TSTP Solution File: SYN442-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN442-1 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.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 23:55:25 EDT 2022
% Result : Unsatisfiable 0.84s 0.80s
% Output : Proof 1.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN442-1 : TPTP v8.1.0. Released v2.1.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Sep 5 04:00:17 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.84/0.80 % SZS status Unsatisfiable
% 0.84/0.80 % SZS output start Proof
% 0.84/0.80 tff(c3_1_type, type, (
% 0.84/0.80 c3_1: $i > $o)).
% 0.84/0.80 tff(a179_type, type, (
% 0.84/0.80 a179: $i)).
% 0.84/0.80 tff(c2_1_type, type, (
% 0.84/0.80 c2_1: $i > $o)).
% 0.84/0.80 tff(c1_1_type, type, (
% 0.84/0.80 c1_1: $i > $o)).
% 0.84/0.80 tff(ndr1_0_type, type, (
% 0.84/0.80 ndr1_0: $o)).
% 0.84/0.80 tff(a131_type, type, (
% 0.84/0.80 a131: $i)).
% 0.84/0.80 tff(hskp5_type, type, (
% 0.84/0.80 hskp5: $o)).
% 0.84/0.80 tff(c0_1_type, type, (
% 0.84/0.80 c0_1: $i > $o)).
% 0.84/0.80 tff(a149_type, type, (
% 0.84/0.80 a149: $i)).
% 0.84/0.80 tff(a144_type, type, (
% 0.84/0.80 a144: $i)).
% 0.84/0.80 tff(hskp13_type, type, (
% 0.84/0.80 hskp13: $o)).
% 0.84/0.80 tff(a159_type, type, (
% 0.84/0.80 a159: $i)).
% 0.84/0.80 tff(hskp4_type, type, (
% 0.84/0.80 hskp4: $o)).
% 0.84/0.80 tff(a136_type, type, (
% 0.84/0.80 a136: $i)).
% 0.84/0.80 tff(hskp9_type, type, (
% 0.84/0.80 hskp9: $o)).
% 0.84/0.80 tff(a128_type, type, (
% 0.84/0.80 a128: $i)).
% 0.84/0.80 tff(hskp3_type, type, (
% 0.84/0.80 hskp3: $o)).
% 0.84/0.80 tff(a145_type, type, (
% 0.84/0.80 a145: $i)).
% 0.84/0.80 tff(hskp14_type, type, (
% 0.84/0.80 hskp14: $o)).
% 0.84/0.80 tff(a170_type, type, (
% 0.84/0.80 a170: $i)).
% 0.84/0.80 tff(hskp21_type, type, (
% 0.84/0.80 hskp21: $o)).
% 0.84/0.80 tff(hskp6_type, type, (
% 0.84/0.80 hskp6: $o)).
% 0.84/0.80 tff(hskp15_type, type, (
% 0.84/0.80 hskp15: $o)).
% 0.84/0.80 tff(a150_type, type, (
% 0.84/0.80 a150: $i)).
% 0.84/0.80 tff(hskp29_type, type, (
% 0.84/0.80 hskp29: $o)).
% 0.84/0.80 tff(a125_type, type, (
% 0.84/0.80 a125: $i)).
% 0.84/0.80 tff(hskp1_type, type, (
% 0.84/0.80 hskp1: $o)).
% 0.84/0.80 tff(hskp18_type, type, (
% 0.84/0.80 hskp18: $o)).
% 0.84/0.80 tff(a139_type, type, (
% 0.84/0.80 a139: $i)).
% 0.84/0.80 tff(hskp11_type, type, (
% 0.84/0.80 hskp11: $o)).
% 0.84/0.80 tff(a140_type, type, (
% 0.84/0.80 a140: $i)).
% 0.84/0.80 tff(a199_type, type, (
% 0.84/0.80 a199: $i)).
% 0.84/0.80 tff(hskp30_type, type, (
% 0.84/0.80 hskp30: $o)).
% 0.84/0.80 tff(hskp10_type, type, (
% 0.84/0.80 hskp10: $o)).
% 0.84/0.80 tff(a138_type, type, (
% 0.84/0.80 a138: $i)).
% 0.84/0.80 tff(a151_type, type, (
% 0.84/0.80 a151: $i)).
% 0.84/0.80 tff(hskp16_type, type, (
% 0.84/0.80 hskp16: $o)).
% 0.84/0.80 tff(hskp12_type, type, (
% 0.84/0.80 hskp12: $o)).
% 0.84/0.80 tff(a133_type, type, (
% 0.84/0.80 a133: $i)).
% 0.84/0.80 tff(a158_type, type, (
% 0.84/0.80 a158: $i)).
% 0.84/0.80 tff(hskp17_type, type, (
% 0.84/0.80 hskp17: $o)).
% 0.84/0.80 tff(a162_type, type, (
% 0.84/0.80 a162: $i)).
% 0.84/0.80 tff(hskp19_type, type, (
% 0.84/0.80 hskp19: $o)).
% 0.84/0.80 tff(hskp8_type, type, (
% 0.84/0.80 hskp8: $o)).
% 0.84/0.80 tff(a135_type, type, (
% 0.84/0.80 a135: $i)).
% 0.84/0.80 tff(a168_type, type, (
% 0.84/0.80 a168: $i)).
% 0.84/0.80 tff(hskp20_type, type, (
% 0.84/0.80 hskp20: $o)).
% 0.84/0.80 tff(hskp22_type, type, (
% 0.84/0.80 hskp22: $o)).
% 0.84/0.80 tff(a137_type, type, (
% 0.84/0.80 a137: $i)).
% 0.84/0.80 tff(hskp27_type, type, (
% 0.84/0.80 hskp27: $o)).
% 0.84/0.80 tff(a124_type, type, (
% 0.84/0.80 a124: $i)).
% 0.84/0.80 tff(hskp0_type, type, (
% 0.84/0.80 hskp0: $o)).
% 0.84/0.80 tff(a143_type, type, (
% 0.84/0.80 a143: $i)).
% 0.84/0.80 tff(hskp28_type, type, (
% 0.84/0.80 hskp28: $o)).
% 0.84/0.80 tff(a183_type, type, (
% 0.84/0.80 a183: $i)).
% 0.84/0.80 tff(hskp24_type, type, (
% 0.84/0.80 hskp24: $o)).
% 0.84/0.80 tff(a130_type, type, (
% 0.84/0.80 a130: $i)).
% 0.84/0.80 tff(1,plain,
% 0.84/0.80 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W))))),
% 0.84/0.80 inference(bind,[status(th)],[])).
% 0.84/0.80 tff(2,plain,
% 0.84/0.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.84/0.80 inference(quant_intro,[status(thm)],[1])).
% 0.84/0.80 tff(3,plain,
% 0.84/0.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.84/0.80 inference(rewrite,[status(thm)],[])).
% 0.84/0.80 tff(4,plain,
% 0.84/0.80 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(W)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(W))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c2_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c2_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c2_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))))),
% 0.84/0.80 inference(bind,[status(th)],[])).
% 0.84/0.80 tff(5,plain,
% 0.84/0.80 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.84/0.80 inference(quant_intro,[status(thm)],[4])).
% 0.84/0.80 tff(6,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause181')).
% 0.84/0.80 tff(7,plain,
% 0.84/0.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.84/0.80 tff(8,plain,
% 0.84/0.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.84/0.80 tff(9,plain,(
% 0.84/0.80 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.84/0.80 inference(skolemize,[status(sab)],[8])).
% 0.84/0.80 tff(10,plain,
% 0.84/0.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.84/0.80 tff(11,assumption,(~hskp13), introduced(assumption)).
% 0.84/0.80 tff(12,plain,
% 0.84/0.80 (^[V: $i, U: $i] : refl((hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 0.84/0.80 inference(bind,[status(th)],[])).
% 0.84/0.80 tff(13,plain,
% 0.84/0.80 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.84/0.80 inference(quant_intro,[status(thm)],[12])).
% 0.84/0.80 tff(14,plain,
% 0.84/0.80 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.84/0.80 inference(rewrite,[status(thm)],[])).
% 0.84/0.80 tff(15,plain,
% 0.84/0.80 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_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)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp13) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp13))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp13) <=> (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 0.84/0.80 inference(bind,[status(th)],[])).
% 0.84/0.80 tff(16,plain,
% 0.84/0.80 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp13) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.84/0.80 inference(quant_intro,[status(thm)],[15])).
% 0.84/0.80 tff(17,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause177')).
% 0.84/0.80 tff(18,plain,
% 0.84/0.80 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.84/0.80 tff(19,plain,
% 0.84/0.80 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.84/0.80 tff(20,plain,(
% 0.84/0.80 ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.84/0.80 inference(skolemize,[status(sab)],[19])).
% 0.84/0.80 tff(21,plain,
% 0.84/0.80 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.84/0.80 tff(22,plain,
% 0.84/0.80 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))),
% 0.84/0.80 inference(bind,[status(th)],[])).
% 0.84/0.80 tff(23,plain,
% 0.84/0.80 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.84/0.80 inference(quant_intro,[status(thm)],[22])).
% 0.84/0.80 tff(24,plain,
% 0.84/0.80 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.84/0.80 inference(rewrite,[status(thm)],[])).
% 0.84/0.80 tff(25,plain,
% 0.84/0.80 (^[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) | c0_1(U) | c2_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp9) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | hskp9))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))))),
% 0.84/0.80 inference(bind,[status(th)],[])).
% 0.84/0.80 tff(26,plain,
% 0.84/0.80 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.84/0.80 inference(quant_intro,[status(thm)],[25])).
% 0.84/0.80 tff(27,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause160')).
% 0.84/0.80 tff(28,plain,
% 0.84/0.80 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.84/0.80 tff(29,plain,
% 0.84/0.80 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.84/0.80 tff(30,plain,(
% 0.84/0.80 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.84/0.80 inference(skolemize,[status(sab)],[29])).
% 0.84/0.80 tff(31,plain,
% 0.84/0.80 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.84/0.80 tff(32,plain,
% 0.84/0.80 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))),
% 0.84/0.80 inference(bind,[status(th)],[])).
% 0.84/0.80 tff(33,plain,
% 0.84/0.80 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.84/0.80 inference(quant_intro,[status(thm)],[32])).
% 0.84/0.80 tff(34,plain,
% 0.84/0.80 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.84/0.80 inference(rewrite,[status(thm)],[])).
% 0.84/0.80 tff(35,plain,
% 0.84/0.80 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp3) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp3))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))))),
% 0.84/0.80 inference(bind,[status(th)],[])).
% 0.84/0.80 tff(36,plain,
% 0.84/0.80 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.84/0.80 inference(quant_intro,[status(thm)],[35])).
% 0.84/0.80 tff(37,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause162')).
% 0.84/0.80 tff(38,plain,
% 0.84/0.80 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.84/0.80 tff(39,plain,
% 0.84/0.80 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.84/0.80 tff(40,plain,(
% 0.84/0.80 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.84/0.80 inference(skolemize,[status(sab)],[39])).
% 0.84/0.80 tff(41,plain,
% 0.84/0.80 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.84/0.80 tff(42,plain,
% 0.84/0.80 (^[U: $i] : refl((hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) <=> (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))))),
% 0.84/0.80 inference(bind,[status(th)],[])).
% 0.84/0.80 tff(43,plain,
% 0.84/0.80 (![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 0.84/0.80 inference(quant_intro,[status(thm)],[42])).
% 0.84/0.80 tff(44,plain,
% 0.84/0.80 (![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 0.84/0.80 inference(rewrite,[status(thm)],[])).
% 0.84/0.80 tff(45,plain,
% 0.84/0.80 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp14) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp14))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp14) | hskp3) <=> ((hskp14 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp3))), rewrite(((hskp14 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp3) <=> (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp14) | hskp3) <=> (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))))),
% 0.84/0.80 inference(bind,[status(th)],[])).
% 0.84/0.80 tff(46,plain,
% 0.84/0.80 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp14) | hskp3) <=> ![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 0.84/0.80 inference(quant_intro,[status(thm)],[45])).
% 0.84/0.80 tff(47,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp14) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause138')).
% 0.84/0.80 tff(48,plain,
% 0.84/0.80 (![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.84/0.80 tff(49,plain,
% 0.84/0.80 (![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.84/0.80 tff(50,plain,(
% 0.84/0.80 ![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 0.84/0.80 inference(skolemize,[status(sab)],[49])).
% 0.84/0.80 tff(51,plain,
% 0.84/0.80 (![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.84/0.80 tff(52,assumption,(~hskp3), introduced(assumption)).
% 0.84/0.80 tff(53,assumption,(~hskp21), introduced(assumption)).
% 0.84/0.80 tff(54,plain,
% 0.84/0.80 (^[U: $i] : refl((hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 0.84/0.80 inference(bind,[status(th)],[])).
% 0.84/0.80 tff(55,plain,
% 0.84/0.80 (![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.84/0.80 inference(quant_intro,[status(thm)],[54])).
% 0.84/0.80 tff(56,plain,
% 0.84/0.80 (![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.84/0.80 inference(rewrite,[status(thm)],[])).
% 0.84/0.80 tff(57,plain,
% 0.84/0.80 (^[U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp15))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.84/0.80 inference(bind,[status(th)],[])).
% 0.84/0.80 tff(58,plain,
% 0.84/0.80 (![U: $i] : (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) <=> ![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.84/0.80 inference(quant_intro,[status(thm)],[57])).
% 0.84/0.80 tff(59,axiom,(![U: $i] : (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause147')).
% 0.84/0.80 tff(60,plain,
% 0.84/0.80 (![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.84/0.81 tff(61,plain,
% 0.84/0.81 (![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.84/0.81 tff(62,plain,(
% 0.84/0.81 ![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.84/0.81 inference(skolemize,[status(sab)],[61])).
% 0.84/0.81 tff(63,plain,
% 0.84/0.81 (![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.84/0.81 tff(64,plain,
% 0.84/0.81 (^[U: $i] : refl((hskp29 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp29 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))),
% 0.84/0.81 inference(bind,[status(th)],[])).
% 0.84/0.81 tff(65,plain,
% 0.84/0.81 (![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.84/0.81 inference(quant_intro,[status(thm)],[64])).
% 0.84/0.81 tff(66,plain,
% 0.84/0.81 (![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.84/0.81 inference(rewrite,[status(thm)],[])).
% 0.84/0.81 tff(67,plain,
% 0.84/0.81 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp29) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp29))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp29) <=> (hskp29 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp29) <=> (hskp29 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp29) | hskp3) <=> ((hskp29 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp3))), rewrite(((hskp29 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp3) <=> (hskp29 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp29) | hskp3) <=> (hskp29 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))))),
% 0.84/0.81 inference(bind,[status(th)],[])).
% 0.84/0.81 tff(68,plain,
% 0.84/0.81 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp29) | hskp3) <=> ![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.84/0.81 inference(quant_intro,[status(thm)],[67])).
% 0.84/0.81 tff(69,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp29) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause140')).
% 0.84/0.81 tff(70,plain,
% 0.84/0.81 (![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.84/0.81 tff(71,plain,
% 0.84/0.81 (![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.84/0.81 tff(72,plain,(
% 0.84/0.81 ![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.84/0.81 inference(skolemize,[status(sab)],[71])).
% 0.84/0.81 tff(73,plain,
% 0.84/0.81 (![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[72, 65])).
% 0.84/0.81 tff(74,assumption,(~hskp15), introduced(assumption)).
% 0.84/0.81 tff(75,plain,
% 0.84/0.81 (^[U: $i] : refl((hskp3 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> (hskp3 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))),
% 0.84/0.81 inference(bind,[status(th)],[])).
% 0.84/0.81 tff(76,plain,
% 0.84/0.81 (![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.84/0.81 inference(quant_intro,[status(thm)],[75])).
% 0.84/0.81 tff(77,plain,
% 0.84/0.81 (![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.84/0.81 inference(rewrite,[status(thm)],[])).
% 0.84/0.81 tff(78,plain,
% 0.84/0.81 (^[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) | c3_1(U) | c2_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp1) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp1))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp1) | hskp3) <=> ((hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp3))), rewrite(((hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp3) <=> (hskp3 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp1) | hskp3) <=> (hskp3 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))))),
% 0.84/0.81 inference(bind,[status(th)],[])).
% 0.84/0.81 tff(79,plain,
% 0.84/0.81 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp1) | hskp3) <=> ![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.84/0.81 inference(quant_intro,[status(thm)],[78])).
% 0.84/0.81 tff(80,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp1) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause145')).
% 0.84/0.81 tff(81,plain,
% 0.84/0.81 (![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.84/0.81 tff(82,plain,
% 0.84/0.81 (![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.84/0.81 tff(83,plain,(
% 0.84/0.81 ![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.84/0.81 inference(skolemize,[status(sab)],[82])).
% 0.84/0.81 tff(84,plain,
% 0.84/0.81 (![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[83, 76])).
% 0.84/0.81 tff(85,plain,
% 0.84/0.81 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W))))),
% 0.84/0.81 inference(bind,[status(th)],[])).
% 0.84/0.81 tff(86,plain,
% 0.84/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | 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)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.84/0.81 inference(quant_intro,[status(thm)],[85])).
% 0.84/0.81 tff(87,plain,
% 0.84/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | 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)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.84/0.81 inference(rewrite,[status(thm)],[])).
% 0.84/0.81 tff(88,plain,
% 0.84/0.81 (^[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))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c2_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c2_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c2_1(V)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c2_1(V)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))))),
% 0.84/0.81 inference(bind,[status(th)],[])).
% 0.84/0.81 tff(89,plain,
% 0.84/0.81 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c2_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) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.84/0.81 inference(quant_intro,[status(thm)],[88])).
% 0.84/0.81 tff(90,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c2_1(V)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause184')).
% 0.84/0.81 tff(91,plain,
% 0.84/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.84/0.81 tff(92,plain,
% 0.84/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.84/0.81 tff(93,plain,(
% 0.84/0.81 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.84/0.81 inference(skolemize,[status(sab)],[92])).
% 0.84/0.81 tff(94,plain,
% 0.84/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[93, 86])).
% 0.84/0.81 tff(95,assumption,(~hskp18), introduced(assumption)).
% 0.84/0.81 tff(96,assumption,(hskp10), introduced(assumption)).
% 0.84/0.81 tff(97,plain,
% 0.84/0.81 (((~hskp10) | (~c1_1(a138))) <=> ((~hskp10) | (~c1_1(a138)))),
% 0.84/0.81 inference(rewrite,[status(thm)],[])).
% 0.84/0.81 tff(98,plain,
% 0.84/0.81 (((~c1_1(a138)) | (~hskp10)) <=> ((~hskp10) | (~c1_1(a138)))),
% 0.84/0.81 inference(rewrite,[status(thm)],[])).
% 0.84/0.81 tff(99,axiom,((~c1_1(a138)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause113')).
% 0.84/0.81 tff(100,plain,
% 0.84/0.81 ((~hskp10) | (~c1_1(a138))),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.84/0.81 tff(101,plain,
% 0.84/0.81 ((~hskp10) | (~c1_1(a138))),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[100, 97])).
% 0.84/0.81 tff(102,plain,
% 0.84/0.81 (~c1_1(a138)),
% 0.84/0.81 inference(unit_resolution,[status(thm)],[101, 96])).
% 0.84/0.81 tff(103,plain,
% 0.84/0.81 (((~hskp10) | c3_1(a138)) <=> ((~hskp10) | c3_1(a138))),
% 0.84/0.81 inference(rewrite,[status(thm)],[])).
% 0.84/0.81 tff(104,axiom,((~hskp10) | c3_1(a138)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause69')).
% 0.84/0.81 tff(105,plain,
% 0.84/0.81 ((~hskp10) | c3_1(a138)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.84/0.81 tff(106,plain,
% 0.84/0.81 ((~hskp10) | c3_1(a138)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[105, 103])).
% 0.84/0.81 tff(107,plain,
% 0.84/0.81 ((~hskp10) | c3_1(a138)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[106, 103])).
% 0.84/0.81 tff(108,plain,
% 0.84/0.81 ((~hskp10) | c3_1(a138)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.84/0.81 tff(109,plain,
% 0.84/0.81 ((~hskp10) | c3_1(a138)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[108, 103])).
% 0.84/0.81 tff(110,plain,
% 0.84/0.81 ((~hskp10) | c3_1(a138)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[109, 103])).
% 0.84/0.81 tff(111,plain,
% 0.84/0.81 ((~hskp10) | c3_1(a138)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[110, 103])).
% 0.84/0.81 tff(112,plain,
% 0.84/0.81 ((~hskp10) | c3_1(a138)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[111, 103])).
% 0.84/0.81 tff(113,plain,
% 0.84/0.81 (c3_1(a138)),
% 0.84/0.81 inference(unit_resolution,[status(thm)],[112, 96])).
% 0.84/0.81 tff(114,plain,
% 0.84/0.81 (((~hskp10) | c0_1(a138)) <=> ((~hskp10) | c0_1(a138))),
% 0.84/0.81 inference(rewrite,[status(thm)],[])).
% 0.84/0.81 tff(115,axiom,((~hskp10) | c0_1(a138)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause68')).
% 0.84/0.81 tff(116,plain,
% 0.84/0.81 ((~hskp10) | c0_1(a138)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.84/0.81 tff(117,plain,
% 0.84/0.81 ((~hskp10) | c0_1(a138)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[116, 114])).
% 0.84/0.81 tff(118,plain,
% 0.84/0.81 ((~hskp10) | c0_1(a138)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[117, 114])).
% 0.84/0.81 tff(119,plain,
% 0.84/0.81 ((~hskp10) | c0_1(a138)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.84/0.81 tff(120,plain,
% 0.84/0.81 ((~hskp10) | c0_1(a138)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[119, 114])).
% 0.84/0.81 tff(121,plain,
% 0.84/0.81 ((~hskp10) | c0_1(a138)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[120, 114])).
% 0.84/0.81 tff(122,plain,
% 0.84/0.81 ((~hskp10) | c0_1(a138)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[121, 114])).
% 0.84/0.81 tff(123,plain,
% 0.84/0.81 ((~hskp10) | c0_1(a138)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[122, 114])).
% 0.84/0.81 tff(124,plain,
% 0.84/0.81 (c0_1(a138)),
% 0.84/0.81 inference(unit_resolution,[status(thm)],[123, 96])).
% 0.84/0.81 tff(125,plain,
% 0.84/0.81 (^[U: $i] : refl((hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) <=> (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))))),
% 0.84/0.81 inference(bind,[status(th)],[])).
% 0.84/0.81 tff(126,plain,
% 0.84/0.81 (![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.84/0.81 inference(quant_intro,[status(thm)],[125])).
% 0.84/0.81 tff(127,plain,
% 0.84/0.81 (![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.84/0.81 inference(rewrite,[status(thm)],[])).
% 0.84/0.81 tff(128,plain,
% 0.84/0.81 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp18) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | hskp18))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | hskp18) <=> (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp18) <=> (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp18) | hskp21) <=> ((hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | hskp21))), rewrite(((hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | hskp21) <=> (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp18) | hskp21) <=> (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))))),
% 0.84/0.81 inference(bind,[status(th)],[])).
% 0.84/0.81 tff(129,plain,
% 0.84/0.81 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp18) | hskp21) <=> ![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.84/0.81 inference(quant_intro,[status(thm)],[128])).
% 0.84/0.81 tff(130,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp18) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause146')).
% 0.84/0.81 tff(131,plain,
% 0.84/0.81 (![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.84/0.81 tff(132,plain,
% 0.84/0.81 (![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[131, 127])).
% 0.84/0.81 tff(133,plain,(
% 0.84/0.81 ![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.84/0.81 inference(skolemize,[status(sab)],[132])).
% 0.84/0.81 tff(134,plain,
% 0.84/0.81 (![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[133, 126])).
% 0.84/0.81 tff(135,plain,
% 0.84/0.81 (^[U: $i] : refl((hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 0.84/0.81 inference(bind,[status(th)],[])).
% 0.84/0.81 tff(136,plain,
% 0.84/0.81 (![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.84/0.81 inference(quant_intro,[status(thm)],[135])).
% 0.84/0.81 tff(137,plain,
% 0.84/0.81 (![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.84/0.81 inference(rewrite,[status(thm)],[])).
% 0.84/0.81 tff(138,plain,
% 0.84/0.81 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp16) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp16))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp16) <=> (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp16) <=> (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp16) | hskp21) <=> ((hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp21))), rewrite(((hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp21) <=> (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp16) | hskp21) <=> (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.84/0.81 inference(bind,[status(th)],[])).
% 0.84/0.81 tff(139,plain,
% 0.84/0.81 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp16) | hskp21) <=> ![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.84/0.81 inference(quant_intro,[status(thm)],[138])).
% 0.84/0.81 tff(140,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp16) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause149')).
% 0.84/0.81 tff(141,plain,
% 0.84/0.81 (![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.84/0.81 tff(142,plain,
% 0.84/0.81 (![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[141, 137])).
% 0.84/0.81 tff(143,plain,(
% 0.84/0.81 ![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.84/0.81 inference(skolemize,[status(sab)],[142])).
% 0.84/0.81 tff(144,plain,
% 0.84/0.81 (![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[143, 136])).
% 0.84/0.81 tff(145,assumption,(~c1_1(a138)), introduced(assumption)).
% 0.84/0.81 tff(146,assumption,(c3_1(a138)), introduced(assumption)).
% 0.84/0.81 tff(147,assumption,(c0_1(a138)), introduced(assumption)).
% 0.84/0.81 tff(148,assumption,(~ndr1_0), introduced(assumption)).
% 0.84/0.81 tff(149,plain,
% 0.84/0.81 ((ndr1_0 | (~hskp10)) <=> (ndr1_0 | (~hskp10))),
% 0.84/0.81 inference(rewrite,[status(thm)],[])).
% 0.84/0.81 tff(150,plain,
% 0.84/0.81 (((~hskp10) | ndr1_0) <=> (ndr1_0 | (~hskp10))),
% 0.84/0.81 inference(rewrite,[status(thm)],[])).
% 0.84/0.81 tff(151,axiom,((~hskp10) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause22')).
% 0.84/0.81 tff(152,plain,
% 0.84/0.81 (ndr1_0 | (~hskp10)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.84/0.81 tff(153,plain,
% 0.84/0.81 (ndr1_0 | (~hskp10)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[152, 149])).
% 0.84/0.81 tff(154,plain,
% 0.84/0.81 (~hskp10),
% 0.84/0.81 inference(unit_resolution,[status(thm)],[153, 148])).
% 0.84/0.81 tff(155,plain,
% 0.84/0.81 (((~hskp30) | ndr1_0) <=> ((~hskp30) | ndr1_0)),
% 0.84/0.81 inference(rewrite,[status(thm)],[])).
% 0.84/0.81 tff(156,axiom,((~hskp30) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause2')).
% 0.84/0.81 tff(157,plain,
% 0.84/0.81 ((~hskp30) | ndr1_0),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.84/0.81 tff(158,plain,
% 0.84/0.81 ((~hskp30) | ndr1_0),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[157, 155])).
% 0.84/0.81 tff(159,plain,
% 0.84/0.81 ((~hskp30) | ndr1_0),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[158, 155])).
% 0.84/0.81 tff(160,plain,
% 0.84/0.81 ((~hskp30) | ndr1_0),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[159, 155])).
% 0.84/0.81 tff(161,plain,
% 0.84/0.81 ((~hskp30) | ndr1_0),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[160, 155])).
% 0.84/0.81 tff(162,plain,
% 0.84/0.81 ((~hskp30) | ndr1_0),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[161, 155])).
% 0.84/0.81 tff(163,plain,
% 0.84/0.81 ((~hskp30) | ndr1_0),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[162, 155])).
% 0.84/0.81 tff(164,plain,
% 0.84/0.81 ((~hskp30) | ndr1_0),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[163, 155])).
% 0.84/0.81 tff(165,plain,
% 0.84/0.81 (~hskp30),
% 0.84/0.81 inference(unit_resolution,[status(thm)],[164, 148])).
% 0.84/0.81 tff(166,plain,
% 0.84/0.81 ((ndr1_0 | (~hskp18)) <=> (ndr1_0 | (~hskp18))),
% 0.84/0.81 inference(rewrite,[status(thm)],[])).
% 0.84/0.81 tff(167,plain,
% 0.84/0.81 (((~hskp18) | ndr1_0) <=> (ndr1_0 | (~hskp18))),
% 0.84/0.81 inference(rewrite,[status(thm)],[])).
% 0.84/0.81 tff(168,axiom,((~hskp18) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause14')).
% 0.84/0.81 tff(169,plain,
% 0.84/0.81 (ndr1_0 | (~hskp18)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.84/0.81 tff(170,plain,
% 0.84/0.81 (ndr1_0 | (~hskp18)),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[169, 166])).
% 0.84/0.81 tff(171,plain,
% 0.84/0.81 (~hskp18),
% 0.84/0.81 inference(unit_resolution,[status(thm)],[170, 148])).
% 0.84/0.81 tff(172,plain,
% 0.84/0.81 ((hskp30 | hskp18 | hskp10) <=> (hskp30 | hskp18 | hskp10)),
% 0.84/0.81 inference(rewrite,[status(thm)],[])).
% 0.84/0.81 tff(173,plain,
% 0.84/0.81 (((hskp30 | hskp10) | hskp18) <=> (hskp30 | hskp18 | hskp10)),
% 0.84/0.81 inference(rewrite,[status(thm)],[])).
% 0.84/0.81 tff(174,plain,
% 0.84/0.81 ((hskp30 | hskp10) <=> (hskp30 | hskp10)),
% 0.84/0.81 inference(rewrite,[status(thm)],[])).
% 0.84/0.81 tff(175,plain,
% 0.84/0.81 (((hskp30 | hskp10) | hskp18) <=> ((hskp30 | hskp10) | hskp18)),
% 0.84/0.81 inference(monotonicity,[status(thm)],[174])).
% 0.84/0.81 tff(176,plain,
% 0.84/0.81 (((hskp30 | hskp10) | hskp18) <=> (hskp30 | hskp18 | hskp10)),
% 0.84/0.81 inference(transitivity,[status(thm)],[175, 173])).
% 0.84/0.81 tff(177,axiom,((hskp30 | hskp10) | hskp18), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause33')).
% 0.84/0.81 tff(178,plain,
% 0.84/0.81 (hskp30 | hskp18 | hskp10),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.84/0.81 tff(179,plain,
% 0.84/0.81 (hskp30 | hskp18 | hskp10),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[178, 172])).
% 0.84/0.81 tff(180,plain,
% 0.84/0.81 (hskp30 | hskp18 | hskp10),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[179, 172])).
% 0.84/0.81 tff(181,plain,
% 0.84/0.81 (hskp30 | hskp18 | hskp10),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[180, 172])).
% 0.84/0.81 tff(182,plain,
% 0.84/0.81 (hskp30 | hskp18 | hskp10),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[181, 172])).
% 0.84/0.81 tff(183,plain,
% 0.84/0.81 (hskp30 | hskp18 | hskp10),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[182, 172])).
% 0.84/0.81 tff(184,plain,
% 0.84/0.81 (hskp30 | hskp18 | hskp10),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[183, 172])).
% 0.84/0.81 tff(185,plain,
% 0.84/0.81 (hskp30 | hskp18 | hskp10),
% 0.84/0.81 inference(modus_ponens,[status(thm)],[184, 172])).
% 0.84/0.81 tff(186,plain,
% 0.84/0.81 ($false),
% 0.84/0.81 inference(unit_resolution,[status(thm)],[185, 171, 165, 154])).
% 0.84/0.81 tff(187,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.84/0.81 tff(188,plain,
% 0.84/0.81 (((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp16 | c1_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)))) <=> ((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp16 | c1_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)))),
% 0.84/0.81 inference(rewrite,[status(thm)],[])).
% 0.84/0.81 tff(189,plain,
% 0.84/0.81 ((hskp21 | hskp16 | (~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138))) <=> (hskp21 | hskp16 | c1_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)))),
% 0.84/0.81 inference(rewrite,[status(thm)],[])).
% 0.84/0.81 tff(190,plain,
% 0.84/0.81 (((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp16 | (~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)))) <=> ((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp16 | c1_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138))))),
% 0.84/0.81 inference(monotonicity,[status(thm)],[189])).
% 0.84/0.81 tff(191,plain,
% 0.84/0.81 (((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp16 | (~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)))) <=> ((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp16 | c1_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)))),
% 0.84/0.81 inference(transitivity,[status(thm)],[190, 188])).
% 0.84/0.82 tff(192,plain,
% 0.84/0.82 ((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp16 | (~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)))),
% 0.84/0.82 inference(quant_inst,[status(thm)],[])).
% 0.84/0.82 tff(193,plain,
% 0.84/0.82 ((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp16 | c1_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138))),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.84/0.82 tff(194,plain,
% 0.84/0.82 (hskp21 | hskp16),
% 0.84/0.82 inference(unit_resolution,[status(thm)],[193, 187, 147, 146, 145, 144])).
% 0.84/0.82 tff(195,plain,
% 0.84/0.82 (hskp16),
% 0.84/0.82 inference(unit_resolution,[status(thm)],[194, 53])).
% 0.84/0.82 tff(196,plain,
% 0.84/0.82 (((~hskp16) | (~c2_1(a151))) <=> ((~hskp16) | (~c2_1(a151)))),
% 0.84/0.82 inference(rewrite,[status(thm)],[])).
% 0.84/0.82 tff(197,plain,
% 0.84/0.82 (((~c2_1(a151)) | (~hskp16)) <=> ((~hskp16) | (~c2_1(a151)))),
% 0.84/0.82 inference(rewrite,[status(thm)],[])).
% 0.84/0.82 tff(198,axiom,((~c2_1(a151)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause102')).
% 0.84/0.82 tff(199,plain,
% 0.84/0.82 ((~hskp16) | (~c2_1(a151))),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.84/0.82 tff(200,plain,
% 0.84/0.82 ((~hskp16) | (~c2_1(a151))),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[199, 196])).
% 0.84/0.82 tff(201,plain,
% 0.84/0.82 (~c2_1(a151)),
% 0.84/0.82 inference(unit_resolution,[status(thm)],[200, 195])).
% 0.84/0.82 tff(202,plain,
% 0.84/0.82 (((~hskp16) | c1_1(a151)) <=> ((~hskp16) | c1_1(a151))),
% 0.84/0.82 inference(rewrite,[status(thm)],[])).
% 0.84/0.82 tff(203,axiom,((~hskp16) | c1_1(a151)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause62')).
% 0.84/0.82 tff(204,plain,
% 0.84/0.82 ((~hskp16) | c1_1(a151)),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.84/0.82 tff(205,plain,
% 0.84/0.82 ((~hskp16) | c1_1(a151)),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[204, 202])).
% 0.84/0.82 tff(206,plain,
% 0.84/0.82 ((~hskp16) | c1_1(a151)),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[205, 202])).
% 0.84/0.82 tff(207,plain,
% 0.84/0.82 ((~hskp16) | c1_1(a151)),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[206, 202])).
% 0.84/0.82 tff(208,plain,
% 0.84/0.82 ((~hskp16) | c1_1(a151)),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[207, 202])).
% 0.84/0.82 tff(209,plain,
% 0.84/0.82 ((~hskp16) | c1_1(a151)),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[208, 202])).
% 0.84/0.82 tff(210,plain,
% 0.84/0.82 ((~hskp16) | c1_1(a151)),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[209, 202])).
% 0.84/0.82 tff(211,plain,
% 0.84/0.82 ((~hskp16) | c1_1(a151)),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[210, 202])).
% 0.84/0.82 tff(212,plain,
% 0.84/0.82 (c1_1(a151)),
% 0.84/0.82 inference(unit_resolution,[status(thm)],[211, 195])).
% 0.84/0.82 tff(213,plain,
% 0.84/0.82 (((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | c2_1(a151) | (~ndr1_0) | c3_1(a151) | (~c1_1(a151)))) <=> ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp21 | hskp18 | c2_1(a151) | (~ndr1_0) | c3_1(a151) | (~c1_1(a151)))),
% 0.84/0.82 inference(rewrite,[status(thm)],[])).
% 0.84/0.82 tff(214,plain,
% 0.84/0.82 ((hskp21 | hskp18 | (~ndr1_0) | c3_1(a151) | c2_1(a151) | (~c1_1(a151))) <=> (hskp21 | hskp18 | c2_1(a151) | (~ndr1_0) | c3_1(a151) | (~c1_1(a151)))),
% 0.84/0.82 inference(rewrite,[status(thm)],[])).
% 0.84/0.82 tff(215,plain,
% 0.84/0.82 (((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | (~ndr1_0) | c3_1(a151) | c2_1(a151) | (~c1_1(a151)))) <=> ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | c2_1(a151) | (~ndr1_0) | c3_1(a151) | (~c1_1(a151))))),
% 0.84/0.82 inference(monotonicity,[status(thm)],[214])).
% 0.84/0.82 tff(216,plain,
% 0.84/0.82 (((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | (~ndr1_0) | c3_1(a151) | c2_1(a151) | (~c1_1(a151)))) <=> ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp21 | hskp18 | c2_1(a151) | (~ndr1_0) | c3_1(a151) | (~c1_1(a151)))),
% 0.84/0.82 inference(transitivity,[status(thm)],[215, 213])).
% 0.84/0.82 tff(217,plain,
% 0.84/0.82 ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | (~ndr1_0) | c3_1(a151) | c2_1(a151) | (~c1_1(a151)))),
% 0.84/0.82 inference(quant_inst,[status(thm)],[])).
% 0.84/0.82 tff(218,plain,
% 0.84/0.82 ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp21 | hskp18 | c2_1(a151) | (~ndr1_0) | c3_1(a151) | (~c1_1(a151))),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.84/0.82 tff(219,plain,
% 0.84/0.82 (c3_1(a151)),
% 0.84/0.82 inference(unit_resolution,[status(thm)],[218, 187, 53, 95, 212, 201, 134])).
% 0.84/0.82 tff(220,plain,
% 0.84/0.82 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_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) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W))))),
% 0.84/0.82 inference(bind,[status(th)],[])).
% 0.84/0.82 tff(221,plain,
% 0.84/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 0.84/0.82 inference(quant_intro,[status(thm)],[220])).
% 0.84/0.82 tff(222,plain,
% 0.84/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 0.84/0.82 inference(rewrite,[status(thm)],[])).
% 0.84/0.82 tff(223,plain,
% 0.84/0.82 (^[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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(W)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(W))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(W)) | (~c3_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(W)) | (~c3_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(W)) | (~c3_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(W)) | (~c3_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(W)) | (~c3_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(W)) | (~c3_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c2_1(W)) | (~c3_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c2_1(W)) | (~c3_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))))),
% 0.84/0.82 inference(bind,[status(th)],[])).
% 0.84/0.82 tff(224,plain,
% 0.84/0.82 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 0.84/0.82 inference(quant_intro,[status(thm)],[223])).
% 0.84/0.82 tff(225,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause182')).
% 0.84/0.82 tff(226,plain,
% 0.84/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.84/0.82 tff(227,plain,
% 0.84/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[226, 222])).
% 0.84/0.82 tff(228,plain,(
% 0.84/0.82 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 0.84/0.82 inference(skolemize,[status(sab)],[227])).
% 0.84/0.82 tff(229,plain,
% 0.84/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[228, 221])).
% 0.84/0.82 tff(230,plain,
% 0.84/0.82 (^[U: $i] : refl((hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 0.84/0.82 inference(bind,[status(th)],[])).
% 0.84/0.82 tff(231,plain,
% 0.84/0.82 (![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.84/0.82 inference(quant_intro,[status(thm)],[230])).
% 0.84/0.82 tff(232,plain,
% 0.84/0.82 (![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.84/0.82 inference(rewrite,[status(thm)],[])).
% 0.84/0.82 tff(233,plain,
% 0.84/0.82 (^[U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp12) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp12))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.84/0.82 inference(bind,[status(th)],[])).
% 0.84/0.82 tff(234,plain,
% 0.84/0.82 (![U: $i] : (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp12) <=> ![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.84/0.82 inference(quant_intro,[status(thm)],[233])).
% 0.84/0.82 tff(235,axiom,(![U: $i] : (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause148')).
% 0.84/0.82 tff(236,plain,
% 0.84/0.82 (![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.84/0.82 tff(237,plain,
% 0.84/0.82 (![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[236, 232])).
% 0.84/0.82 tff(238,plain,(
% 0.84/0.82 ![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.84/0.82 inference(skolemize,[status(sab)],[237])).
% 0.84/0.82 tff(239,plain,
% 0.84/0.82 (![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[238, 231])).
% 0.84/0.82 tff(240,plain,
% 0.84/0.82 (((~hskp16) | c0_1(a151)) <=> ((~hskp16) | c0_1(a151))),
% 0.84/0.82 inference(rewrite,[status(thm)],[])).
% 0.84/0.82 tff(241,axiom,((~hskp16) | c0_1(a151)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause61')).
% 0.84/0.82 tff(242,plain,
% 0.84/0.82 ((~hskp16) | c0_1(a151)),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.84/0.82 tff(243,plain,
% 0.84/0.82 ((~hskp16) | c0_1(a151)),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[242, 240])).
% 0.84/0.82 tff(244,plain,
% 0.84/0.82 ((~hskp16) | c0_1(a151)),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[243, 240])).
% 0.84/0.82 tff(245,plain,
% 0.84/0.82 ((~hskp16) | c0_1(a151)),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[244, 240])).
% 0.84/0.82 tff(246,plain,
% 0.84/0.82 ((~hskp16) | c0_1(a151)),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[245, 240])).
% 0.84/0.82 tff(247,plain,
% 0.84/0.82 ((~hskp16) | c0_1(a151)),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[246, 240])).
% 0.84/0.82 tff(248,plain,
% 0.84/0.82 ((~hskp16) | c0_1(a151)),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[247, 240])).
% 0.84/0.82 tff(249,plain,
% 0.84/0.82 ((~hskp16) | c0_1(a151)),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[248, 240])).
% 0.84/0.82 tff(250,plain,
% 0.84/0.82 (c0_1(a151)),
% 0.84/0.82 inference(unit_resolution,[status(thm)],[249, 195])).
% 0.84/0.82 tff(251,plain,
% 0.84/0.82 (((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | c2_1(a151) | (~ndr1_0) | (~c1_1(a151)) | (~c0_1(a151)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp15 | c2_1(a151) | (~ndr1_0) | (~c1_1(a151)) | (~c0_1(a151)))),
% 0.84/0.82 inference(rewrite,[status(thm)],[])).
% 0.84/0.82 tff(252,plain,
% 0.84/0.82 ((hskp15 | (~ndr1_0) | c2_1(a151) | (~c1_1(a151)) | (~c0_1(a151))) <=> (hskp15 | c2_1(a151) | (~ndr1_0) | (~c1_1(a151)) | (~c0_1(a151)))),
% 0.84/0.82 inference(rewrite,[status(thm)],[])).
% 0.84/0.82 tff(253,plain,
% 0.84/0.82 (((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | (~ndr1_0) | c2_1(a151) | (~c1_1(a151)) | (~c0_1(a151)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | c2_1(a151) | (~ndr1_0) | (~c1_1(a151)) | (~c0_1(a151))))),
% 0.84/0.82 inference(monotonicity,[status(thm)],[252])).
% 0.84/0.82 tff(254,plain,
% 0.84/0.82 (((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | (~ndr1_0) | c2_1(a151) | (~c1_1(a151)) | (~c0_1(a151)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp15 | c2_1(a151) | (~ndr1_0) | (~c1_1(a151)) | (~c0_1(a151)))),
% 0.84/0.82 inference(transitivity,[status(thm)],[253, 251])).
% 0.84/0.82 tff(255,plain,
% 0.84/0.82 ((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | (~ndr1_0) | c2_1(a151) | (~c1_1(a151)) | (~c0_1(a151)))),
% 0.84/0.82 inference(quant_inst,[status(thm)],[])).
% 0.84/0.82 tff(256,plain,
% 0.84/0.82 ((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp15 | c2_1(a151) | (~ndr1_0) | (~c1_1(a151)) | (~c0_1(a151))),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[255, 254])).
% 0.84/0.82 tff(257,plain,
% 0.84/0.82 (hskp15),
% 0.84/0.82 inference(unit_resolution,[status(thm)],[256, 187, 250, 212, 201, 63])).
% 0.84/0.82 tff(258,plain,
% 0.84/0.82 (((~hskp15) | c3_1(a149)) <=> ((~hskp15) | c3_1(a149))),
% 0.84/0.82 inference(rewrite,[status(thm)],[])).
% 0.84/0.82 tff(259,axiom,((~hskp15) | c3_1(a149)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause63')).
% 0.84/0.82 tff(260,plain,
% 0.84/0.82 ((~hskp15) | c3_1(a149)),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.84/0.82 tff(261,plain,
% 0.84/0.82 ((~hskp15) | c3_1(a149)),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[260, 258])).
% 0.84/0.82 tff(262,plain,
% 0.84/0.82 ((~hskp15) | c3_1(a149)),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[261, 258])).
% 0.84/0.82 tff(263,plain,
% 0.84/0.82 ((~hskp15) | c3_1(a149)),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[262, 258])).
% 0.84/0.82 tff(264,plain,
% 0.84/0.82 ((~hskp15) | c3_1(a149)),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[263, 258])).
% 0.84/0.82 tff(265,plain,
% 0.84/0.82 ((~hskp15) | c3_1(a149)),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[264, 258])).
% 0.84/0.82 tff(266,plain,
% 0.84/0.82 ((~hskp15) | c3_1(a149)),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[265, 258])).
% 0.84/0.82 tff(267,plain,
% 0.84/0.82 ((~hskp15) | c3_1(a149)),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[266, 258])).
% 0.84/0.82 tff(268,plain,
% 0.84/0.82 (c3_1(a149)),
% 0.84/0.82 inference(unit_resolution,[status(thm)],[267, 257])).
% 0.84/0.82 tff(269,assumption,(~c3_1(a128)), introduced(assumption)).
% 0.84/0.82 tff(270,plain,
% 0.84/0.82 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 0.84/0.82 inference(bind,[status(th)],[])).
% 0.84/0.82 tff(271,plain,
% 0.84/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_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) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.84/0.82 inference(quant_intro,[status(thm)],[270])).
% 0.84/0.82 tff(272,plain,
% 0.84/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_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) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.84/0.82 inference(rewrite,[status(thm)],[])).
% 0.84/0.82 tff(273,plain,
% 0.84/0.82 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c0_1(W))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 0.84/0.82 inference(bind,[status(th)],[])).
% 0.84/0.82 tff(274,plain,
% 0.84/0.82 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.84/0.82 inference(quant_intro,[status(thm)],[273])).
% 0.84/0.82 tff(275,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause178')).
% 0.84/0.82 tff(276,plain,
% 0.84/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[275, 274])).
% 0.84/0.82 tff(277,plain,
% 0.84/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[276, 272])).
% 0.84/0.82 tff(278,plain,(
% 0.84/0.82 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.84/0.82 inference(skolemize,[status(sab)],[277])).
% 0.84/0.82 tff(279,plain,
% 0.84/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[278, 271])).
% 0.84/0.82 tff(280,assumption,(~c2_1(a128)), introduced(assumption)).
% 0.84/0.82 tff(281,plain,
% 0.84/0.82 (^[V: $i, U: $i] : refl((hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))))),
% 0.84/0.82 inference(bind,[status(th)],[])).
% 0.84/0.82 tff(282,plain,
% 0.84/0.82 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.84/0.82 inference(quant_intro,[status(thm)],[281])).
% 0.84/0.82 tff(283,plain,
% 0.84/0.82 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.84/0.82 inference(rewrite,[status(thm)],[])).
% 0.84/0.82 tff(284,plain,
% 0.84/0.82 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) <=> ((~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(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp17) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) | hskp17))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))))),
% 0.84/0.82 inference(bind,[status(th)],[])).
% 0.84/0.82 tff(285,plain,
% 0.84/0.82 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp17) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.84/0.82 inference(quant_intro,[status(thm)],[284])).
% 0.84/0.82 tff(286,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause170')).
% 0.84/0.82 tff(287,plain,
% 0.84/0.82 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[286, 285])).
% 0.84/0.82 tff(288,plain,
% 0.84/0.82 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.84/0.82 inference(modus_ponens,[status(thm)],[287, 283])).
% 0.84/0.82 tff(289,plain,(
% 0.84/0.82 ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.84/0.83 inference(skolemize,[status(sab)],[288])).
% 0.84/0.83 tff(290,plain,
% 0.84/0.83 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[289, 282])).
% 0.84/0.83 tff(291,assumption,(~c0_1(a128)), introduced(assumption)).
% 0.84/0.83 tff(292,plain,
% 0.84/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a138) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a138)) | (~c0_1(a138)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a138) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a138)) | (~c0_1(a138)))),
% 0.84/0.83 inference(rewrite,[status(thm)],[])).
% 0.84/0.83 tff(293,plain,
% 0.84/0.83 (((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a128) | c1_1(a128) | c0_1(a128)) <=> (c1_1(a138) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a138)) | (~c0_1(a138)))),
% 0.84/0.83 inference(rewrite,[status(thm)],[])).
% 0.84/0.83 tff(294,plain,
% 0.84/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a128) | c1_1(a128) | c0_1(a128))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a138) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a138)) | (~c0_1(a138))))),
% 0.84/0.83 inference(monotonicity,[status(thm)],[293])).
% 0.84/0.83 tff(295,plain,
% 0.84/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a128) | c1_1(a128) | c0_1(a128))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a138) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a138)) | (~c0_1(a138)))),
% 0.84/0.83 inference(transitivity,[status(thm)],[294, 292])).
% 0.84/0.83 tff(296,plain,
% 0.84/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a128) | c1_1(a128) | c0_1(a128))),
% 0.84/0.83 inference(quant_inst,[status(thm)],[])).
% 0.84/0.83 tff(297,plain,
% 0.84/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a138) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a138)) | (~c0_1(a138))),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[296, 295])).
% 0.84/0.83 tff(298,plain,
% 0.84/0.83 (c0_1(a128) | c1_1(a128)),
% 0.84/0.83 inference(unit_resolution,[status(thm)],[297, 187, 147, 146, 145, 280, 269, 279])).
% 0.84/0.83 tff(299,plain,
% 0.84/0.83 (c1_1(a128)),
% 0.84/0.83 inference(unit_resolution,[status(thm)],[298, 291])).
% 0.84/0.83 tff(300,plain,
% 0.84/0.83 (((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)))) <=> ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp21 | hskp18 | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)))),
% 0.84/0.83 inference(rewrite,[status(thm)],[])).
% 0.84/0.83 tff(301,plain,
% 0.84/0.83 ((hskp21 | hskp18 | (~ndr1_0) | c3_1(a128) | c2_1(a128) | (~c1_1(a128))) <=> (hskp21 | hskp18 | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)))),
% 0.84/0.83 inference(rewrite,[status(thm)],[])).
% 0.84/0.83 tff(302,plain,
% 0.84/0.83 (((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | (~ndr1_0) | c3_1(a128) | c2_1(a128) | (~c1_1(a128)))) <=> ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128))))),
% 0.84/0.83 inference(monotonicity,[status(thm)],[301])).
% 0.84/0.83 tff(303,plain,
% 0.84/0.83 (((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | (~ndr1_0) | c3_1(a128) | c2_1(a128) | (~c1_1(a128)))) <=> ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp21 | hskp18 | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)))),
% 0.84/0.83 inference(transitivity,[status(thm)],[302, 300])).
% 0.84/0.83 tff(304,plain,
% 0.84/0.83 ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | (~ndr1_0) | c3_1(a128) | c2_1(a128) | (~c1_1(a128)))),
% 0.84/0.83 inference(quant_inst,[status(thm)],[])).
% 0.84/0.83 tff(305,plain,
% 0.84/0.83 ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp21 | hskp18 | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128))),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[304, 303])).
% 0.84/0.83 tff(306,plain,
% 0.84/0.83 (hskp21 | c2_1(a128) | (~c1_1(a128))),
% 0.84/0.83 inference(unit_resolution,[status(thm)],[305, 187, 95, 269, 134])).
% 0.84/0.83 tff(307,plain,
% 0.84/0.83 (hskp21),
% 0.84/0.83 inference(unit_resolution,[status(thm)],[306, 299, 280])).
% 0.84/0.83 tff(308,plain,
% 0.84/0.83 (((~hskp21) | (~c2_1(a170))) <=> ((~hskp21) | (~c2_1(a170)))),
% 0.84/0.83 inference(rewrite,[status(thm)],[])).
% 0.84/0.83 tff(309,plain,
% 0.84/0.83 (((~c2_1(a170)) | (~hskp21)) <=> ((~hskp21) | (~c2_1(a170)))),
% 0.84/0.83 inference(rewrite,[status(thm)],[])).
% 0.84/0.83 tff(310,axiom,((~c2_1(a170)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause94')).
% 0.84/0.83 tff(311,plain,
% 0.84/0.83 ((~hskp21) | (~c2_1(a170))),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[310, 309])).
% 0.84/0.83 tff(312,plain,
% 0.84/0.83 ((~hskp21) | (~c2_1(a170))),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[311, 308])).
% 0.84/0.83 tff(313,plain,
% 0.84/0.83 (~c2_1(a170)),
% 0.84/0.83 inference(unit_resolution,[status(thm)],[312, 307])).
% 0.84/0.83 tff(314,plain,
% 0.84/0.83 (((~hskp21) | (~c0_1(a170))) <=> ((~hskp21) | (~c0_1(a170)))),
% 0.84/0.83 inference(rewrite,[status(thm)],[])).
% 0.84/0.83 tff(315,plain,
% 0.84/0.83 (((~c0_1(a170)) | (~hskp21)) <=> ((~hskp21) | (~c0_1(a170)))),
% 0.84/0.83 inference(rewrite,[status(thm)],[])).
% 0.84/0.83 tff(316,axiom,((~c0_1(a170)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause93')).
% 0.84/0.83 tff(317,plain,
% 0.84/0.83 ((~hskp21) | (~c0_1(a170))),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[316, 315])).
% 0.84/0.83 tff(318,plain,
% 0.84/0.83 ((~hskp21) | (~c0_1(a170))),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[317, 314])).
% 0.84/0.83 tff(319,plain,
% 0.84/0.83 (~c0_1(a170)),
% 0.84/0.83 inference(unit_resolution,[status(thm)],[318, 307])).
