
% 1.47/1.24 tff(304,plain,
% 1.47/1.24 ((~hskp18) | c2_1(a129)),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[303, 299])).
% 1.47/1.24 tff(305,plain,
% 1.47/1.24 ((~hskp18) | c2_1(a129)),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[304, 299])).
% 1.47/1.24 tff(306,plain,
% 1.47/1.24 ((~hskp18) | c2_1(a129)),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[305, 299])).
% 1.47/1.24 tff(307,plain,
% 1.47/1.24 ((~hskp18) | c2_1(a129)),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[306, 299])).
% 1.47/1.24 tff(308,plain,
% 1.47/1.24 ((~hskp18) | c2_1(a129)),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[307, 299])).
% 1.47/1.24 tff(309,plain,
% 1.47/1.24 (c2_1(a129)),
% 1.47/1.24 inference(unit_resolution,[status(thm)],[308, 292])).
% 1.47/1.24 tff(310,plain,
% 1.47/1.24 (((~hskp18) | c0_1(a129)) <=> ((~hskp18) | c0_1(a129))),
% 1.47/1.24 inference(rewrite,[status(thm)],[])).
% 1.47/1.24 tff(311,axiom,((~hskp18) | c0_1(a129)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause62')).
% 1.47/1.24 tff(312,plain,
% 1.47/1.24 ((~hskp18) | c0_1(a129)),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[311, 310])).
% 1.47/1.24 tff(313,plain,
% 1.47/1.24 ((~hskp18) | c0_1(a129)),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[312, 310])).
% 1.47/1.24 tff(314,plain,
% 1.47/1.24 ((~hskp18) | c0_1(a129)),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[313, 310])).
% 1.47/1.24 tff(315,plain,
% 1.47/1.24 ((~hskp18) | c0_1(a129)),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[314, 310])).
% 1.47/1.24 tff(316,plain,
% 1.47/1.24 ((~hskp18) | c0_1(a129)),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[315, 310])).
% 1.47/1.24 tff(317,plain,
% 1.47/1.24 ((~hskp18) | c0_1(a129)),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[316, 310])).
% 1.47/1.24 tff(318,plain,
% 1.47/1.24 ((~hskp18) | c0_1(a129)),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[317, 310])).
% 1.47/1.24 tff(319,plain,
% 1.47/1.24 ((~hskp18) | c0_1(a129)),
% 1.47/1.24 inference(modus_ponens,[status(thm)],[318, 310])).
% 1.47/1.24 tff(320,plain,
% 1.47/1.24 (c0_1(a129)),
% 1.47/1.24 inference(unit_resolution,[status(thm)],[319, 292])).
% 1.47/1.24 tff(321,plain,
% 1.47/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a129) | c3_1(a103) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | c1_1(a97) | (~c2_1(a103)) | (~c0_1(a103)) | (~c2_1(a129)) | (~c0_1(a129)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a129) | c3_1(a103) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | c1_1(a97) | (~c2_1(a103)) | (~c0_1(a103)) | (~c2_1(a129)) | (~c0_1(a129)))),
% 1.47/1.24 inference(rewrite,[status(thm)],[])).
% 1.47/1.24 tff(322,plain,
% 1.47/1.24 (((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c2_1(a97) | c1_1(a97) | (~c0_1(a97))) <=> (c1_1(a129) | c3_1(a103) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | c1_1(a97) | (~c2_1(a103)) | (~c0_1(a103)) | (~c2_1(a129)) | (~c0_1(a129)))),
% 1.47/1.24 inference(rewrite,[status(thm)],[])).
% 1.47/1.24 tff(323,plain,
% 1.47/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c2_1(a97) | c1_1(a97) | (~c0_1(a97)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a129) | c3_1(a103) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | c1_1(a97) | (~c2_1(a103)) | (~c0_1(a103)) | (~c2_1(a129)) | (~c0_1(a129))))),
% 1.47/1.25 inference(monotonicity,[status(thm)],[322])).
% 1.47/1.25 tff(324,plain,
% 1.47/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c2_1(a97) | c1_1(a97) | (~c0_1(a97)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a129) | c3_1(a103) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | c1_1(a97) | (~c2_1(a103)) | (~c0_1(a103)) | (~c2_1(a129)) | (~c0_1(a129)))),
% 1.47/1.25 inference(transitivity,[status(thm)],[323, 321])).
% 1.47/1.25 tff(325,plain,
% 1.47/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c2_1(a97) | c1_1(a97) | (~c0_1(a97)))),
% 1.47/1.25 inference(quant_inst,[status(thm)],[])).
% 1.47/1.25 tff(326,plain,
% 1.47/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a129) | c3_1(a103) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | c1_1(a97) | (~c2_1(a103)) | (~c0_1(a103)) | (~c2_1(a129)) | (~c0_1(a129))),
% 1.47/1.25 inference(modus_ponens,[status(thm)],[325, 324])).
% 1.47/1.25 tff(327,plain,
% 1.47/1.25 ($false),
% 1.47/1.25 inference(unit_resolution,[status(thm)],[326, 126, 320, 309, 161, 174, 246, 298, 160, 31, 143, 245])).
% 1.47/1.25 tff(328,plain,(c1_1(a97) | (~c0_1(a103)) | (~c2_1(a103)) | (~c0_1(a97)) | c3_1(a103) | c2_1(a97) | c3_1(a97)), inference(lemma,lemma(discharge,[]))).
% 1.47/1.25 tff(329,plain,
% 1.47/1.25 (c1_1(a97)),
% 1.47/1.25 inference(unit_resolution,[status(thm)],[328, 159, 158, 244, 147, 243, 237])).
% 1.47/1.25 tff(330,assumption,(c1_1(a97)), introduced(assumption)).
% 1.47/1.25 tff(331,plain,
% 1.47/1.25 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))),
% 1.47/1.25 inference(bind,[status(th)],[])).
% 1.47/1.25 tff(332,plain,
% 1.47/1.25 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.47/1.25 inference(quant_intro,[status(thm)],[331])).
% 1.47/1.25 tff(333,plain,
% 1.47/1.25 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.47/1.25 inference(rewrite,[status(thm)],[])).
% 1.47/1.25 tff(334,plain,
% 1.47/1.25 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp28) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp28))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))))),
% 1.47/1.25 inference(bind,[status(th)],[])).
% 1.47/1.25 tff(335,plain,
% 1.47/1.25 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.47/1.25 inference(quant_intro,[status(thm)],[334])).
% 1.47/1.25 tff(336,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp28)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause176')).
% 1.47/1.25 tff(337,plain,
% 1.47/1.25 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.47/1.25 inference(modus_ponens,[status(thm)],[336, 335])).
% 1.47/1.25 tff(338,plain,
% 1.47/1.25 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.47/1.25 inference(modus_ponens,[status(thm)],[337, 333])).
% 1.47/1.25 tff(339,plain,(
% 1.47/1.25 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.47/1.25 inference(skolemize,[status(sab)],[338])).
% 1.47/1.25 tff(340,plain,
% 1.47/1.25 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.47/1.25 inference(modus_ponens,[status(thm)],[339, 332])).
% 1.47/1.25 tff(341,assumption,(hskp21), introduced(assumption)).
% 1.47/1.25 tff(342,plain,
% 1.47/1.25 (~c2_1(a136)),
% 1.47/1.25 inference(unit_resolution,[status(thm)],[187, 341])).
% 1.47/1.25 tff(343,plain,
% 1.47/1.25 (~c1_1(a136)),
% 1.47/1.25 inference(unit_resolution,[status(thm)],[193, 341])).
% 1.47/1.25 tff(344,plain,
% 1.47/1.25 (c3_1(a136)),
% 1.47/1.25 inference(unit_resolution,[status(thm)],[221, 341])).
% 1.47/1.25 tff(345,plain,
% 1.47/1.25 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp28 | c1_1(a136) | c2_1(a136) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c3_1(a136)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp28 | c1_1(a136) | c2_1(a136) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c3_1(a136)))),
% 1.47/1.25 inference(rewrite,[status(thm)],[])).
% 1.47/1.25 tff(346,plain,
% 1.47/1.25 ((hskp28 | (~ndr1_0) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c2_1(a136) | c1_1(a136) | (~c3_1(a136))) <=> (hskp28 | c1_1(a136) | c2_1(a136) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c3_1(a136)))),
% 1.47/1.25 inference(rewrite,[status(thm)],[])).
% 1.47/1.25 tff(347,plain,
% 1.47/1.25 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c2_1(a136) | c1_1(a136) | (~c3_1(a136)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp28 | c1_1(a136) | c2_1(a136) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c3_1(a136))))),
% 1.47/1.25 inference(monotonicity,[status(thm)],[346])).
% 1.47/1.25 tff(348,plain,
% 1.47/1.25 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c2_1(a136) | c1_1(a136) | (~c3_1(a136)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp28 | c1_1(a136) | c2_1(a136) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c3_1(a136)))),
% 1.47/1.25 inference(transitivity,[status(thm)],[347, 345])).
% 1.47/1.25 tff(349,plain,
% 1.47/1.25 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c2_1(a136) | c1_1(a136) | (~c3_1(a136)))),
% 1.47/1.25 inference(quant_inst,[status(thm)],[])).
% 1.47/1.25 tff(350,plain,
% 1.47/1.25 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp28 | c1_1(a136) | c2_1(a136) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c3_1(a136))),
% 1.47/1.25 inference(modus_ponens,[status(thm)],[349, 348])).
% 1.47/1.25 tff(351,plain,
% 1.47/1.25 ($false),
% 1.47/1.25 inference(unit_resolution,[status(thm)],[350, 126, 145, 344, 246, 343, 342, 31, 340, 330])).
% 1.47/1.25 tff(352,plain,((~hskp21) | hskp28 | (~c0_1(a97)) | c2_1(a97) | (~c1_1(a97))), inference(lemma,lemma(discharge,[]))).
% 1.47/1.25 tff(353,plain,
% 1.47/1.25 (~hskp21),
% 1.47/1.25 inference(unit_resolution,[status(thm)],[352, 145, 244, 243, 329])).
% 1.47/1.25 tff(354,assumption,(~c1_1(a103)), introduced(assumption)).
% 1.47/1.25 tff(355,plain,
% 1.47/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a103) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | c1_1(a97) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a103) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | c1_1(a97) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103))),
% 1.47/1.25 inference(rewrite,[status(thm)],[])).
% 1.47/1.25 tff(356,plain,
% 1.47/1.25 (((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c2_1(a97) | c1_1(a97) | (~c0_1(a97))) <=> (c3_1(a103) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | c1_1(a97) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103))),
% 1.47/1.25 inference(rewrite,[status(thm)],[])).
% 1.47/1.25 tff(357,plain,
% 1.47/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c2_1(a97) | c1_1(a97) | (~c0_1(a97)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a103) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | c1_1(a97) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103)))),
% 1.47/1.25 inference(monotonicity,[status(thm)],[356])).
% 1.47/1.25 tff(358,plain,
% 1.47/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c2_1(a97) | c1_1(a97) | (~c0_1(a97)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a103) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | c1_1(a97) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103))),
% 1.47/1.25 inference(transitivity,[status(thm)],[357, 355])).
% 1.47/1.25 tff(359,plain,
% 1.47/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c2_1(a97) | c1_1(a97) | (~c0_1(a97)))),
% 1.47/1.25 inference(quant_inst,[status(thm)],[])).
% 1.47/1.25 tff(360,plain,
% 1.47/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a103) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | c1_1(a97) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103)),
% 1.47/1.25 inference(modus_ponens,[status(thm)],[359, 358])).
% 1.47/1.25 tff(361,plain,
% 1.47/1.25 ($false),
% 1.47/1.25 inference(unit_resolution,[status(thm)],[360, 126, 161, 174, 246, 160, 31, 143, 354, 245])).
% 1.47/1.25 tff(362,plain,(c1_1(a103) | (~c0_1(a103)) | (~c2_1(a103)) | (~c0_1(a97)) | c3_1(a103) | c2_1(a97) | c1_1(a97)), inference(lemma,lemma(discharge,[]))).
% 1.47/1.25 tff(363,plain,
% 1.47/1.25 (c1_1(a97)),
% 1.47/1.25 inference(unit_resolution,[status(thm)],[362, 354, 158, 244, 147, 243, 159])).
% 1.47/1.25 tff(364,plain,
% 1.47/1.25 (hskp21 | c1_1(a103)),
% 1.47/1.25 inference(unit_resolution,[status(thm)],[180, 126, 144, 158, 147, 173])).
% 1.47/1.25 tff(365,plain,
% 1.47/1.25 (hskp21),
% 1.47/1.25 inference(unit_resolution,[status(thm)],[364, 354])).
% 1.47/1.25 tff(366,plain,
% 1.47/1.25 (~c2_1(a136)),
% 1.47/1.25 inference(unit_resolution,[status(thm)],[187, 365])).
% 1.47/1.25 tff(367,plain,
% 1.47/1.25 (~c1_1(a136)),
% 1.47/1.25 inference(unit_resolution,[status(thm)],[193, 365])).
% 1.47/1.25 tff(368,plain,
% 1.47/1.25 (c3_1(a136)),
% 1.47/1.25 inference(unit_resolution,[status(thm)],[221, 365])).
% 1.47/1.25 tff(369,plain,
% 1.47/1.25 ($false),
% 1.47/1.25 inference(unit_resolution,[status(thm)],[350, 126, 145, 368, 244, 367, 366, 243, 340, 363])).
% 1.47/1.25 tff(370,plain,(c1_1(a103) | hskp28 | hskp22), inference(lemma,lemma(discharge,[]))).
% 1.47/1.25 tff(371,plain,
% 1.47/1.25 (c1_1(a103)),
% 1.47/1.25 inference(unit_resolution,[status(thm)],[370, 145, 144])).
% 1.47/1.25 tff(372,plain,
% 1.47/1.25 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))))),
% 1.47/1.25 inference(bind,[status(th)],[])).
% 1.47/1.25 tff(373,plain,
% 1.47/1.25 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.47/1.25 inference(quant_intro,[status(thm)],[372])).
% 1.47/1.25 tff(374,plain,
% 1.47/1.25 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.47/1.25 inference(rewrite,[status(thm)],[])).
% 1.47/1.25 tff(375,plain,
% 1.47/1.25 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(V)) | (~c1_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(V)) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(V)) | (~c2_1(W)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(V)) | (~c2_1(W)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_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)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))))),
% 1.47/1.25 inference(bind,[status(th)],[])).
% 1.47/1.25 tff(376,plain,
% 1.47/1.25 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.47/1.25 inference(quant_intro,[status(thm)],[375])).
% 1.47/1.25 tff(377,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause198')).
% 1.47/1.25 tff(378,plain,
% 1.47/1.25 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.47/1.25 inference(modus_ponens,[status(thm)],[377, 376])).
% 1.47/1.25 tff(379,plain,
% 1.47/1.25 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.47/1.25 inference(modus_ponens,[status(thm)],[378, 374])).
% 1.47/1.25 tff(380,plain,(
% 1.47/1.25 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.47/1.25 inference(skolemize,[status(sab)],[379])).
% 1.47/1.25 tff(381,plain,
% 1.47/1.25 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.47/1.25 inference(modus_ponens,[status(thm)],[380, 373])).
% 1.47/1.25 tff(382,plain,
% 1.47/1.25 (^[U: $i] : refl((hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))))),
% 1.47/1.25 inference(bind,[status(th)],[])).
% 1.47/1.25 tff(383,plain,
% 1.47/1.25 (![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.47/1.25 inference(quant_intro,[status(thm)],[382])).
% 1.47/1.25 tff(384,plain,
% 1.47/1.25 (![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.47/1.25 inference(rewrite,[status(thm)],[])).
% 1.47/1.25 tff(385,plain,
% 1.47/1.25 (^[U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp6) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp6))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))))),
% 1.47/1.25 inference(bind,[status(th)],[])).
% 1.47/1.25 tff(386,plain,
% 1.47/1.25 (![U: $i] : (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp6) <=> ![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.47/1.25 inference(quant_intro,[status(thm)],[385])).
% 1.47/1.25 tff(387,axiom,(![U: $i] : (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause150')).
% 1.47/1.25 tff(388,plain,
% 1.47/1.25 (![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.47/1.25 inference(modus_ponens,[status(thm)],[387, 386])).
% 1.47/1.25 tff(389,plain,
% 1.47/1.25 (![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.47/1.25 inference(modus_ponens,[status(thm)],[388, 384])).
% 1.47/1.25 tff(390,plain,(
% 1.47/1.25 ![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.47/1.25 inference(skolemize,[status(sab)],[389])).
% 1.47/1.25 tff(391,plain,
% 1.47/1.25 (![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.47/1.25 inference(modus_ponens,[status(thm)],[390, 383])).
% 1.47/1.25 tff(392,plain,
% 1.47/1.25 (((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp6 | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | (~c1_1(a103)))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp6 | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | (~c1_1(a103)))),
% 1.47/1.25 inference(rewrite,[status(thm)],[])).
% 1.47/1.25 tff(393,plain,
% 1.47/1.25 ((hskp6 | (~ndr1_0) | c3_1(a103) | (~c0_1(a103)) | (~c1_1(a103))) <=> (hskp6 | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | (~c1_1(a103)))),
% 1.47/1.25 inference(rewrite,[status(thm)],[])).
% 1.47/1.25 tff(394,plain,
% 1.47/1.25 (((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp6 | (~ndr1_0) | c3_1(a103) | (~c0_1(a103)) | (~c1_1(a103)))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp6 | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | (~c1_1(a103))))),
% 1.47/1.25 inference(monotonicity,[status(thm)],[393])).
% 1.47/1.25 tff(395,plain,
% 1.47/1.25 (((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp6 | (~ndr1_0) | c3_1(a103) | (~c0_1(a103)) | (~c1_1(a103)))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp6 | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | (~c1_1(a103)))),
% 1.47/1.25 inference(transitivity,[status(thm)],[394, 392])).
% 1.47/1.25 tff(396,plain,
% 1.47/1.25 ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp6 | (~ndr1_0) | c3_1(a103) | (~c0_1(a103)) | (~c1_1(a103)))),
% 1.47/1.25 inference(quant_inst,[status(thm)],[])).
% 1.47/1.25 tff(397,plain,
% 1.47/1.25 ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp6 | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | (~c1_1(a103))),
% 1.47/1.25 inference(modus_ponens,[status(thm)],[396, 395])).
% 1.47/1.25 tff(398,plain,
% 1.47/1.25 (hskp6 | (~c1_1(a103))),
% 1.47/1.25 inference(unit_resolution,[status(thm)],[397, 126, 159, 147, 391])).
% 1.47/1.25 tff(399,plain,
% 1.47/1.25 (hskp6),
% 1.47/1.25 inference(unit_resolution,[status(thm)],[398, 371])).
% 1.47/1.25 tff(400,plain,
% 1.47/1.25 (((~hskp6) | (~c3_1(a105))) <=> ((~hskp6) | (~c3_1(a105)))),
% 1.47/1.25 inference(rewrite,[status(thm)],[])).
% 1.47/1.25 tff(401,plain,
% 1.47/1.25 (((~c3_1(a105)) | (~hskp6)) <=> ((~hskp6) | (~c3_1(a105)))),
% 1.47/1.25 inference(rewrite,[status(thm)],[])).
% 1.47/1.25 tff(402,axiom,((~c3_1(a105)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause122')).
% 1.47/1.25 tff(403,plain,
% 1.47/1.25 ((~hskp6) | (~c3_1(a105))),
% 1.47/1.25 inference(modus_ponens,[status(thm)],[402, 401])).
% 1.47/1.25 tff(404,plain,
% 1.47/1.25 ((~hskp6) | (~c3_1(a105))),
% 1.47/1.25 inference(modus_ponens,[status(thm)],[403, 400])).
% 1.47/1.25 tff(405,plain,
% 1.47/1.25 (~c3_1(a105)),
% 1.47/1.25 inference(unit_resolution,[status(thm)],[404, 399])).
% 1.47/1.25 tff(406,plain,
% 1.47/1.25 (((~hskp6) | c2_1(a105)) <=> ((~hskp6) | c2_1(a105))),
% 1.47/1.25 inference(rewrite,[status(thm)],[])).
% 1.47/1.25 tff(407,axiom,((~hskp6) | c2_1(a105)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause78')).
% 1.47/1.25 tff(408,plain,
% 1.47/1.25 ((~hskp6) | c2_1(a105)),
% 1.47/1.25 inference(modus_ponens,[status(thm)],[407, 406])).
% 1.47/1.25 tff(409,plain,
% 1.47/1.25 ((~hskp6) | c2_1(a105)),
% 1.47/1.25 inference(modus_ponens,[status(thm)],[408, 406])).
% 1.47/1.25 tff(410,plain,
% 1.47/1.25 ((~hskp6) | c2_1(a105)),
% 1.47/1.25 inference(modus_ponens,[status(thm)],[409, 406])).
% 1.47/1.25 tff(411,plain,
% 1.47/1.25 ((~hskp6) | c2_1(a105)),
% 1.47/1.25 inference(modus_ponens,[status(thm)],[410, 406])).
% 1.47/1.25 tff(412,plain,
% 1.47/1.25 ((~hskp6) | c2_1(a105)),
% 1.47/1.25 inference(modus_ponens,[status(thm)],[411, 406])).
% 1.47/1.25 tff(413,plain,
% 1.47/1.25 ((~hskp6) | c2_1(a105)),
% 1.47/1.25 inference(modus_ponens,[status(thm)],[412, 406])).
% 1.47/1.25 tff(414,plain,
% 1.47/1.25 ((~hskp6) | c2_1(a105)),
% 1.47/1.25 inference(modus_ponens,[status(thm)],[413, 406])).
% 1.47/1.25 tff(415,plain,
% 1.47/1.25 ((~hskp6) | c2_1(a105)),
% 1.47/1.25 inference(modus_ponens,[status(thm)],[414, 406])).
% 1.47/1.25 tff(416,plain,
% 1.47/1.25 (c2_1(a105)),
% 1.47/1.25 inference(unit_resolution,[status(thm)],[415, 399])).
% 1.47/1.25 tff(417,plain,
% 1.47/1.25 (((~hskp6) | c1_1(a105)) <=> ((~hskp6) | c1_1(a105))),
% 1.47/1.25 inference(rewrite,[status(thm)],[])).
% 1.47/1.25 tff(418,axiom,((~hskp6) | c1_1(a105)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause77')).
% 1.47/1.25 tff(419,plain,
% 1.47/1.25 ((~hskp6) | c1_1(a105)),
% 1.47/1.25 inference(modus_ponens,[status(thm)],[418, 417])).
% 1.47/1.25 tff(420,plain,
% 1.47/1.25 ((~hskp6) | c1_1(a105)),
% 1.47/1.25 inference(modus_ponens,[status(thm)],[419, 417])).
% 1.47/1.25 tff(421,plain,
% 1.47/1.25 ((~hskp6) | c1_1(a105)),
% 1.47/1.25 inference(modus_ponens,[status(thm)],[420, 417])).
% 1.47/1.25 tff(422,plain,
% 1.47/1.25 ((~hskp6) | c1_1(a105)),
% 1.47/1.25 inference(modus_ponens,[status(thm)],[421, 417])).
% 1.47/1.25 tff(423,plain,
% 1.47/1.25 ((~hskp6) | c1_1(a105)),
% 1.47/1.25 inference(modus_ponens,[status(thm)],[422, 417])).
% 1.47/1.25 tff(424,plain,
% 1.47/1.25 ((~hskp6) | c1_1(a105)),
% 1.47/1.25 inference(modus_ponens,[status(thm)],[423, 417])).
% 1.47/1.25 tff(425,plain,
% 1.47/1.25 ((~hskp6) | c1_1(a105)),
% 1.47/1.25 inference(modus_ponens,[status(thm)],[424, 417])).
% 1.47/1.25 tff(426,plain,
% 1.47/1.25 ((~hskp6) | c1_1(a105)),
% 1.47/1.25 inference(modus_ponens,[status(thm)],[425, 417])).
% 1.47/1.25 tff(427,plain,
% 1.47/1.25 (c1_1(a105)),
% 1.47/1.25 inference(unit_resolution,[status(thm)],[426, 399])).
% 1.47/1.25 tff(428,assumption,(~c1_1(a122)), introduced(assumption)).
% 1.47/1.25 tff(429,plain,
% 1.47/1.25 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)))),
% 1.47/1.25 inference(bind,[status(th)],[])).
% 1.47/1.25 tff(430,plain,
% 1.47/1.25 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 1.47/1.25 inference(quant_intro,[status(thm)],[429])).
% 1.47/1.25 tff(431,plain,
% 1.47/1.25 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 1.47/1.25 inference(rewrite,[status(thm)],[])).
% 1.47/1.25 tff(432,plain,
% 1.47/1.25 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))))),
% 1.47/1.26 inference(bind,[status(th)],[])).
% 1.47/1.26 tff(433,plain,
% 1.47/1.26 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 1.47/1.26 inference(quant_intro,[status(thm)],[432])).
% 1.47/1.26 tff(434,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause189')).
% 1.47/1.26 tff(435,plain,
% 1.47/1.26 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 1.47/1.26 inference(modus_ponens,[status(thm)],[434, 433])).
% 1.47/1.26 tff(436,plain,
% 1.47/1.26 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 1.47/1.26 inference(modus_ponens,[status(thm)],[435, 431])).
% 1.47/1.26 tff(437,plain,(
% 1.47/1.26 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 1.47/1.26 inference(skolemize,[status(sab)],[436])).
% 1.47/1.26 tff(438,plain,
% 1.47/1.26 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 1.47/1.26 inference(modus_ponens,[status(thm)],[437, 430])).
% 1.47/1.26 tff(439,assumption,(~c3_1(a105)), introduced(assumption)).
% 1.47/1.26 tff(440,assumption,(~c2_1(a122)), introduced(assumption)).
% 1.47/1.26 tff(441,assumption,(c2_1(a105)), introduced(assumption)).
% 1.47/1.26 tff(442,assumption,(c1_1(a105)), introduced(assumption)).
% 1.47/1.26 tff(443,plain,
% 1.47/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a122) | c2_1(a122) | c3_1(a105) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c1_1(a97)) | (~c2_1(a105)) | (~c1_1(a105)) | c3_1(a122))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a122) | c2_1(a122) | c3_1(a105) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c1_1(a97)) | (~c2_1(a105)) | (~c1_1(a105)) | c3_1(a122))),
% 1.47/1.26 inference(rewrite,[status(thm)],[])).
% 1.47/1.26 tff(444,plain,
% 1.47/1.26 (((~ndr1_0) | c3_1(a105) | (~c2_1(a105)) | (~c1_1(a105)) | c2_1(a97) | c3_1(a97) | (~c1_1(a97)) | c2_1(a122) | c1_1(a122) | c3_1(a122)) <=> (c1_1(a122) | c2_1(a122) | c3_1(a105) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c1_1(a97)) | (~c2_1(a105)) | (~c1_1(a105)) | c3_1(a122))),
% 1.47/1.26 inference(rewrite,[status(thm)],[])).
% 1.47/1.26 tff(445,plain,
% 1.47/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a105) | (~c2_1(a105)) | (~c1_1(a105)) | c2_1(a97) | c3_1(a97) | (~c1_1(a97)) | c2_1(a122) | c1_1(a122) | c3_1(a122))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a122) | c2_1(a122) | c3_1(a105) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c1_1(a97)) | (~c2_1(a105)) | (~c1_1(a105)) | c3_1(a122)))),
% 1.47/1.26 inference(monotonicity,[status(thm)],[444])).
% 1.47/1.26 tff(446,plain,
% 1.47/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a105) | (~c2_1(a105)) | (~c1_1(a105)) | c2_1(a97) | c3_1(a97) | (~c1_1(a97)) | c2_1(a122) | c1_1(a122) | c3_1(a122))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a122) | c2_1(a122) | c3_1(a105) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c1_1(a97)) | (~c2_1(a105)) | (~c1_1(a105)) | c3_1(a122))),
% 1.47/1.26 inference(transitivity,[status(thm)],[445, 443])).
% 1.47/1.26 tff(447,plain,
% 1.47/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a105) | (~c2_1(a105)) | (~c1_1(a105)) | c2_1(a97) | c3_1(a97) | (~c1_1(a97)) | c2_1(a122) | c1_1(a122) | c3_1(a122))),
% 1.47/1.26 inference(quant_inst,[status(thm)],[])).
% 1.47/1.26 tff(448,plain,
% 1.47/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a122) | c2_1(a122) | c3_1(a105) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c1_1(a97)) | (~c2_1(a105)) | (~c1_1(a105)) | c3_1(a122)),
% 1.47/1.26 inference(modus_ponens,[status(thm)],[447, 446])).
% 1.47/1.26 tff(449,plain,
% 1.47/1.26 (c3_1(a122)),
% 1.47/1.26 inference(unit_resolution,[status(thm)],[448, 126, 442, 441, 428, 440, 439, 31, 53, 438, 330])).
% 1.47/1.26 tff(450,plain,
% 1.47/1.26 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp28 | c1_1(a122) | c2_1(a122) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c3_1(a122)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp28 | c1_1(a122) | c2_1(a122) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c3_1(a122)))),
% 1.47/1.26 inference(rewrite,[status(thm)],[])).
% 1.47/1.26 tff(451,plain,
% 1.47/1.26 ((hskp28 | (~ndr1_0) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c2_1(a122) | c1_1(a122) | (~c3_1(a122))) <=> (hskp28 | c1_1(a122) | c2_1(a122) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c3_1(a122)))),
% 1.47/1.26 inference(rewrite,[status(thm)],[])).
% 1.47/1.26 tff(452,plain,
% 1.47/1.26 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c2_1(a122) | c1_1(a122) | (~c3_1(a122)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp28 | c1_1(a122) | c2_1(a122) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c3_1(a122))))),
% 1.47/1.26 inference(monotonicity,[status(thm)],[451])).
% 1.47/1.26 tff(453,plain,
% 1.47/1.26 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c2_1(a122) | c1_1(a122) | (~c3_1(a122)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp28 | c1_1(a122) | c2_1(a122) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c3_1(a122)))),
% 1.47/1.26 inference(transitivity,[status(thm)],[452, 450])).
% 1.47/1.26 tff(454,plain,
% 1.47/1.26 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c2_1(a122) | c1_1(a122) | (~c3_1(a122)))),
% 1.47/1.26 inference(quant_inst,[status(thm)],[])).
% 1.47/1.26 tff(455,plain,
% 1.47/1.26 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp28 | c1_1(a122) | c2_1(a122) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c3_1(a122))),
% 1.47/1.26 inference(modus_ponens,[status(thm)],[454, 453])).
% 1.47/1.26 tff(456,plain,
% 1.47/1.26 ($false),
% 1.47/1.26 inference(unit_resolution,[status(thm)],[455, 126, 145, 246, 428, 440, 31, 340, 330, 449])).
% 1.47/1.26 tff(457,plain,(c2_1(a122) | hskp28 | (~c0_1(a97)) | c1_1(a122) | c2_1(a97) | (~c1_1(a97)) | (~c1_1(a105)) | (~c2_1(a105)) | c3_1(a105) | c3_1(a97)), inference(lemma,lemma(discharge,[]))).
% 1.47/1.26 tff(458,plain,
% 1.47/1.26 (c2_1(a122)),
% 1.47/1.26 inference(unit_resolution,[status(thm)],[457, 428, 244, 145, 243, 329, 427, 416, 405, 237])).
% 1.47/1.26 tff(459,plain,
% 1.47/1.26 (((~hskp16) | (~c2_1(a122))) <=> ((~hskp16) | (~c2_1(a122)))),
% 1.47/1.26 inference(rewrite,[status(thm)],[])).
% 1.47/1.26 tff(460,plain,
% 1.47/1.26 (((~c2_1(a122)) | (~hskp16)) <=> ((~hskp16) | (~c2_1(a122)))),
% 1.47/1.26 inference(rewrite,[status(thm)],[])).
% 1.47/1.26 tff(461,axiom,((~c2_1(a122)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause105')).
% 1.47/1.26 tff(462,plain,
% 1.47/1.26 ((~hskp16) | (~c2_1(a122))),
% 1.47/1.26 inference(modus_ponens,[status(thm)],[461, 460])).
% 1.47/1.26 tff(463,plain,
% 1.47/1.26 ((~hskp16) | (~c2_1(a122))),
% 1.47/1.26 inference(modus_ponens,[status(thm)],[462, 459])).
% 1.47/1.26 tff(464,plain,
% 1.47/1.26 (~hskp16),
% 1.47/1.26 inference(unit_resolution,[status(thm)],[463, 458])).
% 1.47/1.26 tff(465,plain,
% 1.47/1.26 (^[U: $i] : refl((hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 1.47/1.26 inference(bind,[status(th)],[])).
% 1.47/1.26 tff(466,plain,
% 1.47/1.26 (![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.47/1.26 inference(quant_intro,[status(thm)],[465])).
% 1.47/1.26 tff(467,plain,
% 1.47/1.26 (![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.47/1.26 inference(rewrite,[status(thm)],[])).
% 1.47/1.26 tff(468,plain,
% 1.47/1.26 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp16) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp16))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp16) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp16) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp16) | hskp25) <=> ((hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp25))), rewrite(((hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp25) <=> (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp16) | hskp25) <=> (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 1.47/1.26 inference(bind,[status(th)],[])).
% 1.47/1.26 tff(469,plain,
% 1.47/1.26 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp16) | hskp25) <=> ![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.47/1.26 inference(quant_intro,[status(thm)],[468])).
% 1.47/1.26 tff(470,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp16) | hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause158')).
% 1.47/1.26 tff(471,plain,
% 1.47/1.26 (![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.47/1.26 inference(modus_ponens,[status(thm)],[470, 469])).
% 1.47/1.26 tff(472,plain,
% 1.47/1.26 (![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.47/1.26 inference(modus_ponens,[status(thm)],[471, 467])).
% 1.47/1.26 tff(473,plain,(
% 1.47/1.26 ![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.47/1.26 inference(skolemize,[status(sab)],[472])).
% 1.47/1.26 tff(474,plain,
% 1.47/1.26 (![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.47/1.26 inference(modus_ponens,[status(thm)],[473, 466])).
% 1.47/1.26 tff(475,plain,
% 1.47/1.26 (((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp25 | hskp16 | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)))) <=> ((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp25 | hskp16 | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)))),
% 1.47/1.26 inference(rewrite,[status(thm)],[])).
% 1.47/1.26 tff(476,plain,
% 1.47/1.26 ((hskp25 | hskp16 | (~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103))) <=> (hskp25 | hskp16 | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)))),
% 1.47/1.26 inference(rewrite,[status(thm)],[])).
% 1.47/1.26 tff(477,plain,
% 1.47/1.26 (((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp25 | hskp16 | (~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)))) <=> ((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp25 | hskp16 | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103))))),
% 1.47/1.26 inference(monotonicity,[status(thm)],[476])).
% 1.47/1.26 tff(478,plain,
% 1.47/1.26 (((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp25 | hskp16 | (~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)))) <=> ((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp25 | hskp16 | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)))),
% 1.47/1.26 inference(transitivity,[status(thm)],[477, 475])).
% 1.47/1.26 tff(479,plain,
% 1.47/1.26 ((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp25 | hskp16 | (~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)))),
% 1.47/1.26 inference(quant_inst,[status(thm)],[])).
% 1.47/1.26 tff(480,plain,
% 1.47/1.26 ((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp25 | hskp16 | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103))),
% 1.47/1.26 inference(modus_ponens,[status(thm)],[479, 478])).
% 1.47/1.26 tff(481,plain,
% 1.47/1.26 (hskp25 | hskp16),
% 1.47/1.26 inference(unit_resolution,[status(thm)],[480, 126, 159, 158, 147, 474])).
% 1.47/1.26 tff(482,plain,
% 1.47/1.26 (hskp25),
% 1.47/1.26 inference(unit_resolution,[status(thm)],[481, 464])).
% 1.47/1.26 tff(483,plain,
% 1.47/1.26 (((~hskp25) | (~c0_1(a173))) <=> ((~hskp25) | (~c0_1(a173)))),
% 1.47/1.26 inference(rewrite,[status(thm)],[])).
% 1.47/1.26 tff(484,plain,
% 1.47/1.26 (((~c0_1(a173)) | (~hskp25)) <=> ((~hskp25) | (~c0_1(a173)))),
% 1.47/1.26 inference(rewrite,[status(thm)],[])).
% 1.47/1.26 tff(485,axiom,((~c0_1(a173)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause88')).
% 1.47/1.26 tff(486,plain,
% 1.47/1.26 ((~hskp25) | (~c0_1(a173))),
% 1.47/1.26 inference(modus_ponens,[status(thm)],[485, 484])).
% 1.47/1.26 tff(487,plain,
% 1.47/1.26 ((~hskp25) | (~c0_1(a173))),
% 1.47/1.26 inference(modus_ponens,[status(thm)],[486, 483])).
% 1.47/1.26 tff(488,plain,
% 1.47/1.26 (~c0_1(a173)),
% 1.47/1.26 inference(unit_resolution,[status(thm)],[487, 482])).
% 1.47/1.26 tff(489,plain,
% 1.47/1.26 (((~hskp25) | c1_1(a173)) <=> ((~hskp25) | c1_1(a173))),
% 1.47/1.26 inference(rewrite,[status(thm)],[])).
% 1.47/1.26 tff(490,axiom,((~hskp25) | c1_1(a173)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause54')).
% 1.47/1.26 tff(491,plain,
% 1.47/1.26 ((~hskp25) | c1_1(a173)),
% 1.47/1.26 inference(modus_ponens,[status(thm)],[490, 489])).
% 1.47/1.26 tff(492,plain,
% 1.47/1.26 ((~hskp25) | c1_1(a173)),
% 1.47/1.26 inference(modus_ponens,[status(thm)],[491, 489])).
% 1.47/1.26 tff(493,plain,
% 1.47/1.26 ((~hskp25) | c1_1(a173)),
% 1.47/1.26 inference(modus_ponens,[status(thm)],[492, 489])).
% 1.47/1.26 tff(494,plain,
% 1.47/1.26 ((~hskp25) | c1_1(a173)),
% 1.47/1.26 inference(modus_ponens,[status(thm)],[493, 489])).
% 1.47/1.26 tff(495,plain,
% 1.47/1.26 ((~hskp25) | c1_1(a173)),
% 1.47/1.26 inference(modus_ponens,[status(thm)],[494, 489])).
% 1.47/1.26 tff(496,plain,
% 1.47/1.26 ((~hskp25) | c1_1(a173)),
% 1.47/1.26 inference(modus_ponens,[status(thm)],[495, 489])).
% 1.47/1.26 tff(497,plain,
% 1.47/1.26 ((~hskp25) | c1_1(a173)),
% 1.47/1.26 inference(modus_ponens,[status(thm)],[496, 489])).
% 1.47/1.26 tff(498,plain,
% 1.47/1.26 ((~hskp25) | c1_1(a173)),
% 1.47/1.26 inference(modus_ponens,[status(thm)],[497, 489])).
% 1.47/1.26 tff(499,plain,
% 1.47/1.26 (c1_1(a173)),
% 1.47/1.26 inference(unit_resolution,[status(thm)],[498, 482])).
% 1.47/1.26 tff(500,plain,
% 1.47/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a173) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a103)) | (~c2_1(a173)) | (~c1_1(a173)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a173) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a103)) | (~c2_1(a173)) | (~c1_1(a173)))),
% 1.47/1.26 inference(rewrite,[status(thm)],[])).
% 1.47/1.26 tff(501,plain,
% 1.47/1.26 (((~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a103)) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a173) | (~c2_1(a173)) | (~c1_1(a173))) <=> (c0_1(a173) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a103)) | (~c2_1(a173)) | (~c1_1(a173)))),
% 1.47/1.26 inference(rewrite,[status(thm)],[])).
% 1.47/1.26 tff(502,plain,
% 1.47/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a103)) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a173) | (~c2_1(a173)) | (~c1_1(a173)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a173) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a103)) | (~c2_1(a173)) | (~c1_1(a173))))),
% 1.47/1.26 inference(monotonicity,[status(thm)],[501])).
% 1.47/1.26 tff(503,plain,
% 1.47/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a103)) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a173) | (~c2_1(a173)) | (~c1_1(a173)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a173) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a103)) | (~c2_1(a173)) | (~c1_1(a173)))),
% 1.47/1.26 inference(transitivity,[status(thm)],[502, 500])).
% 1.47/1.26 tff(504,plain,
% 1.47/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a103)) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a173) | (~c2_1(a173)) | (~c1_1(a173)))),
% 1.47/1.26 inference(quant_inst,[status(thm)],[])).
% 1.47/1.26 tff(505,plain,
% 1.47/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a173) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a103)) | (~c2_1(a173)) | (~c1_1(a173))),
% 1.47/1.26 inference(modus_ponens,[status(thm)],[504, 503])).
% 1.47/1.26 tff(506,plain,
% 1.47/1.26 (~c2_1(a173)),
% 1.47/1.26 inference(unit_resolution,[status(thm)],[505, 126, 499, 159, 158, 244, 488, 243, 381, 371, 329])).
% 1.47/1.26 tff(507,assumption,(~hskp21), introduced(assumption)).
% 1.47/1.26 tff(508,plain,
% 1.47/1.26 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | c1_1(a122) | (~c2_1(a122)) | (~ndr1_0) | c3_1(a122))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp22 | hskp21 | c1_1(a122) | (~c2_1(a122)) | (~ndr1_0) | c3_1(a122))),
% 1.47/1.26 inference(rewrite,[status(thm)],[])).
% 1.47/1.26 tff(509,plain,
% 1.47/1.26 ((hskp22 | hskp21 | (~ndr1_0) | c1_1(a122) | c3_1(a122) | (~c2_1(a122))) <=> (hskp22 | hskp21 | c1_1(a122) | (~c2_1(a122)) | (~ndr1_0) | c3_1(a122))),
% 1.47/1.26 inference(rewrite,[status(thm)],[])).
% 1.47/1.26 tff(510,plain,
% 1.47/1.26 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c1_1(a122) | c3_1(a122) | (~c2_1(a122)))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | c1_1(a122) | (~c2_1(a122)) | (~ndr1_0) | c3_1(a122)))),
% 1.47/1.26 inference(monotonicity,[status(thm)],[509])).
% 1.47/1.26 tff(511,plain,
% 1.47/1.26 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c1_1(a122) | c3_1(a122) | (~c2_1(a122)))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp22 | hskp21 | c1_1(a122) | (~c2_1(a122)) | (~ndr1_0) | c3_1(a122))),
% 1.47/1.26 inference(transitivity,[status(thm)],[510, 508])).
% 1.47/1.26 tff(512,plain,
% 1.47/1.26 ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c1_1(a122) | c3_1(a122) | (~c2_1(a122)))),
% 1.47/1.26 inference(quant_inst,[status(thm)],[])).
% 1.47/1.26 tff(513,plain,
% 1.47/1.26 ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp22 | hskp21 | c1_1(a122) | (~c2_1(a122)) | (~ndr1_0) | c3_1(a122)),
% 1.47/1.26 inference(modus_ponens,[status(thm)],[512, 511])).
% 1.47/1.26 tff(514,plain,
% 1.47/1.26 ((~c2_1(a122)) | c3_1(a122)),
% 1.47/1.26 inference(unit_resolution,[status(thm)],[513, 126, 144, 507, 428, 173])).
% 1.47/1.26 tff(515,plain,
% 1.47/1.26 (c3_1(a122)),
% 1.47/1.26 inference(unit_resolution,[status(thm)],[514, 458])).
% 1.47/1.26 tff(516,plain,
% 1.47/1.26 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)))),
% 1.47/1.26 inference(bind,[status(th)],[])).
% 1.47/1.26 tff(517,plain,
% 1.47/1.26 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.47/1.26 inference(quant_intro,[status(thm)],[516])).
% 1.47/1.26 tff(518,plain,
% 1.47/1.26 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.47/1.26 inference(rewrite,[status(thm)],[])).
% 1.47/1.26 tff(519,plain,
% 1.47/1.26 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))))),
% 1.47/1.27 inference(bind,[status(th)],[])).
% 1.47/1.27 tff(520,plain,
% 1.47/1.27 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.47/1.27 inference(quant_intro,[status(thm)],[519])).
% 1.47/1.27 tff(521,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause191')).
% 1.47/1.27 tff(522,plain,
% 1.47/1.27 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.47/1.27 inference(modus_ponens,[status(thm)],[521, 520])).
% 1.47/1.27 tff(523,plain,
% 1.47/1.27 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.47/1.27 inference(modus_ponens,[status(thm)],[522, 518])).
% 1.47/1.27 tff(524,plain,(
% 1.47/1.27 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.47/1.27 inference(skolemize,[status(sab)],[523])).
% 1.47/1.27 tff(525,plain,
% 1.47/1.27 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.47/1.27 inference(modus_ponens,[status(thm)],[524, 517])).
% 1.47/1.27 tff(526,plain,
% 1.47/1.27 (((~hskp25) | (~c3_1(a173))) <=> ((~hskp25) | (~c3_1(a173)))),
% 1.47/1.27 inference(rewrite,[status(thm)],[])).
% 1.47/1.27 tff(527,plain,
% 1.47/1.27 (((~c3_1(a173)) | (~hskp25)) <=> ((~hskp25) | (~c3_1(a173)))),
% 1.47/1.27 inference(rewrite,[status(thm)],[])).
% 1.47/1.27 tff(528,axiom,((~c3_1(a173)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause89')).
% 1.47/1.27 tff(529,plain,
% 1.47/1.27 ((~hskp25) | (~c3_1(a173))),
% 1.47/1.27 inference(modus_ponens,[status(thm)],[528, 527])).
% 1.47/1.27 tff(530,plain,
% 1.47/1.27 ((~hskp25) | (~c3_1(a173))),
% 1.47/1.27 inference(modus_ponens,[status(thm)],[529, 526])).
% 1.47/1.27 tff(531,plain,
% 1.47/1.27 (~c3_1(a173)),
% 1.47/1.27 inference(unit_resolution,[status(thm)],[530, 482])).
% 1.47/1.27 tff(532,plain,
% 1.47/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | (c1_1(a122) | (~c2_1(a122)) | (~ndr1_0) | (~c0_1(a122)) | (~c3_1(a122)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a122) | (~c2_1(a122)) | (~ndr1_0) | (~c0_1(a122)) | (~c3_1(a122)))),
% 1.47/1.27 inference(rewrite,[status(thm)],[])).
% 1.47/1.27 tff(533,plain,
% 1.47/1.27 (((~ndr1_0) | (~c2_1(a122)) | (~c3_1(a122)) | (~c0_1(a122)) | c1_1(a122) | (~c2_1(a122)) | (~c3_1(a122)) | c1_1(a122) | (~c0_1(a122)) | (~c2_1(a122))) <=> (c1_1(a122) | (~c2_1(a122)) | (~ndr1_0) | (~c0_1(a122)) | (~c3_1(a122)))),
% 1.47/1.27 inference(rewrite,[status(thm)],[])).
% 1.47/1.27 tff(534,plain,
% 1.47/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a122)) | (~c3_1(a122)) | (~c0_1(a122)) | c1_1(a122) | (~c2_1(a122)) | (~c3_1(a122)) | c1_1(a122) | (~c0_1(a122)) | (~c2_1(a122)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | (c1_1(a122) | (~c2_1(a122)) | (~ndr1_0) | (~c0_1(a122)) | (~c3_1(a122))))),
% 1.47/1.27 inference(monotonicity,[status(thm)],[533])).
% 1.47/1.27 tff(535,plain,
% 1.47/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a122)) | (~c3_1(a122)) | (~c0_1(a122)) | c1_1(a122) | (~c2_1(a122)) | (~c3_1(a122)) | c1_1(a122) | (~c0_1(a122)) | (~c2_1(a122)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a122) | (~c2_1(a122)) | (~ndr1_0) | (~c0_1(a122)) | (~c3_1(a122)))),
% 1.47/1.27 inference(transitivity,[status(thm)],[534, 532])).
% 1.47/1.27 tff(536,plain,
% 1.47/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a122)) | (~c3_1(a122)) | (~c0_1(a122)) | c1_1(a122) | (~c2_1(a122)) | (~c3_1(a122)) | c1_1(a122) | (~c0_1(a122)) | (~c2_1(a122)))),
% 1.47/1.27 inference(quant_inst,[status(thm)],[])).
% 1.47/1.27 tff(537,plain,
% 1.47/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a122) | (~c2_1(a122)) | (~ndr1_0) | (~c0_1(a122)) | (~c3_1(a122))),
% 1.47/1.27 inference(modus_ponens,[status(thm)],[536, 535])).
% 1.47/1.27 tff(538,plain,
% 1.47/1.27 (~c0_1(a122)),
% 1.47/1.27 inference(unit_resolution,[status(thm)],[537, 126, 428, 458, 10, 515])).
% 1.47/1.27 tff(539,plain,
% 1.47/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a122) | c0_1(a173) | c3_1(a173) | (~c2_1(a122)) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c3_1(a122)) | c2_1(a173))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a122) | c0_1(a173) | c3_1(a173) | (~c2_1(a122)) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c3_1(a122)) | c2_1(a173))),
% 1.47/1.27 inference(rewrite,[status(thm)],[])).
% 1.47/1.27 tff(540,plain,
% 1.47/1.27 (((~ndr1_0) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a122) | (~c2_1(a122)) | (~c3_1(a122)) | c2_1(a173) | c0_1(a173) | c3_1(a173)) <=> (c0_1(a122) | c0_1(a173) | c3_1(a173) | (~c2_1(a122)) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c3_1(a122)) | c2_1(a173))),
% 1.47/1.27 inference(rewrite,[status(thm)],[])).
% 1.47/1.27 tff(541,plain,
% 1.47/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a122) | (~c2_1(a122)) | (~c3_1(a122)) | c2_1(a173) | c0_1(a173) | c3_1(a173))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a122) | c0_1(a173) | c3_1(a173) | (~c2_1(a122)) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c3_1(a122)) | c2_1(a173)))),
% 1.47/1.27 inference(monotonicity,[status(thm)],[540])).
% 1.47/1.27 tff(542,plain,
% 1.47/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a122) | (~c2_1(a122)) | (~c3_1(a122)) | c2_1(a173) | c0_1(a173) | c3_1(a173))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a122) | c0_1(a173) | c3_1(a173) | (~c2_1(a122)) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c3_1(a122)) | c2_1(a173))),
% 1.47/1.27 inference(transitivity,[status(thm)],[541, 539])).
% 1.47/1.27 tff(543,plain,
% 1.47/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a122) | (~c2_1(a122)) | (~c3_1(a122)) | c2_1(a173) | c0_1(a173) | c3_1(a173))),
% 1.47/1.27 inference(quant_inst,[status(thm)],[])).
% 1.47/1.27 tff(544,plain,
% 1.47/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a122) | c0_1(a173) | c3_1(a173) | (~c2_1(a122)) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c3_1(a122)) | c2_1(a173)),
% 1.47/1.27 inference(modus_ponens,[status(thm)],[543, 542])).
% 1.47/1.27 tff(545,plain,
% 1.47/1.27 ($false),
% 1.47/1.27 inference(unit_resolution,[status(thm)],[544, 126, 538, 244, 488, 531, 458, 243, 525, 329, 515, 506])).
% 1.47/1.27 tff(546,plain,(c1_1(a122) | hskp22 | hskp21 | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.47/1.27 tff(547,plain,
% 1.47/1.27 (c1_1(a122)),
% 1.47/1.27 inference(unit_resolution,[status(thm)],[546, 353, 144, 145])).
% 1.47/1.27 tff(548,plain,
% 1.47/1.27 (((~hskp16) | (~c1_1(a122))) <=> ((~hskp16) | (~c1_1(a122)))),
% 1.47/1.27 inference(rewrite,[status(thm)],[])).
% 1.47/1.27 tff(549,plain,
% 1.47/1.27 (((~c1_1(a122)) | (~hskp16)) <=> ((~hskp16) | (~c1_1(a122)))),
% 1.47/1.27 inference(rewrite,[status(thm)],[])).
% 1.47/1.27 tff(550,axiom,((~c1_1(a122)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause104')).
% 1.47/1.27 tff(551,plain,
% 1.47/1.27 ((~hskp16) | (~c1_1(a122))),
% 1.47/1.27 inference(modus_ponens,[status(thm)],[550, 549])).
% 1.47/1.27 tff(552,plain,
% 1.47/1.27 ((~hskp16) | (~c1_1(a122))),
% 1.47/1.27 inference(modus_ponens,[status(thm)],[551, 548])).
% 1.47/1.27 tff(553,plain,
% 1.47/1.27 (~hskp16),
% 1.47/1.27 inference(unit_resolution,[status(thm)],[552, 547])).
% 1.47/1.27 tff(554,plain,
% 1.47/1.27 (c1_1(a122)),
% 1.47/1.27 inference(unit_resolution,[status(thm)],[546, 507, 144, 145])).
% 1.47/1.27 tff(555,plain,
% 1.47/1.27 (~hskp16),
% 1.47/1.27 inference(unit_resolution,[status(thm)],[552, 554])).
% 1.47/1.27 tff(556,plain,
% 1.47/1.27 (hskp25),
% 1.47/1.27 inference(unit_resolution,[status(thm)],[481, 555])).
% 1.47/1.27 tff(557,plain,
% 1.47/1.27 (~c0_1(a173)),
% 1.47/1.27 inference(unit_resolution,[status(thm)],[487, 556])).
% 1.47/1.27 tff(558,plain,
% 1.47/1.27 (c1_1(a173)),
% 1.47/1.27 inference(unit_resolution,[status(thm)],[498, 556])).
% 1.47/1.27 tff(559,plain,
% 1.47/1.27 (~c2_1(a173)),
% 1.47/1.27 inference(unit_resolution,[status(thm)],[505, 126, 558, 159, 158, 244, 557, 243, 381, 371, 329])).
% 1.47/1.27 tff(560,plain,
% 1.47/1.27 (^[U: $i] : refl((hskp16 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> (hskp16 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))),
% 1.47/1.27 inference(bind,[status(th)],[])).
% 1.47/1.27 tff(561,plain,
% 1.47/1.27 (![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.47/1.27 inference(quant_intro,[status(thm)],[560])).
% 1.47/1.27 tff(562,plain,
% 1.47/1.27 (![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.47/1.27 inference(rewrite,[status(thm)],[])).
% 1.47/1.27 tff(563,plain,
% 1.47/1.27 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp16) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp16))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp16) <=> (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp16) <=> (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp16) | hskp2) <=> ((hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp2))), rewrite(((hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp2) <=> (hskp16 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp16) | hskp2) <=> (hskp16 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))))),
% 1.47/1.27 inference(bind,[status(th)],[])).
% 1.47/1.27 tff(564,plain,
% 1.47/1.27 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp16) | hskp2) <=> ![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.47/1.27 inference(quant_intro,[status(thm)],[563])).
% 1.47/1.27 tff(565,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp16) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause148')).
% 1.47/1.27 tff(566,plain,
% 1.47/1.27 (![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.47/1.27 inference(modus_ponens,[status(thm)],[565, 564])).
% 1.47/1.27 tff(567,plain,
% 1.47/1.27 (![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.47/1.27 inference(modus_ponens,[status(thm)],[566, 562])).
% 1.47/1.27 tff(568,plain,(
% 1.47/1.27 ![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.47/1.27 inference(skolemize,[status(sab)],[567])).
% 1.47/1.27 tff(569,plain,
% 1.47/1.27 (![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.47/1.27 inference(modus_ponens,[status(thm)],[568, 561])).
% 1.47/1.27 tff(570,plain,
% 1.47/1.27 (((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp16 | hskp2 | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)))) <=> ((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp16 | hskp2 | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)))),
% 1.47/1.27 inference(rewrite,[status(thm)],[])).
% 1.47/1.27 tff(571,plain,
% 1.47/1.27 ((hskp16 | hskp2 | (~ndr1_0) | c2_1(a97) | c3_1(a97) | (~c0_1(a97))) <=> (hskp16 | hskp2 | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)))),
% 1.47/1.27 inference(rewrite,[status(thm)],[])).
% 1.47/1.27 tff(572,plain,
% 1.47/1.27 (((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp16 | hskp2 | (~ndr1_0) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)))) <=> ((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp16 | hskp2 | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97))))),
% 1.47/1.27 inference(monotonicity,[status(thm)],[571])).
% 1.47/1.27 tff(573,plain,
% 1.47/1.27 (((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp16 | hskp2 | (~ndr1_0) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)))) <=> ((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp16 | hskp2 | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)))),
% 1.53/1.27 inference(transitivity,[status(thm)],[572, 570])).
% 1.53/1.27 tff(574,plain,
% 1.53/1.27 ((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp16 | hskp2 | (~ndr1_0) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)))),
% 1.53/1.27 inference(quant_inst,[status(thm)],[])).
% 1.53/1.27 tff(575,plain,
% 1.53/1.27 ((~![U: $i] : (hskp16 | hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp16 | hskp2 | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97))),
% 1.53/1.27 inference(modus_ponens,[status(thm)],[574, 573])).
% 1.53/1.27 tff(576,plain,
% 1.53/1.27 (hskp16 | hskp2),
% 1.53/1.27 inference(unit_resolution,[status(thm)],[575, 126, 244, 243, 237, 569])).
% 1.53/1.27 tff(577,plain,
% 1.53/1.27 (hskp2),
% 1.53/1.27 inference(unit_resolution,[status(thm)],[576, 555])).
% 1.53/1.27 tff(578,plain,
% 1.53/1.27 (((~hskp2) | c2_1(a99)) <=> ((~hskp2) | c2_1(a99))),
% 1.53/1.27 inference(rewrite,[status(thm)],[])).
% 1.53/1.27 tff(579,axiom,((~hskp2) | c2_1(a99)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause84')).
% 1.53/1.27 tff(580,plain,
% 1.53/1.27 ((~hskp2) | c2_1(a99)),
% 1.53/1.27 inference(modus_ponens,[status(thm)],[579, 578])).
% 1.53/1.27 tff(581,plain,
% 1.53/1.27 ((~hskp2) | c2_1(a99)),
% 1.53/1.27 inference(modus_ponens,[status(thm)],[580, 578])).
% 1.53/1.27 tff(582,plain,
% 1.53/1.27 ((~hskp2) | c2_1(a99)),
% 1.53/1.27 inference(modus_ponens,[status(thm)],[581, 578])).
% 1.53/1.27 tff(583,plain,
% 1.53/1.27 ((~hskp2) | c2_1(a99)),
% 1.53/1.27 inference(modus_ponens,[status(thm)],[582, 578])).
% 1.53/1.27 tff(584,plain,
% 1.53/1.27 ((~hskp2) | c2_1(a99)),
% 1.53/1.27 inference(modus_ponens,[status(thm)],[583, 578])).
% 1.53/1.27 tff(585,plain,
% 1.53/1.27 ((~hskp2) | c2_1(a99)),
% 1.53/1.27 inference(modus_ponens,[status(thm)],[584, 578])).
% 1.53/1.27 tff(586,plain,
% 1.53/1.27 ((~hskp2) | c2_1(a99)),
% 1.53/1.27 inference(modus_ponens,[status(thm)],[585, 578])).
% 1.53/1.27 tff(587,plain,
% 1.53/1.27 ((~hskp2) | c2_1(a99)),
% 1.53/1.27 inference(modus_ponens,[status(thm)],[586, 578])).
% 1.53/1.27 tff(588,plain,
% 1.53/1.27 (c2_1(a99)),
% 1.53/1.27 inference(unit_resolution,[status(thm)],[587, 577])).
% 1.53/1.27 tff(589,assumption,(~c1_1(a99)), introduced(assumption)).
% 1.53/1.27 tff(590,plain,
% 1.53/1.27 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c3_1(a99))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp22 | hskp21 | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c3_1(a99))),
% 1.53/1.27 inference(rewrite,[status(thm)],[])).
% 1.53/1.27 tff(591,plain,
% 1.53/1.27 ((hskp22 | hskp21 | (~ndr1_0) | c1_1(a99) | c3_1(a99) | (~c2_1(a99))) <=> (hskp22 | hskp21 | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c3_1(a99))),
% 1.53/1.27 inference(rewrite,[status(thm)],[])).
% 1.53/1.27 tff(592,plain,
% 1.53/1.27 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c1_1(a99) | c3_1(a99) | (~c2_1(a99)))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c3_1(a99)))),
% 1.53/1.27 inference(monotonicity,[status(thm)],[591])).
% 1.53/1.27 tff(593,plain,
% 1.53/1.27 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c1_1(a99) | c3_1(a99) | (~c2_1(a99)))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp22 | hskp21 | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c3_1(a99))),
% 1.53/1.27 inference(transitivity,[status(thm)],[592, 590])).
% 1.53/1.27 tff(594,plain,
% 1.53/1.27 ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c1_1(a99) | c3_1(a99) | (~c2_1(a99)))),
% 1.53/1.27 inference(quant_inst,[status(thm)],[])).
% 1.53/1.27 tff(595,plain,
% 1.53/1.27 ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp22 | hskp21 | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c3_1(a99)),
% 1.53/1.27 inference(modus_ponens,[status(thm)],[594, 593])).
% 1.53/1.27 tff(596,plain,
% 1.53/1.27 (hskp21 | (~c2_1(a99)) | c3_1(a99)),
% 1.53/1.27 inference(unit_resolution,[status(thm)],[595, 126, 144, 589, 173])).
% 1.53/1.27 tff(597,plain,
% 1.53/1.27 (c3_1(a99)),
% 1.53/1.27 inference(unit_resolution,[status(thm)],[596, 588, 507])).
% 1.53/1.28 tff(598,plain,
% 1.53/1.28 (((~hskp2) | (~c0_1(a99))) <=> ((~hskp2) | (~c0_1(a99)))),
% 1.53/1.28 inference(rewrite,[status(thm)],[])).
% 1.53/1.28 tff(599,plain,
% 1.53/1.28 (((~c0_1(a99)) | (~hskp2)) <=> ((~hskp2) | (~c0_1(a99)))),
% 1.53/1.28 inference(rewrite,[status(thm)],[])).
% 1.53/1.28 tff(600,axiom,((~c0_1(a99)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause127')).
% 1.53/1.28 tff(601,plain,
% 1.53/1.28 ((~hskp2) | (~c0_1(a99))),
% 1.53/1.28 inference(modus_ponens,[status(thm)],[600, 599])).
% 1.53/1.28 tff(602,plain,
% 1.53/1.28 ((~hskp2) | (~c0_1(a99))),
% 1.53/1.28 inference(modus_ponens,[status(thm)],[601, 598])).
% 1.53/1.28 tff(603,plain,
% 1.53/1.28 (~c0_1(a99)),
% 1.53/1.28 inference(unit_resolution,[status(thm)],[602, 577])).
% 1.53/1.28 tff(604,plain,
% 1.53/1.28 (~c3_1(a173)),
% 1.53/1.28 inference(unit_resolution,[status(thm)],[530, 556])).
% 1.53/1.28 tff(605,plain,
% 1.53/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a173) | c3_1(a173) | c0_1(a99) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c2_1(a99)) | (~c3_1(a99)) | c2_1(a173))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a173) | c3_1(a173) | c0_1(a99) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c2_1(a99)) | (~c3_1(a99)) | c2_1(a173))),
% 1.53/1.28 inference(rewrite,[status(thm)],[])).
% 1.53/1.28 tff(606,plain,
% 1.53/1.28 (((~ndr1_0) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a99) | (~c2_1(a99)) | (~c3_1(a99)) | c2_1(a173) | c0_1(a173) | c3_1(a173)) <=> (c0_1(a173) | c3_1(a173) | c0_1(a99) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c2_1(a99)) | (~c3_1(a99)) | c2_1(a173))),
% 1.53/1.28 inference(rewrite,[status(thm)],[])).
% 1.53/1.28 tff(607,plain,
% 1.53/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a99) | (~c2_1(a99)) | (~c3_1(a99)) | c2_1(a173) | c0_1(a173) | c3_1(a173))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a173) | c3_1(a173) | c0_1(a99) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c2_1(a99)) | (~c3_1(a99)) | c2_1(a173)))),
% 1.53/1.28 inference(monotonicity,[status(thm)],[606])).
% 1.53/1.28 tff(608,plain,
% 1.53/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a99) | (~c2_1(a99)) | (~c3_1(a99)) | c2_1(a173) | c0_1(a173) | c3_1(a173))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a173) | c3_1(a173) | c0_1(a99) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c2_1(a99)) | (~c3_1(a99)) | c2_1(a173))),
% 1.53/1.28 inference(transitivity,[status(thm)],[607, 605])).
% 1.53/1.28 tff(609,plain,
% 1.53/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a99) | (~c2_1(a99)) | (~c3_1(a99)) | c2_1(a173) | c0_1(a173) | c3_1(a173))),
% 1.53/1.28 inference(quant_inst,[status(thm)],[])).
% 1.53/1.28 tff(610,plain,
% 1.53/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a173) | c3_1(a173) | c0_1(a99) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | (~c2_1(a99)) | (~c3_1(a99)) | c2_1(a173)),
% 1.53/1.28 inference(modus_ponens,[status(thm)],[609, 608])).
% 1.53/1.28 tff(611,plain,
% 1.53/1.28 ($false),
% 1.53/1.28 inference(unit_resolution,[status(thm)],[610, 126, 588, 244, 557, 604, 603, 243, 525, 597, 329, 559])).
% 1.53/1.28 tff(612,plain,(hskp21 | hskp22 | c1_1(a99) | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.53/1.28 tff(613,plain,
% 1.53/1.28 (c1_1(a99)),
% 1.53/1.28 inference(unit_resolution,[status(thm)],[612, 353, 144, 145])).
% 1.53/1.28 tff(614,plain,
% 1.53/1.28 (((~hskp2) | (~c1_1(a99))) <=> ((~hskp2) | (~c1_1(a99)))),
% 1.53/1.28 inference(rewrite,[status(thm)],[])).
% 1.53/1.28 tff(615,plain,
% 1.53/1.28 (((~c1_1(a99)) | (~hskp2)) <=> ((~hskp2) | (~c1_1(a99)))),
% 1.53/1.28 inference(rewrite,[status(thm)],[])).
% 1.53/1.28 tff(616,axiom,((~c1_1(a99)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause128')).
% 1.53/1.28 tff(617,plain,
% 1.53/1.28 ((~hskp2) | (~c1_1(a99))),
% 1.53/1.28 inference(modus_ponens,[status(thm)],[616, 615])).
% 1.53/1.28 tff(618,plain,
% 1.53/1.28 ((~hskp2) | (~c1_1(a99))),
% 1.53/1.28 inference(modus_ponens,[status(thm)],[617, 614])).
% 1.53/1.28 tff(619,plain,
% 1.53/1.28 (~hskp2),
% 1.53/1.28 inference(unit_resolution,[status(thm)],[618, 613])).
% 1.53/1.28 tff(620,plain,
% 1.53/1.28 ($false),
% 1.53/1.28 inference(unit_resolution,[status(thm)],[576, 619, 553])).
% 1.53/1.28 tff(621,plain,(hskp28 | hskp22), inference(lemma,lemma(discharge,[]))).
% 1.53/1.28 tff(622,plain,
% 1.53/1.28 (hskp28),
% 1.53/1.28 inference(unit_resolution,[status(thm)],[621, 144])).
% 1.53/1.28 tff(623,plain,
% 1.53/1.28 (((~hskp28) | c0_1(a137)) <=> ((~hskp28) | c0_1(a137))),
% 1.53/1.28 inference(rewrite,[status(thm)],[])).
% 1.53/1.28 tff(624,axiom,((~hskp28) | c0_1(a137)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause46')).
% 1.53/1.28 tff(625,plain,
% 1.53/1.28 ((~hskp28) | c0_1(a137)),
% 1.53/1.28 inference(modus_ponens,[status(thm)],[624, 623])).
% 1.53/1.28 tff(626,plain,
% 1.53/1.28 ((~hskp28) | c0_1(a137)),
% 1.53/1.28 inference(modus_ponens,[status(thm)],[625, 623])).
% 1.53/1.28 tff(627,plain,
% 1.53/1.28 ((~hskp28) | c0_1(a137)),
% 1.53/1.28 inference(modus_ponens,[status(thm)],[626, 623])).
% 1.53/1.28 tff(628,plain,
% 1.53/1.28 ((~hskp28) | c0_1(a137)),
% 1.53/1.28 inference(modus_ponens,[status(thm)],[627, 623])).
% 1.53/1.28 tff(629,plain,
% 1.53/1.28 ((~hskp28) | c0_1(a137)),
% 1.53/1.28 inference(modus_ponens,[status(thm)],[628, 623])).
% 1.53/1.28 tff(630,plain,
% 1.53/1.28 ((~hskp28) | c0_1(a137)),
% 1.53/1.28 inference(modus_ponens,[status(thm)],[629, 623])).
% 1.53/1.28 tff(631,plain,
% 1.53/1.28 ((~hskp28) | c0_1(a137)),
% 1.53/1.28 inference(modus_ponens,[status(thm)],[630, 623])).
% 1.53/1.28 tff(632,plain,
% 1.53/1.28 ((~hskp28) | c0_1(a137)),
% 1.53/1.28 inference(modus_ponens,[status(thm)],[631, 623])).
% 1.53/1.28 tff(633,plain,
% 1.53/1.28 (c0_1(a137)),
% 1.53/1.28 inference(unit_resolution,[status(thm)],[632, 622])).
% 1.53/1.28 tff(634,plain,
% 1.53/1.28 (((~hskp28) | c2_1(a137)) <=> ((~hskp28) | c2_1(a137))),
% 1.53/1.28 inference(rewrite,[status(thm)],[])).
% 1.53/1.28 tff(635,axiom,((~hskp28) | c2_1(a137)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause48')).
% 1.53/1.28 tff(636,plain,
% 1.53/1.28 ((~hskp28) | c2_1(a137)),
% 1.53/1.28 inference(modus_ponens,[status(thm)],[635, 634])).
% 1.53/1.28 tff(637,plain,
% 1.53/1.28 ((~hskp28) | c2_1(a137)),
% 1.53/1.28 inference(modus_ponens,[status(thm)],[636, 634])).
% 1.53/1.28 tff(638,plain,
% 1.53/1.28 ((~hskp28) | c2_1(a137)),
% 1.53/1.28 inference(modus_ponens,[status(thm)],[637, 634])).
% 1.53/1.28 tff(639,plain,
% 1.53/1.28 ((~hskp28) | c2_1(a137)),
% 1.53/1.28 inference(modus_ponens,[status(thm)],[638, 634])).
% 1.53/1.28 tff(640,plain,
% 1.53/1.28 ((~hskp28) | c2_1(a137)),
% 1.53/1.28 inference(modus_ponens,[status(thm)],[639, 634])).
% 1.53/1.28 tff(641,plain,
% 1.53/1.28 ((~hskp28) | c2_1(a137)),
% 1.53/1.28 inference(modus_ponens,[status(thm)],[640, 634])).
% 1.53/1.28 tff(642,plain,
% 1.53/1.28 ((~hskp28) | c2_1(a137)),
% 1.53/1.28 inference(modus_ponens,[status(thm)],[641, 634])).
% 1.53/1.28 tff(643,plain,
% 1.53/1.28 ((~hskp28) | c2_1(a137)),
% 1.53/1.28 inference(modus_ponens,[status(thm)],[642, 634])).
% 1.53/1.28 tff(644,plain,
% 1.53/1.28 (c2_1(a137)),
% 1.53/1.28 inference(unit_resolution,[status(thm)],[643, 622])).
% 1.53/1.28 tff(645,plain,
% 1.53/1.28 (((~hskp28) | c1_1(a137)) <=> ((~hskp28) | c1_1(a137))),
% 1.53/1.28 inference(rewrite,[status(thm)],[])).
% 1.53/1.28 tff(646,axiom,((~hskp28) | c1_1(a137)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause47')).
% 1.53/1.28 tff(647,plain,
% 1.53/1.28 ((~hskp28) | c1_1(a137)),
% 1.53/1.28 inference(modus_ponens,[status(thm)],[646, 645])).
% 1.53/1.28 tff(648,plain,
% 1.53/1.28 ((~hskp28) | c1_1(a137)),
% 1.53/1.28 inference(modus_ponens,[status(thm)],[647, 645])).
% 1.53/1.28 tff(649,plain,
% 1.53/1.28 ((~hskp28) | c1_1(a137)),
% 1.53/1.28 inference(modus_ponens,[status(thm)],[648, 645])).
% 1.53/1.28 tff(650,plain,
% 1.53/1.28 ((~hskp28) | c1_1(a137)),
% 1.53/1.28 inference(modus_ponens,[status(thm)],[649, 645])).
% 1.53/1.28 tff(651,plain,
% 1.53/1.28 ((~hskp28) | c1_1(a137)),
% 1.53/1.28 inference(modus_ponens,[status(thm)],[650, 645])).
% 1.53/1.28 tff(652,plain,
% 1.53/1.28 ((~hskp28) | c1_1(a137)),
% 1.53/1.28 inference(modus_ponens,[status(thm)],[651, 645])).
% 1.53/1.28 tff(653,plain,
% 1.53/1.28 ((~hskp28) | c1_1(a137)),
% 1.53/1.28 inference(modus_ponens,[status(thm)],[652, 645])).
% 1.53/1.28 tff(654,plain,
% 1.53/1.28 ((~hskp28) | c1_1(a137)),
% 1.53/1.28 inference(modus_ponens,[status(thm)],[653, 645])).
% 1.53/1.28 tff(655,plain,
% 1.53/1.28 (c1_1(a137)),
% 1.53/1.28 inference(unit_resolution,[status(thm)],[654, 622])).
% 1.53/1.28 tff(656,plain,
% 1.53/1.28 (((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp0 | (~ndr1_0) | (~c0_1(a137)) | c3_1(a137) | (~c1_1(a137)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp0 | (~ndr1_0) | (~c0_1(a137)) | c3_1(a137) | (~c1_1(a137)))),
% 1.53/1.28 inference(rewrite,[status(thm)],[])).
% 1.53/1.28 tff(657,plain,
% 1.53/1.28 ((hskp0 | (~ndr1_0) | c3_1(a137) | (~c0_1(a137)) | (~c1_1(a137))) <=> (hskp0 | (~ndr1_0) | (~c0_1(a137)) | c3_1(a137) | (~c1_1(a137)))),
% 1.53/1.28 inference(rewrite,[status(thm)],[])).
% 1.53/1.28 tff(658,plain,
% 1.53/1.28 (((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp0 | (~ndr1_0) | c3_1(a137) | (~c0_1(a137)) | (~c1_1(a137)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp0 | (~ndr1_0) | (~c0_1(a137)) | c3_1(a137) | (~c1_1(a137))))),
% 1.53/1.28 inference(monotonicity,[status(thm)],[657])).
% 1.53/1.28 tff(659,plain,
% 1.53/1.28 (((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp0 | (~ndr1_0) | c3_1(a137) | (~c0_1(a137)) | (~c1_1(a137)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp0 | (~ndr1_0) | (~c0_1(a137)) | c3_1(a137) | (~c1_1(a137)))),
% 1.53/1.28 inference(transitivity,[status(thm)],[658, 656])).
% 1.53/1.28 tff(660,plain,
% 1.53/1.28 ((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp0 | (~ndr1_0) | c3_1(a137) | (~c0_1(a137)) | (~c1_1(a137)))),
% 1.53/1.28 inference(quant_inst,[status(thm)],[])).
% 1.53/1.28 tff(661,plain,
% 1.53/1.28 ((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp0 | (~ndr1_0) | (~c0_1(a137)) | c3_1(a137) | (~c1_1(a137))),
% 1.53/1.28 inference(modus_ponens,[status(thm)],[660, 659])).
% 1.53/1.28 tff(662,plain,
% 1.53/1.28 (hskp0 | c3_1(a137)),
% 1.53/1.28 inference(unit_resolution,[status(thm)],[661, 126, 633, 655, 75])).
% 1.53/1.28 tff(663,plain,
% 1.53/1.28 (c3_1(a137)),
% 1.53/1.28 inference(unit_resolution,[status(thm)],[662, 94])).
% 1.53/1.28 tff(664,assumption,(c0_1(a137)), introduced(assumption)).
% 1.53/1.28 tff(665,assumption,(c3_1(a137)), introduced(assumption)).
% 1.53/1.28 tff(666,assumption,(c1_1(a137)), introduced(assumption)).
% 1.53/1.28 tff(667,assumption,(c2_1(a137)), introduced(assumption)).
% 1.53/1.28 tff(668,assumption,(hskp18), introduced(assumption)).
% 1.53/1.28 tff(669,plain,
% 1.53/1.28 (~c1_1(a129)),
% 1.53/1.28 inference(unit_resolution,[status(thm)],[297, 668])).
% 1.53/1.28 tff(670,plain,
% 1.53/1.28 (c0_1(a129)),
% 1.53/1.28 inference(unit_resolution,[status(thm)],[319, 668])).
% 1.53/1.28 tff(671,plain,
% 1.53/1.28 (c2_1(a129)),
% 1.53/1.28 inference(unit_resolution,[status(thm)],[308, 668])).
% 1.53/1.28 tff(672,assumption,(~c1_1(a129)), introduced(assumption)).
% 1.53/1.28 tff(673,plain,
% 1.53/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | (c1_1(a129) | (~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | (~c3_1(a137)) | (~c2_1(a129)) | (~c0_1(a129)) | (~c3_1(a129)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a129) | (~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | (~c3_1(a137)) | (~c2_1(a129)) | (~c0_1(a129)) | (~c3_1(a129)))),
% 1.53/1.28 inference(rewrite,[status(thm)],[])).
% 1.53/1.28 tff(674,plain,
% 1.53/1.28 (((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | c1_1(a129) | (~c2_1(a129)) | (~c3_1(a129)) | c1_1(a129) | (~c0_1(a129)) | (~c2_1(a129))) <=> (c1_1(a129) | (~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | (~c3_1(a137)) | (~c2_1(a129)) | (~c0_1(a129)) | (~c3_1(a129)))),
% 1.53/1.28 inference(rewrite,[status(thm)],[])).
% 1.53/1.28 tff(675,plain,
% 1.53/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | c1_1(a129) | (~c2_1(a129)) | (~c3_1(a129)) | c1_1(a129) | (~c0_1(a129)) | (~c2_1(a129)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | (c1_1(a129) | (~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | (~c3_1(a137)) | (~c2_1(a129)) | (~c0_1(a129)) | (~c3_1(a129))))),
% 1.53/1.28 inference(monotonicity,[status(thm)],[674])).
% 1.53/1.28 tff(676,plain,
% 1.53/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | c1_1(a129) | (~c2_1(a129)) | (~c3_1(a129)) | c1_1(a129) | (~c0_1(a129)) | (~c2_1(a129)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a129) | (~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | (~c3_1(a137)) | (~c2_1(a129)) | (~c0_1(a129)) | (~c3_1(a129)))),
% 1.53/1.28 inference(transitivity,[status(thm)],[675, 673])).
% 1.53/1.28 tff(677,plain,
% 1.53/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | c1_1(a129) | (~c2_1(a129)) | (~c3_1(a129)) | c1_1(a129) | (~c0_1(a129)) | (~c2_1(a129)))),
% 1.53/1.28 inference(quant_inst,[status(thm)],[])).
% 1.53/1.28 tff(678,plain,
% 1.53/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a129) | (~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | (~c3_1(a137)) | (~c2_1(a129)) | (~c0_1(a129)) | (~c3_1(a129))),
% 1.53/1.28 inference(modus_ponens,[status(thm)],[677, 676])).
% 1.53/1.28 tff(679,plain,
% 1.53/1.28 ((~c2_1(a129)) | (~c0_1(a129)) | (~c3_1(a129))),
% 1.53/1.28 inference(unit_resolution,[status(thm)],[678, 126, 664, 667, 672, 10, 665])).
% 1.53/1.28 tff(680,plain,
% 1.53/1.28 (~c3_1(a129)),
% 1.53/1.28 inference(unit_resolution,[status(thm)],[679, 671, 670])).
% 1.53/1.28 tff(681,plain,
% 1.53/1.28 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W))))),
% 1.53/1.28 inference(bind,[status(th)],[])).
% 1.53/1.28 tff(682,plain,
% 1.53/1.28 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_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)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.53/1.28 inference(quant_intro,[status(thm)],[681])).
% 1.53/1.28 tff(683,plain,
% 1.53/1.28 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_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)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.53/1.28 inference(rewrite,[status(thm)],[])).
% 1.53/1.28 tff(684,plain,
% 1.53/1.28 (^[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))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_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) | (~c2_1(U)) | (~c3_1(U)) | (~c1_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) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_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) | (~c2_1(U)) | (~c3_1(U)) | (~c1_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)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_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)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_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)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_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)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))))),
% 1.53/1.28 inference(bind,[status(th)],[])).
% 1.53/1.28 tff(685,plain,
% 1.53/1.28 (![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)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.53/1.28 inference(quant_intro,[status(thm)],[684])).
% 1.53/1.28 tff(686,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)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause197')).
% 1.53/1.28 tff(687,plain,
% 1.53/1.28 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.53/1.28 inference(modus_ponens,[status(thm)],[686, 685])).
% 1.53/1.28 tff(688,plain,
% 1.53/1.28 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.53/1.28 inference(modus_ponens,[status(thm)],[687, 683])).
% 1.53/1.28 tff(689,plain,(
% 1.53/1.28 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.53/1.28 inference(skolemize,[status(sab)],[688])).
% 1.53/1.28 tff(690,plain,
% 1.53/1.28 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.53/1.28 inference(modus_ponens,[status(thm)],[689, 682])).
% 1.53/1.28 tff(691,plain,
% 1.53/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c1_1(a129) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a129) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129))),
% 1.53/1.28 inference(rewrite,[status(thm)],[])).
% 1.53/1.28 tff(692,plain,
% 1.53/1.28 (((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c1_1(a129) | c3_1(a129) | (~c2_1(a129))) <=> (c1_1(a129) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129))),
% 1.53/1.28 inference(rewrite,[status(thm)],[])).
% 1.53/1.28 tff(693,plain,
% 1.53/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c1_1(a129) | c3_1(a129) | (~c2_1(a129)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c1_1(a129) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129)))),
% 1.53/1.28 inference(monotonicity,[status(thm)],[692])).
% 1.53/1.28 tff(694,plain,
% 1.53/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c1_1(a129) | c3_1(a129) | (~c2_1(a129)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a129) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129))),
% 1.53/1.28 inference(transitivity,[status(thm)],[693, 691])).
% 1.53/1.28 tff(695,plain,
% 1.53/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c1_1(a129) | c3_1(a129) | (~c2_1(a129)))),
% 1.53/1.28 inference(quant_inst,[status(thm)],[])).
% 1.53/1.28 tff(696,plain,
% 1.53/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a129) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129)),
% 1.53/1.28 inference(modus_ponens,[status(thm)],[695, 694])).
% 1.53/1.28 tff(697,plain,
% 1.53/1.28 ((~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129)),
% 1.53/1.28 inference(unit_resolution,[status(thm)],[696, 126, 666, 667, 672, 690, 665])).
% 1.53/1.28 tff(698,plain,
% 1.53/1.28 ($false),
% 1.53/1.28 inference(unit_resolution,[status(thm)],[697, 680, 671, 670])).
% 1.53/1.28 tff(699,plain,((~hskp18) | (~c1_1(a137)) | (~c2_1(a137)) | c1_1(a129) | (~c3_1(a137)) | (~c0_1(a137))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.28 tff(700,plain,
% 1.53/1.28 ($false),
% 1.53/1.28 inference(unit_resolution,[status(thm)],[699, 669, 668, 667, 666, 665, 664])).
% 1.53/1.28 tff(701,plain,((~hskp18) | (~c2_1(a137)) | (~c1_1(a137)) | (~c3_1(a137)) | (~c0_1(a137))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.28 tff(702,plain,
% 1.53/1.28 (~hskp18),
% 1.53/1.28 inference(unit_resolution,[status(thm)],[701, 663, 655, 644, 633])).
% 1.53/1.28 tff(703,plain,
% 1.53/1.28 (hskp0 | c3_1(a137)),
% 1.53/1.28 inference(unit_resolution,[status(thm)],[661, 126, 664, 666, 75])).
% 1.53/1.28 tff(704,plain,
% 1.53/1.28 (c3_1(a137)),
% 1.53/1.28 inference(unit_resolution,[status(thm)],[703, 94])).
% 1.53/1.28 tff(705,plain,
% 1.53/1.28 (^[V: $i, U: $i] : refl((hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))),
% 1.53/1.28 inference(bind,[status(th)],[])).
% 1.53/1.28 tff(706,plain,
% 1.53/1.28 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.53/1.28 inference(quant_intro,[status(thm)],[705])).
% 1.53/1.28 tff(707,plain,
% 1.53/1.28 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.53/1.28 inference(rewrite,[status(thm)],[])).
% 1.53/1.28 tff(708,plain,
% 1.53/1.28 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp18) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp18))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp18) <=> (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp18) <=> (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))))),
% 1.53/1.28 inference(bind,[status(th)],[])).
% 1.53/1.28 tff(709,plain,
% 1.53/1.28 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp18) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.53/1.29 inference(quant_intro,[status(thm)],[708])).
% 1.53/1.29 tff(710,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause179')).
% 1.53/1.29 tff(711,plain,
% 1.53/1.29 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.53/1.29 inference(modus_ponens,[status(thm)],[710, 709])).
% 1.53/1.29 tff(712,plain,
% 1.53/1.29 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.53/1.29 inference(modus_ponens,[status(thm)],[711, 707])).
% 1.53/1.29 tff(713,plain,(
% 1.53/1.29 ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.53/1.29 inference(skolemize,[status(sab)],[712])).
% 1.53/1.29 tff(714,plain,
% 1.53/1.29 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.53/1.29 inference(modus_ponens,[status(thm)],[713, 706])).
% 1.53/1.29 tff(715,assumption,(hskp20), introduced(assumption)).
% 1.53/1.29 tff(716,plain,
% 1.53/1.29 (((~hskp20) | (~c3_1(a132))) <=> ((~hskp20) | (~c3_1(a132)))),
% 1.53/1.29 inference(rewrite,[status(thm)],[])).
% 1.53/1.29 tff(717,plain,
% 1.53/1.29 (((~c3_1(a132)) | (~hskp20)) <=> ((~hskp20) | (~c3_1(a132)))),
% 1.53/1.29 inference(rewrite,[status(thm)],[])).
% 1.53/1.29 tff(718,axiom,((~c3_1(a132)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause99')).
% 1.53/1.29 tff(719,plain,
% 1.53/1.29 ((~hskp20) | (~c3_1(a132))),
% 1.53/1.29 inference(modus_ponens,[status(thm)],[718, 717])).
% 1.53/1.29 tff(720,plain,
% 1.53/1.29 ((~hskp20) | (~c3_1(a132))),
% 1.53/1.29 inference(modus_ponens,[status(thm)],[719, 716])).
% 1.53/1.29 tff(721,plain,
% 1.53/1.29 (~c3_1(a132)),
% 1.53/1.29 inference(unit_resolution,[status(thm)],[720, 715])).
% 1.53/1.29 tff(722,plain,
% 1.53/1.29 (((~hskp20) | (~c1_1(a132))) <=> ((~hskp20) | (~c1_1(a132)))),
% 1.53/1.29 inference(rewrite,[status(thm)],[])).
% 1.53/1.29 tff(723,plain,
% 1.53/1.29 (((~c1_1(a132)) | (~hskp20)) <=> ((~hskp20) | (~c1_1(a132)))),
% 1.53/1.29 inference(rewrite,[status(thm)],[])).
% 1.53/1.29 tff(724,axiom,((~c1_1(a132)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause97')).
% 1.53/1.29 tff(725,plain,
% 1.53/1.29 ((~hskp20) | (~c1_1(a132))),
% 1.53/1.29 inference(modus_ponens,[status(thm)],[724, 723])).
% 1.53/1.29 tff(726,plain,
% 1.53/1.29 ((~hskp20) | (~c1_1(a132))),
% 1.53/1.29 inference(modus_ponens,[status(thm)],[725, 722])).
% 1.53/1.29 tff(727,plain,
% 1.53/1.29 (~c1_1(a132)),
% 1.53/1.29 inference(unit_resolution,[status(thm)],[726, 715])).
% 1.53/1.29 tff(728,plain,
% 1.53/1.29 (~hskp18),
% 1.53/1.29 inference(unit_resolution,[status(thm)],[701, 704, 666, 667, 664])).
% 1.53/1.29 tff(729,plain,
% 1.53/1.29 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp18 | c1_1(a132) | c3_1(a132) | (~ndr1_0) | (~c0_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c0_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a132) | c3_1(a132) | (~ndr1_0) | (~c0_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c0_1(a132)))),
% 1.53/1.29 inference(rewrite,[status(thm)],[])).
% 1.53/1.29 tff(730,plain,
% 1.53/1.29 ((hskp18 | (~ndr1_0) | (~c3_1(a137)) | (~c0_1(a137)) | (~c1_1(a137)) | c1_1(a132) | c3_1(a132) | (~c0_1(a132))) <=> (hskp18 | c1_1(a132) | c3_1(a132) | (~ndr1_0) | (~c0_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c0_1(a132)))),
% 1.53/1.29 inference(rewrite,[status(thm)],[])).
% 1.53/1.29 tff(731,plain,
% 1.53/1.29 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c3_1(a137)) | (~c0_1(a137)) | (~c1_1(a137)) | c1_1(a132) | c3_1(a132) | (~c0_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp18 | c1_1(a132) | c3_1(a132) | (~ndr1_0) | (~c0_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c0_1(a132))))),
% 1.53/1.29 inference(monotonicity,[status(thm)],[730])).
% 1.53/1.29 tff(732,plain,
% 1.53/1.29 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c3_1(a137)) | (~c0_1(a137)) | (~c1_1(a137)) | c1_1(a132) | c3_1(a132) | (~c0_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a132) | c3_1(a132) | (~ndr1_0) | (~c0_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c0_1(a132)))),
% 1.53/1.29 inference(transitivity,[status(thm)],[731, 729])).
% 1.53/1.29 tff(733,plain,
% 1.53/1.29 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c3_1(a137)) | (~c0_1(a137)) | (~c1_1(a137)) | c1_1(a132) | c3_1(a132) | (~c0_1(a132)))),
% 1.53/1.29 inference(quant_inst,[status(thm)],[])).
% 1.53/1.29 tff(734,plain,
% 1.53/1.29 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a132) | c3_1(a132) | (~ndr1_0) | (~c0_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c0_1(a132))),
% 1.53/1.29 inference(modus_ponens,[status(thm)],[733, 732])).
% 1.53/1.29 tff(735,plain,
% 1.53/1.29 (~c0_1(a132)),
% 1.53/1.29 inference(unit_resolution,[status(thm)],[734, 126, 728, 664, 666, 727, 721, 714, 704])).
% 1.53/1.29 tff(736,plain,
% 1.53/1.29 (((~hskp20) | (~c2_1(a132))) <=> ((~hskp20) | (~c2_1(a132)))),
% 1.53/1.29 inference(rewrite,[status(thm)],[])).
% 1.53/1.29 tff(737,plain,
% 1.53/1.29 (((~c2_1(a132)) | (~hskp20)) <=> ((~hskp20) | (~c2_1(a132)))),
% 1.53/1.29 inference(rewrite,[status(thm)],[])).
% 1.53/1.29 tff(738,axiom,((~c2_1(a132)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause98')).
% 1.53/1.29 tff(739,plain,
% 1.53/1.29 ((~hskp20) | (~c2_1(a132))),
% 1.53/1.29 inference(modus_ponens,[status(thm)],[738, 737])).
% 1.53/1.29 tff(740,plain,
% 1.53/1.29 ((~hskp20) | (~c2_1(a132))),
% 1.53/1.29 inference(modus_ponens,[status(thm)],[739, 736])).
% 1.53/1.29 tff(741,plain,
% 1.53/1.29 (~c2_1(a132)),
% 1.53/1.29 inference(unit_resolution,[status(thm)],[740, 715])).
% 1.53/1.29 tff(742,plain,
% 1.53/1.29 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp18 | c1_1(a132) | c2_1(a132) | c3_1(a132) | (~ndr1_0))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp19 | hskp18 | c1_1(a132) | c2_1(a132) | c3_1(a132) | (~ndr1_0))),
% 1.53/1.29 inference(rewrite,[status(thm)],[])).
% 1.53/1.29 tff(743,plain,
% 1.53/1.29 ((hskp19 | hskp18 | (~ndr1_0) | c2_1(a132) | c1_1(a132) | c3_1(a132)) <=> (hskp19 | hskp18 | c1_1(a132) | c2_1(a132) | c3_1(a132) | (~ndr1_0))),
% 1.53/1.29 inference(rewrite,[status(thm)],[])).
% 1.53/1.29 tff(744,plain,
% 1.53/1.29 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a132) | c1_1(a132) | c3_1(a132))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp18 | c1_1(a132) | c2_1(a132) | c3_1(a132) | (~ndr1_0)))),
% 1.53/1.29 inference(monotonicity,[status(thm)],[743])).
% 1.53/1.29 tff(745,plain,
% 1.53/1.29 (((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a132) | c1_1(a132) | c3_1(a132))) <=> ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp19 | hskp18 | c1_1(a132) | c2_1(a132) | c3_1(a132) | (~ndr1_0))),
% 1.53/1.29 inference(transitivity,[status(thm)],[744, 742])).
% 1.53/1.29 tff(746,plain,
% 1.53/1.29 ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp19 | hskp18 | (~ndr1_0) | c2_1(a132) | c1_1(a132) | c3_1(a132))),
% 1.53/1.29 inference(quant_inst,[status(thm)],[])).
% 1.53/1.29 tff(747,plain,
% 1.53/1.29 ((~![U: $i] : (hskp19 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp19 | hskp18 | c1_1(a132) | c2_1(a132) | c3_1(a132) | (~ndr1_0)),
% 1.53/1.29 inference(modus_ponens,[status(thm)],[746, 745])).
% 1.53/1.29 tff(748,plain,
% 1.53/1.29 (hskp19),
% 1.53/1.29 inference(unit_resolution,[status(thm)],[747, 126, 728, 727, 741, 721, 30])).
% 1.53/1.29 tff(749,plain,
% 1.53/1.29 (~c2_1(a130)),
% 1.53/1.29 inference(unit_resolution,[status(thm)],[252, 748])).
% 1.53/1.29 tff(750,plain,
% 1.53/1.29 (c3_1(a130)),
% 1.53/1.29 inference(unit_resolution,[status(thm)],[263, 748])).
% 1.53/1.29 tff(751,plain,
% 1.53/1.29 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a132) | c2_1(a132) | c2_1(a130) | (~ndr1_0) | c0_1(a130) | (~c3_1(a130)) | c0_1(a132))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a132) | c2_1(a132) | c2_1(a130) | (~ndr1_0) | c0_1(a130) | (~c3_1(a130)) | c0_1(a132))),
% 1.53/1.29 inference(rewrite,[status(thm)],[])).
% 1.53/1.29 tff(752,plain,
% 1.53/1.29 ((hskp0 | (~ndr1_0) | c2_1(a130) | c0_1(a130) | (~c3_1(a130)) | c2_1(a132) | c1_1(a132) | c0_1(a132)) <=> (hskp0 | c1_1(a132) | c2_1(a132) | c2_1(a130) | (~ndr1_0) | c0_1(a130) | (~c3_1(a130)) | c0_1(a132))),
% 1.53/1.29 inference(rewrite,[status(thm)],[])).
% 1.53/1.29 tff(753,plain,
% 1.53/1.29 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a130) | c0_1(a130) | (~c3_1(a130)) | c2_1(a132) | c1_1(a132) | c0_1(a132))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a132) | c2_1(a132) | c2_1(a130) | (~ndr1_0) | c0_1(a130) | (~c3_1(a130)) | c0_1(a132)))),
% 1.53/1.29 inference(monotonicity,[status(thm)],[752])).
% 1.53/1.29 tff(754,plain,
% 1.53/1.29 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a130) | c0_1(a130) | (~c3_1(a130)) | c2_1(a132) | c1_1(a132) | c0_1(a132))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a132) | c2_1(a132) | c2_1(a130) | (~ndr1_0) | c0_1(a130) | (~c3_1(a130)) | c0_1(a132))),
% 1.53/1.29 inference(transitivity,[status(thm)],[753, 751])).
% 1.53/1.29 tff(755,plain,
% 1.53/1.29 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a130) | c0_1(a130) | (~c3_1(a130)) | c2_1(a132) | c1_1(a132) | c0_1(a132))),
% 1.53/1.29 inference(quant_inst,[status(thm)],[])).
% 1.53/1.29 tff(756,plain,
% 1.53/1.29 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a132) | c2_1(a132) | c2_1(a130) | (~ndr1_0) | c0_1(a130) | (~c3_1(a130)) | c0_1(a132)),
% 1.53/1.29 inference(modus_ponens,[status(thm)],[755, 754])).
% 1.53/1.29 tff(757,plain,
% 1.53/1.29 (c0_1(a130)),
% 1.53/1.29 inference(unit_resolution,[status(thm)],[756, 126, 94, 750, 727, 741, 749, 211, 735])).
% 1.53/1.29 tff(758,plain,
% 1.53/1.29 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 1.53/1.29 inference(bind,[status(th)],[])).
% 1.53/1.29 tff(759,plain,
% 1.53/1.29 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.53/1.29 inference(quant_intro,[status(thm)],[758])).
% 1.53/1.29 tff(760,plain,
% 1.53/1.29 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.53/1.29 inference(rewrite,[status(thm)],[])).
% 1.53/1.29 tff(761,plain,
% 1.53/1.29 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp2) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp2))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp2) <=> (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 1.53/1.29 inference(bind,[status(th)],[])).
% 1.53/1.29 tff(762,plain,
% 1.53/1.29 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.53/1.29 inference(quant_intro,[status(thm)],[761])).
% 1.53/1.29 tff(763,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause185')).
% 1.53/1.29 tff(764,plain,
% 1.53/1.29 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.53/1.29 inference(modus_ponens,[status(thm)],[763, 762])).
% 1.53/1.29 tff(765,plain,
% 1.53/1.29 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.53/1.29 inference(modus_ponens,[status(thm)],[764, 760])).
% 1.53/1.29 tff(766,plain,(
% 1.53/1.29 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.53/1.29 inference(skolemize,[status(sab)],[765])).
% 1.53/1.29 tff(767,plain,
% 1.53/1.29 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.53/1.29 inference(modus_ponens,[status(thm)],[766, 759])).