% 0.84/0.83 tff(320,plain,
% 0.84/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a170) | c2_1(a170) | c1_1(a138) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c1_1(a170))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a170) | c2_1(a170) | c1_1(a138) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c1_1(a170))),
% 0.84/0.83 inference(rewrite,[status(thm)],[])).
% 0.84/0.83 tff(321,plain,
% 0.84/0.83 (((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a170) | c1_1(a170) | c0_1(a170)) <=> (c0_1(a170) | c2_1(a170) | c1_1(a138) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c1_1(a170))),
% 0.84/0.83 inference(rewrite,[status(thm)],[])).
% 0.84/0.83 tff(322,plain,
% 0.84/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a170) | c1_1(a170) | c0_1(a170))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a170) | c2_1(a170) | c1_1(a138) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c1_1(a170)))),
% 0.84/0.83 inference(monotonicity,[status(thm)],[321])).
% 0.84/0.83 tff(323,plain,
% 0.84/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a170) | c1_1(a170) | c0_1(a170))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a170) | c2_1(a170) | c1_1(a138) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c1_1(a170))),
% 0.84/0.83 inference(transitivity,[status(thm)],[322, 320])).
% 0.84/0.83 tff(324,plain,
% 0.84/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a170) | c1_1(a170) | c0_1(a170))),
% 0.84/0.83 inference(quant_inst,[status(thm)],[])).
% 0.84/0.83 tff(325,plain,
% 0.84/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a170) | c2_1(a170) | c1_1(a138) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c1_1(a170)),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[324, 323])).
% 0.84/0.83 tff(326,plain,
% 0.84/0.83 (c1_1(a170)),
% 0.84/0.83 inference(unit_resolution,[status(thm)],[325, 187, 147, 146, 319, 313, 145, 291, 280, 269, 279])).
% 0.84/0.83 tff(327,plain,
% 0.84/0.83 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))),
% 0.84/0.83 inference(bind,[status(th)],[])).
% 0.84/0.83 tff(328,plain,
% 0.84/0.83 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.84/0.83 inference(quant_intro,[status(thm)],[327])).
% 0.84/0.83 tff(329,plain,
% 0.84/0.83 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.84/0.83 inference(rewrite,[status(thm)],[])).
% 0.84/0.83 tff(330,plain,
% 0.84/0.83 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp6) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp6))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp6) <=> (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))))),
% 0.84/0.83 inference(bind,[status(th)],[])).
% 0.84/0.83 tff(331,plain,
% 0.84/0.83 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.84/0.83 inference(quant_intro,[status(thm)],[330])).
% 0.84/0.83 tff(332,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause165')).
% 0.84/0.83 tff(333,plain,
% 0.84/0.83 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[332, 331])).
% 0.84/0.83 tff(334,plain,
% 0.84/0.83 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[333, 329])).
% 0.84/0.83 tff(335,plain,(
% 0.84/0.83 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.84/0.83 inference(skolemize,[status(sab)],[334])).
% 0.84/0.83 tff(336,plain,
% 0.84/0.83 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[335, 328])).
% 0.84/0.83 tff(337,plain,
% 0.84/0.83 (((~hskp21) | c3_1(a170)) <=> ((~hskp21) | c3_1(a170))),
% 0.84/0.83 inference(rewrite,[status(thm)],[])).
% 0.84/0.83 tff(338,axiom,((~hskp21) | c3_1(a170)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause55')).
% 0.84/0.83 tff(339,plain,
% 0.84/0.83 ((~hskp21) | c3_1(a170)),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[338, 337])).
% 0.84/0.83 tff(340,plain,
% 0.84/0.83 ((~hskp21) | c3_1(a170)),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[339, 337])).
% 0.84/0.83 tff(341,plain,
% 0.84/0.83 ((~hskp21) | c3_1(a170)),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[340, 337])).
% 0.84/0.83 tff(342,plain,
% 0.84/0.83 ((~hskp21) | c3_1(a170)),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[341, 337])).
% 0.84/0.83 tff(343,plain,
% 0.84/0.83 ((~hskp21) | c3_1(a170)),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[342, 337])).
% 0.84/0.83 tff(344,plain,
% 0.84/0.83 ((~hskp21) | c3_1(a170)),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[343, 337])).
% 0.84/0.83 tff(345,plain,
% 0.84/0.83 ((~hskp21) | c3_1(a170)),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[344, 337])).
% 0.84/0.83 tff(346,plain,
% 0.84/0.83 ((~hskp21) | c3_1(a170)),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[345, 337])).
% 0.84/0.83 tff(347,plain,
% 0.84/0.83 (c3_1(a170)),
% 0.84/0.83 inference(unit_resolution,[status(thm)],[346, 307])).
% 0.84/0.83 tff(348,plain,
% 0.84/0.83 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a170) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a170)) | (~c1_1(a170)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a170) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a170)) | (~c1_1(a170)))),
% 0.84/0.83 inference(rewrite,[status(thm)],[])).
% 0.84/0.83 tff(349,plain,
% 0.84/0.83 ((hskp6 | (~ndr1_0) | c0_1(a170) | (~c3_1(a170)) | (~c1_1(a170)) | c3_1(a128) | c0_1(a128) | (~c1_1(a128))) <=> (hskp6 | c0_1(a170) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a170)) | (~c1_1(a170)))),
% 0.84/0.83 inference(rewrite,[status(thm)],[])).
% 0.84/0.83 tff(350,plain,
% 0.84/0.83 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a170) | (~c3_1(a170)) | (~c1_1(a170)) | c3_1(a128) | c0_1(a128) | (~c1_1(a128)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a170) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a170)) | (~c1_1(a170))))),
% 0.84/0.83 inference(monotonicity,[status(thm)],[349])).
% 0.84/0.83 tff(351,plain,
% 0.84/0.83 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a170) | (~c3_1(a170)) | (~c1_1(a170)) | c3_1(a128) | c0_1(a128) | (~c1_1(a128)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a170) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a170)) | (~c1_1(a170)))),
% 0.84/0.83 inference(transitivity,[status(thm)],[350, 348])).
% 0.84/0.83 tff(352,plain,
% 0.84/0.83 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a170) | (~c3_1(a170)) | (~c1_1(a170)) | c3_1(a128) | c0_1(a128) | (~c1_1(a128)))),
% 0.84/0.83 inference(quant_inst,[status(thm)],[])).
% 0.84/0.83 tff(353,plain,
% 0.84/0.83 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a170) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a170)) | (~c1_1(a170))),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[352, 351])).
% 0.84/0.83 tff(354,plain,
% 0.84/0.83 (hskp6 | (~c1_1(a170))),
% 0.84/0.83 inference(unit_resolution,[status(thm)],[353, 187, 347, 319, 291, 269, 336, 299])).
% 0.84/0.83 tff(355,plain,
% 0.84/0.83 (hskp6),
% 0.84/0.83 inference(unit_resolution,[status(thm)],[354, 326])).
% 0.84/0.83 tff(356,plain,
% 0.84/0.83 (((~hskp6) | (~c2_1(a133))) <=> ((~hskp6) | (~c2_1(a133)))),
% 0.84/0.83 inference(rewrite,[status(thm)],[])).
% 0.84/0.83 tff(357,plain,
% 0.84/0.83 (((~c2_1(a133)) | (~hskp6)) <=> ((~hskp6) | (~c2_1(a133)))),
% 0.84/0.83 inference(rewrite,[status(thm)],[])).
% 0.84/0.83 tff(358,axiom,((~c2_1(a133)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause120')).
% 0.84/0.83 tff(359,plain,
% 0.84/0.83 ((~hskp6) | (~c2_1(a133))),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[358, 357])).
% 0.84/0.83 tff(360,plain,
% 0.84/0.83 ((~hskp6) | (~c2_1(a133))),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[359, 356])).
% 0.84/0.83 tff(361,plain,
% 0.84/0.83 (~c2_1(a133)),
% 0.84/0.83 inference(unit_resolution,[status(thm)],[360, 355])).
% 0.84/0.83 tff(362,plain,
% 0.84/0.83 (((~hskp6) | (~c1_1(a133))) <=> ((~hskp6) | (~c1_1(a133)))),
% 0.84/0.83 inference(rewrite,[status(thm)],[])).
% 0.84/0.83 tff(363,plain,
% 0.84/0.83 (((~c1_1(a133)) | (~hskp6)) <=> ((~hskp6) | (~c1_1(a133)))),
% 0.84/0.83 inference(rewrite,[status(thm)],[])).
% 0.84/0.83 tff(364,axiom,((~c1_1(a133)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause119')).
% 0.84/0.83 tff(365,plain,
% 0.84/0.83 ((~hskp6) | (~c1_1(a133))),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[364, 363])).
% 0.84/0.83 tff(366,plain,
% 0.84/0.83 ((~hskp6) | (~c1_1(a133))),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[365, 362])).
% 0.84/0.83 tff(367,plain,
% 0.84/0.83 (~c1_1(a133)),
% 0.84/0.83 inference(unit_resolution,[status(thm)],[366, 355])).
% 0.84/0.83 tff(368,plain,
% 0.84/0.83 (((~hskp6) | (~c0_1(a133))) <=> ((~hskp6) | (~c0_1(a133)))),
% 0.84/0.83 inference(rewrite,[status(thm)],[])).
% 0.84/0.83 tff(369,plain,
% 0.84/0.83 (((~c0_1(a133)) | (~hskp6)) <=> ((~hskp6) | (~c0_1(a133)))),
% 0.84/0.83 inference(rewrite,[status(thm)],[])).
% 0.84/0.83 tff(370,axiom,((~c0_1(a133)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause118')).
% 0.84/0.83 tff(371,plain,
% 0.84/0.83 ((~hskp6) | (~c0_1(a133))),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[370, 369])).
% 0.84/0.83 tff(372,plain,
% 0.84/0.83 ((~hskp6) | (~c0_1(a133))),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[371, 368])).
% 0.84/0.83 tff(373,plain,
% 0.84/0.83 (~c0_1(a133)),
% 0.84/0.83 inference(unit_resolution,[status(thm)],[372, 355])).
% 0.84/0.83 tff(374,plain,
% 0.84/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a138) | c0_1(a133) | c1_1(a133) | c2_1(a133) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a138) | c0_1(a133) | c1_1(a133) | c2_1(a133) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)))),
% 0.84/0.83 inference(rewrite,[status(thm)],[])).
% 0.84/0.83 tff(375,plain,
% 0.84/0.83 (((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a133) | c1_1(a133) | c0_1(a133)) <=> (c1_1(a138) | c0_1(a133) | c1_1(a133) | c2_1(a133) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)))),
% 0.84/0.83 inference(rewrite,[status(thm)],[])).
% 0.84/0.83 tff(376,plain,
% 0.84/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a133) | c1_1(a133) | c0_1(a133))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a138) | c0_1(a133) | c1_1(a133) | c2_1(a133) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138))))),
% 0.84/0.83 inference(monotonicity,[status(thm)],[375])).
% 0.84/0.83 tff(377,plain,
% 0.84/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a133) | c1_1(a133) | c0_1(a133))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a138) | c0_1(a133) | c1_1(a133) | c2_1(a133) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)))),
% 0.84/0.83 inference(transitivity,[status(thm)],[376, 374])).
% 0.84/0.83 tff(378,plain,
% 0.84/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a133) | c1_1(a133) | c0_1(a133))),
% 0.84/0.83 inference(quant_inst,[status(thm)],[])).
% 0.84/0.83 tff(379,plain,
% 0.84/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a138) | c0_1(a133) | c1_1(a133) | c2_1(a133) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138))),
% 0.84/0.83 inference(modus_ponens,[status(thm)],[378, 377])).
% 0.84/0.83 tff(380,plain,
% 0.84/0.83 ($false),
% 0.84/0.83 inference(unit_resolution,[status(thm)],[379, 187, 147, 146, 145, 373, 367, 361, 291, 280, 269, 279])).
% 0.84/0.83 tff(381,plain,(c0_1(a128) | (~c0_1(a138)) | (~c3_1(a138)) | c1_1(a138) | c2_1(a128) | c3_1(a128) | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.84/0.83 tff(382,plain,
% 0.84/0.83 (c0_1(a128)),
% 0.84/0.83 inference(unit_resolution,[status(thm)],[381, 280, 146, 145, 147, 269, 95])).
% 0.84/0.83 tff(383,plain,
% 0.84/0.83 (~c1_1(a128)),
% 0.84/0.83 inference(unit_resolution,[status(thm)],[306, 53, 280])).
% 0.84/0.83 tff(384,plain,
% 0.84/0.83 (^[V: $i, U: $i] : refl((hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))),
% 0.84/0.83 inference(bind,[status(th)],[])).
% 0.84/0.83 tff(385,plain,
% 0.84/0.83 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.84/0.83 inference(quant_intro,[status(thm)],[384])).
% 0.84/0.83 tff(386,plain,
% 0.84/0.83 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.84/0.83 inference(rewrite,[status(thm)],[])).
% 0.84/0.83 tff(387,plain,
% 0.84/0.83 (^[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))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp19) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp19))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp19) <=> (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp19) <=> (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))))),
% 0.84/0.84 inference(bind,[status(th)],[])).
% 0.84/0.84 tff(388,plain,
% 0.84/0.84 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp19) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.84/0.84 inference(quant_intro,[status(thm)],[387])).
% 0.84/0.84 tff(389,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause168')).
% 0.84/0.84 tff(390,plain,
% 0.84/0.84 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.84/0.84 inference(modus_ponens,[status(thm)],[389, 388])).
% 0.84/0.84 tff(391,plain,
% 0.84/0.84 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.84/0.84 inference(modus_ponens,[status(thm)],[390, 386])).
% 0.84/0.84 tff(392,plain,(
% 0.84/0.84 ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.84/0.84 inference(skolemize,[status(sab)],[391])).
% 0.84/0.84 tff(393,plain,
% 0.84/0.84 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.84/0.84 inference(modus_ponens,[status(thm)],[392, 385])).
% 0.84/0.84 tff(394,plain,
% 0.84/0.84 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | c1_1(a138) | (~c0_1(a128)) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a138)) | (~c0_1(a138)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp19 | c1_1(a138) | (~c0_1(a128)) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a138)) | (~c0_1(a138)))),
% 0.84/0.84 inference(rewrite,[status(thm)],[])).
% 0.84/0.84 tff(395,plain,
% 0.84/0.84 ((hskp19 | (~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a128) | c1_1(a128) | (~c0_1(a128))) <=> (hskp19 | c1_1(a138) | (~c0_1(a128)) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a138)) | (~c0_1(a138)))),
% 0.84/0.84 inference(rewrite,[status(thm)],[])).
% 0.84/0.84 tff(396,plain,
% 0.84/0.84 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | (~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a128) | c1_1(a128) | (~c0_1(a128)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | c1_1(a138) | (~c0_1(a128)) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a138)) | (~c0_1(a138))))),
% 0.84/0.84 inference(monotonicity,[status(thm)],[395])).
% 0.84/0.84 tff(397,plain,
% 0.84/0.84 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | (~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a128) | c1_1(a128) | (~c0_1(a128)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp19 | c1_1(a138) | (~c0_1(a128)) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a138)) | (~c0_1(a138)))),
% 0.84/0.84 inference(transitivity,[status(thm)],[396, 394])).
% 0.84/0.84 tff(398,plain,
% 0.84/0.84 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | (~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a128) | c1_1(a128) | (~c0_1(a128)))),
% 0.84/0.84 inference(quant_inst,[status(thm)],[])).
% 0.84/0.84 tff(399,plain,
% 0.84/0.84 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp19 | c1_1(a138) | (~c0_1(a128)) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a138)) | (~c0_1(a138))),
% 0.84/0.84 inference(modus_ponens,[status(thm)],[398, 397])).
% 0.84/0.84 tff(400,plain,
% 0.84/0.84 (hskp19 | (~c0_1(a128)) | c1_1(a128)),
% 0.84/0.84 inference(unit_resolution,[status(thm)],[399, 187, 147, 146, 145, 269, 393])).
% 0.84/0.84 tff(401,plain,
% 0.84/0.84 (hskp19),
% 0.84/0.84 inference(unit_resolution,[status(thm)],[400, 383, 382])).
% 0.84/0.84 tff(402,plain,
% 0.84/0.84 (((~hskp19) | (~c2_1(a162))) <=> ((~hskp19) | (~c2_1(a162)))),
% 0.84/0.84 inference(rewrite,[status(thm)],[])).
% 0.84/0.84 tff(403,plain,
% 0.84/0.84 (((~c2_1(a162)) | (~hskp19)) <=> ((~hskp19) | (~c2_1(a162)))),
% 0.84/0.84 inference(rewrite,[status(thm)],[])).
% 0.84/0.84 tff(404,axiom,((~c2_1(a162)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause97')).
% 0.84/0.84 tff(405,plain,
% 0.84/0.84 ((~hskp19) | (~c2_1(a162))),
% 0.84/0.84 inference(modus_ponens,[status(thm)],[404, 403])).
% 0.84/0.84 tff(406,plain,
% 0.84/0.84 ((~hskp19) | (~c2_1(a162))),
% 0.84/0.84 inference(modus_ponens,[status(thm)],[405, 402])).
% 0.84/0.84 tff(407,plain,
% 0.84/0.84 (~c2_1(a162)),
% 0.84/0.84 inference(unit_resolution,[status(thm)],[406, 401])).
% 0.84/0.84 tff(408,plain,
% 0.84/0.84 (((~hskp19) | c3_1(a162)) <=> ((~hskp19) | c3_1(a162))),
% 0.84/0.84 inference(rewrite,[status(thm)],[])).
% 0.84/0.84 tff(409,axiom,((~hskp19) | c3_1(a162)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause58')).
% 0.84/0.84 tff(410,plain,
% 0.84/0.84 ((~hskp19) | c3_1(a162)),
% 0.84/0.84 inference(modus_ponens,[status(thm)],[409, 408])).
% 0.84/0.84 tff(411,plain,
% 0.84/0.84 ((~hskp19) | c3_1(a162)),
% 0.84/0.84 inference(modus_ponens,[status(thm)],[410, 408])).
% 0.84/0.84 tff(412,plain,
% 0.84/0.84 ((~hskp19) | c3_1(a162)),
% 0.84/0.84 inference(modus_ponens,[status(thm)],[411, 408])).
% 0.84/0.84 tff(413,plain,
% 0.84/0.84 ((~hskp19) | c3_1(a162)),
% 0.84/0.84 inference(modus_ponens,[status(thm)],[412, 408])).
% 0.84/0.84 tff(414,plain,
% 0.84/0.84 ((~hskp19) | c3_1(a162)),
% 0.84/0.84 inference(modus_ponens,[status(thm)],[413, 408])).
% 0.84/0.84 tff(415,plain,
% 0.84/0.84 ((~hskp19) | c3_1(a162)),
% 0.84/0.84 inference(modus_ponens,[status(thm)],[414, 408])).
% 0.84/0.84 tff(416,plain,
% 0.84/0.84 ((~hskp19) | c3_1(a162)),
% 0.84/0.84 inference(modus_ponens,[status(thm)],[415, 408])).
% 0.84/0.84 tff(417,plain,
% 0.84/0.84 ((~hskp19) | c3_1(a162)),
% 0.84/0.84 inference(modus_ponens,[status(thm)],[416, 408])).
% 0.84/0.84 tff(418,plain,
% 0.84/0.84 (c3_1(a162)),
% 0.84/0.84 inference(unit_resolution,[status(thm)],[417, 401])).
% 0.84/0.84 tff(419,plain,
% 0.84/0.84 (((~hskp19) | c0_1(a162)) <=> ((~hskp19) | c0_1(a162))),
% 0.84/0.84 inference(rewrite,[status(thm)],[])).
% 0.84/0.84 tff(420,axiom,((~hskp19) | c0_1(a162)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause57')).
% 0.84/0.84 tff(421,plain,
% 0.84/0.84 ((~hskp19) | c0_1(a162)),
% 0.84/0.84 inference(modus_ponens,[status(thm)],[420, 419])).
% 0.84/0.84 tff(422,plain,
% 0.84/0.84 ((~hskp19) | c0_1(a162)),
% 0.84/0.84 inference(modus_ponens,[status(thm)],[421, 419])).
% 0.84/0.84 tff(423,plain,
% 0.84/0.84 ((~hskp19) | c0_1(a162)),
% 0.84/0.84 inference(modus_ponens,[status(thm)],[422, 419])).
% 0.84/0.84 tff(424,plain,
% 0.84/0.84 ((~hskp19) | c0_1(a162)),
% 0.84/0.84 inference(modus_ponens,[status(thm)],[423, 419])).
% 0.84/0.84 tff(425,plain,
% 0.84/0.84 ((~hskp19) | c0_1(a162)),
% 0.84/0.84 inference(modus_ponens,[status(thm)],[424, 419])).
% 0.84/0.84 tff(426,plain,
% 0.84/0.84 ((~hskp19) | c0_1(a162)),
% 0.84/0.84 inference(modus_ponens,[status(thm)],[425, 419])).
% 0.84/0.84 tff(427,plain,
% 0.84/0.84 ((~hskp19) | c0_1(a162)),
% 0.84/0.84 inference(modus_ponens,[status(thm)],[426, 419])).
% 0.84/0.84 tff(428,plain,
% 0.84/0.84 ((~hskp19) | c0_1(a162)),
% 0.84/0.84 inference(modus_ponens,[status(thm)],[427, 419])).
% 0.84/0.84 tff(429,plain,
% 0.84/0.84 (c0_1(a162)),
% 0.84/0.84 inference(unit_resolution,[status(thm)],[428, 401])).
% 0.84/0.84 tff(430,plain,
% 0.84/0.84 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp17 | c2_1(a162) | (~c0_1(a128)) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a162)) | (~c0_1(a162)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp17 | c2_1(a162) | (~c0_1(a128)) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a162)) | (~c0_1(a162)))),
% 0.84/0.84 inference(rewrite,[status(thm)],[])).
% 0.84/0.84 tff(431,plain,
% 0.84/0.84 ((hskp17 | (~ndr1_0) | c2_1(a162) | (~c3_1(a162)) | (~c0_1(a162)) | c3_1(a128) | c2_1(a128) | (~c0_1(a128))) <=> (hskp17 | c2_1(a162) | (~c0_1(a128)) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a162)) | (~c0_1(a162)))),
% 0.84/0.84 inference(rewrite,[status(thm)],[])).
% 0.84/0.84 tff(432,plain,
% 0.84/0.84 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a162) | (~c3_1(a162)) | (~c0_1(a162)) | c3_1(a128) | c2_1(a128) | (~c0_1(a128)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp17 | c2_1(a162) | (~c0_1(a128)) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a162)) | (~c0_1(a162))))),
% 0.84/0.84 inference(monotonicity,[status(thm)],[431])).
% 0.84/0.84 tff(433,plain,
% 0.84/0.84 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a162) | (~c3_1(a162)) | (~c0_1(a162)) | c3_1(a128) | c2_1(a128) | (~c0_1(a128)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp17 | c2_1(a162) | (~c0_1(a128)) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a162)) | (~c0_1(a162)))),
% 0.84/0.84 inference(transitivity,[status(thm)],[432, 430])).
% 0.84/0.84 tff(434,plain,
% 0.84/0.84 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a162) | (~c3_1(a162)) | (~c0_1(a162)) | c3_1(a128) | c2_1(a128) | (~c0_1(a128)))),
% 0.84/0.84 inference(quant_inst,[status(thm)],[])).
% 0.84/0.84 tff(435,plain,
% 0.84/0.84 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp17 | c2_1(a162) | (~c0_1(a128)) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a162)) | (~c0_1(a162))),
% 0.84/0.84 inference(modus_ponens,[status(thm)],[434, 433])).
% 0.84/0.84 tff(436,plain,
% 0.84/0.84 (hskp17),
% 0.84/0.84 inference(unit_resolution,[status(thm)],[435, 187, 429, 418, 407, 382, 280, 269, 290])).
% 0.84/0.84 tff(437,plain,
% 0.84/0.84 (((~hskp17) | (~c3_1(a158))) <=> ((~hskp17) | (~c3_1(a158)))),
% 0.84/0.84 inference(rewrite,[status(thm)],[])).
% 0.84/0.84 tff(438,plain,
% 0.84/0.84 (((~c3_1(a158)) | (~hskp17)) <=> ((~hskp17) | (~c3_1(a158)))),
% 0.84/0.84 inference(rewrite,[status(thm)],[])).
% 0.84/0.84 tff(439,axiom,((~c3_1(a158)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause101')).
% 0.84/0.84 tff(440,plain,
% 0.84/0.84 ((~hskp17) | (~c3_1(a158))),
% 0.84/0.84 inference(modus_ponens,[status(thm)],[439, 438])).
% 0.84/0.84 tff(441,plain,
% 0.84/0.84 ((~hskp17) | (~c3_1(a158))),
% 0.84/0.84 inference(modus_ponens,[status(thm)],[440, 437])).
% 0.84/0.84 tff(442,plain,
% 0.84/0.84 (~c3_1(a158)),
% 0.84/0.84 inference(unit_resolution,[status(thm)],[441, 436])).
% 0.84/0.84 tff(443,plain,
% 0.84/0.84 (((~hskp17) | (~c2_1(a158))) <=> ((~hskp17) | (~c2_1(a158)))),
% 0.84/0.84 inference(rewrite,[status(thm)],[])).
% 0.84/0.84 tff(444,plain,
% 0.84/0.84 (((~c2_1(a158)) | (~hskp17)) <=> ((~hskp17) | (~c2_1(a158)))),
% 0.84/0.84 inference(rewrite,[status(thm)],[])).
% 0.84/0.84 tff(445,axiom,((~c2_1(a158)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause100')).
% 0.84/0.84 tff(446,plain,
% 0.84/0.84 ((~hskp17) | (~c2_1(a158))),
% 0.84/0.84 inference(modus_ponens,[status(thm)],[445, 444])).
% 0.84/0.84 tff(447,plain,
% 0.84/0.84 ((~hskp17) | (~c2_1(a158))),
% 0.84/0.84 inference(modus_ponens,[status(thm)],[446, 443])).
% 0.84/0.84 tff(448,plain,
% 0.84/0.84 (~c2_1(a158)),
% 0.84/0.84 inference(unit_resolution,[status(thm)],[447, 436])).
% 0.84/0.84 tff(449,plain,
% 0.84/0.84 (((~hskp17) | c1_1(a158)) <=> ((~hskp17) | c1_1(a158))),
% 0.84/0.84 inference(rewrite,[status(thm)],[])).
% 0.84/0.84 tff(450,axiom,((~hskp17) | c1_1(a158)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause60')).
% 0.84/0.84 tff(451,plain,
% 0.84/0.84 ((~hskp17) | c1_1(a158)),
% 0.84/0.84 inference(modus_ponens,[status(thm)],[450, 449])).
% 0.84/0.84 tff(452,plain,
% 0.84/0.84 ((~hskp17) | c1_1(a158)),
% 0.84/0.84 inference(modus_ponens,[status(thm)],[451, 449])).
% 0.84/0.84 tff(453,plain,
% 0.84/0.84 ((~hskp17) | c1_1(a158)),
% 0.84/0.84 inference(modus_ponens,[status(thm)],[452, 449])).
% 0.84/0.84 tff(454,plain,
% 0.84/0.84 ((~hskp17) | c1_1(a158)),
% 0.84/0.84 inference(modus_ponens,[status(thm)],[453, 449])).
% 0.84/0.84 tff(455,plain,
% 0.84/0.84 ((~hskp17) | c1_1(a158)),
% 0.84/0.84 inference(modus_ponens,[status(thm)],[454, 449])).
% 0.84/0.84 tff(456,plain,
% 0.84/0.84 ((~hskp17) | c1_1(a158)),
% 0.84/0.84 inference(modus_ponens,[status(thm)],[455, 449])).
% 0.84/0.84 tff(457,plain,
% 0.84/0.84 ((~hskp17) | c1_1(a158)),
% 0.84/0.84 inference(modus_ponens,[status(thm)],[456, 449])).
% 0.84/0.84 tff(458,plain,
% 0.84/0.84 ((~hskp17) | c1_1(a158)),
% 0.84/0.84 inference(modus_ponens,[status(thm)],[457, 449])).
% 0.84/0.84 tff(459,plain,
% 0.84/0.84 (c1_1(a158)),
% 0.84/0.84 inference(unit_resolution,[status(thm)],[458, 436])).
% 0.84/0.84 tff(460,plain,
% 0.84/0.84 (((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | c2_1(a158) | c3_1(a158) | (~ndr1_0) | (~c1_1(a158)))) <=> ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp21 | hskp18 | c2_1(a158) | c3_1(a158) | (~ndr1_0) | (~c1_1(a158)))),
% 0.84/0.84 inference(rewrite,[status(thm)],[])).
% 0.84/0.84 tff(461,plain,
% 0.84/0.84 ((hskp21 | hskp18 | (~ndr1_0) | c3_1(a158) | c2_1(a158) | (~c1_1(a158))) <=> (hskp21 | hskp18 | c2_1(a158) | c3_1(a158) | (~ndr1_0) | (~c1_1(a158)))),
% 0.84/0.84 inference(rewrite,[status(thm)],[])).
% 0.84/0.84 tff(462,plain,
% 0.84/0.84 (((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | (~ndr1_0) | c3_1(a158) | c2_1(a158) | (~c1_1(a158)))) <=> ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | c2_1(a158) | c3_1(a158) | (~ndr1_0) | (~c1_1(a158))))),
% 0.84/0.84 inference(monotonicity,[status(thm)],[461])).
% 0.84/0.84 tff(463,plain,
% 0.84/0.84 (((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | (~ndr1_0) | c3_1(a158) | c2_1(a158) | (~c1_1(a158)))) <=> ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp21 | hskp18 | c2_1(a158) | c3_1(a158) | (~ndr1_0) | (~c1_1(a158)))),
% 0.84/0.84 inference(transitivity,[status(thm)],[462, 460])).
% 0.84/0.84 tff(464,plain,
% 0.84/0.84 ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | (~ndr1_0) | c3_1(a158) | c2_1(a158) | (~c1_1(a158)))),
% 0.84/0.84 inference(quant_inst,[status(thm)],[])).
% 0.84/0.84 tff(465,plain,
% 0.84/0.84 ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp21 | hskp18 | c2_1(a158) | c3_1(a158) | (~ndr1_0) | (~c1_1(a158))),
% 0.84/0.84 inference(modus_ponens,[status(thm)],[464, 463])).
% 0.84/0.84 tff(466,plain,
% 0.84/0.84 ($false),
% 0.84/0.84 inference(unit_resolution,[status(thm)],[465, 187, 53, 95, 459, 448, 442, 134])).
% 0.84/0.84 tff(467,plain,(hskp21 | hskp18 | c2_1(a128) | c3_1(a128) | (~c0_1(a138)) | (~c3_1(a138)) | c1_1(a138)), inference(lemma,lemma(discharge,[]))).
% 0.84/0.84 tff(468,plain,
% 0.84/0.84 (hskp21),
% 0.84/0.84 inference(unit_resolution,[status(thm)],[467, 280, 95, 269, 147, 146, 145])).
% 0.84/0.84 tff(469,plain,
% 0.84/0.84 (~c0_1(a170)),
% 0.84/0.84 inference(unit_resolution,[status(thm)],[318, 468])).
% 0.84/0.84 tff(470,plain,
% 0.84/0.84 (~c2_1(a170)),
% 0.84/0.84 inference(unit_resolution,[status(thm)],[312, 468])).
% 0.84/0.84 tff(471,assumption,(~c2_1(a170)), introduced(assumption)).
% 0.84/0.84 tff(472,assumption,(~c0_1(a170)), introduced(assumption)).
% 0.84/0.84 tff(473,assumption,(~c3_1(a170)), introduced(assumption)).
% 0.84/0.84 tff(474,plain,
% 0.84/0.84 (~hskp21),
% 0.84/0.84 inference(unit_resolution,[status(thm)],[346, 473])).
% 0.84/0.84 tff(475,plain,
% 0.84/0.84 (((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | c3_1(a170) | c2_1(a170) | (~ndr1_0) | (~c1_1(a170)))) <=> ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp21 | hskp18 | c3_1(a170) | c2_1(a170) | (~ndr1_0) | (~c1_1(a170)))),
% 0.84/0.84 inference(rewrite,[status(thm)],[])).
% 0.84/0.84 tff(476,plain,
% 0.84/0.84 ((hskp21 | hskp18 | (~ndr1_0) | c3_1(a170) | c2_1(a170) | (~c1_1(a170))) <=> (hskp21 | hskp18 | c3_1(a170) | c2_1(a170) | (~ndr1_0) | (~c1_1(a170)))),
% 0.84/0.84 inference(rewrite,[status(thm)],[])).
% 0.84/0.84 tff(477,plain,
% 0.84/0.84 (((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | (~ndr1_0) | c3_1(a170) | c2_1(a170) | (~c1_1(a170)))) <=> ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | c3_1(a170) | c2_1(a170) | (~ndr1_0) | (~c1_1(a170))))),
% 0.84/0.84 inference(monotonicity,[status(thm)],[476])).
% 0.84/0.84 tff(478,plain,
% 0.84/0.84 (((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | (~ndr1_0) | c3_1(a170) | c2_1(a170) | (~c1_1(a170)))) <=> ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp21 | hskp18 | c3_1(a170) | c2_1(a170) | (~ndr1_0) | (~c1_1(a170)))),
% 0.84/0.84 inference(transitivity,[status(thm)],[477, 475])).
% 0.84/0.84 tff(479,plain,
% 0.84/0.84 ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | (~ndr1_0) | c3_1(a170) | c2_1(a170) | (~c1_1(a170)))),
% 0.84/0.84 inference(quant_inst,[status(thm)],[])).
% 0.84/0.84 tff(480,plain,
% 0.84/0.84 ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp21 | hskp18 | c3_1(a170) | c2_1(a170) | (~ndr1_0) | (~c1_1(a170))),
% 0.84/0.84 inference(modus_ponens,[status(thm)],[479, 478])).
% 0.84/0.84 tff(481,plain,
% 0.84/0.84 (hskp21 | c3_1(a170) | (~c1_1(a170))),
% 0.84/0.84 inference(unit_resolution,[status(thm)],[480, 187, 95, 471, 134])).
% 0.84/0.84 tff(482,plain,
% 0.84/0.84 (~c1_1(a170)),
% 0.84/0.84 inference(unit_resolution,[status(thm)],[481, 474, 473])).
% 0.84/0.84 tff(483,plain,
% 0.84/0.84 (~c1_1(a128)),
% 0.84/0.84 inference(unit_resolution,[status(thm)],[306, 474, 280])).
% 0.84/0.84 tff(484,plain,
% 0.84/0.84 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 0.84/0.84 inference(bind,[status(th)],[])).
% 0.84/0.84 tff(485,plain,
% 0.84/0.84 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.84/0.84 inference(quant_intro,[status(thm)],[484])).
% 0.84/0.84 tff(486,plain,
% 0.84/0.84 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.84/0.84 inference(rewrite,[status(thm)],[])).
% 0.84/0.84 tff(487,plain,
% 0.84/0.84 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c0_1(W))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c0_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 0.84/0.84 inference(bind,[status(th)],[])).
% 0.84/0.84 tff(488,plain,
% 0.84/0.84 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.84/0.84 inference(quant_intro,[status(thm)],[487])).
% 0.84/0.84 tff(489,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause174')).
% 0.84/0.84 tff(490,plain,
% 0.84/0.84 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[489, 488])).
% 0.84/0.85 tff(491,plain,
% 0.84/0.85 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[490, 486])).
% 0.84/0.85 tff(492,plain,(
% 0.84/0.85 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.84/0.85 inference(skolemize,[status(sab)],[491])).
% 0.84/0.85 tff(493,plain,
% 0.84/0.85 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[492, 485])).
% 0.84/0.85 tff(494,assumption,(c0_1(a128)), introduced(assumption)).
% 0.84/0.85 tff(495,plain,
% 0.84/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a170) | c0_1(a170) | c2_1(a170) | (~c0_1(a128)) | c2_1(a128) | (~ndr1_0) | c1_1(a128) | c1_1(a170))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a170) | c0_1(a170) | c2_1(a170) | (~c0_1(a128)) | c2_1(a128) | (~ndr1_0) | c1_1(a128) | c1_1(a170))),
% 0.84/0.85 inference(rewrite,[status(thm)],[])).
% 0.84/0.85 tff(496,plain,
% 0.84/0.85 (((~ndr1_0) | c1_1(a128) | c2_1(a128) | (~c0_1(a128)) | c3_1(a170) | c1_1(a170) | c0_1(a170) | c2_1(a170) | c1_1(a170) | c0_1(a170)) <=> (c3_1(a170) | c0_1(a170) | c2_1(a170) | (~c0_1(a128)) | c2_1(a128) | (~ndr1_0) | c1_1(a128) | c1_1(a170))),
% 0.84/0.85 inference(rewrite,[status(thm)],[])).
% 0.84/0.85 tff(497,plain,
% 0.84/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a128) | c2_1(a128) | (~c0_1(a128)) | c3_1(a170) | c1_1(a170) | c0_1(a170) | c2_1(a170) | c1_1(a170) | c0_1(a170))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a170) | c0_1(a170) | c2_1(a170) | (~c0_1(a128)) | c2_1(a128) | (~ndr1_0) | c1_1(a128) | c1_1(a170)))),
% 0.84/0.85 inference(monotonicity,[status(thm)],[496])).
% 0.84/0.85 tff(498,plain,
% 0.84/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a128) | c2_1(a128) | (~c0_1(a128)) | c3_1(a170) | c1_1(a170) | c0_1(a170) | c2_1(a170) | c1_1(a170) | c0_1(a170))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a170) | c0_1(a170) | c2_1(a170) | (~c0_1(a128)) | c2_1(a128) | (~ndr1_0) | c1_1(a128) | c1_1(a170))),
% 0.84/0.85 inference(transitivity,[status(thm)],[497, 495])).
% 0.84/0.85 tff(499,plain,
% 0.84/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a128) | c2_1(a128) | (~c0_1(a128)) | c3_1(a170) | c1_1(a170) | c0_1(a170) | c2_1(a170) | c1_1(a170) | c0_1(a170))),
% 0.84/0.85 inference(quant_inst,[status(thm)],[])).
% 0.84/0.85 tff(500,plain,
% 0.84/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a170) | c0_1(a170) | c2_1(a170) | (~c0_1(a128)) | c2_1(a128) | (~ndr1_0) | c1_1(a128) | c1_1(a170)),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[499, 498])).
% 0.84/0.85 tff(501,plain,
% 0.84/0.85 ($false),
% 0.84/0.85 inference(unit_resolution,[status(thm)],[500, 187, 473, 472, 471, 494, 280, 493, 483, 482])).
% 0.84/0.85 tff(502,plain,(c3_1(a170) | c0_1(a170) | c2_1(a170) | (~c0_1(a128)) | c2_1(a128) | hskp18 | c3_1(a128)), inference(lemma,lemma(discharge,[]))).
% 0.84/0.85 tff(503,plain,
% 0.84/0.85 (c3_1(a170)),
% 0.84/0.85 inference(unit_resolution,[status(thm)],[502, 471, 472, 382, 280, 95, 269])).
% 0.84/0.85 tff(504,plain,
% 0.84/0.85 (((~hskp3) | (~c0_1(a128))) <=> ((~hskp3) | (~c0_1(a128)))),
% 0.84/0.85 inference(rewrite,[status(thm)],[])).
% 0.84/0.85 tff(505,plain,
% 0.84/0.85 (((~c0_1(a128)) | (~hskp3)) <=> ((~hskp3) | (~c0_1(a128)))),
% 0.84/0.85 inference(rewrite,[status(thm)],[])).
% 0.84/0.85 tff(506,axiom,((~c0_1(a128)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause123')).
% 0.84/0.85 tff(507,plain,
% 0.84/0.85 ((~hskp3) | (~c0_1(a128))),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[506, 505])).
% 0.84/0.85 tff(508,plain,
% 0.84/0.85 ((~hskp3) | (~c0_1(a128))),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[507, 504])).
% 0.84/0.85 tff(509,plain,
% 0.84/0.85 (~hskp3),
% 0.84/0.85 inference(unit_resolution,[status(thm)],[508, 382])).
% 0.84/0.85 tff(510,plain,
% 0.84/0.85 (((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp14 | hskp3 | c0_1(a170) | c2_1(a170) | (~ndr1_0) | (~c3_1(a170)))) <=> ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp14 | hskp3 | c0_1(a170) | c2_1(a170) | (~ndr1_0) | (~c3_1(a170)))),
% 0.84/0.85 inference(rewrite,[status(thm)],[])).
% 0.84/0.85 tff(511,plain,
% 0.84/0.85 ((hskp14 | hskp3 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c3_1(a170))) <=> (hskp14 | hskp3 | c0_1(a170) | c2_1(a170) | (~ndr1_0) | (~c3_1(a170)))),
% 0.84/0.85 inference(rewrite,[status(thm)],[])).
% 0.84/0.85 tff(512,plain,
% 0.84/0.85 (((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp14 | hskp3 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c3_1(a170)))) <=> ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp14 | hskp3 | c0_1(a170) | c2_1(a170) | (~ndr1_0) | (~c3_1(a170))))),
% 0.84/0.85 inference(monotonicity,[status(thm)],[511])).
% 0.84/0.85 tff(513,plain,
% 0.84/0.85 (((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp14 | hskp3 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c3_1(a170)))) <=> ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp14 | hskp3 | c0_1(a170) | c2_1(a170) | (~ndr1_0) | (~c3_1(a170)))),
% 0.84/0.85 inference(transitivity,[status(thm)],[512, 510])).
% 0.84/0.85 tff(514,plain,
% 0.84/0.85 ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp14 | hskp3 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c3_1(a170)))),
% 0.84/0.85 inference(quant_inst,[status(thm)],[])).
% 0.84/0.85 tff(515,plain,
% 0.84/0.85 ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp14 | hskp3 | c0_1(a170) | c2_1(a170) | (~ndr1_0) | (~c3_1(a170))),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[514, 513])).
% 0.84/0.85 tff(516,plain,
% 0.84/0.85 (hskp14 | c2_1(a170) | (~c3_1(a170))),
% 0.84/0.85 inference(unit_resolution,[status(thm)],[515, 187, 509, 472, 51])).
% 0.84/0.85 tff(517,plain,
% 0.84/0.85 (hskp14),
% 0.84/0.85 inference(unit_resolution,[status(thm)],[516, 503, 471])).
% 0.84/0.85 tff(518,plain,
% 0.84/0.85 (((~hskp14) | (~c3_1(a145))) <=> ((~hskp14) | (~c3_1(a145)))),
% 0.84/0.85 inference(rewrite,[status(thm)],[])).
% 0.84/0.85 tff(519,plain,
% 0.84/0.85 (((~c3_1(a145)) | (~hskp14)) <=> ((~hskp14) | (~c3_1(a145)))),
% 0.84/0.85 inference(rewrite,[status(thm)],[])).
% 0.84/0.85 tff(520,axiom,((~c3_1(a145)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause107')).
% 0.84/0.85 tff(521,plain,
% 0.84/0.85 ((~hskp14) | (~c3_1(a145))),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[520, 519])).
% 0.84/0.85 tff(522,plain,
% 0.84/0.85 ((~hskp14) | (~c3_1(a145))),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[521, 518])).
% 0.84/0.85 tff(523,plain,
% 0.84/0.85 (~c3_1(a145)),
% 0.84/0.85 inference(unit_resolution,[status(thm)],[522, 517])).
% 0.84/0.85 tff(524,plain,
% 0.84/0.85 (((~hskp14) | (~c1_1(a145))) <=> ((~hskp14) | (~c1_1(a145)))),
% 0.84/0.85 inference(rewrite,[status(thm)],[])).
% 0.84/0.85 tff(525,plain,
% 0.84/0.85 (((~c1_1(a145)) | (~hskp14)) <=> ((~hskp14) | (~c1_1(a145)))),
% 0.84/0.85 inference(rewrite,[status(thm)],[])).
% 0.84/0.85 tff(526,axiom,((~c1_1(a145)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause106')).
% 0.84/0.85 tff(527,plain,
% 0.84/0.85 ((~hskp14) | (~c1_1(a145))),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[526, 525])).
% 0.84/0.85 tff(528,plain,
% 0.84/0.85 ((~hskp14) | (~c1_1(a145))),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[527, 524])).
% 0.84/0.85 tff(529,plain,
% 0.84/0.85 (~c1_1(a145)),
% 0.84/0.85 inference(unit_resolution,[status(thm)],[528, 517])).
% 0.84/0.85 tff(530,plain,
% 0.84/0.85 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c0_1(a170) | c2_1(a170) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c2_1(a145)) | (~c3_1(a170)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a170) | c2_1(a170) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c2_1(a145)) | (~c3_1(a170)))),
% 0.84/0.85 inference(rewrite,[status(thm)],[])).
% 0.84/0.85 tff(531,plain,
% 0.84/0.85 ((hskp3 | (~ndr1_0) | c3_1(a145) | c1_1(a145) | (~c2_1(a145)) | c0_1(a170) | c2_1(a170) | (~c3_1(a170))) <=> (hskp3 | c0_1(a170) | c2_1(a170) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c2_1(a145)) | (~c3_1(a170)))),
% 0.84/0.85 inference(rewrite,[status(thm)],[])).
% 0.84/0.85 tff(532,plain,
% 0.84/0.85 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a145) | c1_1(a145) | (~c2_1(a145)) | c0_1(a170) | c2_1(a170) | (~c3_1(a170)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c0_1(a170) | c2_1(a170) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c2_1(a145)) | (~c3_1(a170))))),
% 0.84/0.85 inference(monotonicity,[status(thm)],[531])).
% 0.84/0.85 tff(533,plain,
% 0.84/0.85 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a145) | c1_1(a145) | (~c2_1(a145)) | c0_1(a170) | c2_1(a170) | (~c3_1(a170)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a170) | c2_1(a170) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c2_1(a145)) | (~c3_1(a170)))),
% 0.84/0.85 inference(transitivity,[status(thm)],[532, 530])).
% 0.84/0.85 tff(534,plain,
% 0.84/0.85 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a145) | c1_1(a145) | (~c2_1(a145)) | c0_1(a170) | c2_1(a170) | (~c3_1(a170)))),
% 0.84/0.85 inference(quant_inst,[status(thm)],[])).
% 0.84/0.85 tff(535,plain,
% 0.84/0.85 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a170) | c2_1(a170) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c2_1(a145)) | (~c3_1(a170))),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[534, 533])).
% 0.84/0.85 tff(536,plain,
% 0.84/0.85 (~c2_1(a145)),
% 0.84/0.85 inference(unit_resolution,[status(thm)],[535, 187, 509, 503, 472, 471, 529, 523, 41])).
% 0.84/0.85 tff(537,plain,
% 0.84/0.85 (((~hskp14) | (~c0_1(a145))) <=> ((~hskp14) | (~c0_1(a145)))),
% 0.84/0.85 inference(rewrite,[status(thm)],[])).
% 0.84/0.85 tff(538,plain,
% 0.84/0.85 (((~c0_1(a145)) | (~hskp14)) <=> ((~hskp14) | (~c0_1(a145)))),
% 0.84/0.85 inference(rewrite,[status(thm)],[])).
% 0.84/0.85 tff(539,axiom,((~c0_1(a145)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause105')).
% 0.84/0.85 tff(540,plain,
% 0.84/0.85 ((~hskp14) | (~c0_1(a145))),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[539, 538])).
% 0.84/0.85 tff(541,plain,
% 0.84/0.85 ((~hskp14) | (~c0_1(a145))),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[540, 537])).
% 0.84/0.85 tff(542,plain,
% 0.84/0.85 (~c0_1(a145)),
% 0.84/0.85 inference(unit_resolution,[status(thm)],[541, 517])).
% 0.84/0.85 tff(543,plain,
% 0.84/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a145) | c1_1(a145) | c3_1(a145) | c1_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a145))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a145) | c1_1(a145) | c3_1(a145) | c1_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a145))),
% 0.84/0.85 inference(rewrite,[status(thm)],[])).
% 0.84/0.85 tff(544,plain,
% 0.84/0.85 (((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a145) | c0_1(a145) | c2_1(a145) | c2_1(a145) | c1_1(a145) | c0_1(a145)) <=> (c0_1(a145) | c1_1(a145) | c3_1(a145) | c1_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a145))),
% 0.84/0.85 inference(rewrite,[status(thm)],[])).
% 0.84/0.85 tff(545,plain,
% 0.84/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a145) | c0_1(a145) | c2_1(a145) | c2_1(a145) | c1_1(a145) | c0_1(a145))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a145) | c1_1(a145) | c3_1(a145) | c1_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a145)))),
% 0.84/0.85 inference(monotonicity,[status(thm)],[544])).
% 0.84/0.85 tff(546,plain,
% 0.84/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a145) | c0_1(a145) | c2_1(a145) | c2_1(a145) | c1_1(a145) | c0_1(a145))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a145) | c1_1(a145) | c3_1(a145) | c1_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a145))),
% 0.84/0.85 inference(transitivity,[status(thm)],[545, 543])).
% 0.84/0.85 tff(547,plain,
% 0.84/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a145) | c0_1(a145) | c2_1(a145) | c2_1(a145) | c1_1(a145) | c0_1(a145))),
% 0.84/0.85 inference(quant_inst,[status(thm)],[])).
% 0.84/0.85 tff(548,plain,
% 0.84/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a145) | c1_1(a145) | c3_1(a145) | c1_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a145)),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[547, 546])).
% 0.84/0.85 tff(549,plain,
% 0.84/0.85 ($false),
% 0.84/0.85 inference(unit_resolution,[status(thm)],[548, 187, 147, 146, 542, 529, 523, 145, 279, 536])).
% 0.84/0.85 tff(550,plain,(c2_1(a170) | (~c0_1(a138)) | (~c3_1(a138)) | c1_1(a138) | c0_1(a170) | c2_1(a128) | hskp18 | c3_1(a128)), inference(lemma,lemma(discharge,[]))).
% 0.84/0.85 tff(551,plain,
% 0.84/0.85 ($false),
% 0.84/0.85 inference(unit_resolution,[status(thm)],[550, 470, 469, 146, 145, 147, 280, 95, 269])).
% 0.84/0.85 tff(552,plain,(c2_1(a128) | (~c3_1(a138)) | c1_1(a138) | (~c0_1(a138)) | hskp18 | c3_1(a128)), inference(lemma,lemma(discharge,[]))).
% 0.84/0.85 tff(553,plain,
% 0.84/0.85 (c2_1(a128)),
% 0.84/0.85 inference(unit_resolution,[status(thm)],[552, 269, 145, 147, 95, 146])).
% 0.84/0.85 tff(554,plain,
% 0.84/0.85 (((~hskp15) | (~c2_1(a149))) <=> ((~hskp15) | (~c2_1(a149)))),
% 0.84/0.85 inference(rewrite,[status(thm)],[])).
% 0.84/0.85 tff(555,plain,
% 0.84/0.85 (((~c2_1(a149)) | (~hskp15)) <=> ((~hskp15) | (~c2_1(a149)))),
% 0.84/0.85 inference(rewrite,[status(thm)],[])).
% 0.84/0.85 tff(556,axiom,((~c2_1(a149)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause104')).
% 0.84/0.85 tff(557,plain,
% 0.84/0.85 ((~hskp15) | (~c2_1(a149))),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[556, 555])).
% 0.84/0.85 tff(558,plain,
% 0.84/0.85 ((~hskp15) | (~c2_1(a149))),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[557, 554])).
% 0.84/0.85 tff(559,plain,
% 0.84/0.85 (~c2_1(a149)),
% 0.84/0.85 inference(unit_resolution,[status(thm)],[558, 257])).
% 0.84/0.85 tff(560,plain,
% 0.84/0.85 (((~hskp15) | (~c1_1(a149))) <=> ((~hskp15) | (~c1_1(a149)))),
% 0.84/0.85 inference(rewrite,[status(thm)],[])).
% 0.84/0.85 tff(561,plain,
% 0.84/0.85 (((~c1_1(a149)) | (~hskp15)) <=> ((~hskp15) | (~c1_1(a149)))),
% 0.84/0.85 inference(rewrite,[status(thm)],[])).
% 0.84/0.85 tff(562,axiom,((~c1_1(a149)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause103')).
% 0.84/0.85 tff(563,plain,
% 0.84/0.85 ((~hskp15) | (~c1_1(a149))),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[562, 561])).
% 0.84/0.85 tff(564,plain,
% 0.84/0.85 ((~hskp15) | (~c1_1(a149))),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[563, 560])).
% 0.84/0.85 tff(565,plain,
% 0.84/0.85 (~c1_1(a149)),
% 0.84/0.85 inference(unit_resolution,[status(thm)],[564, 257])).
% 0.84/0.85 tff(566,assumption,(c3_1(a151)), introduced(assumption)).
% 0.84/0.85 tff(567,assumption,(~c1_1(a128)), introduced(assumption)).
% 0.84/0.85 tff(568,plain,
% 0.84/0.85 (^[U: $i] : refl((hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))),
% 0.84/0.85 inference(bind,[status(th)],[])).
% 0.84/0.85 tff(569,plain,
% 0.84/0.85 (![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.84/0.85 inference(quant_intro,[status(thm)],[568])).
% 0.84/0.85 tff(570,plain,
% 0.84/0.85 (![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.84/0.85 inference(rewrite,[status(thm)],[])).
% 0.84/0.85 tff(571,plain,
% 0.84/0.85 (^[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)) | hskp1) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp1))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp1) | hskp3) <=> ((hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp3))), rewrite(((hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp3) <=> (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp1) | hskp3) <=> (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))))),
% 0.84/0.85 inference(bind,[status(th)],[])).
% 0.84/0.85 tff(572,plain,
% 0.84/0.85 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp1) | hskp3) <=> ![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.84/0.85 inference(quant_intro,[status(thm)],[571])).
% 0.84/0.85 tff(573,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp1) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause131')).
% 0.84/0.85 tff(574,plain,
% 0.84/0.85 (![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[573, 572])).
% 0.84/0.85 tff(575,plain,
% 0.84/0.85 (![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[574, 570])).
% 0.84/0.85 tff(576,plain,(
% 0.84/0.85 ![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.84/0.85 inference(skolemize,[status(sab)],[575])).
% 0.84/0.85 tff(577,plain,
% 0.84/0.85 (![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[576, 569])).
% 0.84/0.85 tff(578,assumption,(c2_1(a128)), introduced(assumption)).
% 0.84/0.85 tff(579,plain,
% 0.84/0.85 (((~hskp3) | (~c2_1(a128))) <=> ((~hskp3) | (~c2_1(a128)))),
% 0.84/0.85 inference(rewrite,[status(thm)],[])).
% 0.84/0.85 tff(580,plain,
% 0.84/0.85 (((~c2_1(a128)) | (~hskp3)) <=> ((~hskp3) | (~c2_1(a128)))),
% 0.84/0.85 inference(rewrite,[status(thm)],[])).
% 0.84/0.85 tff(581,axiom,((~c2_1(a128)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause124')).
% 0.84/0.85 tff(582,plain,
% 0.84/0.85 ((~hskp3) | (~c2_1(a128))),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[581, 580])).
% 0.84/0.85 tff(583,plain,
% 0.84/0.85 ((~hskp3) | (~c2_1(a128))),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[582, 579])).
% 0.84/0.85 tff(584,plain,
% 0.84/0.85 (~hskp3),
% 0.84/0.85 inference(unit_resolution,[status(thm)],[583, 578])).
% 0.84/0.85 tff(585,plain,
% 0.84/0.85 (((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp1 | c0_1(a128) | (~c2_1(a128)) | (~ndr1_0) | c1_1(a128))) <=> ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp3 | hskp1 | c0_1(a128) | (~c2_1(a128)) | (~ndr1_0) | c1_1(a128))),
% 0.84/0.85 inference(rewrite,[status(thm)],[])).
% 0.84/0.85 tff(586,plain,
% 0.84/0.85 ((hskp3 | hskp1 | (~ndr1_0) | c1_1(a128) | c0_1(a128) | (~c2_1(a128))) <=> (hskp3 | hskp1 | c0_1(a128) | (~c2_1(a128)) | (~ndr1_0) | c1_1(a128))),
% 0.84/0.85 inference(rewrite,[status(thm)],[])).
% 0.84/0.85 tff(587,plain,
% 0.84/0.85 (((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp1 | (~ndr1_0) | c1_1(a128) | c0_1(a128) | (~c2_1(a128)))) <=> ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp1 | c0_1(a128) | (~c2_1(a128)) | (~ndr1_0) | c1_1(a128)))),
% 0.84/0.85 inference(monotonicity,[status(thm)],[586])).
% 0.84/0.85 tff(588,plain,
% 0.84/0.85 (((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp1 | (~ndr1_0) | c1_1(a128) | c0_1(a128) | (~c2_1(a128)))) <=> ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp3 | hskp1 | c0_1(a128) | (~c2_1(a128)) | (~ndr1_0) | c1_1(a128))),
% 0.84/0.85 inference(transitivity,[status(thm)],[587, 585])).
% 0.84/0.85 tff(589,plain,
% 0.84/0.85 ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp1 | (~ndr1_0) | c1_1(a128) | c0_1(a128) | (~c2_1(a128)))),
% 0.84/0.85 inference(quant_inst,[status(thm)],[])).
% 0.84/0.85 tff(590,plain,
% 0.84/0.85 ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp3 | hskp1 | c0_1(a128) | (~c2_1(a128)) | (~ndr1_0) | c1_1(a128)),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[589, 588])).
% 0.84/0.85 tff(591,plain,
% 0.84/0.85 (hskp1 | c0_1(a128) | c1_1(a128)),
% 0.84/0.85 inference(unit_resolution,[status(thm)],[590, 187, 584, 578, 577])).
% 0.84/0.85 tff(592,plain,
% 0.84/0.85 (hskp1),
% 0.84/0.85 inference(unit_resolution,[status(thm)],[591, 567, 291])).
% 0.84/0.85 tff(593,plain,
% 0.84/0.85 (((~hskp1) | (~c3_1(a125))) <=> ((~hskp1) | (~c3_1(a125)))),
% 0.84/0.85 inference(rewrite,[status(thm)],[])).
% 0.84/0.85 tff(594,plain,
% 0.84/0.85 (((~c3_1(a125)) | (~hskp1)) <=> ((~hskp1) | (~c3_1(a125)))),
% 0.84/0.85 inference(rewrite,[status(thm)],[])).
% 0.84/0.85 tff(595,axiom,((~c3_1(a125)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause128')).
% 0.84/0.85 tff(596,plain,
% 0.84/0.85 ((~hskp1) | (~c3_1(a125))),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[595, 594])).
% 0.84/0.85 tff(597,plain,
% 0.84/0.85 ((~hskp1) | (~c3_1(a125))),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[596, 593])).
% 0.84/0.85 tff(598,plain,
% 0.84/0.85 (~c3_1(a125)),
% 0.84/0.85 inference(unit_resolution,[status(thm)],[597, 592])).
% 0.84/0.85 tff(599,plain,
% 0.84/0.85 (((~hskp1) | c1_1(a125)) <=> ((~hskp1) | c1_1(a125))),
% 0.84/0.85 inference(rewrite,[status(thm)],[])).
% 0.84/0.85 tff(600,axiom,((~hskp1) | c1_1(a125)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause81')).
% 0.84/0.85 tff(601,plain,
% 0.84/0.85 ((~hskp1) | c1_1(a125)),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[600, 599])).
% 0.84/0.85 tff(602,plain,
% 0.84/0.85 ((~hskp1) | c1_1(a125)),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[601, 599])).
% 0.84/0.85 tff(603,plain,
% 0.84/0.85 ((~hskp1) | c1_1(a125)),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[602, 599])).
% 0.84/0.85 tff(604,plain,
% 0.84/0.85 ((~hskp1) | c1_1(a125)),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[603, 599])).
% 0.84/0.85 tff(605,plain,
% 0.84/0.85 ((~hskp1) | c1_1(a125)),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[604, 599])).
% 0.84/0.85 tff(606,plain,
% 0.84/0.85 ((~hskp1) | c1_1(a125)),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[605, 599])).
% 0.84/0.85 tff(607,plain,
% 0.84/0.85 ((~hskp1) | c1_1(a125)),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[606, 599])).
% 0.84/0.85 tff(608,plain,
% 0.84/0.85 ((~hskp1) | c1_1(a125)),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[607, 599])).
% 0.84/0.85 tff(609,plain,
% 0.84/0.85 (c1_1(a125)),
% 0.84/0.85 inference(unit_resolution,[status(thm)],[608, 592])).
% 0.84/0.85 tff(610,plain,
% 0.84/0.85 (((~hskp1) | c0_1(a125)) <=> ((~hskp1) | c0_1(a125))),
% 0.84/0.85 inference(rewrite,[status(thm)],[])).
% 0.84/0.85 tff(611,axiom,((~hskp1) | c0_1(a125)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause80')).
% 0.84/0.85 tff(612,plain,
% 0.84/0.85 ((~hskp1) | c0_1(a125)),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[611, 610])).
% 0.84/0.85 tff(613,plain,
% 0.84/0.85 ((~hskp1) | c0_1(a125)),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[612, 610])).
% 0.84/0.85 tff(614,plain,
% 0.84/0.85 ((~hskp1) | c0_1(a125)),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[613, 610])).
% 0.84/0.85 tff(615,plain,
% 0.84/0.85 ((~hskp1) | c0_1(a125)),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[614, 610])).
% 0.84/0.85 tff(616,plain,
% 0.84/0.85 ((~hskp1) | c0_1(a125)),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[615, 610])).
% 0.84/0.85 tff(617,plain,
% 0.84/0.85 ((~hskp1) | c0_1(a125)),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[616, 610])).
% 0.84/0.85 tff(618,plain,
% 0.84/0.85 ((~hskp1) | c0_1(a125)),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[617, 610])).
% 0.84/0.85 tff(619,plain,
% 0.84/0.85 ((~hskp1) | c0_1(a125)),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[618, 610])).
% 0.84/0.85 tff(620,plain,
% 0.84/0.85 (c0_1(a125)),
% 0.84/0.85 inference(unit_resolution,[status(thm)],[619, 592])).
% 0.84/0.85 tff(621,plain,
% 0.84/0.85 (((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | c3_1(a125) | (~ndr1_0) | (~c0_1(a125)) | (~c1_1(a125)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp12 | c3_1(a125) | (~ndr1_0) | (~c0_1(a125)) | (~c1_1(a125)))),
% 0.84/0.85 inference(rewrite,[status(thm)],[])).
% 0.84/0.85 tff(622,plain,
% 0.84/0.85 ((hskp12 | (~ndr1_0) | c3_1(a125) | (~c1_1(a125)) | (~c0_1(a125))) <=> (hskp12 | c3_1(a125) | (~ndr1_0) | (~c0_1(a125)) | (~c1_1(a125)))),
% 0.84/0.85 inference(rewrite,[status(thm)],[])).
% 0.84/0.85 tff(623,plain,
% 0.84/0.85 (((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | c3_1(a125) | (~c1_1(a125)) | (~c0_1(a125)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | c3_1(a125) | (~ndr1_0) | (~c0_1(a125)) | (~c1_1(a125))))),
% 0.84/0.85 inference(monotonicity,[status(thm)],[622])).
% 0.84/0.85 tff(624,plain,
% 0.84/0.85 (((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | c3_1(a125) | (~c1_1(a125)) | (~c0_1(a125)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp12 | c3_1(a125) | (~ndr1_0) | (~c0_1(a125)) | (~c1_1(a125)))),
% 0.84/0.85 inference(transitivity,[status(thm)],[623, 621])).
% 0.84/0.85 tff(625,plain,
% 0.84/0.85 ((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | c3_1(a125) | (~c1_1(a125)) | (~c0_1(a125)))),
% 0.84/0.85 inference(quant_inst,[status(thm)],[])).
% 0.84/0.85 tff(626,plain,
% 0.84/0.85 ((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp12 | c3_1(a125) | (~ndr1_0) | (~c0_1(a125)) | (~c1_1(a125))),
% 0.84/0.85 inference(modus_ponens,[status(thm)],[625, 624])).
% 0.84/0.85 tff(627,plain,
% 0.84/0.85 (hskp12),
% 0.84/0.85 inference(unit_resolution,[status(thm)],[626, 187, 620, 609, 598, 239])).
% 0.84/0.85 tff(628,plain,
% 0.84/0.85 (((~hskp12) | (~c0_1(a140))) <=> ((~hskp12) | (~c0_1(a140)))),
% 0.84/0.85 inference(rewrite,[status(thm)],[])).
% 0.84/0.85 tff(629,plain,
% 0.84/0.85 (((~c0_1(a140)) | (~hskp12)) <=> ((~hskp12) | (~c0_1(a140)))),
% 0.84/0.85 inference(rewrite,[status(thm)],[])).
% 0.84/0.85 tff(630,axiom,((~c0_1(a140)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause110')).
% 0.84/0.86 tff(631,plain,
% 0.84/0.86 ((~hskp12) | (~c0_1(a140))),
% 0.84/0.86 inference(modus_ponens,[status(thm)],[630, 629])).
% 0.84/0.86 tff(632,plain,
% 0.84/0.86 ((~hskp12) | (~c0_1(a140))),
% 0.84/0.86 inference(modus_ponens,[status(thm)],[631, 628])).
% 0.84/0.86 tff(633,plain,
% 0.84/0.86 (~c0_1(a140)),
% 0.84/0.86 inference(unit_resolution,[status(thm)],[632, 627])).
% 0.84/0.86 tff(634,assumption,(~c2_1(a149)), introduced(assumption)).
% 0.84/0.86 tff(635,assumption,(~c1_1(a149)), introduced(assumption)).
% 0.84/0.86 tff(636,assumption,(~c2_1(a151)), introduced(assumption)).
% 0.84/0.86 tff(637,plain,
% 0.84/0.86 (((~hskp12) | c3_1(a140)) <=> ((~hskp12) | c3_1(a140))),
% 0.84/0.86 inference(rewrite,[status(thm)],[])).
% 0.84/0.86 tff(638,axiom,((~hskp12) | c3_1(a140)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause66')).
% 0.84/0.86 tff(639,plain,
% 0.84/0.86 ((~hskp12) | c3_1(a140)),
% 0.84/0.86 inference(modus_ponens,[status(thm)],[638, 637])).
% 0.84/0.86 tff(640,plain,
% 0.84/0.86 ((~hskp12) | c3_1(a140)),
% 0.84/0.86 inference(modus_ponens,[status(thm)],[639, 637])).
% 0.84/0.86 tff(641,plain,
% 0.84/0.86 ((~hskp12) | c3_1(a140)),
% 0.84/0.86 inference(modus_ponens,[status(thm)],[640, 637])).
% 0.84/0.86 tff(642,plain,
% 0.84/0.86 ((~hskp12) | c3_1(a140)),
% 0.84/0.86 inference(modus_ponens,[status(thm)],[641, 637])).
% 0.84/0.86 tff(643,plain,
% 0.84/0.86 ((~hskp12) | c3_1(a140)),
% 0.84/0.86 inference(modus_ponens,[status(thm)],[642, 637])).
% 0.84/0.86 tff(644,plain,
% 0.84/0.86 ((~hskp12) | c3_1(a140)),
% 0.84/0.86 inference(modus_ponens,[status(thm)],[643, 637])).
% 0.84/0.86 tff(645,plain,
% 0.84/0.86 ((~hskp12) | c3_1(a140)),
% 0.84/0.86 inference(modus_ponens,[status(thm)],[644, 637])).
% 0.84/0.86 tff(646,plain,
% 0.84/0.86 ((~hskp12) | c3_1(a140)),
% 0.84/0.86 inference(modus_ponens,[status(thm)],[645, 637])).
% 0.84/0.86 tff(647,plain,
% 0.84/0.86 (c3_1(a140)),
% 0.84/0.86 inference(unit_resolution,[status(thm)],[646, 627])).
% 0.84/0.86 tff(648,assumption,(c3_1(a149)), introduced(assumption)).
% 0.84/0.86 tff(649,assumption,(c1_1(a151)), introduced(assumption)).
% 0.84/0.86 tff(650,plain,
% 0.84/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c2_1(a151) | c1_1(a149) | c2_1(a149) | c0_1(a140) | (~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c3_1(a149)) | (~c3_1(a151)) | (~c1_1(a151)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a151) | c1_1(a149) | c2_1(a149) | c0_1(a140) | (~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c3_1(a149)) | (~c3_1(a151)) | (~c1_1(a151)))),
% 0.84/0.86 inference(rewrite,[status(thm)],[])).
% 0.84/0.86 tff(651,plain,
% 0.84/0.86 (((~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c1_1(a151)) | c1_1(a149) | c2_1(a149) | (~c3_1(a149)) | c0_1(a140) | (~c2_1(a140)) | (~c3_1(a140))) <=> (c2_1(a151) | c1_1(a149) | c2_1(a149) | c0_1(a140) | (~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c3_1(a149)) | (~c3_1(a151)) | (~c1_1(a151)))),
% 0.84/0.86 inference(rewrite,[status(thm)],[])).
% 0.84/0.86 tff(652,plain,
% 0.84/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c1_1(a151)) | c1_1(a149) | c2_1(a149) | (~c3_1(a149)) | c0_1(a140) | (~c2_1(a140)) | (~c3_1(a140)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c2_1(a151) | c1_1(a149) | c2_1(a149) | c0_1(a140) | (~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c3_1(a149)) | (~c3_1(a151)) | (~c1_1(a151))))),
% 0.84/0.86 inference(monotonicity,[status(thm)],[651])).
% 0.84/0.86 tff(653,plain,
% 0.84/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c1_1(a151)) | c1_1(a149) | c2_1(a149) | (~c3_1(a149)) | c0_1(a140) | (~c2_1(a140)) | (~c3_1(a140)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a151) | c1_1(a149) | c2_1(a149) | c0_1(a140) | (~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c3_1(a149)) | (~c3_1(a151)) | (~c1_1(a151)))),
% 0.84/0.86 inference(transitivity,[status(thm)],[652, 650])).
% 0.84/0.86 tff(654,plain,
% 0.84/0.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c1_1(a151)) | c1_1(a149) | c2_1(a149) | (~c3_1(a149)) | c0_1(a140) | (~c2_1(a140)) | (~c3_1(a140)))),
% 0.84/0.86 inference(quant_inst,[status(thm)],[])).
% 0.84/0.86 tff(655,plain,
% 0.84/0.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a151) | c1_1(a149) | c2_1(a149) | c0_1(a140) | (~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c3_1(a149)) | (~c3_1(a151)) | (~c1_1(a151))),
% 0.84/0.86 inference(modus_ponens,[status(thm)],[654, 653])).
% 0.84/0.86 tff(656,plain,
% 0.84/0.86 (~c2_1(a140)),
% 0.84/0.86 inference(unit_resolution,[status(thm)],[655, 187, 649, 648, 647, 636, 635, 634, 633, 229, 566])).
% 0.84/0.86 tff(657,plain,
% 0.84/0.86 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c0_1(a140) | (~c2_1(a128)) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | c2_1(a140) | (~c3_1(a140)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a140) | (~c2_1(a128)) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | c2_1(a140) | (~c3_1(a140)))),
% 0.84/0.86 inference(rewrite,[status(thm)],[])).
% 0.84/0.86 tff(658,plain,
% 0.84/0.86 ((hskp3 | (~ndr1_0) | c3_1(a128) | c1_1(a128) | (~c2_1(a128)) | c0_1(a140) | c2_1(a140) | (~c3_1(a140))) <=> (hskp3 | c0_1(a140) | (~c2_1(a128)) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | c2_1(a140) | (~c3_1(a140)))),
% 0.84/0.86 inference(rewrite,[status(thm)],[])).
% 0.84/0.86 tff(659,plain,
% 0.84/0.86 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a128) | c1_1(a128) | (~c2_1(a128)) | c0_1(a140) | c2_1(a140) | (~c3_1(a140)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c0_1(a140) | (~c2_1(a128)) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | c2_1(a140) | (~c3_1(a140))))),
% 0.95/0.86 inference(monotonicity,[status(thm)],[658])).
% 0.95/0.86 tff(660,plain,
% 0.95/0.86 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a128) | c1_1(a128) | (~c2_1(a128)) | c0_1(a140) | c2_1(a140) | (~c3_1(a140)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a140) | (~c2_1(a128)) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | c2_1(a140) | (~c3_1(a140)))),
% 0.95/0.86 inference(transitivity,[status(thm)],[659, 657])).
% 0.95/0.86 tff(661,plain,
% 0.95/0.86 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a128) | c1_1(a128) | (~c2_1(a128)) | c0_1(a140) | c2_1(a140) | (~c3_1(a140)))),
% 0.95/0.86 inference(quant_inst,[status(thm)],[])).
% 0.95/0.86 tff(662,plain,
% 0.95/0.86 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a140) | (~c2_1(a128)) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | c2_1(a140) | (~c3_1(a140))),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[661, 660])).
% 0.95/0.86 tff(663,plain,
% 0.95/0.86 ($false),
% 0.95/0.86 inference(unit_resolution,[status(thm)],[662, 187, 584, 647, 633, 578, 269, 41, 567, 656])).
% 0.95/0.86 tff(664,plain,(c1_1(a128) | (~c2_1(a128)) | c3_1(a128) | (~c1_1(a151)) | (~c3_1(a149)) | c2_1(a151) | c1_1(a149) | c2_1(a149) | (~c3_1(a151)) | c0_1(a128)), inference(lemma,lemma(discharge,[]))).
% 0.95/0.86 tff(665,plain,
% 0.95/0.86 (c1_1(a128)),
% 0.95/0.86 inference(unit_resolution,[status(thm)],[664, 291, 269, 212, 268, 201, 565, 559, 219, 553])).
% 0.95/0.86 tff(666,assumption,(~hskp1), introduced(assumption)).
% 0.95/0.86 tff(667,assumption,(c1_1(a128)), introduced(assumption)).
% 0.95/0.86 tff(668,plain,
% 0.95/0.86 (^[V: $i, U: $i] : refl((hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))),
% 0.95/0.86 inference(bind,[status(th)],[])).
% 0.95/0.86 tff(669,plain,
% 0.95/0.86 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.95/0.86 inference(quant_intro,[status(thm)],[668])).
% 0.95/0.86 tff(670,plain,
% 0.95/0.86 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.95/0.86 inference(rewrite,[status(thm)],[])).
% 0.95/0.86 tff(671,plain,
% 0.95/0.86 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | hskp18) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp18))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp18) <=> (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | hskp18) <=> (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))))),
% 0.95/0.86 inference(bind,[status(th)],[])).
% 0.95/0.86 tff(672,plain,
% 0.95/0.86 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | hskp18) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.95/0.86 inference(quant_intro,[status(thm)],[671])).
% 0.95/0.86 tff(673,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause175')).
% 0.95/0.86 tff(674,plain,
% 0.95/0.86 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[673, 672])).
% 0.95/0.86 tff(675,plain,
% 0.95/0.86 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[674, 670])).
% 0.95/0.86 tff(676,plain,(
% 0.95/0.86 ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.95/0.86 inference(skolemize,[status(sab)],[675])).
% 0.95/0.86 tff(677,plain,
% 0.95/0.86 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[676, 669])).
% 0.95/0.86 tff(678,assumption,(hskp8), introduced(assumption)).
% 0.95/0.86 tff(679,plain,
% 0.95/0.86 (((~hskp8) | c3_1(a135)) <=> ((~hskp8) | c3_1(a135))),
% 0.95/0.86 inference(rewrite,[status(thm)],[])).
% 0.95/0.86 tff(680,axiom,((~hskp8) | c3_1(a135)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 0.95/0.86 tff(681,plain,
% 0.95/0.86 ((~hskp8) | c3_1(a135)),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[680, 679])).
% 0.95/0.86 tff(682,plain,
% 0.95/0.86 ((~hskp8) | c3_1(a135)),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[681, 679])).
% 0.95/0.86 tff(683,plain,
% 0.95/0.86 ((~hskp8) | c3_1(a135)),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[682, 679])).
% 0.95/0.86 tff(684,plain,
% 0.95/0.86 ((~hskp8) | c3_1(a135)),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[683, 679])).
% 0.95/0.86 tff(685,plain,
% 0.95/0.86 ((~hskp8) | c3_1(a135)),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[684, 679])).
% 0.95/0.86 tff(686,plain,
% 0.95/0.86 ((~hskp8) | c3_1(a135)),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[685, 679])).
% 0.95/0.86 tff(687,plain,
% 0.95/0.86 ((~hskp8) | c3_1(a135)),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[686, 679])).
% 0.95/0.86 tff(688,plain,
% 0.95/0.86 ((~hskp8) | c3_1(a135)),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[687, 679])).
% 0.95/0.86 tff(689,plain,
% 0.95/0.86 (c3_1(a135)),
% 0.95/0.86 inference(unit_resolution,[status(thm)],[688, 678])).
% 0.95/0.86 tff(690,plain,
% 0.95/0.86 (((~hskp8) | c2_1(a135)) <=> ((~hskp8) | c2_1(a135))),
% 0.95/0.86 inference(rewrite,[status(thm)],[])).
% 0.95/0.86 tff(691,axiom,((~hskp8) | c2_1(a135)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause72')).
% 0.95/0.86 tff(692,plain,
% 0.95/0.86 ((~hskp8) | c2_1(a135)),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[691, 690])).
% 0.95/0.86 tff(693,plain,
% 0.95/0.86 ((~hskp8) | c2_1(a135)),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[692, 690])).
% 0.95/0.86 tff(694,plain,
% 0.95/0.86 ((~hskp8) | c2_1(a135)),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[693, 690])).
% 0.95/0.86 tff(695,plain,
% 0.95/0.86 ((~hskp8) | c2_1(a135)),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[694, 690])).
% 0.95/0.86 tff(696,plain,
% 0.95/0.86 ((~hskp8) | c2_1(a135)),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[695, 690])).
% 0.95/0.86 tff(697,plain,
% 0.95/0.86 ((~hskp8) | c2_1(a135)),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[696, 690])).
% 0.95/0.86 tff(698,plain,
% 0.95/0.86 ((~hskp8) | c2_1(a135)),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[697, 690])).
% 0.95/0.86 tff(699,plain,
% 0.95/0.86 ((~hskp8) | c2_1(a135)),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[698, 690])).
% 0.95/0.86 tff(700,plain,
% 0.95/0.86 (c2_1(a135)),
% 0.95/0.86 inference(unit_resolution,[status(thm)],[699, 678])).
% 0.95/0.86 tff(701,plain,
% 0.95/0.86 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | c0_1(a128) | (~c2_1(a128)) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a135)) | (~c2_1(a135)) | (~c0_1(a135)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp18 | c0_1(a128) | (~c2_1(a128)) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a135)) | (~c2_1(a135)) | (~c0_1(a135)))),
% 0.95/0.86 inference(rewrite,[status(thm)],[])).
% 0.95/0.86 tff(702,plain,
% 0.95/0.86 ((hskp18 | (~ndr1_0) | (~c2_1(a135)) | (~c3_1(a135)) | (~c0_1(a135)) | c0_1(a128) | (~c2_1(a128)) | (~c1_1(a128))) <=> (hskp18 | c0_1(a128) | (~c2_1(a128)) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a135)) | (~c2_1(a135)) | (~c0_1(a135)))),
% 0.95/0.86 inference(rewrite,[status(thm)],[])).
% 0.95/0.86 tff(703,plain,
% 0.95/0.86 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | (~c2_1(a135)) | (~c3_1(a135)) | (~c0_1(a135)) | c0_1(a128) | (~c2_1(a128)) | (~c1_1(a128)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | c0_1(a128) | (~c2_1(a128)) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a135)) | (~c2_1(a135)) | (~c0_1(a135))))),
% 0.95/0.86 inference(monotonicity,[status(thm)],[702])).
% 0.95/0.86 tff(704,plain,
% 0.95/0.86 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | (~c2_1(a135)) | (~c3_1(a135)) | (~c0_1(a135)) | c0_1(a128) | (~c2_1(a128)) | (~c1_1(a128)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp18 | c0_1(a128) | (~c2_1(a128)) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a135)) | (~c2_1(a135)) | (~c0_1(a135)))),
% 0.95/0.86 inference(transitivity,[status(thm)],[703, 701])).
% 0.95/0.86 tff(705,plain,
% 0.95/0.86 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | (~c2_1(a135)) | (~c3_1(a135)) | (~c0_1(a135)) | c0_1(a128) | (~c2_1(a128)) | (~c1_1(a128)))),
% 0.95/0.86 inference(quant_inst,[status(thm)],[])).
% 0.95/0.86 tff(706,plain,
% 0.95/0.86 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp18 | c0_1(a128) | (~c2_1(a128)) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a135)) | (~c2_1(a135)) | (~c0_1(a135))),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[705, 704])).
% 0.95/0.86 tff(707,plain,
% 0.95/0.86 (~c0_1(a135)),
% 0.95/0.86 inference(unit_resolution,[status(thm)],[706, 187, 95, 700, 689, 291, 578, 677, 667])).
% 0.95/0.86 tff(708,plain,
% 0.95/0.86 (((~hskp8) | (~c1_1(a135))) <=> ((~hskp8) | (~c1_1(a135)))),
% 0.95/0.86 inference(rewrite,[status(thm)],[])).
% 0.95/0.86 tff(709,plain,
% 0.95/0.86 (((~c1_1(a135)) | (~hskp8)) <=> ((~hskp8) | (~c1_1(a135)))),
% 0.95/0.86 inference(rewrite,[status(thm)],[])).
% 0.95/0.86 tff(710,axiom,((~c1_1(a135)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause115')).
% 0.95/0.86 tff(711,plain,
% 0.95/0.86 ((~hskp8) | (~c1_1(a135))),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[710, 709])).
% 0.95/0.86 tff(712,plain,
% 0.95/0.86 ((~hskp8) | (~c1_1(a135))),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[711, 708])).
% 0.95/0.86 tff(713,plain,
% 0.95/0.86 (~c1_1(a135)),
% 0.95/0.86 inference(unit_resolution,[status(thm)],[712, 678])).
% 0.95/0.86 tff(714,plain,
% 0.95/0.86 (((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp1 | c1_1(a135) | (~ndr1_0) | (~c2_1(a135)) | c0_1(a135))) <=> ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp3 | hskp1 | c1_1(a135) | (~ndr1_0) | (~c2_1(a135)) | c0_1(a135))),
% 0.95/0.86 inference(rewrite,[status(thm)],[])).
% 0.95/0.86 tff(715,plain,
% 0.95/0.86 ((hskp3 | hskp1 | (~ndr1_0) | c1_1(a135) | c0_1(a135) | (~c2_1(a135))) <=> (hskp3 | hskp1 | c1_1(a135) | (~ndr1_0) | (~c2_1(a135)) | c0_1(a135))),
% 0.95/0.86 inference(rewrite,[status(thm)],[])).
% 0.95/0.86 tff(716,plain,
% 0.95/0.86 (((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp1 | (~ndr1_0) | c1_1(a135) | c0_1(a135) | (~c2_1(a135)))) <=> ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp1 | c1_1(a135) | (~ndr1_0) | (~c2_1(a135)) | c0_1(a135)))),
% 0.95/0.86 inference(monotonicity,[status(thm)],[715])).
% 0.95/0.86 tff(717,plain,
% 0.95/0.86 (((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp1 | (~ndr1_0) | c1_1(a135) | c0_1(a135) | (~c2_1(a135)))) <=> ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp3 | hskp1 | c1_1(a135) | (~ndr1_0) | (~c2_1(a135)) | c0_1(a135))),
% 0.95/0.86 inference(transitivity,[status(thm)],[716, 714])).
% 0.95/0.86 tff(718,plain,
% 0.95/0.86 ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp1 | (~ndr1_0) | c1_1(a135) | c0_1(a135) | (~c2_1(a135)))),
% 0.95/0.86 inference(quant_inst,[status(thm)],[])).
% 0.95/0.86 tff(719,plain,
% 0.95/0.86 ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp3 | hskp1 | c1_1(a135) | (~ndr1_0) | (~c2_1(a135)) | c0_1(a135)),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[718, 717])).
% 0.95/0.86 tff(720,plain,
% 0.95/0.86 ($false),
% 0.95/0.86 inference(unit_resolution,[status(thm)],[719, 187, 584, 666, 700, 713, 577, 707])).
% 0.95/0.86 tff(721,plain,((~hskp8) | hskp1 | hskp18 | c0_1(a128) | (~c2_1(a128)) | (~c1_1(a128))), inference(lemma,lemma(discharge,[]))).
% 0.95/0.86 tff(722,plain,
% 0.95/0.86 (~hskp8),
% 0.95/0.86 inference(unit_resolution,[status(thm)],[721, 666, 95, 291, 553, 665])).
% 0.95/0.86 tff(723,plain,
% 0.95/0.86 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))),
% 0.95/0.86 inference(bind,[status(th)],[])).
% 0.95/0.86 tff(724,plain,
% 0.95/0.86 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.95/0.86 inference(quant_intro,[status(thm)],[723])).
% 0.95/0.86 tff(725,plain,
% 0.95/0.86 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.95/0.86 inference(rewrite,[status(thm)],[])).
% 0.95/0.86 tff(726,plain,
% 0.95/0.86 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~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(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp8) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp8))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))))),
% 0.95/0.86 inference(bind,[status(th)],[])).
% 0.95/0.86 tff(727,plain,
% 0.95/0.86 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.95/0.86 inference(quant_intro,[status(thm)],[726])).
% 0.95/0.86 tff(728,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause169')).
% 0.95/0.86 tff(729,plain,
% 0.95/0.86 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[728, 727])).
% 0.95/0.86 tff(730,plain,
% 0.95/0.86 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[729, 725])).
% 0.95/0.86 tff(731,plain,(
% 0.95/0.86 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.95/0.86 inference(skolemize,[status(sab)],[730])).
% 0.95/0.86 tff(732,plain,
% 0.95/0.86 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[731, 724])).
% 0.95/0.86 tff(733,plain,
% 0.95/0.86 (~hskp3),
% 0.95/0.86 inference(unit_resolution,[status(thm)],[583, 553])).
% 0.95/0.86 tff(734,assumption,(hskp14), introduced(assumption)).
% 0.95/0.86 tff(735,plain,
% 0.95/0.86 (~c1_1(a145)),
% 0.95/0.86 inference(unit_resolution,[status(thm)],[528, 734])).
% 0.95/0.86 tff(736,plain,
% 0.95/0.86 (~c0_1(a145)),
% 0.95/0.86 inference(unit_resolution,[status(thm)],[541, 734])).
% 0.95/0.86 tff(737,plain,
% 0.95/0.86 (((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp1 | c0_1(a145) | c1_1(a145) | (~ndr1_0) | (~c2_1(a145)))) <=> ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp3 | hskp1 | c0_1(a145) | c1_1(a145) | (~ndr1_0) | (~c2_1(a145)))),
% 0.95/0.86 inference(rewrite,[status(thm)],[])).
% 0.95/0.86 tff(738,plain,
% 0.95/0.86 ((hskp3 | hskp1 | (~ndr1_0) | c1_1(a145) | c0_1(a145) | (~c2_1(a145))) <=> (hskp3 | hskp1 | c0_1(a145) | c1_1(a145) | (~ndr1_0) | (~c2_1(a145)))),
% 0.95/0.86 inference(rewrite,[status(thm)],[])).
% 0.95/0.86 tff(739,plain,
% 0.95/0.86 (((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp1 | (~ndr1_0) | c1_1(a145) | c0_1(a145) | (~c2_1(a145)))) <=> ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp1 | c0_1(a145) | c1_1(a145) | (~ndr1_0) | (~c2_1(a145))))),
% 0.95/0.86 inference(monotonicity,[status(thm)],[738])).
% 0.95/0.86 tff(740,plain,
% 0.95/0.86 (((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp1 | (~ndr1_0) | c1_1(a145) | c0_1(a145) | (~c2_1(a145)))) <=> ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp3 | hskp1 | c0_1(a145) | c1_1(a145) | (~ndr1_0) | (~c2_1(a145)))),
% 0.95/0.86 inference(transitivity,[status(thm)],[739, 737])).
% 0.95/0.86 tff(741,plain,
% 0.95/0.86 ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp1 | (~ndr1_0) | c1_1(a145) | c0_1(a145) | (~c2_1(a145)))),
% 0.95/0.86 inference(quant_inst,[status(thm)],[])).
% 0.95/0.86 tff(742,plain,
% 0.95/0.86 ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp3 | hskp1 | c0_1(a145) | c1_1(a145) | (~ndr1_0) | (~c2_1(a145))),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[741, 740])).
% 0.95/0.86 tff(743,plain,
% 0.95/0.86 (~c2_1(a145)),
% 0.95/0.86 inference(unit_resolution,[status(thm)],[742, 187, 52, 666, 736, 735, 577])).
% 0.95/0.86 tff(744,plain,
% 0.95/0.86 (~c3_1(a145)),
% 0.95/0.86 inference(unit_resolution,[status(thm)],[522, 734])).
% 0.95/0.86 tff(745,plain,
% 0.95/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a149) | c2_1(a149) | c0_1(a145) | c3_1(a145) | c1_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a145) | c0_1(a149))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c2_1(a149) | c0_1(a145) | c3_1(a145) | c1_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a145) | c0_1(a149))),
% 0.95/0.86 inference(rewrite,[status(thm)],[])).
% 0.95/0.86 tff(746,plain,
% 0.95/0.86 (((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a145) | c0_1(a145) | c2_1(a145) | c2_1(a149) | c1_1(a149) | c0_1(a149)) <=> (c1_1(a149) | c2_1(a149) | c0_1(a145) | c3_1(a145) | c1_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a145) | c0_1(a149))),
% 0.95/0.86 inference(rewrite,[status(thm)],[])).
% 0.95/0.86 tff(747,plain,
% 0.95/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a145) | c0_1(a145) | c2_1(a145) | c2_1(a149) | c1_1(a149) | c0_1(a149))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a149) | c2_1(a149) | c0_1(a145) | c3_1(a145) | c1_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a145) | c0_1(a149)))),
% 0.95/0.86 inference(monotonicity,[status(thm)],[746])).
% 0.95/0.86 tff(748,plain,
% 0.95/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a145) | c0_1(a145) | c2_1(a145) | c2_1(a149) | c1_1(a149) | c0_1(a149))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c2_1(a149) | c0_1(a145) | c3_1(a145) | c1_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a145) | c0_1(a149))),
% 0.95/0.86 inference(transitivity,[status(thm)],[747, 745])).
% 0.95/0.86 tff(749,plain,
% 0.95/0.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a145) | c0_1(a145) | c2_1(a145) | c2_1(a149) | c1_1(a149) | c0_1(a149))),
% 0.95/0.86 inference(quant_inst,[status(thm)],[])).
% 0.95/0.86 tff(750,plain,
% 0.95/0.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c2_1(a149) | c0_1(a145) | c3_1(a145) | c1_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a145) | c0_1(a149)),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[749, 748])).
% 0.95/0.86 tff(751,plain,
% 0.95/0.86 (c0_1(a149)),
% 0.95/0.86 inference(unit_resolution,[status(thm)],[750, 187, 147, 146, 635, 634, 736, 744, 145, 279, 743])).
% 0.95/0.86 tff(752,plain,
% 0.95/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a149) | c0_1(a145) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a149)) | (~c0_1(a149)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c0_1(a145) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a149)) | (~c0_1(a149)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(753,plain,
% 0.95/0.87 (((~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a145) | c0_1(a145) | c2_1(a145) | c2_1(a145) | c1_1(a145) | c0_1(a145)) <=> (c1_1(a149) | c0_1(a145) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a149)) | (~c0_1(a149)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(754,plain,
% 0.95/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a145) | c0_1(a145) | c2_1(a145) | c2_1(a145) | c1_1(a145) | c0_1(a145))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a149) | c0_1(a145) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a149)) | (~c0_1(a149))))),
% 0.95/0.87 inference(monotonicity,[status(thm)],[753])).
% 0.95/0.87 tff(755,plain,
% 0.95/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a145) | c0_1(a145) | c2_1(a145) | c2_1(a145) | c1_1(a145) | c0_1(a145))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c0_1(a145) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a149)) | (~c0_1(a149)))),
% 0.95/0.87 inference(transitivity,[status(thm)],[754, 752])).
% 0.95/0.87 tff(756,plain,
% 0.95/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a145) | c0_1(a145) | c2_1(a145) | c2_1(a145) | c1_1(a145) | c0_1(a145))),
% 0.95/0.87 inference(quant_inst,[status(thm)],[])).
% 0.95/0.87 tff(757,plain,
% 0.95/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c0_1(a145) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a149)) | (~c0_1(a149))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[756, 755])).
% 0.95/0.87 tff(758,plain,
% 0.95/0.87 ($false),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[757, 187, 648, 635, 736, 735, 744, 279, 751, 743])).
% 0.95/0.87 tff(759,plain,((~hskp14) | (~c3_1(a149)) | c1_1(a149) | (~c0_1(a138)) | (~c3_1(a138)) | c2_1(a149) | c1_1(a138) | hskp3 | hskp1), inference(lemma,lemma(discharge,[]))).
% 0.95/0.87 tff(760,plain,
% 0.95/0.87 (~hskp14),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[759, 666, 565, 147, 146, 559, 145, 733, 268])).
% 0.95/0.87 tff(761,plain,
% 0.95/0.87 (((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp14 | hskp3 | c2_1(a149) | (~ndr1_0) | (~c3_1(a149)) | c0_1(a149))) <=> ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp14 | hskp3 | c2_1(a149) | (~ndr1_0) | (~c3_1(a149)) | c0_1(a149))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(762,plain,
% 0.95/0.87 ((hskp14 | hskp3 | (~ndr1_0) | c0_1(a149) | c2_1(a149) | (~c3_1(a149))) <=> (hskp14 | hskp3 | c2_1(a149) | (~ndr1_0) | (~c3_1(a149)) | c0_1(a149))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(763,plain,
% 0.95/0.87 (((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp14 | hskp3 | (~ndr1_0) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)))) <=> ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp14 | hskp3 | c2_1(a149) | (~ndr1_0) | (~c3_1(a149)) | c0_1(a149)))),
% 0.95/0.87 inference(monotonicity,[status(thm)],[762])).
% 0.95/0.87 tff(764,plain,
% 0.95/0.87 (((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp14 | hskp3 | (~ndr1_0) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)))) <=> ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp14 | hskp3 | c2_1(a149) | (~ndr1_0) | (~c3_1(a149)) | c0_1(a149))),
% 0.95/0.87 inference(transitivity,[status(thm)],[763, 761])).
% 0.95/0.87 tff(765,plain,
% 0.95/0.87 ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp14 | hskp3 | (~ndr1_0) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)))),
% 0.95/0.87 inference(quant_inst,[status(thm)],[])).
% 0.95/0.87 tff(766,plain,
% 0.95/0.87 ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp14 | hskp3 | c2_1(a149) | (~ndr1_0) | (~c3_1(a149)) | c0_1(a149)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[765, 764])).
% 0.95/0.87 tff(767,plain,
% 0.95/0.87 (hskp14 | c0_1(a149)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[766, 187, 733, 268, 559, 51])).
% 0.95/0.87 tff(768,plain,
% 0.95/0.87 (c0_1(a149)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[767, 760])).
% 0.95/0.87 tff(769,assumption,(hskp6), introduced(assumption)).
% 0.95/0.87 tff(770,plain,
% 0.95/0.87 (~c2_1(a133)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[360, 769])).
% 0.95/0.87 tff(771,plain,
% 0.95/0.87 (~c0_1(a133)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[372, 769])).
% 0.95/0.87 tff(772,assumption,(~hskp14), introduced(assumption)).
% 0.95/0.87 tff(773,plain,
% 0.95/0.87 (((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp14 | hskp3 | c0_1(a133) | c2_1(a133) | (~ndr1_0) | (~c3_1(a133)))) <=> ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp14 | hskp3 | c0_1(a133) | c2_1(a133) | (~ndr1_0) | (~c3_1(a133)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(774,plain,
% 0.95/0.87 ((hskp14 | hskp3 | (~ndr1_0) | c0_1(a133) | c2_1(a133) | (~c3_1(a133))) <=> (hskp14 | hskp3 | c0_1(a133) | c2_1(a133) | (~ndr1_0) | (~c3_1(a133)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(775,plain,
% 0.95/0.87 (((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp14 | hskp3 | (~ndr1_0) | c0_1(a133) | c2_1(a133) | (~c3_1(a133)))) <=> ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp14 | hskp3 | c0_1(a133) | c2_1(a133) | (~ndr1_0) | (~c3_1(a133))))),
% 0.95/0.87 inference(monotonicity,[status(thm)],[774])).
% 0.95/0.87 tff(776,plain,
% 0.95/0.87 (((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp14 | hskp3 | (~ndr1_0) | c0_1(a133) | c2_1(a133) | (~c3_1(a133)))) <=> ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp14 | hskp3 | c0_1(a133) | c2_1(a133) | (~ndr1_0) | (~c3_1(a133)))),
% 0.95/0.87 inference(transitivity,[status(thm)],[775, 773])).
% 0.95/0.87 tff(777,plain,
% 0.95/0.87 ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp14 | hskp3 | (~ndr1_0) | c0_1(a133) | c2_1(a133) | (~c3_1(a133)))),
% 0.95/0.87 inference(quant_inst,[status(thm)],[])).
% 0.95/0.87 tff(778,plain,
% 0.95/0.87 ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp14 | hskp3 | c0_1(a133) | c2_1(a133) | (~ndr1_0) | (~c3_1(a133))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[777, 776])).
% 0.95/0.87 tff(779,plain,
% 0.95/0.87 (~c3_1(a133)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[778, 187, 772, 52, 771, 770, 51])).
% 0.95/0.87 tff(780,assumption,(c0_1(a149)), introduced(assumption)).
% 0.95/0.87 tff(781,plain,
% 0.95/0.87 (~c1_1(a133)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[366, 769])).
% 0.95/0.87 tff(782,plain,
% 0.95/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a149) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | c3_1(a133) | (~c3_1(a149)) | (~c0_1(a149)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | c3_1(a133) | (~c3_1(a149)) | (~c0_1(a149)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(783,plain,
% 0.95/0.87 (((~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a133) | c0_1(a133) | c2_1(a133) | c2_1(a133) | c1_1(a133) | c0_1(a133)) <=> (c1_1(a149) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | c3_1(a133) | (~c3_1(a149)) | (~c0_1(a149)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(784,plain,
% 0.95/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a133) | c0_1(a133) | c2_1(a133) | c2_1(a133) | c1_1(a133) | c0_1(a133))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a149) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | c3_1(a133) | (~c3_1(a149)) | (~c0_1(a149))))),
% 0.95/0.87 inference(monotonicity,[status(thm)],[783])).
% 0.95/0.87 tff(785,plain,
% 0.95/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a133) | c0_1(a133) | c2_1(a133) | c2_1(a133) | c1_1(a133) | c0_1(a133))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | c3_1(a133) | (~c3_1(a149)) | (~c0_1(a149)))),
% 0.95/0.87 inference(transitivity,[status(thm)],[784, 782])).
% 0.95/0.87 tff(786,plain,
% 0.95/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a133) | c0_1(a133) | c2_1(a133) | c2_1(a133) | c1_1(a133) | c0_1(a133))),
% 0.95/0.87 inference(quant_inst,[status(thm)],[])).
% 0.95/0.87 tff(787,plain,
% 0.95/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | c3_1(a133) | (~c3_1(a149)) | (~c0_1(a149))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[786, 785])).
% 0.95/0.87 tff(788,plain,
% 0.95/0.87 ($false),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[787, 187, 648, 635, 771, 781, 770, 279, 780, 779])).
% 0.95/0.87 tff(789,plain,((~hskp6) | (~c3_1(a149)) | c1_1(a149) | (~c0_1(a149)) | hskp14 | hskp3), inference(lemma,lemma(discharge,[]))).
% 0.95/0.87 tff(790,plain,
% 0.95/0.87 (~hskp6),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[789, 768, 565, 268, 760, 733])).
% 0.95/0.87 tff(791,plain,
% 0.95/0.87 ((hskp21 | hskp9 | hskp6) <=> (hskp21 | hskp9 | hskp6)),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(792,plain,
% 0.95/0.87 (((hskp21 | hskp9) | hskp6) <=> (hskp21 | hskp9 | hskp6)),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(793,plain,
% 0.95/0.87 ((hskp9 | hskp21) <=> (hskp21 | hskp9)),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(794,plain,
% 0.95/0.87 (((hskp9 | hskp21) | hskp6) <=> ((hskp21 | hskp9) | hskp6)),
% 0.95/0.87 inference(monotonicity,[status(thm)],[793])).
% 0.95/0.87 tff(795,plain,
% 0.95/0.87 (((hskp9 | hskp21) | hskp6) <=> (hskp21 | hskp9 | hskp6)),
% 0.95/0.87 inference(transitivity,[status(thm)],[794, 792])).
% 0.95/0.87 tff(796,axiom,((hskp9 | hskp21) | hskp6), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause34')).
% 0.95/0.87 tff(797,plain,
% 0.95/0.87 (hskp21 | hskp9 | hskp6),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[796, 795])).
% 0.95/0.87 tff(798,plain,
% 0.95/0.87 (hskp21 | hskp9 | hskp6),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[797, 791])).
% 0.95/0.87 tff(799,plain,
% 0.95/0.87 (hskp21 | hskp9 | hskp6),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[798, 791])).
% 0.95/0.87 tff(800,plain,
% 0.95/0.87 (hskp21 | hskp9 | hskp6),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[799, 791])).
% 0.95/0.87 tff(801,plain,
% 0.95/0.87 (hskp21 | hskp9 | hskp6),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[800, 791])).
% 0.95/0.87 tff(802,plain,
% 0.95/0.87 (hskp21 | hskp9 | hskp6),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[801, 791])).
% 0.95/0.87 tff(803,plain,
% 0.95/0.87 (hskp21 | hskp9 | hskp6),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[802, 791])).
% 0.95/0.87 tff(804,plain,
% 0.95/0.87 (hskp21 | hskp9 | hskp6),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[803, 791])).
% 0.95/0.87 tff(805,plain,
% 0.95/0.87 (hskp9),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[804, 790, 53])).
% 0.95/0.87 tff(806,plain,
% 0.95/0.87 (((~hskp9) | (~c3_1(a136))) <=> ((~hskp9) | (~c3_1(a136)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(807,plain,
% 0.95/0.87 (((~c3_1(a136)) | (~hskp9)) <=> ((~hskp9) | (~c3_1(a136)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(808,axiom,((~c3_1(a136)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause114')).
% 0.95/0.87 tff(809,plain,
% 0.95/0.87 ((~hskp9) | (~c3_1(a136))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[808, 807])).
% 0.95/0.87 tff(810,plain,
% 0.95/0.87 ((~hskp9) | (~c3_1(a136))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[809, 806])).
% 0.95/0.87 tff(811,plain,
% 0.95/0.87 (~c3_1(a136)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[810, 805])).
% 0.95/0.87 tff(812,plain,
% 0.95/0.87 (((~hskp9) | c2_1(a136)) <=> ((~hskp9) | c2_1(a136))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(813,axiom,((~hskp9) | c2_1(a136)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause71')).
% 0.95/0.87 tff(814,plain,
% 0.95/0.87 ((~hskp9) | c2_1(a136)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[813, 812])).
% 0.95/0.87 tff(815,plain,
% 0.95/0.87 ((~hskp9) | c2_1(a136)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[814, 812])).
% 0.95/0.87 tff(816,plain,
% 0.95/0.87 ((~hskp9) | c2_1(a136)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[815, 812])).
% 0.95/0.87 tff(817,plain,
% 0.95/0.87 ((~hskp9) | c2_1(a136)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[816, 812])).
% 0.95/0.87 tff(818,plain,
% 0.95/0.87 ((~hskp9) | c2_1(a136)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[817, 812])).
% 0.95/0.87 tff(819,plain,
% 0.95/0.87 ((~hskp9) | c2_1(a136)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[818, 812])).
% 0.95/0.87 tff(820,plain,
% 0.95/0.87 ((~hskp9) | c2_1(a136)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[819, 812])).
% 0.95/0.87 tff(821,plain,
% 0.95/0.87 ((~hskp9) | c2_1(a136)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[820, 812])).
% 0.95/0.87 tff(822,plain,
% 0.95/0.87 (c2_1(a136)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[821, 805])).
% 0.95/0.87 tff(823,plain,
% 0.95/0.87 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp8 | c2_1(a151) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a151)) | (~c0_1(a151)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp8 | c2_1(a151) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a151)) | (~c0_1(a151)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(824,plain,
% 0.95/0.87 ((hskp8 | (~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c0_1(a151)) | c3_1(a136) | c1_1(a136) | (~c2_1(a136))) <=> (hskp8 | c2_1(a151) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a151)) | (~c0_1(a151)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(825,plain,
% 0.95/0.87 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c0_1(a151)) | c3_1(a136) | c1_1(a136) | (~c2_1(a136)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp8 | c2_1(a151) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a151)) | (~c0_1(a151))))),
% 0.95/0.87 inference(monotonicity,[status(thm)],[824])).
% 0.95/0.87 tff(826,plain,
% 0.95/0.87 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c0_1(a151)) | c3_1(a136) | c1_1(a136) | (~c2_1(a136)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp8 | c2_1(a151) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a151)) | (~c0_1(a151)))),
% 0.95/0.87 inference(transitivity,[status(thm)],[825, 823])).
% 0.95/0.87 tff(827,plain,
% 0.95/0.87 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c0_1(a151)) | c3_1(a136) | c1_1(a136) | (~c2_1(a136)))),
% 0.95/0.87 inference(quant_inst,[status(thm)],[])).
% 0.95/0.87 tff(828,plain,
% 0.95/0.87 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp8 | c2_1(a151) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a151)) | (~c0_1(a151))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[827, 826])).
% 0.95/0.87 tff(829,plain,
% 0.95/0.87 (hskp8 | c1_1(a136)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[828, 187, 250, 822, 201, 811, 732, 219])).
% 0.95/0.87 tff(830,plain,
% 0.95/0.87 (c1_1(a136)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[829, 722])).
% 0.95/0.87 tff(831,plain,
% 0.95/0.87 (((~hskp9) | c0_1(a136)) <=> ((~hskp9) | c0_1(a136))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(832,axiom,((~hskp9) | c0_1(a136)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause70')).
% 0.95/0.87 tff(833,plain,
% 0.95/0.87 ((~hskp9) | c0_1(a136)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[832, 831])).
% 0.95/0.87 tff(834,plain,
% 0.95/0.87 ((~hskp9) | c0_1(a136)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[833, 831])).
% 0.95/0.87 tff(835,plain,
% 0.95/0.87 ((~hskp9) | c0_1(a136)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[834, 831])).
% 0.95/0.87 tff(836,plain,
% 0.95/0.87 ((~hskp9) | c0_1(a136)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[835, 831])).
% 0.95/0.87 tff(837,plain,
% 0.95/0.87 ((~hskp9) | c0_1(a136)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[836, 831])).
% 0.95/0.87 tff(838,plain,
% 0.95/0.87 ((~hskp9) | c0_1(a136)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[837, 831])).
% 0.95/0.87 tff(839,plain,
% 0.95/0.87 ((~hskp9) | c0_1(a136)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[838, 831])).
% 0.95/0.87 tff(840,plain,
% 0.95/0.87 ((~hskp9) | c0_1(a136)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[839, 831])).
% 0.95/0.87 tff(841,plain,
% 0.95/0.87 (c0_1(a136)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[840, 805])).
% 0.95/0.87 tff(842,plain,
% 0.95/0.87 (((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | c3_1(a136) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp12 | c3_1(a136) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(843,plain,
% 0.95/0.87 ((hskp12 | (~ndr1_0) | c3_1(a136) | (~c1_1(a136)) | (~c0_1(a136))) <=> (hskp12 | c3_1(a136) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(844,plain,
% 0.95/0.87 (((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | c3_1(a136) | (~c1_1(a136)) | (~c0_1(a136)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | c3_1(a136) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136))))),
% 0.95/0.87 inference(monotonicity,[status(thm)],[843])).
% 0.95/0.87 tff(845,plain,
% 0.95/0.87 (((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | c3_1(a136) | (~c1_1(a136)) | (~c0_1(a136)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp12 | c3_1(a136) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)))),
% 0.95/0.87 inference(transitivity,[status(thm)],[844, 842])).
% 0.95/0.87 tff(846,plain,
% 0.95/0.87 ((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | c3_1(a136) | (~c1_1(a136)) | (~c0_1(a136)))),
% 0.95/0.87 inference(quant_inst,[status(thm)],[])).
% 0.95/0.87 tff(847,plain,
% 0.95/0.87 ((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp12 | c3_1(a136) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[846, 845])).