% 1.53/1.29 tff(768,plain,
% 1.53/1.29 (c1_1(a130)),
% 1.53/1.29 inference(unit_resolution,[status(thm)],[274, 748])).
% 1.53/1.29 tff(769,plain,
% 1.53/1.29 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | c2_1(a130) | (~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | (~c1_1(a137)) | (~c3_1(a130)) | (~c1_1(a130)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c2_1(a130) | (~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | (~c1_1(a137)) | (~c3_1(a130)) | (~c1_1(a130)))),
% 1.53/1.29 inference(rewrite,[status(thm)],[])).
% 1.53/1.29 tff(770,plain,
% 1.53/1.29 ((hskp2 | (~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | (~c1_1(a137)) | c2_1(a130) | (~c3_1(a130)) | (~c1_1(a130))) <=> (hskp2 | c2_1(a130) | (~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | (~c1_1(a137)) | (~c3_1(a130)) | (~c1_1(a130)))),
% 1.53/1.29 inference(rewrite,[status(thm)],[])).
% 1.53/1.29 tff(771,plain,
% 1.53/1.29 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | (~c1_1(a137)) | c2_1(a130) | (~c3_1(a130)) | (~c1_1(a130)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | c2_1(a130) | (~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | (~c1_1(a137)) | (~c3_1(a130)) | (~c1_1(a130))))),
% 1.53/1.29 inference(monotonicity,[status(thm)],[770])).
% 1.53/1.29 tff(772,plain,
% 1.53/1.29 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | (~c1_1(a137)) | c2_1(a130) | (~c3_1(a130)) | (~c1_1(a130)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c2_1(a130) | (~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | (~c1_1(a137)) | (~c3_1(a130)) | (~c1_1(a130)))),
% 1.53/1.29 inference(transitivity,[status(thm)],[771, 769])).
% 1.53/1.29 tff(773,plain,
% 1.53/1.29 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp2 | (~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | (~c1_1(a137)) | c2_1(a130) | (~c3_1(a130)) | (~c1_1(a130)))),
% 1.53/1.29 inference(quant_inst,[status(thm)],[])).
% 1.53/1.29 tff(774,plain,
% 1.53/1.29 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp2 | c2_1(a130) | (~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | (~c1_1(a137)) | (~c3_1(a130)) | (~c1_1(a130))),
% 1.53/1.29 inference(modus_ponens,[status(thm)],[773, 772])).
% 1.53/1.29 tff(775,plain,
% 1.53/1.29 (hskp2),
% 1.53/1.29 inference(unit_resolution,[status(thm)],[774, 126, 664, 666, 667, 768, 750, 749, 767])).
% 1.53/1.29 tff(776,plain,
% 1.53/1.29 (~c0_1(a99)),
% 1.53/1.29 inference(unit_resolution,[status(thm)],[602, 775])).
% 1.53/1.29 tff(777,plain,
% 1.53/1.29 (c2_1(a99)),
% 1.53/1.29 inference(unit_resolution,[status(thm)],[587, 775])).
% 1.53/1.29 tff(778,plain,
% 1.53/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a132) | c3_1(a132) | c2_1(a130) | c0_1(a99) | (~ndr1_0) | (~c2_1(a99)) | (~c3_1(a99)) | (~c0_1(a130)) | (~c1_1(a130)) | c0_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a132) | c3_1(a132) | c2_1(a130) | c0_1(a99) | (~ndr1_0) | (~c2_1(a99)) | (~c3_1(a99)) | (~c0_1(a130)) | (~c1_1(a130)) | c0_1(a132))),
% 1.53/1.29 inference(rewrite,[status(thm)],[])).
% 1.53/1.29 tff(779,plain,
% 1.53/1.29 (((~ndr1_0) | c2_1(a130) | (~c0_1(a130)) | (~c1_1(a130)) | c0_1(a99) | (~c2_1(a99)) | (~c3_1(a99)) | c2_1(a132) | c0_1(a132) | c3_1(a132)) <=> (c2_1(a132) | c3_1(a132) | c2_1(a130) | c0_1(a99) | (~ndr1_0) | (~c2_1(a99)) | (~c3_1(a99)) | (~c0_1(a130)) | (~c1_1(a130)) | c0_1(a132))),
% 1.53/1.29 inference(rewrite,[status(thm)],[])).
% 1.53/1.29 tff(780,plain,
% 1.53/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a130) | (~c0_1(a130)) | (~c1_1(a130)) | c0_1(a99) | (~c2_1(a99)) | (~c3_1(a99)) | c2_1(a132) | c0_1(a132) | c3_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a132) | c3_1(a132) | c2_1(a130) | c0_1(a99) | (~ndr1_0) | (~c2_1(a99)) | (~c3_1(a99)) | (~c0_1(a130)) | (~c1_1(a130)) | c0_1(a132)))),
% 1.53/1.29 inference(monotonicity,[status(thm)],[779])).
% 1.53/1.29 tff(781,plain,
% 1.53/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a130) | (~c0_1(a130)) | (~c1_1(a130)) | c0_1(a99) | (~c2_1(a99)) | (~c3_1(a99)) | c2_1(a132) | c0_1(a132) | c3_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a132) | c3_1(a132) | c2_1(a130) | c0_1(a99) | (~ndr1_0) | (~c2_1(a99)) | (~c3_1(a99)) | (~c0_1(a130)) | (~c1_1(a130)) | c0_1(a132))),
% 1.53/1.29 inference(transitivity,[status(thm)],[780, 778])).
% 1.53/1.29 tff(782,plain,
% 1.53/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a130) | (~c0_1(a130)) | (~c1_1(a130)) | c0_1(a99) | (~c2_1(a99)) | (~c3_1(a99)) | c2_1(a132) | c0_1(a132) | c3_1(a132))),
% 1.53/1.29 inference(quant_inst,[status(thm)],[])).
% 1.53/1.29 tff(783,plain,
% 1.53/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a132) | c3_1(a132) | c2_1(a130) | c0_1(a99) | (~ndr1_0) | (~c2_1(a99)) | (~c3_1(a99)) | (~c0_1(a130)) | (~c1_1(a130)) | c0_1(a132)),
% 1.53/1.29 inference(modus_ponens,[status(thm)],[782, 781])).
% 1.53/1.29 tff(784,plain,
% 1.53/1.29 (~c3_1(a99)),
% 1.53/1.29 inference(unit_resolution,[status(thm)],[783, 126, 768, 777, 741, 721, 749, 776, 525, 735, 757])).
% 1.53/1.29 tff(785,plain,
% 1.53/1.29 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 1.53/1.29 inference(bind,[status(th)],[])).
% 1.53/1.29 tff(786,plain,
% 1.53/1.29 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.53/1.29 inference(quant_intro,[status(thm)],[785])).
% 1.53/1.29 tff(787,plain,
% 1.53/1.29 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.53/1.29 inference(rewrite,[status(thm)],[])).
% 1.53/1.29 tff(788,plain,
% 1.53/1.29 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c2_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c2_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) | (~c2_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | 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) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | 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(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 1.53/1.30 inference(bind,[status(th)],[])).
% 1.53/1.30 tff(789,plain,
% 1.53/1.30 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.53/1.30 inference(quant_intro,[status(thm)],[788])).
% 1.53/1.30 tff(790,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause186')).
% 1.53/1.30 tff(791,plain,
% 1.53/1.30 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.53/1.30 inference(modus_ponens,[status(thm)],[790, 789])).
% 1.53/1.30 tff(792,plain,
% 1.53/1.30 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.53/1.30 inference(modus_ponens,[status(thm)],[791, 787])).
% 1.53/1.30 tff(793,plain,(
% 1.53/1.30 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.53/1.30 inference(skolemize,[status(sab)],[792])).
% 1.53/1.30 tff(794,plain,
% 1.53/1.30 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.53/1.30 inference(modus_ponens,[status(thm)],[793, 786])).
% 1.53/1.30 tff(795,plain,
% 1.53/1.30 (~c1_1(a99)),
% 1.53/1.30 inference(unit_resolution,[status(thm)],[618, 775])).
% 1.53/1.30 tff(796,plain,
% 1.53/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a132) | c2_1(a132) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c3_1(a99) | c0_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a132) | c2_1(a132) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c3_1(a99) | c0_1(a132))),
% 1.53/1.30 inference(rewrite,[status(thm)],[])).
% 1.53/1.30 tff(797,plain,
% 1.53/1.30 (((~ndr1_0) | c0_1(a99) | c3_1(a99) | (~c2_1(a99)) | c1_1(a99) | c0_1(a99) | (~c2_1(a99)) | c2_1(a132) | c1_1(a132) | c0_1(a132)) <=> (c1_1(a132) | c2_1(a132) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c3_1(a99) | c0_1(a132))),
% 1.53/1.30 inference(rewrite,[status(thm)],[])).
% 1.53/1.30 tff(798,plain,
% 1.53/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a99) | c3_1(a99) | (~c2_1(a99)) | c1_1(a99) | c0_1(a99) | (~c2_1(a99)) | c2_1(a132) | c1_1(a132) | c0_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a132) | c2_1(a132) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c3_1(a99) | c0_1(a132)))),
% 1.53/1.30 inference(monotonicity,[status(thm)],[797])).
% 1.53/1.30 tff(799,plain,
% 1.53/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a99) | c3_1(a99) | (~c2_1(a99)) | c1_1(a99) | c0_1(a99) | (~c2_1(a99)) | c2_1(a132) | c1_1(a132) | c0_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a132) | c2_1(a132) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c3_1(a99) | c0_1(a132))),
% 1.53/1.30 inference(transitivity,[status(thm)],[798, 796])).
% 1.53/1.30 tff(800,plain,
% 1.53/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a99) | c3_1(a99) | (~c2_1(a99)) | c1_1(a99) | c0_1(a99) | (~c2_1(a99)) | c2_1(a132) | c1_1(a132) | c0_1(a132))),
% 1.53/1.30 inference(quant_inst,[status(thm)],[])).
% 1.53/1.30 tff(801,plain,
% 1.53/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a132) | c2_1(a132) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c3_1(a99) | c0_1(a132)),
% 1.53/1.30 inference(modus_ponens,[status(thm)],[800, 799])).
% 1.53/1.30 tff(802,plain,
% 1.53/1.30 ($false),
% 1.53/1.30 inference(unit_resolution,[status(thm)],[801, 126, 777, 727, 741, 776, 795, 794, 784, 735])).
% 1.53/1.30 tff(803,plain,((~hskp20) | hskp0 | (~c0_1(a137)) | (~c1_1(a137)) | (~c2_1(a137))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.30 tff(804,plain,
% 1.53/1.30 (~hskp20),
% 1.53/1.30 inference(unit_resolution,[status(thm)],[803, 94, 633, 655, 644])).
% 1.53/1.30 tff(805,plain,
% 1.53/1.30 ((hskp20 | hskp18 | hskp4) <=> (hskp20 | hskp18 | hskp4)),
% 1.53/1.30 inference(rewrite,[status(thm)],[])).
% 1.53/1.30 tff(806,plain,
% 1.53/1.30 (((hskp18 | hskp4) | hskp20) <=> (hskp20 | hskp18 | hskp4)),
% 1.53/1.30 inference(rewrite,[status(thm)],[])).
% 1.53/1.30 tff(807,axiom,((hskp18 | hskp4) | hskp20), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause35')).
% 1.53/1.30 tff(808,plain,
% 1.53/1.30 (hskp20 | hskp18 | hskp4),
% 1.53/1.30 inference(modus_ponens,[status(thm)],[807, 806])).
% 1.53/1.30 tff(809,plain,
% 1.53/1.30 (hskp20 | hskp18 | hskp4),
% 1.53/1.30 inference(modus_ponens,[status(thm)],[808, 805])).
% 1.53/1.30 tff(810,plain,
% 1.53/1.30 (hskp20 | hskp18 | hskp4),
% 1.53/1.30 inference(modus_ponens,[status(thm)],[809, 805])).
% 1.53/1.30 tff(811,plain,
% 1.53/1.30 (hskp20 | hskp18 | hskp4),
% 1.53/1.30 inference(modus_ponens,[status(thm)],[810, 805])).
% 1.53/1.30 tff(812,plain,
% 1.53/1.30 (hskp20 | hskp18 | hskp4),
% 1.53/1.30 inference(modus_ponens,[status(thm)],[811, 805])).
% 1.53/1.30 tff(813,plain,
% 1.53/1.30 (hskp20 | hskp18 | hskp4),
% 1.53/1.30 inference(modus_ponens,[status(thm)],[812, 805])).
% 1.53/1.30 tff(814,plain,
% 1.53/1.30 (hskp20 | hskp18 | hskp4),
% 1.53/1.30 inference(modus_ponens,[status(thm)],[813, 805])).
% 1.53/1.30 tff(815,plain,
% 1.53/1.30 (hskp20 | hskp18 | hskp4),
% 1.53/1.30 inference(modus_ponens,[status(thm)],[814, 805])).
% 1.53/1.30 tff(816,plain,
% 1.53/1.30 (hskp4),
% 1.53/1.30 inference(unit_resolution,[status(thm)],[815, 804, 702])).
% 1.53/1.30 tff(817,plain,
% 1.53/1.30 (~c3_1(a103)),
% 1.53/1.30 inference(unit_resolution,[status(thm)],[81, 816])).
% 1.53/1.30 tff(818,plain,
% 1.53/1.30 (c0_1(a103)),
% 1.53/1.30 inference(unit_resolution,[status(thm)],[92, 816])).
% 1.53/1.30 tff(819,plain,
% 1.53/1.30 (c2_1(a103)),
% 1.53/1.30 inference(unit_resolution,[status(thm)],[157, 816])).
% 1.53/1.30 tff(820,plain,
% 1.53/1.30 ($false),
% 1.53/1.30 inference(unit_resolution,[status(thm)],[230, 819, 818, 94, 817, 144])).
% 1.53/1.30 tff(821,plain,(hskp0 | hskp22), inference(lemma,lemma(discharge,[]))).
% 1.53/1.30 tff(822,plain,
% 1.53/1.30 (hskp0),
% 1.53/1.30 inference(unit_resolution,[status(thm)],[821, 144])).
% 1.53/1.30 tff(823,plain,
% 1.53/1.30 (~c3_1(a97)),
% 1.53/1.30 inference(unit_resolution,[status(thm)],[236, 822])).
% 1.53/1.30 tff(824,plain,
% 1.53/1.30 (~c2_1(a97)),
% 1.53/1.30 inference(unit_resolution,[status(thm)],[242, 822])).
% 1.53/1.30 tff(825,plain,
% 1.53/1.30 (^[U: $i] : refl((hskp18 | hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> (hskp18 | hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))),
% 1.53/1.30 inference(bind,[status(th)],[])).
% 1.53/1.30 tff(826,plain,
% 1.53/1.30 (![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.53/1.30 inference(quant_intro,[status(thm)],[825])).
% 1.53/1.30 tff(827,plain,
% 1.53/1.30 (![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.53/1.30 inference(rewrite,[status(thm)],[])).
% 1.53/1.30 tff(828,plain,
% 1.53/1.30 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp18) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp18))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp18) <=> (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp18) <=> (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp18) | hskp11) <=> ((hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp11))), rewrite(((hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp11) <=> (hskp18 | hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp18) | hskp11) <=> (hskp18 | hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))))),
% 1.53/1.30 inference(bind,[status(th)],[])).
% 1.53/1.30 tff(829,plain,
% 1.53/1.30 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp18) | hskp11) <=> ![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.53/1.30 inference(quant_intro,[status(thm)],[828])).
% 1.53/1.30 tff(830,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp18) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause147')).
% 1.53/1.30 tff(831,plain,
% 1.53/1.30 (![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.53/1.30 inference(modus_ponens,[status(thm)],[830, 829])).
% 1.53/1.30 tff(832,plain,
% 1.53/1.30 (![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.53/1.30 inference(modus_ponens,[status(thm)],[831, 827])).
% 1.53/1.30 tff(833,plain,(
% 1.53/1.30 ![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.53/1.30 inference(skolemize,[status(sab)],[832])).
% 1.53/1.30 tff(834,plain,
% 1.53/1.30 (![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.53/1.30 inference(modus_ponens,[status(thm)],[833, 826])).
% 1.53/1.30 tff(835,plain,
% 1.53/1.30 (c0_1(a97)),
% 1.53/1.30 inference(unit_resolution,[status(thm)],[64, 822])).
% 1.53/1.30 tff(836,plain,
% 1.53/1.30 (((~![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp18 | hskp11 | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)))) <=> ((~![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp18 | hskp11 | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)))),
% 1.53/1.30 inference(rewrite,[status(thm)],[])).
% 1.53/1.30 tff(837,plain,
% 1.53/1.30 ((hskp18 | hskp11 | (~ndr1_0) | c2_1(a97) | c3_1(a97) | (~c0_1(a97))) <=> (hskp18 | hskp11 | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)))),
% 1.53/1.30 inference(rewrite,[status(thm)],[])).
% 1.53/1.30 tff(838,plain,
% 1.53/1.30 (((~![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp18 | hskp11 | (~ndr1_0) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)))) <=> ((~![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp18 | hskp11 | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97))))),
% 1.53/1.30 inference(monotonicity,[status(thm)],[837])).
% 1.53/1.30 tff(839,plain,
% 1.53/1.30 (((~![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp18 | hskp11 | (~ndr1_0) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)))) <=> ((~![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp18 | hskp11 | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)))),
% 1.53/1.30 inference(transitivity,[status(thm)],[838, 836])).
% 1.53/1.30 tff(840,plain,
% 1.53/1.30 ((~![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp18 | hskp11 | (~ndr1_0) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)))),
% 1.53/1.30 inference(quant_inst,[status(thm)],[])).
% 1.53/1.30 tff(841,plain,
% 1.53/1.30 ((~![U: $i] : (hskp18 | hskp11 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp18 | hskp11 | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97))),
% 1.53/1.30 inference(modus_ponens,[status(thm)],[840, 839])).
% 1.53/1.30 tff(842,plain,
% 1.53/1.30 (hskp18 | hskp11),
% 1.53/1.30 inference(unit_resolution,[status(thm)],[841, 126, 835, 824, 823, 834])).
% 1.53/1.30 tff(843,plain,
% 1.53/1.30 (hskp11),
% 1.53/1.30 inference(unit_resolution,[status(thm)],[842, 52])).
% 1.53/1.30 tff(844,plain,
% 1.53/1.30 (((~hskp11) | (~c1_1(a112))) <=> ((~hskp11) | (~c1_1(a112)))),
% 1.53/1.30 inference(rewrite,[status(thm)],[])).
% 1.53/1.30 tff(845,plain,
% 1.53/1.30 (((~c1_1(a112)) | (~hskp11)) <=> ((~hskp11) | (~c1_1(a112)))),
% 1.53/1.30 inference(rewrite,[status(thm)],[])).
% 1.53/1.30 tff(846,axiom,((~c1_1(a112)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause115')).
% 1.53/1.30 tff(847,plain,
% 1.53/1.30 ((~hskp11) | (~c1_1(a112))),
% 1.53/1.30 inference(modus_ponens,[status(thm)],[846, 845])).
% 1.53/1.30 tff(848,plain,
% 1.53/1.30 ((~hskp11) | (~c1_1(a112))),
% 1.53/1.30 inference(modus_ponens,[status(thm)],[847, 844])).
% 1.53/1.30 tff(849,plain,
% 1.53/1.30 (~c1_1(a112)),
% 1.53/1.30 inference(unit_resolution,[status(thm)],[848, 843])).
% 1.53/1.30 tff(850,plain,
% 1.53/1.30 (((~hskp11) | (~c0_1(a112))) <=> ((~hskp11) | (~c0_1(a112)))),
% 1.53/1.30 inference(rewrite,[status(thm)],[])).
% 1.53/1.30 tff(851,plain,
% 1.53/1.30 (((~c0_1(a112)) | (~hskp11)) <=> ((~hskp11) | (~c0_1(a112)))),
% 1.53/1.30 inference(rewrite,[status(thm)],[])).
% 1.53/1.30 tff(852,axiom,((~c0_1(a112)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause114')).
% 1.53/1.30 tff(853,plain,
% 1.53/1.30 ((~hskp11) | (~c0_1(a112))),
% 1.53/1.30 inference(modus_ponens,[status(thm)],[852, 851])).
% 1.53/1.30 tff(854,plain,
% 1.53/1.30 ((~hskp11) | (~c0_1(a112))),
% 1.53/1.30 inference(modus_ponens,[status(thm)],[853, 850])).
% 1.53/1.30 tff(855,plain,
% 1.53/1.30 (~c0_1(a112)),
% 1.53/1.30 inference(unit_resolution,[status(thm)],[854, 843])).
% 1.53/1.30 tff(856,assumption,(~hskp4), introduced(assumption)).
% 1.53/1.30 tff(857,plain,
% 1.53/1.30 (hskp20),
% 1.53/1.30 inference(unit_resolution,[status(thm)],[815, 52, 856])).
% 1.53/1.30 tff(858,plain,
% 1.53/1.30 (~c3_1(a132)),
% 1.53/1.30 inference(unit_resolution,[status(thm)],[720, 857])).
% 1.53/1.30 tff(859,plain,
% 1.53/1.30 (~c2_1(a132)),
% 1.53/1.30 inference(unit_resolution,[status(thm)],[740, 857])).
% 1.53/1.30 tff(860,plain,
% 1.53/1.30 (~c1_1(a132)),
% 1.53/1.30 inference(unit_resolution,[status(thm)],[726, 857])).
% 1.53/1.30 tff(861,plain,
% 1.53/1.30 (hskp19),
% 1.53/1.30 inference(unit_resolution,[status(thm)],[747, 126, 52, 860, 859, 858, 30])).
% 1.53/1.30 tff(862,plain,
% 1.53/1.30 (c1_1(a97)),
% 1.53/1.30 inference(unit_resolution,[status(thm)],[283, 861, 31, 53, 246])).
% 1.53/1.30 tff(863,plain,
% 1.53/1.30 (((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp6 | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp6 | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)))),
% 1.53/1.30 inference(rewrite,[status(thm)],[])).
% 1.53/1.30 tff(864,plain,
% 1.53/1.30 ((hskp6 | (~ndr1_0) | c3_1(a97) | (~c0_1(a97)) | (~c1_1(a97))) <=> (hskp6 | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)))),
% 1.53/1.30 inference(rewrite,[status(thm)],[])).
% 1.53/1.30 tff(865,plain,
% 1.53/1.30 (((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp6 | (~ndr1_0) | c3_1(a97) | (~c0_1(a97)) | (~c1_1(a97)))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp6 | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97))))),
% 1.53/1.30 inference(monotonicity,[status(thm)],[864])).
% 1.53/1.30 tff(866,plain,
% 1.53/1.30 (((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp6 | (~ndr1_0) | c3_1(a97) | (~c0_1(a97)) | (~c1_1(a97)))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp6 | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)))),
% 1.53/1.30 inference(transitivity,[status(thm)],[865, 863])).
% 1.53/1.30 tff(867,plain,
% 1.53/1.30 ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp6 | (~ndr1_0) | c3_1(a97) | (~c0_1(a97)) | (~c1_1(a97)))),
% 1.53/1.30 inference(quant_inst,[status(thm)],[])).
% 1.53/1.30 tff(868,plain,
% 1.53/1.30 ((~![U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp6 | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97))),
% 1.53/1.30 inference(modus_ponens,[status(thm)],[867, 866])).
% 1.53/1.30 tff(869,plain,
% 1.53/1.30 (hskp6 | (~c1_1(a97))),
% 1.53/1.30 inference(unit_resolution,[status(thm)],[868, 126, 246, 53, 391])).
% 1.53/1.30 tff(870,plain,
% 1.53/1.30 (hskp6),
% 1.53/1.30 inference(unit_resolution,[status(thm)],[869, 862])).
% 1.53/1.30 tff(871,plain,
% 1.53/1.30 (~c3_1(a105)),
% 1.53/1.30 inference(unit_resolution,[status(thm)],[404, 870])).
% 1.53/1.30 tff(872,plain,
% 1.53/1.30 (c2_1(a105)),
% 1.53/1.30 inference(unit_resolution,[status(thm)],[415, 870])).
% 1.53/1.30 tff(873,plain,
% 1.53/1.30 (c1_1(a105)),
% 1.53/1.30 inference(unit_resolution,[status(thm)],[426, 870])).
% 1.53/1.30 tff(874,plain,
% 1.53/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a132) | c2_1(a132) | c3_1(a132) | c3_1(a105) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c1_1(a97)) | (~c2_1(a105)) | (~c1_1(a105)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a132) | c2_1(a132) | c3_1(a132) | c3_1(a105) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c1_1(a97)) | (~c2_1(a105)) | (~c1_1(a105)))),
% 1.53/1.30 inference(rewrite,[status(thm)],[])).
% 1.53/1.30 tff(875,plain,
% 1.53/1.30 (((~ndr1_0) | c3_1(a105) | (~c2_1(a105)) | (~c1_1(a105)) | c2_1(a97) | c3_1(a97) | (~c1_1(a97)) | c2_1(a132) | c1_1(a132) | c3_1(a132)) <=> (c1_1(a132) | c2_1(a132) | c3_1(a132) | c3_1(a105) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c1_1(a97)) | (~c2_1(a105)) | (~c1_1(a105)))),
% 1.53/1.30 inference(rewrite,[status(thm)],[])).
% 1.53/1.30 tff(876,plain,
% 1.53/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a105) | (~c2_1(a105)) | (~c1_1(a105)) | c2_1(a97) | c3_1(a97) | (~c1_1(a97)) | c2_1(a132) | c1_1(a132) | c3_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a132) | c2_1(a132) | c3_1(a132) | c3_1(a105) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c1_1(a97)) | (~c2_1(a105)) | (~c1_1(a105))))),
% 1.53/1.30 inference(monotonicity,[status(thm)],[875])).
% 1.53/1.30 tff(877,plain,
% 1.53/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a105) | (~c2_1(a105)) | (~c1_1(a105)) | c2_1(a97) | c3_1(a97) | (~c1_1(a97)) | c2_1(a132) | c1_1(a132) | c3_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a132) | c2_1(a132) | c3_1(a132) | c3_1(a105) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c1_1(a97)) | (~c2_1(a105)) | (~c1_1(a105)))),
% 1.53/1.30 inference(transitivity,[status(thm)],[876, 874])).
% 1.53/1.30 tff(878,plain,
% 1.53/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a105) | (~c2_1(a105)) | (~c1_1(a105)) | c2_1(a97) | c3_1(a97) | (~c1_1(a97)) | c2_1(a132) | c1_1(a132) | c3_1(a132))),
% 1.53/1.30 inference(quant_inst,[status(thm)],[])).
% 1.53/1.30 tff(879,plain,
% 1.53/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a132) | c2_1(a132) | c3_1(a132) | c3_1(a105) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c1_1(a97)) | (~c2_1(a105)) | (~c1_1(a105))),
% 1.53/1.31 inference(modus_ponens,[status(thm)],[878, 877])).
% 1.53/1.31 tff(880,plain,
% 1.53/1.31 ($false),
% 1.53/1.31 inference(unit_resolution,[status(thm)],[879, 126, 873, 872, 860, 859, 858, 871, 31, 53, 438, 862])).
% 1.53/1.31 tff(881,plain,(hskp18 | c2_1(a97) | c3_1(a97) | (~c0_1(a97)) | hskp4), inference(lemma,lemma(discharge,[]))).
% 1.53/1.31 tff(882,plain,
% 1.53/1.31 (hskp18),
% 1.53/1.31 inference(unit_resolution,[status(thm)],[881, 856, 823, 835, 824])).
% 1.53/1.31 tff(883,plain,
% 1.53/1.31 (~c1_1(a129)),
% 1.53/1.31 inference(unit_resolution,[status(thm)],[297, 882])).
% 1.53/1.31 tff(884,plain,
% 1.53/1.31 (c2_1(a129)),
% 1.53/1.31 inference(unit_resolution,[status(thm)],[308, 882])).
% 1.53/1.31 tff(885,plain,
% 1.53/1.31 (c0_1(a129)),
% 1.53/1.31 inference(unit_resolution,[status(thm)],[319, 882])).
% 1.53/1.31 tff(886,plain,
% 1.53/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | (c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | (~c3_1(a129)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | (~c3_1(a129)))),
% 1.53/1.31 inference(rewrite,[status(thm)],[])).
% 1.53/1.31 tff(887,plain,
% 1.53/1.31 (((~ndr1_0) | (~c2_1(a129)) | (~c3_1(a129)) | (~c0_1(a129)) | c1_1(a129) | (~c2_1(a129)) | (~c3_1(a129)) | c1_1(a129) | (~c0_1(a129)) | (~c2_1(a129))) <=> (c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | (~c3_1(a129)))),
% 1.53/1.31 inference(rewrite,[status(thm)],[])).
% 1.53/1.31 tff(888,plain,
% 1.53/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a129)) | (~c3_1(a129)) | (~c0_1(a129)) | c1_1(a129) | (~c2_1(a129)) | (~c3_1(a129)) | c1_1(a129) | (~c0_1(a129)) | (~c2_1(a129)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | (c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | (~c3_1(a129))))),
% 1.53/1.31 inference(monotonicity,[status(thm)],[887])).
% 1.53/1.31 tff(889,plain,
% 1.53/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a129)) | (~c3_1(a129)) | (~c0_1(a129)) | c1_1(a129) | (~c2_1(a129)) | (~c3_1(a129)) | c1_1(a129) | (~c0_1(a129)) | (~c2_1(a129)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | (~c3_1(a129)))),
% 1.53/1.31 inference(transitivity,[status(thm)],[888, 886])).
% 1.53/1.31 tff(890,plain,
% 1.53/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a129)) | (~c3_1(a129)) | (~c0_1(a129)) | c1_1(a129) | (~c2_1(a129)) | (~c3_1(a129)) | c1_1(a129) | (~c0_1(a129)) | (~c2_1(a129)))),
% 1.53/1.31 inference(quant_inst,[status(thm)],[])).
% 1.53/1.31 tff(891,plain,
% 1.53/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | (~c3_1(a129))),
% 1.53/1.31 inference(modus_ponens,[status(thm)],[890, 889])).
% 1.53/1.31 tff(892,plain,
% 1.53/1.31 (~c3_1(a129)),
% 1.53/1.31 inference(unit_resolution,[status(thm)],[891, 126, 885, 884, 883, 10])).
% 1.53/1.31 tff(893,plain,
% 1.53/1.31 (^[U: $i] : refl((hskp7 | hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp7 | hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 1.53/1.31 inference(bind,[status(th)],[])).
% 1.53/1.31 tff(894,plain,
% 1.53/1.31 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.53/1.31 inference(quant_intro,[status(thm)],[893])).
% 1.53/1.31 tff(895,plain,
% 1.53/1.31 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.53/1.31 inference(rewrite,[status(thm)],[])).
% 1.53/1.31 tff(896,plain,
% 1.53/1.31 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp4) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp4))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp4) | hskp7) <=> ((hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp7))), rewrite(((hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp7) <=> (hskp7 | hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp4) | hskp7) <=> (hskp7 | hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 1.53/1.31 inference(bind,[status(th)],[])).
% 1.53/1.31 tff(897,plain,
% 1.53/1.31 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp4) | hskp7) <=> ![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.53/1.31 inference(quant_intro,[status(thm)],[896])).
% 1.53/1.31 tff(898,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp4) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause152')).
% 1.53/1.31 tff(899,plain,
% 1.53/1.31 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.53/1.31 inference(modus_ponens,[status(thm)],[898, 897])).
% 1.53/1.31 tff(900,plain,
% 1.53/1.31 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.53/1.31 inference(modus_ponens,[status(thm)],[899, 895])).
% 1.53/1.31 tff(901,plain,(
% 1.53/1.31 ![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.53/1.31 inference(skolemize,[status(sab)],[900])).
% 1.53/1.31 tff(902,plain,
% 1.53/1.31 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.53/1.31 inference(modus_ponens,[status(thm)],[901, 894])).
% 1.53/1.31 tff(903,plain,
% 1.53/1.31 (((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | hskp4 | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)))) <=> ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp7 | hskp4 | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)))),
% 1.53/1.31 inference(rewrite,[status(thm)],[])).
% 1.53/1.31 tff(904,plain,
% 1.53/1.31 ((hskp7 | hskp4 | (~ndr1_0) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129))) <=> (hskp7 | hskp4 | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)))),
% 1.53/1.31 inference(rewrite,[status(thm)],[])).
% 1.53/1.31 tff(905,plain,
% 1.53/1.31 (((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | hskp4 | (~ndr1_0) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)))) <=> ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | hskp4 | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129))))),
% 1.53/1.31 inference(monotonicity,[status(thm)],[904])).
% 1.53/1.31 tff(906,plain,
% 1.53/1.31 (((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | hskp4 | (~ndr1_0) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)))) <=> ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp7 | hskp4 | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)))),
% 1.53/1.31 inference(transitivity,[status(thm)],[905, 903])).
% 1.53/1.31 tff(907,plain,
% 1.53/1.31 ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp7 | hskp4 | (~ndr1_0) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)))),
% 1.53/1.31 inference(quant_inst,[status(thm)],[])).
% 1.53/1.31 tff(908,plain,
% 1.53/1.31 ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp7 | hskp4 | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129))),
% 1.53/1.31 inference(modus_ponens,[status(thm)],[907, 906])).
% 1.53/1.31 tff(909,plain,
% 1.53/1.31 (hskp7),
% 1.53/1.31 inference(unit_resolution,[status(thm)],[908, 126, 856, 885, 884, 883, 902])).
% 1.53/1.31 tff(910,plain,
% 1.53/1.31 (((~hskp7) | c3_1(a106)) <=> ((~hskp7) | c3_1(a106))),
% 1.53/1.31 inference(rewrite,[status(thm)],[])).
% 1.53/1.31 tff(911,axiom,((~hskp7) | c3_1(a106)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause76')).
% 1.53/1.31 tff(912,plain,
% 1.53/1.31 ((~hskp7) | c3_1(a106)),
% 1.53/1.31 inference(modus_ponens,[status(thm)],[911, 910])).
% 1.53/1.31 tff(913,plain,
% 1.53/1.31 ((~hskp7) | c3_1(a106)),
% 1.53/1.31 inference(modus_ponens,[status(thm)],[912, 910])).
% 1.53/1.31 tff(914,plain,
% 1.53/1.31 ((~hskp7) | c3_1(a106)),
% 1.53/1.31 inference(modus_ponens,[status(thm)],[913, 910])).
% 1.53/1.31 tff(915,plain,
% 1.53/1.31 ((~hskp7) | c3_1(a106)),
% 1.53/1.31 inference(modus_ponens,[status(thm)],[914, 910])).
% 1.53/1.31 tff(916,plain,
% 1.53/1.31 ((~hskp7) | c3_1(a106)),
% 1.53/1.31 inference(modus_ponens,[status(thm)],[915, 910])).
% 1.53/1.31 tff(917,plain,
% 1.53/1.31 ((~hskp7) | c3_1(a106)),
% 1.53/1.31 inference(modus_ponens,[status(thm)],[916, 910])).
% 1.53/1.31 tff(918,plain,
% 1.53/1.31 ((~hskp7) | c3_1(a106)),
% 1.53/1.31 inference(modus_ponens,[status(thm)],[917, 910])).
% 1.53/1.31 tff(919,plain,
% 1.53/1.31 ((~hskp7) | c3_1(a106)),
% 1.53/1.31 inference(modus_ponens,[status(thm)],[918, 910])).
% 1.53/1.31 tff(920,plain,
% 1.53/1.31 (c3_1(a106)),
% 1.53/1.31 inference(unit_resolution,[status(thm)],[919, 909])).
% 1.53/1.31 tff(921,plain,
% 1.53/1.31 (((~hskp7) | c2_1(a106)) <=> ((~hskp7) | c2_1(a106))),
% 1.53/1.31 inference(rewrite,[status(thm)],[])).
% 1.53/1.31 tff(922,axiom,((~hskp7) | c2_1(a106)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause75')).
% 1.53/1.31 tff(923,plain,
% 1.53/1.31 ((~hskp7) | c2_1(a106)),
% 1.53/1.31 inference(modus_ponens,[status(thm)],[922, 921])).
% 1.53/1.31 tff(924,plain,
% 1.53/1.31 ((~hskp7) | c2_1(a106)),
% 1.53/1.31 inference(modus_ponens,[status(thm)],[923, 921])).
% 1.53/1.31 tff(925,plain,
% 1.53/1.31 ((~hskp7) | c2_1(a106)),
% 1.53/1.31 inference(modus_ponens,[status(thm)],[924, 921])).
% 1.53/1.31 tff(926,plain,
% 1.53/1.31 ((~hskp7) | c2_1(a106)),
% 1.53/1.31 inference(modus_ponens,[status(thm)],[925, 921])).
% 1.53/1.31 tff(927,plain,
% 1.53/1.31 ((~hskp7) | c2_1(a106)),
% 1.53/1.31 inference(modus_ponens,[status(thm)],[926, 921])).
% 1.53/1.31 tff(928,plain,
% 1.53/1.31 ((~hskp7) | c2_1(a106)),
% 1.53/1.31 inference(modus_ponens,[status(thm)],[927, 921])).
% 1.53/1.31 tff(929,plain,
% 1.53/1.31 ((~hskp7) | c2_1(a106)),
% 1.53/1.31 inference(modus_ponens,[status(thm)],[928, 921])).
% 1.53/1.31 tff(930,plain,
% 1.53/1.31 ((~hskp7) | c2_1(a106)),
% 1.53/1.31 inference(modus_ponens,[status(thm)],[929, 921])).
% 1.53/1.31 tff(931,plain,
% 1.53/1.31 (c2_1(a106)),
% 1.53/1.31 inference(unit_resolution,[status(thm)],[930, 909])).
% 1.53/1.31 tff(932,plain,
% 1.53/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c1_1(a129) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | (~c1_1(a106)) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a129) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | (~c1_1(a106)) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129))),
% 1.53/1.31 inference(rewrite,[status(thm)],[])).
% 1.53/1.31 tff(933,plain,
% 1.53/1.31 (((~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | (~c1_1(a106)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c1_1(a129) | c3_1(a129) | (~c2_1(a129))) <=> (c1_1(a129) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | (~c1_1(a106)) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129))),
% 1.53/1.31 inference(rewrite,[status(thm)],[])).
% 1.53/1.31 tff(934,plain,
% 1.53/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | (~c1_1(a106)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c1_1(a129) | c3_1(a129) | (~c2_1(a129)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c1_1(a129) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | (~c1_1(a106)) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129)))),
% 1.53/1.31 inference(monotonicity,[status(thm)],[933])).
% 1.53/1.31 tff(935,plain,
% 1.53/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | (~c1_1(a106)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c1_1(a129) | c3_1(a129) | (~c2_1(a129)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a129) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | (~c1_1(a106)) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129))),
% 1.53/1.31 inference(transitivity,[status(thm)],[934, 932])).
% 1.53/1.31 tff(936,plain,
% 1.53/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | (~c1_1(a106)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c1_1(a129) | c3_1(a129) | (~c2_1(a129)))),
% 1.53/1.31 inference(quant_inst,[status(thm)],[])).
% 1.53/1.31 tff(937,plain,
% 1.53/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a129) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | (~c1_1(a106)) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129)),
% 1.53/1.31 inference(modus_ponens,[status(thm)],[936, 935])).
% 1.53/1.31 tff(938,plain,
% 1.53/1.31 (~c1_1(a106)),
% 1.53/1.31 inference(unit_resolution,[status(thm)],[937, 126, 885, 884, 931, 920, 883, 690, 892])).
% 1.53/1.31 tff(939,plain,
% 1.53/1.31 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | c3_1(a129))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp22 | hskp21 | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | c3_1(a129))),
% 1.53/1.31 inference(rewrite,[status(thm)],[])).
% 1.53/1.31 tff(940,plain,
% 1.53/1.31 ((hskp22 | hskp21 | (~ndr1_0) | c1_1(a129) | c3_1(a129) | (~c2_1(a129))) <=> (hskp22 | hskp21 | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | c3_1(a129))),
% 1.53/1.31 inference(rewrite,[status(thm)],[])).
% 1.53/1.31 tff(941,plain,
% 1.53/1.31 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c1_1(a129) | c3_1(a129) | (~c2_1(a129)))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | c3_1(a129)))),
% 1.53/1.31 inference(monotonicity,[status(thm)],[940])).
% 1.53/1.31 tff(942,plain,
% 1.53/1.31 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c1_1(a129) | c3_1(a129) | (~c2_1(a129)))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp22 | hskp21 | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | c3_1(a129))),
% 1.53/1.31 inference(transitivity,[status(thm)],[941, 939])).
% 1.53/1.31 tff(943,plain,
% 1.53/1.31 ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c1_1(a129) | c3_1(a129) | (~c2_1(a129)))),
% 1.53/1.31 inference(quant_inst,[status(thm)],[])).
% 1.53/1.31 tff(944,plain,
% 1.53/1.31 ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp22 | hskp21 | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | c3_1(a129)),
% 1.53/1.31 inference(modus_ponens,[status(thm)],[943, 942])).
% 1.53/1.31 tff(945,plain,
% 1.53/1.31 (hskp21),
% 1.53/1.31 inference(unit_resolution,[status(thm)],[944, 126, 144, 884, 883, 173, 892])).
% 1.53/1.31 tff(946,plain,
% 1.53/1.31 (~c2_1(a136)),
% 1.53/1.31 inference(unit_resolution,[status(thm)],[187, 945])).
% 1.53/1.31 tff(947,plain,
% 1.53/1.31 (~c1_1(a136)),
% 1.53/1.31 inference(unit_resolution,[status(thm)],[193, 945])).
% 1.53/1.31 tff(948,plain,
% 1.53/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a136) | c2_1(a136) | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129) | (~c0_1(a136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a136) | c2_1(a136) | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129) | (~c0_1(a136)))),
% 1.53/1.31 inference(rewrite,[status(thm)],[])).
% 1.53/1.31 tff(949,plain,
% 1.53/1.31 (((~ndr1_0) | c3_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c2_1(a136) | c1_1(a136) | (~c0_1(a136))) <=> (c1_1(a136) | c2_1(a136) | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129) | (~c0_1(a136)))),
% 1.53/1.31 inference(rewrite,[status(thm)],[])).
% 1.53/1.31 tff(950,plain,
% 1.53/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c2_1(a136) | c1_1(a136) | (~c0_1(a136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a136) | c2_1(a136) | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129) | (~c0_1(a136))))),
% 1.53/1.31 inference(monotonicity,[status(thm)],[949])).
% 1.53/1.31 tff(951,plain,
% 1.53/1.31 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c2_1(a136) | c1_1(a136) | (~c0_1(a136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a136) | c2_1(a136) | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129) | (~c0_1(a136)))),
% 1.53/1.31 inference(transitivity,[status(thm)],[950, 948])).
% 1.53/1.31 tff(952,plain,
% 1.53/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c2_1(a136) | c1_1(a136) | (~c0_1(a136)))),
% 1.53/1.31 inference(quant_inst,[status(thm)],[])).
% 1.53/1.31 tff(953,plain,
% 1.53/1.31 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a136) | c2_1(a136) | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129) | (~c0_1(a136))),
% 1.53/1.31 inference(modus_ponens,[status(thm)],[952, 951])).
% 1.53/1.31 tff(954,plain,
% 1.53/1.31 (~c0_1(a136)),
% 1.53/1.31 inference(unit_resolution,[status(thm)],[953, 126, 885, 884, 947, 946, 883, 143, 892])).
% 1.53/1.31 tff(955,plain,
% 1.53/1.31 (^[U: $i] : refl((hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))),
% 1.53/1.31 inference(bind,[status(th)],[])).
% 1.53/1.31 tff(956,plain,
% 1.53/1.31 (![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.53/1.31 inference(quant_intro,[status(thm)],[955])).
% 1.53/1.31 tff(957,plain,
% 1.53/1.31 (![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.53/1.31 inference(rewrite,[status(thm)],[])).
% 1.53/1.31 tff(958,plain,
% 1.53/1.31 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp4) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp4))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp4) | hskp5) <=> ((hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp5))), rewrite(((hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp5) <=> (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp4) | hskp5) <=> (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))))),
% 1.53/1.31 inference(bind,[status(th)],[])).
% 1.53/1.31 tff(959,plain,
% 1.53/1.31 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp4) | hskp5) <=> ![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.53/1.31 inference(quant_intro,[status(thm)],[958])).
% 1.53/1.31 tff(960,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp4) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause136')).
% 1.53/1.31 tff(961,plain,
% 1.53/1.31 (![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.53/1.31 inference(modus_ponens,[status(thm)],[960, 959])).
% 1.53/1.31 tff(962,plain,
% 1.53/1.31 (![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.53/1.31 inference(modus_ponens,[status(thm)],[961, 957])).
% 1.53/1.31 tff(963,plain,(
% 1.53/1.31 ![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.53/1.31 inference(skolemize,[status(sab)],[962])).
% 1.53/1.31 tff(964,plain,
% 1.53/1.31 (![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.53/1.31 inference(modus_ponens,[status(thm)],[963, 956])).
% 1.53/1.31 tff(965,plain,
% 1.53/1.31 (((~hskp7) | (~c0_1(a106))) <=> ((~hskp7) | (~c0_1(a106)))),
% 1.53/1.31 inference(rewrite,[status(thm)],[])).
% 1.53/1.31 tff(966,plain,
% 1.53/1.31 (((~c0_1(a106)) | (~hskp7)) <=> ((~hskp7) | (~c0_1(a106)))),
% 1.53/1.31 inference(rewrite,[status(thm)],[])).
% 1.53/1.31 tff(967,axiom,((~c0_1(a106)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause121')).
% 1.53/1.31 tff(968,plain,
% 1.53/1.31 ((~hskp7) | (~c0_1(a106))),
% 1.53/1.31 inference(modus_ponens,[status(thm)],[967, 966])).
% 1.53/1.31 tff(969,plain,
% 1.53/1.31 ((~hskp7) | (~c0_1(a106))),
% 1.53/1.31 inference(modus_ponens,[status(thm)],[968, 965])).
% 1.53/1.31 tff(970,plain,
% 1.53/1.31 (~c0_1(a106)),
% 1.53/1.31 inference(unit_resolution,[status(thm)],[969, 909])).
% 1.53/1.31 tff(971,plain,
% 1.53/1.31 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp5 | hskp4 | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | c1_1(a106))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp5 | hskp4 | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | c1_1(a106))),
% 1.53/1.31 inference(rewrite,[status(thm)],[])).
% 1.53/1.31 tff(972,plain,
% 1.53/1.31 ((hskp5 | hskp4 | (~ndr1_0) | c1_1(a106) | c0_1(a106) | (~c2_1(a106))) <=> (hskp5 | hskp4 | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | c1_1(a106))),
% 1.53/1.31 inference(rewrite,[status(thm)],[])).
% 1.53/1.31 tff(973,plain,
% 1.53/1.31 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp5 | hskp4 | (~ndr1_0) | c1_1(a106) | c0_1(a106) | (~c2_1(a106)))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp5 | hskp4 | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | c1_1(a106)))),
% 1.53/1.31 inference(monotonicity,[status(thm)],[972])).
% 1.53/1.31 tff(974,plain,
% 1.53/1.31 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp5 | hskp4 | (~ndr1_0) | c1_1(a106) | c0_1(a106) | (~c2_1(a106)))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp5 | hskp4 | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | c1_1(a106))),
% 1.53/1.31 inference(transitivity,[status(thm)],[973, 971])).
% 1.53/1.31 tff(975,plain,
% 1.53/1.31 ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp5 | hskp4 | (~ndr1_0) | c1_1(a106) | c0_1(a106) | (~c2_1(a106)))),
% 1.53/1.31 inference(quant_inst,[status(thm)],[])).
% 1.53/1.31 tff(976,plain,
% 1.53/1.31 ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp5 | hskp4 | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | c1_1(a106)),
% 1.53/1.31 inference(modus_ponens,[status(thm)],[975, 974])).
% 1.53/1.31 tff(977,plain,
% 1.53/1.31 (hskp5),
% 1.53/1.31 inference(unit_resolution,[status(thm)],[976, 126, 856, 931, 970, 964, 938])).
% 1.53/1.31 tff(978,plain,
% 1.53/1.31 (((~hskp5) | (~c3_1(a104))) <=> ((~hskp5) | (~c3_1(a104)))),
% 1.53/1.32 inference(rewrite,[status(thm)],[])).
% 1.53/1.32 tff(979,plain,
% 1.53/1.32 (((~c3_1(a104)) | (~hskp5)) <=> ((~hskp5) | (~c3_1(a104)))),
% 1.53/1.32 inference(rewrite,[status(thm)],[])).
% 1.53/1.32 tff(980,axiom,((~c3_1(a104)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause124')).
% 1.53/1.32 tff(981,plain,
% 1.53/1.32 ((~hskp5) | (~c3_1(a104))),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[980, 979])).
% 1.53/1.32 tff(982,plain,
% 1.53/1.32 ((~hskp5) | (~c3_1(a104))),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[981, 978])).
% 1.53/1.32 tff(983,plain,
% 1.53/1.32 (~c3_1(a104)),
% 1.53/1.32 inference(unit_resolution,[status(thm)],[982, 977])).
% 1.53/1.32 tff(984,plain,
% 1.53/1.32 (((~hskp5) | (~c0_1(a104))) <=> ((~hskp5) | (~c0_1(a104)))),
% 1.53/1.32 inference(rewrite,[status(thm)],[])).