% 0.95/0.87 tff(848,plain,
% 0.95/0.87 (hskp12 | (~c1_1(a136))),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[847, 187, 841, 811, 239])).
% 0.95/0.87 tff(849,plain,
% 0.95/0.87 (hskp12),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[848, 830])).
% 0.95/0.87 tff(850,plain,
% 0.95/0.87 (~c0_1(a140)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[632, 849])).
% 0.95/0.87 tff(851,plain,
% 0.95/0.87 (c3_1(a140)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[646, 849])).
% 0.95/0.87 tff(852,plain,
% 0.95/0.87 (((~hskp12) | c1_1(a140)) <=> ((~hskp12) | c1_1(a140))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(853,axiom,((~hskp12) | c1_1(a140)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause65')).
% 0.95/0.87 tff(854,plain,
% 0.95/0.87 ((~hskp12) | c1_1(a140)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[853, 852])).
% 0.95/0.87 tff(855,plain,
% 0.95/0.87 ((~hskp12) | c1_1(a140)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[854, 852])).
% 0.95/0.87 tff(856,plain,
% 0.95/0.87 ((~hskp12) | c1_1(a140)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[855, 852])).
% 0.95/0.87 tff(857,plain,
% 0.95/0.87 ((~hskp12) | c1_1(a140)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[856, 852])).
% 0.95/0.87 tff(858,plain,
% 0.95/0.87 ((~hskp12) | c1_1(a140)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[857, 852])).
% 0.95/0.87 tff(859,plain,
% 0.95/0.87 ((~hskp12) | c1_1(a140)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[858, 852])).
% 0.95/0.87 tff(860,plain,
% 0.95/0.87 ((~hskp12) | c1_1(a140)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[859, 852])).
% 0.95/0.87 tff(861,plain,
% 0.95/0.87 ((~hskp12) | c1_1(a140)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[860, 852])).
% 0.95/0.87 tff(862,plain,
% 0.95/0.87 (c1_1(a140)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[861, 849])).
% 0.95/0.87 tff(863,plain,
% 0.95/0.87 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a140) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a140)) | (~c1_1(a140)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a140) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a140)) | (~c1_1(a140)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(864,plain,
% 0.95/0.87 ((hskp6 | (~ndr1_0) | c0_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | c3_1(a128) | c0_1(a128) | (~c1_1(a128))) <=> (hskp6 | c0_1(a140) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a140)) | (~c1_1(a140)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(865,plain,
% 0.95/0.87 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | c3_1(a128) | c0_1(a128) | (~c1_1(a128)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a140) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a140)) | (~c1_1(a140))))),
% 0.95/0.87 inference(monotonicity,[status(thm)],[864])).
% 0.95/0.87 tff(866,plain,
% 0.95/0.87 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | c3_1(a128) | c0_1(a128) | (~c1_1(a128)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a140) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a140)) | (~c1_1(a140)))),
% 0.95/0.87 inference(transitivity,[status(thm)],[865, 863])).
% 0.95/0.87 tff(867,plain,
% 0.95/0.87 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | c3_1(a128) | c0_1(a128) | (~c1_1(a128)))),
% 0.95/0.87 inference(quant_inst,[status(thm)],[])).
% 0.95/0.87 tff(868,plain,
% 0.95/0.87 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a140) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a140)) | (~c1_1(a140))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[867, 866])).
% 0.95/0.87 tff(869,plain,
% 0.95/0.87 ($false),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[868, 187, 790, 862, 851, 850, 291, 269, 336, 665])).
% 0.95/0.87 tff(870,plain,(hskp1 | c0_1(a128) | c3_1(a128) | hskp18 | hskp21 | (~c0_1(a138)) | (~c3_1(a138)) | c1_1(a138)), inference(lemma,lemma(discharge,[]))).
% 0.95/0.87 tff(871,plain,
% 0.95/0.87 (hskp1),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[870, 291, 269, 95, 53, 147, 146, 145])).
% 0.95/0.87 tff(872,plain,
% 0.95/0.87 (~c3_1(a125)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[597, 871])).
% 0.95/0.87 tff(873,plain,
% 0.95/0.87 (c1_1(a125)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[608, 871])).
% 0.95/0.87 tff(874,plain,
% 0.95/0.87 (c0_1(a125)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[619, 871])).
% 0.95/0.87 tff(875,plain,
% 0.95/0.87 (hskp12),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[626, 187, 874, 873, 872, 239])).
% 0.95/0.87 tff(876,plain,
% 0.95/0.87 (~c0_1(a140)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[632, 875])).
% 0.95/0.87 tff(877,plain,
% 0.95/0.87 (c3_1(a140)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[646, 875])).
% 0.95/0.87 tff(878,plain,
% 0.95/0.87 (c1_1(a140)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[861, 875])).
% 0.95/0.87 tff(879,plain,
% 0.95/0.87 (hskp6),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[868, 187, 878, 877, 876, 291, 269, 336, 665])).
% 0.95/0.87 tff(880,plain,
% 0.95/0.87 (~c2_1(a133)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[360, 879])).
% 0.95/0.87 tff(881,plain,
% 0.95/0.87 (~c1_1(a133)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[366, 879])).
% 0.95/0.87 tff(882,plain,
% 0.95/0.87 (~c0_1(a133)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[372, 879])).
% 0.95/0.88 tff(883,plain,
% 0.95/0.88 (~c2_1(a140)),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[655, 187, 212, 268, 877, 201, 565, 559, 876, 229, 219])).
% 0.95/0.88 tff(884,plain,
% 0.95/0.88 (((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp14 | hskp3 | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)))) <=> ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp14 | hskp3 | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(885,plain,
% 0.95/0.88 ((hskp14 | hskp3 | (~ndr1_0) | c0_1(a140) | c2_1(a140) | (~c3_1(a140))) <=> (hskp14 | hskp3 | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(886,plain,
% 0.95/0.88 (((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp14 | hskp3 | (~ndr1_0) | c0_1(a140) | c2_1(a140) | (~c3_1(a140)))) <=> ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp14 | hskp3 | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140))))),
% 0.95/0.88 inference(monotonicity,[status(thm)],[885])).
% 0.95/0.88 tff(887,plain,
% 0.95/0.88 (((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp14 | hskp3 | (~ndr1_0) | c0_1(a140) | c2_1(a140) | (~c3_1(a140)))) <=> ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp14 | hskp3 | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)))),
% 0.95/0.88 inference(transitivity,[status(thm)],[886, 884])).
% 0.95/0.88 tff(888,plain,
% 0.95/0.88 ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp14 | hskp3 | (~ndr1_0) | c0_1(a140) | c2_1(a140) | (~c3_1(a140)))),
% 0.95/0.88 inference(quant_inst,[status(thm)],[])).
% 0.95/0.88 tff(889,plain,
% 0.95/0.88 ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp14 | hskp3 | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140))),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[888, 887])).
% 0.95/0.88 tff(890,plain,
% 0.95/0.88 (hskp14 | c2_1(a140)),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[889, 187, 733, 877, 876, 51])).
% 0.95/0.88 tff(891,plain,
% 0.95/0.88 (hskp14),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[890, 883])).
% 0.95/0.88 tff(892,plain,
% 0.95/0.88 (~c3_1(a145)),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[522, 891])).
% 0.95/0.88 tff(893,plain,
% 0.95/0.88 (~c0_1(a145)),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[541, 891])).
% 0.95/0.88 tff(894,plain,
% 0.95/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a145) | c3_1(a145) | c1_1(a138) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a145))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a145) | c3_1(a145) | c1_1(a138) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a145))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(895,plain,
% 0.95/0.88 (((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a145) | c0_1(a145) | c2_1(a145) | c2_1(a133) | c1_1(a133) | c0_1(a133)) <=> (c0_1(a145) | c3_1(a145) | c1_1(a138) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a145))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(896,plain,
% 0.95/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a145) | c0_1(a145) | c2_1(a145) | c2_1(a133) | c1_1(a133) | c0_1(a133))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a145) | c3_1(a145) | c1_1(a138) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a145)))),
% 0.95/0.88 inference(monotonicity,[status(thm)],[895])).
% 0.95/0.88 tff(897,plain,
% 0.95/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a145) | c0_1(a145) | c2_1(a145) | c2_1(a133) | c1_1(a133) | c0_1(a133))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a145) | c3_1(a145) | c1_1(a138) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a145))),
% 0.95/0.88 inference(transitivity,[status(thm)],[896, 894])).
% 0.95/0.88 tff(898,plain,
% 0.95/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a145) | c0_1(a145) | c2_1(a145) | c2_1(a133) | c1_1(a133) | c0_1(a133))),
% 0.95/0.88 inference(quant_inst,[status(thm)],[])).
% 0.95/0.88 tff(899,plain,
% 0.95/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a145) | c3_1(a145) | c1_1(a138) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a145)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[898, 897])).
% 0.95/0.88 tff(900,plain,
% 0.95/0.88 (c2_1(a145)),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[899, 187, 147, 146, 893, 892, 145, 882, 881, 880, 279])).
% 0.95/0.88 tff(901,plain,
% 0.95/0.88 (~c1_1(a145)),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[528, 891])).
% 0.95/0.88 tff(902,plain,
% 0.95/0.88 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c1_1(a145) | c3_1(a145) | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)) | (~c2_1(a145)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c1_1(a145) | c3_1(a145) | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)) | (~c2_1(a145)))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(903,plain,
% 0.95/0.88 ((hskp3 | (~ndr1_0) | c3_1(a145) | c1_1(a145) | (~c2_1(a145)) | c0_1(a140) | c2_1(a140) | (~c3_1(a140))) <=> (hskp3 | c1_1(a145) | c3_1(a145) | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)) | (~c2_1(a145)))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(904,plain,
% 0.95/0.88 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a145) | c1_1(a145) | (~c2_1(a145)) | c0_1(a140) | c2_1(a140) | (~c3_1(a140)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c1_1(a145) | c3_1(a145) | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)) | (~c2_1(a145))))),
% 0.95/0.88 inference(monotonicity,[status(thm)],[903])).
% 0.95/0.88 tff(905,plain,
% 0.95/0.88 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a145) | c1_1(a145) | (~c2_1(a145)) | c0_1(a140) | c2_1(a140) | (~c3_1(a140)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c1_1(a145) | c3_1(a145) | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)) | (~c2_1(a145)))),
% 0.95/0.88 inference(transitivity,[status(thm)],[904, 902])).
% 0.95/0.88 tff(906,plain,
% 0.95/0.88 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a145) | c1_1(a145) | (~c2_1(a145)) | c0_1(a140) | c2_1(a140) | (~c3_1(a140)))),
% 0.95/0.88 inference(quant_inst,[status(thm)],[])).
% 0.95/0.88 tff(907,plain,
% 0.95/0.88 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c1_1(a145) | c3_1(a145) | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)) | (~c2_1(a145))),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[906, 905])).
% 0.95/0.88 tff(908,plain,
% 0.95/0.88 ($false),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[907, 187, 733, 877, 901, 892, 876, 41, 883, 900])).
% 0.95/0.88 tff(909,plain,(c0_1(a128) | (~c0_1(a138)) | (~c3_1(a138)) | c1_1(a138) | c3_1(a128) | hskp18 | hskp21), inference(lemma,lemma(discharge,[]))).
% 0.95/0.88 tff(910,plain,
% 0.95/0.88 (c0_1(a128)),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[909, 53, 146, 145, 269, 95, 147])).
% 0.95/0.88 tff(911,plain,
% 0.95/0.88 (c3_1(a151)),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[218, 187, 53, 95, 649, 636, 134])).
% 0.95/0.88 tff(912,plain,
% 0.95/0.88 (^[V: $i, U: $i] : refl((hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 0.95/0.88 inference(bind,[status(th)],[])).
% 0.95/0.88 tff(913,plain,
% 0.95/0.88 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.95/0.88 inference(quant_intro,[status(thm)],[912])).
% 0.95/0.88 tff(914,plain,
% 0.95/0.88 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(915,plain,
% 0.95/0.88 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c1_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)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~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)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp20) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp20))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 0.95/0.88 inference(bind,[status(th)],[])).
% 0.95/0.88 tff(916,plain,
% 0.95/0.88 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp20) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.95/0.88 inference(quant_intro,[status(thm)],[915])).
% 0.95/0.88 tff(917,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause173')).
% 0.95/0.88 tff(918,plain,
% 0.95/0.88 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[917, 916])).
% 0.95/0.88 tff(919,plain,
% 0.95/0.88 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[918, 914])).
% 0.95/0.88 tff(920,plain,(
% 0.95/0.88 ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.95/0.88 inference(skolemize,[status(sab)],[919])).
% 0.95/0.88 tff(921,plain,
% 0.95/0.88 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[920, 913])).
% 0.95/0.88 tff(922,plain,
% 0.95/0.88 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | c2_1(a151) | (~c0_1(a128)) | (~c2_1(a128)) | (~ndr1_0) | c1_1(a128) | (~c3_1(a151)) | (~c1_1(a151)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c2_1(a151) | (~c0_1(a128)) | (~c2_1(a128)) | (~ndr1_0) | c1_1(a128) | (~c3_1(a151)) | (~c1_1(a151)))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(923,plain,
% 0.95/0.88 ((hskp20 | (~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c1_1(a151)) | c1_1(a128) | (~c2_1(a128)) | (~c0_1(a128))) <=> (hskp20 | c2_1(a151) | (~c0_1(a128)) | (~c2_1(a128)) | (~ndr1_0) | c1_1(a128) | (~c3_1(a151)) | (~c1_1(a151)))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(924,plain,
% 0.95/0.88 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c1_1(a151)) | c1_1(a128) | (~c2_1(a128)) | (~c0_1(a128)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | c2_1(a151) | (~c0_1(a128)) | (~c2_1(a128)) | (~ndr1_0) | c1_1(a128) | (~c3_1(a151)) | (~c1_1(a151))))),
% 0.95/0.88 inference(monotonicity,[status(thm)],[923])).
% 0.95/0.88 tff(925,plain,
% 0.95/0.88 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c1_1(a151)) | c1_1(a128) | (~c2_1(a128)) | (~c0_1(a128)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c2_1(a151) | (~c0_1(a128)) | (~c2_1(a128)) | (~ndr1_0) | c1_1(a128) | (~c3_1(a151)) | (~c1_1(a151)))),
% 0.95/0.88 inference(transitivity,[status(thm)],[924, 922])).
% 0.95/0.88 tff(926,plain,
% 0.95/0.88 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c1_1(a151)) | c1_1(a128) | (~c2_1(a128)) | (~c0_1(a128)))),
% 0.95/0.88 inference(quant_inst,[status(thm)],[])).
% 0.95/0.88 tff(927,plain,
% 0.95/0.88 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c2_1(a151) | (~c0_1(a128)) | (~c2_1(a128)) | (~ndr1_0) | c1_1(a128) | (~c3_1(a151)) | (~c1_1(a151))),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[926, 925])).
% 0.95/0.88 tff(928,plain,
% 0.95/0.88 (hskp20),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[927, 187, 649, 636, 494, 578, 921, 567, 911])).
% 0.95/0.88 tff(929,plain,
% 0.95/0.88 (((~hskp20) | (~c2_1(a168))) <=> ((~hskp20) | (~c2_1(a168)))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(930,plain,
% 0.95/0.88 (((~c2_1(a168)) | (~hskp20)) <=> ((~hskp20) | (~c2_1(a168)))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(931,axiom,((~c2_1(a168)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause96')).
% 0.95/0.88 tff(932,plain,
% 0.95/0.88 ((~hskp20) | (~c2_1(a168))),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[931, 930])).
% 0.95/0.88 tff(933,plain,
% 0.95/0.88 ((~hskp20) | (~c2_1(a168))),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[932, 929])).
% 0.95/0.88 tff(934,plain,
% 0.95/0.88 (~c2_1(a168)),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[933, 928])).
% 0.95/0.88 tff(935,plain,
% 0.95/0.88 (((~hskp20) | c1_1(a168)) <=> ((~hskp20) | c1_1(a168))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(936,axiom,((~hskp20) | c1_1(a168)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause56')).
% 0.95/0.88 tff(937,plain,
% 0.95/0.88 ((~hskp20) | c1_1(a168)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[936, 935])).
% 0.95/0.88 tff(938,plain,
% 0.95/0.88 ((~hskp20) | c1_1(a168)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[937, 935])).
% 0.95/0.88 tff(939,plain,
% 0.95/0.88 ((~hskp20) | c1_1(a168)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[938, 935])).
% 0.95/0.88 tff(940,plain,
% 0.95/0.88 ((~hskp20) | c1_1(a168)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[939, 935])).
% 0.95/0.88 tff(941,plain,
% 0.95/0.88 ((~hskp20) | c1_1(a168)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[940, 935])).
% 0.95/0.88 tff(942,plain,
% 0.95/0.88 ((~hskp20) | c1_1(a168)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[941, 935])).
% 0.95/0.88 tff(943,plain,
% 0.95/0.88 ((~hskp20) | c1_1(a168)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[942, 935])).
% 0.95/0.88 tff(944,plain,
% 0.95/0.88 ((~hskp20) | c1_1(a168)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[943, 935])).
% 0.95/0.88 tff(945,plain,
% 0.95/0.88 (c1_1(a168)),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[944, 928])).
% 0.95/0.88 tff(946,plain,
% 0.95/0.88 (((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | c2_1(a168) | (~ndr1_0) | c3_1(a168) | (~c1_1(a168)))) <=> ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp21 | hskp18 | c2_1(a168) | (~ndr1_0) | c3_1(a168) | (~c1_1(a168)))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(947,plain,
% 0.95/0.88 ((hskp21 | hskp18 | (~ndr1_0) | c3_1(a168) | c2_1(a168) | (~c1_1(a168))) <=> (hskp21 | hskp18 | c2_1(a168) | (~ndr1_0) | c3_1(a168) | (~c1_1(a168)))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(948,plain,
% 0.95/0.88 (((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | (~ndr1_0) | c3_1(a168) | c2_1(a168) | (~c1_1(a168)))) <=> ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | c2_1(a168) | (~ndr1_0) | c3_1(a168) | (~c1_1(a168))))),
% 0.95/0.88 inference(monotonicity,[status(thm)],[947])).
% 0.95/0.88 tff(949,plain,
% 0.95/0.88 (((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | (~ndr1_0) | c3_1(a168) | c2_1(a168) | (~c1_1(a168)))) <=> ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp21 | hskp18 | c2_1(a168) | (~ndr1_0) | c3_1(a168) | (~c1_1(a168)))),
% 0.95/0.88 inference(transitivity,[status(thm)],[948, 946])).
% 0.95/0.88 tff(950,plain,
% 0.95/0.88 ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | (~ndr1_0) | c3_1(a168) | c2_1(a168) | (~c1_1(a168)))),
% 0.95/0.88 inference(quant_inst,[status(thm)],[])).
% 0.95/0.88 tff(951,plain,
% 0.95/0.88 ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp21 | hskp18 | c2_1(a168) | (~ndr1_0) | c3_1(a168) | (~c1_1(a168))),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[950, 949])).
% 0.95/0.88 tff(952,plain,
% 0.95/0.88 (c3_1(a168)),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[951, 187, 53, 95, 945, 934, 134])).
% 0.95/0.88 tff(953,plain,
% 0.95/0.88 (((~hskp20) | (~c0_1(a168))) <=> ((~hskp20) | (~c0_1(a168)))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(954,plain,
% 0.95/0.88 (((~c0_1(a168)) | (~hskp20)) <=> ((~hskp20) | (~c0_1(a168)))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(955,axiom,((~c0_1(a168)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause95')).
% 0.95/0.88 tff(956,plain,
% 0.95/0.88 ((~hskp20) | (~c0_1(a168))),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[955, 954])).
% 0.95/0.88 tff(957,plain,
% 0.95/0.88 ((~hskp20) | (~c0_1(a168))),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[956, 953])).
% 0.95/0.88 tff(958,plain,
% 0.95/0.88 (~c0_1(a168)),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[957, 928])).
% 0.95/0.88 tff(959,plain,
% 0.95/0.88 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c0_1(a168) | c2_1(a168) | (~c2_1(a128)) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a168)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a168) | c2_1(a168) | (~c2_1(a128)) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a168)))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(960,plain,
% 0.95/0.88 ((hskp3 | (~ndr1_0) | c3_1(a128) | c1_1(a128) | (~c2_1(a128)) | c0_1(a168) | c2_1(a168) | (~c3_1(a168))) <=> (hskp3 | c0_1(a168) | c2_1(a168) | (~c2_1(a128)) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a168)))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(961,plain,
% 0.95/0.88 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a128) | c1_1(a128) | (~c2_1(a128)) | c0_1(a168) | c2_1(a168) | (~c3_1(a168)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c0_1(a168) | c2_1(a168) | (~c2_1(a128)) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a168))))),
% 0.95/0.88 inference(monotonicity,[status(thm)],[960])).
% 0.95/0.88 tff(962,plain,
% 0.95/0.88 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a128) | c1_1(a128) | (~c2_1(a128)) | c0_1(a168) | c2_1(a168) | (~c3_1(a168)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a168) | c2_1(a168) | (~c2_1(a128)) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a168)))),
% 0.95/0.88 inference(transitivity,[status(thm)],[961, 959])).
% 0.95/0.88 tff(963,plain,
% 0.95/0.88 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a128) | c1_1(a128) | (~c2_1(a128)) | c0_1(a168) | c2_1(a168) | (~c3_1(a168)))),
% 0.95/0.88 inference(quant_inst,[status(thm)],[])).
% 0.95/0.88 tff(964,plain,
% 0.95/0.88 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a168) | c2_1(a168) | (~c2_1(a128)) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a168))),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[963, 962])).
% 0.95/0.88 tff(965,plain,
% 0.95/0.88 ($false),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[964, 187, 584, 958, 934, 578, 269, 41, 567, 952])).
% 0.95/0.88 tff(966,plain,(c1_1(a128) | (~c2_1(a128)) | c3_1(a128) | hskp21 | hskp18 | (~c1_1(a151)) | c2_1(a151) | (~c0_1(a128))), inference(lemma,lemma(discharge,[]))).
% 0.95/0.88 tff(967,plain,
% 0.95/0.88 (c1_1(a128)),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[966, 53, 269, 553, 95, 212, 201, 910])).
% 0.95/0.88 tff(968,plain,
% 0.95/0.88 (((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | (~c0_1(a128)) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp12 | (~c0_1(a128)) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(969,plain,
% 0.95/0.88 ((hskp12 | (~ndr1_0) | c3_1(a128) | (~c1_1(a128)) | (~c0_1(a128))) <=> (hskp12 | (~c0_1(a128)) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(970,plain,
% 0.95/0.88 (((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | c3_1(a128) | (~c1_1(a128)) | (~c0_1(a128)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | (~c0_1(a128)) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128))))),
% 0.95/0.88 inference(monotonicity,[status(thm)],[969])).
% 0.95/0.88 tff(971,plain,
% 0.95/0.88 (((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | c3_1(a128) | (~c1_1(a128)) | (~c0_1(a128)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp12 | (~c0_1(a128)) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)))),
% 0.95/0.88 inference(transitivity,[status(thm)],[970, 968])).
% 0.95/0.88 tff(972,plain,
% 0.95/0.88 ((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | c3_1(a128) | (~c1_1(a128)) | (~c0_1(a128)))),
% 0.95/0.88 inference(quant_inst,[status(thm)],[])).
% 0.95/0.88 tff(973,plain,
% 0.95/0.88 ((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp12 | (~c0_1(a128)) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128))),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[972, 971])).
% 0.95/0.88 tff(974,plain,
% 0.95/0.88 (hskp12 | (~c0_1(a128)) | (~c1_1(a128))),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[973, 187, 269, 239])).
% 0.95/0.88 tff(975,plain,
% 0.95/0.88 (hskp12),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[974, 967, 910])).
% 0.95/0.88 tff(976,plain,
% 0.95/0.88 (~c0_1(a140)),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[632, 975])).
% 0.95/0.88 tff(977,plain,
% 0.95/0.88 (c3_1(a140)),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[646, 975])).
% 0.95/0.88 tff(978,plain,
% 0.95/0.88 (~c2_1(a140)),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[655, 187, 212, 268, 977, 201, 565, 559, 976, 229, 219])).
% 0.95/0.88 tff(979,plain,
% 0.95/0.88 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~c0_1(a128)) | (~c2_1(a128)) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | (~c0_1(a128)) | (~c2_1(a128)) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(980,plain,
% 0.95/0.88 ((hskp13 | (~ndr1_0) | (~c2_1(a128)) | (~c1_1(a128)) | (~c0_1(a128)) | c3_1(a128) | (~c1_1(a128)) | (~c0_1(a128))) <=> (hskp13 | (~c0_1(a128)) | (~c2_1(a128)) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(981,plain,
% 0.95/0.88 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a128)) | (~c1_1(a128)) | (~c0_1(a128)) | c3_1(a128) | (~c1_1(a128)) | (~c0_1(a128)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~c0_1(a128)) | (~c2_1(a128)) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128))))),
% 0.95/0.88 inference(monotonicity,[status(thm)],[980])).
% 0.95/0.88 tff(982,plain,
% 0.95/0.88 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a128)) | (~c1_1(a128)) | (~c0_1(a128)) | c3_1(a128) | (~c1_1(a128)) | (~c0_1(a128)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | (~c0_1(a128)) | (~c2_1(a128)) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)))),
% 0.95/0.88 inference(transitivity,[status(thm)],[981, 979])).
% 0.95/0.88 tff(983,plain,
% 0.95/0.88 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a128)) | (~c1_1(a128)) | (~c0_1(a128)) | c3_1(a128) | (~c1_1(a128)) | (~c0_1(a128)))),
% 0.95/0.88 inference(quant_inst,[status(thm)],[])).
% 0.95/0.88 tff(984,plain,
% 0.95/0.88 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | (~c0_1(a128)) | (~c2_1(a128)) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128))),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[983, 982])).
% 0.95/0.88 tff(985,plain,
% 0.95/0.88 (hskp13 | (~c0_1(a128)) | (~c1_1(a128))),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[984, 187, 553, 269, 21])).
% 0.95/0.88 tff(986,plain,
% 0.95/0.88 (hskp13),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[985, 967, 910])).
% 0.95/0.88 tff(987,plain,
% 0.95/0.88 (((~hskp13) | (~c3_1(a144))) <=> ((~hskp13) | (~c3_1(a144)))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(988,plain,
% 0.95/0.88 (((~c3_1(a144)) | (~hskp13)) <=> ((~hskp13) | (~c3_1(a144)))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(989,axiom,((~c3_1(a144)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause109')).
% 0.95/0.88 tff(990,plain,
% 0.95/0.88 ((~hskp13) | (~c3_1(a144))),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[989, 988])).
% 0.95/0.88 tff(991,plain,
% 0.95/0.88 ((~hskp13) | (~c3_1(a144))),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[990, 987])).
% 0.95/0.88 tff(992,plain,
% 0.95/0.88 (~c3_1(a144)),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[991, 986])).
% 0.95/0.88 tff(993,plain,
% 0.95/0.88 (((~hskp13) | c2_1(a144)) <=> ((~hskp13) | c2_1(a144))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(994,axiom,((~hskp13) | c2_1(a144)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause64')).
% 0.95/0.88 tff(995,plain,
% 0.95/0.88 ((~hskp13) | c2_1(a144)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[994, 993])).
% 0.95/0.88 tff(996,plain,
% 0.95/0.88 ((~hskp13) | c2_1(a144)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[995, 993])).
% 0.95/0.89 tff(997,plain,
% 0.95/0.89 ((~hskp13) | c2_1(a144)),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[996, 993])).
% 0.95/0.89 tff(998,plain,
% 0.95/0.89 ((~hskp13) | c2_1(a144)),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[997, 993])).
% 0.95/0.89 tff(999,plain,
% 0.95/0.89 ((~hskp13) | c2_1(a144)),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[998, 993])).
% 0.95/0.89 tff(1000,plain,
% 0.95/0.89 ((~hskp13) | c2_1(a144)),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[999, 993])).
% 0.95/0.89 tff(1001,plain,
% 0.95/0.89 ((~hskp13) | c2_1(a144)),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[1000, 993])).
% 0.95/0.89 tff(1002,plain,
% 0.95/0.89 ((~hskp13) | c2_1(a144)),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[1001, 993])).
% 0.95/0.89 tff(1003,plain,
% 0.95/0.89 (c2_1(a144)),
% 0.95/0.89 inference(unit_resolution,[status(thm)],[1002, 986])).
% 0.95/0.89 tff(1004,plain,
% 0.95/0.89 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c3_1(a144) | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)) | c1_1(a144) | (~c2_1(a144)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c3_1(a144) | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)) | c1_1(a144) | (~c2_1(a144)))),
% 0.95/0.89 inference(rewrite,[status(thm)],[])).
% 0.95/0.89 tff(1005,plain,
% 0.95/0.89 ((hskp3 | (~ndr1_0) | c3_1(a144) | c1_1(a144) | (~c2_1(a144)) | c0_1(a140) | c2_1(a140) | (~c3_1(a140))) <=> (hskp3 | c3_1(a144) | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)) | c1_1(a144) | (~c2_1(a144)))),
% 0.95/0.89 inference(rewrite,[status(thm)],[])).
% 0.95/0.89 tff(1006,plain,
% 0.95/0.89 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a144) | c1_1(a144) | (~c2_1(a144)) | c0_1(a140) | c2_1(a140) | (~c3_1(a140)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c3_1(a144) | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)) | c1_1(a144) | (~c2_1(a144))))),
% 0.95/0.89 inference(monotonicity,[status(thm)],[1005])).
% 0.95/0.89 tff(1007,plain,
% 0.95/0.89 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a144) | c1_1(a144) | (~c2_1(a144)) | c0_1(a140) | c2_1(a140) | (~c3_1(a140)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c3_1(a144) | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)) | c1_1(a144) | (~c2_1(a144)))),
% 0.95/0.89 inference(transitivity,[status(thm)],[1006, 1004])).
% 0.95/0.89 tff(1008,plain,
% 0.95/0.89 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a144) | c1_1(a144) | (~c2_1(a144)) | c0_1(a140) | c2_1(a140) | (~c3_1(a140)))),
% 0.95/0.89 inference(quant_inst,[status(thm)],[])).
% 0.95/0.89 tff(1009,plain,
% 0.95/0.89 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c3_1(a144) | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)) | c1_1(a144) | (~c2_1(a144))),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[1008, 1007])).
% 0.95/0.89 tff(1010,plain,
% 0.95/0.89 (c1_1(a144)),
% 0.95/0.89 inference(unit_resolution,[status(thm)],[1009, 187, 733, 1003, 977, 992, 976, 41, 978])).
% 0.95/0.89 tff(1011,plain,
% 0.95/0.89 (((~hskp13) | (~c0_1(a144))) <=> ((~hskp13) | (~c0_1(a144)))),
% 0.95/0.89 inference(rewrite,[status(thm)],[])).
% 0.95/0.89 tff(1012,plain,
% 0.95/0.89 (((~c0_1(a144)) | (~hskp13)) <=> ((~hskp13) | (~c0_1(a144)))),
% 0.95/0.89 inference(rewrite,[status(thm)],[])).
% 0.95/0.89 tff(1013,axiom,((~c0_1(a144)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause108')).
% 0.95/0.89 tff(1014,plain,
% 0.95/0.89 ((~hskp13) | (~c0_1(a144))),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[1013, 1012])).
% 0.95/0.89 tff(1015,plain,
% 0.95/0.89 ((~hskp13) | (~c0_1(a144))),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[1014, 1011])).
% 0.95/0.89 tff(1016,plain,
% 0.95/0.89 (~c0_1(a144)),
% 0.95/0.89 inference(unit_resolution,[status(thm)],[1015, 986])).
% 0.95/0.89 tff(1017,plain,
% 0.95/0.89 (c1_1(a140)),
% 0.95/0.89 inference(unit_resolution,[status(thm)],[861, 975])).
% 0.95/0.89 tff(1018,plain,
% 0.95/0.89 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a144) | c3_1(a144) | c0_1(a140) | (~ndr1_0) | (~c3_1(a140)) | (~c1_1(a140)) | (~c1_1(a144)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a144) | c3_1(a144) | c0_1(a140) | (~ndr1_0) | (~c3_1(a140)) | (~c1_1(a140)) | (~c1_1(a144)))),
% 0.95/0.89 inference(rewrite,[status(thm)],[])).
% 0.95/0.89 tff(1019,plain,
% 0.95/0.89 ((hskp6 | (~ndr1_0) | c0_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | c3_1(a144) | c0_1(a144) | (~c1_1(a144))) <=> (hskp6 | c0_1(a144) | c3_1(a144) | c0_1(a140) | (~ndr1_0) | (~c3_1(a140)) | (~c1_1(a140)) | (~c1_1(a144)))),
% 0.95/0.89 inference(rewrite,[status(thm)],[])).
% 0.95/0.89 tff(1020,plain,
% 0.95/0.89 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | c3_1(a144) | c0_1(a144) | (~c1_1(a144)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a144) | c3_1(a144) | c0_1(a140) | (~ndr1_0) | (~c3_1(a140)) | (~c1_1(a140)) | (~c1_1(a144))))),
% 0.95/0.89 inference(monotonicity,[status(thm)],[1019])).
% 0.95/0.89 tff(1021,plain,
% 0.95/0.89 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | c3_1(a144) | c0_1(a144) | (~c1_1(a144)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a144) | c3_1(a144) | c0_1(a140) | (~ndr1_0) | (~c3_1(a140)) | (~c1_1(a140)) | (~c1_1(a144)))),
% 0.95/0.89 inference(transitivity,[status(thm)],[1020, 1018])).
% 0.95/0.89 tff(1022,plain,
% 0.95/0.89 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | c3_1(a144) | c0_1(a144) | (~c1_1(a144)))),
% 0.95/0.89 inference(quant_inst,[status(thm)],[])).
% 0.95/0.89 tff(1023,plain,
% 0.95/0.89 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a144) | c3_1(a144) | c0_1(a140) | (~ndr1_0) | (~c3_1(a140)) | (~c1_1(a140)) | (~c1_1(a144))),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[1022, 1021])).
% 0.95/0.89 tff(1024,plain,
% 0.95/0.89 (hskp6 | (~c1_1(a144))),
% 0.95/0.89 inference(unit_resolution,[status(thm)],[1023, 187, 1017, 977, 1016, 992, 976, 336])).
% 0.95/0.89 tff(1025,plain,
% 0.95/0.89 (hskp6),
% 0.95/0.89 inference(unit_resolution,[status(thm)],[1024, 1010])).
% 0.95/0.89 tff(1026,plain,
% 0.95/0.89 (~c2_1(a133)),
% 0.95/0.89 inference(unit_resolution,[status(thm)],[360, 1025])).
% 0.95/0.89 tff(1027,plain,
% 0.95/0.89 (~c1_1(a133)),
% 0.95/0.89 inference(unit_resolution,[status(thm)],[366, 1025])).
% 0.95/0.89 tff(1028,plain,
% 0.95/0.89 (~c0_1(a133)),
% 0.95/0.89 inference(unit_resolution,[status(thm)],[372, 1025])).
% 0.95/0.89 tff(1029,plain,
% 0.95/0.89 (hskp14),
% 0.95/0.89 inference(unit_resolution,[status(thm)],[889, 187, 733, 977, 976, 51, 978])).
% 0.95/0.89 tff(1030,plain,
% 0.95/0.89 (~c3_1(a145)),
% 0.95/0.89 inference(unit_resolution,[status(thm)],[522, 1029])).
% 0.95/0.89 tff(1031,plain,
% 0.95/0.89 (~c0_1(a145)),
% 0.95/0.89 inference(unit_resolution,[status(thm)],[541, 1029])).
% 0.95/0.89 tff(1032,plain,
% 0.95/0.89 (c2_1(a145)),
% 0.95/0.89 inference(unit_resolution,[status(thm)],[899, 187, 147, 146, 1031, 1030, 145, 1028, 1027, 1026, 279])).
% 0.95/0.89 tff(1033,plain,
% 0.95/0.89 (^[V: $i, U: $i] : refl((hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 0.95/0.89 inference(bind,[status(th)],[])).
% 0.95/0.89 tff(1034,plain,
% 0.95/0.89 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.95/0.89 inference(quant_intro,[status(thm)],[1033])).
% 0.95/0.89 tff(1035,plain,
% 0.95/0.89 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.95/0.89 inference(rewrite,[status(thm)],[])).
% 0.95/0.89 tff(1036,plain,
% 0.95/0.89 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp22) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp22))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp22) <=> (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp22) <=> (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 0.95/0.89 inference(bind,[status(th)],[])).
% 0.95/0.89 tff(1037,plain,
% 0.95/0.89 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp22) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.95/0.89 inference(quant_intro,[status(thm)],[1036])).
% 0.95/0.89 tff(1038,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause176')).
% 0.95/0.89 tff(1039,plain,
% 0.95/0.89 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[1038, 1037])).
% 0.95/0.89 tff(1040,plain,
% 0.95/0.89 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[1039, 1035])).
% 0.95/0.89 tff(1041,plain,(
% 0.95/0.89 ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.95/0.89 inference(skolemize,[status(sab)],[1040])).
% 0.95/0.89 tff(1042,plain,
% 0.95/0.89 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[1041, 1034])).
% 0.98/0.89 tff(1043,plain,
% 0.98/0.89 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp22 | c2_1(a151) | (~c0_1(a128)) | (~c2_1(a128)) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a151)) | (~c0_1(a151)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp22 | c2_1(a151) | (~c0_1(a128)) | (~c2_1(a128)) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a151)) | (~c0_1(a151)))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(1044,plain,
% 0.98/0.89 ((hskp22 | (~ndr1_0) | (~c2_1(a128)) | (~c1_1(a128)) | (~c0_1(a128)) | c2_1(a151) | (~c3_1(a151)) | (~c0_1(a151))) <=> (hskp22 | c2_1(a151) | (~c0_1(a128)) | (~c2_1(a128)) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a151)) | (~c0_1(a151)))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(1045,plain,
% 0.98/0.89 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | (~c2_1(a128)) | (~c1_1(a128)) | (~c0_1(a128)) | c2_1(a151) | (~c3_1(a151)) | (~c0_1(a151)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp22 | c2_1(a151) | (~c0_1(a128)) | (~c2_1(a128)) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a151)) | (~c0_1(a151))))),
% 0.98/0.89 inference(monotonicity,[status(thm)],[1044])).
% 0.98/0.89 tff(1046,plain,
% 0.98/0.89 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | (~c2_1(a128)) | (~c1_1(a128)) | (~c0_1(a128)) | c2_1(a151) | (~c3_1(a151)) | (~c0_1(a151)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp22 | c2_1(a151) | (~c0_1(a128)) | (~c2_1(a128)) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a151)) | (~c0_1(a151)))),
% 0.98/0.89 inference(transitivity,[status(thm)],[1045, 1043])).
% 0.98/0.89 tff(1047,plain,
% 0.98/0.89 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | (~c2_1(a128)) | (~c1_1(a128)) | (~c0_1(a128)) | c2_1(a151) | (~c3_1(a151)) | (~c0_1(a151)))),
% 0.98/0.89 inference(quant_inst,[status(thm)],[])).
% 0.98/0.89 tff(1048,plain,
% 0.98/0.89 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp22 | c2_1(a151) | (~c0_1(a128)) | (~c2_1(a128)) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a151)) | (~c0_1(a151))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[1047, 1046])).
% 0.98/0.89 tff(1049,plain,
% 0.98/0.89 (hskp22 | (~c0_1(a128)) | (~c1_1(a128))),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[1048, 187, 250, 201, 553, 1042, 219])).
% 0.98/0.89 tff(1050,plain,
% 0.98/0.89 (hskp22),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[1049, 967, 910])).
% 0.98/0.89 tff(1051,plain,
% 0.98/0.89 (((~hskp22) | (~c1_1(a179))) <=> ((~hskp22) | (~c1_1(a179)))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(1052,plain,
% 0.98/0.89 (((~c1_1(a179)) | (~hskp22)) <=> ((~hskp22) | (~c1_1(a179)))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(1053,axiom,((~c1_1(a179)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause92')).
% 0.98/0.89 tff(1054,plain,
% 0.98/0.89 ((~hskp22) | (~c1_1(a179))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[1053, 1052])).
% 0.98/0.89 tff(1055,plain,
% 0.98/0.89 ((~hskp22) | (~c1_1(a179))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[1054, 1051])).
% 0.98/0.89 tff(1056,plain,
% 0.98/0.89 (~c1_1(a179)),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[1055, 1050])).
% 0.98/0.89 tff(1057,plain,
% 0.98/0.89 (((~hskp22) | c2_1(a179)) <=> ((~hskp22) | c2_1(a179))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(1058,axiom,((~hskp22) | c2_1(a179)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause54')).
% 0.98/0.89 tff(1059,plain,
% 0.98/0.89 ((~hskp22) | c2_1(a179)),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[1058, 1057])).
% 0.98/0.89 tff(1060,plain,
% 0.98/0.89 ((~hskp22) | c2_1(a179)),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[1059, 1057])).
% 0.98/0.89 tff(1061,plain,
% 0.98/0.89 ((~hskp22) | c2_1(a179)),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[1060, 1057])).
% 0.98/0.89 tff(1062,plain,
% 0.98/0.89 ((~hskp22) | c2_1(a179)),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[1061, 1057])).
% 0.98/0.89 tff(1063,plain,
% 0.98/0.89 ((~hskp22) | c2_1(a179)),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[1062, 1057])).
% 0.98/0.89 tff(1064,plain,
% 0.98/0.89 ((~hskp22) | c2_1(a179)),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[1063, 1057])).
% 0.98/0.89 tff(1065,plain,
% 0.98/0.89 ((~hskp22) | c2_1(a179)),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[1064, 1057])).
% 0.98/0.89 tff(1066,plain,
% 0.98/0.89 ((~hskp22) | c2_1(a179)),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[1065, 1057])).
% 0.98/0.89 tff(1067,plain,
% 0.98/0.89 (c2_1(a179)),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[1066, 1050])).
% 0.98/0.89 tff(1068,plain,
% 0.98/0.89 (((~hskp22) | c0_1(a179)) <=> ((~hskp22) | c0_1(a179))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(1069,axiom,((~hskp22) | c0_1(a179)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause53')).
% 0.98/0.89 tff(1070,plain,
% 0.98/0.89 ((~hskp22) | c0_1(a179)),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[1069, 1068])).
% 0.98/0.89 tff(1071,plain,
% 0.98/0.89 ((~hskp22) | c0_1(a179)),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[1070, 1068])).
% 0.98/0.89 tff(1072,plain,
% 0.98/0.89 ((~hskp22) | c0_1(a179)),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[1071, 1068])).
% 0.98/0.89 tff(1073,plain,
% 0.98/0.89 ((~hskp22) | c0_1(a179)),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[1072, 1068])).
% 0.98/0.89 tff(1074,plain,
% 0.98/0.89 ((~hskp22) | c0_1(a179)),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[1073, 1068])).
% 0.98/0.89 tff(1075,plain,
% 0.98/0.89 ((~hskp22) | c0_1(a179)),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[1074, 1068])).
% 0.98/0.89 tff(1076,plain,
% 0.98/0.89 ((~hskp22) | c0_1(a179)),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[1075, 1068])).
% 0.98/0.89 tff(1077,plain,
% 0.98/0.89 ((~hskp22) | c0_1(a179)),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[1076, 1068])).
% 0.98/0.89 tff(1078,plain,
% 0.98/0.89 (c0_1(a179)),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[1077, 1050])).
% 0.98/0.89 tff(1079,plain,
% 0.98/0.89 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | c1_1(a179) | c2_1(a151) | (~ndr1_0) | (~c3_1(a151)) | (~c1_1(a151)) | (~c2_1(a179)) | (~c0_1(a179)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c1_1(a179) | c2_1(a151) | (~ndr1_0) | (~c3_1(a151)) | (~c1_1(a151)) | (~c2_1(a179)) | (~c0_1(a179)))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(1080,plain,
% 0.98/0.89 ((hskp20 | (~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c1_1(a151)) | c1_1(a179) | (~c2_1(a179)) | (~c0_1(a179))) <=> (hskp20 | c1_1(a179) | c2_1(a151) | (~ndr1_0) | (~c3_1(a151)) | (~c1_1(a151)) | (~c2_1(a179)) | (~c0_1(a179)))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(1081,plain,
% 0.98/0.89 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c1_1(a151)) | c1_1(a179) | (~c2_1(a179)) | (~c0_1(a179)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | c1_1(a179) | c2_1(a151) | (~ndr1_0) | (~c3_1(a151)) | (~c1_1(a151)) | (~c2_1(a179)) | (~c0_1(a179))))),
% 0.98/0.89 inference(monotonicity,[status(thm)],[1080])).
% 0.98/0.89 tff(1082,plain,
% 0.98/0.89 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c1_1(a151)) | c1_1(a179) | (~c2_1(a179)) | (~c0_1(a179)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c1_1(a179) | c2_1(a151) | (~ndr1_0) | (~c3_1(a151)) | (~c1_1(a151)) | (~c2_1(a179)) | (~c0_1(a179)))),
% 0.98/0.89 inference(transitivity,[status(thm)],[1081, 1079])).
% 0.98/0.89 tff(1083,plain,
% 0.98/0.89 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c1_1(a151)) | c1_1(a179) | (~c2_1(a179)) | (~c0_1(a179)))),
% 0.98/0.89 inference(quant_inst,[status(thm)],[])).
% 0.98/0.89 tff(1084,plain,
% 0.98/0.89 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c1_1(a179) | c2_1(a151) | (~ndr1_0) | (~c3_1(a151)) | (~c1_1(a151)) | (~c2_1(a179)) | (~c0_1(a179))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[1083, 1082])).
% 0.98/0.89 tff(1085,plain,
% 0.98/0.89 (hskp20),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[1084, 187, 1078, 1067, 212, 1056, 201, 921, 219])).
% 0.98/0.89 tff(1086,plain,
% 0.98/0.89 (~c2_1(a168)),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[933, 1085])).
% 0.98/0.89 tff(1087,plain,
% 0.98/0.89 (c1_1(a168)),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[944, 1085])).
% 0.98/0.89 tff(1088,plain,
% 0.98/0.89 (c3_1(a168)),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[951, 187, 53, 95, 1087, 1086, 134])).
% 0.98/0.89 tff(1089,plain,
% 0.98/0.89 (~c1_1(a145)),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[528, 1029])).
% 0.98/0.89 tff(1090,plain,
% 0.98/0.89 (~c0_1(a168)),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[957, 1085])).
% 0.98/0.89 tff(1091,plain,
% 0.98/0.89 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c0_1(a168) | c2_1(a168) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c2_1(a145)) | (~c3_1(a168)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a168) | c2_1(a168) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c2_1(a145)) | (~c3_1(a168)))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(1092,plain,
% 0.98/0.89 ((hskp3 | (~ndr1_0) | c3_1(a145) | c1_1(a145) | (~c2_1(a145)) | c0_1(a168) | c2_1(a168) | (~c3_1(a168))) <=> (hskp3 | c0_1(a168) | c2_1(a168) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c2_1(a145)) | (~c3_1(a168)))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(1093,plain,
% 0.98/0.89 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a145) | c1_1(a145) | (~c2_1(a145)) | c0_1(a168) | c2_1(a168) | (~c3_1(a168)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c0_1(a168) | c2_1(a168) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c2_1(a145)) | (~c3_1(a168))))),
% 0.98/0.89 inference(monotonicity,[status(thm)],[1092])).
% 0.98/0.89 tff(1094,plain,
% 0.98/0.89 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a145) | c1_1(a145) | (~c2_1(a145)) | c0_1(a168) | c2_1(a168) | (~c3_1(a168)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a168) | c2_1(a168) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c2_1(a145)) | (~c3_1(a168)))),
% 0.98/0.89 inference(transitivity,[status(thm)],[1093, 1091])).
% 0.98/0.89 tff(1095,plain,
% 0.98/0.89 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a145) | c1_1(a145) | (~c2_1(a145)) | c0_1(a168) | c2_1(a168) | (~c3_1(a168)))),
% 0.98/0.89 inference(quant_inst,[status(thm)],[])).
% 0.98/0.89 tff(1096,plain,
% 0.98/0.89 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a168) | c2_1(a168) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c2_1(a145)) | (~c3_1(a168))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[1095, 1094])).
% 0.98/0.89 tff(1097,plain,
% 0.98/0.89 ($false),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[1096, 187, 733, 1090, 1086, 1089, 1030, 41, 1088, 1032])).
% 0.98/0.89 tff(1098,plain,(hskp21 | (~c0_1(a138)) | (~c3_1(a138)) | c1_1(a138) | hskp18 | c3_1(a128)), inference(lemma,lemma(discharge,[]))).
% 0.98/0.89 tff(1099,plain,
% 0.98/0.89 (hskp21),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[1098, 269, 146, 145, 95, 147])).
% 0.98/0.89 tff(1100,plain,
% 0.98/0.89 (~c2_1(a170)),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[312, 1099])).
% 0.98/0.89 tff(1101,plain,
% 0.98/0.89 (~c0_1(a170)),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[318, 1099])).
% 0.98/0.89 tff(1102,plain,
% 0.98/0.89 (c3_1(a170)),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[346, 1099])).
% 0.98/0.89 tff(1103,plain,
% 0.98/0.89 (hskp14),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[515, 187, 733, 1102, 1101, 1100, 51])).
% 0.98/0.89 tff(1104,plain,
% 0.98/0.89 (~c3_1(a145)),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[522, 1103])).
% 0.98/0.89 tff(1105,plain,
% 0.98/0.89 (~c1_1(a145)),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[528, 1103])).
% 0.98/0.89 tff(1106,plain,
% 0.98/0.89 (~c2_1(a145)),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[535, 187, 733, 1102, 1101, 1100, 1105, 1104, 41])).
% 0.98/0.89 tff(1107,plain,
% 0.98/0.89 (~c0_1(a145)),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[541, 1103])).
% 0.98/0.89 tff(1108,plain,
% 0.98/0.89 ($false),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[548, 187, 147, 146, 1107, 1105, 1104, 145, 279, 1106])).
% 0.98/0.89 tff(1109,plain,(c3_1(a128) | (~c0_1(a138)) | (~c3_1(a138)) | c1_1(a138) | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.98/0.89 tff(1110,plain,
% 0.98/0.89 (c3_1(a128)),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[1109, 147, 146, 145, 95])).
% 0.98/0.89 tff(1111,plain,
% 0.98/0.89 (((~hskp3) | (~c3_1(a128))) <=> ((~hskp3) | (~c3_1(a128)))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(1112,plain,
% 0.98/0.89 (((~c3_1(a128)) | (~hskp3)) <=> ((~hskp3) | (~c3_1(a128)))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(1113,axiom,((~c3_1(a128)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause125')).
% 0.98/0.89 tff(1114,plain,
% 0.98/0.89 ((~hskp3) | (~c3_1(a128))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[1113, 1112])).
% 0.98/0.89 tff(1115,plain,
% 0.98/0.89 ((~hskp3) | (~c3_1(a128))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[1114, 1111])).
% 0.98/0.89 tff(1116,plain,
% 0.98/0.89 (~hskp3),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[1115, 1110])).
% 0.98/0.89 tff(1117,plain,
% 0.98/0.89 (hskp14 | c0_1(a149)),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[766, 187, 52, 648, 634, 51])).
% 0.98/0.89 tff(1118,plain,
% 0.98/0.89 (c0_1(a149)),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[1117, 772])).
% 0.98/0.89 tff(1119,plain,
% 0.98/0.89 (~hskp6),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[789, 772, 52, 635, 1118, 648])).
% 0.98/0.89 tff(1120,plain,
% 0.98/0.89 (hskp9),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[804, 1119, 53])).
% 0.98/0.89 tff(1121,plain,
% 0.98/0.89 (c0_1(a136)),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[840, 1120])).
% 0.98/0.89 tff(1122,plain,
% 0.98/0.89 (~c3_1(a136)),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[810, 1120])).
% 0.98/0.89 tff(1123,plain,
% 0.98/0.89 (c2_1(a136)),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[821, 1120])).
% 0.98/0.89 tff(1124,assumption,(~c1_1(a136)), introduced(assumption)).
% 0.98/0.89 tff(1125,assumption,(c2_1(a136)), introduced(assumption)).
% 0.98/0.89 tff(1126,assumption,(c0_1(a136)), introduced(assumption)).
% 0.98/0.89 tff(1127,plain,
% 0.98/0.89 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | c2_1(a151) | (~ndr1_0) | c1_1(a136) | (~c0_1(a136)) | (~c2_1(a136)) | (~c3_1(a151)) | (~c1_1(a151)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c2_1(a151) | (~ndr1_0) | c1_1(a136) | (~c0_1(a136)) | (~c2_1(a136)) | (~c3_1(a151)) | (~c1_1(a151)))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(1128,plain,
% 0.98/0.89 ((hskp20 | (~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c1_1(a151)) | c1_1(a136) | (~c2_1(a136)) | (~c0_1(a136))) <=> (hskp20 | c2_1(a151) | (~ndr1_0) | c1_1(a136) | (~c0_1(a136)) | (~c2_1(a136)) | (~c3_1(a151)) | (~c1_1(a151)))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(1129,plain,
% 0.98/0.89 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c1_1(a151)) | c1_1(a136) | (~c2_1(a136)) | (~c0_1(a136)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | c2_1(a151) | (~ndr1_0) | c1_1(a136) | (~c0_1(a136)) | (~c2_1(a136)) | (~c3_1(a151)) | (~c1_1(a151))))),
% 0.98/0.89 inference(monotonicity,[status(thm)],[1128])).
% 0.98/0.89 tff(1130,plain,
% 0.98/0.89 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c1_1(a151)) | c1_1(a136) | (~c2_1(a136)) | (~c0_1(a136)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c2_1(a151) | (~ndr1_0) | c1_1(a136) | (~c0_1(a136)) | (~c2_1(a136)) | (~c3_1(a151)) | (~c1_1(a151)))),
% 0.98/0.89 inference(transitivity,[status(thm)],[1129, 1127])).
% 0.98/0.89 tff(1131,plain,
% 0.98/0.89 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c1_1(a151)) | c1_1(a136) | (~c2_1(a136)) | (~c0_1(a136)))),
% 0.98/0.89 inference(quant_inst,[status(thm)],[])).
% 0.98/0.89 tff(1132,plain,
% 0.98/0.89 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c2_1(a151) | (~ndr1_0) | c1_1(a136) | (~c0_1(a136)) | (~c2_1(a136)) | (~c3_1(a151)) | (~c1_1(a151))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[1131, 1130])).