% 1.53/1.32 tff(985,plain,
% 1.53/1.32 (((~c0_1(a104)) | (~hskp5)) <=> ((~hskp5) | (~c0_1(a104)))),
% 1.53/1.32 inference(rewrite,[status(thm)],[])).
% 1.53/1.32 tff(986,axiom,((~c0_1(a104)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause123')).
% 1.53/1.32 tff(987,plain,
% 1.53/1.32 ((~hskp5) | (~c0_1(a104))),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[986, 985])).
% 1.53/1.32 tff(988,plain,
% 1.53/1.32 ((~hskp5) | (~c0_1(a104))),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[987, 984])).
% 1.53/1.32 tff(989,plain,
% 1.53/1.32 (~c0_1(a104)),
% 1.53/1.32 inference(unit_resolution,[status(thm)],[988, 977])).
% 1.53/1.32 tff(990,plain,
% 1.53/1.32 (((~hskp5) | c2_1(a104)) <=> ((~hskp5) | c2_1(a104))),
% 1.53/1.32 inference(rewrite,[status(thm)],[])).
% 1.53/1.32 tff(991,axiom,((~hskp5) | c2_1(a104)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause79')).
% 1.53/1.32 tff(992,plain,
% 1.53/1.32 ((~hskp5) | c2_1(a104)),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[991, 990])).
% 1.53/1.32 tff(993,plain,
% 1.53/1.32 ((~hskp5) | c2_1(a104)),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[992, 990])).
% 1.53/1.32 tff(994,plain,
% 1.53/1.32 ((~hskp5) | c2_1(a104)),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[993, 990])).
% 1.53/1.32 tff(995,plain,
% 1.53/1.32 ((~hskp5) | c2_1(a104)),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[994, 990])).
% 1.53/1.32 tff(996,plain,
% 1.53/1.32 ((~hskp5) | c2_1(a104)),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[995, 990])).
% 1.53/1.32 tff(997,plain,
% 1.53/1.32 ((~hskp5) | c2_1(a104)),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[996, 990])).
% 1.53/1.32 tff(998,plain,
% 1.53/1.32 ((~hskp5) | c2_1(a104)),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[997, 990])).
% 1.53/1.32 tff(999,plain,
% 1.53/1.32 ((~hskp5) | c2_1(a104)),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[998, 990])).
% 1.53/1.32 tff(1000,plain,
% 1.53/1.32 (c2_1(a104)),
% 1.53/1.32 inference(unit_resolution,[status(thm)],[999, 977])).
% 1.53/1.32 tff(1001,plain,
% 1.53/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a136) | c2_1(a136) | c0_1(a106) | c0_1(a104) | c3_1(a104) | (~ndr1_0) | (~c2_1(a104)) | (~c2_1(a106)) | c1_1(a106) | c0_1(a136))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a136) | c2_1(a136) | c0_1(a106) | c0_1(a104) | c3_1(a104) | (~ndr1_0) | (~c2_1(a104)) | (~c2_1(a106)) | c1_1(a106) | c0_1(a136))),
% 1.53/1.32 inference(rewrite,[status(thm)],[])).
% 1.53/1.32 tff(1002,plain,
% 1.53/1.32 (((~ndr1_0) | c0_1(a104) | c3_1(a104) | (~c2_1(a104)) | c1_1(a106) | c0_1(a106) | (~c2_1(a106)) | c2_1(a136) | c1_1(a136) | c0_1(a136)) <=> (c1_1(a136) | c2_1(a136) | c0_1(a106) | c0_1(a104) | c3_1(a104) | (~ndr1_0) | (~c2_1(a104)) | (~c2_1(a106)) | c1_1(a106) | c0_1(a136))),
% 1.53/1.32 inference(rewrite,[status(thm)],[])).
% 1.53/1.32 tff(1003,plain,
% 1.53/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a104) | c3_1(a104) | (~c2_1(a104)) | c1_1(a106) | c0_1(a106) | (~c2_1(a106)) | c2_1(a136) | c1_1(a136) | c0_1(a136))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a136) | c2_1(a136) | c0_1(a106) | c0_1(a104) | c3_1(a104) | (~ndr1_0) | (~c2_1(a104)) | (~c2_1(a106)) | c1_1(a106) | c0_1(a136)))),
% 1.53/1.32 inference(monotonicity,[status(thm)],[1002])).
% 1.53/1.32 tff(1004,plain,
% 1.53/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a104) | c3_1(a104) | (~c2_1(a104)) | c1_1(a106) | c0_1(a106) | (~c2_1(a106)) | c2_1(a136) | c1_1(a136) | c0_1(a136))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a136) | c2_1(a136) | c0_1(a106) | c0_1(a104) | c3_1(a104) | (~ndr1_0) | (~c2_1(a104)) | (~c2_1(a106)) | c1_1(a106) | c0_1(a136))),
% 1.53/1.32 inference(transitivity,[status(thm)],[1003, 1001])).
% 1.53/1.32 tff(1005,plain,
% 1.53/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a104) | c3_1(a104) | (~c2_1(a104)) | c1_1(a106) | c0_1(a106) | (~c2_1(a106)) | c2_1(a136) | c1_1(a136) | c0_1(a136))),
% 1.53/1.32 inference(quant_inst,[status(thm)],[])).
% 1.53/1.32 tff(1006,plain,
% 1.53/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a136) | c2_1(a136) | c0_1(a106) | c0_1(a104) | c3_1(a104) | (~ndr1_0) | (~c2_1(a104)) | (~c2_1(a106)) | c1_1(a106) | c0_1(a136)),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[1005, 1004])).
% 1.53/1.32 tff(1007,plain,
% 1.53/1.32 ($false),
% 1.53/1.32 inference(unit_resolution,[status(thm)],[1006, 126, 931, 1000, 947, 946, 970, 989, 983, 794, 954, 938])).
% 1.53/1.32 tff(1008,plain,(hskp4 | hskp22), inference(lemma,lemma(discharge,[]))).
% 1.53/1.32 tff(1009,plain,
% 1.53/1.32 (hskp4),
% 1.53/1.32 inference(unit_resolution,[status(thm)],[1008, 144])).
% 1.53/1.32 tff(1010,plain,
% 1.53/1.32 (c0_1(a103)),
% 1.53/1.32 inference(unit_resolution,[status(thm)],[92, 1009])).
% 1.53/1.32 tff(1011,plain,
% 1.53/1.32 (~c3_1(a103)),
% 1.53/1.32 inference(unit_resolution,[status(thm)],[81, 1009])).
% 1.53/1.32 tff(1012,plain,
% 1.53/1.32 (c2_1(a103)),
% 1.53/1.32 inference(unit_resolution,[status(thm)],[157, 1009])).
% 1.53/1.32 tff(1013,plain,
% 1.53/1.32 (c1_1(a97)),
% 1.53/1.32 inference(unit_resolution,[status(thm)],[328, 1012, 823, 835, 1011, 824, 1010])).
% 1.53/1.32 tff(1014,plain,
% 1.53/1.32 (^[U: $i] : refl((hskp18 | hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> (hskp18 | hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))))),
% 1.53/1.32 inference(bind,[status(th)],[])).
% 1.53/1.32 tff(1015,plain,
% 1.53/1.32 (![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.53/1.32 inference(quant_intro,[status(thm)],[1014])).
% 1.53/1.32 tff(1016,plain,
% 1.53/1.32 (![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.53/1.32 inference(rewrite,[status(thm)],[])).
% 1.53/1.32 tff(1017,plain,
% 1.53/1.32 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp18) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp18))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp18) <=> (hskp18 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp18) <=> (hskp18 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp18) | hskp8) <=> ((hskp18 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp8))), rewrite(((hskp18 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp8) <=> (hskp18 | hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp18) | hskp8) <=> (hskp18 | hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))))),
% 1.53/1.32 inference(bind,[status(th)],[])).
% 1.53/1.32 tff(1018,plain,
% 1.53/1.32 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp18) | hskp8) <=> ![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.53/1.32 inference(quant_intro,[status(thm)],[1017])).
% 1.53/1.32 tff(1019,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp18) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause157')).
% 1.53/1.32 tff(1020,plain,
% 1.53/1.32 (![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[1019, 1018])).
% 1.53/1.32 tff(1021,plain,
% 1.53/1.32 (![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[1020, 1016])).
% 1.53/1.32 tff(1022,plain,(
% 1.53/1.32 ![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.53/1.32 inference(skolemize,[status(sab)],[1021])).
% 1.53/1.32 tff(1023,plain,
% 1.53/1.32 (![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[1022, 1015])).
% 1.53/1.32 tff(1024,plain,
% 1.53/1.32 (((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp18 | hskp8 | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)))) <=> ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp18 | hskp8 | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)))),
% 1.53/1.32 inference(rewrite,[status(thm)],[])).
% 1.53/1.32 tff(1025,plain,
% 1.53/1.32 ((hskp18 | hskp8 | (~ndr1_0) | c3_1(a97) | (~c0_1(a97)) | (~c1_1(a97))) <=> (hskp18 | hskp8 | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)))),
% 1.53/1.32 inference(rewrite,[status(thm)],[])).
% 1.53/1.32 tff(1026,plain,
% 1.53/1.32 (((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp18 | hskp8 | (~ndr1_0) | c3_1(a97) | (~c0_1(a97)) | (~c1_1(a97)))) <=> ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp18 | hskp8 | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97))))),
% 1.53/1.32 inference(monotonicity,[status(thm)],[1025])).
% 1.53/1.32 tff(1027,plain,
% 1.53/1.32 (((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp18 | hskp8 | (~ndr1_0) | c3_1(a97) | (~c0_1(a97)) | (~c1_1(a97)))) <=> ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp18 | hskp8 | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)))),
% 1.53/1.32 inference(transitivity,[status(thm)],[1026, 1024])).
% 1.53/1.32 tff(1028,plain,
% 1.53/1.32 ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp18 | hskp8 | (~ndr1_0) | c3_1(a97) | (~c0_1(a97)) | (~c1_1(a97)))),
% 1.53/1.32 inference(quant_inst,[status(thm)],[])).
% 1.53/1.32 tff(1029,plain,
% 1.53/1.32 ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp18 | hskp8 | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97))),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[1028, 1027])).
% 1.53/1.32 tff(1030,plain,
% 1.53/1.32 (hskp18 | hskp8 | (~c1_1(a97))),
% 1.53/1.32 inference(unit_resolution,[status(thm)],[1029, 126, 835, 823, 1023])).
% 1.53/1.32 tff(1031,plain,
% 1.53/1.32 (hskp8),
% 1.53/1.32 inference(unit_resolution,[status(thm)],[1030, 52, 1013])).
% 1.53/1.32 tff(1032,plain,
% 1.53/1.32 (((~hskp8) | c3_1(a107)) <=> ((~hskp8) | c3_1(a107))),
% 1.53/1.32 inference(rewrite,[status(thm)],[])).
% 1.53/1.32 tff(1033,axiom,((~hskp8) | c3_1(a107)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause74')).
% 1.53/1.32 tff(1034,plain,
% 1.53/1.32 ((~hskp8) | c3_1(a107)),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[1033, 1032])).
% 1.53/1.32 tff(1035,plain,
% 1.53/1.32 ((~hskp8) | c3_1(a107)),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[1034, 1032])).
% 1.53/1.32 tff(1036,plain,
% 1.53/1.32 ((~hskp8) | c3_1(a107)),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[1035, 1032])).
% 1.53/1.32 tff(1037,plain,
% 1.53/1.32 ((~hskp8) | c3_1(a107)),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[1036, 1032])).
% 1.53/1.32 tff(1038,plain,
% 1.53/1.32 ((~hskp8) | c3_1(a107)),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[1037, 1032])).
% 1.53/1.32 tff(1039,plain,
% 1.53/1.32 ((~hskp8) | c3_1(a107)),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[1038, 1032])).
% 1.53/1.32 tff(1040,plain,
% 1.53/1.32 ((~hskp8) | c3_1(a107)),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[1039, 1032])).
% 1.53/1.32 tff(1041,plain,
% 1.53/1.32 ((~hskp8) | c3_1(a107)),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[1040, 1032])).
% 1.53/1.32 tff(1042,plain,
% 1.53/1.32 (c3_1(a107)),
% 1.53/1.32 inference(unit_resolution,[status(thm)],[1041, 1031])).
% 1.53/1.32 tff(1043,plain,
% 1.53/1.32 (((~hskp11) | c3_1(a112)) <=> ((~hskp11) | c3_1(a112))),
% 1.53/1.32 inference(rewrite,[status(thm)],[])).
% 1.53/1.32 tff(1044,axiom,((~hskp11) | c3_1(a112)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause70')).
% 1.53/1.32 tff(1045,plain,
% 1.53/1.32 ((~hskp11) | c3_1(a112)),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[1044, 1043])).
% 1.53/1.32 tff(1046,plain,
% 1.53/1.32 ((~hskp11) | c3_1(a112)),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[1045, 1043])).
% 1.53/1.32 tff(1047,plain,
% 1.53/1.32 ((~hskp11) | c3_1(a112)),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[1046, 1043])).
% 1.53/1.32 tff(1048,plain,
% 1.53/1.32 ((~hskp11) | c3_1(a112)),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[1047, 1043])).
% 1.53/1.32 tff(1049,plain,
% 1.53/1.32 ((~hskp11) | c3_1(a112)),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[1048, 1043])).
% 1.53/1.32 tff(1050,plain,
% 1.53/1.32 ((~hskp11) | c3_1(a112)),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[1049, 1043])).
% 1.53/1.32 tff(1051,plain,
% 1.53/1.32 ((~hskp11) | c3_1(a112)),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[1050, 1043])).
% 1.53/1.32 tff(1052,plain,
% 1.53/1.32 ((~hskp11) | c3_1(a112)),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[1051, 1043])).
% 1.53/1.32 tff(1053,plain,
% 1.53/1.32 (c3_1(a112)),
% 1.53/1.32 inference(unit_resolution,[status(thm)],[1052, 843])).
% 1.53/1.32 tff(1054,plain,
% 1.53/1.32 (((~hskp8) | (~c2_1(a107))) <=> ((~hskp8) | (~c2_1(a107)))),
% 1.53/1.32 inference(rewrite,[status(thm)],[])).
% 1.53/1.32 tff(1055,plain,
% 1.53/1.32 (((~c2_1(a107)) | (~hskp8)) <=> ((~hskp8) | (~c2_1(a107)))),
% 1.53/1.32 inference(rewrite,[status(thm)],[])).
% 1.53/1.32 tff(1056,axiom,((~c2_1(a107)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause120')).
% 1.53/1.32 tff(1057,plain,
% 1.53/1.32 ((~hskp8) | (~c2_1(a107))),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[1056, 1055])).
% 1.53/1.32 tff(1058,plain,
% 1.53/1.32 ((~hskp8) | (~c2_1(a107))),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[1057, 1054])).
% 1.53/1.32 tff(1059,plain,
% 1.53/1.32 (~c2_1(a107)),
% 1.53/1.32 inference(unit_resolution,[status(thm)],[1058, 1031])).
% 1.53/1.32 tff(1060,assumption,(hskp9), introduced(assumption)).
% 1.53/1.32 tff(1061,plain,
% 1.53/1.32 (((~hskp9) | (~c0_1(a108))) <=> ((~hskp9) | (~c0_1(a108)))),
% 1.53/1.32 inference(rewrite,[status(thm)],[])).
% 1.53/1.32 tff(1062,plain,
% 1.53/1.32 (((~c0_1(a108)) | (~hskp9)) <=> ((~hskp9) | (~c0_1(a108)))),
% 1.53/1.32 inference(rewrite,[status(thm)],[])).
% 1.53/1.32 tff(1063,axiom,((~c0_1(a108)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause118')).
% 1.53/1.32 tff(1064,plain,
% 1.53/1.32 ((~hskp9) | (~c0_1(a108))),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[1063, 1062])).
% 1.53/1.32 tff(1065,plain,
% 1.53/1.32 ((~hskp9) | (~c0_1(a108))),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[1064, 1061])).
% 1.53/1.32 tff(1066,plain,
% 1.53/1.32 (~c0_1(a108)),
% 1.53/1.32 inference(unit_resolution,[status(thm)],[1065, 1060])).
% 1.53/1.32 tff(1067,plain,
% 1.53/1.32 (((~hskp9) | c2_1(a108)) <=> ((~hskp9) | c2_1(a108))),
% 1.53/1.32 inference(rewrite,[status(thm)],[])).
% 1.53/1.32 tff(1068,axiom,((~hskp9) | c2_1(a108)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 1.53/1.32 tff(1069,plain,
% 1.53/1.32 ((~hskp9) | c2_1(a108)),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[1068, 1067])).
% 1.53/1.32 tff(1070,plain,
% 1.53/1.32 ((~hskp9) | c2_1(a108)),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[1069, 1067])).
% 1.53/1.32 tff(1071,plain,
% 1.53/1.32 ((~hskp9) | c2_1(a108)),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[1070, 1067])).
% 1.53/1.32 tff(1072,plain,
% 1.53/1.32 ((~hskp9) | c2_1(a108)),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[1071, 1067])).
% 1.53/1.32 tff(1073,plain,
% 1.53/1.32 ((~hskp9) | c2_1(a108)),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[1072, 1067])).
% 1.53/1.32 tff(1074,plain,
% 1.53/1.32 ((~hskp9) | c2_1(a108)),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[1073, 1067])).
% 1.53/1.32 tff(1075,plain,
% 1.53/1.32 ((~hskp9) | c2_1(a108)),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[1074, 1067])).
% 1.53/1.32 tff(1076,plain,
% 1.53/1.32 ((~hskp9) | c2_1(a108)),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[1075, 1067])).
% 1.53/1.32 tff(1077,plain,
% 1.53/1.32 (c2_1(a108)),
% 1.53/1.32 inference(unit_resolution,[status(thm)],[1076, 1060])).
% 1.53/1.32 tff(1078,plain,
% 1.53/1.32 (((~hskp9) | c1_1(a108)) <=> ((~hskp9) | c1_1(a108))),
% 1.53/1.32 inference(rewrite,[status(thm)],[])).
% 1.53/1.32 tff(1079,axiom,((~hskp9) | c1_1(a108)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause72')).
% 1.53/1.32 tff(1080,plain,
% 1.53/1.32 ((~hskp9) | c1_1(a108)),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[1079, 1078])).
% 1.53/1.32 tff(1081,plain,
% 1.53/1.32 ((~hskp9) | c1_1(a108)),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[1080, 1078])).
% 1.53/1.32 tff(1082,plain,
% 1.53/1.32 ((~hskp9) | c1_1(a108)),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[1081, 1078])).
% 1.53/1.32 tff(1083,plain,
% 1.53/1.32 ((~hskp9) | c1_1(a108)),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[1082, 1078])).
% 1.53/1.32 tff(1084,plain,
% 1.53/1.32 ((~hskp9) | c1_1(a108)),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[1083, 1078])).
% 1.53/1.32 tff(1085,plain,
% 1.53/1.32 ((~hskp9) | c1_1(a108)),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[1084, 1078])).
% 1.53/1.32 tff(1086,plain,
% 1.53/1.32 ((~hskp9) | c1_1(a108)),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[1085, 1078])).
% 1.53/1.32 tff(1087,plain,
% 1.53/1.32 ((~hskp9) | c1_1(a108)),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[1086, 1078])).
% 1.53/1.32 tff(1088,plain,
% 1.53/1.32 (c1_1(a108)),
% 1.53/1.32 inference(unit_resolution,[status(thm)],[1087, 1060])).
% 1.53/1.32 tff(1089,plain,
% 1.53/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a108) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c2_1(a137)) | (~c0_1(a137)) | (~c1_1(a97)) | (~c1_1(a137)) | (~c1_1(a108)) | (~c2_1(a108)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a108) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c2_1(a137)) | (~c0_1(a137)) | (~c1_1(a97)) | (~c1_1(a137)) | (~c1_1(a108)) | (~c2_1(a108)))),
% 1.53/1.32 inference(rewrite,[status(thm)],[])).
% 1.53/1.32 tff(1090,plain,
% 1.53/1.32 (((~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | (~c1_1(a137)) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a108) | (~c2_1(a108)) | (~c1_1(a108))) <=> (c0_1(a108) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c2_1(a137)) | (~c0_1(a137)) | (~c1_1(a97)) | (~c1_1(a137)) | (~c1_1(a108)) | (~c2_1(a108)))),
% 1.53/1.32 inference(rewrite,[status(thm)],[])).
% 1.53/1.32 tff(1091,plain,
% 1.53/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | (~c1_1(a137)) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a108) | (~c2_1(a108)) | (~c1_1(a108)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a108) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c2_1(a137)) | (~c0_1(a137)) | (~c1_1(a97)) | (~c1_1(a137)) | (~c1_1(a108)) | (~c2_1(a108))))),
% 1.53/1.32 inference(monotonicity,[status(thm)],[1090])).
% 1.53/1.32 tff(1092,plain,
% 1.53/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | (~c1_1(a137)) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a108) | (~c2_1(a108)) | (~c1_1(a108)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a108) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c2_1(a137)) | (~c0_1(a137)) | (~c1_1(a97)) | (~c1_1(a137)) | (~c1_1(a108)) | (~c2_1(a108)))),
% 1.53/1.32 inference(transitivity,[status(thm)],[1091, 1089])).
% 1.53/1.32 tff(1093,plain,
% 1.53/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | (~c1_1(a137)) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a108) | (~c2_1(a108)) | (~c1_1(a108)))),
% 1.53/1.32 inference(quant_inst,[status(thm)],[])).
% 1.53/1.32 tff(1094,plain,
% 1.53/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a108) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c2_1(a137)) | (~c0_1(a137)) | (~c1_1(a97)) | (~c1_1(a137)) | (~c1_1(a108)) | (~c2_1(a108))),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[1093, 1092])).
% 1.53/1.32 tff(1095,plain,
% 1.53/1.32 ($false),
% 1.53/1.32 inference(unit_resolution,[status(thm)],[1094, 126, 664, 666, 667, 1088, 1077, 246, 1066, 31, 381, 330])).
% 1.53/1.32 tff(1096,plain,((~hskp9) | (~c0_1(a137)) | (~c1_1(a137)) | (~c2_1(a137)) | (~c0_1(a97)) | c2_1(a97) | (~c1_1(a97))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.32 tff(1097,plain,
% 1.53/1.32 (~hskp9),
% 1.53/1.32 inference(unit_resolution,[status(thm)],[1096, 633, 655, 644, 835, 824, 1013])).
% 1.53/1.32 tff(1098,plain,
% 1.53/1.32 (((~hskp8) | (~c0_1(a107))) <=> ((~hskp8) | (~c0_1(a107)))),
% 1.53/1.32 inference(rewrite,[status(thm)],[])).
% 1.53/1.32 tff(1099,plain,
% 1.53/1.32 (((~c0_1(a107)) | (~hskp8)) <=> ((~hskp8) | (~c0_1(a107)))),
% 1.53/1.32 inference(rewrite,[status(thm)],[])).
% 1.53/1.32 tff(1100,axiom,((~c0_1(a107)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause119')).
% 1.53/1.32 tff(1101,plain,
% 1.53/1.32 ((~hskp8) | (~c0_1(a107))),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[1100, 1099])).
% 1.53/1.32 tff(1102,plain,
% 1.53/1.32 ((~hskp8) | (~c0_1(a107))),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[1101, 1098])).
% 1.53/1.32 tff(1103,plain,
% 1.53/1.32 (~c0_1(a107)),
% 1.53/1.32 inference(unit_resolution,[status(thm)],[1102, 1031])).
% 1.53/1.32 tff(1104,assumption,(~hskp17), introduced(assumption)).
% 1.53/1.32 tff(1105,plain,
% 1.53/1.32 (^[U: $i] : refl((hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))),
% 1.53/1.32 inference(bind,[status(th)],[])).
% 1.53/1.32 tff(1106,plain,
% 1.53/1.32 (![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.53/1.32 inference(quant_intro,[status(thm)],[1105])).
% 1.53/1.32 tff(1107,plain,
% 1.53/1.32 (![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.53/1.32 inference(rewrite,[status(thm)],[])).
% 1.53/1.32 tff(1108,plain,
% 1.53/1.32 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp9) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp9))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp9) <=> (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp9) <=> (hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp9) | hskp17) <=> ((hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp17))), rewrite(((hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp17) <=> (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp9) | hskp17) <=> (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))))),
% 1.53/1.32 inference(bind,[status(th)],[])).
% 1.53/1.32 tff(1109,plain,
% 1.53/1.32 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp9) | hskp17) <=> ![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.53/1.32 inference(quant_intro,[status(thm)],[1108])).
% 1.53/1.32 tff(1110,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp9) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause151')).
% 1.53/1.32 tff(1111,plain,
% 1.53/1.32 (![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[1110, 1109])).
% 1.53/1.32 tff(1112,plain,
% 1.53/1.32 (![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[1111, 1107])).
% 1.53/1.32 tff(1113,plain,(
% 1.53/1.32 ![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.53/1.32 inference(skolemize,[status(sab)],[1112])).
% 1.53/1.32 tff(1114,plain,
% 1.53/1.32 (![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.53/1.32 inference(modus_ponens,[status(thm)],[1113, 1106])).
% 1.53/1.32 tff(1115,assumption,(~c0_1(a112)), introduced(assumption)).
% 1.53/1.32 tff(1116,assumption,(c3_1(a112)), introduced(assumption)).
% 1.53/1.32 tff(1117,assumption,(~hskp9), introduced(assumption)).
% 1.53/1.32 tff(1118,plain,
% 1.53/1.32 (((~![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp9 | c0_1(a112) | (~ndr1_0) | (~c2_1(a112)) | (~c3_1(a112)))) <=> ((~![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp17 | hskp9 | c0_1(a112) | (~ndr1_0) | (~c2_1(a112)) | (~c3_1(a112)))),
% 1.53/1.33 inference(rewrite,[status(thm)],[])).
% 1.53/1.33 tff(1119,plain,
% 1.53/1.33 ((hskp17 | hskp9 | (~ndr1_0) | c0_1(a112) | (~c2_1(a112)) | (~c3_1(a112))) <=> (hskp17 | hskp9 | c0_1(a112) | (~ndr1_0) | (~c2_1(a112)) | (~c3_1(a112)))),
% 1.53/1.33 inference(rewrite,[status(thm)],[])).
% 1.53/1.33 tff(1120,plain,
% 1.53/1.33 (((~![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp9 | (~ndr1_0) | c0_1(a112) | (~c2_1(a112)) | (~c3_1(a112)))) <=> ((~![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp9 | c0_1(a112) | (~ndr1_0) | (~c2_1(a112)) | (~c3_1(a112))))),
% 1.53/1.33 inference(monotonicity,[status(thm)],[1119])).
% 1.53/1.33 tff(1121,plain,
% 1.53/1.33 (((~![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp9 | (~ndr1_0) | c0_1(a112) | (~c2_1(a112)) | (~c3_1(a112)))) <=> ((~![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp17 | hskp9 | c0_1(a112) | (~ndr1_0) | (~c2_1(a112)) | (~c3_1(a112)))),
% 1.53/1.33 inference(transitivity,[status(thm)],[1120, 1118])).
% 1.53/1.33 tff(1122,plain,
% 1.53/1.33 ((~![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp9 | (~ndr1_0) | c0_1(a112) | (~c2_1(a112)) | (~c3_1(a112)))),
% 1.53/1.33 inference(quant_inst,[status(thm)],[])).
% 1.53/1.33 tff(1123,plain,
% 1.53/1.33 ((~![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp17 | hskp9 | c0_1(a112) | (~ndr1_0) | (~c2_1(a112)) | (~c3_1(a112))),
% 1.53/1.33 inference(modus_ponens,[status(thm)],[1122, 1121])).
% 1.53/1.33 tff(1124,plain,
% 1.53/1.33 (hskp17 | (~c2_1(a112))),
% 1.53/1.33 inference(unit_resolution,[status(thm)],[1123, 126, 1117, 1116, 1115, 1114])).
% 1.53/1.33 tff(1125,plain,
% 1.53/1.33 (~c2_1(a112)),
% 1.53/1.33 inference(unit_resolution,[status(thm)],[1124, 1104])).
% 1.53/1.33 tff(1126,plain,
% 1.53/1.33 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))))),
% 1.53/1.33 inference(bind,[status(th)],[])).
% 1.53/1.33 tff(1127,plain,
% 1.53/1.33 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_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) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.53/1.33 inference(quant_intro,[status(thm)],[1126])).
% 1.53/1.33 tff(1128,plain,
% 1.53/1.33 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_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) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.53/1.33 inference(rewrite,[status(thm)],[])).
% 1.53/1.33 tff(1129,plain,
% 1.53/1.33 (^[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))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_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) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_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) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_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) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_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) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))))),
% 1.53/1.33 inference(bind,[status(th)],[])).
% 1.53/1.33 tff(1130,plain,
% 1.53/1.33 (![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_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) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.53/1.33 inference(quant_intro,[status(thm)],[1129])).
% 1.53/1.33 tff(1131,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause192')).
% 1.53/1.33 tff(1132,plain,
% 1.53/1.33 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.53/1.33 inference(modus_ponens,[status(thm)],[1131, 1130])).
% 1.53/1.33 tff(1133,plain,
% 1.53/1.33 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.53/1.33 inference(modus_ponens,[status(thm)],[1132, 1128])).
% 1.53/1.33 tff(1134,plain,(
% 1.53/1.33 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.53/1.33 inference(skolemize,[status(sab)],[1133])).
% 1.53/1.33 tff(1135,plain,
% 1.53/1.33 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.53/1.33 inference(modus_ponens,[status(thm)],[1134, 1127])).
% 1.53/1.33 tff(1136,assumption,(~c0_1(a107)), introduced(assumption)).
% 1.53/1.33 tff(1137,assumption,(~c1_1(a112)), introduced(assumption)).
% 1.53/1.33 tff(1138,assumption,(c3_1(a107)), introduced(assumption)).
% 1.53/1.33 tff(1139,plain,
% 1.53/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a112) | c1_1(a112) | c0_1(a107) | (~ndr1_0) | (~c3_1(a107)) | (~c1_1(a107)) | c2_1(a112) | (~c3_1(a112)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a112) | c1_1(a112) | c0_1(a107) | (~ndr1_0) | (~c3_1(a107)) | (~c1_1(a107)) | c2_1(a112) | (~c3_1(a112)))),
% 1.53/1.33 inference(rewrite,[status(thm)],[])).
% 1.53/1.33 tff(1140,plain,
% 1.53/1.33 (((~ndr1_0) | c2_1(a112) | c1_1(a112) | (~c3_1(a112)) | c0_1(a107) | (~c3_1(a107)) | (~c1_1(a107)) | c2_1(a112) | c0_1(a112) | (~c3_1(a112))) <=> (c0_1(a112) | c1_1(a112) | c0_1(a107) | (~ndr1_0) | (~c3_1(a107)) | (~c1_1(a107)) | c2_1(a112) | (~c3_1(a112)))),
% 1.53/1.33 inference(rewrite,[status(thm)],[])).
% 1.53/1.33 tff(1141,plain,
% 1.53/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a112) | c1_1(a112) | (~c3_1(a112)) | c0_1(a107) | (~c3_1(a107)) | (~c1_1(a107)) | c2_1(a112) | c0_1(a112) | (~c3_1(a112)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a112) | c1_1(a112) | c0_1(a107) | (~ndr1_0) | (~c3_1(a107)) | (~c1_1(a107)) | c2_1(a112) | (~c3_1(a112))))),
% 1.53/1.33 inference(monotonicity,[status(thm)],[1140])).
% 1.53/1.33 tff(1142,plain,
% 1.53/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a112) | c1_1(a112) | (~c3_1(a112)) | c0_1(a107) | (~c3_1(a107)) | (~c1_1(a107)) | c2_1(a112) | c0_1(a112) | (~c3_1(a112)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a112) | c1_1(a112) | c0_1(a107) | (~ndr1_0) | (~c3_1(a107)) | (~c1_1(a107)) | c2_1(a112) | (~c3_1(a112)))),
% 1.53/1.33 inference(transitivity,[status(thm)],[1141, 1139])).
% 1.53/1.33 tff(1143,plain,
% 1.53/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a112) | c1_1(a112) | (~c3_1(a112)) | c0_1(a107) | (~c3_1(a107)) | (~c1_1(a107)) | c2_1(a112) | c0_1(a112) | (~c3_1(a112)))),
% 1.53/1.33 inference(quant_inst,[status(thm)],[])).
% 1.53/1.33 tff(1144,plain,
% 1.53/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a112) | c1_1(a112) | c0_1(a107) | (~ndr1_0) | (~c3_1(a107)) | (~c1_1(a107)) | c2_1(a112) | (~c3_1(a112))),
% 1.53/1.33 inference(modus_ponens,[status(thm)],[1143, 1142])).
% 1.53/1.33 tff(1145,plain,
% 1.53/1.33 (~c1_1(a107)),
% 1.53/1.33 inference(unit_resolution,[status(thm)],[1144, 126, 1116, 1138, 1115, 1137, 1136, 1135, 1125])).
% 1.53/1.33 tff(1146,plain,
% 1.53/1.33 ((hskp19 | hskp18 | hskp17) <=> (hskp19 | hskp18 | hskp17)),
% 1.53/1.33 inference(rewrite,[status(thm)],[])).
% 1.53/1.33 tff(1147,plain,
% 1.53/1.33 (((hskp18 | hskp19) | hskp17) <=> (hskp19 | hskp18 | hskp17)),
% 1.53/1.33 inference(rewrite,[status(thm)],[])).
% 1.53/1.33 tff(1148,axiom,((hskp18 | hskp19) | hskp17), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause36')).
% 1.53/1.33 tff(1149,plain,
% 1.53/1.33 (hskp19 | hskp18 | hskp17),
% 1.53/1.33 inference(modus_ponens,[status(thm)],[1148, 1147])).
% 1.53/1.33 tff(1150,plain,
% 1.53/1.33 (hskp19 | hskp18 | hskp17),
% 1.53/1.33 inference(modus_ponens,[status(thm)],[1149, 1146])).
% 1.53/1.33 tff(1151,plain,
% 1.53/1.33 (hskp19 | hskp18 | hskp17),
% 1.53/1.33 inference(modus_ponens,[status(thm)],[1150, 1146])).
% 1.53/1.33 tff(1152,plain,
% 1.53/1.33 (hskp19 | hskp18 | hskp17),
% 1.53/1.33 inference(modus_ponens,[status(thm)],[1151, 1146])).
% 1.53/1.33 tff(1153,plain,
% 1.53/1.33 (hskp19 | hskp18 | hskp17),
% 1.53/1.33 inference(modus_ponens,[status(thm)],[1152, 1146])).
% 1.53/1.33 tff(1154,plain,
% 1.53/1.33 (hskp19 | hskp18 | hskp17),
% 1.53/1.33 inference(modus_ponens,[status(thm)],[1153, 1146])).
% 1.53/1.33 tff(1155,plain,
% 1.53/1.33 (hskp19 | hskp18 | hskp17),
% 1.53/1.33 inference(modus_ponens,[status(thm)],[1154, 1146])).
% 1.53/1.33 tff(1156,plain,
% 1.53/1.33 (hskp19 | hskp18 | hskp17),
% 1.53/1.33 inference(modus_ponens,[status(thm)],[1155, 1146])).
% 1.53/1.33 tff(1157,plain,
% 1.53/1.33 (hskp19),
% 1.53/1.33 inference(unit_resolution,[status(thm)],[1156, 1104, 52])).
% 1.53/1.33 tff(1158,plain,
% 1.53/1.33 (~c2_1(a130)),
% 1.53/1.33 inference(unit_resolution,[status(thm)],[252, 1157])).
% 1.53/1.33 tff(1159,plain,
% 1.53/1.33 (c3_1(a130)),
% 1.53/1.33 inference(unit_resolution,[status(thm)],[263, 1157])).
% 1.53/1.33 tff(1160,plain,
% 1.53/1.33 (c1_1(a130)),
% 1.53/1.33 inference(unit_resolution,[status(thm)],[274, 1157])).
% 1.53/1.33 tff(1161,plain,
% 1.53/1.33 (hskp2),
% 1.53/1.33 inference(unit_resolution,[status(thm)],[774, 126, 664, 666, 667, 1160, 1159, 1158, 767])).
% 1.53/1.33 tff(1162,plain,
% 1.53/1.33 (~c1_1(a99)),
% 1.53/1.33 inference(unit_resolution,[status(thm)],[618, 1161])).
% 1.53/1.33 tff(1163,plain,
% 1.53/1.33 (~c0_1(a99)),
% 1.53/1.33 inference(unit_resolution,[status(thm)],[602, 1161])).
% 1.53/1.33 tff(1164,assumption,(~c2_1(a107)), introduced(assumption)).
% 1.53/1.33 tff(1165,plain,
% 1.53/1.33 (c2_1(a99)),
% 1.53/1.33 inference(unit_resolution,[status(thm)],[587, 1161])).
% 1.53/1.33 tff(1166,plain,
% 1.53/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a107) | c2_1(a107) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c3_1(a99) | c1_1(a107))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a107) | c2_1(a107) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c3_1(a99) | c1_1(a107))),
% 1.53/1.33 inference(rewrite,[status(thm)],[])).
% 1.53/1.33 tff(1167,plain,
% 1.53/1.33 (((~ndr1_0) | c0_1(a99) | c3_1(a99) | (~c2_1(a99)) | c1_1(a99) | c0_1(a99) | (~c2_1(a99)) | c2_1(a107) | c1_1(a107) | c0_1(a107)) <=> (c0_1(a107) | c2_1(a107) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c3_1(a99) | c1_1(a107))),
% 1.53/1.33 inference(rewrite,[status(thm)],[])).
% 1.53/1.33 tff(1168,plain,
% 1.53/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a99) | c3_1(a99) | (~c2_1(a99)) | c1_1(a99) | c0_1(a99) | (~c2_1(a99)) | c2_1(a107) | c1_1(a107) | c0_1(a107))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a107) | c2_1(a107) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c3_1(a99) | c1_1(a107)))),
% 1.53/1.33 inference(monotonicity,[status(thm)],[1167])).
% 1.53/1.33 tff(1169,plain,
% 1.53/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a99) | c3_1(a99) | (~c2_1(a99)) | c1_1(a99) | c0_1(a99) | (~c2_1(a99)) | c2_1(a107) | c1_1(a107) | c0_1(a107))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a107) | c2_1(a107) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c3_1(a99) | c1_1(a107))),
% 1.53/1.33 inference(transitivity,[status(thm)],[1168, 1166])).
% 1.53/1.33 tff(1170,plain,
% 1.53/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a99) | c3_1(a99) | (~c2_1(a99)) | c1_1(a99) | c0_1(a99) | (~c2_1(a99)) | c2_1(a107) | c1_1(a107) | c0_1(a107))),
% 1.53/1.33 inference(quant_inst,[status(thm)],[])).
% 1.53/1.33 tff(1171,plain,
% 1.53/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a107) | c2_1(a107) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c3_1(a99) | c1_1(a107)),
% 1.53/1.33 inference(modus_ponens,[status(thm)],[1170, 1169])).
% 1.53/1.33 tff(1172,plain,
% 1.53/1.33 (c3_1(a99)),
% 1.53/1.33 inference(unit_resolution,[status(thm)],[1171, 126, 1165, 1136, 1164, 1163, 1162, 794, 1145])).
% 1.53/1.33 tff(1173,plain,
% 1.53/1.33 (((~![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp9 | c0_1(a99) | (~ndr1_0) | (~c2_1(a99)) | (~c3_1(a99)))) <=> ((~![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp17 | hskp9 | c0_1(a99) | (~ndr1_0) | (~c2_1(a99)) | (~c3_1(a99)))),
% 1.53/1.33 inference(rewrite,[status(thm)],[])).
% 1.53/1.33 tff(1174,plain,
% 1.53/1.33 ((hskp17 | hskp9 | (~ndr1_0) | c0_1(a99) | (~c2_1(a99)) | (~c3_1(a99))) <=> (hskp17 | hskp9 | c0_1(a99) | (~ndr1_0) | (~c2_1(a99)) | (~c3_1(a99)))),
% 1.53/1.33 inference(rewrite,[status(thm)],[])).
% 1.53/1.33 tff(1175,plain,
% 1.53/1.33 (((~![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp9 | (~ndr1_0) | c0_1(a99) | (~c2_1(a99)) | (~c3_1(a99)))) <=> ((~![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp9 | c0_1(a99) | (~ndr1_0) | (~c2_1(a99)) | (~c3_1(a99))))),
% 1.53/1.33 inference(monotonicity,[status(thm)],[1174])).
% 1.53/1.33 tff(1176,plain,
% 1.53/1.33 (((~![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp9 | (~ndr1_0) | c0_1(a99) | (~c2_1(a99)) | (~c3_1(a99)))) <=> ((~![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp17 | hskp9 | c0_1(a99) | (~ndr1_0) | (~c2_1(a99)) | (~c3_1(a99)))),
% 1.53/1.33 inference(transitivity,[status(thm)],[1175, 1173])).
% 1.53/1.33 tff(1177,plain,
% 1.53/1.33 ((~![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp9 | (~ndr1_0) | c0_1(a99) | (~c2_1(a99)) | (~c3_1(a99)))),
% 1.53/1.33 inference(quant_inst,[status(thm)],[])).
% 1.53/1.33 tff(1178,plain,
% 1.53/1.33 ((~![U: $i] : (hskp17 | hskp9 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp17 | hskp9 | c0_1(a99) | (~ndr1_0) | (~c2_1(a99)) | (~c3_1(a99))),
% 1.53/1.33 inference(modus_ponens,[status(thm)],[1177, 1176])).
% 1.53/1.33 tff(1179,plain,
% 1.53/1.33 ($false),
% 1.53/1.33 inference(unit_resolution,[status(thm)],[1178, 126, 1104, 1117, 1165, 1163, 1114, 1172])).
% 1.53/1.33 tff(1180,plain,(hskp17 | hskp9 | c0_1(a107) | c2_1(a107) | (~c0_1(a137)) | (~c1_1(a137)) | (~c2_1(a137)) | (~c3_1(a112)) | (~c3_1(a107)) | c0_1(a112) | c1_1(a112) | hskp18), inference(lemma,lemma(discharge,[]))).
% 1.53/1.33 tff(1181,plain,
% 1.53/1.33 (hskp17),
% 1.53/1.33 inference(unit_resolution,[status(thm)],[1180, 1103, 1097, 1059, 633, 655, 644, 1053, 1042, 855, 849, 52])).
% 1.53/1.33 tff(1182,plain,
% 1.53/1.33 (((~hskp17) | (~c3_1(a124))) <=> ((~hskp17) | (~c3_1(a124)))),
% 1.53/1.33 inference(rewrite,[status(thm)],[])).
% 1.53/1.33 tff(1183,plain,
% 1.53/1.33 (((~c3_1(a124)) | (~hskp17)) <=> ((~hskp17) | (~c3_1(a124)))),
% 1.53/1.33 inference(rewrite,[status(thm)],[])).
% 1.53/1.33 tff(1184,axiom,((~c3_1(a124)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause103')).
% 1.53/1.33 tff(1185,plain,
% 1.53/1.33 ((~hskp17) | (~c3_1(a124))),
% 1.53/1.33 inference(modus_ponens,[status(thm)],[1184, 1183])).
% 1.53/1.33 tff(1186,plain,
% 1.53/1.33 ((~hskp17) | (~c3_1(a124))),
% 1.53/1.33 inference(modus_ponens,[status(thm)],[1185, 1182])).
% 1.53/1.33 tff(1187,plain,
% 1.53/1.33 (~c3_1(a124)),
% 1.53/1.33 inference(unit_resolution,[status(thm)],[1186, 1181])).
% 1.53/1.33 tff(1188,plain,
% 1.53/1.33 (((~hskp17) | (~c1_1(a124))) <=> ((~hskp17) | (~c1_1(a124)))),
% 1.53/1.33 inference(rewrite,[status(thm)],[])).
% 1.53/1.33 tff(1189,plain,
% 1.53/1.33 (((~c1_1(a124)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a124)))),
% 1.53/1.33 inference(rewrite,[status(thm)],[])).
% 1.53/1.33 tff(1190,axiom,((~c1_1(a124)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause102')).
% 1.53/1.33 tff(1191,plain,
% 1.53/1.33 ((~hskp17) | (~c1_1(a124))),
% 1.53/1.33 inference(modus_ponens,[status(thm)],[1190, 1189])).
% 1.53/1.33 tff(1192,plain,
% 1.53/1.33 ((~hskp17) | (~c1_1(a124))),
% 1.53/1.33 inference(modus_ponens,[status(thm)],[1191, 1188])).
% 1.53/1.33 tff(1193,plain,
% 1.53/1.33 (~c1_1(a124)),
% 1.53/1.33 inference(unit_resolution,[status(thm)],[1192, 1181])).
% 1.53/1.33 tff(1194,plain,
% 1.53/1.33 (((~hskp17) | c2_1(a124)) <=> ((~hskp17) | c2_1(a124))),
% 1.53/1.33 inference(rewrite,[status(thm)],[])).
% 1.53/1.33 tff(1195,axiom,((~hskp17) | c2_1(a124)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause64')).
% 1.53/1.33 tff(1196,plain,
% 1.53/1.33 ((~hskp17) | c2_1(a124)),
% 1.53/1.33 inference(modus_ponens,[status(thm)],[1195, 1194])).
% 1.53/1.33 tff(1197,plain,
% 1.53/1.33 ((~hskp17) | c2_1(a124)),
% 1.53/1.33 inference(modus_ponens,[status(thm)],[1196, 1194])).
% 1.53/1.33 tff(1198,plain,
% 1.53/1.33 ((~hskp17) | c2_1(a124)),
% 1.53/1.33 inference(modus_ponens,[status(thm)],[1197, 1194])).
% 1.53/1.33 tff(1199,plain,
% 1.53/1.33 ((~hskp17) | c2_1(a124)),
% 1.53/1.33 inference(modus_ponens,[status(thm)],[1198, 1194])).
% 1.53/1.33 tff(1200,plain,
% 1.53/1.33 ((~hskp17) | c2_1(a124)),
% 1.53/1.33 inference(modus_ponens,[status(thm)],[1199, 1194])).
% 1.53/1.33 tff(1201,plain,
% 1.53/1.33 ((~hskp17) | c2_1(a124)),
% 1.53/1.33 inference(modus_ponens,[status(thm)],[1200, 1194])).
% 1.53/1.33 tff(1202,plain,
% 1.53/1.33 ((~hskp17) | c2_1(a124)),
% 1.53/1.33 inference(modus_ponens,[status(thm)],[1201, 1194])).
% 1.53/1.33 tff(1203,plain,
% 1.53/1.33 ((~hskp17) | c2_1(a124)),
% 1.53/1.33 inference(modus_ponens,[status(thm)],[1202, 1194])).
% 1.53/1.33 tff(1204,plain,
% 1.53/1.33 (c2_1(a124)),
% 1.53/1.33 inference(unit_resolution,[status(thm)],[1203, 1181])).
% 1.53/1.33 tff(1205,assumption,(~hskp19), introduced(assumption)).
% 1.53/1.33 tff(1206,plain,
% 1.53/1.33 (^[U: $i] : refl((hskp19 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp19 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))),
% 1.53/1.33 inference(bind,[status(th)],[])).
% 1.53/1.33 tff(1207,plain,
% 1.53/1.33 (![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.53/1.33 inference(quant_intro,[status(thm)],[1206])).
% 1.53/1.33 tff(1208,plain,
% 1.53/1.33 (![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.53/1.33 inference(rewrite,[status(thm)],[])).
% 1.53/1.33 tff(1209,plain,
% 1.53/1.33 (^[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)) | hskp1) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp1))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp1) | hskp19) <=> ((hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp19))), rewrite(((hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp19) <=> (hskp19 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp1) | hskp19) <=> (hskp19 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))))),
% 1.53/1.33 inference(bind,[status(th)],[])).
% 1.53/1.33 tff(1210,plain,
% 1.53/1.33 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp1) | hskp19) <=> ![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.53/1.33 inference(quant_intro,[status(thm)],[1209])).
% 1.53/1.33 tff(1211,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp1) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause145')).
% 1.53/1.33 tff(1212,plain,
% 1.53/1.33 (![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.53/1.33 inference(modus_ponens,[status(thm)],[1211, 1210])).
% 1.53/1.34 tff(1213,plain,
% 1.53/1.34 (![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.53/1.34 inference(modus_ponens,[status(thm)],[1212, 1208])).
% 1.53/1.34 tff(1214,plain,(
% 1.53/1.34 ![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.53/1.34 inference(skolemize,[status(sab)],[1213])).
% 1.53/1.34 tff(1215,plain,
% 1.53/1.34 (![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.53/1.34 inference(modus_ponens,[status(thm)],[1214, 1207])).
% 1.53/1.34 tff(1216,assumption,(~c3_1(a124)), introduced(assumption)).
% 1.53/1.34 tff(1217,assumption,(~c1_1(a124)), introduced(assumption)).
% 1.53/1.34 tff(1218,assumption,(c2_1(a124)), introduced(assumption)).
% 1.53/1.34 tff(1219,plain,
% 1.53/1.34 (((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp19 | hskp1 | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)))) <=> ((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp19 | hskp1 | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)))),
% 1.53/1.34 inference(rewrite,[status(thm)],[])).
% 1.53/1.34 tff(1220,plain,
% 1.53/1.34 ((hskp19 | hskp1 | (~ndr1_0) | c1_1(a124) | c3_1(a124) | (~c2_1(a124))) <=> (hskp19 | hskp1 | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)))),
% 1.53/1.34 inference(rewrite,[status(thm)],[])).
% 1.53/1.34 tff(1221,plain,
% 1.53/1.34 (((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp19 | hskp1 | (~ndr1_0) | c1_1(a124) | c3_1(a124) | (~c2_1(a124)))) <=> ((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp19 | hskp1 | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124))))),
% 1.53/1.34 inference(monotonicity,[status(thm)],[1220])).
% 1.53/1.34 tff(1222,plain,
% 1.53/1.34 (((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp19 | hskp1 | (~ndr1_0) | c1_1(a124) | c3_1(a124) | (~c2_1(a124)))) <=> ((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp19 | hskp1 | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)))),
% 1.53/1.34 inference(transitivity,[status(thm)],[1221, 1219])).
% 1.53/1.34 tff(1223,plain,
% 1.53/1.34 ((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp19 | hskp1 | (~ndr1_0) | c1_1(a124) | c3_1(a124) | (~c2_1(a124)))),
% 1.53/1.34 inference(quant_inst,[status(thm)],[])).
% 1.53/1.34 tff(1224,plain,
% 1.53/1.34 ((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp19 | hskp1 | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124))),
% 1.53/1.34 inference(modus_ponens,[status(thm)],[1223, 1222])).
% 1.53/1.34 tff(1225,plain,
% 1.53/1.34 (hskp19 | hskp1),
% 1.53/1.34 inference(unit_resolution,[status(thm)],[1224, 126, 1218, 1217, 1216, 1215])).
% 1.53/1.34 tff(1226,plain,
% 1.53/1.34 (hskp1),
% 1.53/1.34 inference(unit_resolution,[status(thm)],[1225, 1205])).
% 1.53/1.34 tff(1227,plain,
% 1.53/1.34 (((~hskp1) | (~c3_1(a98))) <=> ((~hskp1) | (~c3_1(a98)))),
% 1.53/1.34 inference(rewrite,[status(thm)],[])).
% 1.53/1.34 tff(1228,plain,
% 1.53/1.34 (((~c3_1(a98)) | (~hskp1)) <=> ((~hskp1) | (~c3_1(a98)))),
% 1.53/1.34 inference(rewrite,[status(thm)],[])).
% 1.53/1.34 tff(1229,axiom,((~c3_1(a98)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause130')).
% 1.53/1.34 tff(1230,plain,
% 1.53/1.34 ((~hskp1) | (~c3_1(a98))),
% 1.53/1.34 inference(modus_ponens,[status(thm)],[1229, 1228])).
% 1.53/1.34 tff(1231,plain,
% 1.53/1.34 ((~hskp1) | (~c3_1(a98))),
% 1.53/1.34 inference(modus_ponens,[status(thm)],[1230, 1227])).
% 1.53/1.34 tff(1232,plain,
% 1.53/1.34 (~c3_1(a98)),
% 1.53/1.34 inference(unit_resolution,[status(thm)],[1231, 1226])).
% 1.53/1.34 tff(1233,plain,
% 1.53/1.34 (((~hskp1) | (~c1_1(a98))) <=> ((~hskp1) | (~c1_1(a98)))),
% 1.53/1.34 inference(rewrite,[status(thm)],[])).
% 1.53/1.34 tff(1234,plain,
% 1.53/1.34 (((~c1_1(a98)) | (~hskp1)) <=> ((~hskp1) | (~c1_1(a98)))),
% 1.53/1.34 inference(rewrite,[status(thm)],[])).
% 1.53/1.34 tff(1235,axiom,((~c1_1(a98)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 1.53/1.34 tff(1236,plain,
% 1.53/1.34 ((~hskp1) | (~c1_1(a98))),
% 1.53/1.34 inference(modus_ponens,[status(thm)],[1235, 1234])).
% 1.53/1.34 tff(1237,plain,
% 1.53/1.34 ((~hskp1) | (~c1_1(a98))),
% 1.53/1.34 inference(modus_ponens,[status(thm)],[1236, 1233])).
% 1.53/1.34 tff(1238,plain,
% 1.53/1.34 (~c1_1(a98)),
% 1.53/1.34 inference(unit_resolution,[status(thm)],[1237, 1226])).
% 1.53/1.34 tff(1239,plain,
% 1.53/1.34 (((~hskp1) | c0_1(a98)) <=> ((~hskp1) | c0_1(a98))),
% 1.53/1.34 inference(rewrite,[status(thm)],[])).
% 1.53/1.34 tff(1240,axiom,((~hskp1) | c0_1(a98)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause85')).
% 1.53/1.34 tff(1241,plain,
% 1.53/1.34 ((~hskp1) | c0_1(a98)),
% 1.53/1.34 inference(modus_ponens,[status(thm)],[1240, 1239])).
% 1.53/1.34 tff(1242,plain,
% 1.53/1.34 ((~hskp1) | c0_1(a98)),
% 1.53/1.34 inference(modus_ponens,[status(thm)],[1241, 1239])).
% 1.53/1.34 tff(1243,plain,
% 1.53/1.34 ((~hskp1) | c0_1(a98)),
% 1.53/1.34 inference(modus_ponens,[status(thm)],[1242, 1239])).
% 1.53/1.34 tff(1244,plain,
% 1.53/1.34 ((~hskp1) | c0_1(a98)),
% 1.53/1.34 inference(modus_ponens,[status(thm)],[1243, 1239])).
% 1.53/1.34 tff(1245,plain,
% 1.53/1.34 ((~hskp1) | c0_1(a98)),
% 1.53/1.34 inference(modus_ponens,[status(thm)],[1244, 1239])).
% 1.53/1.34 tff(1246,plain,
% 1.53/1.34 ((~hskp1) | c0_1(a98)),
% 1.53/1.34 inference(modus_ponens,[status(thm)],[1245, 1239])).
% 1.53/1.34 tff(1247,plain,
% 1.53/1.34 ((~hskp1) | c0_1(a98)),
% 1.53/1.34 inference(modus_ponens,[status(thm)],[1246, 1239])).
% 1.53/1.34 tff(1248,plain,
% 1.53/1.34 ((~hskp1) | c0_1(a98)),
% 1.53/1.34 inference(modus_ponens,[status(thm)],[1247, 1239])).
% 1.53/1.34 tff(1249,plain,
% 1.53/1.34 (c0_1(a98)),
% 1.53/1.34 inference(unit_resolution,[status(thm)],[1248, 1226])).
% 1.53/1.34 tff(1250,plain,
% 1.53/1.34 (^[U: $i] : refl((hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))))),
% 1.53/1.34 inference(bind,[status(th)],[])).
% 1.53/1.34 tff(1251,plain,
% 1.53/1.34 (![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.53/1.34 inference(quant_intro,[status(thm)],[1250])).
% 1.53/1.34 tff(1252,plain,
% 1.53/1.34 (![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.53/1.34 inference(rewrite,[status(thm)],[])).
% 1.53/1.34 tff(1253,plain,
% 1.53/1.34 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp27))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) | hskp19) <=> ((hskp27 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp19))), rewrite(((hskp27 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp19) <=> (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) | hskp19) <=> (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))))),
% 1.53/1.34 inference(bind,[status(th)],[])).
% 1.53/1.34 tff(1254,plain,
% 1.53/1.34 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) | hskp19) <=> ![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.53/1.34 inference(quant_intro,[status(thm)],[1253])).
% 1.53/1.34 tff(1255,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause156')).
% 1.53/1.34 tff(1256,plain,
% 1.53/1.34 (![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.53/1.34 inference(modus_ponens,[status(thm)],[1255, 1254])).
% 1.53/1.34 tff(1257,plain,
% 1.53/1.34 (![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.53/1.34 inference(modus_ponens,[status(thm)],[1256, 1252])).
% 1.53/1.34 tff(1258,plain,(
% 1.53/1.34 ![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.53/1.34 inference(skolemize,[status(sab)],[1257])).
% 1.53/1.34 tff(1259,plain,
% 1.53/1.34 (![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 1.53/1.34 inference(modus_ponens,[status(thm)],[1258, 1251])).
% 1.53/1.34 tff(1260,plain,
% 1.53/1.34 (((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp27 | hskp19 | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)))) <=> ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp27 | hskp19 | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)))),
% 1.53/1.34 inference(rewrite,[status(thm)],[])).
% 1.53/1.34 tff(1261,plain,
% 1.53/1.34 ((hskp27 | hskp19 | (~ndr1_0) | c3_1(a97) | (~c0_1(a97)) | (~c1_1(a97))) <=> (hskp27 | hskp19 | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)))),
% 1.53/1.34 inference(rewrite,[status(thm)],[])).
% 1.53/1.34 tff(1262,plain,
% 1.53/1.34 (((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp27 | hskp19 | (~ndr1_0) | c3_1(a97) | (~c0_1(a97)) | (~c1_1(a97)))) <=> ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp27 | hskp19 | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97))))),
% 1.53/1.34 inference(monotonicity,[status(thm)],[1261])).
% 1.53/1.34 tff(1263,plain,
% 1.53/1.34 (((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp27 | hskp19 | (~ndr1_0) | c3_1(a97) | (~c0_1(a97)) | (~c1_1(a97)))) <=> ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp27 | hskp19 | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)))),
% 1.53/1.34 inference(transitivity,[status(thm)],[1262, 1260])).
% 1.53/1.34 tff(1264,plain,
% 1.53/1.34 ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp27 | hskp19 | (~ndr1_0) | c3_1(a97) | (~c0_1(a97)) | (~c1_1(a97)))),
% 1.53/1.34 inference(quant_inst,[status(thm)],[])).
% 1.53/1.34 tff(1265,plain,
% 1.53/1.34 ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp27 | hskp19 | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97))),
% 1.53/1.34 inference(modus_ponens,[status(thm)],[1264, 1263])).
% 1.53/1.34 tff(1266,plain,
% 1.53/1.34 (hskp27 | hskp19 | (~c1_1(a97))),
% 1.53/1.34 inference(unit_resolution,[status(thm)],[1265, 126, 246, 53, 1259])).
% 1.53/1.34 tff(1267,plain,
% 1.53/1.34 (hskp27),
% 1.53/1.34 inference(unit_resolution,[status(thm)],[1266, 1205, 330])).
% 1.53/1.34 tff(1268,plain,
% 1.53/1.34 (((~hskp27) | c3_1(a101)) <=> ((~hskp27) | c3_1(a101))),
% 1.53/1.34 inference(rewrite,[status(thm)],[])).
% 1.53/1.34 tff(1269,axiom,((~hskp27) | c3_1(a101)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause51')).
% 1.53/1.34 tff(1270,plain,
% 1.53/1.34 ((~hskp27) | c3_1(a101)),
% 1.53/1.34 inference(modus_ponens,[status(thm)],[1269, 1268])).
% 1.53/1.34 tff(1271,plain,
% 1.53/1.34 ((~hskp27) | c3_1(a101)),
% 1.53/1.34 inference(modus_ponens,[status(thm)],[1270, 1268])).
% 1.53/1.34 tff(1272,plain,
% 1.53/1.34 ((~hskp27) | c3_1(a101)),
% 1.53/1.34 inference(modus_ponens,[status(thm)],[1271, 1268])).
% 1.53/1.34 tff(1273,plain,
% 1.53/1.34 ((~hskp27) | c3_1(a101)),
% 1.53/1.34 inference(modus_ponens,[status(thm)],[1272, 1268])).
% 1.53/1.34 tff(1274,plain,
% 1.53/1.34 ((~hskp27) | c3_1(a101)),
% 1.53/1.34 inference(modus_ponens,[status(thm)],[1273, 1268])).
% 1.53/1.34 tff(1275,plain,
% 1.53/1.34 ((~hskp27) | c3_1(a101)),
% 1.53/1.34 inference(modus_ponens,[status(thm)],[1274, 1268])).
% 1.53/1.34 tff(1276,plain,
% 1.53/1.34 ((~hskp27) | c3_1(a101)),
% 1.53/1.34 inference(modus_ponens,[status(thm)],[1275, 1268])).
% 1.53/1.34 tff(1277,plain,
% 1.53/1.34 ((~hskp27) | c3_1(a101)),
% 1.53/1.34 inference(modus_ponens,[status(thm)],[1276, 1268])).
% 1.53/1.34 tff(1278,plain,
% 1.53/1.34 (c3_1(a101)),
% 1.53/1.34 inference(unit_resolution,[status(thm)],[1277, 1267])).
% 1.53/1.34 tff(1279,plain,
% 1.53/1.34 (((~hskp27) | c1_1(a101)) <=> ((~hskp27) | c1_1(a101))),
% 1.53/1.34 inference(rewrite,[status(thm)],[])).
% 1.53/1.34 tff(1280,axiom,((~hskp27) | c1_1(a101)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause50')).
% 1.53/1.34 tff(1281,plain,
% 1.53/1.34 ((~hskp27) | c1_1(a101)),
% 1.53/1.34 inference(modus_ponens,[status(thm)],[1280, 1279])).
% 1.53/1.34 tff(1282,plain,
% 1.53/1.34 ((~hskp27) | c1_1(a101)),
% 1.53/1.34 inference(modus_ponens,[status(thm)],[1281, 1279])).
% 1.53/1.34 tff(1283,plain,
% 1.53/1.34 ((~hskp27) | c1_1(a101)),
% 1.53/1.34 inference(modus_ponens,[status(thm)],[1282, 1279])).
% 1.53/1.34 tff(1284,plain,
% 1.53/1.34 ((~hskp27) | c1_1(a101)),
% 1.53/1.34 inference(modus_ponens,[status(thm)],[1283, 1279])).
% 1.53/1.34 tff(1285,plain,
% 1.53/1.34 ((~hskp27) | c1_1(a101)),
% 1.53/1.34 inference(modus_ponens,[status(thm)],[1284, 1279])).
% 1.53/1.34 tff(1286,plain,
% 1.53/1.34 ((~hskp27) | c1_1(a101)),
% 1.53/1.34 inference(modus_ponens,[status(thm)],[1285, 1279])).
% 1.53/1.34 tff(1287,plain,
% 1.53/1.34 ((~hskp27) | c1_1(a101)),
% 1.53/1.34 inference(modus_ponens,[status(thm)],[1286, 1279])).
% 1.53/1.34 tff(1288,plain,
% 1.53/1.34 ((~hskp27) | c1_1(a101)),
% 1.53/1.34 inference(modus_ponens,[status(thm)],[1287, 1279])).
% 1.53/1.34 tff(1289,plain,
% 1.53/1.34 (c1_1(a101)),
% 1.53/1.34 inference(unit_resolution,[status(thm)],[1288, 1267])).
% 1.53/1.34 tff(1290,plain,
% 1.53/1.34 (((~hskp27) | c0_1(a101)) <=> ((~hskp27) | c0_1(a101))),
% 1.53/1.34 inference(rewrite,[status(thm)],[])).
% 1.53/1.34 tff(1291,axiom,((~hskp27) | c0_1(a101)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause49')).
% 1.53/1.34 tff(1292,plain,
% 1.53/1.34 ((~hskp27) | c0_1(a101)),
% 1.53/1.34 inference(modus_ponens,[status(thm)],[1291, 1290])).
% 1.53/1.34 tff(1293,plain,
% 1.53/1.34 ((~hskp27) | c0_1(a101)),
% 1.53/1.34 inference(modus_ponens,[status(thm)],[1292, 1290])).
% 1.53/1.34 tff(1294,plain,
% 1.53/1.34 ((~hskp27) | c0_1(a101)),
% 1.53/1.34 inference(modus_ponens,[status(thm)],[1293, 1290])).
% 1.53/1.34 tff(1295,plain,
% 1.53/1.34 ((~hskp27) | c0_1(a101)),
% 1.53/1.34 inference(modus_ponens,[status(thm)],[1294, 1290])).
% 1.53/1.34 tff(1296,plain,
% 1.53/1.34 ((~hskp27) | c0_1(a101)),
% 1.53/1.34 inference(modus_ponens,[status(thm)],[1295, 1290])).
% 1.53/1.34 tff(1297,plain,
% 1.53/1.34 ((~hskp27) | c0_1(a101)),
% 1.53/1.34 inference(modus_ponens,[status(thm)],[1296, 1290])).
% 1.53/1.34 tff(1298,plain,
% 1.53/1.34 ((~hskp27) | c0_1(a101)),
% 1.53/1.34 inference(modus_ponens,[status(thm)],[1297, 1290])).
% 1.53/1.34 tff(1299,plain,
% 1.53/1.34 ((~hskp27) | c0_1(a101)),
% 1.53/1.34 inference(modus_ponens,[status(thm)],[1298, 1290])).
% 1.53/1.34 tff(1300,plain,
% 1.53/1.34 (c0_1(a101)),
% 1.53/1.34 inference(unit_resolution,[status(thm)],[1299, 1267])).
% 1.53/1.34 tff(1301,plain,
% 1.53/1.34 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp18 | c1_1(a98) | c3_1(a98) | (~ndr1_0) | (~c0_1(a98)) | (~c0_1(a101)) | (~c1_1(a101)) | (~c3_1(a101)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a98) | c3_1(a98) | (~ndr1_0) | (~c0_1(a98)) | (~c0_1(a101)) | (~c1_1(a101)) | (~c3_1(a101)))),
% 1.53/1.34 inference(rewrite,[status(thm)],[])).
% 1.53/1.34 tff(1302,plain,
% 1.53/1.34 ((hskp18 | (~ndr1_0) | (~c3_1(a101)) | (~c0_1(a101)) | (~c1_1(a101)) | c1_1(a98) | c3_1(a98) | (~c0_1(a98))) <=> (hskp18 | c1_1(a98) | c3_1(a98) | (~ndr1_0) | (~c0_1(a98)) | (~c0_1(a101)) | (~c1_1(a101)) | (~c3_1(a101)))),
% 1.53/1.34 inference(rewrite,[status(thm)],[])).
% 1.53/1.34 tff(1303,plain,
% 1.53/1.34 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c3_1(a101)) | (~c0_1(a101)) | (~c1_1(a101)) | c1_1(a98) | c3_1(a98) | (~c0_1(a98)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp18 | c1_1(a98) | c3_1(a98) | (~ndr1_0) | (~c0_1(a98)) | (~c0_1(a101)) | (~c1_1(a101)) | (~c3_1(a101))))),
% 1.53/1.34 inference(monotonicity,[status(thm)],[1302])).
% 1.53/1.34 tff(1304,plain,
% 1.53/1.34 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c3_1(a101)) | (~c0_1(a101)) | (~c1_1(a101)) | c1_1(a98) | c3_1(a98) | (~c0_1(a98)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a98) | c3_1(a98) | (~ndr1_0) | (~c0_1(a98)) | (~c0_1(a101)) | (~c1_1(a101)) | (~c3_1(a101)))),
% 1.53/1.34 inference(transitivity,[status(thm)],[1303, 1301])).
% 1.53/1.34 tff(1305,plain,
% 1.53/1.34 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c3_1(a101)) | (~c0_1(a101)) | (~c1_1(a101)) | c1_1(a98) | c3_1(a98) | (~c0_1(a98)))),
% 1.53/1.34 inference(quant_inst,[status(thm)],[])).
% 1.53/1.34 tff(1306,plain,
% 1.53/1.34 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a98) | c3_1(a98) | (~ndr1_0) | (~c0_1(a98)) | (~c0_1(a101)) | (~c1_1(a101)) | (~c3_1(a101))),
% 1.53/1.34 inference(modus_ponens,[status(thm)],[1305, 1304])).
% 1.53/1.34 tff(1307,plain,
% 1.53/1.34 ($false),
% 1.53/1.34 inference(unit_resolution,[status(thm)],[1306, 126, 52, 1300, 1289, 1278, 1249, 1238, 1232, 714])).
% 1.53/1.34 tff(1308,plain,(hskp19 | hskp18 | (~c2_1(a124)) | c1_1(a124) | c3_1(a124) | (~c1_1(a97)) | (~c0_1(a97)) | c3_1(a97)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.34 tff(1309,plain,
% 1.53/1.34 (hskp19),
% 1.53/1.34 inference(unit_resolution,[status(thm)],[1308, 52, 1204, 1193, 1187, 1013, 835, 823])).
% 1.53/1.34 tff(1310,plain,
% 1.53/1.34 (~c2_1(a130)),
% 1.53/1.34 inference(unit_resolution,[status(thm)],[252, 1309])).
% 1.53/1.34 tff(1311,plain,
% 1.53/1.34 (c3_1(a130)),
% 1.53/1.34 inference(unit_resolution,[status(thm)],[263, 1309])).
% 1.53/1.34 tff(1312,plain,
% 1.53/1.34 (c1_1(a130)),
% 1.53/1.34 inference(unit_resolution,[status(thm)],[274, 1309])).
% 1.53/1.34 tff(1313,plain,
% 1.53/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a130) | c1_1(a124) | c3_1(a124) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a124)) | (~c3_1(a130)) | (~c1_1(a130)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a130) | c1_1(a124) | c3_1(a124) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a124)) | (~c3_1(a130)) | (~c1_1(a130)))),
% 1.53/1.34 inference(rewrite,[status(thm)],[])).
% 1.53/1.34 tff(1314,plain,
% 1.53/1.34 (((~ndr1_0) | c2_1(a130) | (~c3_1(a130)) | (~c1_1(a130)) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)) | c1_1(a124) | c3_1(a124) | (~c0_1(a124))) <=> (c2_1(a130) | c1_1(a124) | c3_1(a124) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a124)) | (~c3_1(a130)) | (~c1_1(a130)))),
% 1.53/1.34 inference(rewrite,[status(thm)],[])).
% 1.53/1.34 tff(1315,plain,
% 1.53/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a130) | (~c3_1(a130)) | (~c1_1(a130)) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)) | c1_1(a124) | c3_1(a124) | (~c0_1(a124)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a130) | c1_1(a124) | c3_1(a124) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a124)) | (~c3_1(a130)) | (~c1_1(a130))))),
% 1.53/1.34 inference(monotonicity,[status(thm)],[1314])).
% 1.53/1.34 tff(1316,plain,
% 1.53/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a130) | (~c3_1(a130)) | (~c1_1(a130)) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)) | c1_1(a124) | c3_1(a124) | (~c0_1(a124)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a130) | c1_1(a124) | c3_1(a124) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a124)) | (~c3_1(a130)) | (~c1_1(a130)))),
% 1.53/1.34 inference(transitivity,[status(thm)],[1315, 1313])).
% 1.53/1.34 tff(1317,plain,
% 1.53/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a130) | (~c3_1(a130)) | (~c1_1(a130)) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)) | c1_1(a124) | c3_1(a124) | (~c0_1(a124)))),
% 1.53/1.34 inference(quant_inst,[status(thm)],[])).
% 1.53/1.34 tff(1318,plain,
% 1.53/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a130) | c1_1(a124) | c3_1(a124) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a124)) | (~c3_1(a130)) | (~c1_1(a130))),
% 1.53/1.34 inference(modus_ponens,[status(thm)],[1317, 1316])).
% 1.53/1.34 tff(1319,plain,
% 1.53/1.34 (~c0_1(a124)),
% 1.53/1.34 inference(unit_resolution,[status(thm)],[1318, 126, 1312, 1311, 835, 1310, 1193, 1187, 824, 823, 20])).
% 1.53/1.34 tff(1320,plain,
% 1.53/1.34 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)))),
% 1.53/1.34 inference(bind,[status(th)],[])).
% 1.53/1.34 tff(1321,plain,
% 1.53/1.34 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.53/1.34 inference(quant_intro,[status(thm)],[1320])).
% 1.53/1.34 tff(1322,plain,
% 1.53/1.34 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.53/1.34 inference(rewrite,[status(thm)],[])).
% 1.53/1.34 tff(1323,plain,
% 1.53/1.34 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_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))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_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))) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))))),
% 1.53/1.35 inference(bind,[status(th)],[])).
% 1.53/1.35 tff(1324,plain,
% 1.53/1.35 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.53/1.35 inference(quant_intro,[status(thm)],[1323])).
% 1.53/1.35 tff(1325,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause190')).
% 1.53/1.35 tff(1326,plain,
% 1.53/1.35 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.53/1.35 inference(modus_ponens,[status(thm)],[1325, 1324])).
% 1.53/1.35 tff(1327,plain,
% 1.53/1.35 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.53/1.35 inference(modus_ponens,[status(thm)],[1326, 1322])).
% 1.53/1.35 tff(1328,plain,(
% 1.53/1.35 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.53/1.35 inference(skolemize,[status(sab)],[1327])).
% 1.53/1.35 tff(1329,plain,
% 1.53/1.35 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.53/1.35 inference(modus_ponens,[status(thm)],[1328, 1321])).
% 1.53/1.35 tff(1330,assumption,(hskp17), introduced(assumption)).
% 1.53/1.35 tff(1331,plain,
% 1.53/1.35 (~c3_1(a124)),
% 1.53/1.35 inference(unit_resolution,[status(thm)],[1186, 1330])).
% 1.53/1.35 tff(1332,plain,
% 1.53/1.35 (~c1_1(a124)),
% 1.53/1.35 inference(unit_resolution,[status(thm)],[1192, 1330])).
% 1.53/1.35 tff(1333,plain,
% 1.53/1.35 (c2_1(a124)),
% 1.53/1.35 inference(unit_resolution,[status(thm)],[1203, 1330])).
% 1.53/1.35 tff(1334,plain,
% 1.53/1.35 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp22 | hskp21 | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)))),
% 1.53/1.35 inference(rewrite,[status(thm)],[])).
% 1.53/1.35 tff(1335,plain,
% 1.53/1.35 ((hskp22 | hskp21 | (~ndr1_0) | c1_1(a124) | c3_1(a124) | (~c2_1(a124))) <=> (hskp22 | hskp21 | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)))),
% 1.53/1.35 inference(rewrite,[status(thm)],[])).
% 1.53/1.35 tff(1336,plain,
% 1.53/1.35 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c1_1(a124) | c3_1(a124) | (~c2_1(a124)))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124))))),
% 1.53/1.35 inference(monotonicity,[status(thm)],[1335])).
% 1.53/1.35 tff(1337,plain,
% 1.53/1.35 (((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c1_1(a124) | c3_1(a124) | (~c2_1(a124)))) <=> ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp22 | hskp21 | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)))),
% 1.53/1.35 inference(transitivity,[status(thm)],[1336, 1334])).
% 1.53/1.35 tff(1338,plain,
% 1.53/1.35 ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp22 | hskp21 | (~ndr1_0) | c1_1(a124) | c3_1(a124) | (~c2_1(a124)))),
% 1.53/1.35 inference(quant_inst,[status(thm)],[])).
% 1.53/1.35 tff(1339,plain,
% 1.53/1.35 ((~![U: $i] : (hskp22 | hskp21 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp22 | hskp21 | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124))),
% 1.53/1.35 inference(modus_ponens,[status(thm)],[1338, 1337])).
% 1.53/1.35 tff(1340,plain,
% 1.53/1.35 ($false),
% 1.53/1.35 inference(unit_resolution,[status(thm)],[1339, 126, 144, 507, 1333, 1332, 1331, 173])).
% 1.53/1.35 tff(1341,plain,((~hskp17) | hskp22 | hskp21), inference(lemma,lemma(discharge,[]))).
% 1.53/1.35 tff(1342,plain,
% 1.53/1.35 (hskp21),
% 1.53/1.35 inference(unit_resolution,[status(thm)],[1341, 1181, 144])).
% 1.53/1.35 tff(1343,plain,
% 1.53/1.35 (~c1_1(a136)),
% 1.53/1.35 inference(unit_resolution,[status(thm)],[193, 1342])).
% 1.53/1.35 tff(1344,plain,
% 1.53/1.35 (c3_1(a136)),
% 1.53/1.35 inference(unit_resolution,[status(thm)],[221, 1342])).
% 1.53/1.35 tff(1345,plain,
% 1.53/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a136) | c1_1(a124) | c3_1(a124) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a124) | (~c0_1(a136)) | (~c3_1(a136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a136) | c1_1(a124) | c3_1(a124) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a124) | (~c0_1(a136)) | (~c3_1(a136)))),
% 1.53/1.35 inference(rewrite,[status(thm)],[])).
% 1.53/1.35 tff(1346,plain,
% 1.53/1.35 (((~ndr1_0) | c3_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c1_1(a136) | (~c3_1(a136)) | (~c0_1(a136)) | c1_1(a124) | c0_1(a124) | c3_1(a124)) <=> (c1_1(a136) | c1_1(a124) | c3_1(a124) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a124) | (~c0_1(a136)) | (~c3_1(a136)))),
% 1.53/1.35 inference(rewrite,[status(thm)],[])).
% 1.53/1.35 tff(1347,plain,
% 1.53/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c1_1(a136) | (~c3_1(a136)) | (~c0_1(a136)) | c1_1(a124) | c0_1(a124) | c3_1(a124))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a136) | c1_1(a124) | c3_1(a124) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a124) | (~c0_1(a136)) | (~c3_1(a136))))),
% 1.53/1.35 inference(monotonicity,[status(thm)],[1346])).
% 1.53/1.35 tff(1348,plain,
% 1.53/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c1_1(a136) | (~c3_1(a136)) | (~c0_1(a136)) | c1_1(a124) | c0_1(a124) | c3_1(a124))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a136) | c1_1(a124) | c3_1(a124) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a124) | (~c0_1(a136)) | (~c3_1(a136)))),
% 1.53/1.35 inference(transitivity,[status(thm)],[1347, 1345])).
% 1.53/1.35 tff(1349,plain,
% 1.53/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c1_1(a136) | (~c3_1(a136)) | (~c0_1(a136)) | c1_1(a124) | c0_1(a124) | c3_1(a124))),
% 1.53/1.35 inference(quant_inst,[status(thm)],[])).
% 1.53/1.35 tff(1350,plain,
% 1.53/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a136) | c1_1(a124) | c3_1(a124) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a124) | (~c0_1(a136)) | (~c3_1(a136))),
% 1.53/1.35 inference(modus_ponens,[status(thm)],[1349, 1348])).
% 1.53/1.35 tff(1351,plain,
% 1.53/1.35 (c0_1(a124) | (~c0_1(a136))),
% 1.53/1.35 inference(unit_resolution,[status(thm)],[1350, 126, 1344, 835, 1343, 1193, 1187, 823, 1329, 1013])).
% 1.53/1.35 tff(1352,plain,
% 1.53/1.35 (~c0_1(a136)),
% 1.53/1.35 inference(unit_resolution,[status(thm)],[1351, 1319])).
% 1.53/1.35 tff(1353,plain,
% 1.53/1.35 (~c2_1(a136)),
% 1.53/1.35 inference(unit_resolution,[status(thm)],[187, 1342])).
% 1.53/1.35 tff(1354,plain,
% 1.53/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a136) | c2_1(a136) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | c0_1(a124) | c0_1(a136))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a136) | c2_1(a136) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | c0_1(a124) | c0_1(a136))),
% 1.53/1.35 inference(rewrite,[status(thm)],[])).
% 1.53/1.35 tff(1355,plain,
% 1.53/1.35 (((~ndr1_0) | c0_1(a124) | c3_1(a124) | (~c2_1(a124)) | c1_1(a124) | c0_1(a124) | (~c2_1(a124)) | c2_1(a136) | c1_1(a136) | c0_1(a136)) <=> (c1_1(a136) | c2_1(a136) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | c0_1(a124) | c0_1(a136))),
% 1.53/1.35 inference(rewrite,[status(thm)],[])).
% 1.53/1.35 tff(1356,plain,
% 1.53/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a124) | c3_1(a124) | (~c2_1(a124)) | c1_1(a124) | c0_1(a124) | (~c2_1(a124)) | c2_1(a136) | c1_1(a136) | c0_1(a136))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a136) | c2_1(a136) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | c0_1(a124) | c0_1(a136)))),
% 1.53/1.35 inference(monotonicity,[status(thm)],[1355])).
% 1.53/1.35 tff(1357,plain,
% 1.53/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a124) | c3_1(a124) | (~c2_1(a124)) | c1_1(a124) | c0_1(a124) | (~c2_1(a124)) | c2_1(a136) | c1_1(a136) | c0_1(a136))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a136) | c2_1(a136) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | c0_1(a124) | c0_1(a136))),
% 1.53/1.35 inference(transitivity,[status(thm)],[1356, 1354])).
% 1.53/1.35 tff(1358,plain,
% 1.53/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a124) | c3_1(a124) | (~c2_1(a124)) | c1_1(a124) | c0_1(a124) | (~c2_1(a124)) | c2_1(a136) | c1_1(a136) | c0_1(a136))),
% 1.53/1.35 inference(quant_inst,[status(thm)],[])).
% 1.53/1.35 tff(1359,plain,
% 1.53/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a136) | c2_1(a136) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | c0_1(a124) | c0_1(a136)),
% 1.53/1.35 inference(modus_ponens,[status(thm)],[1358, 1357])).
% 1.53/1.35 tff(1360,plain,
% 1.53/1.35 ($false),
% 1.53/1.35 inference(unit_resolution,[status(thm)],[1359, 126, 1204, 1343, 1353, 1193, 1187, 794, 1319, 1352])).
% 1.53/1.35 tff(1361,plain,(hskp18 | hskp22), inference(lemma,lemma(discharge,[]))).
% 1.53/1.35 tff(1362,plain,
% 1.53/1.35 (hskp18),
% 1.53/1.35 inference(unit_resolution,[status(thm)],[1361, 144])).
% 1.53/1.35 tff(1363,plain,
% 1.53/1.35 (~c1_1(a129)),
% 1.53/1.35 inference(unit_resolution,[status(thm)],[297, 1362])).
% 1.53/1.35 tff(1364,plain,
% 1.53/1.35 (c2_1(a129)),
% 1.53/1.35 inference(unit_resolution,[status(thm)],[308, 1362])).
% 1.53/1.35 tff(1365,plain,
% 1.53/1.35 (c0_1(a129)),
% 1.53/1.35 inference(unit_resolution,[status(thm)],[319, 1362])).
% 1.53/1.35 tff(1366,plain,
% 1.53/1.35 (~c3_1(a129)),
% 1.53/1.35 inference(unit_resolution,[status(thm)],[891, 126, 1365, 1364, 1363, 10])).
% 1.53/1.35 tff(1367,plain,
% 1.53/1.35 (hskp21),
% 1.53/1.35 inference(unit_resolution,[status(thm)],[944, 126, 144, 1364, 1363, 173, 1366])).
% 1.53/1.35 tff(1368,plain,
% 1.53/1.35 (~c2_1(a136)),
% 1.53/1.35 inference(unit_resolution,[status(thm)],[187, 1367])).
% 1.53/1.35 tff(1369,plain,
% 1.53/1.35 (~c1_1(a136)),
% 1.53/1.35 inference(unit_resolution,[status(thm)],[193, 1367])).
% 1.53/1.35 tff(1370,plain,
% 1.53/1.35 (~c0_1(a136)),
% 1.53/1.35 inference(unit_resolution,[status(thm)],[953, 126, 1365, 1364, 1369, 1368, 1363, 143, 1366])).
% 1.53/1.35 tff(1371,assumption,(hskp16), introduced(assumption)).
% 1.53/1.35 tff(1372,plain,
% 1.53/1.35 (~c2_1(a122)),
% 1.53/1.35 inference(unit_resolution,[status(thm)],[463, 1371])).
% 1.53/1.35 tff(1373,plain,
% 1.53/1.35 (((~hskp16) | c0_1(a122)) <=> ((~hskp16) | c0_1(a122))),
% 1.53/1.35 inference(rewrite,[status(thm)],[])).
% 1.53/1.35 tff(1374,axiom,((~hskp16) | c0_1(a122)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause65')).
% 1.60/1.35 tff(1375,plain,
% 1.60/1.35 ((~hskp16) | c0_1(a122)),
% 1.60/1.35 inference(modus_ponens,[status(thm)],[1374, 1373])).
% 1.60/1.35 tff(1376,plain,
% 1.60/1.35 ((~hskp16) | c0_1(a122)),
% 1.60/1.35 inference(modus_ponens,[status(thm)],[1375, 1373])).
% 1.60/1.35 tff(1377,plain,
% 1.60/1.35 ((~hskp16) | c0_1(a122)),
% 1.60/1.35 inference(modus_ponens,[status(thm)],[1376, 1373])).
% 1.60/1.35 tff(1378,plain,
% 1.60/1.35 ((~hskp16) | c0_1(a122)),
% 1.60/1.35 inference(modus_ponens,[status(thm)],[1377, 1373])).
% 1.60/1.35 tff(1379,plain,
% 1.60/1.35 ((~hskp16) | c0_1(a122)),
% 1.60/1.35 inference(modus_ponens,[status(thm)],[1378, 1373])).
% 1.60/1.35 tff(1380,plain,
% 1.60/1.35 ((~hskp16) | c0_1(a122)),
% 1.60/1.35 inference(modus_ponens,[status(thm)],[1379, 1373])).
% 1.60/1.35 tff(1381,plain,
% 1.60/1.35 ((~hskp16) | c0_1(a122)),
% 1.60/1.35 inference(modus_ponens,[status(thm)],[1380, 1373])).
% 1.60/1.35 tff(1382,plain,
% 1.60/1.35 ((~hskp16) | c0_1(a122)),
% 1.60/1.35 inference(modus_ponens,[status(thm)],[1381, 1373])).
% 1.60/1.35 tff(1383,plain,
% 1.60/1.35 (c0_1(a122)),
% 1.60/1.35 inference(unit_resolution,[status(thm)],[1382, 1371])).
% 1.60/1.35 tff(1384,plain,
% 1.60/1.35 (~c1_1(a122)),
% 1.60/1.35 inference(unit_resolution,[status(thm)],[552, 1371])).
% 1.60/1.35 tff(1385,assumption,(c0_1(a122)), introduced(assumption)).
% 1.60/1.35 tff(1386,plain,
% 1.60/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a129) | c1_1(a122) | c2_1(a122) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c0_1(a122)) | (~c2_1(a129)) | (~c0_1(a129)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a129) | c1_1(a122) | c2_1(a122) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c0_1(a122)) | (~c2_1(a129)) | (~c0_1(a129)))),
% 1.60/1.35 inference(rewrite,[status(thm)],[])).
% 1.60/1.35 tff(1387,plain,
% 1.60/1.35 (((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c2_1(a122) | c1_1(a122) | (~c0_1(a122))) <=> (c1_1(a129) | c1_1(a122) | c2_1(a122) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c0_1(a122)) | (~c2_1(a129)) | (~c0_1(a129)))),
% 1.60/1.35 inference(rewrite,[status(thm)],[])).
% 1.60/1.35 tff(1388,plain,
% 1.60/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c2_1(a122) | c1_1(a122) | (~c0_1(a122)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a129) | c1_1(a122) | c2_1(a122) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c0_1(a122)) | (~c2_1(a129)) | (~c0_1(a129))))),
% 1.60/1.35 inference(monotonicity,[status(thm)],[1387])).
% 1.60/1.35 tff(1389,plain,
% 1.60/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c2_1(a122) | c1_1(a122) | (~c0_1(a122)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a129) | c1_1(a122) | c2_1(a122) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c0_1(a122)) | (~c2_1(a129)) | (~c0_1(a129)))),
% 1.60/1.35 inference(transitivity,[status(thm)],[1388, 1386])).
% 1.60/1.35 tff(1390,plain,
% 1.60/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c2_1(a122) | c1_1(a122) | (~c0_1(a122)))),
% 1.60/1.35 inference(quant_inst,[status(thm)],[])).
% 1.60/1.35 tff(1391,plain,
% 1.60/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a129) | c1_1(a122) | c2_1(a122) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c0_1(a122)) | (~c2_1(a129)) | (~c0_1(a129))),
% 1.60/1.35 inference(modus_ponens,[status(thm)],[1390, 1389])).
% 1.60/1.35 tff(1392,plain,
% 1.60/1.35 ((~c0_1(a122)) | (~c2_1(a129)) | (~c0_1(a129))),
% 1.60/1.35 inference(unit_resolution,[status(thm)],[1391, 126, 161, 174, 672, 428, 440, 160, 143])).
% 1.60/1.35 tff(1393,plain,
% 1.60/1.35 ($false),
% 1.60/1.35 inference(unit_resolution,[status(thm)],[1392, 671, 670, 1385])).
% 1.60/1.35 tff(1394,plain,((~hskp18) | (~c0_1(a122)) | (~c0_1(a103)) | (~c2_1(a103)) | c1_1(a129) | c1_1(a122) | c2_1(a122) | c3_1(a103)), inference(lemma,lemma(discharge,[]))).
% 1.60/1.35 tff(1395,plain,
% 1.60/1.35 ($false),
% 1.60/1.35 inference(unit_resolution,[status(thm)],[1394, 1384, 1383, 161, 174, 669, 668, 1372, 160])).
% 1.60/1.35 tff(1396,plain,((~hskp16) | (~c0_1(a103)) | (~c2_1(a103)) | (~hskp18) | c3_1(a103)), inference(lemma,lemma(discharge,[]))).
% 1.60/1.35 tff(1397,plain,
% 1.60/1.35 (~hskp16),
% 1.60/1.35 inference(unit_resolution,[status(thm)],[1396, 1010, 1012, 1362, 1011])).
% 1.60/1.35 tff(1398,plain,
% 1.60/1.35 (hskp16 | hskp2),
% 1.60/1.35 inference(unit_resolution,[status(thm)],[575, 126, 835, 824, 823, 569])).
% 1.60/1.35 tff(1399,plain,
% 1.60/1.35 (hskp2),
% 1.60/1.35 inference(unit_resolution,[status(thm)],[1398, 1397])).
% 1.60/1.35 tff(1400,plain,
% 1.60/1.35 (~c1_1(a99)),
% 1.60/1.35 inference(unit_resolution,[status(thm)],[618, 1399])).
% 1.60/1.35 tff(1401,plain,
% 1.60/1.35 (~c0_1(a99)),
% 1.60/1.35 inference(unit_resolution,[status(thm)],[602, 1399])).
% 1.60/1.35 tff(1402,plain,
% 1.60/1.35 (~c3_1(a137)),
% 1.60/1.35 inference(unit_resolution,[status(thm)],[701, 1362, 655, 644, 633])).
% 1.60/1.35 tff(1403,plain,
% 1.60/1.35 (((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp25 | hskp16 | (~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | c3_1(a137))) <=> ((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp25 | hskp16 | (~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | c3_1(a137))),
% 1.60/1.35 inference(rewrite,[status(thm)],[])).
% 1.60/1.35 tff(1404,plain,
% 1.60/1.35 ((hskp25 | hskp16 | (~ndr1_0) | c3_1(a137) | (~c2_1(a137)) | (~c0_1(a137))) <=> (hskp25 | hskp16 | (~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | c3_1(a137))),
% 1.60/1.35 inference(rewrite,[status(thm)],[])).
% 1.60/1.35 tff(1405,plain,
% 1.60/1.35 (((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp25 | hskp16 | (~ndr1_0) | c3_1(a137) | (~c2_1(a137)) | (~c0_1(a137)))) <=> ((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp25 | hskp16 | (~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | c3_1(a137)))),
% 1.60/1.35 inference(monotonicity,[status(thm)],[1404])).
% 1.60/1.35 tff(1406,plain,
% 1.60/1.35 (((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp25 | hskp16 | (~ndr1_0) | c3_1(a137) | (~c2_1(a137)) | (~c0_1(a137)))) <=> ((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp25 | hskp16 | (~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | c3_1(a137))),
% 1.60/1.35 inference(transitivity,[status(thm)],[1405, 1403])).
% 1.60/1.35 tff(1407,plain,
% 1.60/1.35 ((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp25 | hskp16 | (~ndr1_0) | c3_1(a137) | (~c2_1(a137)) | (~c0_1(a137)))),
% 1.60/1.35 inference(quant_inst,[status(thm)],[])).
% 1.60/1.35 tff(1408,plain,
% 1.60/1.35 ((~![U: $i] : (hskp25 | hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp25 | hskp16 | (~ndr1_0) | (~c2_1(a137)) | (~c0_1(a137)) | c3_1(a137)),
% 1.60/1.35 inference(modus_ponens,[status(thm)],[1407, 1406])).
% 1.60/1.35 tff(1409,plain,
% 1.60/1.35 (hskp25 | hskp16 | c3_1(a137)),
% 1.60/1.35 inference(unit_resolution,[status(thm)],[1408, 126, 633, 644, 474])).
% 1.60/1.35 tff(1410,plain,
% 1.60/1.35 (hskp25),
% 1.60/1.35 inference(unit_resolution,[status(thm)],[1409, 1397, 1402])).
% 1.60/1.35 tff(1411,plain,
% 1.60/1.35 (~c3_1(a173)),
% 1.60/1.35 inference(unit_resolution,[status(thm)],[530, 1410])).
% 1.60/1.35 tff(1412,plain,
% 1.60/1.35 (~c0_1(a173)),
% 1.60/1.35 inference(unit_resolution,[status(thm)],[487, 1410])).
% 1.60/1.35 tff(1413,plain,
% 1.60/1.35 (c2_1(a99)),
% 1.60/1.35 inference(unit_resolution,[status(thm)],[587, 1399])).
% 1.60/1.35 tff(1414,plain,
% 1.60/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a173) | c3_1(a173) | c1_1(a136) | c2_1(a136) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c0_1(a136) | (~c2_1(a173)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a173) | c3_1(a173) | c1_1(a136) | c2_1(a136) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c0_1(a136) | (~c2_1(a173)))),
% 1.60/1.36 inference(rewrite,[status(thm)],[])).
% 1.60/1.36 tff(1415,plain,
% 1.60/1.36 (((~ndr1_0) | c0_1(a173) | c3_1(a173) | (~c2_1(a173)) | c1_1(a99) | c0_1(a99) | (~c2_1(a99)) | c2_1(a136) | c1_1(a136) | c0_1(a136)) <=> (c0_1(a173) | c3_1(a173) | c1_1(a136) | c2_1(a136) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c0_1(a136) | (~c2_1(a173)))),
% 1.60/1.36 inference(rewrite,[status(thm)],[])).
% 1.60/1.36 tff(1416,plain,
% 1.60/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a173) | c3_1(a173) | (~c2_1(a173)) | c1_1(a99) | c0_1(a99) | (~c2_1(a99)) | c2_1(a136) | c1_1(a136) | c0_1(a136))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a173) | c3_1(a173) | c1_1(a136) | c2_1(a136) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c0_1(a136) | (~c2_1(a173))))),
% 1.60/1.36 inference(monotonicity,[status(thm)],[1415])).
% 1.60/1.36 tff(1417,plain,
% 1.60/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a173) | c3_1(a173) | (~c2_1(a173)) | c1_1(a99) | c0_1(a99) | (~c2_1(a99)) | c2_1(a136) | c1_1(a136) | c0_1(a136))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a173) | c3_1(a173) | c1_1(a136) | c2_1(a136) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c0_1(a136) | (~c2_1(a173)))),
% 1.60/1.36 inference(transitivity,[status(thm)],[1416, 1414])).
% 1.60/1.36 tff(1418,plain,
% 1.60/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c0_1(a173) | c3_1(a173) | (~c2_1(a173)) | c1_1(a99) | c0_1(a99) | (~c2_1(a99)) | c2_1(a136) | c1_1(a136) | c0_1(a136))),
% 1.60/1.36 inference(quant_inst,[status(thm)],[])).
% 1.60/1.36 tff(1419,plain,
% 1.60/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a173) | c3_1(a173) | c1_1(a136) | c2_1(a136) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c0_1(a136) | (~c2_1(a173))),
% 1.60/1.36 inference(modus_ponens,[status(thm)],[1418, 1417])).
% 1.60/1.36 tff(1420,plain,
% 1.60/1.36 (~c2_1(a173)),
% 1.60/1.36 inference(unit_resolution,[status(thm)],[1419, 126, 1413, 1412, 1411, 1369, 1368, 1401, 1400, 794, 1370])).
% 1.60/1.36 tff(1421,plain,
% 1.60/1.36 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)))),
% 1.60/1.36 inference(bind,[status(th)],[])).
% 1.60/1.36 tff(1422,plain,
% 1.60/1.36 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.60/1.36 inference(quant_intro,[status(thm)],[1421])).
% 1.60/1.36 tff(1423,plain,
% 1.60/1.36 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.60/1.36 inference(rewrite,[status(thm)],[])).
% 1.60/1.36 tff(1424,plain,
% 1.60/1.36 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c0_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) | c0_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) | c0_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)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c0_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)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))))),
% 1.60/1.36 inference(bind,[status(th)],[])).
% 1.60/1.36 tff(1425,plain,
% 1.60/1.36 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.60/1.36 inference(quant_intro,[status(thm)],[1424])).
% 1.60/1.36 tff(1426,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause187')).
% 1.60/1.36 tff(1427,plain,
% 1.60/1.36 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.60/1.36 inference(modus_ponens,[status(thm)],[1426, 1425])).
% 1.60/1.36 tff(1428,plain,
% 1.60/1.36 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.60/1.36 inference(modus_ponens,[status(thm)],[1427, 1423])).
% 1.60/1.36 tff(1429,plain,(
% 1.60/1.36 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.60/1.36 inference(skolemize,[status(sab)],[1428])).
% 1.60/1.36 tff(1430,plain,
% 1.60/1.36 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.60/1.36 inference(modus_ponens,[status(thm)],[1429, 1422])).