% 0.98/0.89 tff(1133,plain,
% 0.98/0.89 (hskp20),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[1132, 187, 649, 1126, 1125, 636, 921, 911, 1124])).
% 0.98/0.89 tff(1134,plain,
% 0.98/0.89 (~c2_1(a168)),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[933, 1133])).
% 0.98/0.89 tff(1135,plain,
% 0.98/0.89 (c1_1(a168)),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[944, 1133])).
% 0.98/0.89 tff(1136,plain,
% 0.98/0.89 (c3_1(a168)),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[951, 187, 53, 95, 1135, 1134, 134])).
% 0.98/0.89 tff(1137,assumption,(~c3_1(a136)), introduced(assumption)).
% 0.98/0.89 tff(1138,plain,
% 0.98/0.89 (~c0_1(a168)),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[957, 1133])).
% 0.98/0.89 tff(1139,plain,
% 0.98/0.89 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c0_1(a168) | c2_1(a168) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a168)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a168) | c2_1(a168) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a168)))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(1140,plain,
% 0.98/0.89 ((hskp3 | (~ndr1_0) | c3_1(a136) | c1_1(a136) | (~c2_1(a136)) | c0_1(a168) | c2_1(a168) | (~c3_1(a168))) <=> (hskp3 | c0_1(a168) | c2_1(a168) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a168)))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(1141,plain,
% 0.98/0.89 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a136) | c1_1(a136) | (~c2_1(a136)) | c0_1(a168) | c2_1(a168) | (~c3_1(a168)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c0_1(a168) | c2_1(a168) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a168))))),
% 0.98/0.89 inference(monotonicity,[status(thm)],[1140])).
% 0.98/0.89 tff(1142,plain,
% 0.98/0.89 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a136) | c1_1(a136) | (~c2_1(a136)) | c0_1(a168) | c2_1(a168) | (~c3_1(a168)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a168) | c2_1(a168) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a168)))),
% 0.98/0.89 inference(transitivity,[status(thm)],[1141, 1139])).
% 0.98/0.89 tff(1143,plain,
% 0.98/0.89 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a136) | c1_1(a136) | (~c2_1(a136)) | c0_1(a168) | c2_1(a168) | (~c3_1(a168)))),
% 0.98/0.89 inference(quant_inst,[status(thm)],[])).
% 0.98/0.89 tff(1144,plain,
% 0.98/0.89 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a168) | c2_1(a168) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a168))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[1143, 1142])).
% 0.98/0.89 tff(1145,plain,
% 0.98/0.89 ($false),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[1144, 187, 52, 1125, 1138, 1134, 1137, 41, 1124, 1136])).
% 0.98/0.89 tff(1146,plain,(c1_1(a136) | hskp3 | (~c2_1(a136)) | c3_1(a136) | hskp21 | hskp18 | (~c1_1(a151)) | (~c0_1(a136)) | c2_1(a151)), inference(lemma,lemma(discharge,[]))).
% 0.98/0.89 tff(1147,plain,
% 0.98/0.89 (c1_1(a136)),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[1146, 1123, 52, 1122, 53, 95, 649, 1121, 636])).
% 0.98/0.89 tff(1148,plain,
% 0.98/0.89 (hskp12 | (~c1_1(a136))),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[847, 187, 1121, 1122, 239])).
% 0.98/0.89 tff(1149,plain,
% 0.98/0.89 (hskp12),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[1148, 1147])).
% 0.98/0.89 tff(1150,plain,
% 0.98/0.89 (~c0_1(a140)),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[632, 1149])).
% 0.98/0.90 tff(1151,plain,
% 0.98/0.90 (c3_1(a140)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[646, 1149])).
% 0.98/0.90 tff(1152,plain,
% 0.98/0.90 (c2_1(a140)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[889, 187, 772, 52, 1151, 1150, 51])).
% 0.98/0.90 tff(1153,plain,
% 0.98/0.90 ($false),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[655, 187, 649, 648, 1151, 636, 635, 634, 1150, 229, 911, 1152])).
% 0.98/0.90 tff(1154,plain,(hskp14 | (~c1_1(a151)) | (~c3_1(a149)) | c2_1(a151) | c1_1(a149) | c2_1(a149) | hskp3 | hskp21 | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.98/0.90 tff(1155,plain,
% 0.98/0.90 (hskp14),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[1154, 212, 268, 201, 565, 559, 1116, 53, 95])).
% 0.98/0.90 tff(1156,plain,
% 0.98/0.90 (hskp1),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[759, 1155, 565, 147, 146, 559, 145, 1116, 268])).
% 0.98/0.90 tff(1157,plain,
% 0.98/0.90 (~c3_1(a125)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[597, 1156])).
% 0.98/0.90 tff(1158,plain,
% 0.98/0.90 (c1_1(a125)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[608, 1156])).
% 0.98/0.90 tff(1159,plain,
% 0.98/0.90 (c0_1(a125)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[619, 1156])).
% 0.98/0.90 tff(1160,plain,
% 0.98/0.90 (hskp12),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[626, 187, 1159, 1158, 1157, 239])).
% 0.98/0.90 tff(1161,plain,
% 0.98/0.90 (~c0_1(a140)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[632, 1160])).
% 0.98/0.90 tff(1162,plain,
% 0.98/0.90 (c3_1(a140)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[646, 1160])).
% 0.98/0.90 tff(1163,plain,
% 0.98/0.90 (~c2_1(a140)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[655, 187, 212, 268, 1162, 201, 565, 559, 1161, 229, 219])).
% 0.98/0.90 tff(1164,plain,
% 0.98/0.90 (~c3_1(a145)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[522, 1155])).
% 0.98/0.90 tff(1165,plain,
% 0.98/0.90 (~c1_1(a145)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[528, 1155])).
% 0.98/0.90 tff(1166,plain,
% 0.98/0.90 (~c2_1(a145)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[907, 187, 1116, 1162, 1165, 1164, 1161, 41, 1163])).
% 0.98/0.90 tff(1167,plain,
% 0.98/0.90 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)))),
% 0.98/0.90 inference(bind,[status(th)],[])).
% 0.98/0.90 tff(1168,plain,
% 0.98/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 0.98/0.90 inference(quant_intro,[status(thm)],[1167])).
% 0.98/0.90 tff(1169,plain,
% 0.98/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(1170,plain,
% 0.98/0.90 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c1_1(W))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c1_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c1_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))))),
% 0.98/0.90 inference(bind,[status(th)],[])).
% 0.98/0.90 tff(1171,plain,
% 0.98/0.90 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c3_1(V)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 0.98/0.90 inference(quant_intro,[status(thm)],[1170])).
% 0.98/0.90 tff(1172,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c3_1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause180')).
% 0.98/0.90 tff(1173,plain,
% 0.98/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1172, 1171])).
% 0.98/0.90 tff(1174,plain,
% 0.98/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1173, 1169])).
% 0.98/0.90 tff(1175,plain,(
% 0.98/0.90 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 0.98/0.90 inference(skolemize,[status(sab)],[1174])).
% 0.98/0.90 tff(1176,plain,
% 0.98/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1175, 1168])).
% 0.98/0.90 tff(1177,plain,
% 0.98/0.90 (((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | c3_1(a125) | (~ndr1_0) | c2_1(a125) | (~c1_1(a125)))) <=> ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp21 | hskp18 | c3_1(a125) | (~ndr1_0) | c2_1(a125) | (~c1_1(a125)))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(1178,plain,
% 0.98/0.90 ((hskp21 | hskp18 | (~ndr1_0) | c3_1(a125) | c2_1(a125) | (~c1_1(a125))) <=> (hskp21 | hskp18 | c3_1(a125) | (~ndr1_0) | c2_1(a125) | (~c1_1(a125)))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(1179,plain,
% 0.98/0.90 (((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | (~ndr1_0) | c3_1(a125) | c2_1(a125) | (~c1_1(a125)))) <=> ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | c3_1(a125) | (~ndr1_0) | c2_1(a125) | (~c1_1(a125))))),
% 0.98/0.90 inference(monotonicity,[status(thm)],[1178])).
% 0.98/0.90 tff(1180,plain,
% 0.98/0.90 (((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | (~ndr1_0) | c3_1(a125) | c2_1(a125) | (~c1_1(a125)))) <=> ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp21 | hskp18 | c3_1(a125) | (~ndr1_0) | c2_1(a125) | (~c1_1(a125)))),
% 0.98/0.90 inference(transitivity,[status(thm)],[1179, 1177])).
% 0.98/0.90 tff(1181,plain,
% 0.98/0.90 ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | (~ndr1_0) | c3_1(a125) | c2_1(a125) | (~c1_1(a125)))),
% 0.98/0.90 inference(quant_inst,[status(thm)],[])).
% 0.98/0.90 tff(1182,plain,
% 0.98/0.90 ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp21 | hskp18 | c3_1(a125) | (~ndr1_0) | c2_1(a125) | (~c1_1(a125))),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1181, 1180])).
% 0.98/0.90 tff(1183,plain,
% 0.98/0.90 (c2_1(a125)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[1182, 187, 53, 95, 1158, 1157, 134])).
% 0.98/0.90 tff(1184,plain,
% 0.98/0.90 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | c3_1(a125) | (~ndr1_0) | (~c0_1(a125)) | (~c2_1(a125)) | (~c1_1(a125)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | c3_1(a125) | (~ndr1_0) | (~c0_1(a125)) | (~c2_1(a125)) | (~c1_1(a125)))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(1185,plain,
% 0.98/0.90 ((hskp13 | (~ndr1_0) | (~c2_1(a125)) | (~c1_1(a125)) | (~c0_1(a125)) | c3_1(a125) | (~c1_1(a125)) | (~c0_1(a125))) <=> (hskp13 | c3_1(a125) | (~ndr1_0) | (~c0_1(a125)) | (~c2_1(a125)) | (~c1_1(a125)))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(1186,plain,
% 0.98/0.90 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a125)) | (~c1_1(a125)) | (~c0_1(a125)) | c3_1(a125) | (~c1_1(a125)) | (~c0_1(a125)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | c3_1(a125) | (~ndr1_0) | (~c0_1(a125)) | (~c2_1(a125)) | (~c1_1(a125))))),
% 0.98/0.90 inference(monotonicity,[status(thm)],[1185])).
% 0.98/0.90 tff(1187,plain,
% 0.98/0.90 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a125)) | (~c1_1(a125)) | (~c0_1(a125)) | c3_1(a125) | (~c1_1(a125)) | (~c0_1(a125)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | c3_1(a125) | (~ndr1_0) | (~c0_1(a125)) | (~c2_1(a125)) | (~c1_1(a125)))),
% 0.98/0.90 inference(transitivity,[status(thm)],[1186, 1184])).
% 0.98/0.90 tff(1188,plain,
% 0.98/0.90 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a125)) | (~c1_1(a125)) | (~c0_1(a125)) | c3_1(a125) | (~c1_1(a125)) | (~c0_1(a125)))),
% 0.98/0.90 inference(quant_inst,[status(thm)],[])).
% 0.98/0.90 tff(1189,plain,
% 0.98/0.90 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | c3_1(a125) | (~ndr1_0) | (~c0_1(a125)) | (~c2_1(a125)) | (~c1_1(a125))),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1188, 1187])).
% 0.98/0.90 tff(1190,plain,
% 0.98/0.90 (hskp13),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[1189, 187, 1159, 1158, 1157, 21, 1183])).
% 0.98/0.90 tff(1191,plain,
% 0.98/0.90 (~c3_1(a144)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[991, 1190])).
% 0.98/0.90 tff(1192,plain,
% 0.98/0.90 (~c0_1(a144)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[1015, 1190])).
% 0.98/0.90 tff(1193,plain,
% 0.98/0.90 (c2_1(a144)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[1002, 1190])).
% 0.98/0.90 tff(1194,plain,
% 0.98/0.90 (^[V: $i, U: $i] : refl((hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))),
% 0.98/0.90 inference(bind,[status(th)],[])).
% 0.98/0.90 tff(1195,plain,
% 0.98/0.90 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.98/0.90 inference(quant_intro,[status(thm)],[1194])).
% 0.98/0.90 tff(1196,plain,
% 0.98/0.90 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(1197,plain,
% 0.98/0.90 (^[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) | c0_1(U) | c2_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp27) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | hskp27))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))))),
% 0.98/0.90 inference(bind,[status(th)],[])).
% 0.98/0.90 tff(1198,plain,
% 0.98/0.90 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp27) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.98/0.90 inference(quant_intro,[status(thm)],[1197])).
% 0.98/0.90 tff(1199,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause161')).
% 0.98/0.90 tff(1200,plain,
% 0.98/0.90 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1199, 1198])).
% 0.98/0.90 tff(1201,plain,
% 0.98/0.90 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1200, 1196])).
% 0.98/0.90 tff(1202,plain,(
% 0.98/0.90 ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.98/0.90 inference(skolemize,[status(sab)],[1201])).
% 0.98/0.90 tff(1203,plain,
% 0.98/0.90 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1202, 1195])).
% 0.98/0.90 tff(1204,plain,
% 0.98/0.90 (~c0_1(a145)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[541, 1155])).
% 0.98/0.90 tff(1205,plain,
% 0.98/0.90 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | c0_1(a145) | c3_1(a145) | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)) | c2_1(a145))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c0_1(a145) | c3_1(a145) | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)) | c2_1(a145))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(1206,plain,
% 0.98/0.90 ((hskp27 | (~ndr1_0) | c0_1(a140) | c2_1(a140) | (~c3_1(a140)) | c3_1(a145) | c0_1(a145) | c2_1(a145)) <=> (hskp27 | c0_1(a145) | c3_1(a145) | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)) | c2_1(a145))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(1207,plain,
% 0.98/0.90 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a140) | c2_1(a140) | (~c3_1(a140)) | c3_1(a145) | c0_1(a145) | c2_1(a145))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | c0_1(a145) | c3_1(a145) | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)) | c2_1(a145)))),
% 0.98/0.90 inference(monotonicity,[status(thm)],[1206])).
% 0.98/0.90 tff(1208,plain,
% 0.98/0.90 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a140) | c2_1(a140) | (~c3_1(a140)) | c3_1(a145) | c0_1(a145) | c2_1(a145))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c0_1(a145) | c3_1(a145) | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)) | c2_1(a145))),
% 0.98/0.90 inference(transitivity,[status(thm)],[1207, 1205])).
% 0.98/0.90 tff(1209,plain,
% 0.98/0.90 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a140) | c2_1(a140) | (~c3_1(a140)) | c3_1(a145) | c0_1(a145) | c2_1(a145))),
% 0.98/0.90 inference(quant_inst,[status(thm)],[])).
% 0.98/0.90 tff(1210,plain,
% 0.98/0.90 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c0_1(a145) | c3_1(a145) | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)) | c2_1(a145)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1209, 1208])).
% 0.98/0.90 tff(1211,plain,
% 0.98/0.90 (hskp27),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[1210, 187, 1162, 1204, 1164, 1161, 1203, 1166, 1163])).
% 0.98/0.90 tff(1212,plain,
% 0.98/0.90 (((~hskp27) | c3_1(a137)) <=> ((~hskp27) | c3_1(a137))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(1213,axiom,((~hskp27) | c3_1(a137)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause48')).
% 0.98/0.90 tff(1214,plain,
% 0.98/0.90 ((~hskp27) | c3_1(a137)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1213, 1212])).
% 0.98/0.90 tff(1215,plain,
% 0.98/0.90 ((~hskp27) | c3_1(a137)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1214, 1212])).
% 0.98/0.90 tff(1216,plain,
% 0.98/0.90 ((~hskp27) | c3_1(a137)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1215, 1212])).
% 0.98/0.90 tff(1217,plain,
% 0.98/0.90 ((~hskp27) | c3_1(a137)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1216, 1212])).
% 0.98/0.90 tff(1218,plain,
% 0.98/0.90 ((~hskp27) | c3_1(a137)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1217, 1212])).
% 0.98/0.90 tff(1219,plain,
% 0.98/0.90 ((~hskp27) | c3_1(a137)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1218, 1212])).
% 0.98/0.90 tff(1220,plain,
% 0.98/0.90 ((~hskp27) | c3_1(a137)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1219, 1212])).
% 0.98/0.90 tff(1221,plain,
% 0.98/0.90 ((~hskp27) | c3_1(a137)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1220, 1212])).
% 0.98/0.90 tff(1222,plain,
% 0.98/0.90 (c3_1(a137)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[1221, 1211])).
% 0.98/0.90 tff(1223,plain,
% 0.98/0.90 (((~hskp27) | c2_1(a137)) <=> ((~hskp27) | c2_1(a137))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(1224,axiom,((~hskp27) | c2_1(a137)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause47')).
% 0.98/0.90 tff(1225,plain,
% 0.98/0.90 ((~hskp27) | c2_1(a137)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1224, 1223])).
% 0.98/0.90 tff(1226,plain,
% 0.98/0.90 ((~hskp27) | c2_1(a137)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1225, 1223])).
% 0.98/0.90 tff(1227,plain,
% 0.98/0.90 ((~hskp27) | c2_1(a137)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1226, 1223])).
% 0.98/0.90 tff(1228,plain,
% 0.98/0.90 ((~hskp27) | c2_1(a137)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1227, 1223])).
% 0.98/0.90 tff(1229,plain,
% 0.98/0.90 ((~hskp27) | c2_1(a137)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1228, 1223])).
% 0.98/0.90 tff(1230,plain,
% 0.98/0.90 ((~hskp27) | c2_1(a137)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1229, 1223])).
% 0.98/0.90 tff(1231,plain,
% 0.98/0.90 ((~hskp27) | c2_1(a137)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1230, 1223])).
% 0.98/0.90 tff(1232,plain,
% 0.98/0.90 ((~hskp27) | c2_1(a137)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1231, 1223])).
% 0.98/0.90 tff(1233,plain,
% 0.98/0.90 (c2_1(a137)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[1232, 1211])).
% 0.98/0.90 tff(1234,plain,
% 0.98/0.90 (((~hskp27) | c1_1(a137)) <=> ((~hskp27) | c1_1(a137))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(1235,axiom,((~hskp27) | c1_1(a137)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause46')).
% 0.98/0.90 tff(1236,plain,
% 0.98/0.90 ((~hskp27) | c1_1(a137)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1235, 1234])).
% 0.98/0.90 tff(1237,plain,
% 0.98/0.90 ((~hskp27) | c1_1(a137)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1236, 1234])).
% 0.98/0.90 tff(1238,plain,
% 0.98/0.90 ((~hskp27) | c1_1(a137)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1237, 1234])).
% 0.98/0.90 tff(1239,plain,
% 0.98/0.90 ((~hskp27) | c1_1(a137)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1238, 1234])).
% 0.98/0.90 tff(1240,plain,
% 0.98/0.90 ((~hskp27) | c1_1(a137)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1239, 1234])).
% 0.98/0.90 tff(1241,plain,
% 0.98/0.90 ((~hskp27) | c1_1(a137)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1240, 1234])).
% 0.98/0.90 tff(1242,plain,
% 0.98/0.90 ((~hskp27) | c1_1(a137)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1241, 1234])).
% 0.98/0.90 tff(1243,plain,
% 0.98/0.90 ((~hskp27) | c1_1(a137)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1242, 1234])).
% 0.98/0.90 tff(1244,plain,
% 0.98/0.90 (c1_1(a137)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[1243, 1211])).
% 0.98/0.90 tff(1245,plain,
% 0.98/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a145) | c3_1(a145) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a144)) | c2_1(a145))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a145) | c3_1(a145) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a144)) | c2_1(a145))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(1246,plain,
% 0.98/0.90 (((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a145) | c1_1(a145) | c3_1(a145)) <=> (c1_1(a145) | c3_1(a145) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a144)) | c2_1(a145))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(1247,plain,
% 0.98/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a145) | c1_1(a145) | c3_1(a145))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a145) | c3_1(a145) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a144)) | c2_1(a145)))),
% 0.98/0.90 inference(monotonicity,[status(thm)],[1246])).
% 0.98/0.90 tff(1248,plain,
% 0.98/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a145) | c1_1(a145) | c3_1(a145))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a145) | c3_1(a145) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a144)) | c2_1(a145))),
% 0.98/0.90 inference(transitivity,[status(thm)],[1247, 1245])).
% 0.98/0.90 tff(1249,plain,
% 0.98/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a145) | c1_1(a145) | c3_1(a145))),
% 0.98/0.90 inference(quant_inst,[status(thm)],[])).
% 0.98/0.90 tff(1250,plain,
% 0.98/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a145) | c3_1(a145) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a144)) | c2_1(a145)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1249, 1248])).
% 0.98/0.90 tff(1251,plain,
% 0.98/0.90 ($false),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[1250, 187, 1244, 1233, 1222, 1193, 1165, 1164, 1192, 1191, 1176, 1166])).
% 0.98/0.90 tff(1252,plain,(hskp21 | hskp18 | (~c0_1(a138)) | (~c3_1(a138)) | c1_1(a138)), inference(lemma,lemma(discharge,[]))).
% 0.98/0.90 tff(1253,plain,
% 0.98/0.90 (hskp21),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[1252, 124, 95, 113, 102])).
% 0.98/0.90 tff(1254,plain,
% 0.98/0.90 (~c2_1(a170)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[312, 1253])).
% 0.98/0.90 tff(1255,plain,
% 0.98/0.90 (~c0_1(a170)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[318, 1253])).
% 0.98/0.90 tff(1256,plain,
% 0.98/0.90 (c3_1(a170)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[346, 1253])).
% 0.98/0.90 tff(1257,plain,
% 0.98/0.90 (c3_1(a128)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[1109, 124, 113, 102, 95])).
% 0.98/0.90 tff(1258,plain,
% 0.98/0.90 (~hskp3),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[1115, 1257])).
% 0.98/0.90 tff(1259,plain,
% 0.98/0.90 (hskp14),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[515, 187, 1258, 1256, 1255, 1254, 51])).
% 0.98/0.90 tff(1260,plain,
% 0.98/0.90 (~c3_1(a145)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[522, 1259])).
% 0.98/0.90 tff(1261,plain,
% 0.98/0.90 (~c1_1(a145)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[528, 1259])).
% 0.98/0.90 tff(1262,plain,
% 0.98/0.90 (~c2_1(a145)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[535, 187, 1258, 1256, 1255, 1254, 1261, 1260, 41])).
% 0.98/0.90 tff(1263,plain,
% 0.98/0.90 (~c0_1(a145)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[541, 1259])).
% 0.98/0.90 tff(1264,plain,
% 0.98/0.90 ($false),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[548, 187, 124, 113, 1263, 1261, 1260, 102, 279, 1262])).
% 0.98/0.90 tff(1265,plain,((~hskp10) | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.98/0.90 tff(1266,plain,
% 0.98/0.90 (~hskp10),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[1265, 95])).
% 0.98/0.90 tff(1267,plain,
% 0.98/0.90 (hskp30),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[185, 1266, 95])).
% 0.98/0.90 tff(1268,plain,
% 0.98/0.90 (((~hskp30) | c2_1(a199)) <=> ((~hskp30) | c2_1(a199))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(1269,axiom,((~hskp30) | c2_1(a199)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause39')).
% 0.98/0.90 tff(1270,plain,
% 0.98/0.90 ((~hskp30) | c2_1(a199)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1269, 1268])).
% 0.98/0.90 tff(1271,plain,
% 0.98/0.90 ((~hskp30) | c2_1(a199)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1270, 1268])).
% 0.98/0.90 tff(1272,plain,
% 0.98/0.90 ((~hskp30) | c2_1(a199)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1271, 1268])).
% 0.98/0.90 tff(1273,plain,
% 0.98/0.90 ((~hskp30) | c2_1(a199)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1272, 1268])).
% 0.98/0.90 tff(1274,plain,
% 0.98/0.90 ((~hskp30) | c2_1(a199)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1273, 1268])).
% 0.98/0.90 tff(1275,plain,
% 0.98/0.90 ((~hskp30) | c2_1(a199)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1274, 1268])).
% 0.98/0.90 tff(1276,plain,
% 0.98/0.90 ((~hskp30) | c2_1(a199)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1275, 1268])).
% 0.98/0.90 tff(1277,plain,
% 0.98/0.90 ((~hskp30) | c2_1(a199)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1276, 1268])).
% 0.98/0.90 tff(1278,plain,
% 0.98/0.90 (c2_1(a199)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[1277, 1267])).
% 0.98/0.90 tff(1279,plain,
% 0.98/0.90 (((~hskp30) | c1_1(a199)) <=> ((~hskp30) | c1_1(a199))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(1280,axiom,((~hskp30) | c1_1(a199)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause38')).
% 0.98/0.90 tff(1281,plain,
% 0.98/0.90 ((~hskp30) | c1_1(a199)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1280, 1279])).
% 0.98/0.90 tff(1282,plain,
% 0.98/0.90 ((~hskp30) | c1_1(a199)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1281, 1279])).
% 0.98/0.90 tff(1283,plain,
% 0.98/0.90 ((~hskp30) | c1_1(a199)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1282, 1279])).
% 0.98/0.90 tff(1284,plain,
% 0.98/0.90 ((~hskp30) | c1_1(a199)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1283, 1279])).
% 0.98/0.90 tff(1285,plain,
% 0.98/0.90 ((~hskp30) | c1_1(a199)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1284, 1279])).
% 0.98/0.90 tff(1286,plain,
% 0.98/0.90 ((~hskp30) | c1_1(a199)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1285, 1279])).
% 0.98/0.90 tff(1287,plain,
% 0.98/0.90 ((~hskp30) | c1_1(a199)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1286, 1279])).
% 0.98/0.90 tff(1288,plain,
% 0.98/0.90 ((~hskp30) | c1_1(a199)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1287, 1279])).
% 0.98/0.90 tff(1289,plain,
% 0.98/0.90 (c1_1(a199)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[1288, 1267])).
% 0.98/0.90 tff(1290,plain,
% 0.98/0.90 (((~hskp30) | c0_1(a199)) <=> ((~hskp30) | c0_1(a199))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(1291,axiom,((~hskp30) | c0_1(a199)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause37')).
% 0.98/0.90 tff(1292,plain,
% 0.98/0.90 ((~hskp30) | c0_1(a199)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1291, 1290])).
% 0.98/0.90 tff(1293,plain,
% 0.98/0.90 ((~hskp30) | c0_1(a199)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1292, 1290])).
% 0.98/0.90 tff(1294,plain,
% 0.98/0.90 ((~hskp30) | c0_1(a199)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1293, 1290])).
% 0.98/0.90 tff(1295,plain,
% 0.98/0.90 ((~hskp30) | c0_1(a199)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1294, 1290])).
% 0.98/0.90 tff(1296,plain,
% 0.98/0.90 ((~hskp30) | c0_1(a199)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1295, 1290])).
% 0.98/0.90 tff(1297,plain,
% 0.98/0.90 ((~hskp30) | c0_1(a199)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1296, 1290])).
% 0.98/0.90 tff(1298,plain,
% 0.98/0.90 ((~hskp30) | c0_1(a199)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1297, 1290])).
% 0.98/0.90 tff(1299,plain,
% 0.98/0.90 ((~hskp30) | c0_1(a199)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[1298, 1290])).
% 0.98/0.90 tff(1300,plain,
% 0.98/0.90 (c0_1(a199)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[1299, 1267])).
% 0.98/0.90 tff(1301,plain,
% 0.98/0.90 (^[U: $i] : refl((hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 0.98/0.90 inference(bind,[status(th)],[])).
% 0.98/0.90 tff(1302,plain,
% 0.98/0.90 (![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.98/0.90 inference(quant_intro,[status(thm)],[1301])).
% 0.98/0.90 tff(1303,plain,
% 0.98/0.90 (![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(1304,plain,
% 0.98/0.90 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp10) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp10))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp10) | hskp15) <=> ((hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp15))), rewrite(((hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp15) <=> (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp10) | hskp15) <=> (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.98/0.91 inference(bind,[status(th)],[])).
% 0.98/0.91 tff(1305,plain,
% 0.98/0.91 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp10) | hskp15) <=> ![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.98/0.91 inference(quant_intro,[status(thm)],[1304])).
% 0.98/0.91 tff(1306,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp10) | hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause155')).
% 0.98/0.91 tff(1307,plain,
% 0.98/0.91 (![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[1306, 1305])).
% 0.98/0.91 tff(1308,plain,
% 0.98/0.91 (![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[1307, 1303])).
% 0.98/0.91 tff(1309,plain,(
% 0.98/0.91 ![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.98/0.91 inference(skolemize,[status(sab)],[1308])).
% 0.98/0.91 tff(1310,plain,
% 0.98/0.91 (![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[1309, 1302])).
% 0.98/0.91 tff(1311,assumption,(c1_1(a199)), introduced(assumption)).
% 0.98/0.91 tff(1312,assumption,(c0_1(a199)), introduced(assumption)).
% 0.98/0.91 tff(1313,assumption,(~hskp10), introduced(assumption)).
% 0.98/0.91 tff(1314,plain,
% 0.98/0.91 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | (~c0_1(a199)) | (~c3_1(a199)) | (~c1_1(a199)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp15 | hskp10 | (~ndr1_0) | (~c0_1(a199)) | (~c3_1(a199)) | (~c1_1(a199)))),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(1315,plain,
% 0.98/0.91 ((hskp15 | hskp10 | (~ndr1_0) | (~c3_1(a199)) | (~c1_1(a199)) | (~c0_1(a199))) <=> (hskp15 | hskp10 | (~ndr1_0) | (~c0_1(a199)) | (~c3_1(a199)) | (~c1_1(a199)))),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(1316,plain,
% 0.98/0.91 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(a199)) | (~c1_1(a199)) | (~c0_1(a199)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | (~c0_1(a199)) | (~c3_1(a199)) | (~c1_1(a199))))),
% 0.98/0.91 inference(monotonicity,[status(thm)],[1315])).
% 0.98/0.91 tff(1317,plain,
% 0.98/0.91 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(a199)) | (~c1_1(a199)) | (~c0_1(a199)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp15 | hskp10 | (~ndr1_0) | (~c0_1(a199)) | (~c3_1(a199)) | (~c1_1(a199)))),
% 0.98/0.91 inference(transitivity,[status(thm)],[1316, 1314])).
% 0.98/0.91 tff(1318,plain,
% 0.98/0.91 ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(a199)) | (~c1_1(a199)) | (~c0_1(a199)))),
% 0.98/0.91 inference(quant_inst,[status(thm)],[])).
% 0.98/0.91 tff(1319,plain,
% 0.98/0.91 ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp15 | hskp10 | (~ndr1_0) | (~c0_1(a199)) | (~c3_1(a199)) | (~c1_1(a199))),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[1318, 1317])).
% 0.98/0.91 tff(1320,plain,
% 0.98/0.91 (hskp15 | (~c3_1(a199))),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[1319, 187, 1313, 1312, 1311, 1310])).
% 0.98/0.91 tff(1321,plain,
% 0.98/0.91 (~c3_1(a199)),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[1320, 74])).
% 0.98/0.91 tff(1322,assumption,(c2_1(a199)), introduced(assumption)).
% 0.98/0.91 tff(1323,plain,
% 0.98/0.91 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | c3_1(a199) | (~c1_1(a199)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | c3_1(a199) | (~c1_1(a199)))),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(1324,plain,
% 0.98/0.91 ((hskp13 | (~ndr1_0) | (~c2_1(a199)) | (~c1_1(a199)) | (~c0_1(a199)) | c3_1(a199) | (~c1_1(a199)) | (~c0_1(a199))) <=> (hskp13 | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | c3_1(a199) | (~c1_1(a199)))),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(1325,plain,
% 0.98/0.91 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a199)) | (~c1_1(a199)) | (~c0_1(a199)) | c3_1(a199) | (~c1_1(a199)) | (~c0_1(a199)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | c3_1(a199) | (~c1_1(a199))))),
% 0.98/0.91 inference(monotonicity,[status(thm)],[1324])).
% 0.98/0.91 tff(1326,plain,
% 0.98/0.91 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a199)) | (~c1_1(a199)) | (~c0_1(a199)) | c3_1(a199) | (~c1_1(a199)) | (~c0_1(a199)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | c3_1(a199) | (~c1_1(a199)))),
% 0.98/0.91 inference(transitivity,[status(thm)],[1325, 1323])).
% 0.98/0.91 tff(1327,plain,
% 0.98/0.91 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a199)) | (~c1_1(a199)) | (~c0_1(a199)) | c3_1(a199) | (~c1_1(a199)) | (~c0_1(a199)))),
% 0.98/0.91 inference(quant_inst,[status(thm)],[])).
% 0.98/0.91 tff(1328,plain,
% 0.98/0.91 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | c3_1(a199) | (~c1_1(a199))),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[1327, 1326])).
% 0.98/0.91 tff(1329,plain,
% 0.98/0.91 (hskp13),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[1328, 187, 1312, 1311, 1322, 21, 1321])).
% 0.98/0.91 tff(1330,plain,
% 0.98/0.91 (~c3_1(a144)),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[991, 1329])).
% 0.98/0.91 tff(1331,plain,
% 0.98/0.91 (~c0_1(a144)),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[1015, 1329])).
% 0.98/0.91 tff(1332,plain,
% 0.98/0.91 (c2_1(a144)),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[1002, 1329])).
% 0.98/0.91 tff(1333,plain,
% 0.98/0.91 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp29 | hskp3 | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a144)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp29 | hskp3 | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a144)))),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(1334,plain,
% 0.98/0.91 ((hskp29 | hskp3 | (~ndr1_0) | c3_1(a144) | c0_1(a144) | (~c2_1(a144))) <=> (hskp29 | hskp3 | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a144)))),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(1335,plain,
% 0.98/0.91 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp29 | hskp3 | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a144))))),
% 0.98/0.91 inference(monotonicity,[status(thm)],[1334])).
% 0.98/0.91 tff(1336,plain,
% 0.98/0.91 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp29 | hskp3 | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a144)))),
% 0.98/0.91 inference(transitivity,[status(thm)],[1335, 1333])).
% 0.98/0.91 tff(1337,plain,
% 0.98/0.91 ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)))),
% 0.98/0.91 inference(quant_inst,[status(thm)],[])).
% 0.98/0.91 tff(1338,plain,
% 0.98/0.91 ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp29 | hskp3 | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a144))),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[1337, 1336])).
% 0.98/0.91 tff(1339,plain,
% 0.98/0.91 (hskp29),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[1338, 187, 52, 1332, 1331, 1330, 73])).
% 0.98/0.91 tff(1340,plain,
% 0.98/0.91 (((~hskp29) | c3_1(a150)) <=> ((~hskp29) | c3_1(a150))),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(1341,axiom,((~hskp29) | c3_1(a150)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause42')).
% 0.98/0.91 tff(1342,plain,
% 0.98/0.91 ((~hskp29) | c3_1(a150)),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[1341, 1340])).
% 0.98/0.91 tff(1343,plain,
% 0.98/0.91 ((~hskp29) | c3_1(a150)),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[1342, 1340])).
% 0.98/0.91 tff(1344,plain,
% 0.98/0.91 ((~hskp29) | c3_1(a150)),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[1343, 1340])).
% 0.98/0.91 tff(1345,plain,
% 0.98/0.91 ((~hskp29) | c3_1(a150)),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[1344, 1340])).
% 0.98/0.91 tff(1346,plain,
% 0.98/0.91 ((~hskp29) | c3_1(a150)),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[1345, 1340])).
% 0.98/0.91 tff(1347,plain,
% 0.98/0.91 ((~hskp29) | c3_1(a150)),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[1346, 1340])).
% 0.98/0.91 tff(1348,plain,
% 0.98/0.91 ((~hskp29) | c3_1(a150)),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[1347, 1340])).
% 0.98/0.91 tff(1349,plain,
% 0.98/0.91 ((~hskp29) | c3_1(a150)),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[1348, 1340])).
% 0.98/0.91 tff(1350,plain,
% 0.98/0.91 (c3_1(a150)),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[1349, 1339])).
% 0.98/0.91 tff(1351,plain,
% 0.98/0.91 (((~hskp29) | c1_1(a150)) <=> ((~hskp29) | c1_1(a150))),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(1352,axiom,((~hskp29) | c1_1(a150)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause41')).
% 0.98/0.91 tff(1353,plain,
% 0.98/0.91 ((~hskp29) | c1_1(a150)),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[1352, 1351])).
% 0.98/0.91 tff(1354,plain,
% 0.98/0.91 ((~hskp29) | c1_1(a150)),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[1353, 1351])).
% 0.98/0.91 tff(1355,plain,
% 0.98/0.91 ((~hskp29) | c1_1(a150)),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[1354, 1351])).
% 0.98/0.91 tff(1356,plain,
% 0.98/0.91 ((~hskp29) | c1_1(a150)),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[1355, 1351])).
% 0.98/0.91 tff(1357,plain,
% 0.98/0.91 ((~hskp29) | c1_1(a150)),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[1356, 1351])).
% 0.98/0.91 tff(1358,plain,
% 0.98/0.91 ((~hskp29) | c1_1(a150)),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[1357, 1351])).
% 0.98/0.91 tff(1359,plain,
% 0.98/0.91 ((~hskp29) | c1_1(a150)),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[1358, 1351])).
% 0.98/0.91 tff(1360,plain,
% 0.98/0.91 ((~hskp29) | c1_1(a150)),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[1359, 1351])).
% 0.98/0.91 tff(1361,plain,
% 0.98/0.91 (c1_1(a150)),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[1360, 1339])).
% 0.98/0.91 tff(1362,plain,
% 0.98/0.91 (((~hskp29) | c0_1(a150)) <=> ((~hskp29) | c0_1(a150))),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(1363,axiom,((~hskp29) | c0_1(a150)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause40')).
% 0.98/0.91 tff(1364,plain,
% 0.98/0.91 ((~hskp29) | c0_1(a150)),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[1363, 1362])).
% 0.98/0.91 tff(1365,plain,
% 0.98/0.91 ((~hskp29) | c0_1(a150)),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[1364, 1362])).
% 0.98/0.91 tff(1366,plain,
% 0.98/0.91 ((~hskp29) | c0_1(a150)),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[1365, 1362])).
% 0.98/0.91 tff(1367,plain,
% 0.98/0.91 ((~hskp29) | c0_1(a150)),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[1366, 1362])).
% 0.98/0.91 tff(1368,plain,
% 0.98/0.91 ((~hskp29) | c0_1(a150)),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[1367, 1362])).
% 0.98/0.91 tff(1369,plain,
% 0.98/0.91 ((~hskp29) | c0_1(a150)),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[1368, 1362])).
% 0.98/0.91 tff(1370,plain,
% 0.98/0.91 ((~hskp29) | c0_1(a150)),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[1369, 1362])).
% 0.98/0.91 tff(1371,plain,
% 0.98/0.91 ((~hskp29) | c0_1(a150)),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[1370, 1362])).
% 0.98/0.91 tff(1372,plain,
% 0.98/0.91 (c0_1(a150)),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[1371, 1339])).
% 0.98/0.91 tff(1373,plain,
% 0.98/0.91 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(a150)) | (~c0_1(a150)) | (~c1_1(a150)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp15 | hskp10 | (~ndr1_0) | (~c3_1(a150)) | (~c0_1(a150)) | (~c1_1(a150)))),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(1374,plain,
% 0.98/0.91 ((hskp15 | hskp10 | (~ndr1_0) | (~c3_1(a150)) | (~c1_1(a150)) | (~c0_1(a150))) <=> (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(a150)) | (~c0_1(a150)) | (~c1_1(a150)))),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(1375,plain,
% 0.98/0.91 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(a150)) | (~c1_1(a150)) | (~c0_1(a150)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(a150)) | (~c0_1(a150)) | (~c1_1(a150))))),
% 0.98/0.91 inference(monotonicity,[status(thm)],[1374])).
% 0.98/0.91 tff(1376,plain,
% 0.98/0.91 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(a150)) | (~c1_1(a150)) | (~c0_1(a150)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp15 | hskp10 | (~ndr1_0) | (~c3_1(a150)) | (~c0_1(a150)) | (~c1_1(a150)))),
% 0.98/0.91 inference(transitivity,[status(thm)],[1375, 1373])).
% 0.98/0.91 tff(1377,plain,
% 0.98/0.91 ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(a150)) | (~c1_1(a150)) | (~c0_1(a150)))),
% 0.98/0.91 inference(quant_inst,[status(thm)],[])).
% 0.98/0.91 tff(1378,plain,
% 0.98/0.91 ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp15 | hskp10 | (~ndr1_0) | (~c3_1(a150)) | (~c0_1(a150)) | (~c1_1(a150))),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[1377, 1376])).
% 0.98/0.91 tff(1379,plain,
% 0.98/0.91 ($false),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[1378, 187, 74, 1313, 1372, 1361, 1350, 1310])).
% 0.98/0.91 tff(1380,plain,(hskp15 | hskp10 | hskp3 | (~c0_1(a199)) | (~c1_1(a199)) | (~c2_1(a199))), inference(lemma,lemma(discharge,[]))).
% 0.98/0.91 tff(1381,plain,
% 0.98/0.91 (hskp15),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[1380, 52, 1266, 1300, 1289, 1278])).
% 0.98/0.91 tff(1382,plain,
% 0.98/0.91 (~c2_1(a149)),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[558, 1381])).
% 0.98/0.91 tff(1383,plain,
% 0.98/0.91 (~c1_1(a149)),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[564, 1381])).
% 0.98/0.91 tff(1384,plain,
% 0.98/0.91 (c3_1(a149)),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[267, 1381])).
% 0.98/0.91 tff(1385,plain,
% 0.98/0.91 (hskp14 | c0_1(a149)),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[766, 187, 52, 1384, 1382, 51])).
% 0.98/0.91 tff(1386,plain,
% 0.98/0.91 (c0_1(a149)),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[1385, 772])).
% 0.98/0.91 tff(1387,plain,
% 0.98/0.91 (((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp16 | c1_1(a149) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)))) <=> ((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp16 | c1_1(a149) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)))),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(1388,plain,
% 0.98/0.91 ((hskp21 | hskp16 | (~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149))) <=> (hskp21 | hskp16 | c1_1(a149) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)))),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(1389,plain,
% 0.98/0.91 (((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp16 | (~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149)))) <=> ((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp16 | c1_1(a149) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149))))),
% 0.98/0.91 inference(monotonicity,[status(thm)],[1388])).
% 0.98/0.91 tff(1390,plain,
% 0.98/0.91 (((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp16 | (~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149)))) <=> ((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp16 | c1_1(a149) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)))),
% 0.98/0.91 inference(transitivity,[status(thm)],[1389, 1387])).
% 0.98/0.91 tff(1391,plain,
% 0.98/0.91 ((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp16 | (~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149)))),
% 0.98/0.91 inference(quant_inst,[status(thm)],[])).
% 0.98/0.91 tff(1392,plain,
% 0.98/0.91 ((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp16 | c1_1(a149) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149))),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[1391, 1390])).
% 0.98/0.91 tff(1393,plain,
% 0.98/0.91 (hskp21 | hskp16 | (~c0_1(a149))),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[1392, 187, 1384, 1383, 144])).
% 0.98/0.91 tff(1394,plain,
% 0.98/0.91 (hskp16),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[1393, 1386, 53])).
% 0.98/0.91 tff(1395,plain,
% 0.98/0.91 (c1_1(a151)),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[211, 1394])).
% 0.98/0.91 tff(1396,plain,
% 0.98/0.91 (~c2_1(a151)),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[200, 1394])).
% 0.98/0.91 tff(1397,plain,
% 0.98/0.91 ($false),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[1154, 1396, 1395, 1384, 772, 1383, 1382, 52, 53, 95])).
% 0.98/0.91 tff(1398,plain,(hskp14 | hskp3 | hskp21 | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.98/0.91 tff(1399,plain,
% 0.98/0.91 (hskp14),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[1398, 53, 52, 95])).
% 0.98/0.91 tff(1400,plain,
% 0.98/0.91 (~c0_1(a145)),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[541, 1399])).
% 0.98/0.91 tff(1401,plain,
% 0.98/0.91 (~c3_1(a145)),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[522, 1399])).
% 0.98/0.91 tff(1402,plain,
% 0.98/0.91 (~c1_1(a145)),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[528, 1399])).
% 0.98/0.91 tff(1403,assumption,(~c0_1(a149)), introduced(assumption)).
% 0.98/0.91 tff(1404,assumption,(~c3_1(a145)), introduced(assumption)).
% 0.98/0.91 tff(1405,assumption,(~c1_1(a145)), introduced(assumption)).
% 0.98/0.91 tff(1406,plain,
% 0.98/0.91 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c2_1(a149) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c2_1(a145)) | (~c3_1(a149)) | c0_1(a149))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a149) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c2_1(a145)) | (~c3_1(a149)) | c0_1(a149))),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(1407,plain,
% 0.98/0.91 ((hskp3 | (~ndr1_0) | c3_1(a145) | c1_1(a145) | (~c2_1(a145)) | c0_1(a149) | c2_1(a149) | (~c3_1(a149))) <=> (hskp3 | c2_1(a149) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c2_1(a145)) | (~c3_1(a149)) | c0_1(a149))),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(1408,plain,
% 0.98/0.91 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a145) | c1_1(a145) | (~c2_1(a145)) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c2_1(a149) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c2_1(a145)) | (~c3_1(a149)) | c0_1(a149)))),
% 0.98/0.91 inference(monotonicity,[status(thm)],[1407])).
% 0.98/0.91 tff(1409,plain,
% 0.98/0.91 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a145) | c1_1(a145) | (~c2_1(a145)) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a149) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c2_1(a145)) | (~c3_1(a149)) | c0_1(a149))),
% 0.98/0.91 inference(transitivity,[status(thm)],[1408, 1406])).
% 0.98/0.91 tff(1410,plain,
% 0.98/0.91 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a145) | c1_1(a145) | (~c2_1(a145)) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)))),
% 0.98/0.91 inference(quant_inst,[status(thm)],[])).
% 0.98/0.91 tff(1411,plain,
% 0.98/0.91 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a149) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c2_1(a145)) | (~c3_1(a149)) | c0_1(a149)),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[1410, 1409])).
% 0.98/0.91 tff(1412,plain,
% 0.98/0.91 (~c2_1(a145)),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[1411, 187, 52, 648, 634, 1405, 1404, 41, 1403])).
% 0.98/0.91 tff(1413,assumption,(~c0_1(a145)), introduced(assumption)).
% 0.98/0.91 tff(1414,plain,
% 0.98/0.91 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c2_1(a149) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a149)) | c0_1(a149))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c2_1(a149) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a149)) | c0_1(a149))),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(1415,plain,
% 0.98/0.91 ((hskp9 | (~ndr1_0) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)) | c3_1(a145) | c0_1(a145) | c2_1(a145)) <=> (hskp9 | c2_1(a149) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a149)) | c0_1(a149))),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(1416,plain,
% 0.98/0.91 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)) | c3_1(a145) | c0_1(a145) | c2_1(a145))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c2_1(a149) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a149)) | c0_1(a149)))),
% 0.98/0.91 inference(monotonicity,[status(thm)],[1415])).
% 0.98/0.91 tff(1417,plain,
% 0.98/0.91 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)) | c3_1(a145) | c0_1(a145) | c2_1(a145))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c2_1(a149) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a149)) | c0_1(a149))),
% 0.98/0.91 inference(transitivity,[status(thm)],[1416, 1414])).
% 0.98/0.91 tff(1418,plain,
% 0.98/0.91 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)) | c3_1(a145) | c0_1(a145) | c2_1(a145))),
% 0.98/0.91 inference(quant_inst,[status(thm)],[])).
% 0.98/0.91 tff(1419,plain,
% 0.98/0.91 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c2_1(a149) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a149)) | c0_1(a149)),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[1418, 1417])).
% 0.98/0.91 tff(1420,plain,
% 0.98/0.91 (hskp9),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[1419, 187, 648, 634, 1413, 1404, 31, 1403, 1412])).
% 0.98/0.91 tff(1421,plain,
% 0.98/0.91 (~c3_1(a136)),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[810, 1420])).
% 0.98/0.91 tff(1422,plain,
% 0.98/0.91 (c2_1(a136)),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[821, 1420])).
% 0.98/0.91 tff(1423,plain,
% 0.98/0.91 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c2_1(a149) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a149)) | c0_1(a149))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a149) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a149)) | c0_1(a149))),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(1424,plain,
% 0.98/0.91 ((hskp3 | (~ndr1_0) | c3_1(a136) | c1_1(a136) | (~c2_1(a136)) | c0_1(a149) | c2_1(a149) | (~c3_1(a149))) <=> (hskp3 | c2_1(a149) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a149)) | c0_1(a149))),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(1425,plain,
% 0.98/0.91 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a136) | c1_1(a136) | (~c2_1(a136)) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c2_1(a149) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a149)) | c0_1(a149)))),
% 0.98/0.91 inference(monotonicity,[status(thm)],[1424])).
% 0.98/0.91 tff(1426,plain,
% 0.98/0.91 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a136) | c1_1(a136) | (~c2_1(a136)) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a149) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a149)) | c0_1(a149))),
% 0.98/0.91 inference(transitivity,[status(thm)],[1425, 1423])).
% 0.98/0.91 tff(1427,plain,
% 0.98/0.91 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a136) | c1_1(a136) | (~c2_1(a136)) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)))),
% 0.98/0.91 inference(quant_inst,[status(thm)],[])).
% 0.98/0.91 tff(1428,plain,
% 0.98/0.91 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a149) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a149)) | c0_1(a149)),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[1427, 1426])).
% 0.98/0.91 tff(1429,plain,
% 0.98/0.91 (c1_1(a136)),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[1428, 187, 52, 648, 1422, 634, 1421, 41, 1403])).
% 0.98/0.91 tff(1430,plain,
% 0.98/0.91 (c0_1(a136)),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[840, 1420])).
% 0.98/0.91 tff(1431,plain,
% 0.98/0.91 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | c3_1(a136) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | c3_1(a136) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)))),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(1432,plain,
% 0.98/0.91 ((hskp13 | (~ndr1_0) | (~c2_1(a136)) | (~c1_1(a136)) | (~c0_1(a136)) | c3_1(a136) | (~c1_1(a136)) | (~c0_1(a136))) <=> (hskp13 | c3_1(a136) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)))),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(1433,plain,
% 0.98/0.91 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a136)) | (~c1_1(a136)) | (~c0_1(a136)) | c3_1(a136) | (~c1_1(a136)) | (~c0_1(a136)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | c3_1(a136) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136))))),
% 0.98/0.91 inference(monotonicity,[status(thm)],[1432])).
% 0.98/0.91 tff(1434,plain,
% 0.98/0.91 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a136)) | (~c1_1(a136)) | (~c0_1(a136)) | c3_1(a136) | (~c1_1(a136)) | (~c0_1(a136)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | c3_1(a136) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)))),
% 0.98/0.91 inference(transitivity,[status(thm)],[1433, 1431])).
% 0.98/0.91 tff(1435,plain,
% 0.98/0.91 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a136)) | (~c1_1(a136)) | (~c0_1(a136)) | c3_1(a136) | (~c1_1(a136)) | (~c0_1(a136)))),
% 0.98/0.92 inference(quant_inst,[status(thm)],[])).
% 0.98/0.92 tff(1436,plain,
% 0.98/0.92 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | c3_1(a136) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136))),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[1435, 1434])).
% 0.98/0.92 tff(1437,plain,
% 0.98/0.92 (hskp13 | (~c1_1(a136))),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[1436, 187, 1430, 1422, 1421, 21])).
% 0.98/0.92 tff(1438,plain,
% 0.98/0.92 (hskp13),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[1437, 1429])).
% 0.98/0.92 tff(1439,plain,
% 0.98/0.92 (~c3_1(a144)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[991, 1438])).
% 0.98/0.92 tff(1440,plain,
% 0.98/0.92 (~c0_1(a144)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[1015, 1438])).
% 0.98/0.92 tff(1441,plain,
% 0.98/0.92 (c2_1(a144)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[1002, 1438])).
% 0.98/0.92 tff(1442,plain,
% 0.98/0.92 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | c2_1(a149) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a149)) | c0_1(a149))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c2_1(a149) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a149)) | c0_1(a149))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(1443,plain,
% 0.98/0.92 ((hskp27 | (~ndr1_0) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)) | c3_1(a145) | c0_1(a145) | c2_1(a145)) <=> (hskp27 | c2_1(a149) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a149)) | c0_1(a149))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(1444,plain,
% 0.98/0.92 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)) | c3_1(a145) | c0_1(a145) | c2_1(a145))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | c2_1(a149) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a149)) | c0_1(a149)))),
% 0.98/0.92 inference(monotonicity,[status(thm)],[1443])).
% 0.98/0.92 tff(1445,plain,
% 0.98/0.92 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)) | c3_1(a145) | c0_1(a145) | c2_1(a145))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c2_1(a149) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a149)) | c0_1(a149))),
% 0.98/0.92 inference(transitivity,[status(thm)],[1444, 1442])).
% 0.98/0.92 tff(1446,plain,
% 0.98/0.92 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)) | c3_1(a145) | c0_1(a145) | c2_1(a145))),
% 0.98/0.92 inference(quant_inst,[status(thm)],[])).
% 0.98/0.92 tff(1447,plain,
% 0.98/0.92 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c2_1(a149) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a149)) | c0_1(a149)),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[1446, 1445])).
% 0.98/0.92 tff(1448,plain,
% 0.98/0.92 (hskp27),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[1447, 187, 648, 634, 1413, 1404, 1203, 1403, 1412])).
% 0.98/0.92 tff(1449,plain,
% 0.98/0.92 (c3_1(a137)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[1221, 1448])).
% 0.98/0.92 tff(1450,plain,
% 0.98/0.92 (c2_1(a137)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[1232, 1448])).
% 0.98/0.92 tff(1451,plain,
% 0.98/0.92 (c1_1(a137)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[1243, 1448])).
% 0.98/0.92 tff(1452,plain,
% 0.98/0.92 ($false),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[1250, 187, 1451, 1450, 1449, 1441, 1405, 1404, 1440, 1439, 1176, 1412])).
% 0.98/0.92 tff(1453,plain,(c0_1(a149) | c1_1(a145) | c3_1(a145) | hskp3 | (~c3_1(a149)) | c2_1(a149) | c0_1(a145)), inference(lemma,lemma(discharge,[]))).
% 0.98/0.92 tff(1454,plain,
% 0.98/0.92 (c0_1(a149)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[1453, 1402, 1401, 52, 1384, 1382, 1400])).
% 0.98/0.92 tff(1455,plain,
% 0.98/0.92 (hskp16),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[1393, 1454, 53])).
% 0.98/0.92 tff(1456,plain,
% 0.98/0.92 (~c2_1(a151)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[200, 1455])).
% 0.98/0.92 tff(1457,plain,
% 0.98/0.92 (c1_1(a151)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[211, 1455])).
% 0.98/0.92 tff(1458,plain,
% 0.98/0.92 (c3_1(a151)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[218, 187, 53, 95, 1457, 1456, 134])).
% 0.98/0.92 tff(1459,plain,
% 0.98/0.92 (^[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))))),
% 0.98/0.92 inference(bind,[status(th)],[])).
% 0.98/0.92 tff(1460,plain,
% 0.98/0.92 (![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)))),
% 0.98/0.92 inference(quant_intro,[status(thm)],[1459])).
% 0.98/0.92 tff(1461,plain,
% 0.98/0.92 (![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)))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(1462,plain,
% 0.98/0.92 (^[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))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c2_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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_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)))))),
% 0.98/0.92 inference(bind,[status(th)],[])).
% 0.98/0.92 tff(1463,plain,
% 0.98/0.92 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_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)))),
% 0.98/0.92 inference(quant_intro,[status(thm)],[1462])).
% 0.98/0.92 tff(1464,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause183')).
% 0.98/0.92 tff(1465,plain,
% 0.98/0.92 (![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)))),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[1464, 1463])).
% 0.98/0.92 tff(1466,plain,
% 0.98/0.92 (![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)))),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[1465, 1461])).
% 0.98/0.92 tff(1467,plain,(
% 0.98/0.92 ![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)))),
% 0.98/0.92 inference(skolemize,[status(sab)],[1466])).
% 0.98/0.92 tff(1468,plain,
% 0.98/0.92 (![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)))),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[1467, 1460])).
% 0.98/0.92 tff(1469,plain,
% 0.98/0.92 (^[U: $i] : refl((hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))),
% 0.98/0.92 inference(bind,[status(th)],[])).
% 0.98/0.92 tff(1470,plain,
% 0.98/0.92 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.98/0.92 inference(quant_intro,[status(thm)],[1469])).
% 0.98/0.92 tff(1471,plain,
% 0.98/0.92 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(1472,plain,
% 0.98/0.92 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp10) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp10))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp10) <=> (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp10) <=> (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp10) | hskp11) <=> ((hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp11))), rewrite(((hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp11) <=> (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp10) | hskp11) <=> (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))))),
% 0.98/0.92 inference(bind,[status(th)],[])).
% 0.98/0.92 tff(1473,plain,
% 0.98/0.92 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp10) | hskp11) <=> ![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.98/0.92 inference(quant_intro,[status(thm)],[1472])).
% 0.98/0.92 tff(1474,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp10) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause135')).
% 0.98/0.92 tff(1475,plain,
% 0.98/0.92 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[1474, 1473])).
% 0.98/0.92 tff(1476,plain,
% 0.98/0.92 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[1475, 1471])).
% 0.98/0.92 tff(1477,plain,(
% 0.98/0.92 ![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.98/0.92 inference(skolemize,[status(sab)],[1476])).
% 0.98/0.92 tff(1478,plain,
% 0.98/0.92 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[1477, 1470])).
% 0.98/0.92 tff(1479,plain,
% 0.98/0.92 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp22 | c2_1(a149) | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | (~c1_1(a199)) | (~c3_1(a149)) | (~c0_1(a149)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp22 | c2_1(a149) | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | (~c1_1(a199)) | (~c3_1(a149)) | (~c0_1(a149)))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(1480,plain,
% 0.98/0.92 ((hskp22 | (~ndr1_0) | (~c2_1(a199)) | (~c1_1(a199)) | (~c0_1(a199)) | c2_1(a149) | (~c3_1(a149)) | (~c0_1(a149))) <=> (hskp22 | c2_1(a149) | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | (~c1_1(a199)) | (~c3_1(a149)) | (~c0_1(a149)))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(1481,plain,
% 0.98/0.92 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | (~c2_1(a199)) | (~c1_1(a199)) | (~c0_1(a199)) | c2_1(a149) | (~c3_1(a149)) | (~c0_1(a149)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp22 | c2_1(a149) | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | (~c1_1(a199)) | (~c3_1(a149)) | (~c0_1(a149))))),
% 0.98/0.92 inference(monotonicity,[status(thm)],[1480])).
% 0.98/0.92 tff(1482,plain,
% 0.98/0.92 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | (~c2_1(a199)) | (~c1_1(a199)) | (~c0_1(a199)) | c2_1(a149) | (~c3_1(a149)) | (~c0_1(a149)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp22 | c2_1(a149) | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | (~c1_1(a199)) | (~c3_1(a149)) | (~c0_1(a149)))),
% 0.98/0.92 inference(transitivity,[status(thm)],[1481, 1479])).
% 0.98/0.92 tff(1483,plain,
% 0.98/0.92 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | (~c2_1(a199)) | (~c1_1(a199)) | (~c0_1(a199)) | c2_1(a149) | (~c3_1(a149)) | (~c0_1(a149)))),
% 0.98/0.92 inference(quant_inst,[status(thm)],[])).
% 0.98/0.92 tff(1484,plain,
% 0.98/0.92 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp22 | c2_1(a149) | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | (~c1_1(a199)) | (~c3_1(a149)) | (~c0_1(a149))),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[1483, 1482])).
% 0.98/0.92 tff(1485,plain,
% 0.98/0.92 (hskp22 | (~c0_1(a149))),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[1484, 187, 1300, 1289, 1278, 1384, 1382, 1042])).
% 0.98/0.92 tff(1486,plain,
% 0.98/0.92 (hskp22),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[1485, 1454])).
% 0.98/0.92 tff(1487,plain,
% 0.98/0.92 (~c1_1(a179)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[1055, 1486])).
% 0.98/0.92 tff(1488,plain,
% 0.98/0.92 (c2_1(a179)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[1066, 1486])).
% 0.98/0.92 tff(1489,plain,
% 0.98/0.92 (c0_1(a179)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[1077, 1486])).
% 0.98/0.92 tff(1490,plain,
% 0.98/0.92 (hskp20 | (~c3_1(a151))),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[1084, 187, 1489, 1488, 1457, 1487, 1456, 921])).
% 0.98/0.92 tff(1491,plain,
% 0.98/0.92 (hskp20),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[1490, 1458])).
% 0.98/0.92 tff(1492,plain,
% 0.98/0.92 (~c2_1(a168)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[933, 1491])).
% 0.98/0.92 tff(1493,plain,
% 0.98/0.92 (~c0_1(a168)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[957, 1491])).
% 0.98/0.92 tff(1494,plain,
% 0.98/0.92 (c1_1(a168)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[944, 1491])).
% 0.98/0.92 tff(1495,plain,
% 0.98/0.92 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | c0_1(a168) | c2_1(a168) | (~ndr1_0) | (~c1_1(a168)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp11 | hskp10 | c0_1(a168) | c2_1(a168) | (~ndr1_0) | (~c1_1(a168)))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(1496,plain,
% 0.98/0.92 ((hskp11 | hskp10 | (~ndr1_0) | c0_1(a168) | c2_1(a168) | (~c1_1(a168))) <=> (hskp11 | hskp10 | c0_1(a168) | c2_1(a168) | (~ndr1_0) | (~c1_1(a168)))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(1497,plain,
% 0.98/0.92 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c0_1(a168) | c2_1(a168) | (~c1_1(a168)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | c0_1(a168) | c2_1(a168) | (~ndr1_0) | (~c1_1(a168))))),
% 0.98/0.92 inference(monotonicity,[status(thm)],[1496])).
% 0.98/0.92 tff(1498,plain,
% 0.98/0.92 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c0_1(a168) | c2_1(a168) | (~c1_1(a168)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp11 | hskp10 | c0_1(a168) | c2_1(a168) | (~ndr1_0) | (~c1_1(a168)))),
% 0.98/0.92 inference(transitivity,[status(thm)],[1497, 1495])).
% 0.98/0.92 tff(1499,plain,
% 0.98/0.92 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c0_1(a168) | c2_1(a168) | (~c1_1(a168)))),
% 0.98/0.92 inference(quant_inst,[status(thm)],[])).
% 0.98/0.92 tff(1500,plain,
% 0.98/0.92 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp11 | hskp10 | c0_1(a168) | c2_1(a168) | (~ndr1_0) | (~c1_1(a168))),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[1499, 1498])).
% 0.98/0.92 tff(1501,plain,
% 0.98/0.92 (hskp11),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[1500, 187, 1266, 1494, 1493, 1492, 1478])).
% 0.98/0.92 tff(1502,plain,
% 0.98/0.92 (((~hskp11) | (~c3_1(a139))) <=> ((~hskp11) | (~c3_1(a139)))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(1503,plain,
% 0.98/0.92 (((~c3_1(a139)) | (~hskp11)) <=> ((~hskp11) | (~c3_1(a139)))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(1504,axiom,((~c3_1(a139)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause112')).
% 0.98/0.92 tff(1505,plain,
% 0.98/0.92 ((~hskp11) | (~c3_1(a139))),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[1504, 1503])).
% 0.98/0.92 tff(1506,plain,
% 0.98/0.92 ((~hskp11) | (~c3_1(a139))),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[1505, 1502])).
% 0.98/0.92 tff(1507,plain,
% 0.98/0.92 (~c3_1(a139)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[1506, 1501])).
% 0.98/0.92 tff(1508,plain,
% 0.98/0.92 (((~hskp11) | (~c1_1(a139))) <=> ((~hskp11) | (~c1_1(a139)))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(1509,plain,
% 0.98/0.92 (((~c1_1(a139)) | (~hskp11)) <=> ((~hskp11) | (~c1_1(a139)))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(1510,axiom,((~c1_1(a139)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause111')).
% 0.98/0.92 tff(1511,plain,
% 0.98/0.92 ((~hskp11) | (~c1_1(a139))),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[1510, 1509])).
% 0.98/0.92 tff(1512,plain,
% 0.98/0.92 ((~hskp11) | (~c1_1(a139))),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[1511, 1508])).
% 0.98/0.92 tff(1513,plain,
% 0.98/0.92 (~c1_1(a139)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[1512, 1501])).
% 0.98/0.92 tff(1514,plain,
% 0.98/0.92 (((~hskp11) | c0_1(a139)) <=> ((~hskp11) | c0_1(a139))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(1515,axiom,((~hskp11) | c0_1(a139)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause67')).
% 0.98/0.92 tff(1516,plain,
% 0.98/0.92 ((~hskp11) | c0_1(a139)),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[1515, 1514])).
% 0.98/0.92 tff(1517,plain,
% 0.98/0.92 ((~hskp11) | c0_1(a139)),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[1516, 1514])).
% 0.98/0.92 tff(1518,plain,
% 0.98/0.92 ((~hskp11) | c0_1(a139)),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[1517, 1514])).
% 0.98/0.92 tff(1519,plain,
% 0.98/0.92 ((~hskp11) | c0_1(a139)),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[1518, 1514])).
% 0.98/0.92 tff(1520,plain,
% 0.98/0.92 ((~hskp11) | c0_1(a139)),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[1519, 1514])).
% 0.98/0.92 tff(1521,plain,
% 0.98/0.92 ((~hskp11) | c0_1(a139)),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[1520, 1514])).
% 0.98/0.92 tff(1522,plain,
% 0.98/0.92 ((~hskp11) | c0_1(a139)),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[1521, 1514])).
% 0.98/0.92 tff(1523,plain,
% 0.98/0.92 ((~hskp11) | c0_1(a139)),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[1522, 1514])).
% 0.98/0.92 tff(1524,plain,
% 0.98/0.92 (c0_1(a139)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[1523, 1501])).
% 0.98/0.92 tff(1525,plain,
% 0.98/0.92 (c0_1(a151)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[249, 1455])).
% 0.98/0.92 tff(1526,plain,
% 0.98/0.92 (c3_1(a168)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[951, 187, 53, 95, 1494, 1492, 134])).
% 0.98/0.92 tff(1527,plain,
% 0.98/0.92 ((~c2_1(a145)) | (~c3_1(a168))),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[1096, 187, 52, 1493, 1492, 1402, 1401, 41])).
% 0.98/0.92 tff(1528,plain,
% 0.98/0.92 (~c2_1(a145)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[1527, 1526])).
% 0.98/0.92 tff(1529,plain,
% 0.98/0.92 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | c0_1(a168) | c2_1(a168) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a168)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c0_1(a168) | c2_1(a168) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a168)))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(1530,plain,
% 0.98/0.92 ((hskp27 | (~ndr1_0) | c0_1(a168) | c2_1(a168) | (~c3_1(a168)) | c3_1(a145) | c0_1(a145) | c2_1(a145)) <=> (hskp27 | c0_1(a168) | c2_1(a168) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a168)))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(1531,plain,
% 0.98/0.92 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a168) | c2_1(a168) | (~c3_1(a168)) | c3_1(a145) | c0_1(a145) | c2_1(a145))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | c0_1(a168) | c2_1(a168) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a168))))),
% 0.98/0.92 inference(monotonicity,[status(thm)],[1530])).
% 0.98/0.92 tff(1532,plain,
% 0.98/0.92 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a168) | c2_1(a168) | (~c3_1(a168)) | c3_1(a145) | c0_1(a145) | c2_1(a145))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c0_1(a168) | c2_1(a168) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a168)))),
% 0.98/0.92 inference(transitivity,[status(thm)],[1531, 1529])).
% 0.98/0.92 tff(1533,plain,
% 0.98/0.92 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a168) | c2_1(a168) | (~c3_1(a168)) | c3_1(a145) | c0_1(a145) | c2_1(a145))),
% 0.98/0.92 inference(quant_inst,[status(thm)],[])).
% 0.98/0.92 tff(1534,plain,
% 0.98/0.92 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c0_1(a168) | c2_1(a168) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a168))),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[1533, 1532])).
% 0.98/0.92 tff(1535,plain,
% 0.98/0.92 (hskp27 | c2_1(a145) | (~c3_1(a168))),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[1534, 187, 1493, 1492, 1400, 1401, 1203])).
% 0.98/0.92 tff(1536,plain,
% 0.98/0.92 (hskp27),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[1535, 1528, 1526])).
% 0.98/0.92 tff(1537,plain,
% 0.98/0.92 (c3_1(a137)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[1221, 1536])).
% 0.98/0.92 tff(1538,plain,
% 0.98/0.92 (c2_1(a137)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[1232, 1536])).
% 0.98/0.92 tff(1539,plain,
% 0.98/0.92 (c1_1(a137)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[1243, 1536])).
% 0.98/0.92 tff(1540,plain,
% 0.98/0.92 (((~![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(a151) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c0_1(a139)) | (~c3_1(a151)) | (~c0_1(a151)))) <=> ((~![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(a151) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c0_1(a139)) | (~c3_1(a151)) | (~c0_1(a151)))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(1541,plain,
% 0.98/0.92 (((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a151) | (~c3_1(a151)) | (~c0_1(a151)) | c1_1(a139) | c3_1(a139) | (~c0_1(a139))) <=> (c2_1(a151) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c0_1(a139)) | (~c3_1(a151)) | (~c0_1(a151)))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(1542,plain,
% 0.98/0.92 (((~![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(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a151) | (~c3_1(a151)) | (~c0_1(a151)) | c1_1(a139) | c3_1(a139) | (~c0_1(a139)))) <=> ((~![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(a151) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c0_1(a139)) | (~c3_1(a151)) | (~c0_1(a151))))),
% 0.98/0.92 inference(monotonicity,[status(thm)],[1541])).
% 0.98/0.92 tff(1543,plain,
% 0.98/0.92 (((~![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(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a151) | (~c3_1(a151)) | (~c0_1(a151)) | c1_1(a139) | c3_1(a139) | (~c0_1(a139)))) <=> ((~![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(a151) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c0_1(a139)) | (~c3_1(a151)) | (~c0_1(a151)))),
% 0.98/0.92 inference(transitivity,[status(thm)],[1542, 1540])).
% 0.98/0.92 tff(1544,plain,
% 0.98/0.92 ((~![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(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a151) | (~c3_1(a151)) | (~c0_1(a151)) | c1_1(a139) | c3_1(a139) | (~c0_1(a139)))),
% 0.98/0.92 inference(quant_inst,[status(thm)],[])).
% 0.98/0.92 tff(1545,plain,
% 0.98/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a151) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c0_1(a139)) | (~c3_1(a151)) | (~c0_1(a151))),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[1544, 1543])).
% 0.98/0.92 tff(1546,plain,
% 0.98/0.92 ($false),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[1545, 187, 1539, 1538, 1537, 1525, 1524, 1456, 1513, 1507, 1468, 1458])).
% 0.98/0.92 tff(1547,plain,(hskp21 | hskp3 | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.98/0.92 tff(1548,plain,
% 0.98/0.92 (hskp21),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[1547, 52, 95])).
% 0.98/0.92 tff(1549,plain,
% 0.98/0.92 (~c2_1(a170)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[312, 1548])).
% 0.98/0.92 tff(1550,plain,
% 0.98/0.92 (~c0_1(a170)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[318, 1548])).
% 0.98/0.92 tff(1551,plain,
% 0.98/0.92 (c3_1(a170)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[346, 1548])).
% 0.98/0.92 tff(1552,plain,
% 0.98/0.92 (hskp14),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[515, 187, 52, 1551, 1550, 1549, 51])).
% 0.98/0.92 tff(1553,plain,
% 0.98/0.92 (~c0_1(a145)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[541, 1552])).
% 0.98/0.92 tff(1554,plain,
% 0.98/0.92 (~c3_1(a145)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[522, 1552])).
% 0.98/0.92 tff(1555,plain,
% 0.98/0.92 (~c1_1(a145)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[528, 1552])).
% 0.98/0.92 tff(1556,plain,
% 0.98/0.92 (c0_1(a149)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[1453, 1555, 1554, 52, 1384, 1382, 1553])).
% 0.98/0.92 tff(1557,plain,
% 0.98/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a170) | c2_1(a170) | c1_1(a149) | c2_1(a149) | c0_1(a145) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c0_1(a149)) | c1_1(a170))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a170) | c2_1(a170) | c1_1(a149) | c2_1(a149) | c0_1(a145) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c0_1(a149)) | c1_1(a170))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(1558,plain,
% 0.98/0.92 (((~ndr1_0) | c1_1(a149) | c2_1(a149) | (~c0_1(a149)) | c3_1(a145) | c1_1(a145) | c0_1(a145) | c2_1(a170) | c1_1(a170) | c0_1(a170)) <=> (c0_1(a170) | c2_1(a170) | c1_1(a149) | c2_1(a149) | c0_1(a145) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c0_1(a149)) | c1_1(a170))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(1559,plain,
% 0.98/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | c2_1(a149) | (~c0_1(a149)) | c3_1(a145) | c1_1(a145) | c0_1(a145) | c2_1(a170) | c1_1(a170) | c0_1(a170))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a170) | c2_1(a170) | c1_1(a149) | c2_1(a149) | c0_1(a145) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c0_1(a149)) | c1_1(a170)))),
% 0.98/0.92 inference(monotonicity,[status(thm)],[1558])).
% 0.98/0.92 tff(1560,plain,
% 0.98/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | c2_1(a149) | (~c0_1(a149)) | c3_1(a145) | c1_1(a145) | c0_1(a145) | c2_1(a170) | c1_1(a170) | c0_1(a170))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a170) | c2_1(a170) | c1_1(a149) | c2_1(a149) | c0_1(a145) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c0_1(a149)) | c1_1(a170))),
% 0.98/0.92 inference(transitivity,[status(thm)],[1559, 1557])).
% 0.98/0.92 tff(1561,plain,
% 0.98/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | c2_1(a149) | (~c0_1(a149)) | c3_1(a145) | c1_1(a145) | c0_1(a145) | c2_1(a170) | c1_1(a170) | c0_1(a170))),
% 0.98/0.92 inference(quant_inst,[status(thm)],[])).
% 0.98/0.92 tff(1562,plain,
% 0.98/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a170) | c2_1(a170) | c1_1(a149) | c2_1(a149) | c0_1(a145) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c0_1(a149)) | c1_1(a170)),
% 1.02/0.93 inference(modus_ponens,[status(thm)],[1561, 1560])).
% 1.02/0.93 tff(1563,plain,
% 1.02/0.93 (c1_1(a170)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1562, 187, 1550, 1549, 1383, 1382, 1553, 1555, 1554, 493, 1556])).
% 1.02/0.93 tff(1564,plain,
% 1.02/0.93 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | c0_1(a170) | c2_1(a170) | (~ndr1_0) | (~c1_1(a170)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp11 | hskp10 | c0_1(a170) | c2_1(a170) | (~ndr1_0) | (~c1_1(a170)))),
% 1.02/0.93 inference(rewrite,[status(thm)],[])).
% 1.02/0.93 tff(1565,plain,
% 1.02/0.93 ((hskp11 | hskp10 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c1_1(a170))) <=> (hskp11 | hskp10 | c0_1(a170) | c2_1(a170) | (~ndr1_0) | (~c1_1(a170)))),
% 1.02/0.93 inference(rewrite,[status(thm)],[])).
% 1.02/0.93 tff(1566,plain,
% 1.02/0.93 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c1_1(a170)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | c0_1(a170) | c2_1(a170) | (~ndr1_0) | (~c1_1(a170))))),
% 1.02/0.93 inference(monotonicity,[status(thm)],[1565])).
% 1.02/0.93 tff(1567,plain,
% 1.02/0.93 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c1_1(a170)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp11 | hskp10 | c0_1(a170) | c2_1(a170) | (~ndr1_0) | (~c1_1(a170)))),
% 1.02/0.93 inference(transitivity,[status(thm)],[1566, 1564])).
% 1.02/0.93 tff(1568,plain,
% 1.02/0.93 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c1_1(a170)))),
% 1.02/0.93 inference(quant_inst,[status(thm)],[])).
% 1.02/0.93 tff(1569,plain,
% 1.02/0.93 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp11 | hskp10 | c0_1(a170) | c2_1(a170) | (~ndr1_0) | (~c1_1(a170))),
% 1.02/0.93 inference(modus_ponens,[status(thm)],[1568, 1567])).
% 1.02/0.93 tff(1570,plain,
% 1.02/0.93 (hskp11 | (~c1_1(a170))),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1569, 187, 1266, 1550, 1549, 1478])).
% 1.02/0.93 tff(1571,plain,
% 1.02/0.93 (hskp11),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1570, 1563])).
% 1.02/0.93 tff(1572,plain,
% 1.02/0.93 (~c3_1(a139)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1506, 1571])).
% 1.02/0.93 tff(1573,plain,
% 1.02/0.93 (~c1_1(a139)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1512, 1571])).
% 1.02/0.93 tff(1574,plain,
% 1.02/0.93 (c0_1(a139)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1523, 1571])).
% 1.02/0.93 tff(1575,plain,
% 1.02/0.93 (~c2_1(a145)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[535, 187, 52, 1551, 1550, 1549, 1555, 1554, 41])).
% 1.02/0.93 tff(1576,plain,
% 1.02/0.93 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | c0_1(a170) | c2_1(a170) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a170)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c0_1(a170) | c2_1(a170) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a170)))),
% 1.02/0.93 inference(rewrite,[status(thm)],[])).
% 1.02/0.93 tff(1577,plain,
% 1.02/0.93 ((hskp27 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c3_1(a170)) | c3_1(a145) | c0_1(a145) | c2_1(a145)) <=> (hskp27 | c0_1(a170) | c2_1(a170) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a170)))),
% 1.02/0.93 inference(rewrite,[status(thm)],[])).
% 1.02/0.93 tff(1578,plain,
% 1.02/0.93 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c3_1(a170)) | c3_1(a145) | c0_1(a145) | c2_1(a145))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | c0_1(a170) | c2_1(a170) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a170))))),
% 1.02/0.93 inference(monotonicity,[status(thm)],[1577])).
% 1.02/0.93 tff(1579,plain,
% 1.02/0.93 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c3_1(a170)) | c3_1(a145) | c0_1(a145) | c2_1(a145))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c0_1(a170) | c2_1(a170) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a170)))),
% 1.02/0.93 inference(transitivity,[status(thm)],[1578, 1576])).
% 1.02/0.93 tff(1580,plain,
% 1.02/0.93 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c3_1(a170)) | c3_1(a145) | c0_1(a145) | c2_1(a145))),
% 1.02/0.93 inference(quant_inst,[status(thm)],[])).
% 1.02/0.93 tff(1581,plain,
% 1.02/0.93 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c0_1(a170) | c2_1(a170) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a170))),
% 1.02/0.93 inference(modus_ponens,[status(thm)],[1580, 1579])).
% 1.02/0.93 tff(1582,plain,
% 1.02/0.93 (hskp27),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1581, 187, 1551, 1550, 1549, 1553, 1554, 1203, 1575])).
% 1.02/0.93 tff(1583,plain,
% 1.02/0.93 (c3_1(a137)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1221, 1582])).
% 1.02/0.93 tff(1584,plain,
% 1.02/0.93 (c2_1(a137)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1232, 1582])).
% 1.02/0.93 tff(1585,plain,
% 1.02/0.93 (c1_1(a137)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1243, 1582])).
% 1.02/0.93 tff(1586,plain,
% 1.02/0.93 (((~![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(a149) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c0_1(a139)) | (~c3_1(a149)) | (~c0_1(a149)))) <=> ((~![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(a149) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c0_1(a139)) | (~c3_1(a149)) | (~c0_1(a149)))),
% 1.02/0.93 inference(rewrite,[status(thm)],[])).
% 1.02/0.93 tff(1587,plain,
% 1.02/0.93 (((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c1_1(a139) | c3_1(a139) | (~c0_1(a139))) <=> (c2_1(a149) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c0_1(a139)) | (~c3_1(a149)) | (~c0_1(a149)))),
% 1.02/0.93 inference(rewrite,[status(thm)],[])).
% 1.02/0.93 tff(1588,plain,
% 1.02/0.93 (((~![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(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c1_1(a139) | c3_1(a139) | (~c0_1(a139)))) <=> ((~![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(a149) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c0_1(a139)) | (~c3_1(a149)) | (~c0_1(a149))))),
% 1.02/0.93 inference(monotonicity,[status(thm)],[1587])).
% 1.02/0.93 tff(1589,plain,
% 1.02/0.93 (((~![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(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c1_1(a139) | c3_1(a139) | (~c0_1(a139)))) <=> ((~![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(a149) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c0_1(a139)) | (~c3_1(a149)) | (~c0_1(a149)))),
% 1.02/0.93 inference(transitivity,[status(thm)],[1588, 1586])).
% 1.02/0.93 tff(1590,plain,
% 1.02/0.93 ((~![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(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c1_1(a139) | c3_1(a139) | (~c0_1(a139)))),
% 1.02/0.93 inference(quant_inst,[status(thm)],[])).
% 1.02/0.93 tff(1591,plain,
% 1.02/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a149) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c0_1(a139)) | (~c3_1(a149)) | (~c0_1(a149))),
% 1.02/0.93 inference(modus_ponens,[status(thm)],[1590, 1589])).
% 1.02/0.93 tff(1592,plain,
% 1.02/0.93 ($false),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1591, 187, 1585, 1584, 1583, 1384, 1574, 1382, 1573, 1572, 1468, 1556])).
% 1.02/0.93 tff(1593,plain,(hskp3 | hskp18), inference(lemma,lemma(discharge,[]))).
% 1.02/0.93 tff(1594,plain,
% 1.02/0.93 (hskp3),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1593, 95])).
% 1.02/0.93 tff(1595,plain,
% 1.02/0.93 (~c0_1(a128)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[508, 1594])).
% 1.02/0.93 tff(1596,plain,
% 1.02/0.93 (~c2_1(a128)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[583, 1594])).
% 1.02/0.93 tff(1597,plain,
% 1.02/0.93 (~c3_1(a128)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1115, 1594])).
% 1.02/0.93 tff(1598,assumption,(~c3_1(a199)), introduced(assumption)).
% 1.02/0.93 tff(1599,plain,
% 1.02/0.93 (hskp13),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1328, 187, 1312, 1311, 1322, 21, 1598])).
% 1.02/0.93 tff(1600,plain,
% 1.02/0.93 (~c3_1(a144)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[991, 1599])).
% 1.02/0.93 tff(1601,plain,
% 1.02/0.93 (~c0_1(a144)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1015, 1599])).
% 1.02/0.93 tff(1602,plain,
% 1.02/0.93 (c2_1(a144)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1002, 1599])).
% 1.02/0.93 tff(1603,assumption,(~c3_1(a144)), introduced(assumption)).
% 1.02/0.93 tff(1604,assumption,(~c0_1(a144)), introduced(assumption)).
% 1.02/0.93 tff(1605,assumption,(c2_1(a144)), introduced(assumption)).
% 1.02/0.93 tff(1606,assumption,(hskp27), introduced(assumption)).
% 1.02/0.93 tff(1607,plain,
% 1.02/0.93 (c3_1(a137)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1221, 1606])).
% 1.02/0.93 tff(1608,plain,
% 1.02/0.93 (c2_1(a137)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1232, 1606])).
% 1.02/0.93 tff(1609,plain,
% 1.02/0.93 (c1_1(a137)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1243, 1606])).
% 1.02/0.93 tff(1610,plain,
% 1.02/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c0_1(a144) | c3_1(a144) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c1_1(a128) | (~c2_1(a144)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c0_1(a144) | c3_1(a144) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c1_1(a128) | (~c2_1(a144)))),
% 1.02/0.93 inference(rewrite,[status(thm)],[])).
% 1.02/0.93 tff(1611,plain,
% 1.02/0.93 (((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a128) | c1_1(a128) | c3_1(a128)) <=> (c0_1(a144) | c3_1(a144) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c1_1(a128) | (~c2_1(a144)))),
% 1.02/0.93 inference(rewrite,[status(thm)],[])).
% 1.02/0.93 tff(1612,plain,
% 1.02/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a128) | c1_1(a128) | c3_1(a128))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c0_1(a144) | c3_1(a144) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c1_1(a128) | (~c2_1(a144))))),
% 1.02/0.93 inference(monotonicity,[status(thm)],[1611])).
% 1.02/0.93 tff(1613,plain,
% 1.02/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a128) | c1_1(a128) | c3_1(a128))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c0_1(a144) | c3_1(a144) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c1_1(a128) | (~c2_1(a144)))),
% 1.02/0.93 inference(transitivity,[status(thm)],[1612, 1610])).
% 1.02/0.93 tff(1614,plain,
% 1.02/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a128) | c1_1(a128) | c3_1(a128))),
% 1.02/0.93 inference(quant_inst,[status(thm)],[])).
% 1.02/0.93 tff(1615,plain,
% 1.02/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c0_1(a144) | c3_1(a144) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c1_1(a128) | (~c2_1(a144))),
% 1.02/0.93 inference(modus_ponens,[status(thm)],[1614, 1613])).
% 1.02/0.93 tff(1616,plain,
% 1.02/0.93 ($false),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1615, 187, 1609, 1608, 1607, 1605, 1604, 1603, 280, 269, 1176, 567])).
% 1.02/0.93 tff(1617,plain,((~hskp27) | (~c2_1(a144)) | c0_1(a144) | c3_1(a144) | c2_1(a128) | c3_1(a128) | c1_1(a128)), inference(lemma,lemma(discharge,[]))).
% 1.02/0.93 tff(1618,plain,
% 1.02/0.93 (~hskp27),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1617, 1602, 1601, 1600, 280, 269, 567])).
% 1.02/0.93 tff(1619,plain,
% 1.02/0.93 (((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | (~c0_1(a199)) | c3_1(a199) | (~c1_1(a199)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp12 | (~ndr1_0) | (~c0_1(a199)) | c3_1(a199) | (~c1_1(a199)))),
% 1.02/0.93 inference(rewrite,[status(thm)],[])).
% 1.02/0.93 tff(1620,plain,
% 1.02/0.93 ((hskp12 | (~ndr1_0) | c3_1(a199) | (~c1_1(a199)) | (~c0_1(a199))) <=> (hskp12 | (~ndr1_0) | (~c0_1(a199)) | c3_1(a199) | (~c1_1(a199)))),
% 1.02/0.93 inference(rewrite,[status(thm)],[])).
% 1.02/0.93 tff(1621,plain,
% 1.02/0.93 (((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | c3_1(a199) | (~c1_1(a199)) | (~c0_1(a199)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | (~c0_1(a199)) | c3_1(a199) | (~c1_1(a199))))),
% 1.02/0.93 inference(monotonicity,[status(thm)],[1620])).
% 1.02/0.93 tff(1622,plain,
% 1.02/0.93 (((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | c3_1(a199) | (~c1_1(a199)) | (~c0_1(a199)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp12 | (~ndr1_0) | (~c0_1(a199)) | c3_1(a199) | (~c1_1(a199)))),
% 1.02/0.93 inference(transitivity,[status(thm)],[1621, 1619])).
% 1.02/0.93 tff(1623,plain,
% 1.02/0.93 ((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | c3_1(a199) | (~c1_1(a199)) | (~c0_1(a199)))),
% 1.02/0.93 inference(quant_inst,[status(thm)],[])).
% 1.02/0.93 tff(1624,plain,
% 1.02/0.93 ((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp12 | (~ndr1_0) | (~c0_1(a199)) | c3_1(a199) | (~c1_1(a199))),
% 1.02/0.93 inference(modus_ponens,[status(thm)],[1623, 1622])).
% 1.02/0.93 tff(1625,plain,
% 1.02/0.93 (hskp12 | c3_1(a199)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1624, 187, 1312, 1311, 239])).
% 1.02/0.93 tff(1626,plain,
% 1.02/0.93 (hskp12),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1625, 1598])).
% 1.02/0.93 tff(1627,plain,
% 1.02/0.93 (~c0_1(a140)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[632, 1626])).
% 1.02/0.93 tff(1628,plain,
% 1.02/0.93 (c3_1(a140)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[646, 1626])).
% 1.02/0.93 tff(1629,plain,
% 1.02/0.93 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | c0_1(a140) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c0_1(a140) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)))),
% 1.02/0.93 inference(rewrite,[status(thm)],[])).
% 1.02/0.93 tff(1630,plain,
% 1.02/0.93 ((hskp27 | (~ndr1_0) | c0_1(a140) | c2_1(a140) | (~c3_1(a140)) | c3_1(a128) | c0_1(a128) | c2_1(a128)) <=> (hskp27 | c0_1(a140) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)))),
% 1.02/0.93 inference(rewrite,[status(thm)],[])).
% 1.02/0.93 tff(1631,plain,
% 1.02/0.93 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a140) | c2_1(a140) | (~c3_1(a140)) | c3_1(a128) | c0_1(a128) | c2_1(a128))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | c0_1(a140) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140))))),
% 1.02/0.93 inference(monotonicity,[status(thm)],[1630])).
% 1.02/0.93 tff(1632,plain,
% 1.02/0.93 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a140) | c2_1(a140) | (~c3_1(a140)) | c3_1(a128) | c0_1(a128) | c2_1(a128))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c0_1(a140) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)))),
% 1.02/0.93 inference(transitivity,[status(thm)],[1631, 1629])).
% 1.02/0.93 tff(1633,plain,
% 1.02/0.93 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a140) | c2_1(a140) | (~c3_1(a140)) | c3_1(a128) | c0_1(a128) | c2_1(a128))),
% 1.02/0.93 inference(quant_inst,[status(thm)],[])).
% 1.02/0.93 tff(1634,plain,
% 1.02/0.93 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c0_1(a140) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140))),
% 1.02/0.93 inference(modus_ponens,[status(thm)],[1633, 1632])).
% 1.02/0.93 tff(1635,plain,
% 1.02/0.93 (hskp27 | c2_1(a140)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1634, 187, 1628, 1627, 291, 280, 269, 1203])).
% 1.02/0.93 tff(1636,plain,
% 1.02/0.93 (c2_1(a140)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1635, 1618])).
% 1.02/0.93 tff(1637,plain,
% 1.02/0.93 (c1_1(a140)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[861, 1626])).
% 1.02/0.93 tff(1638,plain,
% 1.02/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c0_1(a144) | c3_1(a144) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | (~c2_1(a144)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c0_1(a144) | c3_1(a144) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | (~c2_1(a144)))),
% 1.02/0.93 inference(rewrite,[status(thm)],[])).
% 1.02/0.93 tff(1639,plain,
% 1.02/0.93 (((~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a128) | c1_1(a128) | c3_1(a128)) <=> (c0_1(a144) | c3_1(a144) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | (~c2_1(a144)))),
% 1.02/0.93 inference(rewrite,[status(thm)],[])).
% 1.02/0.93 tff(1640,plain,
% 1.02/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a128) | c1_1(a128) | c3_1(a128))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c0_1(a144) | c3_1(a144) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | (~c2_1(a144))))),
% 1.02/0.93 inference(monotonicity,[status(thm)],[1639])).
% 1.02/0.93 tff(1641,plain,
% 1.02/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a128) | c1_1(a128) | c3_1(a128))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c0_1(a144) | c3_1(a144) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | (~c2_1(a144)))),
% 1.02/0.93 inference(transitivity,[status(thm)],[1640, 1638])).
% 1.02/0.93 tff(1642,plain,
% 1.02/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a128) | c1_1(a128) | c3_1(a128))),
% 1.02/0.93 inference(quant_inst,[status(thm)],[])).
% 1.02/0.93 tff(1643,plain,
% 1.02/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c0_1(a144) | c3_1(a144) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | (~c2_1(a144))),
% 1.02/0.93 inference(modus_ponens,[status(thm)],[1642, 1641])).
% 1.02/0.93 tff(1644,plain,
% 1.02/0.93 ($false),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1643, 187, 1602, 1637, 1628, 1601, 1600, 280, 269, 1176, 567, 1636])).
% 1.02/0.93 tff(1645,plain,(c3_1(a199) | c2_1(a128) | c3_1(a128) | c1_1(a128) | c0_1(a128) | (~c0_1(a199)) | (~c1_1(a199)) | (~c2_1(a199))), inference(lemma,lemma(discharge,[]))).
% 1.02/0.93 tff(1646,plain,
% 1.02/0.93 (c3_1(a199)),
% 1.02/0.93 inference(unit_resolution,[status(thm)],[1645, 567, 1597, 1596, 1595, 1300, 1289, 1278])).
% 1.02/0.93 tff(1647,plain,
% 1.02/0.93 (^[U: $i] : refl((hskp18 | hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp18 | hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))),
% 1.02/0.93 inference(bind,[status(th)],[])).
% 1.02/0.93 tff(1648,plain,
% 1.02/0.93 (![U: $i] : (hskp18 | hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp18 | hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.02/0.93 inference(quant_intro,[status(thm)],[1647])).
% 1.02/0.93 tff(1649,plain,
% 1.02/0.93 (![U: $i] : (hskp18 | hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp18 | hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.02/0.93 inference(rewrite,[status(thm)],[])).
% 1.03/0.93 tff(1650,plain,
% 1.03/0.93 (^[U: $i] : 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)) | hskp18) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp18))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp18) <=> (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp18) <=> (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp18) | hskp12) <=> ((hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp12))), rewrite(((hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp12) <=> (hskp18 | hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp18) | hskp12) <=> (hskp18 | hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))))),
% 1.03/0.93 inference(bind,[status(th)],[])).
% 1.03/0.93 tff(1651,plain,
% 1.03/0.93 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp18) | hskp12) <=> ![U: $i] : (hskp18 | hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.03/0.93 inference(quant_intro,[status(thm)],[1650])).
% 1.03/0.93 tff(1652,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp18) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause158')).
% 1.03/0.93 tff(1653,plain,
% 1.03/0.93 (![U: $i] : (hskp18 | hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.03/0.93 inference(modus_ponens,[status(thm)],[1652, 1651])).
% 1.03/0.93 tff(1654,plain,
% 1.03/0.93 (![U: $i] : (hskp18 | hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.03/0.93 inference(modus_ponens,[status(thm)],[1653, 1649])).
% 1.03/0.93 tff(1655,plain,(
% 1.03/0.93 ![U: $i] : (hskp18 | hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.03/0.93 inference(skolemize,[status(sab)],[1654])).
% 1.03/0.93 tff(1656,plain,
% 1.03/0.93 (![U: $i] : (hskp18 | hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.03/0.93 inference(modus_ponens,[status(thm)],[1655, 1648])).
% 1.03/0.93 tff(1657,plain,
% 1.03/0.93 (((~![U: $i] : (hskp18 | hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp12 | (~ndr1_0) | (~c2_1(a199)) | (~c3_1(a199)) | (~c1_1(a199)))) <=> ((~![U: $i] : (hskp18 | hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp18 | hskp12 | (~ndr1_0) | (~c2_1(a199)) | (~c3_1(a199)) | (~c1_1(a199)))),
% 1.03/0.93 inference(rewrite,[status(thm)],[])).
% 1.03/0.93 tff(1658,plain,
% 1.03/0.93 ((~![U: $i] : (hskp18 | hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp12 | (~ndr1_0) | (~c2_1(a199)) | (~c3_1(a199)) | (~c1_1(a199)))),
% 1.03/0.94 inference(quant_inst,[status(thm)],[])).
% 1.03/0.94 tff(1659,plain,
% 1.03/0.94 ((~![U: $i] : (hskp18 | hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp18 | hskp12 | (~ndr1_0) | (~c2_1(a199)) | (~c3_1(a199)) | (~c1_1(a199))),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1658, 1657])).
% 1.03/0.94 tff(1660,plain,
% 1.03/0.94 (hskp12 | (~c3_1(a199))),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[1659, 187, 95, 1289, 1278, 1656])).
% 1.03/0.94 tff(1661,plain,
% 1.03/0.94 (hskp12),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[1660, 1646])).
% 1.03/0.94 tff(1662,plain,
% 1.03/0.94 (~c0_1(a140)),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[632, 1661])).
% 1.03/0.94 tff(1663,plain,
% 1.03/0.94 (c1_1(a140)),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[861, 1661])).
% 1.03/0.94 tff(1664,plain,
% 1.03/0.94 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | c0_1(a140) | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | (~c3_1(a199)) | (~c2_1(a140)) | (~c1_1(a140)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp18 | c0_1(a140) | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | (~c3_1(a199)) | (~c2_1(a140)) | (~c1_1(a140)))),
% 1.03/0.94 inference(rewrite,[status(thm)],[])).
% 1.03/0.94 tff(1665,plain,
% 1.03/0.94 ((hskp18 | (~ndr1_0) | (~c2_1(a199)) | (~c3_1(a199)) | (~c0_1(a199)) | c0_1(a140) | (~c2_1(a140)) | (~c1_1(a140))) <=> (hskp18 | c0_1(a140) | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | (~c3_1(a199)) | (~c2_1(a140)) | (~c1_1(a140)))),
% 1.03/0.94 inference(rewrite,[status(thm)],[])).
% 1.03/0.94 tff(1666,plain,
% 1.03/0.94 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | (~c2_1(a199)) | (~c3_1(a199)) | (~c0_1(a199)) | c0_1(a140) | (~c2_1(a140)) | (~c1_1(a140)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | c0_1(a140) | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | (~c3_1(a199)) | (~c2_1(a140)) | (~c1_1(a140))))),
% 1.03/0.94 inference(monotonicity,[status(thm)],[1665])).
% 1.03/0.94 tff(1667,plain,
% 1.03/0.94 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | (~c2_1(a199)) | (~c3_1(a199)) | (~c0_1(a199)) | c0_1(a140) | (~c2_1(a140)) | (~c1_1(a140)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp18 | c0_1(a140) | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | (~c3_1(a199)) | (~c2_1(a140)) | (~c1_1(a140)))),
% 1.03/0.94 inference(transitivity,[status(thm)],[1666, 1664])).
% 1.03/0.94 tff(1668,plain,
% 1.03/0.94 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | (~c2_1(a199)) | (~c3_1(a199)) | (~c0_1(a199)) | c0_1(a140) | (~c2_1(a140)) | (~c1_1(a140)))),
% 1.03/0.94 inference(quant_inst,[status(thm)],[])).
% 1.03/0.94 tff(1669,plain,
% 1.03/0.94 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp18 | c0_1(a140) | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | (~c3_1(a199)) | (~c2_1(a140)) | (~c1_1(a140))),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1668, 1667])).
% 1.03/0.94 tff(1670,plain,
% 1.03/0.94 (~c2_1(a140)),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[1669, 187, 95, 1300, 1278, 1663, 1662, 677, 1646])).
% 1.03/0.94 tff(1671,plain,
% 1.03/0.94 (hskp15 | (~c3_1(a199))),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[1319, 187, 1266, 1300, 1289, 1310])).
% 1.03/0.94 tff(1672,plain,
% 1.03/0.94 (hskp15),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[1671, 1646])).
% 1.03/0.94 tff(1673,plain,
% 1.03/0.94 (~c1_1(a149)),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[564, 1672])).
% 1.03/0.94 tff(1674,plain,
% 1.03/0.94 (c3_1(a149)),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[267, 1672])).
% 1.03/0.94 tff(1675,plain,
% 1.03/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a149)) | (~c0_1(a149)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a149)) | (~c0_1(a149)))),
% 1.03/0.94 inference(rewrite,[status(thm)],[])).
% 1.03/0.94 tff(1676,plain,
% 1.03/0.94 (((~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a128) | c1_1(a128) | c0_1(a128)) <=> (c1_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a149)) | (~c0_1(a149)))),
% 1.03/0.94 inference(rewrite,[status(thm)],[])).
% 1.03/0.94 tff(1677,plain,
% 1.03/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a128) | c1_1(a128) | c0_1(a128))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a149)) | (~c0_1(a149))))),
% 1.03/0.94 inference(monotonicity,[status(thm)],[1676])).
% 1.03/0.94 tff(1678,plain,
% 1.03/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a128) | c1_1(a128) | c0_1(a128))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a149)) | (~c0_1(a149)))),
% 1.03/0.94 inference(transitivity,[status(thm)],[1677, 1675])).
% 1.03/0.94 tff(1679,plain,
% 1.03/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a128) | c1_1(a128) | c0_1(a128))),
% 1.03/0.94 inference(quant_inst,[status(thm)],[])).
% 1.03/0.94 tff(1680,plain,
% 1.03/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a149)) | (~c0_1(a149))),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1679, 1678])).
% 1.03/0.94 tff(1681,plain,
% 1.03/0.94 (~c0_1(a149)),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[1680, 187, 1674, 1673, 1595, 1596, 1597, 279, 567])).
% 1.03/0.94 tff(1682,plain,
% 1.03/0.94 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 1.03/0.94 inference(bind,[status(th)],[])).
% 1.03/0.94 tff(1683,plain,
% 1.03/0.94 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.03/0.94 inference(quant_intro,[status(thm)],[1682])).
% 1.03/0.94 tff(1684,plain,
% 1.03/0.94 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.03/0.94 inference(rewrite,[status(thm)],[])).
% 1.03/0.94 tff(1685,plain,
% 1.03/0.94 (^[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)) | 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)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp0) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp0))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 1.03/0.94 inference(bind,[status(th)],[])).
% 1.03/0.94 tff(1686,plain,
% 1.03/0.94 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.03/0.94 inference(quant_intro,[status(thm)],[1685])).
% 1.03/0.94 tff(1687,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause159')).
% 1.03/0.94 tff(1688,plain,
% 1.03/0.94 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1687, 1686])).
% 1.03/0.94 tff(1689,plain,
% 1.03/0.94 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1688, 1684])).
% 1.03/0.94 tff(1690,plain,(
% 1.03/0.94 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.03/0.94 inference(skolemize,[status(sab)],[1689])).
% 1.03/0.94 tff(1691,plain,
% 1.03/0.94 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1690, 1683])).
% 1.03/0.94 tff(1692,plain,
% 1.03/0.94 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a149) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a149)) | c0_1(a149))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a149) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a149)) | c0_1(a149))),
% 1.03/0.94 inference(rewrite,[status(thm)],[])).
% 1.03/0.94 tff(1693,plain,
% 1.03/0.94 ((hskp0 | (~ndr1_0) | c1_1(a149) | c0_1(a149) | (~c3_1(a149)) | c3_1(a128) | c1_1(a128) | c0_1(a128)) <=> (hskp0 | c1_1(a149) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a149)) | c0_1(a149))),
% 1.03/0.94 inference(rewrite,[status(thm)],[])).
% 1.03/0.94 tff(1694,plain,
% 1.03/0.94 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a149) | c0_1(a149) | (~c3_1(a149)) | c3_1(a128) | c1_1(a128) | c0_1(a128))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a149) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a149)) | c0_1(a149)))),
% 1.03/0.94 inference(monotonicity,[status(thm)],[1693])).
% 1.03/0.94 tff(1695,plain,
% 1.03/0.94 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a149) | c0_1(a149) | (~c3_1(a149)) | c3_1(a128) | c1_1(a128) | c0_1(a128))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a149) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a149)) | c0_1(a149))),
% 1.03/0.94 inference(transitivity,[status(thm)],[1694, 1692])).
% 1.03/0.94 tff(1696,plain,
% 1.03/0.94 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a149) | c0_1(a149) | (~c3_1(a149)) | c3_1(a128) | c1_1(a128) | c0_1(a128))),
% 1.03/0.94 inference(quant_inst,[status(thm)],[])).
% 1.03/0.94 tff(1697,plain,
% 1.03/0.94 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a149) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a149)) | c0_1(a149)),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1696, 1695])).
% 1.03/0.94 tff(1698,plain,
% 1.03/0.94 (hskp0),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[1697, 187, 1674, 1673, 1595, 1597, 1691, 567, 1681])).
% 1.03/0.94 tff(1699,plain,
% 1.03/0.94 (((~hskp0) | (~c0_1(a124))) <=> ((~hskp0) | (~c0_1(a124)))),
% 1.03/0.94 inference(rewrite,[status(thm)],[])).
% 1.03/0.94 tff(1700,plain,
% 1.03/0.94 (((~c0_1(a124)) | (~hskp0)) <=> ((~hskp0) | (~c0_1(a124)))),
% 1.03/0.94 inference(rewrite,[status(thm)],[])).
% 1.03/0.94 tff(1701,axiom,((~c0_1(a124)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 1.03/0.94 tff(1702,plain,
% 1.03/0.94 ((~hskp0) | (~c0_1(a124))),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1701, 1700])).
% 1.03/0.94 tff(1703,plain,
% 1.03/0.94 ((~hskp0) | (~c0_1(a124))),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1702, 1699])).
% 1.03/0.94 tff(1704,plain,
% 1.03/0.94 (~c0_1(a124)),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[1703, 1698])).
% 1.03/0.94 tff(1705,plain,
% 1.03/0.94 (~c2_1(a149)),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[558, 1672])).
% 1.03/0.94 tff(1706,plain,
% 1.03/0.94 (((~hskp0) | c3_1(a124)) <=> ((~hskp0) | c3_1(a124))),
% 1.03/0.94 inference(rewrite,[status(thm)],[])).
% 1.03/0.94 tff(1707,axiom,((~hskp0) | c3_1(a124)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 1.03/0.94 tff(1708,plain,
% 1.03/0.94 ((~hskp0) | c3_1(a124)),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1707, 1706])).
% 1.03/0.94 tff(1709,plain,
% 1.03/0.94 ((~hskp0) | c3_1(a124)),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1708, 1706])).
% 1.03/0.94 tff(1710,plain,
% 1.03/0.94 ((~hskp0) | c3_1(a124)),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1709, 1706])).
% 1.03/0.94 tff(1711,plain,
% 1.03/0.94 ((~hskp0) | c3_1(a124)),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1710, 1706])).
% 1.03/0.94 tff(1712,plain,
% 1.03/0.94 ((~hskp0) | c3_1(a124)),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1711, 1706])).
% 1.03/0.94 tff(1713,plain,
% 1.03/0.94 ((~hskp0) | c3_1(a124)),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1712, 1706])).
% 1.03/0.94 tff(1714,plain,
% 1.03/0.94 ((~hskp0) | c3_1(a124)),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1713, 1706])).
% 1.03/0.94 tff(1715,plain,
% 1.03/0.94 ((~hskp0) | c3_1(a124)),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1714, 1706])).
% 1.03/0.94 tff(1716,plain,
% 1.03/0.94 (c3_1(a124)),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[1715, 1698])).
% 1.03/0.94 tff(1717,plain,
% 1.03/0.94 (((~hskp0) | c2_1(a124)) <=> ((~hskp0) | c2_1(a124))),
% 1.03/0.94 inference(rewrite,[status(thm)],[])).
% 1.03/0.94 tff(1718,axiom,((~hskp0) | c2_1(a124)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause82')).
% 1.03/0.94 tff(1719,plain,
% 1.03/0.94 ((~hskp0) | c2_1(a124)),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1718, 1717])).
% 1.03/0.94 tff(1720,plain,
% 1.03/0.94 ((~hskp0) | c2_1(a124)),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1719, 1717])).
% 1.03/0.94 tff(1721,plain,
% 1.03/0.94 ((~hskp0) | c2_1(a124)),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1720, 1717])).
% 1.03/0.94 tff(1722,plain,
% 1.03/0.94 ((~hskp0) | c2_1(a124)),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1721, 1717])).
% 1.03/0.94 tff(1723,plain,
% 1.03/0.94 ((~hskp0) | c2_1(a124)),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1722, 1717])).
% 1.03/0.94 tff(1724,plain,
% 1.03/0.94 ((~hskp0) | c2_1(a124)),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1723, 1717])).
% 1.03/0.94 tff(1725,plain,
% 1.03/0.94 ((~hskp0) | c2_1(a124)),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1724, 1717])).
% 1.03/0.94 tff(1726,plain,
% 1.03/0.94 ((~hskp0) | c2_1(a124)),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1725, 1717])).
% 1.03/0.94 tff(1727,plain,
% 1.03/0.94 (c2_1(a124)),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[1726, 1698])).
% 1.03/0.94 tff(1728,plain,
% 1.03/0.94 (c3_1(a140)),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[646, 1661])).
% 1.03/0.94 tff(1729,plain,
% 1.03/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c1_1(a149) | c2_1(a149) | c0_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c3_1(a124)) | c2_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | (~c3_1(a149)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a149) | c2_1(a149) | c0_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c3_1(a124)) | c2_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | (~c3_1(a149)))),
% 1.03/0.94 inference(rewrite,[status(thm)],[])).