% 1.60/1.36 tff(1431,plain,
% 1.60/1.36 (c3_1(a136)),
% 1.60/1.36 inference(unit_resolution,[status(thm)],[221, 1367])).
% 1.60/1.36 tff(1432,plain,
% 1.60/1.36 (c1_1(a173)),
% 1.60/1.36 inference(unit_resolution,[status(thm)],[498, 1410])).
% 1.60/1.36 tff(1433,plain,
% 1.60/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a173) | c3_1(a173) | c1_1(a136) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | c3_1(a99) | c0_1(a136) | (~c3_1(a136)) | (~c1_1(a173)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a173) | c3_1(a173) | c1_1(a136) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | c3_1(a99) | c0_1(a136) | (~c3_1(a136)) | (~c1_1(a173)))),
% 1.60/1.36 inference(rewrite,[status(thm)],[])).
% 1.60/1.36 tff(1434,plain,
% 1.60/1.36 (((~ndr1_0) | c0_1(a173) | c3_1(a173) | (~c1_1(a173)) | c1_1(a136) | c0_1(a136) | (~c3_1(a136)) | c1_1(a99) | c0_1(a99) | c3_1(a99)) <=> (c0_1(a173) | c3_1(a173) | c1_1(a136) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | c3_1(a99) | c0_1(a136) | (~c3_1(a136)) | (~c1_1(a173)))),
% 1.60/1.36 inference(rewrite,[status(thm)],[])).
% 1.60/1.36 tff(1435,plain,
% 1.60/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a173) | c3_1(a173) | (~c1_1(a173)) | c1_1(a136) | c0_1(a136) | (~c3_1(a136)) | c1_1(a99) | c0_1(a99) | c3_1(a99))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a173) | c3_1(a173) | c1_1(a136) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | c3_1(a99) | c0_1(a136) | (~c3_1(a136)) | (~c1_1(a173))))),
% 1.60/1.36 inference(monotonicity,[status(thm)],[1434])).
% 1.60/1.36 tff(1436,plain,
% 1.60/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a173) | c3_1(a173) | (~c1_1(a173)) | c1_1(a136) | c0_1(a136) | (~c3_1(a136)) | c1_1(a99) | c0_1(a99) | c3_1(a99))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a173) | c3_1(a173) | c1_1(a136) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | c3_1(a99) | c0_1(a136) | (~c3_1(a136)) | (~c1_1(a173)))),
% 1.60/1.36 inference(transitivity,[status(thm)],[1435, 1433])).
% 1.60/1.36 tff(1437,plain,
% 1.60/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a173) | c3_1(a173) | (~c1_1(a173)) | c1_1(a136) | c0_1(a136) | (~c3_1(a136)) | c1_1(a99) | c0_1(a99) | c3_1(a99))),
% 1.60/1.36 inference(quant_inst,[status(thm)],[])).
% 1.60/1.36 tff(1438,plain,
% 1.60/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a173) | c3_1(a173) | c1_1(a136) | c0_1(a99) | c1_1(a99) | (~ndr1_0) | c3_1(a99) | c0_1(a136) | (~c3_1(a136)) | (~c1_1(a173))),
% 1.60/1.36 inference(modus_ponens,[status(thm)],[1437, 1436])).
% 1.60/1.36 tff(1439,plain,
% 1.60/1.36 (c3_1(a99)),
% 1.60/1.36 inference(unit_resolution,[status(thm)],[1438, 126, 1432, 1431, 1412, 1411, 1369, 1401, 1400, 1430, 1370])).
% 1.60/1.36 tff(1440,plain,
% 1.60/1.36 ($false),
% 1.60/1.36 inference(unit_resolution,[status(thm)],[610, 126, 1413, 835, 1412, 1411, 1401, 824, 525, 1439, 1013, 1420])).
% 1.60/1.36 tff(1441,plain,(hskp22), inference(lemma,lemma(discharge,[]))).
% 1.60/1.36 tff(1442,plain,
% 1.60/1.36 (((~hskp22) | (~c2_1(a138))) <=> ((~hskp22) | (~c2_1(a138)))),
% 1.60/1.36 inference(rewrite,[status(thm)],[])).
% 1.60/1.36 tff(1443,plain,
% 1.60/1.36 (((~c2_1(a138)) | (~hskp22)) <=> ((~hskp22) | (~c2_1(a138)))),
% 1.60/1.36 inference(rewrite,[status(thm)],[])).
% 1.60/1.36 tff(1444,axiom,((~c2_1(a138)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause94')).
% 1.60/1.36 tff(1445,plain,
% 1.60/1.36 ((~hskp22) | (~c2_1(a138))),
% 1.60/1.36 inference(modus_ponens,[status(thm)],[1444, 1443])).
% 1.60/1.36 tff(1446,plain,
% 1.60/1.36 ((~hskp22) | (~c2_1(a138))),
% 1.60/1.36 inference(modus_ponens,[status(thm)],[1445, 1442])).
% 1.60/1.36 tff(1447,plain,
% 1.60/1.36 (~c2_1(a138)),
% 1.60/1.36 inference(unit_resolution,[status(thm)],[1446, 1441])).
% 1.60/1.36 tff(1448,plain,
% 1.60/1.36 (c2_1(a103)),
% 1.60/1.36 inference(unit_resolution,[status(thm)],[157, 76])).
% 1.60/1.36 tff(1449,plain,
% 1.60/1.36 (((~hskp22) | c0_1(a138)) <=> ((~hskp22) | c0_1(a138))),
% 1.60/1.36 inference(rewrite,[status(thm)],[])).
% 1.60/1.36 tff(1450,axiom,((~hskp22) | c0_1(a138)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause57')).
% 1.60/1.36 tff(1451,plain,
% 1.60/1.36 ((~hskp22) | c0_1(a138)),
% 1.60/1.36 inference(modus_ponens,[status(thm)],[1450, 1449])).
% 1.60/1.36 tff(1452,plain,
% 1.60/1.36 ((~hskp22) | c0_1(a138)),
% 1.60/1.36 inference(modus_ponens,[status(thm)],[1451, 1449])).
% 1.60/1.36 tff(1453,plain,
% 1.60/1.36 ((~hskp22) | c0_1(a138)),
% 1.60/1.36 inference(modus_ponens,[status(thm)],[1452, 1449])).
% 1.60/1.36 tff(1454,plain,
% 1.60/1.36 ((~hskp22) | c0_1(a138)),
% 1.60/1.36 inference(modus_ponens,[status(thm)],[1453, 1449])).
% 1.60/1.36 tff(1455,plain,
% 1.60/1.36 ((~hskp22) | c0_1(a138)),
% 1.60/1.36 inference(modus_ponens,[status(thm)],[1454, 1449])).
% 1.60/1.36 tff(1456,plain,
% 1.60/1.36 ((~hskp22) | c0_1(a138)),
% 1.60/1.36 inference(modus_ponens,[status(thm)],[1455, 1449])).
% 1.60/1.36 tff(1457,plain,
% 1.60/1.36 ((~hskp22) | c0_1(a138)),
% 1.60/1.36 inference(modus_ponens,[status(thm)],[1456, 1449])).
% 1.60/1.36 tff(1458,plain,
% 1.60/1.36 ((~hskp22) | c0_1(a138)),
% 1.60/1.36 inference(modus_ponens,[status(thm)],[1457, 1449])).
% 1.60/1.36 tff(1459,plain,
% 1.60/1.36 (c0_1(a138)),
% 1.60/1.36 inference(unit_resolution,[status(thm)],[1458, 1441])).
% 1.60/1.36 tff(1460,plain,
% 1.60/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a138) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | c1_1(a138) | (~c0_1(a138)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a138) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | c1_1(a138) | (~c0_1(a138)))),
% 1.60/1.36 inference(rewrite,[status(thm)],[])).
% 1.60/1.36 tff(1461,plain,
% 1.60/1.36 (((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c2_1(a138) | c1_1(a138) | (~c0_1(a138))) <=> (c2_1(a138) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | c1_1(a138) | (~c0_1(a138)))),
% 1.60/1.36 inference(rewrite,[status(thm)],[])).
% 1.60/1.36 tff(1462,plain,
% 1.60/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c2_1(a138) | c1_1(a138) | (~c0_1(a138)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a138) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | c1_1(a138) | (~c0_1(a138))))),
% 1.60/1.36 inference(monotonicity,[status(thm)],[1461])).
% 1.60/1.36 tff(1463,plain,
% 1.60/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c2_1(a138) | c1_1(a138) | (~c0_1(a138)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a138) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | c1_1(a138) | (~c0_1(a138)))),
% 1.60/1.36 inference(transitivity,[status(thm)],[1462, 1460])).
% 1.60/1.36 tff(1464,plain,
% 1.60/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c2_1(a138) | c1_1(a138) | (~c0_1(a138)))),
% 1.60/1.36 inference(quant_inst,[status(thm)],[])).
% 1.60/1.36 tff(1465,plain,
% 1.60/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a138) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | c1_1(a138) | (~c0_1(a138))),
% 1.60/1.36 inference(modus_ponens,[status(thm)],[1464, 1463])).
% 1.60/1.36 tff(1466,plain,
% 1.60/1.36 (c1_1(a138)),
% 1.60/1.36 inference(unit_resolution,[status(thm)],[1465, 126, 1459, 93, 1448, 1447, 82, 143, 133])).
% 1.60/1.36 tff(1467,plain,
% 1.60/1.36 (((~hskp22) | c3_1(a138)) <=> ((~hskp22) | c3_1(a138))),
% 1.60/1.36 inference(rewrite,[status(thm)],[])).
% 1.60/1.36 tff(1468,axiom,((~hskp22) | c3_1(a138)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause58')).
% 1.60/1.36 tff(1469,plain,
% 1.60/1.36 ((~hskp22) | c3_1(a138)),
% 1.60/1.36 inference(modus_ponens,[status(thm)],[1468, 1467])).
% 1.60/1.36 tff(1470,plain,
% 1.60/1.36 ((~hskp22) | c3_1(a138)),
% 1.60/1.36 inference(modus_ponens,[status(thm)],[1469, 1467])).
% 1.60/1.36 tff(1471,plain,
% 1.60/1.36 ((~hskp22) | c3_1(a138)),
% 1.60/1.36 inference(modus_ponens,[status(thm)],[1470, 1467])).
% 1.60/1.36 tff(1472,plain,
% 1.60/1.36 ((~hskp22) | c3_1(a138)),
% 1.60/1.36 inference(modus_ponens,[status(thm)],[1471, 1467])).
% 1.60/1.36 tff(1473,plain,
% 1.60/1.36 ((~hskp22) | c3_1(a138)),
% 1.60/1.36 inference(modus_ponens,[status(thm)],[1472, 1467])).
% 1.60/1.36 tff(1474,plain,
% 1.60/1.36 ((~hskp22) | c3_1(a138)),
% 1.60/1.36 inference(modus_ponens,[status(thm)],[1473, 1467])).
% 1.60/1.36 tff(1475,plain,
% 1.60/1.36 ((~hskp22) | c3_1(a138)),
% 1.60/1.36 inference(modus_ponens,[status(thm)],[1474, 1467])).
% 1.60/1.36 tff(1476,plain,
% 1.60/1.36 ((~hskp22) | c3_1(a138)),
% 1.60/1.36 inference(modus_ponens,[status(thm)],[1475, 1467])).
% 1.60/1.36 tff(1477,plain,
% 1.60/1.36 (c3_1(a138)),
% 1.60/1.36 inference(unit_resolution,[status(thm)],[1476, 1441])).
% 1.60/1.36 tff(1478,plain,
% 1.60/1.36 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp18 | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | c1_1(a103) | (~c0_1(a138)) | (~c3_1(a138)) | (~c1_1(a138)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp18 | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | c1_1(a103) | (~c0_1(a138)) | (~c3_1(a138)) | (~c1_1(a138)))),
% 1.60/1.36 inference(rewrite,[status(thm)],[])).
% 1.60/1.36 tff(1479,plain,
% 1.60/1.36 ((hskp18 | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | (~c1_1(a138)) | c1_1(a103) | c3_1(a103) | (~c0_1(a103))) <=> (hskp18 | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | c1_1(a103) | (~c0_1(a138)) | (~c3_1(a138)) | (~c1_1(a138)))),
% 1.60/1.36 inference(rewrite,[status(thm)],[])).
% 1.60/1.36 tff(1480,plain,
% 1.60/1.36 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | (~c1_1(a138)) | c1_1(a103) | c3_1(a103) | (~c0_1(a103)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp18 | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | c1_1(a103) | (~c0_1(a138)) | (~c3_1(a138)) | (~c1_1(a138))))),
% 1.60/1.36 inference(monotonicity,[status(thm)],[1479])).
% 1.60/1.36 tff(1481,plain,
% 1.60/1.36 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | (~c1_1(a138)) | c1_1(a103) | c3_1(a103) | (~c0_1(a103)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp18 | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | c1_1(a103) | (~c0_1(a138)) | (~c3_1(a138)) | (~c1_1(a138)))),
% 1.60/1.36 inference(transitivity,[status(thm)],[1480, 1478])).
% 1.60/1.36 tff(1482,plain,
% 1.60/1.36 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | (~c1_1(a138)) | c1_1(a103) | c3_1(a103) | (~c0_1(a103)))),
% 1.60/1.36 inference(quant_inst,[status(thm)],[])).
% 1.60/1.36 tff(1483,plain,
% 1.60/1.36 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp18 | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | c1_1(a103) | (~c0_1(a138)) | (~c3_1(a138)) | (~c1_1(a138))),
% 1.60/1.36 inference(modus_ponens,[status(thm)],[1482, 1481])).
% 1.60/1.36 tff(1484,plain,
% 1.60/1.36 ($false),
% 1.60/1.36 inference(unit_resolution,[status(thm)],[1483, 126, 52, 1459, 1477, 93, 82, 714, 133, 1466])).
% 1.60/1.36 tff(1485,plain,((~hskp4) | hskp18 | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.60/1.36 tff(1486,plain,
% 1.60/1.36 (~hskp4),
% 1.60/1.36 inference(unit_resolution,[status(thm)],[1485, 52, 65])).
% 1.60/1.36 tff(1487,plain,
% 1.60/1.36 (^[U: $i] : refl((hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 1.60/1.36 inference(bind,[status(th)],[])).
% 1.60/1.36 tff(1488,plain,
% 1.60/1.36 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.60/1.36 inference(quant_intro,[status(thm)],[1487])).
% 1.60/1.36 tff(1489,plain,
% 1.60/1.36 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.60/1.36 inference(rewrite,[status(thm)],[])).
% 1.60/1.36 tff(1490,plain,
% 1.60/1.36 (^[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)) | hskp4) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp4))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp4) <=> (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp4) | hskp7) <=> ((hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp7))), rewrite(((hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp7) <=> (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp4) | hskp7) <=> (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 1.60/1.36 inference(bind,[status(th)],[])).
% 1.60/1.36 tff(1491,plain,
% 1.60/1.36 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp4) | hskp7) <=> ![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.60/1.36 inference(quant_intro,[status(thm)],[1490])).
% 1.60/1.36 tff(1492,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp4) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause155')).
% 1.60/1.36 tff(1493,plain,
% 1.60/1.36 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.60/1.36 inference(modus_ponens,[status(thm)],[1492, 1491])).
% 1.60/1.36 tff(1494,plain,
% 1.60/1.36 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.60/1.36 inference(modus_ponens,[status(thm)],[1493, 1489])).
% 1.60/1.36 tff(1495,plain,(
% 1.60/1.36 ![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.60/1.36 inference(skolemize,[status(sab)],[1494])).
% 1.60/1.36 tff(1496,plain,
% 1.60/1.36 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.60/1.36 inference(modus_ponens,[status(thm)],[1495, 1488])).
% 1.60/1.37 tff(1497,plain,
% 1.60/1.37 (((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp4 | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c3_1(a138)))) <=> ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp7 | hskp4 | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c3_1(a138)))),
% 1.60/1.37 inference(rewrite,[status(thm)],[])).
% 1.60/1.37 tff(1498,plain,
% 1.60/1.37 ((hskp7 | hskp4 | (~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c0_1(a138))) <=> (hskp7 | hskp4 | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c3_1(a138)))),
% 1.60/1.37 inference(rewrite,[status(thm)],[])).
% 1.60/1.37 tff(1499,plain,
% 1.60/1.37 (((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp4 | (~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c0_1(a138)))) <=> ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp4 | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c3_1(a138))))),
% 1.60/1.37 inference(monotonicity,[status(thm)],[1498])).
% 1.60/1.37 tff(1500,plain,
% 1.60/1.37 (((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp4 | (~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c0_1(a138)))) <=> ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp7 | hskp4 | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c3_1(a138)))),
% 1.60/1.37 inference(transitivity,[status(thm)],[1499, 1497])).
% 1.60/1.37 tff(1501,plain,
% 1.60/1.37 ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp4 | (~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c0_1(a138)))),
% 1.60/1.37 inference(quant_inst,[status(thm)],[])).
% 1.60/1.37 tff(1502,plain,
% 1.60/1.37 ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp7 | hskp4 | c2_1(a138) | (~ndr1_0) | (~c0_1(a138)) | (~c3_1(a138))),
% 1.60/1.37 inference(modus_ponens,[status(thm)],[1501, 1500])).
% 1.60/1.37 tff(1503,plain,
% 1.60/1.37 (hskp7 | hskp4),
% 1.60/1.37 inference(unit_resolution,[status(thm)],[1502, 126, 1459, 1477, 1447, 1496])).
% 1.60/1.37 tff(1504,plain,
% 1.60/1.37 (hskp7),
% 1.60/1.37 inference(unit_resolution,[status(thm)],[1503, 856])).
% 1.60/1.37 tff(1505,plain,
% 1.60/1.37 (~c0_1(a106)),
% 1.60/1.37 inference(unit_resolution,[status(thm)],[969, 1504])).
% 1.60/1.37 tff(1506,plain,
% 1.60/1.37 (c3_1(a106)),
% 1.60/1.37 inference(unit_resolution,[status(thm)],[919, 1504])).
% 1.60/1.37 tff(1507,plain,
% 1.60/1.37 (c2_1(a106)),
% 1.60/1.37 inference(unit_resolution,[status(thm)],[930, 1504])).
% 1.60/1.37 tff(1508,plain,
% 1.60/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a97) | c2_1(a138) | c0_1(a106) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | (~c0_1(a138)) | (~c1_1(a138)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a97) | c2_1(a138) | c0_1(a106) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | (~c0_1(a138)) | (~c1_1(a138)))),
% 1.60/1.37 inference(rewrite,[status(thm)],[])).
% 1.60/1.37 tff(1509,plain,
% 1.60/1.37 (((~ndr1_0) | c2_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | c0_1(a106) | (~c2_1(a106)) | (~c3_1(a106)) | c2_1(a97) | c0_1(a97) | c3_1(a97)) <=> (c0_1(a97) | c2_1(a138) | c0_1(a106) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | (~c0_1(a138)) | (~c1_1(a138)))),
% 1.60/1.37 inference(rewrite,[status(thm)],[])).
% 1.60/1.37 tff(1510,plain,
% 1.60/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | c0_1(a106) | (~c2_1(a106)) | (~c3_1(a106)) | c2_1(a97) | c0_1(a97) | c3_1(a97))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a97) | c2_1(a138) | c0_1(a106) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | (~c0_1(a138)) | (~c1_1(a138))))),
% 1.60/1.37 inference(monotonicity,[status(thm)],[1509])).
% 1.60/1.37 tff(1511,plain,
% 1.60/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | c0_1(a106) | (~c2_1(a106)) | (~c3_1(a106)) | c2_1(a97) | c0_1(a97) | c3_1(a97))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a97) | c2_1(a138) | c0_1(a106) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | (~c0_1(a138)) | (~c1_1(a138)))),
% 1.60/1.37 inference(transitivity,[status(thm)],[1510, 1508])).
% 1.60/1.37 tff(1512,plain,
% 1.60/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | c0_1(a106) | (~c2_1(a106)) | (~c3_1(a106)) | c2_1(a97) | c0_1(a97) | c3_1(a97))),
% 1.60/1.37 inference(quant_inst,[status(thm)],[])).
% 1.60/1.37 tff(1513,plain,
% 1.60/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a97) | c2_1(a138) | c0_1(a106) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | (~c0_1(a138)) | (~c1_1(a138))),
% 1.60/1.37 inference(modus_ponens,[status(thm)],[1512, 1511])).
% 1.60/1.37 tff(1514,plain,
% 1.60/1.37 (~c1_1(a138)),
% 1.60/1.37 inference(unit_resolution,[status(thm)],[1513, 126, 1459, 1507, 1506, 54, 1447, 1505, 31, 53, 525])).
% 1.60/1.37 tff(1515,plain,
% 1.60/1.37 (hskp20),
% 1.60/1.37 inference(unit_resolution,[status(thm)],[815, 856, 52])).
% 1.60/1.37 tff(1516,plain,
% 1.60/1.37 (~c3_1(a132)),
% 1.60/1.37 inference(unit_resolution,[status(thm)],[720, 1515])).
% 1.60/1.37 tff(1517,plain,
% 1.60/1.37 (~c2_1(a132)),
% 1.60/1.37 inference(unit_resolution,[status(thm)],[740, 1515])).
% 1.60/1.37 tff(1518,plain,
% 1.60/1.37 (~c1_1(a132)),
% 1.60/1.37 inference(unit_resolution,[status(thm)],[726, 1515])).
% 1.60/1.37 tff(1519,plain,
% 1.60/1.37 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp17 | c1_1(a132) | c2_1(a132) | c3_1(a132) | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp17 | c1_1(a132) | c2_1(a132) | c3_1(a132) | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)))),
% 1.60/1.37 inference(rewrite,[status(thm)],[])).
% 1.60/1.37 tff(1520,plain,
% 1.60/1.37 ((hskp17 | (~ndr1_0) | c0_1(a106) | (~c2_1(a106)) | (~c3_1(a106)) | c2_1(a132) | c1_1(a132) | c3_1(a132)) <=> (hskp17 | c1_1(a132) | c2_1(a132) | c3_1(a132) | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)))),
% 1.60/1.37 inference(rewrite,[status(thm)],[])).
% 1.60/1.37 tff(1521,plain,
% 1.60/1.37 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp17 | (~ndr1_0) | c0_1(a106) | (~c2_1(a106)) | (~c3_1(a106)) | c2_1(a132) | c1_1(a132) | c3_1(a132))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp17 | c1_1(a132) | c2_1(a132) | c3_1(a132) | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106))))),
% 1.60/1.37 inference(monotonicity,[status(thm)],[1520])).
% 1.60/1.37 tff(1522,plain,
% 1.60/1.37 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp17 | (~ndr1_0) | c0_1(a106) | (~c2_1(a106)) | (~c3_1(a106)) | c2_1(a132) | c1_1(a132) | c3_1(a132))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp17 | c1_1(a132) | c2_1(a132) | c3_1(a132) | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)))),
% 1.60/1.37 inference(transitivity,[status(thm)],[1521, 1519])).
% 1.60/1.37 tff(1523,plain,
% 1.60/1.37 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp17 | (~ndr1_0) | c0_1(a106) | (~c2_1(a106)) | (~c3_1(a106)) | c2_1(a132) | c1_1(a132) | c3_1(a132))),
% 1.60/1.37 inference(quant_inst,[status(thm)],[])).
% 1.60/1.37 tff(1524,plain,
% 1.60/1.37 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp17 | c1_1(a132) | c2_1(a132) | c3_1(a132) | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106))),
% 1.60/1.37 inference(modus_ponens,[status(thm)],[1523, 1522])).
% 1.60/1.37 tff(1525,plain,
% 1.60/1.37 (hskp17),
% 1.60/1.37 inference(unit_resolution,[status(thm)],[1524, 126, 1507, 1506, 1518, 1517, 1516, 1505, 51])).
% 1.60/1.37 tff(1526,plain,
% 1.60/1.37 (~c3_1(a124)),
% 1.60/1.37 inference(unit_resolution,[status(thm)],[1186, 1525])).
% 1.60/1.37 tff(1527,plain,
% 1.60/1.37 (~c1_1(a124)),
% 1.60/1.37 inference(unit_resolution,[status(thm)],[1192, 1525])).
% 1.60/1.37 tff(1528,plain,
% 1.60/1.37 (c2_1(a124)),
% 1.60/1.37 inference(unit_resolution,[status(thm)],[1203, 1525])).
% 1.60/1.37 tff(1529,plain,
% 1.60/1.37 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp4 | c2_1(a138) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | c1_1(a138) | (~c0_1(a138)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp4 | c2_1(a138) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | c1_1(a138) | (~c0_1(a138)))),
% 1.60/1.37 inference(rewrite,[status(thm)],[])).
% 1.60/1.37 tff(1530,plain,
% 1.60/1.37 ((hskp4 | (~ndr1_0) | c1_1(a124) | c3_1(a124) | (~c2_1(a124)) | c2_1(a138) | c1_1(a138) | (~c0_1(a138))) <=> (hskp4 | c2_1(a138) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | c1_1(a138) | (~c0_1(a138)))),
% 1.60/1.37 inference(rewrite,[status(thm)],[])).
% 1.60/1.37 tff(1531,plain,
% 1.60/1.37 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a124) | c3_1(a124) | (~c2_1(a124)) | c2_1(a138) | c1_1(a138) | (~c0_1(a138)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp4 | c2_1(a138) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | c1_1(a138) | (~c0_1(a138))))),
% 1.60/1.37 inference(monotonicity,[status(thm)],[1530])).
% 1.60/1.37 tff(1532,plain,
% 1.60/1.37 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a124) | c3_1(a124) | (~c2_1(a124)) | c2_1(a138) | c1_1(a138) | (~c0_1(a138)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp4 | c2_1(a138) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | c1_1(a138) | (~c0_1(a138)))),
% 1.60/1.37 inference(transitivity,[status(thm)],[1531, 1529])).
% 1.60/1.37 tff(1533,plain,
% 1.60/1.37 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a124) | c3_1(a124) | (~c2_1(a124)) | c2_1(a138) | c1_1(a138) | (~c0_1(a138)))),
% 1.60/1.37 inference(quant_inst,[status(thm)],[])).
% 1.60/1.37 tff(1534,plain,
% 1.60/1.37 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp4 | c2_1(a138) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | c1_1(a138) | (~c0_1(a138))),
% 1.60/1.37 inference(modus_ponens,[status(thm)],[1533, 1532])).
% 1.60/1.37 tff(1535,plain,
% 1.60/1.37 ($false),
% 1.60/1.37 inference(unit_resolution,[status(thm)],[1534, 126, 856, 1459, 1528, 1447, 1527, 1526, 41, 1514])).
% 1.60/1.37 tff(1536,plain,(hskp4 | c0_1(a97) | c2_1(a97) | c3_1(a97) | hskp18), inference(lemma,lemma(discharge,[]))).
% 1.60/1.37 tff(1537,plain,
% 1.60/1.37 (c3_1(a97)),
% 1.60/1.37 inference(unit_resolution,[status(thm)],[1536, 1486, 31, 54, 52])).
% 1.60/1.37 tff(1538,plain,
% 1.60/1.37 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a97) | c2_1(a97) | (~c3_1(a97)) | (~ndr1_0) | c1_1(a97))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a97) | c2_1(a97) | (~c3_1(a97)) | (~ndr1_0) | c1_1(a97))),
% 1.60/1.37 inference(rewrite,[status(thm)],[])).
% 1.60/1.37 tff(1539,plain,
% 1.60/1.37 ((hskp0 | (~ndr1_0) | c2_1(a97) | c0_1(a97) | (~c3_1(a97)) | c2_1(a97) | c1_1(a97) | c0_1(a97)) <=> (hskp0 | c0_1(a97) | c2_1(a97) | (~c3_1(a97)) | (~ndr1_0) | c1_1(a97))),
% 1.60/1.37 inference(rewrite,[status(thm)],[])).
% 1.60/1.37 tff(1540,plain,
% 1.60/1.37 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a97) | c0_1(a97) | (~c3_1(a97)) | c2_1(a97) | c1_1(a97) | c0_1(a97))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a97) | c2_1(a97) | (~c3_1(a97)) | (~ndr1_0) | c1_1(a97)))),
% 1.60/1.37 inference(monotonicity,[status(thm)],[1539])).
% 1.60/1.37 tff(1541,plain,
% 1.60/1.37 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a97) | c0_1(a97) | (~c3_1(a97)) | c2_1(a97) | c1_1(a97) | c0_1(a97))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a97) | c2_1(a97) | (~c3_1(a97)) | (~ndr1_0) | c1_1(a97))),
% 1.60/1.37 inference(transitivity,[status(thm)],[1540, 1538])).
% 1.60/1.37 tff(1542,plain,
% 1.60/1.37 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a97) | c0_1(a97) | (~c3_1(a97)) | c2_1(a97) | c1_1(a97) | c0_1(a97))),
% 1.60/1.37 inference(quant_inst,[status(thm)],[])).
% 1.60/1.37 tff(1543,plain,
% 1.60/1.37 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a97) | c2_1(a97) | (~c3_1(a97)) | (~ndr1_0) | c1_1(a97)),
% 1.60/1.37 inference(modus_ponens,[status(thm)],[1542, 1541])).
% 1.60/1.37 tff(1544,plain,
% 1.60/1.37 (hskp0 | c0_1(a97) | (~c3_1(a97)) | c1_1(a97)),
% 1.60/1.37 inference(unit_resolution,[status(thm)],[1543, 126, 31, 211])).
% 1.60/1.37 tff(1545,plain,
% 1.60/1.37 (c1_1(a97)),
% 1.60/1.37 inference(unit_resolution,[status(thm)],[1544, 1537, 54, 65])).
% 1.60/1.37 tff(1546,plain,
% 1.60/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a97) | c2_1(a138) | c2_1(a97) | (~c3_1(a97)) | (~ndr1_0) | (~c1_1(a97)) | c1_1(a138) | (~c3_1(a138)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a97) | c2_1(a138) | c2_1(a97) | (~c3_1(a97)) | (~ndr1_0) | (~c1_1(a97)) | c1_1(a138) | (~c3_1(a138)))),
% 1.60/1.37 inference(rewrite,[status(thm)],[])).
% 1.60/1.37 tff(1547,plain,
% 1.60/1.37 (((~ndr1_0) | c2_1(a138) | c1_1(a138) | (~c3_1(a138)) | c0_1(a97) | (~c3_1(a97)) | (~c1_1(a97)) | c2_1(a97) | c0_1(a97) | (~c3_1(a97))) <=> (c0_1(a97) | c2_1(a138) | c2_1(a97) | (~c3_1(a97)) | (~ndr1_0) | (~c1_1(a97)) | c1_1(a138) | (~c3_1(a138)))),
% 1.60/1.37 inference(rewrite,[status(thm)],[])).
% 1.60/1.37 tff(1548,plain,
% 1.60/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a138) | c1_1(a138) | (~c3_1(a138)) | c0_1(a97) | (~c3_1(a97)) | (~c1_1(a97)) | c2_1(a97) | c0_1(a97) | (~c3_1(a97)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a97) | c2_1(a138) | c2_1(a97) | (~c3_1(a97)) | (~ndr1_0) | (~c1_1(a97)) | c1_1(a138) | (~c3_1(a138))))),
% 1.60/1.37 inference(monotonicity,[status(thm)],[1547])).
% 1.60/1.37 tff(1549,plain,
% 1.60/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a138) | c1_1(a138) | (~c3_1(a138)) | c0_1(a97) | (~c3_1(a97)) | (~c1_1(a97)) | c2_1(a97) | c0_1(a97) | (~c3_1(a97)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a97) | c2_1(a138) | c2_1(a97) | (~c3_1(a97)) | (~ndr1_0) | (~c1_1(a97)) | c1_1(a138) | (~c3_1(a138)))),
% 1.60/1.37 inference(transitivity,[status(thm)],[1548, 1546])).
% 1.60/1.37 tff(1550,plain,
% 1.60/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a138) | c1_1(a138) | (~c3_1(a138)) | c0_1(a97) | (~c3_1(a97)) | (~c1_1(a97)) | c2_1(a97) | c0_1(a97) | (~c3_1(a97)))),
% 1.60/1.37 inference(quant_inst,[status(thm)],[])).
% 1.60/1.37 tff(1551,plain,
% 1.60/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a97) | c2_1(a138) | c2_1(a97) | (~c3_1(a97)) | (~ndr1_0) | (~c1_1(a97)) | c1_1(a138) | (~c3_1(a138))),
% 1.62/1.37 inference(modus_ponens,[status(thm)],[1550, 1549])).
% 1.62/1.37 tff(1552,plain,
% 1.62/1.37 ((~c3_1(a97)) | (~c1_1(a97)) | c1_1(a138)),
% 1.62/1.37 inference(unit_resolution,[status(thm)],[1551, 126, 1477, 54, 1447, 31, 1135])).
% 1.62/1.37 tff(1553,plain,
% 1.62/1.37 (c1_1(a138)),
% 1.62/1.37 inference(unit_resolution,[status(thm)],[1552, 1545, 1537])).
% 1.62/1.37 tff(1554,plain,
% 1.62/1.37 (hskp20),
% 1.62/1.37 inference(unit_resolution,[status(thm)],[815, 1486, 52])).
% 1.62/1.37 tff(1555,plain,
% 1.62/1.37 (~c3_1(a132)),
% 1.62/1.37 inference(unit_resolution,[status(thm)],[720, 1554])).
% 1.62/1.37 tff(1556,plain,
% 1.62/1.37 (~c2_1(a132)),
% 1.62/1.37 inference(unit_resolution,[status(thm)],[740, 1554])).
% 1.62/1.37 tff(1557,plain,
% 1.62/1.37 (~c1_1(a132)),
% 1.62/1.37 inference(unit_resolution,[status(thm)],[726, 1554])).
% 1.62/1.37 tff(1558,plain,
% 1.62/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a138) | c1_1(a132) | c2_1(a132) | c3_1(a132) | (~ndr1_0) | (~c0_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) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a138) | c1_1(a132) | c2_1(a132) | c3_1(a132) | (~ndr1_0) | (~c0_1(a132)) | (~c3_1(a138)) | (~c1_1(a138)))),
% 1.62/1.37 inference(rewrite,[status(thm)],[])).
% 1.62/1.37 tff(1559,plain,
% 1.62/1.37 (((~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138)) | c2_1(a132) | c3_1(a132) | (~c0_1(a132)) | c1_1(a132) | c3_1(a132) | (~c0_1(a132))) <=> (c2_1(a138) | c1_1(a132) | c2_1(a132) | c3_1(a132) | (~ndr1_0) | (~c0_1(a132)) | (~c3_1(a138)) | (~c1_1(a138)))),
% 1.62/1.37 inference(rewrite,[status(thm)],[])).
% 1.62/1.37 tff(1560,plain,
% 1.62/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138)) | c2_1(a132) | c3_1(a132) | (~c0_1(a132)) | c1_1(a132) | c3_1(a132) | (~c0_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a138) | c1_1(a132) | c2_1(a132) | c3_1(a132) | (~ndr1_0) | (~c0_1(a132)) | (~c3_1(a138)) | (~c1_1(a138))))),
% 1.62/1.37 inference(monotonicity,[status(thm)],[1559])).
% 1.62/1.37 tff(1561,plain,
% 1.62/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138)) | c2_1(a132) | c3_1(a132) | (~c0_1(a132)) | c1_1(a132) | c3_1(a132) | (~c0_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a138) | c1_1(a132) | c2_1(a132) | c3_1(a132) | (~ndr1_0) | (~c0_1(a132)) | (~c3_1(a138)) | (~c1_1(a138)))),
% 1.62/1.37 inference(transitivity,[status(thm)],[1560, 1558])).
% 1.62/1.37 tff(1562,plain,
% 1.62/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138)) | c2_1(a132) | c3_1(a132) | (~c0_1(a132)) | c1_1(a132) | c3_1(a132) | (~c0_1(a132)))),
% 1.62/1.37 inference(quant_inst,[status(thm)],[])).
% 1.62/1.37 tff(1563,plain,
% 1.62/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a138) | c1_1(a132) | c2_1(a132) | c3_1(a132) | (~ndr1_0) | (~c0_1(a132)) | (~c3_1(a138)) | (~c1_1(a138))),
% 1.62/1.37 inference(modus_ponens,[status(thm)],[1562, 1561])).
% 1.62/1.37 tff(1564,plain,
% 1.62/1.37 (~c0_1(a132)),
% 1.62/1.37 inference(unit_resolution,[status(thm)],[1563, 126, 1477, 1447, 1557, 1556, 1555, 20, 1553])).
% 1.62/1.37 tff(1565,plain,
% 1.62/1.37 (hskp7),
% 1.62/1.37 inference(unit_resolution,[status(thm)],[1503, 1486])).
% 1.62/1.37 tff(1566,plain,
% 1.62/1.37 (~c0_1(a106)),
% 1.62/1.37 inference(unit_resolution,[status(thm)],[969, 1565])).
% 1.62/1.37 tff(1567,plain,
% 1.62/1.37 (c3_1(a106)),
% 1.62/1.37 inference(unit_resolution,[status(thm)],[919, 1565])).
% 1.62/1.37 tff(1568,plain,
% 1.62/1.37 (c2_1(a106)),
% 1.62/1.37 inference(unit_resolution,[status(thm)],[930, 1565])).
% 1.62/1.37 tff(1569,plain,
% 1.62/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a138) | c2_1(a132) | c3_1(a132) | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | c0_1(a132) | (~c0_1(a138)) | (~c1_1(a138)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a138) | c2_1(a132) | c3_1(a132) | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | c0_1(a132) | (~c0_1(a138)) | (~c1_1(a138)))),
% 1.62/1.38 inference(rewrite,[status(thm)],[])).
% 1.62/1.38 tff(1570,plain,
% 1.62/1.38 (((~ndr1_0) | c2_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | c0_1(a106) | (~c2_1(a106)) | (~c3_1(a106)) | c2_1(a132) | c0_1(a132) | c3_1(a132)) <=> (c2_1(a138) | c2_1(a132) | c3_1(a132) | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | c0_1(a132) | (~c0_1(a138)) | (~c1_1(a138)))),
% 1.62/1.38 inference(rewrite,[status(thm)],[])).
% 1.62/1.38 tff(1571,plain,
% 1.62/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | c0_1(a106) | (~c2_1(a106)) | (~c3_1(a106)) | c2_1(a132) | c0_1(a132) | c3_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a138) | c2_1(a132) | c3_1(a132) | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | c0_1(a132) | (~c0_1(a138)) | (~c1_1(a138))))),
% 1.62/1.38 inference(monotonicity,[status(thm)],[1570])).
% 1.62/1.38 tff(1572,plain,
% 1.62/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | c0_1(a106) | (~c2_1(a106)) | (~c3_1(a106)) | c2_1(a132) | c0_1(a132) | c3_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a138) | c2_1(a132) | c3_1(a132) | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | c0_1(a132) | (~c0_1(a138)) | (~c1_1(a138)))),
% 1.62/1.38 inference(transitivity,[status(thm)],[1571, 1569])).
% 1.62/1.38 tff(1573,plain,
% 1.62/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | c0_1(a106) | (~c2_1(a106)) | (~c3_1(a106)) | c2_1(a132) | c0_1(a132) | c3_1(a132))),
% 1.62/1.38 inference(quant_inst,[status(thm)],[])).
% 1.62/1.38 tff(1574,plain,
% 1.62/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a138) | c2_1(a132) | c3_1(a132) | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | c0_1(a132) | (~c0_1(a138)) | (~c1_1(a138))),
% 1.62/1.38 inference(modus_ponens,[status(thm)],[1573, 1572])).
% 1.62/1.38 tff(1575,plain,
% 1.62/1.38 ($false),
% 1.62/1.38 inference(unit_resolution,[status(thm)],[1574, 126, 1459, 1568, 1567, 1447, 1556, 1555, 1566, 525, 1553, 1564])).
% 1.62/1.38 tff(1576,plain,(hskp18 | c0_1(a97) | c2_1(a97)), inference(lemma,lemma(discharge,[]))).
% 1.62/1.38 tff(1577,plain,
% 1.62/1.38 (hskp18),
% 1.62/1.38 inference(unit_resolution,[status(thm)],[1576, 54, 31])).
% 1.62/1.38 tff(1578,plain,
% 1.62/1.38 (~c1_1(a129)),
% 1.62/1.38 inference(unit_resolution,[status(thm)],[297, 1577])).
% 1.62/1.38 tff(1579,plain,
% 1.62/1.38 (c2_1(a129)),
% 1.62/1.38 inference(unit_resolution,[status(thm)],[308, 1577])).
% 1.62/1.38 tff(1580,plain,
% 1.62/1.38 (c0_1(a129)),
% 1.62/1.38 inference(unit_resolution,[status(thm)],[319, 1577])).
% 1.62/1.38 tff(1581,plain,
% 1.62/1.38 (~c3_1(a129)),
% 1.62/1.38 inference(unit_resolution,[status(thm)],[891, 126, 1580, 1579, 1578, 10])).
% 1.62/1.38 tff(1582,plain,
% 1.62/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a138) | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129) | c1_1(a138) | (~c0_1(a138)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a138) | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129) | c1_1(a138) | (~c0_1(a138)))),
% 1.62/1.38 inference(rewrite,[status(thm)],[])).
% 1.62/1.38 tff(1583,plain,
% 1.62/1.38 (((~ndr1_0) | c3_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c2_1(a138) | c1_1(a138) | (~c0_1(a138))) <=> (c2_1(a138) | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129) | c1_1(a138) | (~c0_1(a138)))),
% 1.62/1.38 inference(rewrite,[status(thm)],[])).
% 1.62/1.38 tff(1584,plain,
% 1.62/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c2_1(a138) | c1_1(a138) | (~c0_1(a138)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a138) | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129) | c1_1(a138) | (~c0_1(a138))))),
% 1.62/1.38 inference(monotonicity,[status(thm)],[1583])).
% 1.62/1.38 tff(1585,plain,
% 1.62/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c2_1(a138) | c1_1(a138) | (~c0_1(a138)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a138) | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129) | c1_1(a138) | (~c0_1(a138)))),
% 1.62/1.38 inference(transitivity,[status(thm)],[1584, 1582])).
% 1.62/1.38 tff(1586,plain,
% 1.62/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c2_1(a138) | c1_1(a138) | (~c0_1(a138)))),
% 1.62/1.38 inference(quant_inst,[status(thm)],[])).
% 1.62/1.38 tff(1587,plain,
% 1.62/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a138) | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129) | c1_1(a138) | (~c0_1(a138))),
% 1.62/1.38 inference(modus_ponens,[status(thm)],[1586, 1585])).
% 1.62/1.38 tff(1588,plain,
% 1.62/1.38 (c1_1(a138)),
% 1.62/1.38 inference(unit_resolution,[status(thm)],[1587, 126, 1459, 1580, 1579, 1447, 1578, 143, 1581])).
% 1.62/1.38 tff(1589,plain,
% 1.62/1.38 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 1.62/1.38 inference(bind,[status(th)],[])).
% 1.62/1.38 tff(1590,plain,
% 1.62/1.38 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.62/1.38 inference(quant_intro,[status(thm)],[1589])).
% 1.62/1.38 tff(1591,plain,
% 1.62/1.38 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.62/1.38 inference(rewrite,[status(thm)],[])).
% 1.62/1.38 tff(1592,plain,
% 1.62/1.38 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp11) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp11))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 1.62/1.38 inference(bind,[status(th)],[])).
% 1.62/1.38 tff(1593,plain,
% 1.62/1.38 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.62/1.38 inference(quant_intro,[status(thm)],[1592])).
% 1.62/1.38 tff(1594,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause183')).
% 1.62/1.38 tff(1595,plain,
% 1.62/1.38 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.62/1.38 inference(modus_ponens,[status(thm)],[1594, 1593])).
% 1.62/1.38 tff(1596,plain,
% 1.62/1.38 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.62/1.38 inference(modus_ponens,[status(thm)],[1595, 1591])).
% 1.62/1.38 tff(1597,plain,(
% 1.62/1.38 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.62/1.38 inference(skolemize,[status(sab)],[1596])).
% 1.62/1.38 tff(1598,plain,
% 1.62/1.38 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.62/1.38 inference(modus_ponens,[status(thm)],[1597, 1590])).
% 1.62/1.38 tff(1599,plain,
% 1.62/1.38 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | c2_1(a138) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129) | (~c3_1(a138)) | (~c1_1(a138)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp11 | c2_1(a138) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129) | (~c3_1(a138)) | (~c1_1(a138)))),
% 1.62/1.38 inference(rewrite,[status(thm)],[])).
% 1.62/1.38 tff(1600,plain,
% 1.62/1.38 ((hskp11 | (~ndr1_0) | c3_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138))) <=> (hskp11 | c2_1(a138) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129) | (~c3_1(a138)) | (~c1_1(a138)))),
% 1.62/1.38 inference(rewrite,[status(thm)],[])).
% 1.62/1.38 tff(1601,plain,
% 1.62/1.38 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | c2_1(a138) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129) | (~c3_1(a138)) | (~c1_1(a138))))),
% 1.62/1.38 inference(monotonicity,[status(thm)],[1600])).
% 1.62/1.38 tff(1602,plain,
% 1.62/1.38 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp11 | c2_1(a138) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129) | (~c3_1(a138)) | (~c1_1(a138)))),
% 1.62/1.38 inference(transitivity,[status(thm)],[1601, 1599])).
% 1.62/1.38 tff(1603,plain,
% 1.62/1.38 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138)))),
% 1.62/1.38 inference(quant_inst,[status(thm)],[])).
% 1.62/1.38 tff(1604,plain,
% 1.62/1.38 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp11 | c2_1(a138) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129) | (~c3_1(a138)) | (~c1_1(a138))),
% 1.62/1.38 inference(modus_ponens,[status(thm)],[1603, 1602])).
% 1.62/1.38 tff(1605,plain,
% 1.62/1.38 (hskp11),
% 1.62/1.38 inference(unit_resolution,[status(thm)],[1604, 126, 1477, 1580, 1579, 1447, 1598, 1588, 1581])).
% 1.62/1.38 tff(1606,plain,
% 1.62/1.38 (~c1_1(a112)),
% 1.62/1.38 inference(unit_resolution,[status(thm)],[848, 1605])).
% 1.62/1.38 tff(1607,plain,
% 1.62/1.38 (~c0_1(a112)),
% 1.62/1.38 inference(unit_resolution,[status(thm)],[854, 1605])).
% 1.62/1.38 tff(1608,plain,
% 1.62/1.38 (c3_1(a112)),
% 1.62/1.38 inference(unit_resolution,[status(thm)],[1052, 1605])).
% 1.62/1.38 tff(1609,assumption,(~c2_1(a112)), introduced(assumption)).
% 1.62/1.38 tff(1610,plain,
% 1.62/1.38 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a112) | c1_1(a112) | (~ndr1_0) | c2_1(a112) | (~c3_1(a112)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a112) | c1_1(a112) | (~ndr1_0) | c2_1(a112) | (~c3_1(a112)))),
% 1.62/1.38 inference(rewrite,[status(thm)],[])).
% 1.62/1.38 tff(1611,plain,
% 1.62/1.38 ((hskp0 | (~ndr1_0) | c2_1(a112) | c0_1(a112) | (~c3_1(a112)) | c2_1(a112) | c1_1(a112) | c0_1(a112)) <=> (hskp0 | c0_1(a112) | c1_1(a112) | (~ndr1_0) | c2_1(a112) | (~c3_1(a112)))),
% 1.62/1.38 inference(rewrite,[status(thm)],[])).
% 1.62/1.38 tff(1612,plain,
% 1.62/1.38 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a112) | c0_1(a112) | (~c3_1(a112)) | c2_1(a112) | c1_1(a112) | c0_1(a112))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a112) | c1_1(a112) | (~ndr1_0) | c2_1(a112) | (~c3_1(a112))))),
% 1.62/1.38 inference(monotonicity,[status(thm)],[1611])).
% 1.62/1.38 tff(1613,plain,
% 1.62/1.38 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a112) | c0_1(a112) | (~c3_1(a112)) | c2_1(a112) | c1_1(a112) | c0_1(a112))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a112) | c1_1(a112) | (~ndr1_0) | c2_1(a112) | (~c3_1(a112)))),
% 1.62/1.38 inference(transitivity,[status(thm)],[1612, 1610])).
% 1.62/1.38 tff(1614,plain,
% 1.62/1.38 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a112) | c0_1(a112) | (~c3_1(a112)) | c2_1(a112) | c1_1(a112) | c0_1(a112))),
% 1.62/1.38 inference(quant_inst,[status(thm)],[])).
% 1.62/1.38 tff(1615,plain,
% 1.62/1.38 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a112) | c1_1(a112) | (~ndr1_0) | c2_1(a112) | (~c3_1(a112))),
% 1.62/1.38 inference(modus_ponens,[status(thm)],[1614, 1613])).
% 1.62/1.38 tff(1616,plain,
% 1.62/1.38 ($false),
% 1.62/1.38 inference(unit_resolution,[status(thm)],[1615, 126, 94, 1116, 1115, 1137, 211, 1609])).
% 1.62/1.38 tff(1617,plain,(c2_1(a112) | hskp0 | (~c3_1(a112)) | c0_1(a112) | c1_1(a112)), inference(lemma,lemma(discharge,[]))).
% 1.62/1.38 tff(1618,plain,
% 1.62/1.38 (c2_1(a112)),
% 1.62/1.38 inference(unit_resolution,[status(thm)],[1617, 65, 1608, 1607, 1606])).