% 1.03/0.94 tff(1730,plain,
% 1.03/0.94 (((~ndr1_0) | c2_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | c1_1(a149) | c2_1(a149) | (~c3_1(a149)) | c0_1(a124) | (~c2_1(a124)) | (~c3_1(a124))) <=> (c1_1(a149) | c2_1(a149) | c0_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c3_1(a124)) | c2_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | (~c3_1(a149)))),
% 1.03/0.94 inference(rewrite,[status(thm)],[])).
% 1.03/0.94 tff(1731,plain,
% 1.03/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | c1_1(a149) | c2_1(a149) | (~c3_1(a149)) | c0_1(a124) | (~c2_1(a124)) | (~c3_1(a124)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c1_1(a149) | c2_1(a149) | c0_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c3_1(a124)) | c2_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | (~c3_1(a149))))),
% 1.03/0.94 inference(monotonicity,[status(thm)],[1730])).
% 1.03/0.94 tff(1732,plain,
% 1.03/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | c1_1(a149) | c2_1(a149) | (~c3_1(a149)) | c0_1(a124) | (~c2_1(a124)) | (~c3_1(a124)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a149) | c2_1(a149) | c0_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c3_1(a124)) | c2_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | (~c3_1(a149)))),
% 1.03/0.94 inference(transitivity,[status(thm)],[1731, 1729])).
% 1.03/0.94 tff(1733,plain,
% 1.03/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | c1_1(a149) | c2_1(a149) | (~c3_1(a149)) | c0_1(a124) | (~c2_1(a124)) | (~c3_1(a124)))),
% 1.03/0.94 inference(quant_inst,[status(thm)],[])).
% 1.03/0.94 tff(1734,plain,
% 1.03/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a149) | c2_1(a149) | c0_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c3_1(a124)) | c2_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | (~c3_1(a149))),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1733, 1732])).
% 1.03/0.94 tff(1735,plain,
% 1.03/0.94 ($false),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[1734, 187, 1674, 1663, 1728, 1727, 1716, 1673, 1705, 1704, 229, 1670])).
% 1.03/0.94 tff(1736,plain,(c1_1(a128) | hskp18), inference(lemma,lemma(discharge,[]))).
% 1.03/0.94 tff(1737,plain,
% 1.03/0.94 (c1_1(a128)),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[1736, 95])).
% 1.03/0.94 tff(1738,plain,
% 1.03/0.94 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | c0_1(a128) | c2_1(a128) | (~ndr1_0) | (~c1_1(a128)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp11 | hskp10 | c0_1(a128) | c2_1(a128) | (~ndr1_0) | (~c1_1(a128)))),
% 1.03/0.94 inference(rewrite,[status(thm)],[])).
% 1.03/0.94 tff(1739,plain,
% 1.03/0.94 ((hskp11 | hskp10 | (~ndr1_0) | c0_1(a128) | c2_1(a128) | (~c1_1(a128))) <=> (hskp11 | hskp10 | c0_1(a128) | c2_1(a128) | (~ndr1_0) | (~c1_1(a128)))),
% 1.03/0.94 inference(rewrite,[status(thm)],[])).
% 1.03/0.94 tff(1740,plain,
% 1.03/0.94 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c0_1(a128) | c2_1(a128) | (~c1_1(a128)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | c0_1(a128) | c2_1(a128) | (~ndr1_0) | (~c1_1(a128))))),
% 1.03/0.94 inference(monotonicity,[status(thm)],[1739])).
% 1.03/0.94 tff(1741,plain,
% 1.03/0.94 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c0_1(a128) | c2_1(a128) | (~c1_1(a128)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp11 | hskp10 | c0_1(a128) | c2_1(a128) | (~ndr1_0) | (~c1_1(a128)))),
% 1.03/0.94 inference(transitivity,[status(thm)],[1740, 1738])).
% 1.03/0.94 tff(1742,plain,
% 1.03/0.94 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c0_1(a128) | c2_1(a128) | (~c1_1(a128)))),
% 1.03/0.94 inference(quant_inst,[status(thm)],[])).
% 1.03/0.94 tff(1743,plain,
% 1.03/0.94 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp11 | hskp10 | c0_1(a128) | c2_1(a128) | (~ndr1_0) | (~c1_1(a128))),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1742, 1741])).
% 1.03/0.94 tff(1744,plain,
% 1.03/0.94 (hskp11 | (~c1_1(a128))),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[1743, 187, 1266, 1595, 1596, 1478])).
% 1.03/0.94 tff(1745,plain,
% 1.03/0.94 (hskp11),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[1744, 1737])).
% 1.03/0.94 tff(1746,plain,
% 1.03/0.94 (~c3_1(a139)),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[1506, 1745])).
% 1.03/0.94 tff(1747,plain,
% 1.03/0.94 (~c1_1(a139)),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[1512, 1745])).
% 1.03/0.94 tff(1748,plain,
% 1.03/0.94 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))),
% 1.03/0.94 inference(bind,[status(th)],[])).
% 1.03/0.94 tff(1749,plain,
% 1.03/0.94 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.03/0.94 inference(quant_intro,[status(thm)],[1748])).
% 1.03/0.94 tff(1750,plain,
% 1.03/0.94 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.03/0.94 inference(rewrite,[status(thm)],[])).
% 1.03/0.94 tff(1751,plain,
% 1.03/0.94 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp16) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp16))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))))),
% 1.03/0.94 inference(bind,[status(th)],[])).
% 1.03/0.94 tff(1752,plain,
% 1.03/0.94 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.03/0.94 inference(quant_intro,[status(thm)],[1751])).
% 1.03/0.94 tff(1753,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause163')).
% 1.03/0.94 tff(1754,plain,
% 1.03/0.94 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1753, 1752])).
% 1.03/0.94 tff(1755,plain,
% 1.03/0.94 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1754, 1750])).
% 1.03/0.94 tff(1756,plain,(
% 1.03/0.94 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.03/0.94 inference(skolemize,[status(sab)],[1755])).
% 1.03/0.94 tff(1757,plain,
% 1.03/0.94 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1756, 1749])).
% 1.03/0.94 tff(1758,plain,
% 1.03/0.94 (hskp21 | (~c1_1(a128))),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[305, 187, 95, 1596, 1597, 134])).
% 1.03/0.94 tff(1759,plain,
% 1.03/0.94 (hskp21),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[1758, 1737])).
% 1.03/0.94 tff(1760,plain,
% 1.03/0.94 (~c2_1(a170)),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[312, 1759])).
% 1.03/0.94 tff(1761,plain,
% 1.03/0.94 (~c0_1(a170)),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[318, 1759])).
% 1.03/0.94 tff(1762,plain,
% 1.03/0.94 (c3_1(a170)),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[346, 1759])).
% 1.03/0.94 tff(1763,plain,
% 1.03/0.94 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c0_1(a170) | c2_1(a170) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a170)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a170) | c2_1(a170) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a170)))),
% 1.03/0.94 inference(rewrite,[status(thm)],[])).
% 1.03/0.94 tff(1764,plain,
% 1.03/0.94 ((hskp9 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c3_1(a170)) | c3_1(a128) | c0_1(a128) | c2_1(a128)) <=> (hskp9 | c0_1(a170) | c2_1(a170) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a170)))),
% 1.03/0.94 inference(rewrite,[status(thm)],[])).
% 1.03/0.94 tff(1765,plain,
% 1.03/0.94 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c3_1(a170)) | c3_1(a128) | c0_1(a128) | c2_1(a128))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c0_1(a170) | c2_1(a170) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a170))))),
% 1.03/0.94 inference(monotonicity,[status(thm)],[1764])).
% 1.03/0.94 tff(1766,plain,
% 1.03/0.94 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c3_1(a170)) | c3_1(a128) | c0_1(a128) | c2_1(a128))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a170) | c2_1(a170) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a170)))),
% 1.03/0.94 inference(transitivity,[status(thm)],[1765, 1763])).
% 1.03/0.94 tff(1767,plain,
% 1.03/0.94 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c3_1(a170)) | c3_1(a128) | c0_1(a128) | c2_1(a128))),
% 1.03/0.94 inference(quant_inst,[status(thm)],[])).
% 1.03/0.94 tff(1768,plain,
% 1.03/0.94 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a170) | c2_1(a170) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a170))),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1767, 1766])).
% 1.03/0.94 tff(1769,plain,
% 1.03/0.94 (hskp9),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[1768, 187, 1762, 1761, 1760, 1595, 1596, 1597, 31])).
% 1.03/0.94 tff(1770,plain,
% 1.03/0.94 (c0_1(a136)),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[840, 1769])).
% 1.03/0.94 tff(1771,plain,
% 1.03/0.94 (~c3_1(a136)),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[810, 1769])).
% 1.03/0.94 tff(1772,plain,
% 1.03/0.94 (c2_1(a136)),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[821, 1769])).
% 1.03/0.94 tff(1773,plain,
% 1.03/0.94 (^[U: $i] : refl((hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 1.03/0.94 inference(bind,[status(th)],[])).
% 1.03/0.94 tff(1774,plain,
% 1.03/0.94 (![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.03/0.94 inference(quant_intro,[status(thm)],[1773])).
% 1.03/0.94 tff(1775,plain,
% 1.03/0.94 (![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.03/0.94 inference(rewrite,[status(thm)],[])).
% 1.03/0.94 tff(1776,plain,
% 1.03/0.94 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp10) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp10))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp10) <=> (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp10) <=> (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp10) | hskp13) <=> ((hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp13))), rewrite(((hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp13) <=> (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp10) | hskp13) <=> (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 1.03/0.95 inference(bind,[status(th)],[])).
% 1.03/0.95 tff(1777,plain,
% 1.03/0.95 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp10) | hskp13) <=> ![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.03/0.95 inference(quant_intro,[status(thm)],[1776])).
% 1.03/0.95 tff(1778,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp10) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause150')).
% 1.03/0.95 tff(1779,plain,
% 1.03/0.95 (![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1778, 1777])).
% 1.03/0.95 tff(1780,plain,
% 1.03/0.95 (![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1779, 1775])).
% 1.03/0.95 tff(1781,plain,(
% 1.03/0.95 ![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.03/0.95 inference(skolemize,[status(sab)],[1780])).
% 1.03/0.95 tff(1782,plain,
% 1.03/0.95 (![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1781, 1774])).
% 1.03/0.95 tff(1783,plain,
% 1.03/0.95 (^[U: $i] : refl((hskp28 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) <=> (hskp28 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))))),
% 1.03/0.95 inference(bind,[status(th)],[])).
% 1.03/0.95 tff(1784,plain,
% 1.03/0.95 (![U: $i] : (hskp28 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp28 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 1.03/0.95 inference(quant_intro,[status(thm)],[1783])).
% 1.03/0.95 tff(1785,plain,
% 1.03/0.95 (![U: $i] : (hskp28 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp28 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 1.03/0.95 inference(rewrite,[status(thm)],[])).
% 1.03/0.95 tff(1786,plain,
% 1.03/0.95 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp28))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) | hskp13) <=> ((hskp28 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp13))), rewrite(((hskp28 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp13) <=> (hskp28 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) | hskp13) <=> (hskp28 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))))),
% 1.03/0.95 inference(bind,[status(th)],[])).
% 1.03/0.95 tff(1787,plain,
% 1.03/0.95 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) | hskp13) <=> ![U: $i] : (hskp28 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 1.03/0.95 inference(quant_intro,[status(thm)],[1786])).
% 1.03/0.95 tff(1788,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause137')).
% 1.03/0.95 tff(1789,plain,
% 1.03/0.95 (![U: $i] : (hskp28 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1788, 1787])).
% 1.03/0.95 tff(1790,plain,
% 1.03/0.95 (![U: $i] : (hskp28 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1789, 1785])).
% 1.03/0.95 tff(1791,plain,(
% 1.03/0.95 ![U: $i] : (hskp28 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 1.03/0.95 inference(skolemize,[status(sab)],[1790])).
% 1.03/0.95 tff(1792,plain,
% 1.03/0.95 (![U: $i] : (hskp28 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1791, 1784])).
% 1.03/0.95 tff(1793,assumption,(c3_1(a170)), introduced(assumption)).
% 1.03/0.95 tff(1794,plain,
% 1.03/0.95 (((~![U: $i] : (hskp28 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp28 | hskp13 | c0_1(a170) | c2_1(a170) | (~ndr1_0) | (~c3_1(a170)))) <=> ((~![U: $i] : (hskp28 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp28 | hskp13 | c0_1(a170) | c2_1(a170) | (~ndr1_0) | (~c3_1(a170)))),
% 1.03/0.95 inference(rewrite,[status(thm)],[])).
% 1.03/0.95 tff(1795,plain,
% 1.03/0.95 ((hskp28 | hskp13 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c3_1(a170))) <=> (hskp28 | hskp13 | c0_1(a170) | c2_1(a170) | (~ndr1_0) | (~c3_1(a170)))),
% 1.03/0.95 inference(rewrite,[status(thm)],[])).
% 1.03/0.95 tff(1796,plain,
% 1.03/0.95 (((~![U: $i] : (hskp28 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp28 | hskp13 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c3_1(a170)))) <=> ((~![U: $i] : (hskp28 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp28 | hskp13 | c0_1(a170) | c2_1(a170) | (~ndr1_0) | (~c3_1(a170))))),
% 1.03/0.95 inference(monotonicity,[status(thm)],[1795])).
% 1.03/0.95 tff(1797,plain,
% 1.03/0.95 (((~![U: $i] : (hskp28 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp28 | hskp13 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c3_1(a170)))) <=> ((~![U: $i] : (hskp28 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp28 | hskp13 | c0_1(a170) | c2_1(a170) | (~ndr1_0) | (~c3_1(a170)))),
% 1.03/0.95 inference(transitivity,[status(thm)],[1796, 1794])).
% 1.03/0.95 tff(1798,plain,
% 1.03/0.95 ((~![U: $i] : (hskp28 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp28 | hskp13 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c3_1(a170)))),
% 1.03/0.95 inference(quant_inst,[status(thm)],[])).
% 1.03/0.95 tff(1799,plain,
% 1.03/0.95 ((~![U: $i] : (hskp28 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp28 | hskp13 | c0_1(a170) | c2_1(a170) | (~ndr1_0) | (~c3_1(a170))),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1798, 1797])).
% 1.03/0.95 tff(1800,plain,
% 1.03/0.95 (hskp28 | hskp13),
% 1.03/0.95 inference(unit_resolution,[status(thm)],[1799, 187, 1793, 472, 471, 1792])).
% 1.03/0.95 tff(1801,plain,
% 1.03/0.95 (hskp28),
% 1.03/0.95 inference(unit_resolution,[status(thm)],[1800, 11])).
% 1.03/0.95 tff(1802,plain,
% 1.03/0.95 (((~hskp28) | c3_1(a143)) <=> ((~hskp28) | c3_1(a143))),
% 1.03/0.95 inference(rewrite,[status(thm)],[])).
% 1.03/0.95 tff(1803,axiom,((~hskp28) | c3_1(a143)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause45')).
% 1.03/0.95 tff(1804,plain,
% 1.03/0.95 ((~hskp28) | c3_1(a143)),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1803, 1802])).
% 1.03/0.95 tff(1805,plain,
% 1.03/0.95 ((~hskp28) | c3_1(a143)),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1804, 1802])).
% 1.03/0.95 tff(1806,plain,
% 1.03/0.95 ((~hskp28) | c3_1(a143)),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1805, 1802])).
% 1.03/0.95 tff(1807,plain,
% 1.03/0.95 ((~hskp28) | c3_1(a143)),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1806, 1802])).
% 1.03/0.95 tff(1808,plain,
% 1.03/0.95 ((~hskp28) | c3_1(a143)),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1807, 1802])).
% 1.03/0.95 tff(1809,plain,
% 1.03/0.95 ((~hskp28) | c3_1(a143)),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1808, 1802])).
% 1.03/0.95 tff(1810,plain,
% 1.03/0.95 ((~hskp28) | c3_1(a143)),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1809, 1802])).
% 1.03/0.95 tff(1811,plain,
% 1.03/0.95 ((~hskp28) | c3_1(a143)),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1810, 1802])).
% 1.03/0.95 tff(1812,plain,
% 1.03/0.95 (c3_1(a143)),
% 1.03/0.95 inference(unit_resolution,[status(thm)],[1811, 1801])).
% 1.03/0.95 tff(1813,plain,
% 1.03/0.95 (((~hskp28) | c0_1(a143)) <=> ((~hskp28) | c0_1(a143))),
% 1.03/0.95 inference(rewrite,[status(thm)],[])).
% 1.03/0.95 tff(1814,axiom,((~hskp28) | c0_1(a143)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause43')).
% 1.03/0.95 tff(1815,plain,
% 1.03/0.95 ((~hskp28) | c0_1(a143)),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1814, 1813])).
% 1.03/0.95 tff(1816,plain,
% 1.03/0.95 ((~hskp28) | c0_1(a143)),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1815, 1813])).
% 1.03/0.95 tff(1817,plain,
% 1.03/0.95 ((~hskp28) | c0_1(a143)),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1816, 1813])).
% 1.03/0.95 tff(1818,plain,
% 1.03/0.95 ((~hskp28) | c0_1(a143)),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1817, 1813])).
% 1.03/0.95 tff(1819,plain,
% 1.03/0.95 ((~hskp28) | c0_1(a143)),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1818, 1813])).
% 1.03/0.95 tff(1820,plain,
% 1.03/0.95 ((~hskp28) | c0_1(a143)),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1819, 1813])).
% 1.03/0.95 tff(1821,plain,
% 1.03/0.95 ((~hskp28) | c0_1(a143)),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1820, 1813])).
% 1.03/0.95 tff(1822,plain,
% 1.03/0.95 ((~hskp28) | c0_1(a143)),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1821, 1813])).
% 1.03/0.95 tff(1823,plain,
% 1.03/0.95 (c0_1(a143)),
% 1.03/0.95 inference(unit_resolution,[status(thm)],[1822, 1801])).
% 1.03/0.95 tff(1824,plain,
% 1.03/0.95 (((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp13 | hskp10 | (~ndr1_0) | c1_1(a143) | (~c0_1(a143)) | (~c3_1(a143)))) <=> ((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp13 | hskp10 | (~ndr1_0) | c1_1(a143) | (~c0_1(a143)) | (~c3_1(a143)))),
% 1.03/0.95 inference(rewrite,[status(thm)],[])).
% 1.03/0.95 tff(1825,plain,
% 1.03/0.95 ((hskp13 | hskp10 | (~ndr1_0) | c1_1(a143) | (~c3_1(a143)) | (~c0_1(a143))) <=> (hskp13 | hskp10 | (~ndr1_0) | c1_1(a143) | (~c0_1(a143)) | (~c3_1(a143)))),
% 1.03/0.95 inference(rewrite,[status(thm)],[])).
% 1.03/0.95 tff(1826,plain,
% 1.03/0.95 (((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp13 | hskp10 | (~ndr1_0) | c1_1(a143) | (~c3_1(a143)) | (~c0_1(a143)))) <=> ((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp13 | hskp10 | (~ndr1_0) | c1_1(a143) | (~c0_1(a143)) | (~c3_1(a143))))),
% 1.03/0.95 inference(monotonicity,[status(thm)],[1825])).
% 1.03/0.95 tff(1827,plain,
% 1.03/0.95 (((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp13 | hskp10 | (~ndr1_0) | c1_1(a143) | (~c3_1(a143)) | (~c0_1(a143)))) <=> ((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp13 | hskp10 | (~ndr1_0) | c1_1(a143) | (~c0_1(a143)) | (~c3_1(a143)))),
% 1.03/0.95 inference(transitivity,[status(thm)],[1826, 1824])).
% 1.03/0.95 tff(1828,plain,
% 1.03/0.95 ((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp13 | hskp10 | (~ndr1_0) | c1_1(a143) | (~c3_1(a143)) | (~c0_1(a143)))),
% 1.03/0.95 inference(quant_inst,[status(thm)],[])).
% 1.03/0.95 tff(1829,plain,
% 1.03/0.95 ((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp13 | hskp10 | (~ndr1_0) | c1_1(a143) | (~c0_1(a143)) | (~c3_1(a143))),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1828, 1827])).
% 1.03/0.95 tff(1830,plain,
% 1.03/0.95 (c1_1(a143)),
% 1.03/0.95 inference(unit_resolution,[status(thm)],[1829, 187, 11, 1313, 1823, 1812, 1782])).
% 1.03/0.95 tff(1831,plain,
% 1.03/0.95 (^[U: $i] : refl((hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 1.03/0.95 inference(bind,[status(th)],[])).
% 1.03/0.95 tff(1832,plain,
% 1.03/0.95 (![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.03/0.95 inference(quant_intro,[status(thm)],[1831])).
% 1.03/0.95 tff(1833,plain,
% 1.03/0.95 (![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.03/0.95 inference(rewrite,[status(thm)],[])).
% 1.03/0.95 tff(1834,plain,
% 1.03/0.95 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp19) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp19))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp19) <=> (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp19) <=> (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp19) | hskp13) <=> ((hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp13))), rewrite(((hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp13) <=> (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp19) | hskp13) <=> (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 1.03/0.95 inference(bind,[status(th)],[])).
% 1.03/0.95 tff(1835,plain,
% 1.03/0.95 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp19) | hskp13) <=> ![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.03/0.95 inference(quant_intro,[status(thm)],[1834])).
% 1.03/0.95 tff(1836,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp19) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause154')).
% 1.03/0.95 tff(1837,plain,
% 1.03/0.95 (![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1836, 1835])).
% 1.03/0.95 tff(1838,plain,
% 1.03/0.95 (![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1837, 1833])).
% 1.03/0.95 tff(1839,plain,(
% 1.03/0.95 ![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.03/0.95 inference(skolemize,[status(sab)],[1838])).
% 1.03/0.95 tff(1840,plain,
% 1.03/0.95 (![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1839, 1832])).
% 1.03/0.95 tff(1841,plain,
% 1.03/0.95 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | (~c1_1(a199)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp19 | hskp13 | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | (~c1_1(a199)))),
% 1.03/0.95 inference(rewrite,[status(thm)],[])).
% 1.03/0.95 tff(1842,plain,
% 1.03/0.95 ((hskp19 | hskp13 | (~ndr1_0) | (~c2_1(a199)) | (~c1_1(a199)) | (~c0_1(a199))) <=> (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | (~c1_1(a199)))),
% 1.03/0.95 inference(rewrite,[status(thm)],[])).
% 1.03/0.95 tff(1843,plain,
% 1.03/0.95 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(a199)) | (~c1_1(a199)) | (~c0_1(a199)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | (~c1_1(a199))))),
% 1.03/0.95 inference(monotonicity,[status(thm)],[1842])).
% 1.03/0.95 tff(1844,plain,
% 1.03/0.95 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(a199)) | (~c1_1(a199)) | (~c0_1(a199)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp19 | hskp13 | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | (~c1_1(a199)))),
% 1.03/0.95 inference(transitivity,[status(thm)],[1843, 1841])).
% 1.03/0.95 tff(1845,plain,
% 1.03/0.95 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(a199)) | (~c1_1(a199)) | (~c0_1(a199)))),
% 1.03/0.95 inference(quant_inst,[status(thm)],[])).
% 1.03/0.95 tff(1846,plain,
% 1.03/0.95 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp19 | hskp13 | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | (~c1_1(a199))),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1845, 1844])).
% 1.03/0.95 tff(1847,plain,
% 1.03/0.95 (hskp19 | hskp13),
% 1.03/0.95 inference(unit_resolution,[status(thm)],[1846, 187, 1312, 1311, 1322, 1840])).
% 1.03/0.95 tff(1848,plain,
% 1.03/0.95 (hskp19),
% 1.03/0.95 inference(unit_resolution,[status(thm)],[1847, 11])).
% 1.03/0.95 tff(1849,plain,
% 1.03/0.95 (c3_1(a162)),
% 1.03/0.95 inference(unit_resolution,[status(thm)],[417, 1848])).
% 1.03/0.95 tff(1850,plain,
% 1.03/0.95 (c0_1(a162)),
% 1.03/0.95 inference(unit_resolution,[status(thm)],[428, 1848])).
% 1.03/0.95 tff(1851,plain,
% 1.03/0.95 (((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp13 | hskp10 | (~ndr1_0) | (~c3_1(a162)) | c1_1(a162) | (~c0_1(a162)))) <=> ((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp13 | hskp10 | (~ndr1_0) | (~c3_1(a162)) | c1_1(a162) | (~c0_1(a162)))),
% 1.03/0.95 inference(rewrite,[status(thm)],[])).
% 1.03/0.95 tff(1852,plain,
% 1.03/0.95 ((hskp13 | hskp10 | (~ndr1_0) | c1_1(a162) | (~c3_1(a162)) | (~c0_1(a162))) <=> (hskp13 | hskp10 | (~ndr1_0) | (~c3_1(a162)) | c1_1(a162) | (~c0_1(a162)))),
% 1.03/0.95 inference(rewrite,[status(thm)],[])).
% 1.03/0.95 tff(1853,plain,
% 1.03/0.95 (((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp13 | hskp10 | (~ndr1_0) | c1_1(a162) | (~c3_1(a162)) | (~c0_1(a162)))) <=> ((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp13 | hskp10 | (~ndr1_0) | (~c3_1(a162)) | c1_1(a162) | (~c0_1(a162))))),
% 1.03/0.95 inference(monotonicity,[status(thm)],[1852])).
% 1.03/0.95 tff(1854,plain,
% 1.03/0.95 (((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp13 | hskp10 | (~ndr1_0) | c1_1(a162) | (~c3_1(a162)) | (~c0_1(a162)))) <=> ((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp13 | hskp10 | (~ndr1_0) | (~c3_1(a162)) | c1_1(a162) | (~c0_1(a162)))),
% 1.03/0.95 inference(transitivity,[status(thm)],[1853, 1851])).
% 1.03/0.95 tff(1855,plain,
% 1.03/0.95 ((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp13 | hskp10 | (~ndr1_0) | c1_1(a162) | (~c3_1(a162)) | (~c0_1(a162)))),
% 1.03/0.95 inference(quant_inst,[status(thm)],[])).
% 1.03/0.95 tff(1856,plain,
% 1.03/0.95 ((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp13 | hskp10 | (~ndr1_0) | (~c3_1(a162)) | c1_1(a162) | (~c0_1(a162))),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1855, 1854])).
% 1.03/0.95 tff(1857,plain,
% 1.03/0.95 (c1_1(a162)),
% 1.03/0.95 inference(unit_resolution,[status(thm)],[1856, 187, 11, 1313, 1850, 1849, 1782])).
% 1.03/0.95 tff(1858,plain,
% 1.03/0.95 (hskp13 | (~c1_1(a136))),
% 1.03/0.95 inference(unit_resolution,[status(thm)],[1436, 187, 1126, 1125, 1137, 21])).
% 1.03/0.95 tff(1859,plain,
% 1.03/0.95 (~c1_1(a136)),
% 1.03/0.95 inference(unit_resolution,[status(thm)],[1858, 11])).
% 1.03/0.95 tff(1860,plain,
% 1.03/0.95 (~c2_1(a162)),
% 1.03/0.95 inference(unit_resolution,[status(thm)],[406, 1848])).
% 1.03/0.95 tff(1861,plain,
% 1.03/0.95 (((~hskp28) | c2_1(a143)) <=> ((~hskp28) | c2_1(a143))),
% 1.03/0.95 inference(rewrite,[status(thm)],[])).
% 1.03/0.95 tff(1862,axiom,((~hskp28) | c2_1(a143)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause44')).
% 1.03/0.95 tff(1863,plain,
% 1.03/0.95 ((~hskp28) | c2_1(a143)),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1862, 1861])).
% 1.03/0.95 tff(1864,plain,
% 1.03/0.95 ((~hskp28) | c2_1(a143)),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1863, 1861])).
% 1.03/0.95 tff(1865,plain,
% 1.03/0.95 ((~hskp28) | c2_1(a143)),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1864, 1861])).
% 1.03/0.95 tff(1866,plain,
% 1.03/0.95 ((~hskp28) | c2_1(a143)),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1865, 1861])).
% 1.03/0.95 tff(1867,plain,
% 1.03/0.95 ((~hskp28) | c2_1(a143)),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1866, 1861])).
% 1.03/0.95 tff(1868,plain,
% 1.03/0.95 ((~hskp28) | c2_1(a143)),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1867, 1861])).
% 1.03/0.95 tff(1869,plain,
% 1.03/0.95 ((~hskp28) | c2_1(a143)),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1868, 1861])).
% 1.03/0.95 tff(1870,plain,
% 1.03/0.95 ((~hskp28) | c2_1(a143)),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1869, 1861])).
% 1.03/0.95 tff(1871,plain,
% 1.03/0.95 (c2_1(a143)),
% 1.03/0.95 inference(unit_resolution,[status(thm)],[1870, 1801])).
% 1.03/0.95 tff(1872,plain,
% 1.03/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a162) | c3_1(a136) | (~ndr1_0) | (~c1_1(a143)) | (~c3_1(a143)) | (~c2_1(a143)) | c1_1(a136) | (~c2_1(a136)) | (~c1_1(a162)) | (~c0_1(a162)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a162) | c3_1(a136) | (~ndr1_0) | (~c1_1(a143)) | (~c3_1(a143)) | (~c2_1(a143)) | c1_1(a136) | (~c2_1(a136)) | (~c1_1(a162)) | (~c0_1(a162)))),
% 1.03/0.95 inference(rewrite,[status(thm)],[])).
% 1.03/0.95 tff(1873,plain,
% 1.03/0.95 (((~ndr1_0) | (~c2_1(a143)) | (~c3_1(a143)) | (~c1_1(a143)) | c2_1(a162) | (~c1_1(a162)) | (~c0_1(a162)) | c1_1(a136) | c3_1(a136) | (~c2_1(a136))) <=> (c2_1(a162) | c3_1(a136) | (~ndr1_0) | (~c1_1(a143)) | (~c3_1(a143)) | (~c2_1(a143)) | c1_1(a136) | (~c2_1(a136)) | (~c1_1(a162)) | (~c0_1(a162)))),
% 1.03/0.95 inference(rewrite,[status(thm)],[])).
% 1.03/0.95 tff(1874,plain,
% 1.03/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a143)) | (~c3_1(a143)) | (~c1_1(a143)) | c2_1(a162) | (~c1_1(a162)) | (~c0_1(a162)) | c1_1(a136) | c3_1(a136) | (~c2_1(a136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a162) | c3_1(a136) | (~ndr1_0) | (~c1_1(a143)) | (~c3_1(a143)) | (~c2_1(a143)) | c1_1(a136) | (~c2_1(a136)) | (~c1_1(a162)) | (~c0_1(a162))))),
% 1.03/0.95 inference(monotonicity,[status(thm)],[1873])).
% 1.03/0.95 tff(1875,plain,
% 1.03/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a143)) | (~c3_1(a143)) | (~c1_1(a143)) | c2_1(a162) | (~c1_1(a162)) | (~c0_1(a162)) | c1_1(a136) | c3_1(a136) | (~c2_1(a136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a162) | c3_1(a136) | (~ndr1_0) | (~c1_1(a143)) | (~c3_1(a143)) | (~c2_1(a143)) | c1_1(a136) | (~c2_1(a136)) | (~c1_1(a162)) | (~c0_1(a162)))),
% 1.03/0.95 inference(transitivity,[status(thm)],[1874, 1872])).
% 1.03/0.95 tff(1876,plain,
% 1.03/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a143)) | (~c3_1(a143)) | (~c1_1(a143)) | c2_1(a162) | (~c1_1(a162)) | (~c0_1(a162)) | c1_1(a136) | c3_1(a136) | (~c2_1(a136)))),
% 1.03/0.95 inference(quant_inst,[status(thm)],[])).
% 1.03/0.95 tff(1877,plain,
% 1.03/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a162) | c3_1(a136) | (~ndr1_0) | (~c1_1(a143)) | (~c3_1(a143)) | (~c2_1(a143)) | c1_1(a136) | (~c2_1(a136)) | (~c1_1(a162)) | (~c0_1(a162))),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1876, 1875])).
% 1.03/0.95 tff(1878,plain,
% 1.03/0.95 ($false),
% 1.03/0.95 inference(unit_resolution,[status(thm)],[1877, 187, 1871, 1812, 1850, 1125, 1860, 1137, 94, 1859, 1857, 1830])).
% 1.03/0.95 tff(1879,plain,(hskp13 | (~c2_1(a136)) | c3_1(a136) | hskp10 | (~c0_1(a136)) | (~c3_1(a170)) | c0_1(a170) | c2_1(a170) | (~c0_1(a199)) | (~c1_1(a199)) | (~c2_1(a199))), inference(lemma,lemma(discharge,[]))).
% 1.03/0.95 tff(1880,plain,
% 1.03/0.95 (hskp13),
% 1.03/0.95 inference(unit_resolution,[status(thm)],[1879, 1772, 1771, 1266, 1770, 1762, 1761, 1760, 1300, 1289, 1278])).
% 1.03/0.95 tff(1881,plain,
% 1.03/0.95 (~c3_1(a144)),
% 1.03/0.95 inference(unit_resolution,[status(thm)],[991, 1880])).
% 1.03/0.95 tff(1882,plain,
% 1.03/0.95 (~c0_1(a144)),
% 1.03/0.95 inference(unit_resolution,[status(thm)],[1015, 1880])).
% 1.03/0.95 tff(1883,plain,
% 1.03/0.95 (c2_1(a144)),
% 1.03/0.95 inference(unit_resolution,[status(thm)],[1002, 1880])).
% 1.03/0.95 tff(1884,plain,
% 1.03/0.95 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp16 | c0_1(a144) | c3_1(a144) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)) | (~c2_1(a144)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp16 | c0_1(a144) | c3_1(a144) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)) | (~c2_1(a144)))),
% 1.03/0.95 inference(rewrite,[status(thm)],[])).
% 1.03/0.95 tff(1885,plain,
% 1.03/0.95 ((hskp16 | (~ndr1_0) | c3_1(a128) | c2_1(a128) | (~c1_1(a128)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144))) <=> (hskp16 | c0_1(a144) | c3_1(a144) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)) | (~c2_1(a144)))),
% 1.03/0.95 inference(rewrite,[status(thm)],[])).
% 1.03/0.95 tff(1886,plain,
% 1.03/0.95 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a128) | c2_1(a128) | (~c1_1(a128)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp16 | c0_1(a144) | c3_1(a144) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)) | (~c2_1(a144))))),
% 1.03/0.95 inference(monotonicity,[status(thm)],[1885])).
% 1.03/0.95 tff(1887,plain,
% 1.03/0.95 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a128) | c2_1(a128) | (~c1_1(a128)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp16 | c0_1(a144) | c3_1(a144) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)) | (~c2_1(a144)))),
% 1.03/0.95 inference(transitivity,[status(thm)],[1886, 1884])).
% 1.03/0.95 tff(1888,plain,
% 1.03/0.95 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a128) | c2_1(a128) | (~c1_1(a128)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)))),
% 1.03/0.95 inference(quant_inst,[status(thm)],[])).
% 1.03/0.95 tff(1889,plain,
% 1.03/0.95 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp16 | c0_1(a144) | c3_1(a144) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)) | (~c2_1(a144))),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1888, 1887])).
% 1.03/0.95 tff(1890,plain,
% 1.03/0.95 (hskp16),
% 1.03/0.95 inference(unit_resolution,[status(thm)],[1889, 187, 1883, 1882, 1881, 1596, 1597, 1757, 1737])).
% 1.03/0.95 tff(1891,plain,
% 1.03/0.95 (~c2_1(a151)),
% 1.03/0.95 inference(unit_resolution,[status(thm)],[200, 1890])).
% 1.03/0.95 tff(1892,plain,
% 1.03/0.95 (c1_1(a151)),
% 1.03/0.95 inference(unit_resolution,[status(thm)],[211, 1890])).
% 1.03/0.95 tff(1893,plain,
% 1.03/0.95 (c0_1(a151)),
% 1.03/0.95 inference(unit_resolution,[status(thm)],[249, 1890])).
% 1.03/0.95 tff(1894,plain,
% 1.03/0.95 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | c0_1(a170) | c2_1(a170) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a170)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c0_1(a170) | c2_1(a170) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a170)))),
% 1.03/0.95 inference(rewrite,[status(thm)],[])).
% 1.03/0.95 tff(1895,plain,
% 1.03/0.95 ((hskp27 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c3_1(a170)) | c3_1(a128) | c0_1(a128) | c2_1(a128)) <=> (hskp27 | c0_1(a170) | c2_1(a170) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a170)))),
% 1.03/0.95 inference(rewrite,[status(thm)],[])).
% 1.03/0.95 tff(1896,plain,
% 1.03/0.95 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c3_1(a170)) | c3_1(a128) | c0_1(a128) | c2_1(a128))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | c0_1(a170) | c2_1(a170) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a170))))),
% 1.03/0.95 inference(monotonicity,[status(thm)],[1895])).
% 1.03/0.95 tff(1897,plain,
% 1.03/0.95 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c3_1(a170)) | c3_1(a128) | c0_1(a128) | c2_1(a128))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c0_1(a170) | c2_1(a170) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a170)))),
% 1.03/0.96 inference(transitivity,[status(thm)],[1896, 1894])).
% 1.03/0.96 tff(1898,plain,
% 1.03/0.96 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c3_1(a170)) | c3_1(a128) | c0_1(a128) | c2_1(a128))),
% 1.03/0.96 inference(quant_inst,[status(thm)],[])).
% 1.03/0.96 tff(1899,plain,
% 1.03/0.96 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c0_1(a170) | c2_1(a170) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a170))),
% 1.03/0.96 inference(modus_ponens,[status(thm)],[1898, 1897])).
% 1.03/0.96 tff(1900,plain,
% 1.03/0.96 (hskp27),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[1899, 187, 1762, 1761, 1760, 1595, 1596, 1597, 1203])).
% 1.03/0.96 tff(1901,plain,
% 1.03/0.96 (c3_1(a137)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[1221, 1900])).
% 1.03/0.96 tff(1902,plain,
% 1.03/0.96 (c2_1(a137)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[1232, 1900])).
% 1.03/0.96 tff(1903,plain,
% 1.03/0.96 (c1_1(a137)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[1243, 1900])).
% 1.03/0.96 tff(1904,plain,
% 1.03/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a151) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a139)) | (~c1_1(a151)) | (~c0_1(a151)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a151) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a139)) | (~c1_1(a151)) | (~c0_1(a151)))),
% 1.03/0.96 inference(rewrite,[status(thm)],[])).
% 1.03/0.96 tff(1905,plain,
% 1.03/0.96 (((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a151) | (~c1_1(a151)) | (~c0_1(a151)) | c1_1(a139) | c3_1(a139) | (~c2_1(a139))) <=> (c2_1(a151) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a139)) | (~c1_1(a151)) | (~c0_1(a151)))),
% 1.03/0.96 inference(rewrite,[status(thm)],[])).
% 1.03/0.96 tff(1906,plain,
% 1.03/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a151) | (~c1_1(a151)) | (~c0_1(a151)) | c1_1(a139) | c3_1(a139) | (~c2_1(a139)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a151) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a139)) | (~c1_1(a151)) | (~c0_1(a151))))),
% 1.03/0.96 inference(monotonicity,[status(thm)],[1905])).
% 1.03/0.96 tff(1907,plain,
% 1.03/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a151) | (~c1_1(a151)) | (~c0_1(a151)) | c1_1(a139) | c3_1(a139) | (~c2_1(a139)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a151) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a139)) | (~c1_1(a151)) | (~c0_1(a151)))),
% 1.03/0.96 inference(transitivity,[status(thm)],[1906, 1904])).
% 1.03/0.96 tff(1908,plain,
% 1.03/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a151) | (~c1_1(a151)) | (~c0_1(a151)) | c1_1(a139) | c3_1(a139) | (~c2_1(a139)))),
% 1.03/0.96 inference(quant_inst,[status(thm)],[])).
% 1.03/0.96 tff(1909,plain,
% 1.03/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a151) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a139)) | (~c1_1(a151)) | (~c0_1(a151))),
% 1.03/0.96 inference(modus_ponens,[status(thm)],[1908, 1907])).
% 1.03/0.96 tff(1910,plain,
% 1.03/0.96 (~c2_1(a139)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[1909, 187, 1903, 1902, 1901, 1893, 1892, 1891, 1747, 1746, 94])).
% 1.03/0.96 tff(1911,plain,
% 1.03/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c0_1(a144) | c3_1(a144) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a139) | (~c2_1(a144)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c0_1(a144) | c3_1(a144) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a139) | (~c2_1(a144)))),
% 1.03/0.96 inference(rewrite,[status(thm)],[])).
% 1.03/0.96 tff(1912,plain,
% 1.03/0.96 (((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a139) | c1_1(a139) | c3_1(a139)) <=> (c0_1(a144) | c3_1(a144) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a139) | (~c2_1(a144)))),
% 1.03/0.96 inference(rewrite,[status(thm)],[])).
% 1.03/0.96 tff(1913,plain,
% 1.03/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a139) | c1_1(a139) | c3_1(a139))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c0_1(a144) | c3_1(a144) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a139) | (~c2_1(a144))))),
% 1.03/0.96 inference(monotonicity,[status(thm)],[1912])).
% 1.03/0.96 tff(1914,plain,
% 1.03/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a139) | c1_1(a139) | c3_1(a139))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c0_1(a144) | c3_1(a144) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a139) | (~c2_1(a144)))),
% 1.03/0.96 inference(transitivity,[status(thm)],[1913, 1911])).
% 1.03/0.96 tff(1915,plain,
% 1.03/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a139) | c1_1(a139) | c3_1(a139))),
% 1.03/0.96 inference(quant_inst,[status(thm)],[])).
% 1.03/0.96 tff(1916,plain,
% 1.03/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c0_1(a144) | c3_1(a144) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a139) | (~c2_1(a144))),
% 1.03/0.96 inference(modus_ponens,[status(thm)],[1915, 1914])).
% 1.03/0.96 tff(1917,plain,
% 1.03/0.96 ($false),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[1916, 187, 1903, 1902, 1901, 1883, 1882, 1881, 1747, 1746, 1176, 1910])).
% 1.03/0.96 tff(1918,plain,(hskp18), inference(lemma,lemma(discharge,[]))).
% 1.03/0.96 tff(1919,plain,
% 1.03/0.96 (((~hskp18) | (~c3_1(a159))) <=> ((~hskp18) | (~c3_1(a159)))),
% 1.03/0.96 inference(rewrite,[status(thm)],[])).
% 1.03/0.96 tff(1920,plain,
% 1.03/0.96 (((~c3_1(a159)) | (~hskp18)) <=> ((~hskp18) | (~c3_1(a159)))),
% 1.03/0.96 inference(rewrite,[status(thm)],[])).
% 1.03/0.96 tff(1921,axiom,((~c3_1(a159)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause99')).
% 1.03/0.96 tff(1922,plain,
% 1.03/0.96 ((~hskp18) | (~c3_1(a159))),
% 1.03/0.96 inference(modus_ponens,[status(thm)],[1921, 1920])).
% 1.03/0.96 tff(1923,plain,
% 1.03/0.96 ((~hskp18) | (~c3_1(a159))),
% 1.03/0.96 inference(modus_ponens,[status(thm)],[1922, 1919])).
% 1.03/0.96 tff(1924,plain,
% 1.03/0.96 (~c3_1(a159)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[1923, 1918])).
% 1.03/0.96 tff(1925,plain,
% 1.03/0.96 (((~hskp18) | (~c2_1(a159))) <=> ((~hskp18) | (~c2_1(a159)))),
% 1.03/0.96 inference(rewrite,[status(thm)],[])).
% 1.03/0.96 tff(1926,plain,
% 1.03/0.96 (((~c2_1(a159)) | (~hskp18)) <=> ((~hskp18) | (~c2_1(a159)))),
% 1.03/0.96 inference(rewrite,[status(thm)],[])).
% 1.03/0.96 tff(1927,axiom,((~c2_1(a159)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause98')).
% 1.03/0.96 tff(1928,plain,
% 1.03/0.96 ((~hskp18) | (~c2_1(a159))),
% 1.03/0.96 inference(modus_ponens,[status(thm)],[1927, 1926])).
% 1.03/0.96 tff(1929,plain,
% 1.03/0.96 ((~hskp18) | (~c2_1(a159))),
% 1.03/0.96 inference(modus_ponens,[status(thm)],[1928, 1925])).
% 1.03/0.96 tff(1930,plain,
% 1.03/0.96 (~c2_1(a159)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[1929, 1918])).
% 1.03/0.96 tff(1931,plain,
% 1.03/0.96 (((~hskp18) | c0_1(a159)) <=> ((~hskp18) | c0_1(a159))),
% 1.03/0.96 inference(rewrite,[status(thm)],[])).
% 1.03/0.96 tff(1932,axiom,((~hskp18) | c0_1(a159)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause59')).
% 1.03/0.96 tff(1933,plain,
% 1.03/0.96 ((~hskp18) | c0_1(a159)),
% 1.03/0.96 inference(modus_ponens,[status(thm)],[1932, 1931])).
% 1.03/0.96 tff(1934,plain,
% 1.03/0.96 ((~hskp18) | c0_1(a159)),
% 1.03/0.96 inference(modus_ponens,[status(thm)],[1933, 1931])).
% 1.03/0.96 tff(1935,plain,
% 1.03/0.96 ((~hskp18) | c0_1(a159)),
% 1.03/0.96 inference(modus_ponens,[status(thm)],[1934, 1931])).
% 1.03/0.96 tff(1936,plain,
% 1.03/0.96 ((~hskp18) | c0_1(a159)),
% 1.03/0.96 inference(modus_ponens,[status(thm)],[1935, 1931])).
% 1.03/0.96 tff(1937,plain,
% 1.03/0.96 ((~hskp18) | c0_1(a159)),
% 1.03/0.96 inference(modus_ponens,[status(thm)],[1936, 1931])).
% 1.03/0.96 tff(1938,plain,
% 1.03/0.96 ((~hskp18) | c0_1(a159)),
% 1.03/0.96 inference(modus_ponens,[status(thm)],[1937, 1931])).
% 1.03/0.96 tff(1939,plain,
% 1.03/0.96 ((~hskp18) | c0_1(a159)),
% 1.03/0.96 inference(modus_ponens,[status(thm)],[1938, 1931])).
% 1.03/0.96 tff(1940,plain,
% 1.03/0.96 ((~hskp18) | c0_1(a159)),
% 1.03/0.96 inference(modus_ponens,[status(thm)],[1939, 1931])).
% 1.03/0.96 tff(1941,plain,
% 1.03/0.96 (c0_1(a159)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[1940, 1918])).
% 1.03/0.96 tff(1942,plain,
% 1.03/0.96 (((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp3 | hskp1 | c2_1(a159) | c3_1(a159) | (~ndr1_0) | (~c0_1(a159)))) <=> ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp3 | hskp1 | c2_1(a159) | c3_1(a159) | (~ndr1_0) | (~c0_1(a159)))),
% 1.03/0.96 inference(rewrite,[status(thm)],[])).
% 1.03/0.96 tff(1943,plain,
% 1.03/0.96 ((hskp3 | hskp1 | (~ndr1_0) | c3_1(a159) | c2_1(a159) | (~c0_1(a159))) <=> (hskp3 | hskp1 | c2_1(a159) | c3_1(a159) | (~ndr1_0) | (~c0_1(a159)))),
% 1.03/0.96 inference(rewrite,[status(thm)],[])).
% 1.03/0.96 tff(1944,plain,
% 1.03/0.96 (((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp3 | hskp1 | (~ndr1_0) | c3_1(a159) | c2_1(a159) | (~c0_1(a159)))) <=> ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp3 | hskp1 | c2_1(a159) | c3_1(a159) | (~ndr1_0) | (~c0_1(a159))))),
% 1.03/0.96 inference(monotonicity,[status(thm)],[1943])).
% 1.03/0.96 tff(1945,plain,
% 1.03/0.96 (((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp3 | hskp1 | (~ndr1_0) | c3_1(a159) | c2_1(a159) | (~c0_1(a159)))) <=> ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp3 | hskp1 | c2_1(a159) | c3_1(a159) | (~ndr1_0) | (~c0_1(a159)))),
% 1.03/0.96 inference(transitivity,[status(thm)],[1944, 1942])).
% 1.03/0.96 tff(1946,plain,
% 1.03/0.96 ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp3 | hskp1 | (~ndr1_0) | c3_1(a159) | c2_1(a159) | (~c0_1(a159)))),
% 1.03/0.96 inference(quant_inst,[status(thm)],[])).
% 1.03/0.96 tff(1947,plain,
% 1.03/0.96 ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp3 | hskp1 | c2_1(a159) | c3_1(a159) | (~ndr1_0) | (~c0_1(a159))),
% 1.03/0.96 inference(modus_ponens,[status(thm)],[1946, 1945])).
% 1.03/0.96 tff(1948,plain,
% 1.03/0.96 (hskp3 | hskp1),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[1947, 187, 1941, 1930, 1924, 84])).
% 1.03/0.96 tff(1949,plain,
% 1.03/0.96 (hskp1),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[1948, 52])).
% 1.03/0.96 tff(1950,plain,
% 1.03/0.96 (c1_1(a125)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[608, 1949])).
% 1.03/0.96 tff(1951,plain,
% 1.03/0.96 (c0_1(a125)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[619, 1949])).
% 1.03/0.96 tff(1952,plain,
% 1.03/0.96 (((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | (~ndr1_0) | c2_1(a125) | (~c0_1(a125)) | (~c1_1(a125)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp15 | (~ndr1_0) | c2_1(a125) | (~c0_1(a125)) | (~c1_1(a125)))),
% 1.03/0.96 inference(rewrite,[status(thm)],[])).
% 1.03/0.96 tff(1953,plain,
% 1.03/0.96 ((hskp15 | (~ndr1_0) | c2_1(a125) | (~c1_1(a125)) | (~c0_1(a125))) <=> (hskp15 | (~ndr1_0) | c2_1(a125) | (~c0_1(a125)) | (~c1_1(a125)))),
% 1.03/0.96 inference(rewrite,[status(thm)],[])).
% 1.03/0.96 tff(1954,plain,
% 1.03/0.96 (((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | (~ndr1_0) | c2_1(a125) | (~c1_1(a125)) | (~c0_1(a125)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | (~ndr1_0) | c2_1(a125) | (~c0_1(a125)) | (~c1_1(a125))))),
% 1.03/0.96 inference(monotonicity,[status(thm)],[1953])).
% 1.03/0.96 tff(1955,plain,
% 1.03/0.96 (((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | (~ndr1_0) | c2_1(a125) | (~c1_1(a125)) | (~c0_1(a125)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp15 | (~ndr1_0) | c2_1(a125) | (~c0_1(a125)) | (~c1_1(a125)))),
% 1.03/0.96 inference(transitivity,[status(thm)],[1954, 1952])).
% 1.03/0.96 tff(1956,plain,
% 1.03/0.96 ((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | (~ndr1_0) | c2_1(a125) | (~c1_1(a125)) | (~c0_1(a125)))),
% 1.03/0.96 inference(quant_inst,[status(thm)],[])).
% 1.03/0.96 tff(1957,plain,
% 1.03/0.96 ((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp15 | (~ndr1_0) | c2_1(a125) | (~c0_1(a125)) | (~c1_1(a125))),
% 1.03/0.96 inference(modus_ponens,[status(thm)],[1956, 1955])).
% 1.03/0.96 tff(1958,plain,
% 1.03/0.96 (hskp15 | c2_1(a125)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[1957, 187, 1951, 1950, 63])).
% 1.03/0.96 tff(1959,plain,
% 1.03/0.96 (c2_1(a125)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[1958, 74])).
% 1.03/0.96 tff(1960,plain,
% 1.03/0.96 (~c3_1(a125)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[597, 1949])).
% 1.03/0.96 tff(1961,plain,
% 1.03/0.96 (hskp13),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[1189, 187, 1951, 1950, 1960, 21, 1959])).
% 1.03/0.96 tff(1962,plain,
% 1.03/0.96 (~c3_1(a144)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[991, 1961])).
% 1.03/0.96 tff(1963,plain,
% 1.03/0.96 (~c0_1(a144)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[1015, 1961])).
% 1.03/0.96 tff(1964,plain,
% 1.03/0.96 (c2_1(a144)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[1002, 1961])).
% 1.03/0.96 tff(1965,plain,
% 1.03/0.96 (hskp29),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[1338, 187, 52, 1964, 1963, 1962, 73])).
% 1.03/0.96 tff(1966,plain,
% 1.03/0.96 (c1_1(a150)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[1360, 1965])).
% 1.03/0.96 tff(1967,plain,
% 1.03/0.96 (c0_1(a150)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[1371, 1965])).
% 1.03/0.96 tff(1968,plain,
% 1.03/0.96 (((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | (~ndr1_0) | c2_1(a150) | (~c0_1(a150)) | (~c1_1(a150)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp15 | (~ndr1_0) | c2_1(a150) | (~c0_1(a150)) | (~c1_1(a150)))),
% 1.03/0.96 inference(rewrite,[status(thm)],[])).
% 1.03/0.96 tff(1969,plain,
% 1.03/0.96 ((hskp15 | (~ndr1_0) | c2_1(a150) | (~c1_1(a150)) | (~c0_1(a150))) <=> (hskp15 | (~ndr1_0) | c2_1(a150) | (~c0_1(a150)) | (~c1_1(a150)))),
% 1.03/0.96 inference(rewrite,[status(thm)],[])).
% 1.03/0.96 tff(1970,plain,
% 1.03/0.96 (((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | (~ndr1_0) | c2_1(a150) | (~c1_1(a150)) | (~c0_1(a150)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | (~ndr1_0) | c2_1(a150) | (~c0_1(a150)) | (~c1_1(a150))))),
% 1.03/0.96 inference(monotonicity,[status(thm)],[1969])).
% 1.03/0.96 tff(1971,plain,
% 1.03/0.96 (((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | (~ndr1_0) | c2_1(a150) | (~c1_1(a150)) | (~c0_1(a150)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp15 | (~ndr1_0) | c2_1(a150) | (~c0_1(a150)) | (~c1_1(a150)))),
% 1.03/0.96 inference(transitivity,[status(thm)],[1970, 1968])).
% 1.03/0.96 tff(1972,plain,
% 1.03/0.96 ((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | (~ndr1_0) | c2_1(a150) | (~c1_1(a150)) | (~c0_1(a150)))),
% 1.03/0.96 inference(quant_inst,[status(thm)],[])).