% 1.62/1.38 tff(1619,plain,
% 1.62/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a97) | c2_1(a138) | c0_1(a112) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c2_1(a112)) | (~c3_1(a112)) | (~c0_1(a138)) | (~c1_1(a138)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a97) | c2_1(a138) | c0_1(a112) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c2_1(a112)) | (~c3_1(a112)) | (~c0_1(a138)) | (~c1_1(a138)))),
% 1.62/1.38 inference(rewrite,[status(thm)],[])).
% 1.62/1.38 tff(1620,plain,
% 1.62/1.38 (((~ndr1_0) | c2_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | c0_1(a112) | (~c2_1(a112)) | (~c3_1(a112)) | c2_1(a97) | c0_1(a97) | c3_1(a97)) <=> (c0_1(a97) | c2_1(a138) | c0_1(a112) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c2_1(a112)) | (~c3_1(a112)) | (~c0_1(a138)) | (~c1_1(a138)))),
% 1.62/1.38 inference(rewrite,[status(thm)],[])).
% 1.62/1.38 tff(1621,plain,
% 1.62/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | c0_1(a112) | (~c2_1(a112)) | (~c3_1(a112)) | c2_1(a97) | c0_1(a97) | c3_1(a97))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a97) | c2_1(a138) | c0_1(a112) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c2_1(a112)) | (~c3_1(a112)) | (~c0_1(a138)) | (~c1_1(a138))))),
% 1.62/1.38 inference(monotonicity,[status(thm)],[1620])).
% 1.62/1.38 tff(1622,plain,
% 1.62/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | c0_1(a112) | (~c2_1(a112)) | (~c3_1(a112)) | c2_1(a97) | c0_1(a97) | c3_1(a97))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a97) | c2_1(a138) | c0_1(a112) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c2_1(a112)) | (~c3_1(a112)) | (~c0_1(a138)) | (~c1_1(a138)))),
% 1.62/1.38 inference(transitivity,[status(thm)],[1621, 1619])).
% 1.62/1.38 tff(1623,plain,
% 1.62/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | c0_1(a112) | (~c2_1(a112)) | (~c3_1(a112)) | c2_1(a97) | c0_1(a97) | c3_1(a97))),
% 1.62/1.38 inference(quant_inst,[status(thm)],[])).
% 1.62/1.38 tff(1624,plain,
% 1.62/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a97) | c2_1(a138) | c0_1(a112) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c2_1(a112)) | (~c3_1(a112)) | (~c0_1(a138)) | (~c1_1(a138))),
% 1.62/1.38 inference(modus_ponens,[status(thm)],[1623, 1622])).
% 1.62/1.38 tff(1625,plain,
% 1.62/1.38 (c3_1(a97) | (~c2_1(a112))),
% 1.62/1.38 inference(unit_resolution,[status(thm)],[1624, 126, 1459, 1608, 54, 1447, 1607, 31, 525, 1588])).
% 1.62/1.38 tff(1626,plain,
% 1.62/1.38 (c3_1(a97)),
% 1.62/1.38 inference(unit_resolution,[status(thm)],[1625, 1618])).
% 1.62/1.38 tff(1627,plain,
% 1.62/1.38 (c1_1(a97)),
% 1.62/1.38 inference(unit_resolution,[status(thm)],[1544, 1626, 54, 65])).
% 1.62/1.38 tff(1628,plain,
% 1.62/1.38 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 1.62/1.38 inference(bind,[status(th)],[])).
% 1.62/1.38 tff(1629,plain,
% 1.62/1.38 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.62/1.38 inference(quant_intro,[status(thm)],[1628])).
% 1.62/1.38 tff(1630,plain,
% 1.62/1.38 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.62/1.38 inference(rewrite,[status(thm)],[])).
% 1.62/1.38 tff(1631,plain,
% 1.62/1.38 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp0) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp0))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 1.62/1.38 inference(bind,[status(th)],[])).
% 1.62/1.38 tff(1632,plain,
% 1.62/1.38 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.62/1.38 inference(quant_intro,[status(thm)],[1631])).
% 1.62/1.38 tff(1633,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause174')).
% 1.62/1.39 tff(1634,plain,
% 1.62/1.39 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.62/1.39 inference(modus_ponens,[status(thm)],[1633, 1632])).
% 1.62/1.39 tff(1635,plain,
% 1.62/1.39 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.62/1.39 inference(modus_ponens,[status(thm)],[1634, 1630])).
% 1.62/1.39 tff(1636,plain,(
% 1.62/1.39 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.62/1.39 inference(skolemize,[status(sab)],[1635])).
% 1.62/1.39 tff(1637,plain,
% 1.62/1.39 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.62/1.39 inference(modus_ponens,[status(thm)],[1636, 1629])).
% 1.62/1.39 tff(1638,plain,
% 1.62/1.39 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp0 | c0_1(a97) | c1_1(a129) | (~c3_1(a97)) | (~ndr1_0) | (~c1_1(a97)) | (~c0_1(a129)) | c3_1(a129))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp0 | c0_1(a97) | c1_1(a129) | (~c3_1(a97)) | (~ndr1_0) | (~c1_1(a97)) | (~c0_1(a129)) | c3_1(a129))),
% 1.62/1.39 inference(rewrite,[status(thm)],[])).
% 1.62/1.39 tff(1639,plain,
% 1.62/1.39 ((hskp0 | (~ndr1_0) | c1_1(a129) | c3_1(a129) | (~c0_1(a129)) | c0_1(a97) | (~c3_1(a97)) | (~c1_1(a97))) <=> (hskp0 | c0_1(a97) | c1_1(a129) | (~c3_1(a97)) | (~ndr1_0) | (~c1_1(a97)) | (~c0_1(a129)) | c3_1(a129))),
% 1.62/1.39 inference(rewrite,[status(thm)],[])).
% 1.62/1.39 tff(1640,plain,
% 1.62/1.39 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp0 | (~ndr1_0) | c1_1(a129) | c3_1(a129) | (~c0_1(a129)) | c0_1(a97) | (~c3_1(a97)) | (~c1_1(a97)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp0 | c0_1(a97) | c1_1(a129) | (~c3_1(a97)) | (~ndr1_0) | (~c1_1(a97)) | (~c0_1(a129)) | c3_1(a129)))),
% 1.62/1.39 inference(monotonicity,[status(thm)],[1639])).
% 1.62/1.39 tff(1641,plain,
% 1.62/1.39 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp0 | (~ndr1_0) | c1_1(a129) | c3_1(a129) | (~c0_1(a129)) | c0_1(a97) | (~c3_1(a97)) | (~c1_1(a97)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp0 | c0_1(a97) | c1_1(a129) | (~c3_1(a97)) | (~ndr1_0) | (~c1_1(a97)) | (~c0_1(a129)) | c3_1(a129))),
% 1.62/1.39 inference(transitivity,[status(thm)],[1640, 1638])).
% 1.62/1.39 tff(1642,plain,
% 1.62/1.39 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp0 | (~ndr1_0) | c1_1(a129) | c3_1(a129) | (~c0_1(a129)) | c0_1(a97) | (~c3_1(a97)) | (~c1_1(a97)))),
% 1.62/1.39 inference(quant_inst,[status(thm)],[])).
% 1.62/1.39 tff(1643,plain,
% 1.62/1.39 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp0 | c0_1(a97) | c1_1(a129) | (~c3_1(a97)) | (~ndr1_0) | (~c1_1(a97)) | (~c0_1(a129)) | c3_1(a129)),
% 1.62/1.39 inference(modus_ponens,[status(thm)],[1642, 1641])).
% 1.62/1.39 tff(1644,plain,
% 1.62/1.39 ((~c3_1(a97)) | (~c1_1(a97))),
% 1.62/1.39 inference(unit_resolution,[status(thm)],[1643, 126, 65, 1580, 54, 1578, 1637, 1581])).
% 1.62/1.39 tff(1645,plain,
% 1.62/1.39 ($false),
% 1.62/1.39 inference(unit_resolution,[status(thm)],[1644, 1627, 1626])).
% 1.62/1.39 tff(1646,plain,(c0_1(a97) | c2_1(a97)), inference(lemma,lemma(discharge,[]))).
% 1.62/1.39 tff(1647,plain,
% 1.62/1.39 (c0_1(a97)),
% 1.62/1.39 inference(unit_resolution,[status(thm)],[1646, 31])).
% 1.62/1.39 tff(1648,plain,
% 1.62/1.39 (hskp4),
% 1.62/1.39 inference(unit_resolution,[status(thm)],[881, 53, 1647, 52, 31])).
% 1.62/1.39 tff(1649,plain,
% 1.62/1.39 (c0_1(a103)),
% 1.62/1.39 inference(unit_resolution,[status(thm)],[92, 1648])).
% 1.62/1.39 tff(1650,plain,
% 1.62/1.39 (~c3_1(a103)),
% 1.62/1.39 inference(unit_resolution,[status(thm)],[81, 1648])).
% 1.62/1.39 tff(1651,plain,
% 1.62/1.39 (c2_1(a103)),
% 1.62/1.39 inference(unit_resolution,[status(thm)],[157, 1648])).
% 1.62/1.39 tff(1652,plain,
% 1.62/1.39 (c1_1(a97)),
% 1.62/1.39 inference(unit_resolution,[status(thm)],[328, 1651, 1647, 53, 1650, 31, 1649])).
% 1.62/1.39 tff(1653,plain,
% 1.62/1.39 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp28 | c2_1(a138) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | c1_1(a138) | (~c3_1(a138)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp28 | c2_1(a138) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | c1_1(a138) | (~c3_1(a138)))),
% 1.62/1.39 inference(rewrite,[status(thm)],[])).
% 1.62/1.39 tff(1654,plain,
% 1.62/1.39 ((hskp28 | (~ndr1_0) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c2_1(a138) | c1_1(a138) | (~c3_1(a138))) <=> (hskp28 | c2_1(a138) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | c1_1(a138) | (~c3_1(a138)))),
% 1.62/1.39 inference(rewrite,[status(thm)],[])).
% 1.62/1.39 tff(1655,plain,
% 1.62/1.39 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c2_1(a138) | c1_1(a138) | (~c3_1(a138)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp28 | c2_1(a138) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | c1_1(a138) | (~c3_1(a138))))),
% 1.62/1.39 inference(monotonicity,[status(thm)],[1654])).
% 1.62/1.39 tff(1656,plain,
% 1.62/1.39 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c2_1(a138) | c1_1(a138) | (~c3_1(a138)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp28 | c2_1(a138) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | c1_1(a138) | (~c3_1(a138)))),
% 1.62/1.39 inference(transitivity,[status(thm)],[1655, 1653])).
% 1.62/1.39 tff(1657,plain,
% 1.62/1.39 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c2_1(a138) | c1_1(a138) | (~c3_1(a138)))),
% 1.62/1.39 inference(quant_inst,[status(thm)],[])).
% 1.62/1.39 tff(1658,plain,
% 1.62/1.39 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp28 | c2_1(a138) | c2_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | c1_1(a138) | (~c3_1(a138))),
% 1.62/1.39 inference(modus_ponens,[status(thm)],[1657, 1656])).
% 1.62/1.39 tff(1659,plain,
% 1.62/1.39 (hskp28 | (~c0_1(a97)) | (~c1_1(a97)) | c1_1(a138)),
% 1.62/1.39 inference(unit_resolution,[status(thm)],[1658, 126, 1477, 1447, 31, 340])).
% 1.62/1.39 tff(1660,plain,
% 1.62/1.39 (c1_1(a138)),
% 1.62/1.39 inference(unit_resolution,[status(thm)],[1659, 145, 1647, 1652])).
% 1.62/1.39 tff(1661,plain,
% 1.62/1.39 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))),
% 1.62/1.39 inference(bind,[status(th)],[])).
% 1.62/1.39 tff(1662,plain,
% 1.62/1.39 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.62/1.39 inference(quant_intro,[status(thm)],[1661])).
% 1.62/1.39 tff(1663,plain,
% 1.62/1.39 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.62/1.39 inference(rewrite,[status(thm)],[])).
% 1.62/1.39 tff(1664,plain,
% 1.62/1.39 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | hskp16) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp16))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))))),
% 1.62/1.39 inference(bind,[status(th)],[])).
% 1.62/1.39 tff(1665,plain,
% 1.62/1.39 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.62/1.39 inference(quant_intro,[status(thm)],[1664])).
% 1.62/1.39 tff(1666,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause178')).
% 1.62/1.39 tff(1667,plain,
% 1.62/1.39 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.62/1.39 inference(modus_ponens,[status(thm)],[1666, 1665])).
% 1.62/1.39 tff(1668,plain,
% 1.62/1.39 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.62/1.39 inference(modus_ponens,[status(thm)],[1667, 1663])).
% 1.62/1.39 tff(1669,plain,(
% 1.62/1.39 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.62/1.39 inference(skolemize,[status(sab)],[1668])).
% 1.62/1.39 tff(1670,plain,
% 1.62/1.39 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.62/1.39 inference(modus_ponens,[status(thm)],[1669, 1662])).
% 1.62/1.39 tff(1671,plain,
% 1.62/1.39 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp16 | c0_1(a108) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a108)) | (~c2_1(a108)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp16 | c0_1(a108) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a108)) | (~c2_1(a108)))),
% 1.62/1.39 inference(rewrite,[status(thm)],[])).
% 1.62/1.39 tff(1672,plain,
% 1.62/1.39 ((hskp16 | (~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a108) | (~c2_1(a108)) | (~c1_1(a108))) <=> (hskp16 | c0_1(a108) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a108)) | (~c2_1(a108)))),
% 1.62/1.39 inference(rewrite,[status(thm)],[])).
% 1.62/1.39 tff(1673,plain,
% 1.62/1.39 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a108) | (~c2_1(a108)) | (~c1_1(a108)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp16 | c0_1(a108) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a108)) | (~c2_1(a108))))),
% 1.62/1.39 inference(monotonicity,[status(thm)],[1672])).
% 1.62/1.39 tff(1674,plain,
% 1.62/1.39 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a108) | (~c2_1(a108)) | (~c1_1(a108)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp16 | c0_1(a108) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a108)) | (~c2_1(a108)))),
% 1.62/1.39 inference(transitivity,[status(thm)],[1673, 1671])).
% 1.62/1.39 tff(1675,plain,
% 1.62/1.39 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a108) | (~c2_1(a108)) | (~c1_1(a108)))),
% 1.62/1.39 inference(quant_inst,[status(thm)],[])).
% 1.62/1.39 tff(1676,plain,
% 1.62/1.39 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp16 | c0_1(a108) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a108)) | (~c2_1(a108))),
% 1.62/1.39 inference(modus_ponens,[status(thm)],[1675, 1674])).
% 1.62/1.39 tff(1677,plain,
% 1.62/1.39 (hskp16),
% 1.62/1.39 inference(unit_resolution,[status(thm)],[1676, 126, 1088, 1077, 161, 174, 1066, 160, 1670])).
% 1.62/1.39 tff(1678,plain,
% 1.62/1.39 (c0_1(a122)),
% 1.62/1.39 inference(unit_resolution,[status(thm)],[1382, 1677])).
% 1.62/1.39 tff(1679,assumption,(c1_1(a138)), introduced(assumption)).
% 1.62/1.39 tff(1680,plain,
% 1.62/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a138) | c0_1(a108) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a103)) | (~c1_1(a108)) | (~c2_1(a108)) | (~c0_1(a138)) | (~c1_1(a138)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a138) | c0_1(a108) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a103)) | (~c1_1(a108)) | (~c2_1(a108)) | (~c0_1(a138)) | (~c1_1(a138)))),
% 1.62/1.39 inference(rewrite,[status(thm)],[])).
% 1.62/1.39 tff(1681,plain,
% 1.62/1.39 (((~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a103)) | c2_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | c0_1(a108) | (~c2_1(a108)) | (~c1_1(a108))) <=> (c2_1(a138) | c0_1(a108) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a103)) | (~c1_1(a108)) | (~c2_1(a108)) | (~c0_1(a138)) | (~c1_1(a138)))),
% 1.62/1.39 inference(rewrite,[status(thm)],[])).
% 1.62/1.39 tff(1682,plain,
% 1.62/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a103)) | c2_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | c0_1(a108) | (~c2_1(a108)) | (~c1_1(a108)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a138) | c0_1(a108) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a103)) | (~c1_1(a108)) | (~c2_1(a108)) | (~c0_1(a138)) | (~c1_1(a138))))),
% 1.62/1.39 inference(monotonicity,[status(thm)],[1681])).
% 1.62/1.39 tff(1683,plain,
% 1.62/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a103)) | c2_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | c0_1(a108) | (~c2_1(a108)) | (~c1_1(a108)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a138) | c0_1(a108) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a103)) | (~c1_1(a108)) | (~c2_1(a108)) | (~c0_1(a138)) | (~c1_1(a138)))),
% 1.62/1.39 inference(transitivity,[status(thm)],[1682, 1680])).
% 1.62/1.39 tff(1684,plain,
% 1.62/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a103)) | c2_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | c0_1(a108) | (~c2_1(a108)) | (~c1_1(a108)))),
% 1.62/1.39 inference(quant_inst,[status(thm)],[])).
% 1.62/1.39 tff(1685,plain,
% 1.62/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a138) | c0_1(a108) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a103)) | (~c1_1(a108)) | (~c2_1(a108)) | (~c0_1(a138)) | (~c1_1(a138))),
% 1.62/1.39 inference(modus_ponens,[status(thm)],[1684, 1683])).
% 1.62/1.39 tff(1686,plain,
% 1.62/1.39 (~c1_1(a103)),
% 1.62/1.39 inference(unit_resolution,[status(thm)],[1685, 126, 1459, 1088, 1077, 161, 174, 1447, 1066, 381, 1679])).
% 1.62/1.39 tff(1687,plain,
% 1.62/1.39 (~c1_1(a122)),
% 1.62/1.39 inference(unit_resolution,[status(thm)],[552, 1677])).
% 1.62/1.39 tff(1688,plain,
% 1.62/1.39 (~c2_1(a122)),
% 1.62/1.39 inference(unit_resolution,[status(thm)],[463, 1677])).
% 1.62/1.39 tff(1689,plain,
% 1.62/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a122) | c2_1(a122) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c0_1(a122)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a122) | c2_1(a122) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c0_1(a122)))),
% 1.62/1.39 inference(rewrite,[status(thm)],[])).
% 1.62/1.39 tff(1690,plain,
% 1.62/1.39 (((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c2_1(a122) | c1_1(a122) | (~c0_1(a122))) <=> (c1_1(a122) | c2_1(a122) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c0_1(a122)))),
% 1.62/1.39 inference(rewrite,[status(thm)],[])).
% 1.62/1.39 tff(1691,plain,
% 1.62/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c2_1(a122) | c1_1(a122) | (~c0_1(a122)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a122) | c2_1(a122) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c0_1(a122))))),
% 1.62/1.39 inference(monotonicity,[status(thm)],[1690])).
% 1.62/1.39 tff(1692,plain,
% 1.62/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c2_1(a122) | c1_1(a122) | (~c0_1(a122)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a122) | c2_1(a122) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c0_1(a122)))),
% 1.62/1.39 inference(transitivity,[status(thm)],[1691, 1689])).
% 1.62/1.39 tff(1693,plain,
% 1.62/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c2_1(a122) | c1_1(a122) | (~c0_1(a122)))),
% 1.62/1.39 inference(quant_inst,[status(thm)],[])).
% 1.62/1.39 tff(1694,plain,
% 1.62/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a122) | c2_1(a122) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a103) | (~c0_1(a122))),
% 1.62/1.40 inference(modus_ponens,[status(thm)],[1693, 1692])).
% 1.62/1.40 tff(1695,plain,
% 1.62/1.40 ($false),
% 1.62/1.40 inference(unit_resolution,[status(thm)],[1694, 126, 1385, 161, 174, 428, 440, 160, 143, 354])).
% 1.62/1.40 tff(1696,plain,(c1_1(a103) | (~c0_1(a122)) | (~c0_1(a103)) | (~c2_1(a103)) | c1_1(a122) | c2_1(a122) | c3_1(a103)), inference(lemma,lemma(discharge,[]))).
% 1.62/1.40 tff(1697,plain,
% 1.62/1.40 ($false),
% 1.62/1.40 inference(unit_resolution,[status(thm)],[1696, 1688, 1687, 160, 174, 161, 1686, 1678])).
% 1.62/1.40 tff(1698,plain,((~hskp9) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | (~c1_1(a138))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.40 tff(1699,plain,
% 1.62/1.40 (~hskp9),
% 1.62/1.40 inference(unit_resolution,[status(thm)],[1698, 1660, 1651, 1649, 1650])).
% 1.62/1.40 tff(1700,plain,
% 1.62/1.40 (hskp18 | hskp11 | c3_1(a97) | (~c0_1(a97))),
% 1.62/1.40 inference(unit_resolution,[status(thm)],[841, 126, 31, 834])).
% 1.62/1.40 tff(1701,plain,
% 1.62/1.40 (hskp11),
% 1.62/1.40 inference(unit_resolution,[status(thm)],[1700, 53, 1647, 52])).
% 1.62/1.40 tff(1702,plain,
% 1.62/1.40 (c3_1(a112)),
% 1.62/1.40 inference(unit_resolution,[status(thm)],[1052, 1701])).
% 1.62/1.40 tff(1703,plain,
% 1.62/1.40 (hskp18 | hskp8 | c3_1(a97) | (~c1_1(a97))),
% 1.62/1.40 inference(unit_resolution,[status(thm)],[1029, 126, 1647, 1023])).
% 1.62/1.40 tff(1704,plain,
% 1.62/1.40 (hskp8),
% 1.62/1.40 inference(unit_resolution,[status(thm)],[1703, 1652, 52, 53])).
% 1.62/1.40 tff(1705,plain,
% 1.62/1.40 (~c0_1(a107)),
% 1.62/1.40 inference(unit_resolution,[status(thm)],[1102, 1704])).
% 1.62/1.40 tff(1706,plain,
% 1.62/1.40 (~c1_1(a112)),
% 1.62/1.40 inference(unit_resolution,[status(thm)],[848, 1701])).
% 1.62/1.40 tff(1707,plain,
% 1.62/1.40 (~c0_1(a112)),
% 1.62/1.40 inference(unit_resolution,[status(thm)],[854, 1701])).
% 1.62/1.40 tff(1708,plain,
% 1.62/1.40 (c3_1(a107)),
% 1.62/1.40 inference(unit_resolution,[status(thm)],[1041, 1704])).
% 1.62/1.40 tff(1709,plain,
% 1.62/1.40 (~c2_1(a107)),
% 1.62/1.40 inference(unit_resolution,[status(thm)],[1058, 1704])).
% 1.62/1.40 tff(1710,plain,
% 1.62/1.40 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp28 | c2_1(a138) | c2_1(a107) | (~ndr1_0) | c1_1(a107) | (~c3_1(a107)) | (~c0_1(a138)) | (~c1_1(a138)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp28 | c2_1(a138) | c2_1(a107) | (~ndr1_0) | c1_1(a107) | (~c3_1(a107)) | (~c0_1(a138)) | (~c1_1(a138)))),
% 1.62/1.40 inference(rewrite,[status(thm)],[])).
% 1.62/1.40 tff(1711,plain,
% 1.62/1.40 ((hskp28 | (~ndr1_0) | c2_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | c2_1(a107) | c1_1(a107) | (~c3_1(a107))) <=> (hskp28 | c2_1(a138) | c2_1(a107) | (~ndr1_0) | c1_1(a107) | (~c3_1(a107)) | (~c0_1(a138)) | (~c1_1(a138)))),
% 1.62/1.40 inference(rewrite,[status(thm)],[])).
% 1.62/1.40 tff(1712,plain,
% 1.62/1.40 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | c2_1(a107) | c1_1(a107) | (~c3_1(a107)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp28 | c2_1(a138) | c2_1(a107) | (~ndr1_0) | c1_1(a107) | (~c3_1(a107)) | (~c0_1(a138)) | (~c1_1(a138))))),
% 1.62/1.40 inference(monotonicity,[status(thm)],[1711])).
% 1.62/1.40 tff(1713,plain,
% 1.62/1.40 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | c2_1(a107) | c1_1(a107) | (~c3_1(a107)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp28 | c2_1(a138) | c2_1(a107) | (~ndr1_0) | c1_1(a107) | (~c3_1(a107)) | (~c0_1(a138)) | (~c1_1(a138)))),
% 1.62/1.40 inference(transitivity,[status(thm)],[1712, 1710])).
% 1.62/1.40 tff(1714,plain,
% 1.62/1.40 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a138) | (~c0_1(a138)) | (~c1_1(a138)) | c2_1(a107) | c1_1(a107) | (~c3_1(a107)))),
% 1.62/1.40 inference(quant_inst,[status(thm)],[])).
% 1.62/1.40 tff(1715,plain,
% 1.62/1.40 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp28 | c2_1(a138) | c2_1(a107) | (~ndr1_0) | c1_1(a107) | (~c3_1(a107)) | (~c0_1(a138)) | (~c1_1(a138))),
% 1.62/1.40 inference(modus_ponens,[status(thm)],[1714, 1713])).
% 1.62/1.40 tff(1716,plain,
% 1.62/1.40 (hskp28 | c1_1(a107) | (~c1_1(a138))),
% 1.62/1.40 inference(unit_resolution,[status(thm)],[1715, 126, 1459, 1708, 1447, 1709, 340])).
% 1.62/1.40 tff(1717,plain,
% 1.62/1.40 (c1_1(a107)),
% 1.62/1.40 inference(unit_resolution,[status(thm)],[1716, 145, 1660])).
% 1.62/1.40 tff(1718,assumption,(c1_1(a107)), introduced(assumption)).
% 1.62/1.40 tff(1719,plain,
% 1.62/1.40 ($false),
% 1.62/1.40 inference(unit_resolution,[status(thm)],[1144, 126, 1116, 1138, 1115, 1137, 1136, 1135, 1718, 1609])).
% 1.62/1.40 tff(1720,plain,(c2_1(a112) | (~c3_1(a112)) | (~c3_1(a107)) | c0_1(a112) | c1_1(a112) | c0_1(a107) | (~c1_1(a107))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.40 tff(1721,plain,
% 1.62/1.40 (c2_1(a112)),
% 1.62/1.40 inference(unit_resolution,[status(thm)],[1720, 1717, 1708, 1707, 1706, 1705, 1702])).
% 1.62/1.40 tff(1722,plain,
% 1.62/1.40 (hskp17 | hskp9 | (~c2_1(a112))),
% 1.62/1.40 inference(unit_resolution,[status(thm)],[1123, 126, 1702, 1707, 1114])).
% 1.62/1.40 tff(1723,plain,
% 1.62/1.40 (hskp17),
% 1.62/1.40 inference(unit_resolution,[status(thm)],[1722, 1721, 1699])).
% 1.62/1.40 tff(1724,plain,
% 1.62/1.40 (~c1_1(a124)),
% 1.62/1.40 inference(unit_resolution,[status(thm)],[1192, 1723])).
% 1.62/1.40 tff(1725,plain,
% 1.62/1.40 (~c3_1(a124)),
% 1.62/1.40 inference(unit_resolution,[status(thm)],[1186, 1723])).
% 1.62/1.40 tff(1726,plain,
% 1.62/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a138) | c1_1(a124) | c3_1(a124) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a124)) | (~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) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a138) | c1_1(a124) | c3_1(a124) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a124)) | (~c3_1(a138)) | (~c1_1(a138)))),
% 1.62/1.40 inference(rewrite,[status(thm)],[])).
% 1.62/1.40 tff(1727,plain,
% 1.62/1.40 (((~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138)) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)) | c1_1(a124) | c3_1(a124) | (~c0_1(a124))) <=> (c2_1(a138) | c1_1(a124) | c3_1(a124) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a124)) | (~c3_1(a138)) | (~c1_1(a138)))),
% 1.62/1.40 inference(rewrite,[status(thm)],[])).
% 1.62/1.40 tff(1728,plain,
% 1.62/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138)) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)) | c1_1(a124) | c3_1(a124) | (~c0_1(a124)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a138) | c1_1(a124) | c3_1(a124) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a124)) | (~c3_1(a138)) | (~c1_1(a138))))),
% 1.62/1.40 inference(monotonicity,[status(thm)],[1727])).
% 1.62/1.40 tff(1729,plain,
% 1.62/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138)) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)) | c1_1(a124) | c3_1(a124) | (~c0_1(a124)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a138) | c1_1(a124) | c3_1(a124) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a124)) | (~c3_1(a138)) | (~c1_1(a138)))),
% 1.62/1.40 inference(transitivity,[status(thm)],[1728, 1726])).
% 1.62/1.40 tff(1730,plain,
% 1.62/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138)) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)) | c1_1(a124) | c3_1(a124) | (~c0_1(a124)))),
% 1.62/1.40 inference(quant_inst,[status(thm)],[])).
% 1.62/1.40 tff(1731,plain,
% 1.62/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a138) | c1_1(a124) | c3_1(a124) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a124)) | (~c3_1(a138)) | (~c1_1(a138))),
% 1.62/1.40 inference(modus_ponens,[status(thm)],[1730, 1729])).
% 1.62/1.40 tff(1732,plain,
% 1.62/1.40 (c3_1(a124) | (~c0_1(a124))),
% 1.62/1.40 inference(unit_resolution,[status(thm)],[1731, 126, 1477, 1647, 1447, 1217, 31, 53, 20, 1679])).
% 1.62/1.40 tff(1733,plain,
% 1.62/1.40 (~c0_1(a124)),
% 1.62/1.40 inference(unit_resolution,[status(thm)],[1732, 1216])).
% 1.62/1.40 tff(1734,plain,
% 1.62/1.40 (hskp6 | c3_1(a97) | (~c1_1(a97))),
% 1.62/1.40 inference(unit_resolution,[status(thm)],[868, 126, 1647, 391])).
% 1.62/1.40 tff(1735,plain,
% 1.62/1.40 (hskp6),
% 1.62/1.40 inference(unit_resolution,[status(thm)],[1734, 1652, 53])).
% 1.62/1.40 tff(1736,plain,
% 1.62/1.40 (c1_1(a105)),
% 1.62/1.40 inference(unit_resolution,[status(thm)],[426, 1735])).
% 1.62/1.40 tff(1737,plain,
% 1.62/1.40 (~c3_1(a105)),
% 1.62/1.40 inference(unit_resolution,[status(thm)],[404, 1735])).
% 1.62/1.40 tff(1738,plain,
% 1.62/1.40 (c2_1(a105)),
% 1.62/1.40 inference(unit_resolution,[status(thm)],[415, 1735])).
% 1.62/1.40 tff(1739,assumption,(~c2_1(a124)), introduced(assumption)).
% 1.62/1.40 tff(1740,plain,
% 1.62/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a124) | c1_1(a124) | c3_1(a124) | c3_1(a105) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c1_1(a97)) | (~c2_1(a105)) | (~c1_1(a105)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a124) | c1_1(a124) | c3_1(a124) | c3_1(a105) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c1_1(a97)) | (~c2_1(a105)) | (~c1_1(a105)))),
% 1.62/1.40 inference(rewrite,[status(thm)],[])).
% 1.62/1.40 tff(1741,plain,
% 1.62/1.40 (((~ndr1_0) | c3_1(a105) | (~c2_1(a105)) | (~c1_1(a105)) | c2_1(a97) | c3_1(a97) | (~c1_1(a97)) | c2_1(a124) | c1_1(a124) | c3_1(a124)) <=> (c2_1(a124) | c1_1(a124) | c3_1(a124) | c3_1(a105) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c1_1(a97)) | (~c2_1(a105)) | (~c1_1(a105)))),
% 1.62/1.40 inference(rewrite,[status(thm)],[])).
% 1.62/1.40 tff(1742,plain,
% 1.62/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a105) | (~c2_1(a105)) | (~c1_1(a105)) | c2_1(a97) | c3_1(a97) | (~c1_1(a97)) | c2_1(a124) | c1_1(a124) | c3_1(a124))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a124) | c1_1(a124) | c3_1(a124) | c3_1(a105) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c1_1(a97)) | (~c2_1(a105)) | (~c1_1(a105))))),
% 1.62/1.40 inference(monotonicity,[status(thm)],[1741])).
% 1.62/1.40 tff(1743,plain,
% 1.62/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a105) | (~c2_1(a105)) | (~c1_1(a105)) | c2_1(a97) | c3_1(a97) | (~c1_1(a97)) | c2_1(a124) | c1_1(a124) | c3_1(a124))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a124) | c1_1(a124) | c3_1(a124) | c3_1(a105) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c1_1(a97)) | (~c2_1(a105)) | (~c1_1(a105)))),
% 1.62/1.40 inference(transitivity,[status(thm)],[1742, 1740])).
% 1.62/1.40 tff(1744,plain,
% 1.62/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a105) | (~c2_1(a105)) | (~c1_1(a105)) | c2_1(a97) | c3_1(a97) | (~c1_1(a97)) | c2_1(a124) | c1_1(a124) | c3_1(a124))),
% 1.62/1.40 inference(quant_inst,[status(thm)],[])).
% 1.62/1.40 tff(1745,plain,
% 1.62/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a124) | c1_1(a124) | c3_1(a124) | c3_1(a105) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c1_1(a97)) | (~c2_1(a105)) | (~c1_1(a105))),
% 1.62/1.40 inference(modus_ponens,[status(thm)],[1744, 1743])).
% 1.62/1.40 tff(1746,plain,
% 1.62/1.40 ($false),
% 1.62/1.40 inference(unit_resolution,[status(thm)],[1745, 126, 1739, 442, 441, 1217, 1216, 439, 31, 53, 438, 330])).
% 1.62/1.40 tff(1747,plain,(c2_1(a124) | (~c1_1(a105)) | (~c2_1(a105)) | c1_1(a124) | c3_1(a124) | c3_1(a105) | c2_1(a97) | c3_1(a97) | (~c1_1(a97))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.40 tff(1748,plain,
% 1.62/1.40 (c2_1(a124)),
% 1.62/1.40 inference(unit_resolution,[status(thm)],[1747, 1216, 1652, 1738, 1217, 1737, 31, 53, 1736])).
% 1.62/1.40 tff(1749,plain,
% 1.62/1.40 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 1.62/1.40 inference(bind,[status(th)],[])).
% 1.62/1.40 tff(1750,plain,
% 1.62/1.40 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.62/1.40 inference(quant_intro,[status(thm)],[1749])).
% 1.62/1.40 tff(1751,plain,
% 1.62/1.40 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.62/1.40 inference(rewrite,[status(thm)],[])).
% 1.62/1.40 tff(1752,plain,
% 1.62/1.40 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp1) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp1))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 1.62/1.40 inference(bind,[status(th)],[])).
% 1.62/1.40 tff(1753,plain,
% 1.62/1.40 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.62/1.40 inference(quant_intro,[status(thm)],[1752])).
% 1.62/1.40 tff(1754,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause163')).
% 1.62/1.40 tff(1755,plain,
% 1.62/1.40 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.62/1.40 inference(modus_ponens,[status(thm)],[1754, 1753])).
% 1.62/1.40 tff(1756,plain,
% 1.62/1.40 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.62/1.40 inference(modus_ponens,[status(thm)],[1755, 1751])).
% 1.62/1.40 tff(1757,plain,(
% 1.62/1.40 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.62/1.40 inference(skolemize,[status(sab)],[1756])).
% 1.62/1.40 tff(1758,plain,
% 1.62/1.40 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.62/1.40 inference(modus_ponens,[status(thm)],[1757, 1750])).
% 1.62/1.40 tff(1759,plain,
% 1.62/1.40 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | c0_1(a124))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | c0_1(a124))),
% 1.62/1.40 inference(rewrite,[status(thm)],[])).
% 1.62/1.40 tff(1760,plain,
% 1.62/1.40 ((hskp1 | (~ndr1_0) | c1_1(a124) | c3_1(a124) | (~c2_1(a124)) | c1_1(a124) | c0_1(a124) | (~c2_1(a124))) <=> (hskp1 | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | c0_1(a124))),
% 1.62/1.40 inference(rewrite,[status(thm)],[])).
% 1.62/1.40 tff(1761,plain,
% 1.62/1.40 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a124) | c3_1(a124) | (~c2_1(a124)) | c1_1(a124) | c0_1(a124) | (~c2_1(a124)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | c0_1(a124)))),
% 1.62/1.40 inference(monotonicity,[status(thm)],[1760])).
% 1.62/1.40 tff(1762,plain,
% 1.62/1.40 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a124) | c3_1(a124) | (~c2_1(a124)) | c1_1(a124) | c0_1(a124) | (~c2_1(a124)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | c0_1(a124))),
% 1.62/1.40 inference(transitivity,[status(thm)],[1761, 1759])).
% 1.62/1.40 tff(1763,plain,
% 1.62/1.40 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a124) | c3_1(a124) | (~c2_1(a124)) | c1_1(a124) | c0_1(a124) | (~c2_1(a124)))),
% 1.62/1.40 inference(quant_inst,[status(thm)],[])).
% 1.62/1.40 tff(1764,plain,
% 1.62/1.40 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | c0_1(a124)),
% 1.62/1.40 inference(modus_ponens,[status(thm)],[1763, 1762])).
% 1.62/1.40 tff(1765,plain,
% 1.62/1.40 (hskp1 | c3_1(a124) | (~c2_1(a124)) | c0_1(a124)),
% 1.62/1.40 inference(unit_resolution,[status(thm)],[1764, 126, 1217, 1758])).
% 1.62/1.40 tff(1766,plain,
% 1.62/1.40 (hskp1),
% 1.62/1.40 inference(unit_resolution,[status(thm)],[1765, 1748, 1216, 1733])).
% 1.62/1.40 tff(1767,plain,
% 1.62/1.40 (~c3_1(a98)),
% 1.62/1.40 inference(unit_resolution,[status(thm)],[1231, 1766])).
% 1.62/1.40 tff(1768,plain,
% 1.62/1.40 (~c1_1(a98)),
% 1.62/1.40 inference(unit_resolution,[status(thm)],[1237, 1766])).
% 1.62/1.40 tff(1769,plain,
% 1.62/1.40 (hskp19),
% 1.62/1.40 inference(unit_resolution,[status(thm)],[1308, 1748, 53, 1217, 1216, 1652, 1647, 52])).
% 1.62/1.40 tff(1770,plain,
% 1.62/1.40 (~c2_1(a130)),
% 1.62/1.40 inference(unit_resolution,[status(thm)],[252, 1769])).
% 1.62/1.40 tff(1771,plain,
% 1.62/1.40 (c0_1(a98)),
% 1.62/1.40 inference(unit_resolution,[status(thm)],[1248, 1766])).
% 1.62/1.40 tff(1772,plain,
% 1.62/1.40 (c3_1(a130)),
% 1.62/1.40 inference(unit_resolution,[status(thm)],[263, 1769])).
% 1.62/1.40 tff(1773,plain,
% 1.62/1.40 (c1_1(a130)),
% 1.62/1.40 inference(unit_resolution,[status(thm)],[274, 1769])).
% 1.62/1.40 tff(1774,plain,
% 1.62/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a130) | c1_1(a98) | c3_1(a98) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a98)) | (~c3_1(a130)) | (~c1_1(a130)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a130) | c1_1(a98) | c3_1(a98) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a98)) | (~c3_1(a130)) | (~c1_1(a130)))),
% 1.62/1.40 inference(rewrite,[status(thm)],[])).
% 1.62/1.40 tff(1775,plain,
% 1.62/1.40 (((~ndr1_0) | c2_1(a130) | (~c3_1(a130)) | (~c1_1(a130)) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)) | c1_1(a98) | c3_1(a98) | (~c0_1(a98))) <=> (c2_1(a130) | c1_1(a98) | c3_1(a98) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a98)) | (~c3_1(a130)) | (~c1_1(a130)))),
% 1.62/1.40 inference(rewrite,[status(thm)],[])).
% 1.62/1.40 tff(1776,plain,
% 1.62/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a130) | (~c3_1(a130)) | (~c1_1(a130)) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)) | c1_1(a98) | c3_1(a98) | (~c0_1(a98)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a130) | c1_1(a98) | c3_1(a98) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a98)) | (~c3_1(a130)) | (~c1_1(a130))))),
% 1.62/1.40 inference(monotonicity,[status(thm)],[1775])).
% 1.62/1.40 tff(1777,plain,
% 1.62/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a130) | (~c3_1(a130)) | (~c1_1(a130)) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)) | c1_1(a98) | c3_1(a98) | (~c0_1(a98)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a130) | c1_1(a98) | c3_1(a98) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a98)) | (~c3_1(a130)) | (~c1_1(a130)))),
% 1.62/1.40 inference(transitivity,[status(thm)],[1776, 1774])).
% 1.62/1.40 tff(1778,plain,
% 1.62/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a130) | (~c3_1(a130)) | (~c1_1(a130)) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)) | c1_1(a98) | c3_1(a98) | (~c0_1(a98)))),
% 1.62/1.40 inference(quant_inst,[status(thm)],[])).
% 1.62/1.40 tff(1779,plain,
% 1.62/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a130) | c1_1(a98) | c3_1(a98) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a98)) | (~c3_1(a130)) | (~c1_1(a130))),
% 1.62/1.40 inference(modus_ponens,[status(thm)],[1778, 1777])).
% 1.62/1.40 tff(1780,plain,
% 1.62/1.40 ($false),
% 1.62/1.40 inference(unit_resolution,[status(thm)],[1779, 126, 1773, 1772, 1771, 1647, 1770, 1768, 1767, 31, 53, 20])).
% 1.62/1.40 tff(1781,plain,(c3_1(a124) | c2_1(a97) | c3_1(a97) | c1_1(a124) | hskp18 | (~c1_1(a138))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.40 tff(1782,plain,
% 1.62/1.40 ($false),
% 1.62/1.40 inference(unit_resolution,[status(thm)],[1781, 1725, 1724, 53, 31, 52, 1660])).
% 1.62/1.40 tff(1783,plain,(hskp28 | c3_1(a97) | c2_1(a97) | hskp18), inference(lemma,lemma(discharge,[]))).
% 1.62/1.40 tff(1784,plain,
% 1.62/1.40 (hskp28),
% 1.62/1.40 inference(unit_resolution,[status(thm)],[1783, 53, 31, 52])).
% 1.62/1.40 tff(1785,plain,
% 1.62/1.40 (c1_1(a137)),
% 1.62/1.40 inference(unit_resolution,[status(thm)],[654, 1784])).
% 1.62/1.40 tff(1786,plain,
% 1.62/1.40 (c2_1(a137)),
% 1.62/1.40 inference(unit_resolution,[status(thm)],[643, 1784])).
% 1.62/1.40 tff(1787,plain,
% 1.62/1.40 (c0_1(a137)),
% 1.62/1.40 inference(unit_resolution,[status(thm)],[632, 1784])).
% 1.62/1.40 tff(1788,plain,
% 1.62/1.40 (~hskp9),
% 1.62/1.40 inference(unit_resolution,[status(thm)],[1096, 1785, 1652, 1786, 1647, 31, 1787])).
% 1.62/1.41 tff(1789,plain,
% 1.62/1.41 (hskp17),
% 1.62/1.41 inference(unit_resolution,[status(thm)],[1180, 1788, 52, 1702, 1709, 1787, 1786, 1705, 1708, 1707, 1706, 1785])).
% 1.62/1.41 tff(1790,plain,
% 1.62/1.41 (~c1_1(a124)),
% 1.62/1.41 inference(unit_resolution,[status(thm)],[1192, 1789])).
% 1.62/1.41 tff(1791,plain,
% 1.62/1.41 (~c3_1(a124)),
% 1.62/1.41 inference(unit_resolution,[status(thm)],[1186, 1789])).
% 1.62/1.41 tff(1792,plain,
% 1.62/1.41 (~c1_1(a138)),
% 1.62/1.41 inference(unit_resolution,[status(thm)],[1781, 1791, 53, 31, 52, 1790])).
% 1.62/1.41 tff(1793,plain,
% 1.62/1.41 (c2_1(a124)),
% 1.62/1.41 inference(unit_resolution,[status(thm)],[1203, 1789])).
% 1.62/1.41 tff(1794,plain,
% 1.62/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a138) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c0_1(a124)) | c1_1(a138) | (~c0_1(a138)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a138) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c0_1(a124)) | c1_1(a138) | (~c0_1(a138)))),
% 1.62/1.41 inference(rewrite,[status(thm)],[])).
% 1.62/1.41 tff(1795,plain,
% 1.62/1.41 (((~ndr1_0) | c3_1(a124) | (~c2_1(a124)) | (~c0_1(a124)) | c1_1(a124) | (~c2_1(a124)) | (~c0_1(a124)) | c2_1(a138) | c1_1(a138) | (~c0_1(a138))) <=> (c2_1(a138) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c0_1(a124)) | c1_1(a138) | (~c0_1(a138)))),
% 1.62/1.41 inference(rewrite,[status(thm)],[])).
% 1.62/1.41 tff(1796,plain,
% 1.62/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a124) | (~c2_1(a124)) | (~c0_1(a124)) | c1_1(a124) | (~c2_1(a124)) | (~c0_1(a124)) | c2_1(a138) | c1_1(a138) | (~c0_1(a138)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a138) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c0_1(a124)) | c1_1(a138) | (~c0_1(a138))))),
% 1.62/1.41 inference(monotonicity,[status(thm)],[1795])).
% 1.62/1.41 tff(1797,plain,
% 1.62/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a124) | (~c2_1(a124)) | (~c0_1(a124)) | c1_1(a124) | (~c2_1(a124)) | (~c0_1(a124)) | c2_1(a138) | c1_1(a138) | (~c0_1(a138)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a138) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c0_1(a124)) | c1_1(a138) | (~c0_1(a138)))),
% 1.62/1.41 inference(transitivity,[status(thm)],[1796, 1794])).
% 1.62/1.41 tff(1798,plain,
% 1.62/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a124) | (~c2_1(a124)) | (~c0_1(a124)) | c1_1(a124) | (~c2_1(a124)) | (~c0_1(a124)) | c2_1(a138) | c1_1(a138) | (~c0_1(a138)))),
% 1.62/1.41 inference(quant_inst,[status(thm)],[])).
% 1.62/1.41 tff(1799,plain,
% 1.62/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a138) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c0_1(a124)) | c1_1(a138) | (~c0_1(a138))),
% 1.62/1.41 inference(modus_ponens,[status(thm)],[1798, 1797])).
% 1.62/1.41 tff(1800,plain,
% 1.62/1.41 (~c0_1(a124)),
% 1.62/1.41 inference(unit_resolution,[status(thm)],[1799, 126, 1459, 1793, 1447, 1790, 1791, 143, 1792])).
% 1.62/1.41 tff(1801,plain,
% 1.62/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a124) | c3_1(a124) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a124) | c1_1(a138) | (~c0_1(a138)) | (~c3_1(a138)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a124) | c3_1(a124) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a124) | c1_1(a138) | (~c0_1(a138)) | (~c3_1(a138)))),
% 1.62/1.41 inference(rewrite,[status(thm)],[])).
% 1.62/1.41 tff(1802,plain,
% 1.62/1.41 (((~ndr1_0) | c3_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c1_1(a124) | c0_1(a124) | c3_1(a124)) <=> (c1_1(a124) | c3_1(a124) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a124) | c1_1(a138) | (~c0_1(a138)) | (~c3_1(a138)))),
% 1.62/1.41 inference(rewrite,[status(thm)],[])).
% 1.62/1.41 tff(1803,plain,
% 1.62/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c1_1(a124) | c0_1(a124) | c3_1(a124))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a124) | c3_1(a124) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a124) | c1_1(a138) | (~c0_1(a138)) | (~c3_1(a138))))),
% 1.62/1.41 inference(monotonicity,[status(thm)],[1802])).
% 1.62/1.41 tff(1804,plain,
% 1.62/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c1_1(a124) | c0_1(a124) | c3_1(a124))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a124) | c3_1(a124) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a124) | c1_1(a138) | (~c0_1(a138)) | (~c3_1(a138)))),
% 1.62/1.41 inference(transitivity,[status(thm)],[1803, 1801])).
% 1.62/1.41 tff(1805,plain,
% 1.62/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a97) | (~c0_1(a97)) | (~c1_1(a97)) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c1_1(a124) | c0_1(a124) | c3_1(a124))),
% 1.62/1.41 inference(quant_inst,[status(thm)],[])).
% 1.62/1.41 tff(1806,plain,
% 1.62/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a124) | c3_1(a124) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c1_1(a97)) | c0_1(a124) | c1_1(a138) | (~c0_1(a138)) | (~c3_1(a138))),
% 1.62/1.41 inference(modus_ponens,[status(thm)],[1805, 1804])).
% 1.62/1.41 tff(1807,plain,
% 1.62/1.41 ($false),
% 1.62/1.41 inference(unit_resolution,[status(thm)],[1806, 126, 1459, 1477, 1647, 1790, 1791, 53, 1329, 1652, 1792, 1800])).
% 1.62/1.41 tff(1808,plain,(c3_1(a97) | c2_1(a97) | hskp18), inference(lemma,lemma(discharge,[]))).
% 1.62/1.41 tff(1809,plain,
% 1.62/1.41 (c3_1(a97)),
% 1.62/1.41 inference(unit_resolution,[status(thm)],[1808, 52, 31])).
% 1.62/1.41 tff(1810,plain,
% 1.62/1.41 (~hskp0),
% 1.62/1.41 inference(unit_resolution,[status(thm)],[236, 1809])).
% 1.62/1.41 tff(1811,plain,
% 1.62/1.41 (~hskp4),
% 1.62/1.41 inference(unit_resolution,[status(thm)],[1485, 1810, 52])).
% 1.62/1.41 tff(1812,plain,
% 1.62/1.41 (hskp7),
% 1.62/1.41 inference(unit_resolution,[status(thm)],[1503, 1811])).
% 1.62/1.41 tff(1813,plain,
% 1.62/1.41 (~c0_1(a106)),
% 1.62/1.41 inference(unit_resolution,[status(thm)],[969, 1812])).
% 1.62/1.41 tff(1814,plain,
% 1.62/1.41 (hskp20),
% 1.62/1.41 inference(unit_resolution,[status(thm)],[815, 1811, 52])).
% 1.62/1.41 tff(1815,plain,
% 1.62/1.41 (~c3_1(a132)),
% 1.62/1.41 inference(unit_resolution,[status(thm)],[720, 1814])).
% 1.62/1.41 tff(1816,plain,
% 1.62/1.41 (~c2_1(a132)),
% 1.62/1.41 inference(unit_resolution,[status(thm)],[740, 1814])).
% 1.62/1.41 tff(1817,plain,
% 1.62/1.41 (~c1_1(a132)),
% 1.62/1.41 inference(unit_resolution,[status(thm)],[726, 1814])).
% 1.62/1.41 tff(1818,plain,
% 1.62/1.41 (c3_1(a106)),
% 1.62/1.41 inference(unit_resolution,[status(thm)],[919, 1812])).
% 1.62/1.41 tff(1819,plain,
% 1.62/1.41 (c2_1(a106)),
% 1.62/1.41 inference(unit_resolution,[status(thm)],[930, 1812])).
% 1.62/1.41 tff(1820,plain,
% 1.62/1.41 (hskp17),
% 1.62/1.41 inference(unit_resolution,[status(thm)],[1524, 126, 1819, 1818, 1817, 1816, 1815, 1813, 51])).
% 1.62/1.41 tff(1821,plain,
% 1.62/1.41 (~c3_1(a124)),
% 1.62/1.41 inference(unit_resolution,[status(thm)],[1186, 1820])).
% 1.62/1.41 tff(1822,plain,
% 1.62/1.41 (~c1_1(a124)),
% 1.62/1.41 inference(unit_resolution,[status(thm)],[1192, 1820])).
% 1.62/1.41 tff(1823,plain,
% 1.62/1.41 (c2_1(a124)),
% 1.62/1.41 inference(unit_resolution,[status(thm)],[1203, 1820])).
% 1.62/1.41 tff(1824,plain,
% 1.62/1.41 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp4 | c1_1(a132) | c2_1(a132) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c0_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp4 | c1_1(a132) | c2_1(a132) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c0_1(a132)))),
% 1.62/1.41 inference(rewrite,[status(thm)],[])).
% 1.62/1.41 tff(1825,plain,
% 1.62/1.41 ((hskp4 | (~ndr1_0) | c1_1(a124) | c3_1(a124) | (~c2_1(a124)) | c2_1(a132) | c1_1(a132) | (~c0_1(a132))) <=> (hskp4 | c1_1(a132) | c2_1(a132) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c0_1(a132)))),
% 1.62/1.41 inference(rewrite,[status(thm)],[])).
% 1.62/1.41 tff(1826,plain,
% 1.62/1.41 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a124) | c3_1(a124) | (~c2_1(a124)) | c2_1(a132) | c1_1(a132) | (~c0_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp4 | c1_1(a132) | c2_1(a132) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c0_1(a132))))),
% 1.62/1.41 inference(monotonicity,[status(thm)],[1825])).
% 1.62/1.41 tff(1827,plain,
% 1.62/1.41 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a124) | c3_1(a124) | (~c2_1(a124)) | c2_1(a132) | c1_1(a132) | (~c0_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp4 | c1_1(a132) | c2_1(a132) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c0_1(a132)))),
% 1.62/1.41 inference(transitivity,[status(thm)],[1826, 1824])).
% 1.62/1.41 tff(1828,plain,
% 1.62/1.41 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a124) | c3_1(a124) | (~c2_1(a124)) | c2_1(a132) | c1_1(a132) | (~c0_1(a132)))),
% 1.62/1.41 inference(quant_inst,[status(thm)],[])).
% 1.62/1.41 tff(1829,plain,
% 1.62/1.41 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp4 | c1_1(a132) | c2_1(a132) | c1_1(a124) | c3_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c0_1(a132))),
% 1.62/1.41 inference(modus_ponens,[status(thm)],[1828, 1827])).
% 1.62/1.41 tff(1830,plain,
% 1.62/1.41 (~c0_1(a132)),
% 1.62/1.41 inference(unit_resolution,[status(thm)],[1829, 126, 1811, 1823, 1817, 1816, 1822, 1821, 41])).
% 1.62/1.41 tff(1831,plain,
% 1.62/1.41 (hskp19),
% 1.62/1.41 inference(unit_resolution,[status(thm)],[747, 126, 52, 1817, 1816, 1815, 30])).
% 1.62/1.41 tff(1832,plain,
% 1.62/1.41 (~c2_1(a130)),
% 1.62/1.41 inference(unit_resolution,[status(thm)],[252, 1831])).
% 1.62/1.41 tff(1833,plain,
% 1.62/1.41 (c1_1(a130)),
% 1.62/1.41 inference(unit_resolution,[status(thm)],[274, 1831])).
% 1.62/1.41 tff(1834,plain,
% 1.62/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a132) | c3_1(a132) | c2_1(a130) | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | (~c0_1(a130)) | (~c1_1(a130)) | c0_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a132) | c3_1(a132) | c2_1(a130) | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | (~c0_1(a130)) | (~c1_1(a130)) | c0_1(a132))),
% 1.62/1.41 inference(rewrite,[status(thm)],[])).
% 1.62/1.41 tff(1835,plain,
% 1.62/1.41 (((~ndr1_0) | c2_1(a130) | (~c0_1(a130)) | (~c1_1(a130)) | c0_1(a106) | (~c2_1(a106)) | (~c3_1(a106)) | c2_1(a132) | c0_1(a132) | c3_1(a132)) <=> (c2_1(a132) | c3_1(a132) | c2_1(a130) | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | (~c0_1(a130)) | (~c1_1(a130)) | c0_1(a132))),
% 1.62/1.41 inference(rewrite,[status(thm)],[])).
% 1.62/1.41 tff(1836,plain,
% 1.62/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a130) | (~c0_1(a130)) | (~c1_1(a130)) | c0_1(a106) | (~c2_1(a106)) | (~c3_1(a106)) | c2_1(a132) | c0_1(a132) | c3_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a132) | c3_1(a132) | c2_1(a130) | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | (~c0_1(a130)) | (~c1_1(a130)) | c0_1(a132)))),
% 1.62/1.41 inference(monotonicity,[status(thm)],[1835])).
% 1.62/1.41 tff(1837,plain,
% 1.62/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a130) | (~c0_1(a130)) | (~c1_1(a130)) | c0_1(a106) | (~c2_1(a106)) | (~c3_1(a106)) | c2_1(a132) | c0_1(a132) | c3_1(a132))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a132) | c3_1(a132) | c2_1(a130) | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | (~c0_1(a130)) | (~c1_1(a130)) | c0_1(a132))),
% 1.62/1.41 inference(transitivity,[status(thm)],[1836, 1834])).
% 1.62/1.41 tff(1838,plain,
% 1.62/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a130) | (~c0_1(a130)) | (~c1_1(a130)) | c0_1(a106) | (~c2_1(a106)) | (~c3_1(a106)) | c2_1(a132) | c0_1(a132) | c3_1(a132))),
% 1.62/1.41 inference(quant_inst,[status(thm)],[])).
% 1.62/1.41 tff(1839,plain,
% 1.62/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a132) | c3_1(a132) | c2_1(a130) | c0_1(a106) | (~ndr1_0) | (~c2_1(a106)) | (~c3_1(a106)) | (~c0_1(a130)) | (~c1_1(a130)) | c0_1(a132)),
% 1.62/1.41 inference(modus_ponens,[status(thm)],[1838, 1837])).
% 1.62/1.41 tff(1840,plain,
% 1.62/1.41 (~c0_1(a130)),
% 1.62/1.41 inference(unit_resolution,[status(thm)],[1839, 126, 1833, 1819, 1818, 1816, 1815, 1832, 1813, 525, 1830])).
% 1.62/1.41 tff(1841,plain,
% 1.62/1.41 (c3_1(a130)),
% 1.62/1.41 inference(unit_resolution,[status(thm)],[263, 1831])).
% 1.62/1.41 tff(1842,plain,
% 1.62/1.41 ($false),
% 1.62/1.41 inference(unit_resolution,[status(thm)],[756, 126, 1810, 1841, 1817, 1816, 1832, 211, 1830, 1840])).
% 1.62/1.41 tff(1843,plain,(hskp18 | c2_1(a97)), inference(lemma,lemma(discharge,[]))).
% 1.62/1.41 tff(1844,plain,
% 1.62/1.41 (hskp18),
% 1.62/1.41 inference(unit_resolution,[status(thm)],[1843, 31])).
% 1.62/1.41 tff(1845,plain,
% 1.62/1.41 (~c1_1(a129)),
% 1.62/1.41 inference(unit_resolution,[status(thm)],[297, 1844])).
% 1.62/1.41 tff(1846,plain,
% 1.62/1.41 (c2_1(a129)),
% 1.62/1.41 inference(unit_resolution,[status(thm)],[308, 1844])).
% 1.62/1.41 tff(1847,plain,
% 1.62/1.41 (c0_1(a129)),
% 1.62/1.41 inference(unit_resolution,[status(thm)],[319, 1844])).
% 1.62/1.41 tff(1848,plain,
% 1.62/1.41 (~c3_1(a129)),
% 1.62/1.41 inference(unit_resolution,[status(thm)],[891, 126, 1847, 1846, 1845, 10])).
% 1.62/1.41 tff(1849,plain,
% 1.62/1.41 (c1_1(a138)),
% 1.62/1.41 inference(unit_resolution,[status(thm)],[1587, 126, 1459, 1847, 1846, 1447, 1845, 143, 1848])).
% 1.62/1.41 tff(1850,plain,
% 1.62/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a138) | c1_1(a129) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a129)) | c3_1(a129) | (~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) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a138) | c1_1(a129) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a129)) | c3_1(a129) | (~c3_1(a138)) | (~c1_1(a138)))),
% 1.62/1.41 inference(rewrite,[status(thm)],[])).
% 1.62/1.41 tff(1851,plain,
% 1.62/1.41 (((~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138)) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)) | c1_1(a129) | c3_1(a129) | (~c0_1(a129))) <=> (c2_1(a138) | c1_1(a129) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a129)) | c3_1(a129) | (~c3_1(a138)) | (~c1_1(a138)))),
% 1.62/1.41 inference(rewrite,[status(thm)],[])).
% 1.62/1.41 tff(1852,plain,
% 1.62/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138)) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)) | c1_1(a129) | c3_1(a129) | (~c0_1(a129)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a138) | c1_1(a129) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a129)) | c3_1(a129) | (~c3_1(a138)) | (~c1_1(a138))))),
% 1.62/1.41 inference(monotonicity,[status(thm)],[1851])).
% 1.62/1.41 tff(1853,plain,
% 1.62/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138)) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)) | c1_1(a129) | c3_1(a129) | (~c0_1(a129)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a138) | c1_1(a129) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a129)) | c3_1(a129) | (~c3_1(a138)) | (~c1_1(a138)))),
% 1.62/1.41 inference(transitivity,[status(thm)],[1852, 1850])).
% 1.62/1.41 tff(1854,plain,
% 1.62/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c1_1(a138)) | c2_1(a97) | c3_1(a97) | (~c0_1(a97)) | c1_1(a129) | c3_1(a129) | (~c0_1(a129)))),
% 1.62/1.41 inference(quant_inst,[status(thm)],[])).
% 1.62/1.41 tff(1855,plain,
% 1.62/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a138) | c1_1(a129) | c2_1(a97) | c3_1(a97) | (~ndr1_0) | (~c0_1(a97)) | (~c0_1(a129)) | c3_1(a129) | (~c3_1(a138)) | (~c1_1(a138))),
% 1.62/1.41 inference(modus_ponens,[status(thm)],[1854, 1853])).
% 1.62/1.41 tff(1856,plain,
% 1.62/1.41 (c3_1(a97) | (~c1_1(a138))),
% 1.62/1.41 inference(unit_resolution,[status(thm)],[1855, 126, 1477, 1847, 1647, 1447, 1845, 31, 20, 1848])).
% 1.62/1.41 tff(1857,plain,
% 1.62/1.41 (c3_1(a97)),
% 1.62/1.41 inference(unit_resolution,[status(thm)],[1856, 1849])).
% 1.62/1.41 tff(1858,plain,
% 1.62/1.41 (~hskp0),
% 1.62/1.41 inference(unit_resolution,[status(thm)],[236, 1857])).
% 1.62/1.41 tff(1859,plain,
% 1.62/1.41 (hskp11),
% 1.62/1.41 inference(unit_resolution,[status(thm)],[1604, 126, 1477, 1847, 1846, 1447, 1598, 1849, 1848])).
% 1.62/1.41 tff(1860,plain,
% 1.62/1.41 (~c1_1(a112)),
% 1.62/1.41 inference(unit_resolution,[status(thm)],[848, 1859])).
% 1.62/1.41 tff(1861,plain,
% 1.62/1.41 (~c0_1(a112)),
% 1.62/1.41 inference(unit_resolution,[status(thm)],[854, 1859])).
% 1.62/1.41 tff(1862,plain,
% 1.62/1.41 (^[V: $i, U: $i] : refl((hskp24 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp24 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 1.62/1.41 inference(bind,[status(th)],[])).
% 1.62/1.41 tff(1863,plain,
% 1.62/1.41 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.62/1.41 inference(quant_intro,[status(thm)],[1862])).
% 1.62/1.41 tff(1864,plain,
% 1.62/1.41 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.62/1.41 inference(rewrite,[status(thm)],[])).
% 1.62/1.41 tff(1865,plain,
% 1.62/1.41 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp24) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp24))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp24) <=> (hskp24 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp24) <=> (hskp24 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 1.62/1.42 inference(bind,[status(th)],[])).
% 1.62/1.42 tff(1866,plain,
% 1.62/1.42 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp24) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.62/1.42 inference(quant_intro,[status(thm)],[1865])).
% 1.62/1.42 tff(1867,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause180')).
% 1.62/1.42 tff(1868,plain,
% 1.62/1.42 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.62/1.42 inference(modus_ponens,[status(thm)],[1867, 1866])).
% 1.62/1.42 tff(1869,plain,
% 1.62/1.42 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.62/1.42 inference(modus_ponens,[status(thm)],[1868, 1864])).
% 1.62/1.42 tff(1870,plain,(
% 1.62/1.42 ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.62/1.42 inference(skolemize,[status(sab)],[1869])).
% 1.62/1.42 tff(1871,plain,
% 1.62/1.42 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.62/1.42 inference(modus_ponens,[status(thm)],[1870, 1863])).
% 1.62/1.42 tff(1872,plain,
% 1.62/1.42 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp24 | c2_1(a138) | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | (~c0_1(a138)) | (~c3_1(a138)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp24 | c2_1(a138) | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | (~c0_1(a138)) | (~c3_1(a138)))),
% 1.62/1.42 inference(rewrite,[status(thm)],[])).
% 1.62/1.42 tff(1873,plain,
% 1.62/1.42 ((hskp24 | (~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129))) <=> (hskp24 | c2_1(a138) | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | (~c0_1(a138)) | (~c3_1(a138)))),
% 1.62/1.42 inference(rewrite,[status(thm)],[])).
% 1.62/1.42 tff(1874,plain,
% 1.62/1.42 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp24 | c2_1(a138) | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | (~c0_1(a138)) | (~c3_1(a138))))),
% 1.62/1.42 inference(monotonicity,[status(thm)],[1873])).
% 1.62/1.42 tff(1875,plain,
% 1.62/1.42 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp24 | c2_1(a138) | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | (~c0_1(a138)) | (~c3_1(a138)))),
% 1.62/1.42 inference(transitivity,[status(thm)],[1874, 1872])).
% 1.62/1.42 tff(1876,plain,
% 1.62/1.42 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | c2_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)))),
% 1.62/1.42 inference(quant_inst,[status(thm)],[])).
% 1.62/1.42 tff(1877,plain,
% 1.62/1.42 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp24 | c2_1(a138) | c1_1(a129) | (~ndr1_0) | (~c2_1(a129)) | (~c0_1(a129)) | (~c0_1(a138)) | (~c3_1(a138))),
% 1.62/1.42 inference(modus_ponens,[status(thm)],[1876, 1875])).
% 1.62/1.42 tff(1878,plain,
% 1.62/1.42 (hskp24),
% 1.62/1.42 inference(unit_resolution,[status(thm)],[1877, 126, 1459, 1477, 1847, 1846, 1447, 1845, 1871])).
% 1.62/1.42 tff(1879,plain,
% 1.62/1.42 (((~hskp24) | (~c3_1(a147))) <=> ((~hskp24) | (~c3_1(a147)))),
% 1.62/1.42 inference(rewrite,[status(thm)],[])).
% 1.62/1.42 tff(1880,plain,
% 1.62/1.42 (((~c3_1(a147)) | (~hskp24)) <=> ((~hskp24) | (~c3_1(a147)))),
% 1.62/1.42 inference(rewrite,[status(thm)],[])).
% 1.62/1.42 tff(1881,axiom,((~c3_1(a147)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause92')).
% 1.62/1.42 tff(1882,plain,
% 1.62/1.42 ((~hskp24) | (~c3_1(a147))),
% 1.62/1.42 inference(modus_ponens,[status(thm)],[1881, 1880])).
% 1.62/1.42 tff(1883,plain,
% 1.62/1.42 ((~hskp24) | (~c3_1(a147))),
% 1.62/1.42 inference(modus_ponens,[status(thm)],[1882, 1879])).
% 1.62/1.42 tff(1884,plain,
% 1.62/1.42 (~c3_1(a147)),
% 1.62/1.42 inference(unit_resolution,[status(thm)],[1883, 1878])).
% 1.62/1.42 tff(1885,plain,
% 1.62/1.42 (((~hskp24) | (~c1_1(a147))) <=> ((~hskp24) | (~c1_1(a147)))),
% 1.62/1.42 inference(rewrite,[status(thm)],[])).
% 1.62/1.42 tff(1886,plain,
% 1.62/1.42 (((~c1_1(a147)) | (~hskp24)) <=> ((~hskp24) | (~c1_1(a147)))),
% 1.62/1.42 inference(rewrite,[status(thm)],[])).
% 1.62/1.42 tff(1887,axiom,((~c1_1(a147)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause91')).
% 1.62/1.42 tff(1888,plain,
% 1.62/1.42 ((~hskp24) | (~c1_1(a147))),
% 1.62/1.42 inference(modus_ponens,[status(thm)],[1887, 1886])).
% 1.62/1.42 tff(1889,plain,
% 1.62/1.42 ((~hskp24) | (~c1_1(a147))),
% 1.62/1.42 inference(modus_ponens,[status(thm)],[1888, 1885])).
% 1.62/1.42 tff(1890,plain,
% 1.62/1.42 (~c1_1(a147)),
% 1.62/1.42 inference(unit_resolution,[status(thm)],[1889, 1878])).
% 1.62/1.42 tff(1891,plain,
% 1.62/1.42 (((~hskp24) | (~c0_1(a147))) <=> ((~hskp24) | (~c0_1(a147)))),
% 1.62/1.42 inference(rewrite,[status(thm)],[])).
% 1.62/1.42 tff(1892,plain,
% 1.62/1.42 (((~c0_1(a147)) | (~hskp24)) <=> ((~hskp24) | (~c0_1(a147)))),
% 1.62/1.42 inference(rewrite,[status(thm)],[])).
% 1.62/1.42 tff(1893,axiom,((~c0_1(a147)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause90')).
% 1.62/1.42 tff(1894,plain,
% 1.62/1.42 ((~hskp24) | (~c0_1(a147))),
% 1.62/1.42 inference(modus_ponens,[status(thm)],[1893, 1892])).
% 1.62/1.42 tff(1895,plain,
% 1.62/1.42 ((~hskp24) | (~c0_1(a147))),
% 1.62/1.42 inference(modus_ponens,[status(thm)],[1894, 1891])).
% 1.62/1.42 tff(1896,plain,
% 1.62/1.42 (~c0_1(a147)),
% 1.62/1.42 inference(unit_resolution,[status(thm)],[1895, 1878])).
% 1.62/1.42 tff(1897,plain,
% 1.62/1.42 (c3_1(a112)),
% 1.62/1.42 inference(unit_resolution,[status(thm)],[1052, 1859])).
% 1.62/1.42 tff(1898,assumption,(hskp6), introduced(assumption)).
% 1.62/1.42 tff(1899,plain,
% 1.62/1.42 (~c3_1(a105)),
% 1.62/1.42 inference(unit_resolution,[status(thm)],[404, 1898])).
% 1.62/1.42 tff(1900,plain,
% 1.62/1.42 (c1_1(a105)),
% 1.62/1.42 inference(unit_resolution,[status(thm)],[426, 1898])).
% 1.62/1.42 tff(1901,plain,
% 1.62/1.42 (((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp0 | c3_1(a105) | (~ndr1_0) | (~c0_1(a105)) | (~c1_1(a105)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp0 | c3_1(a105) | (~ndr1_0) | (~c0_1(a105)) | (~c1_1(a105)))),
% 1.67/1.42 inference(rewrite,[status(thm)],[])).
% 1.67/1.42 tff(1902,plain,
% 1.67/1.42 ((hskp0 | (~ndr1_0) | c3_1(a105) | (~c0_1(a105)) | (~c1_1(a105))) <=> (hskp0 | c3_1(a105) | (~ndr1_0) | (~c0_1(a105)) | (~c1_1(a105)))),
% 1.67/1.42 inference(rewrite,[status(thm)],[])).
% 1.67/1.42 tff(1903,plain,
% 1.67/1.42 (((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp0 | (~ndr1_0) | c3_1(a105) | (~c0_1(a105)) | (~c1_1(a105)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp0 | c3_1(a105) | (~ndr1_0) | (~c0_1(a105)) | (~c1_1(a105))))),
% 1.67/1.42 inference(monotonicity,[status(thm)],[1902])).
% 1.67/1.42 tff(1904,plain,
% 1.67/1.42 (((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp0 | (~ndr1_0) | c3_1(a105) | (~c0_1(a105)) | (~c1_1(a105)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp0 | c3_1(a105) | (~ndr1_0) | (~c0_1(a105)) | (~c1_1(a105)))),
% 1.67/1.42 inference(transitivity,[status(thm)],[1903, 1901])).
% 1.67/1.42 tff(1905,plain,
% 1.67/1.42 ((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp0 | (~ndr1_0) | c3_1(a105) | (~c0_1(a105)) | (~c1_1(a105)))),
% 1.67/1.42 inference(quant_inst,[status(thm)],[])).
% 1.67/1.42 tff(1906,plain,
% 1.67/1.42 ((~![U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp0 | c3_1(a105) | (~ndr1_0) | (~c0_1(a105)) | (~c1_1(a105))),
% 1.67/1.42 inference(modus_ponens,[status(thm)],[1905, 1904])).
% 1.67/1.42 tff(1907,plain,
% 1.67/1.42 (~c0_1(a105)),
% 1.67/1.42 inference(unit_resolution,[status(thm)],[1906, 126, 94, 1900, 1899, 75])).
% 1.67/1.42 tff(1908,assumption,(~c3_1(a147)), introduced(assumption)).
% 1.67/1.42 tff(1909,assumption,(~c1_1(a147)), introduced(assumption)).
% 1.67/1.42 tff(1910,assumption,(~c0_1(a147)), introduced(assumption)).
% 1.67/1.42 tff(1911,plain,
% 1.67/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a147) | c1_1(a147) | c3_1(a147) | c0_1(a112) | c1_1(a112) | c3_1(a105) | (~ndr1_0) | c0_1(a105) | (~c1_1(a105)) | (~c3_1(a112)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a147) | c1_1(a147) | c3_1(a147) | c0_1(a112) | c1_1(a112) | c3_1(a105) | (~ndr1_0) | c0_1(a105) | (~c1_1(a105)) | (~c3_1(a112)))),
% 1.67/1.42 inference(rewrite,[status(thm)],[])).
% 1.67/1.42 tff(1912,plain,
% 1.67/1.42 (((~ndr1_0) | c0_1(a105) | c3_1(a105) | (~c1_1(a105)) | c1_1(a112) | c0_1(a112) | (~c3_1(a112)) | c1_1(a147) | c0_1(a147) | c3_1(a147)) <=> (c0_1(a147) | c1_1(a147) | c3_1(a147) | c0_1(a112) | c1_1(a112) | c3_1(a105) | (~ndr1_0) | c0_1(a105) | (~c1_1(a105)) | (~c3_1(a112)))),
% 1.67/1.42 inference(rewrite,[status(thm)],[])).
% 1.67/1.42 tff(1913,plain,
% 1.67/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a105) | c3_1(a105) | (~c1_1(a105)) | c1_1(a112) | c0_1(a112) | (~c3_1(a112)) | c1_1(a147) | c0_1(a147) | c3_1(a147))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a147) | c1_1(a147) | c3_1(a147) | c0_1(a112) | c1_1(a112) | c3_1(a105) | (~ndr1_0) | c0_1(a105) | (~c1_1(a105)) | (~c3_1(a112))))),
% 1.67/1.42 inference(monotonicity,[status(thm)],[1912])).
% 1.67/1.42 tff(1914,plain,
% 1.67/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a105) | c3_1(a105) | (~c1_1(a105)) | c1_1(a112) | c0_1(a112) | (~c3_1(a112)) | c1_1(a147) | c0_1(a147) | c3_1(a147))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a147) | c1_1(a147) | c3_1(a147) | c0_1(a112) | c1_1(a112) | c3_1(a105) | (~ndr1_0) | c0_1(a105) | (~c1_1(a105)) | (~c3_1(a112)))),
% 1.67/1.42 inference(transitivity,[status(thm)],[1913, 1911])).
% 1.67/1.42 tff(1915,plain,
% 1.67/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a105) | c3_1(a105) | (~c1_1(a105)) | c1_1(a112) | c0_1(a112) | (~c3_1(a112)) | c1_1(a147) | c0_1(a147) | c3_1(a147))),
% 1.67/1.42 inference(quant_inst,[status(thm)],[])).
% 1.67/1.42 tff(1916,plain,
% 1.67/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a147) | c1_1(a147) | c3_1(a147) | c0_1(a112) | c1_1(a112) | c3_1(a105) | (~ndr1_0) | c0_1(a105) | (~c1_1(a105)) | (~c3_1(a112))),
% 1.67/1.42 inference(modus_ponens,[status(thm)],[1915, 1914])).
% 1.67/1.42 tff(1917,plain,
% 1.67/1.42 ($false),
% 1.67/1.42 inference(unit_resolution,[status(thm)],[1916, 126, 1116, 1900, 1910, 1909, 1908, 1115, 1137, 1899, 1430, 1907])).
% 1.67/1.42 tff(1918,plain,((~hskp6) | (~c3_1(a112)) | c0_1(a147) | c1_1(a147) | c3_1(a147) | c0_1(a112) | c1_1(a112) | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.67/1.42 tff(1919,plain,
% 1.67/1.42 (~hskp6),
% 1.67/1.42 inference(unit_resolution,[status(thm)],[1918, 1897, 1896, 1890, 1884, 1861, 1860, 1858])).
% 1.67/1.42 tff(1920,plain,
% 1.67/1.42 (^[U: $i] : refl((hskp9 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp9 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))),
% 1.67/1.42 inference(bind,[status(th)],[])).
% 1.67/1.42 tff(1921,plain,
% 1.67/1.42 (![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.67/1.42 inference(quant_intro,[status(thm)],[1920])).
% 1.67/1.42 tff(1922,plain,
% 1.67/1.42 (![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.67/1.42 inference(rewrite,[status(thm)],[])).
% 1.67/1.42 tff(1923,plain,
% 1.67/1.42 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp9) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp9))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp9) <=> (hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp9) <=> (hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp9) | hskp6) <=> ((hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp6))), rewrite(((hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp6) <=> (hskp9 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp9) | hskp6) <=> (hskp9 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))))),
% 1.67/1.42 inference(bind,[status(th)],[])).
% 1.67/1.42 tff(1924,plain,
% 1.67/1.42 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp9) | hskp6) <=> ![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.67/1.42 inference(quant_intro,[status(thm)],[1923])).
% 1.67/1.42 tff(1925,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp9) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause138')).
% 1.67/1.42 tff(1926,plain,
% 1.67/1.42 (![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.67/1.42 inference(modus_ponens,[status(thm)],[1925, 1924])).
% 1.67/1.42 tff(1927,plain,
% 1.67/1.42 (![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.67/1.42 inference(modus_ponens,[status(thm)],[1926, 1922])).
% 1.67/1.42 tff(1928,plain,(
% 1.67/1.42 ![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.67/1.42 inference(skolemize,[status(sab)],[1927])).
% 1.67/1.42 tff(1929,plain,
% 1.67/1.42 (![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.67/1.42 inference(modus_ponens,[status(thm)],[1928, 1921])).
% 1.67/1.42 tff(1930,plain,
% 1.67/1.42 (((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp9 | hskp6 | c0_1(a112) | c1_1(a112) | (~ndr1_0) | (~c3_1(a112)))) <=> ((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp9 | hskp6 | c0_1(a112) | c1_1(a112) | (~ndr1_0) | (~c3_1(a112)))),
% 1.67/1.42 inference(rewrite,[status(thm)],[])).
% 1.67/1.42 tff(1931,plain,
% 1.67/1.42 ((hskp9 | hskp6 | (~ndr1_0) | c1_1(a112) | c0_1(a112) | (~c3_1(a112))) <=> (hskp9 | hskp6 | c0_1(a112) | c1_1(a112) | (~ndr1_0) | (~c3_1(a112)))),
% 1.67/1.42 inference(rewrite,[status(thm)],[])).
% 1.67/1.42 tff(1932,plain,
% 1.67/1.42 (((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp9 | hskp6 | (~ndr1_0) | c1_1(a112) | c0_1(a112) | (~c3_1(a112)))) <=> ((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp9 | hskp6 | c0_1(a112) | c1_1(a112) | (~ndr1_0) | (~c3_1(a112))))),
% 1.67/1.42 inference(monotonicity,[status(thm)],[1931])).
% 1.67/1.42 tff(1933,plain,
% 1.67/1.42 (((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp9 | hskp6 | (~ndr1_0) | c1_1(a112) | c0_1(a112) | (~c3_1(a112)))) <=> ((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp9 | hskp6 | c0_1(a112) | c1_1(a112) | (~ndr1_0) | (~c3_1(a112)))),
% 1.67/1.42 inference(transitivity,[status(thm)],[1932, 1930])).
% 1.67/1.42 tff(1934,plain,
% 1.67/1.42 ((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp9 | hskp6 | (~ndr1_0) | c1_1(a112) | c0_1(a112) | (~c3_1(a112)))),
% 1.67/1.42 inference(quant_inst,[status(thm)],[])).
% 1.67/1.42 tff(1935,plain,
% 1.67/1.42 ((~![U: $i] : (hskp9 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp9 | hskp6 | c0_1(a112) | c1_1(a112) | (~ndr1_0) | (~c3_1(a112))),
% 1.67/1.42 inference(modus_ponens,[status(thm)],[1934, 1933])).
% 1.67/1.42 tff(1936,plain,
% 1.67/1.42 (hskp9 | hskp6),
% 1.67/1.42 inference(unit_resolution,[status(thm)],[1935, 126, 1897, 1861, 1860, 1929])).
% 1.67/1.42 tff(1937,plain,
% 1.67/1.42 (hskp9),
% 1.67/1.42 inference(unit_resolution,[status(thm)],[1936, 1919])).
% 1.67/1.42 tff(1938,plain,
% 1.67/1.42 (c2_1(a108)),
% 1.67/1.42 inference(unit_resolution,[status(thm)],[1076, 1937])).
% 1.67/1.42 tff(1939,plain,
% 1.67/1.42 (c1_1(a108)),
% 1.67/1.42 inference(unit_resolution,[status(thm)],[1087, 1937])).
% 1.67/1.42 tff(1940,plain,
% 1.67/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c1_1(a129) | (~ndr1_0) | (~c3_1(a108)) | (~c1_1(a108)) | (~c2_1(a108)) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a129) | (~ndr1_0) | (~c3_1(a108)) | (~c1_1(a108)) | (~c2_1(a108)) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129))),
% 1.67/1.42 inference(rewrite,[status(thm)],[])).
% 1.67/1.42 tff(1941,plain,
% 1.67/1.42 (((~ndr1_0) | (~c2_1(a108)) | (~c3_1(a108)) | (~c1_1(a108)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c1_1(a129) | c3_1(a129) | (~c2_1(a129))) <=> (c1_1(a129) | (~ndr1_0) | (~c3_1(a108)) | (~c1_1(a108)) | (~c2_1(a108)) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129))),
% 1.67/1.42 inference(rewrite,[status(thm)],[])).
% 1.67/1.42 tff(1942,plain,
% 1.67/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a108)) | (~c3_1(a108)) | (~c1_1(a108)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c1_1(a129) | c3_1(a129) | (~c2_1(a129)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c1_1(a129) | (~ndr1_0) | (~c3_1(a108)) | (~c1_1(a108)) | (~c2_1(a108)) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129)))),
% 1.67/1.42 inference(monotonicity,[status(thm)],[1941])).
% 1.67/1.42 tff(1943,plain,
% 1.67/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a108)) | (~c3_1(a108)) | (~c1_1(a108)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c1_1(a129) | c3_1(a129) | (~c2_1(a129)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a129) | (~ndr1_0) | (~c3_1(a108)) | (~c1_1(a108)) | (~c2_1(a108)) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129))),
% 1.67/1.43 inference(transitivity,[status(thm)],[1942, 1940])).
% 1.67/1.43 tff(1944,plain,
% 1.67/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a108)) | (~c3_1(a108)) | (~c1_1(a108)) | c1_1(a129) | (~c2_1(a129)) | (~c0_1(a129)) | c1_1(a129) | c3_1(a129) | (~c2_1(a129)))),
% 1.67/1.43 inference(quant_inst,[status(thm)],[])).
% 1.67/1.43 tff(1945,plain,
% 1.67/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a129) | (~ndr1_0) | (~c3_1(a108)) | (~c1_1(a108)) | (~c2_1(a108)) | (~c2_1(a129)) | (~c0_1(a129)) | c3_1(a129)),
% 1.67/1.43 inference(modus_ponens,[status(thm)],[1944, 1943])).
% 1.67/1.43 tff(1946,plain,
% 1.67/1.43 (~c3_1(a108)),
% 1.67/1.43 inference(unit_resolution,[status(thm)],[1945, 126, 1847, 1846, 1939, 1938, 1845, 690, 1848])).
% 1.67/1.43 tff(1947,plain,
% 1.67/1.43 (~c0_1(a108)),
% 1.67/1.43 inference(unit_resolution,[status(thm)],[1065, 1937])).
% 1.67/1.43 tff(1948,plain,
% 1.67/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a147) | c1_1(a147) | c3_1(a147) | c0_1(a112) | c1_1(a112) | c0_1(a108) | (~ndr1_0) | c3_1(a108) | (~c1_1(a108)) | (~c3_1(a112)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a147) | c1_1(a147) | c3_1(a147) | c0_1(a112) | c1_1(a112) | c0_1(a108) | (~ndr1_0) | c3_1(a108) | (~c1_1(a108)) | (~c3_1(a112)))),
% 1.67/1.43 inference(rewrite,[status(thm)],[])).
% 1.67/1.43 tff(1949,plain,
% 1.67/1.43 (((~ndr1_0) | c0_1(a108) | c3_1(a108) | (~c1_1(a108)) | c1_1(a112) | c0_1(a112) | (~c3_1(a112)) | c1_1(a147) | c0_1(a147) | c3_1(a147)) <=> (c0_1(a147) | c1_1(a147) | c3_1(a147) | c0_1(a112) | c1_1(a112) | c0_1(a108) | (~ndr1_0) | c3_1(a108) | (~c1_1(a108)) | (~c3_1(a112)))),
% 1.67/1.43 inference(rewrite,[status(thm)],[])).
% 1.67/1.43 tff(1950,plain,
% 1.67/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a108) | c3_1(a108) | (~c1_1(a108)) | c1_1(a112) | c0_1(a112) | (~c3_1(a112)) | c1_1(a147) | c0_1(a147) | c3_1(a147))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a147) | c1_1(a147) | c3_1(a147) | c0_1(a112) | c1_1(a112) | c0_1(a108) | (~ndr1_0) | c3_1(a108) | (~c1_1(a108)) | (~c3_1(a112))))),
% 1.67/1.43 inference(monotonicity,[status(thm)],[1949])).
% 1.67/1.43 tff(1951,plain,
% 1.67/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a108) | c3_1(a108) | (~c1_1(a108)) | c1_1(a112) | c0_1(a112) | (~c3_1(a112)) | c1_1(a147) | c0_1(a147) | c3_1(a147))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a147) | c1_1(a147) | c3_1(a147) | c0_1(a112) | c1_1(a112) | c0_1(a108) | (~ndr1_0) | c3_1(a108) | (~c1_1(a108)) | (~c3_1(a112)))),
% 1.67/1.43 inference(transitivity,[status(thm)],[1950, 1948])).
% 1.67/1.43 tff(1952,plain,
% 1.67/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c0_1(a108) | c3_1(a108) | (~c1_1(a108)) | c1_1(a112) | c0_1(a112) | (~c3_1(a112)) | c1_1(a147) | c0_1(a147) | c3_1(a147))),
% 1.67/1.43 inference(quant_inst,[status(thm)],[])).
% 1.67/1.43 tff(1953,plain,
% 1.67/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a147) | c1_1(a147) | c3_1(a147) | c0_1(a112) | c1_1(a112) | c0_1(a108) | (~ndr1_0) | c3_1(a108) | (~c1_1(a108)) | (~c3_1(a112))),
% 1.67/1.43 inference(modus_ponens,[status(thm)],[1952, 1951])).
% 1.67/1.43 tff(1954,plain,
% 1.67/1.43 ($false),
% 1.67/1.43 inference(unit_resolution,[status(thm)],[1953, 126, 1897, 1939, 1896, 1890, 1884, 1861, 1860, 1947, 1430, 1946])).
% 1.67/1.43 tff(1955,plain,(c2_1(a97)), inference(lemma,lemma(discharge,[]))).
% 1.67/1.43 tff(1956,plain,
% 1.67/1.43 (~hskp0),
% 1.67/1.43 inference(unit_resolution,[status(thm)],[242, 1955])).
% 1.67/1.43 tff(1957,plain,
% 1.67/1.43 (~hskp4),
% 1.67/1.43 inference(unit_resolution,[status(thm)],[1485, 52, 1956])).
% 1.67/1.43 tff(1958,plain,
% 1.67/1.43 (hskp20),
% 1.67/1.43 inference(unit_resolution,[status(thm)],[815, 52, 1957])).
% 1.67/1.43 tff(1959,plain,
% 1.67/1.43 (~c3_1(a132)),
% 1.67/1.43 inference(unit_resolution,[status(thm)],[720, 1958])).
% 1.67/1.43 tff(1960,plain,
% 1.67/1.43 (~c2_1(a132)),
% 1.67/1.43 inference(unit_resolution,[status(thm)],[740, 1958])).
% 1.67/1.43 tff(1961,plain,
% 1.67/1.43 (~c1_1(a132)),
% 1.67/1.43 inference(unit_resolution,[status(thm)],[726, 1958])).
% 1.67/1.43 tff(1962,plain,
% 1.67/1.43 (hskp19),
% 1.67/1.43 inference(unit_resolution,[status(thm)],[747, 126, 52, 1961, 1960, 1959, 30])).
% 1.67/1.43 tff(1963,plain,
% 1.67/1.43 (~c2_1(a130)),
% 1.67/1.43 inference(unit_resolution,[status(thm)],[252, 1962])).
% 1.67/1.43 tff(1964,plain,
% 1.67/1.43 (c3_1(a130)),
% 1.67/1.43 inference(unit_resolution,[status(thm)],[263, 1962])).
% 1.67/1.43 tff(1965,plain,
% 1.67/1.43 (c1_1(a130)),
% 1.67/1.43 inference(unit_resolution,[status(thm)],[274, 1962])).
% 1.67/1.43 tff(1966,plain,
% 1.67/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a132) | c2_1(a132) | c3_1(a132) | c2_1(a130) | (~ndr1_0) | (~c3_1(a130)) | (~c1_1(a130)) | (~c0_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a132) | c2_1(a132) | c3_1(a132) | c2_1(a130) | (~ndr1_0) | (~c3_1(a130)) | (~c1_1(a130)) | (~c0_1(a132)))),
% 1.67/1.43 inference(rewrite,[status(thm)],[])).
% 1.67/1.43 tff(1967,plain,
% 1.67/1.43 (((~ndr1_0) | c2_1(a130) | (~c3_1(a130)) | (~c1_1(a130)) | c2_1(a132) | c3_1(a132) | (~c0_1(a132)) | c1_1(a132) | c3_1(a132) | (~c0_1(a132))) <=> (c1_1(a132) | c2_1(a132) | c3_1(a132) | c2_1(a130) | (~ndr1_0) | (~c3_1(a130)) | (~c1_1(a130)) | (~c0_1(a132)))),
% 1.67/1.43 inference(rewrite,[status(thm)],[])).
% 1.67/1.43 tff(1968,plain,
% 1.67/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a130) | (~c3_1(a130)) | (~c1_1(a130)) | c2_1(a132) | c3_1(a132) | (~c0_1(a132)) | c1_1(a132) | c3_1(a132) | (~c0_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a132) | c2_1(a132) | c3_1(a132) | c2_1(a130) | (~ndr1_0) | (~c3_1(a130)) | (~c1_1(a130)) | (~c0_1(a132))))),
% 1.67/1.43 inference(monotonicity,[status(thm)],[1967])).
% 1.67/1.43 tff(1969,plain,
% 1.67/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a130) | (~c3_1(a130)) | (~c1_1(a130)) | c2_1(a132) | c3_1(a132) | (~c0_1(a132)) | c1_1(a132) | c3_1(a132) | (~c0_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a132) | c2_1(a132) | c3_1(a132) | c2_1(a130) | (~ndr1_0) | (~c3_1(a130)) | (~c1_1(a130)) | (~c0_1(a132)))),
% 1.67/1.43 inference(transitivity,[status(thm)],[1968, 1966])).
% 1.67/1.43 tff(1970,plain,
% 1.67/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a130) | (~c3_1(a130)) | (~c1_1(a130)) | c2_1(a132) | c3_1(a132) | (~c0_1(a132)) | c1_1(a132) | c3_1(a132) | (~c0_1(a132)))),
% 1.67/1.43 inference(quant_inst,[status(thm)],[])).
% 1.67/1.43 tff(1971,plain,
% 1.67/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a132) | c2_1(a132) | c3_1(a132) | c2_1(a130) | (~ndr1_0) | (~c3_1(a130)) | (~c1_1(a130)) | (~c0_1(a132))),
% 1.67/1.44 inference(modus_ponens,[status(thm)],[1970, 1969])).
% 1.67/1.44 tff(1972,plain,
% 1.67/1.44 (~c0_1(a132)),
% 1.67/1.44 inference(unit_resolution,[status(thm)],[1971, 126, 1965, 1964, 1961, 1960, 1959, 1963, 20])).
% 1.67/1.44 tff(1973,plain,
% 1.67/1.44 (hskp7),
% 1.67/1.44 inference(unit_resolution,[status(thm)],[1503, 1957])).
% 1.67/1.44 tff(1974,plain,
% 1.67/1.44 (~c0_1(a106)),
% 1.67/1.44 inference(unit_resolution,[status(thm)],[969, 1973])).
% 1.67/1.44 tff(1975,plain,
% 1.67/1.44 (c3_1(a106)),
% 1.67/1.44 inference(unit_resolution,[status(thm)],[919, 1973])).
% 1.67/1.44 tff(1976,plain,
% 1.67/1.44 (c2_1(a106)),
% 1.67/1.44 inference(unit_resolution,[status(thm)],[930, 1973])).
% 1.67/1.44 tff(1977,plain,
% 1.67/1.44 (~c0_1(a130)),
% 1.67/1.44 inference(unit_resolution,[status(thm)],[1839, 126, 1965, 1976, 1975, 1960, 1959, 1963, 1974, 525, 1972])).
% 1.67/1.44 tff(1978,plain,
% 1.67/1.44 ($false),
% 1.67/1.44 inference(unit_resolution,[status(thm)],[756, 126, 1956, 1964, 1961, 1960, 1963, 211, 1972, 1977])).
% 1.67/1.44 tff(1979,plain,(hskp18), inference(lemma,lemma(discharge,[]))).
% 1.67/1.44 tff(1980,plain,
% 1.67/1.44 (~c1_1(a129)),
% 1.67/1.44 inference(unit_resolution,[status(thm)],[297, 1979])).
% 1.67/1.44 tff(1981,plain,
% 1.67/1.44 (c2_1(a129)),
% 1.67/1.44 inference(unit_resolution,[status(thm)],[308, 1979])).
% 1.67/1.44 tff(1982,plain,
% 1.67/1.44 (c0_1(a129)),
% 1.67/1.44 inference(unit_resolution,[status(thm)],[319, 1979])).
% 1.67/1.44 tff(1983,plain,
% 1.67/1.44 (~c3_1(a129)),
% 1.67/1.44 inference(unit_resolution,[status(thm)],[891, 126, 1982, 1981, 1980, 10])).
% 1.67/1.44 tff(1984,plain,
% 1.67/1.44 (c1_1(a138)),
% 1.67/1.44 inference(unit_resolution,[status(thm)],[1587, 126, 1459, 1982, 1981, 1447, 1980, 143, 1983])).
% 1.67/1.44 tff(1985,plain,
% 1.67/1.44 (hskp11),
% 1.67/1.44 inference(unit_resolution,[status(thm)],[1604, 126, 1477, 1982, 1981, 1447, 1598, 1984, 1983])).
% 1.67/1.44 tff(1986,plain,
% 1.67/1.44 (~c1_1(a112)),
% 1.67/1.44 inference(unit_resolution,[status(thm)],[848, 1985])).
% 1.67/1.44 tff(1987,plain,
% 1.67/1.44 (~c0_1(a112)),
% 1.67/1.44 inference(unit_resolution,[status(thm)],[854, 1985])).
% 1.67/1.44 tff(1988,plain,
% 1.67/1.44 (c3_1(a112)),
% 1.67/1.44 inference(unit_resolution,[status(thm)],[1052, 1985])).
% 1.67/1.44 tff(1989,plain,
% 1.67/1.44 (hskp24),
% 1.67/1.44 inference(unit_resolution,[status(thm)],[1877, 126, 1459, 1477, 1982, 1981, 1447, 1980, 1871])).
% 1.67/1.44 tff(1990,plain,
% 1.67/1.44 (~c3_1(a147)),
% 1.67/1.44 inference(unit_resolution,[status(thm)],[1883, 1989])).
% 1.67/1.44 tff(1991,plain,
% 1.67/1.44 (~c1_1(a147)),
% 1.67/1.44 inference(unit_resolution,[status(thm)],[1889, 1989])).
% 1.67/1.44 tff(1992,plain,
% 1.67/1.44 (~c0_1(a147)),
% 1.67/1.44 inference(unit_resolution,[status(thm)],[1895, 1989])).
% 1.67/1.44 tff(1993,plain,
% 1.67/1.44 (~hskp6),
% 1.67/1.44 inference(unit_resolution,[status(thm)],[1918, 1988, 1992, 1991, 1990, 1987, 1986, 1956])).
% 1.67/1.44 tff(1994,plain,
% 1.67/1.44 (hskp9),
% 1.67/1.44 inference(unit_resolution,[status(thm)],[1935, 126, 1993, 1988, 1987, 1986, 1929])).
% 1.67/1.44 tff(1995,plain,
% 1.67/1.44 (c2_1(a108)),
% 1.67/1.44 inference(unit_resolution,[status(thm)],[1076, 1994])).
% 1.67/1.44 tff(1996,plain,
% 1.67/1.44 (c1_1(a108)),
% 1.67/1.44 inference(unit_resolution,[status(thm)],[1087, 1994])).
% 1.67/1.44 tff(1997,plain,
% 1.67/1.44 (~c3_1(a108)),
% 1.67/1.44 inference(unit_resolution,[status(thm)],[1945, 126, 1982, 1981, 1996, 1995, 1980, 690, 1983])).
% 1.67/1.44 tff(1998,plain,
% 1.67/1.44 (~c0_1(a108)),
% 1.67/1.44 inference(unit_resolution,[status(thm)],[1065, 1994])).
% 1.67/1.44 tff(1999,plain,
% 1.67/1.44 ($false),
% 1.67/1.44 inference(unit_resolution,[status(thm)],[1953, 126, 1988, 1996, 1992, 1991, 1990, 1987, 1986, 1998, 1430, 1997])).
% 1.67/1.44 % SZS output end Proof
%------------------------------------------------------------------------------