% 1.03/0.96 tff(1973,plain,
% 1.03/0.96 ((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp15 | (~ndr1_0) | c2_1(a150) | (~c0_1(a150)) | (~c1_1(a150))),
% 1.03/0.96 inference(modus_ponens,[status(thm)],[1972, 1971])).
% 1.03/0.96 tff(1974,plain,
% 1.03/0.96 (c2_1(a150)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[1973, 187, 74, 1967, 1966, 63])).
% 1.03/0.96 tff(1975,plain,
% 1.03/0.96 (((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | c2_1(a159) | (~ndr1_0) | (~c1_1(a159)) | (~c0_1(a159)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp15 | c2_1(a159) | (~ndr1_0) | (~c1_1(a159)) | (~c0_1(a159)))),
% 1.03/0.96 inference(rewrite,[status(thm)],[])).
% 1.03/0.96 tff(1976,plain,
% 1.03/0.96 ((hskp15 | (~ndr1_0) | c2_1(a159) | (~c1_1(a159)) | (~c0_1(a159))) <=> (hskp15 | c2_1(a159) | (~ndr1_0) | (~c1_1(a159)) | (~c0_1(a159)))),
% 1.03/0.96 inference(rewrite,[status(thm)],[])).
% 1.03/0.96 tff(1977,plain,
% 1.03/0.96 (((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | (~ndr1_0) | c2_1(a159) | (~c1_1(a159)) | (~c0_1(a159)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | c2_1(a159) | (~ndr1_0) | (~c1_1(a159)) | (~c0_1(a159))))),
% 1.03/0.96 inference(monotonicity,[status(thm)],[1976])).
% 1.03/0.96 tff(1978,plain,
% 1.03/0.96 (((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | (~ndr1_0) | c2_1(a159) | (~c1_1(a159)) | (~c0_1(a159)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp15 | c2_1(a159) | (~ndr1_0) | (~c1_1(a159)) | (~c0_1(a159)))),
% 1.03/0.96 inference(transitivity,[status(thm)],[1977, 1975])).
% 1.03/0.96 tff(1979,plain,
% 1.03/0.96 ((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | (~ndr1_0) | c2_1(a159) | (~c1_1(a159)) | (~c0_1(a159)))),
% 1.03/0.96 inference(quant_inst,[status(thm)],[])).
% 1.03/0.96 tff(1980,plain,
% 1.03/0.96 ((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp15 | c2_1(a159) | (~ndr1_0) | (~c1_1(a159)) | (~c0_1(a159))),
% 1.03/0.96 inference(modus_ponens,[status(thm)],[1979, 1978])).
% 1.03/0.96 tff(1981,plain,
% 1.03/0.96 (hskp15 | (~c1_1(a159))),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[1980, 187, 1941, 1930, 63])).
% 1.03/0.96 tff(1982,plain,
% 1.03/0.96 (~c1_1(a159)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[1981, 74])).
% 1.03/0.96 tff(1983,plain,
% 1.03/0.96 (c3_1(a150)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[1349, 1965])).
% 1.03/0.96 tff(1984,plain,
% 1.03/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a159) | c3_1(a159) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c3_1(a150)) | (~c2_1(a150)) | (~c1_1(a150)) | (~c2_1(a144)) | c1_1(a159))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a159) | c3_1(a159) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c3_1(a150)) | (~c2_1(a150)) | (~c1_1(a150)) | (~c2_1(a144)) | c1_1(a159))),
% 1.03/0.96 inference(rewrite,[status(thm)],[])).
% 1.03/0.96 tff(1985,plain,
% 1.03/0.96 (((~ndr1_0) | (~c2_1(a150)) | (~c3_1(a150)) | (~c1_1(a150)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a159) | c1_1(a159) | c3_1(a159)) <=> (c2_1(a159) | c3_1(a159) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c3_1(a150)) | (~c2_1(a150)) | (~c1_1(a150)) | (~c2_1(a144)) | c1_1(a159))),
% 1.03/0.96 inference(rewrite,[status(thm)],[])).
% 1.03/0.96 tff(1986,plain,
% 1.03/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a150)) | (~c3_1(a150)) | (~c1_1(a150)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a159) | c1_1(a159) | c3_1(a159))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a159) | c3_1(a159) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c3_1(a150)) | (~c2_1(a150)) | (~c1_1(a150)) | (~c2_1(a144)) | c1_1(a159)))),
% 1.03/0.96 inference(monotonicity,[status(thm)],[1985])).
% 1.03/0.96 tff(1987,plain,
% 1.03/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a150)) | (~c3_1(a150)) | (~c1_1(a150)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a159) | c1_1(a159) | c3_1(a159))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a159) | c3_1(a159) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c3_1(a150)) | (~c2_1(a150)) | (~c1_1(a150)) | (~c2_1(a144)) | c1_1(a159))),
% 1.03/0.96 inference(transitivity,[status(thm)],[1986, 1984])).
% 1.03/0.96 tff(1988,plain,
% 1.03/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a150)) | (~c3_1(a150)) | (~c1_1(a150)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a159) | c1_1(a159) | c3_1(a159))),
% 1.03/0.96 inference(quant_inst,[status(thm)],[])).
% 1.03/0.96 tff(1989,plain,
% 1.03/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a159) | c3_1(a159) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c3_1(a150)) | (~c2_1(a150)) | (~c1_1(a150)) | (~c2_1(a144)) | c1_1(a159)),
% 1.03/0.96 inference(modus_ponens,[status(thm)],[1988, 1987])).
% 1.03/0.96 tff(1990,plain,
% 1.03/0.96 ($false),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[1989, 187, 1966, 1983, 1964, 1930, 1924, 1963, 1962, 1176, 1982, 1974])).
% 1.03/0.96 tff(1991,plain,(hskp15 | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.03/0.96 tff(1992,plain,
% 1.03/0.96 (hskp15),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[1991, 52])).
% 1.03/0.96 tff(1993,plain,
% 1.03/0.96 (c3_1(a149)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[267, 1992])).
% 1.03/0.96 tff(1994,plain,
% 1.03/0.96 (~c2_1(a149)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[558, 1992])).
% 1.03/0.96 tff(1995,plain,
% 1.03/0.96 (hskp14 | c0_1(a149)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[766, 187, 52, 1993, 1994, 51])).
% 1.03/0.96 tff(1996,plain,
% 1.03/0.96 (c0_1(a149)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[1995, 772])).
% 1.03/0.96 tff(1997,plain,
% 1.03/0.96 (~c1_1(a149)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[564, 1992])).
% 1.03/0.96 tff(1998,plain,
% 1.03/0.96 (~hskp6),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[789, 772, 52, 1997, 1996, 1993])).
% 1.03/0.96 tff(1999,plain,
% 1.03/0.96 (hskp12),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[626, 187, 1951, 1950, 1960, 239])).
% 1.03/0.96 tff(2000,plain,
% 1.03/0.96 (~c0_1(a140)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[632, 1999])).
% 1.03/0.96 tff(2001,plain,
% 1.03/0.96 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp17 | c2_1(a159) | c3_1(a159) | c2_1(a149) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)) | (~c0_1(a159)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp17 | c2_1(a159) | c3_1(a159) | c2_1(a149) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)) | (~c0_1(a159)))),
% 1.03/0.96 inference(rewrite,[status(thm)],[])).
% 1.03/0.96 tff(2002,plain,
% 1.03/0.96 ((hskp17 | (~ndr1_0) | c2_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a159) | c2_1(a159) | (~c0_1(a159))) <=> (hskp17 | c2_1(a159) | c3_1(a159) | c2_1(a149) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)) | (~c0_1(a159)))),
% 1.03/0.96 inference(rewrite,[status(thm)],[])).
% 1.03/0.96 tff(2003,plain,
% 1.03/0.96 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a159) | c2_1(a159) | (~c0_1(a159)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp17 | c2_1(a159) | c3_1(a159) | c2_1(a149) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)) | (~c0_1(a159))))),
% 1.03/0.96 inference(monotonicity,[status(thm)],[2002])).
% 1.03/0.96 tff(2004,plain,
% 1.03/0.96 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a159) | c2_1(a159) | (~c0_1(a159)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp17 | c2_1(a159) | c3_1(a159) | c2_1(a149) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)) | (~c0_1(a159)))),
% 1.03/0.96 inference(transitivity,[status(thm)],[2003, 2001])).
% 1.03/0.96 tff(2005,plain,
% 1.03/0.96 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a159) | c2_1(a159) | (~c0_1(a159)))),
% 1.03/0.96 inference(quant_inst,[status(thm)],[])).
% 1.03/0.96 tff(2006,plain,
% 1.03/0.96 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp17 | c2_1(a159) | c3_1(a159) | c2_1(a149) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)) | (~c0_1(a159))),
% 1.03/0.96 inference(modus_ponens,[status(thm)],[2005, 2004])).
% 1.03/0.96 tff(2007,plain,
% 1.03/0.96 (hskp17 | (~c0_1(a149))),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[2006, 187, 1941, 1993, 1930, 1924, 1994, 290])).
% 1.03/0.96 tff(2008,plain,
% 1.03/0.96 (hskp17),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[2007, 1996])).
% 1.03/0.96 tff(2009,plain,
% 1.03/0.96 (~c3_1(a158)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[441, 2008])).
% 1.03/0.96 tff(2010,plain,
% 1.03/0.96 (c3_1(a140)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[646, 1999])).
% 1.03/0.96 tff(2011,plain,
% 1.03/0.96 (c1_1(a140)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[861, 1999])).
% 1.03/0.96 tff(2012,plain,
% 1.03/0.96 (c1_1(a158)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[458, 2008])).
% 1.03/0.96 tff(2013,plain,
% 1.03/0.96 (~hskp6),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[789, 1996, 52, 1997, 772, 1993])).
% 1.03/0.96 tff(2014,plain,
% 1.03/0.96 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c3_1(a158) | c0_1(a140) | (~ndr1_0) | (~c3_1(a140)) | (~c1_1(a140)) | (~c1_1(a158)) | c0_1(a158))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c3_1(a158) | c0_1(a140) | (~ndr1_0) | (~c3_1(a140)) | (~c1_1(a140)) | (~c1_1(a158)) | c0_1(a158))),
% 1.03/0.96 inference(rewrite,[status(thm)],[])).
% 1.03/0.96 tff(2015,plain,
% 1.03/0.96 ((hskp6 | (~ndr1_0) | c0_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | c3_1(a158) | c0_1(a158) | (~c1_1(a158))) <=> (hskp6 | c3_1(a158) | c0_1(a140) | (~ndr1_0) | (~c3_1(a140)) | (~c1_1(a140)) | (~c1_1(a158)) | c0_1(a158))),
% 1.03/0.96 inference(rewrite,[status(thm)],[])).
% 1.03/0.96 tff(2016,plain,
% 1.03/0.96 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | c3_1(a158) | c0_1(a158) | (~c1_1(a158)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c3_1(a158) | c0_1(a140) | (~ndr1_0) | (~c3_1(a140)) | (~c1_1(a140)) | (~c1_1(a158)) | c0_1(a158)))),
% 1.03/0.96 inference(monotonicity,[status(thm)],[2015])).
% 1.03/0.96 tff(2017,plain,
% 1.03/0.96 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | c3_1(a158) | c0_1(a158) | (~c1_1(a158)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c3_1(a158) | c0_1(a140) | (~ndr1_0) | (~c3_1(a140)) | (~c1_1(a140)) | (~c1_1(a158)) | c0_1(a158))),
% 1.03/0.96 inference(transitivity,[status(thm)],[2016, 2014])).
% 1.03/0.96 tff(2018,plain,
% 1.03/0.96 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | c3_1(a158) | c0_1(a158) | (~c1_1(a158)))),
% 1.03/0.96 inference(quant_inst,[status(thm)],[])).
% 1.03/0.96 tff(2019,plain,
% 1.03/0.96 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c3_1(a158) | c0_1(a140) | (~ndr1_0) | (~c3_1(a140)) | (~c1_1(a140)) | (~c1_1(a158)) | c0_1(a158)),
% 1.03/0.96 inference(modus_ponens,[status(thm)],[2018, 2017])).
% 1.03/0.96 tff(2020,plain,
% 1.03/0.97 (c0_1(a158)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[2019, 187, 2013, 2012, 2011, 2010, 2009, 2000, 336])).
% 1.03/0.97 tff(2021,plain,
% 1.03/0.97 (hskp14 | c2_1(a140)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[889, 187, 52, 2010, 2000, 51])).
% 1.03/0.97 tff(2022,plain,
% 1.03/0.97 (c2_1(a140)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[2021, 772])).
% 1.03/0.97 tff(2023,plain,
% 1.03/0.97 (hskp9),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[804, 2013, 53])).
% 1.03/0.97 tff(2024,plain,
% 1.03/0.97 (~c3_1(a136)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[810, 2023])).
% 1.03/0.97 tff(2025,plain,
% 1.03/0.97 (c2_1(a136)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[821, 2023])).
% 1.03/0.97 tff(2026,plain,
% 1.03/0.97 (c0_1(a136)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[840, 2023])).
% 1.03/0.97 tff(2027,plain,
% 1.03/0.97 (~c1_1(a136)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[1436, 187, 11, 2026, 2025, 2024, 21])).
% 1.03/0.97 tff(2028,plain,
% 1.03/0.97 (~c2_1(a158)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[447, 2008])).
% 1.03/0.97 tff(2029,plain,
% 1.03/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a158) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | (~c1_1(a158)) | (~c0_1(a158)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a158) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | (~c1_1(a158)) | (~c0_1(a158)))),
% 1.03/0.97 inference(rewrite,[status(thm)],[])).
% 1.03/0.97 tff(2030,plain,
% 1.03/0.97 (((~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | c2_1(a158) | (~c1_1(a158)) | (~c0_1(a158)) | c1_1(a136) | c3_1(a136) | (~c2_1(a136))) <=> (c2_1(a158) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | (~c1_1(a158)) | (~c0_1(a158)))),
% 1.03/0.97 inference(rewrite,[status(thm)],[])).
% 1.03/0.97 tff(2031,plain,
% 1.03/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | c2_1(a158) | (~c1_1(a158)) | (~c0_1(a158)) | c1_1(a136) | c3_1(a136) | (~c2_1(a136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a158) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | (~c1_1(a158)) | (~c0_1(a158))))),
% 1.03/0.97 inference(monotonicity,[status(thm)],[2030])).
% 1.03/0.97 tff(2032,plain,
% 1.03/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | c2_1(a158) | (~c1_1(a158)) | (~c0_1(a158)) | c1_1(a136) | c3_1(a136) | (~c2_1(a136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a158) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | (~c1_1(a158)) | (~c0_1(a158)))),
% 1.03/0.97 inference(transitivity,[status(thm)],[2031, 2029])).
% 1.03/0.97 tff(2033,plain,
% 1.03/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | c2_1(a158) | (~c1_1(a158)) | (~c0_1(a158)) | c1_1(a136) | c3_1(a136) | (~c2_1(a136)))),
% 1.03/0.97 inference(quant_inst,[status(thm)],[])).
% 1.03/0.97 tff(2034,plain,
% 1.03/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a158) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | (~c1_1(a158)) | (~c0_1(a158))),
% 1.03/0.97 inference(modus_ponens,[status(thm)],[2033, 2032])).
% 1.03/0.97 tff(2035,plain,
% 1.03/0.97 ($false),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[2034, 187, 2012, 2011, 2010, 2025, 2028, 2024, 94, 2027, 2022, 2020])).
% 1.03/0.97 tff(2036,plain,(hskp14 | hskp13 | hskp21 | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.03/0.97 tff(2037,plain,
% 1.03/0.97 (hskp14),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[2036, 11, 53, 52])).
% 1.03/0.97 tff(2038,plain,
% 1.03/0.97 (~c1_1(a145)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[528, 2037])).
% 1.03/0.97 tff(2039,plain,
% 1.03/0.97 (~c3_1(a145)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[522, 2037])).
% 1.03/0.97 tff(2040,plain,
% 1.03/0.97 (~c0_1(a145)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[541, 2037])).
% 1.03/0.97 tff(2041,plain,
% 1.03/0.97 (c0_1(a149)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[1453, 2040, 2039, 52, 1993, 1994, 2038])).
% 1.03/0.97 tff(2042,plain,
% 1.03/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a149) | c2_1(a149) | c0_1(a145) | c1_1(a145) | c3_1(a145) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | (~c0_1(a149)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c2_1(a149) | c0_1(a145) | c1_1(a145) | c3_1(a145) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | (~c0_1(a149)))),
% 1.03/0.97 inference(rewrite,[status(thm)],[])).
% 1.03/0.97 tff(2043,plain,
% 1.03/0.97 (((~ndr1_0) | c1_1(a149) | c2_1(a149) | (~c0_1(a149)) | c3_1(a145) | c1_1(a145) | c0_1(a145) | c2_1(a133) | c1_1(a133) | c0_1(a133)) <=> (c1_1(a149) | c2_1(a149) | c0_1(a145) | c1_1(a145) | c3_1(a145) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | (~c0_1(a149)))),
% 1.03/0.97 inference(rewrite,[status(thm)],[])).
% 1.03/0.97 tff(2044,plain,
% 1.03/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | c2_1(a149) | (~c0_1(a149)) | c3_1(a145) | c1_1(a145) | c0_1(a145) | c2_1(a133) | c1_1(a133) | c0_1(a133))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a149) | c2_1(a149) | c0_1(a145) | c1_1(a145) | c3_1(a145) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | (~c0_1(a149))))),
% 1.03/0.97 inference(monotonicity,[status(thm)],[2043])).
% 1.03/0.97 tff(2045,plain,
% 1.03/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | c2_1(a149) | (~c0_1(a149)) | c3_1(a145) | c1_1(a145) | c0_1(a145) | c2_1(a133) | c1_1(a133) | c0_1(a133))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c2_1(a149) | c0_1(a145) | c1_1(a145) | c3_1(a145) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | (~c0_1(a149)))),
% 1.03/0.97 inference(transitivity,[status(thm)],[2044, 2042])).
% 1.03/0.97 tff(2046,plain,
% 1.03/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | c2_1(a149) | (~c0_1(a149)) | c3_1(a145) | c1_1(a145) | c0_1(a145) | c2_1(a133) | c1_1(a133) | c0_1(a133))),
% 1.03/0.97 inference(quant_inst,[status(thm)],[])).
% 1.03/0.97 tff(2047,plain,
% 1.03/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c2_1(a149) | c0_1(a145) | c1_1(a145) | c3_1(a145) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | (~c0_1(a149))),
% 1.03/0.97 inference(modus_ponens,[status(thm)],[2046, 2045])).
% 1.03/0.97 tff(2048,plain,
% 1.03/0.97 ($false),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[2047, 187, 635, 634, 1413, 1405, 1404, 771, 781, 770, 493, 780])).
% 1.03/0.97 tff(2049,plain,((~hskp6) | c1_1(a149) | c2_1(a149) | c0_1(a145) | c1_1(a145) | c3_1(a145) | (~c0_1(a149))), inference(lemma,lemma(discharge,[]))).
% 1.03/0.97 tff(2050,plain,
% 1.03/0.97 (~hskp6),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[2049, 2040, 1994, 1997, 2038, 2039, 2041])).
% 1.03/0.97 tff(2051,plain,
% 1.03/0.97 (hskp17),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[2007, 2041])).
% 1.03/0.97 tff(2052,plain,
% 1.03/0.97 (~c3_1(a158)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[441, 2051])).
% 1.03/0.97 tff(2053,plain,
% 1.03/0.97 (c1_1(a158)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[458, 2051])).
% 1.03/0.97 tff(2054,plain,
% 1.03/0.97 (hskp6 | c0_1(a158)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[2019, 187, 2053, 2011, 2010, 2052, 2000, 336])).
% 1.03/0.97 tff(2055,plain,
% 1.03/0.97 (c0_1(a158)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[2054, 2050])).
% 1.03/0.97 tff(2056,plain,
% 1.03/0.97 (hskp9),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[804, 2050, 53])).
% 1.03/0.97 tff(2057,plain,
% 1.03/0.97 (c2_1(a136)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[821, 2056])).
% 1.03/0.97 tff(2058,plain,
% 1.03/0.97 (c0_1(a136)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[840, 2056])).
% 1.03/0.97 tff(2059,plain,
% 1.03/0.97 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | c3_1(a158) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)) | (~c1_1(a158)) | (~c0_1(a158)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | c3_1(a158) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)) | (~c1_1(a158)) | (~c0_1(a158)))),
% 1.03/0.97 inference(rewrite,[status(thm)],[])).
% 1.03/0.97 tff(2060,plain,
% 1.03/0.97 ((hskp13 | (~ndr1_0) | (~c2_1(a136)) | (~c1_1(a136)) | (~c0_1(a136)) | c3_1(a158) | (~c1_1(a158)) | (~c0_1(a158))) <=> (hskp13 | c3_1(a158) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)) | (~c1_1(a158)) | (~c0_1(a158)))),
% 1.03/0.97 inference(rewrite,[status(thm)],[])).
% 1.03/0.97 tff(2061,plain,
% 1.03/0.97 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a136)) | (~c1_1(a136)) | (~c0_1(a136)) | c3_1(a158) | (~c1_1(a158)) | (~c0_1(a158)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | c3_1(a158) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)) | (~c1_1(a158)) | (~c0_1(a158))))),
% 1.03/0.97 inference(monotonicity,[status(thm)],[2060])).
% 1.03/0.97 tff(2062,plain,
% 1.03/0.97 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a136)) | (~c1_1(a136)) | (~c0_1(a136)) | c3_1(a158) | (~c1_1(a158)) | (~c0_1(a158)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | c3_1(a158) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)) | (~c1_1(a158)) | (~c0_1(a158)))),
% 1.03/0.97 inference(transitivity,[status(thm)],[2061, 2059])).
% 1.03/0.97 tff(2063,plain,
% 1.03/0.97 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a136)) | (~c1_1(a136)) | (~c0_1(a136)) | c3_1(a158) | (~c1_1(a158)) | (~c0_1(a158)))),
% 1.03/0.97 inference(quant_inst,[status(thm)],[])).
% 1.03/0.97 tff(2064,plain,
% 1.03/0.97 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | c3_1(a158) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)) | (~c1_1(a158)) | (~c0_1(a158))),
% 1.03/0.97 inference(modus_ponens,[status(thm)],[2063, 2062])).
% 1.03/0.97 tff(2065,plain,
% 1.03/0.97 (~c1_1(a136)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[2064, 187, 11, 2053, 2058, 2057, 2052, 21, 2055])).
% 1.03/0.97 tff(2066,plain,
% 1.03/0.97 (~c3_1(a136)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[810, 2056])).
% 1.03/0.97 tff(2067,plain,
% 1.03/0.97 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c0_1(a140) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | c2_1(a140) | (~c3_1(a140)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a140) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | c2_1(a140) | (~c3_1(a140)))),
% 1.03/0.97 inference(rewrite,[status(thm)],[])).
% 1.03/0.97 tff(2068,plain,
% 1.03/0.97 ((hskp3 | (~ndr1_0) | c3_1(a136) | c1_1(a136) | (~c2_1(a136)) | c0_1(a140) | c2_1(a140) | (~c3_1(a140))) <=> (hskp3 | c0_1(a140) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | c2_1(a140) | (~c3_1(a140)))),
% 1.03/0.97 inference(rewrite,[status(thm)],[])).
% 1.03/0.97 tff(2069,plain,
% 1.03/0.97 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a136) | c1_1(a136) | (~c2_1(a136)) | c0_1(a140) | c2_1(a140) | (~c3_1(a140)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c0_1(a140) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | c2_1(a140) | (~c3_1(a140))))),
% 1.03/0.97 inference(monotonicity,[status(thm)],[2068])).
% 1.03/0.97 tff(2070,plain,
% 1.03/0.97 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a136) | c1_1(a136) | (~c2_1(a136)) | c0_1(a140) | c2_1(a140) | (~c3_1(a140)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a140) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | c2_1(a140) | (~c3_1(a140)))),
% 1.03/0.97 inference(transitivity,[status(thm)],[2069, 2067])).
% 1.03/0.97 tff(2071,plain,
% 1.03/0.97 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a136) | c1_1(a136) | (~c2_1(a136)) | c0_1(a140) | c2_1(a140) | (~c3_1(a140)))),
% 1.03/0.97 inference(quant_inst,[status(thm)],[])).
% 1.03/0.97 tff(2072,plain,
% 1.03/0.97 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a140) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | c2_1(a140) | (~c3_1(a140))),
% 1.03/0.97 inference(modus_ponens,[status(thm)],[2071, 2070])).
% 1.03/0.97 tff(2073,plain,
% 1.03/0.97 (c2_1(a140)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[2072, 187, 52, 2010, 2057, 2000, 2066, 41, 2065])).
% 1.03/0.97 tff(2074,plain,
% 1.03/0.97 (~c2_1(a158)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[447, 2051])).
% 1.03/0.97 tff(2075,plain,
% 1.03/0.97 ($false),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[2034, 187, 2053, 2011, 2010, 2057, 2074, 2066, 94, 2065, 2073, 2055])).
% 1.03/0.97 tff(2076,plain,(hskp13 | hskp3 | hskp21), inference(lemma,lemma(discharge,[]))).
% 1.03/0.97 tff(2077,plain,
% 1.03/0.97 (hskp13),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[2076, 53, 52])).
% 1.03/0.97 tff(2078,plain,
% 1.03/0.97 (~c3_1(a144)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[991, 2077])).
% 1.03/0.97 tff(2079,plain,
% 1.03/0.97 (~c0_1(a144)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[1015, 2077])).
% 1.03/0.97 tff(2080,plain,
% 1.03/0.97 (hskp6 | (~c1_1(a144))),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[1023, 187, 2011, 2010, 2079, 2078, 2000, 336])).
% 1.03/0.97 tff(2081,plain,
% 1.03/0.97 (~c1_1(a144)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[2080, 1998])).
% 1.03/0.97 tff(2082,plain,
% 1.03/0.97 (hskp21 | hskp16 | (~c0_1(a149))),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[1392, 187, 1993, 1997, 144])).
% 1.03/0.97 tff(2083,plain,
% 1.03/0.97 (hskp16),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[2082, 1996, 53])).
% 1.03/0.97 tff(2084,plain,
% 1.03/0.97 (~c2_1(a151)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[200, 2083])).
% 1.03/0.97 tff(2085,plain,
% 1.03/0.97 (c2_1(a144)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[1002, 2077])).
% 1.03/0.97 tff(2086,plain,
% 1.03/0.97 (c1_1(a151)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[211, 2083])).
% 1.03/0.97 tff(2087,plain,
% 1.03/0.97 (c0_1(a151)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[249, 2083])).
% 1.03/0.97 tff(2088,plain,
% 1.03/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a151) | c3_1(a144) | (~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | c1_1(a144) | (~c2_1(a144)) | (~c1_1(a151)) | (~c0_1(a151)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a151) | c3_1(a144) | (~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | c1_1(a144) | (~c2_1(a144)) | (~c1_1(a151)) | (~c0_1(a151)))),
% 1.03/0.97 inference(rewrite,[status(thm)],[])).
% 1.03/0.97 tff(2089,plain,
% 1.03/0.97 (((~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | c2_1(a151) | (~c1_1(a151)) | (~c0_1(a151)) | c1_1(a144) | c3_1(a144) | (~c2_1(a144))) <=> (c2_1(a151) | c3_1(a144) | (~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | c1_1(a144) | (~c2_1(a144)) | (~c1_1(a151)) | (~c0_1(a151)))),
% 1.03/0.97 inference(rewrite,[status(thm)],[])).
% 1.03/0.97 tff(2090,plain,
% 1.03/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | c2_1(a151) | (~c1_1(a151)) | (~c0_1(a151)) | c1_1(a144) | c3_1(a144) | (~c2_1(a144)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a151) | c3_1(a144) | (~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | c1_1(a144) | (~c2_1(a144)) | (~c1_1(a151)) | (~c0_1(a151))))),
% 1.03/0.97 inference(monotonicity,[status(thm)],[2089])).
% 1.03/0.97 tff(2091,plain,
% 1.03/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | c2_1(a151) | (~c1_1(a151)) | (~c0_1(a151)) | c1_1(a144) | c3_1(a144) | (~c2_1(a144)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a151) | c3_1(a144) | (~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | c1_1(a144) | (~c2_1(a144)) | (~c1_1(a151)) | (~c0_1(a151)))),
% 1.03/0.97 inference(transitivity,[status(thm)],[2090, 2088])).
% 1.03/0.97 tff(2092,plain,
% 1.03/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | c2_1(a151) | (~c1_1(a151)) | (~c0_1(a151)) | c1_1(a144) | c3_1(a144) | (~c2_1(a144)))),
% 1.03/0.97 inference(quant_inst,[status(thm)],[])).
% 1.03/0.97 tff(2093,plain,
% 1.03/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a151) | c3_1(a144) | (~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | c1_1(a144) | (~c2_1(a144)) | (~c1_1(a151)) | (~c0_1(a151))),
% 1.03/0.97 inference(modus_ponens,[status(thm)],[2092, 2091])).
% 1.03/0.97 tff(2094,plain,
% 1.03/0.97 ($false),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[2093, 187, 2087, 2086, 2085, 2011, 2010, 2084, 2078, 94, 2022, 2081])).
% 1.03/0.97 tff(2095,plain,(hskp14 | hskp21 | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.03/0.97 tff(2096,plain,
% 1.03/0.97 (hskp14),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[2095, 53, 52])).
% 1.03/0.97 tff(2097,plain,
% 1.03/0.97 (~c1_1(a145)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[528, 2096])).
% 1.03/0.97 tff(2098,plain,
% 1.03/0.97 (~c3_1(a145)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[522, 2096])).
% 1.03/0.97 tff(2099,plain,
% 1.03/0.97 (~c0_1(a145)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[541, 2096])).
% 1.03/0.97 tff(2100,plain,
% 1.03/0.97 (c0_1(a149)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[1453, 2099, 2098, 52, 1993, 1994, 2097])).
% 1.03/0.97 tff(2101,plain,
% 1.03/0.97 (~hskp6),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[2049, 2099, 1994, 1997, 2097, 2098, 2100])).
% 1.03/0.97 tff(2102,plain,
% 1.03/0.97 (~c1_1(a144)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[2080, 2101])).
% 1.03/0.97 tff(2103,plain,
% 1.03/0.97 (c2_1(a140) | c1_1(a144)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[1009, 187, 52, 2085, 2010, 2078, 2000, 41])).
% 1.03/0.97 tff(2104,plain,
% 1.03/0.97 (c2_1(a140)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[2103, 2102])).
% 1.03/0.97 tff(2105,plain,
% 1.03/0.97 (hskp16),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[2082, 2100, 53])).
% 1.03/0.97 tff(2106,plain,
% 1.03/0.97 (~c2_1(a151)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[200, 2105])).
% 1.03/0.97 tff(2107,plain,
% 1.03/0.97 (c1_1(a151)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[211, 2105])).
% 1.03/0.97 tff(2108,plain,
% 1.03/0.97 (c0_1(a151)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[249, 2105])).
% 1.03/0.97 tff(2109,plain,
% 1.03/0.97 ($false),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[2093, 187, 2108, 2107, 2085, 2011, 2010, 2106, 2078, 94, 2104, 2102])).
% 1.03/0.97 tff(2110,plain,(hskp21 | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.03/0.97 tff(2111,plain,
% 1.03/0.97 (hskp21),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[2110, 52])).
% 1.03/0.97 tff(2112,plain,
% 1.03/0.97 (~c2_1(a170)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[312, 2111])).
% 1.03/0.97 tff(2113,plain,
% 1.03/0.97 (~c0_1(a170)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[318, 2111])).
% 1.03/0.97 tff(2114,plain,
% 1.03/0.97 (c3_1(a170)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[346, 2111])).
% 1.03/0.97 tff(2115,plain,
% 1.03/0.97 (hskp14),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[515, 187, 52, 2114, 2113, 2112, 51])).
% 1.03/0.97 tff(2116,plain,
% 1.03/0.97 (~c3_1(a145)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[522, 2115])).
% 1.03/0.97 tff(2117,plain,
% 1.03/0.97 (~c1_1(a145)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[528, 2115])).
% 1.03/0.97 tff(2118,plain,
% 1.03/0.97 (~c2_1(a145)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[535, 187, 52, 2114, 2113, 2112, 2117, 2116, 41])).
% 1.03/0.97 tff(2119,plain,
% 1.03/0.97 (~c0_1(a145)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[541, 2115])).
% 1.03/0.97 tff(2120,plain,
% 1.03/0.97 (c0_1(a149)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[1453, 2119, 2116, 52, 1993, 1994, 2117])).
% 1.03/0.97 tff(2121,plain,
% 1.03/0.97 ($false),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[757, 187, 1993, 1997, 2119, 2117, 2116, 279, 2120, 2118])).
% 1.03/0.97 tff(2122,plain,(hskp3), inference(lemma,lemma(discharge,[]))).
% 1.03/0.97 tff(2123,plain,
% 1.03/0.97 (~c3_1(a128)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[1115, 2122])).
% 1.03/0.97 tff(2124,plain,
% 1.03/0.97 (~c2_1(a128)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[583, 2122])).
% 1.03/0.97 tff(2125,plain,
% 1.03/0.97 (~c0_1(a128)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[508, 2122])).
% 1.03/0.97 tff(2126,plain,
% 1.03/0.97 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))))),
% 1.03/0.97 inference(bind,[status(th)],[])).
% 1.03/0.97 tff(2127,plain,
% 1.03/0.97 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.03/0.97 inference(quant_intro,[status(thm)],[2126])).
% 1.03/0.97 tff(2128,plain,
% 1.03/0.97 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.03/0.97 inference(rewrite,[status(thm)],[])).
% 1.03/0.97 tff(2129,plain,
% 1.03/0.97 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp16) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) | hskp16))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))))),
% 1.03/0.97 inference(bind,[status(th)],[])).
% 1.03/0.97 tff(2130,plain,
% 1.03/0.97 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.03/0.97 inference(quant_intro,[status(thm)],[2129])).
% 1.03/0.97 tff(2131,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause172')).
% 1.03/0.97 tff(2132,plain,
% 1.03/0.97 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.03/0.97 inference(modus_ponens,[status(thm)],[2131, 2130])).
% 1.03/0.97 tff(2133,plain,
% 1.03/0.97 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.03/0.97 inference(modus_ponens,[status(thm)],[2132, 2128])).
% 1.03/0.97 tff(2134,plain,(
% 1.03/0.97 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.03/0.97 inference(skolemize,[status(sab)],[2133])).
% 1.03/0.97 tff(2135,plain,
% 1.03/0.97 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.03/0.97 inference(modus_ponens,[status(thm)],[2134, 2127])).
% 1.03/0.97 tff(2136,plain,
% 1.03/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a159) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | c1_1(a159) | (~c0_1(a159)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a159) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | c1_1(a159) | (~c0_1(a159)))),
% 1.03/0.97 inference(rewrite,[status(thm)],[])).
% 1.03/0.97 tff(2137,plain,
% 1.03/0.97 (((~ndr1_0) | c1_1(a159) | c2_1(a159) | (~c0_1(a159)) | c3_1(a128) | c1_1(a128) | c0_1(a128) | c2_1(a128) | c1_1(a128) | c0_1(a128)) <=> (c2_1(a159) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | c1_1(a159) | (~c0_1(a159)))),
% 1.03/0.97 inference(rewrite,[status(thm)],[])).
% 1.03/0.97 tff(2138,plain,
% 1.03/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a159) | c2_1(a159) | (~c0_1(a159)) | c3_1(a128) | c1_1(a128) | c0_1(a128) | c2_1(a128) | c1_1(a128) | c0_1(a128))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a159) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | c1_1(a159) | (~c0_1(a159))))),
% 1.03/0.97 inference(monotonicity,[status(thm)],[2137])).
% 1.03/0.97 tff(2139,plain,
% 1.03/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a159) | c2_1(a159) | (~c0_1(a159)) | c3_1(a128) | c1_1(a128) | c0_1(a128) | c2_1(a128) | c1_1(a128) | c0_1(a128))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a159) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | c1_1(a159) | (~c0_1(a159)))),
% 1.03/0.98 inference(transitivity,[status(thm)],[2138, 2136])).
% 1.03/0.98 tff(2140,plain,
% 1.03/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a159) | c2_1(a159) | (~c0_1(a159)) | c3_1(a128) | c1_1(a128) | c0_1(a128) | c2_1(a128) | c1_1(a128) | c0_1(a128))),
% 1.03/0.98 inference(quant_inst,[status(thm)],[])).
% 1.03/0.98 tff(2141,plain,
% 1.03/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a159) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | c1_1(a159) | (~c0_1(a159))),
% 1.03/0.98 inference(modus_ponens,[status(thm)],[2140, 2139])).
% 1.03/0.98 tff(2142,plain,
% 1.03/0.98 (c1_1(a128)),
% 1.03/0.98 inference(unit_resolution,[status(thm)],[2141, 187, 1941, 1930, 2125, 2124, 2123, 493, 1982])).
% 1.03/0.98 tff(2143,plain,
% 1.03/0.98 (^[U: $i] : refl((hskp27 | hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) <=> (hskp27 | hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))))),
% 1.03/0.98 inference(bind,[status(th)],[])).
% 1.03/0.98 tff(2144,plain,
% 1.03/0.98 (![U: $i] : (hskp27 | hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp27 | hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.03/0.98 inference(quant_intro,[status(thm)],[2143])).
% 1.03/0.98 tff(2145,plain,
% 1.03/0.98 (![U: $i] : (hskp27 | hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp27 | hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.03/0.98 inference(rewrite,[status(thm)],[])).
% 1.03/0.98 tff(2146,plain,
% 1.03/0.98 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | 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)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp27) | hskp15) <=> ((hskp27 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | hskp15))), rewrite(((hskp27 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | hskp15) <=> (hskp27 | hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp27) | hskp15) <=> (hskp27 | hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))))),
% 1.03/0.98 inference(bind,[status(th)],[])).
% 1.03/0.98 tff(2147,plain,
% 1.03/0.98 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp27) | hskp15) <=> ![U: $i] : (hskp27 | hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.03/0.98 inference(quant_intro,[status(thm)],[2146])).
% 1.03/0.98 tff(2148,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp27) | hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause139')).
% 1.03/0.98 tff(2149,plain,
% 1.03/0.98 (![U: $i] : (hskp27 | hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.03/0.98 inference(modus_ponens,[status(thm)],[2148, 2147])).
% 1.03/0.98 tff(2150,plain,
% 1.03/0.98 (![U: $i] : (hskp27 | hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.03/0.98 inference(modus_ponens,[status(thm)],[2149, 2145])).
% 1.03/0.98 tff(2151,plain,(
% 1.03/0.98 ![U: $i] : (hskp27 | hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.03/0.98 inference(skolemize,[status(sab)],[2150])).
% 1.03/0.98 tff(2152,plain,
% 1.03/0.98 (![U: $i] : (hskp27 | hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.03/0.98 inference(modus_ponens,[status(thm)],[2151, 2144])).
% 1.03/0.98 tff(2153,plain,
% 1.03/0.98 (((~![U: $i] : (hskp27 | hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp15 | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)))) <=> ((~![U: $i] : (hskp27 | hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp27 | hskp15 | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)))),
% 1.03/0.98 inference(rewrite,[status(thm)],[])).
% 1.03/0.98 tff(2154,plain,
% 1.03/0.98 ((hskp27 | hskp15 | (~ndr1_0) | c3_1(a128) | c0_1(a128) | (~c1_1(a128))) <=> (hskp27 | hskp15 | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)))),
% 1.03/0.98 inference(rewrite,[status(thm)],[])).
% 1.03/0.98 tff(2155,plain,
% 1.03/0.98 (((~![U: $i] : (hskp27 | hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp15 | (~ndr1_0) | c3_1(a128) | c0_1(a128) | (~c1_1(a128)))) <=> ((~![U: $i] : (hskp27 | hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp15 | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128))))),
% 1.03/0.98 inference(monotonicity,[status(thm)],[2154])).
% 1.03/0.98 tff(2156,plain,
% 1.03/0.98 (((~![U: $i] : (hskp27 | hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp15 | (~ndr1_0) | c3_1(a128) | c0_1(a128) | (~c1_1(a128)))) <=> ((~![U: $i] : (hskp27 | hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp27 | hskp15 | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)))),
% 1.03/0.98 inference(transitivity,[status(thm)],[2155, 2153])).
% 1.03/0.98 tff(2157,plain,
% 1.03/0.98 ((~![U: $i] : (hskp27 | hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp15 | (~ndr1_0) | c3_1(a128) | c0_1(a128) | (~c1_1(a128)))),
% 1.03/0.98 inference(quant_inst,[status(thm)],[])).
% 1.03/0.98 tff(2158,plain,
% 1.03/0.98 ((~![U: $i] : (hskp27 | hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp27 | hskp15 | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128))),
% 1.03/0.98 inference(modus_ponens,[status(thm)],[2157, 2156])).
% 1.03/0.98 tff(2159,plain,
% 1.03/0.98 (hskp27 | hskp15 | (~c1_1(a128))),
% 1.03/0.98 inference(unit_resolution,[status(thm)],[2158, 187, 2125, 2123, 2152])).
% 1.03/0.98 tff(2160,plain,
% 1.03/0.98 (hskp27),
% 1.03/0.98 inference(unit_resolution,[status(thm)],[2159, 2142, 74])).
% 1.03/0.98 tff(2161,plain,
% 1.03/0.98 (c3_1(a137)),
% 1.03/0.98 inference(unit_resolution,[status(thm)],[1221, 2160])).
% 1.03/0.98 tff(2162,plain,
% 1.03/0.98 (c2_1(a137)),
% 1.03/0.98 inference(unit_resolution,[status(thm)],[1232, 2160])).
% 1.03/0.98 tff(2163,assumption,(hskp16), introduced(assumption)).
% 1.03/0.98 tff(2164,plain,
% 1.03/0.98 (~c2_1(a151)),
% 1.03/0.98 inference(unit_resolution,[status(thm)],[200, 2163])).
% 1.03/0.98 tff(2165,plain,
% 1.03/0.98 (c1_1(a151)),
% 1.03/0.98 inference(unit_resolution,[status(thm)],[211, 2163])).
% 1.03/0.98 tff(2166,plain,
% 1.03/0.98 (c0_1(a151)),
% 1.03/0.98 inference(unit_resolution,[status(thm)],[249, 2163])).
% 1.03/0.98 tff(2167,plain,
% 1.03/0.98 ($false),
% 1.03/0.98 inference(unit_resolution,[status(thm)],[256, 187, 74, 2166, 2165, 2164, 63])).
% 1.03/0.98 tff(2168,plain,((~hskp16) | hskp15), inference(lemma,lemma(discharge,[]))).
% 1.03/0.98 tff(2169,plain,
% 1.03/0.98 (~hskp16),
% 1.03/0.98 inference(unit_resolution,[status(thm)],[2168, 74])).
% 1.03/0.98 tff(2170,plain,
% 1.03/0.98 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp16 | c2_1(a159) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | c1_1(a159) | (~c0_1(a159)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp16 | c2_1(a159) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | c1_1(a159) | (~c0_1(a159)))),
% 1.03/0.98 inference(rewrite,[status(thm)],[])).
% 1.03/0.98 tff(2171,plain,
% 1.03/0.98 ((hskp16 | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | c1_1(a159) | c2_1(a159) | (~c0_1(a159))) <=> (hskp16 | c2_1(a159) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | c1_1(a159) | (~c0_1(a159)))),
% 1.03/0.98 inference(rewrite,[status(thm)],[])).
% 1.03/0.98 tff(2172,plain,
% 1.03/0.98 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | c1_1(a159) | c2_1(a159) | (~c0_1(a159)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp16 | c2_1(a159) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | c1_1(a159) | (~c0_1(a159))))),
% 1.03/0.98 inference(monotonicity,[status(thm)],[2171])).
% 1.03/0.98 tff(2173,plain,
% 1.03/0.98 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | c1_1(a159) | c2_1(a159) | (~c0_1(a159)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp16 | c2_1(a159) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | c1_1(a159) | (~c0_1(a159)))),
% 1.03/0.98 inference(transitivity,[status(thm)],[2172, 2170])).
% 1.03/0.98 tff(2174,plain,
% 1.03/0.98 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | c1_1(a159) | c2_1(a159) | (~c0_1(a159)))),
% 1.03/0.98 inference(quant_inst,[status(thm)],[])).
% 1.03/0.98 tff(2175,plain,
% 1.03/0.98 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp16 | c2_1(a159) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | c1_1(a159) | (~c0_1(a159))),
% 1.03/0.98 inference(modus_ponens,[status(thm)],[2174, 2173])).
% 1.03/0.98 tff(2176,plain,
% 1.03/0.98 (~c0_1(a137)),
% 1.03/0.98 inference(unit_resolution,[status(thm)],[2175, 187, 2169, 2162, 2161, 1941, 1930, 2135, 1982])).
% 1.03/0.98 tff(2177,plain,
% 1.03/0.98 (c1_1(a137)),
% 1.03/0.98 inference(unit_resolution,[status(thm)],[1243, 2160])).
% 1.03/0.98 tff(2178,plain,
% 1.03/0.98 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a137)) | (~c1_1(a137)) | c0_1(a137) | (~c1_1(a128)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a137)) | (~c1_1(a137)) | c0_1(a137) | (~c1_1(a128)))),
% 1.03/0.98 inference(rewrite,[status(thm)],[])).
% 1.03/0.98 tff(2179,plain,
% 1.03/0.98 ((hskp6 | (~ndr1_0) | c0_1(a137) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a128) | c0_1(a128) | (~c1_1(a128))) <=> (hskp6 | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a137)) | (~c1_1(a137)) | c0_1(a137) | (~c1_1(a128)))),
% 1.03/0.98 inference(rewrite,[status(thm)],[])).
% 1.03/0.98 tff(2180,plain,
% 1.03/0.98 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a137) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a128) | c0_1(a128) | (~c1_1(a128)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a137)) | (~c1_1(a137)) | c0_1(a137) | (~c1_1(a128))))),
% 1.03/0.98 inference(monotonicity,[status(thm)],[2179])).
% 1.03/0.98 tff(2181,plain,
% 1.03/0.98 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a137) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a128) | c0_1(a128) | (~c1_1(a128)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a137)) | (~c1_1(a137)) | c0_1(a137) | (~c1_1(a128)))),
% 1.03/0.98 inference(transitivity,[status(thm)],[2180, 2178])).
% 1.03/0.98 tff(2182,plain,
% 1.03/0.98 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a137) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a128) | c0_1(a128) | (~c1_1(a128)))),
% 1.03/0.98 inference(quant_inst,[status(thm)],[])).
% 1.03/0.98 tff(2183,plain,
% 1.03/0.98 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a137)) | (~c1_1(a137)) | c0_1(a137) | (~c1_1(a128))),
% 1.03/0.98 inference(modus_ponens,[status(thm)],[2182, 2181])).
% 1.03/0.98 tff(2184,plain,
% 1.03/0.98 (hskp6),
% 1.03/0.98 inference(unit_resolution,[status(thm)],[2183, 187, 2177, 2161, 2125, 2123, 336, 2142, 2176])).
% 1.03/0.98 tff(2185,plain,
% 1.03/0.98 (~c2_1(a133)),
% 1.03/0.98 inference(unit_resolution,[status(thm)],[360, 2184])).
% 1.03/0.98 tff(2186,plain,
% 1.03/0.98 (~c1_1(a133)),
% 1.03/0.98 inference(unit_resolution,[status(thm)],[366, 2184])).
% 1.03/0.98 tff(2187,plain,
% 1.03/0.98 (~c0_1(a133)),
% 1.03/0.98 inference(unit_resolution,[status(thm)],[372, 2184])).
% 1.03/0.98 tff(2188,assumption,(~c0_1(a137)), introduced(assumption)).
% 1.03/0.98 tff(2189,assumption,(~c1_1(a159)), introduced(assumption)).
% 1.03/0.98 tff(2190,assumption,(~hskp4), introduced(assumption)).
% 1.03/0.98 tff(2191,plain,
% 1.03/0.98 (^[U: $i] : refl((hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))),
% 1.03/0.98 inference(bind,[status(th)],[])).
% 1.03/0.98 tff(2192,plain,
% 1.03/0.98 (![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.03/0.98 inference(quant_intro,[status(thm)],[2191])).
% 1.03/0.98 tff(2193,plain,
% 1.03/0.98 (![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.03/0.98 inference(rewrite,[status(thm)],[])).
% 1.03/0.98 tff(2194,plain,
% 1.03/0.98 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp4) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp4))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp4) <=> (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp4) | hskp5) <=> ((hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp5))), rewrite(((hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp5) <=> (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp4) | hskp5) <=> (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))))),
% 1.03/0.98 inference(bind,[status(th)],[])).
% 1.03/0.98 tff(2195,plain,
% 1.03/0.98 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp4) | hskp5) <=> ![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.03/0.98 inference(quant_intro,[status(thm)],[2194])).
% 1.03/0.98 tff(2196,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp4) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause143')).
% 1.03/0.98 tff(2197,plain,
% 1.03/0.98 (![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.03/0.98 inference(modus_ponens,[status(thm)],[2196, 2195])).
% 1.03/0.98 tff(2198,plain,
% 1.03/0.98 (![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.03/0.98 inference(modus_ponens,[status(thm)],[2197, 2193])).
% 1.03/0.98 tff(2199,plain,(
% 1.03/0.98 ![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.03/0.98 inference(skolemize,[status(sab)],[2198])).
% 1.03/0.98 tff(2200,plain,
% 1.03/0.98 (![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.03/0.98 inference(modus_ponens,[status(thm)],[2199, 2192])).
% 1.03/0.98 tff(2201,plain,
% 1.03/0.98 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp5 | hskp4 | c3_1(a159) | (~ndr1_0) | c1_1(a159) | (~c0_1(a159)))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp5 | hskp4 | c3_1(a159) | (~ndr1_0) | c1_1(a159) | (~c0_1(a159)))),
% 1.03/0.98 inference(rewrite,[status(thm)],[])).
% 1.03/0.98 tff(2202,plain,
% 1.03/0.98 ((hskp5 | hskp4 | (~ndr1_0) | c3_1(a159) | c1_1(a159) | (~c0_1(a159))) <=> (hskp5 | hskp4 | c3_1(a159) | (~ndr1_0) | c1_1(a159) | (~c0_1(a159)))),
% 1.03/0.98 inference(rewrite,[status(thm)],[])).
% 1.03/0.98 tff(2203,plain,
% 1.03/0.98 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp5 | hskp4 | (~ndr1_0) | c3_1(a159) | c1_1(a159) | (~c0_1(a159)))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp5 | hskp4 | c3_1(a159) | (~ndr1_0) | c1_1(a159) | (~c0_1(a159))))),
% 1.03/0.98 inference(monotonicity,[status(thm)],[2202])).
% 1.03/0.98 tff(2204,plain,
% 1.03/0.98 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp5 | hskp4 | (~ndr1_0) | c3_1(a159) | c1_1(a159) | (~c0_1(a159)))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp5 | hskp4 | c3_1(a159) | (~ndr1_0) | c1_1(a159) | (~c0_1(a159)))),
% 1.03/0.98 inference(transitivity,[status(thm)],[2203, 2201])).
% 1.03/0.98 tff(2205,plain,
% 1.03/0.98 ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp5 | hskp4 | (~ndr1_0) | c3_1(a159) | c1_1(a159) | (~c0_1(a159)))),
% 1.03/0.98 inference(quant_inst,[status(thm)],[])).
% 1.03/0.98 tff(2206,plain,
% 1.03/0.98 ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp5 | hskp4 | c3_1(a159) | (~ndr1_0) | c1_1(a159) | (~c0_1(a159))),
% 1.03/0.98 inference(modus_ponens,[status(thm)],[2205, 2204])).
% 1.03/0.98 tff(2207,plain,
% 1.03/0.98 (hskp5 | hskp4 | c1_1(a159)),
% 1.03/0.98 inference(unit_resolution,[status(thm)],[2206, 187, 1941, 1924, 2200])).
% 1.03/0.98 tff(2208,plain,
% 1.03/0.98 (hskp5),
% 1.03/0.98 inference(unit_resolution,[status(thm)],[2207, 2190, 2189])).
% 1.03/0.98 tff(2209,plain,
% 1.03/0.98 (((~hskp5) | (~c2_1(a131))) <=> ((~hskp5) | (~c2_1(a131)))),
% 1.03/0.98 inference(rewrite,[status(thm)],[])).
% 1.03/0.98 tff(2210,plain,
% 1.03/0.98 (((~c2_1(a131)) | (~hskp5)) <=> ((~hskp5) | (~c2_1(a131)))),
% 1.03/0.98 inference(rewrite,[status(thm)],[])).
% 1.03/0.98 tff(2211,axiom,((~c2_1(a131)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause121')).
% 1.03/0.98 tff(2212,plain,
% 1.03/0.98 ((~hskp5) | (~c2_1(a131))),
% 1.03/0.98 inference(modus_ponens,[status(thm)],[2211, 2210])).
% 1.03/0.98 tff(2213,plain,
% 1.03/0.98 ((~hskp5) | (~c2_1(a131))),
% 1.03/0.98 inference(modus_ponens,[status(thm)],[2212, 2209])).
% 1.03/0.98 tff(2214,plain,
% 1.03/0.98 (~c2_1(a131)),
% 1.03/0.98 inference(unit_resolution,[status(thm)],[2213, 2208])).
% 1.03/0.98 tff(2215,assumption,(~c2_1(a133)), introduced(assumption)).
% 1.03/0.98 tff(2216,assumption,(~c1_1(a133)), introduced(assumption)).
% 1.03/0.98 tff(2217,plain,
% 1.03/0.98 (((~hskp5) | c3_1(a131)) <=> ((~hskp5) | c3_1(a131))),
% 1.03/0.98 inference(rewrite,[status(thm)],[])).
% 1.03/0.98 tff(2218,axiom,((~hskp5) | c3_1(a131)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause76')).
% 1.03/0.98 tff(2219,plain,
% 1.03/0.98 ((~hskp5) | c3_1(a131)),
% 1.03/0.98 inference(modus_ponens,[status(thm)],[2218, 2217])).
% 1.03/0.98 tff(2220,plain,
% 1.03/0.98 ((~hskp5) | c3_1(a131)),
% 1.03/0.98 inference(modus_ponens,[status(thm)],[2219, 2217])).
% 1.03/0.98 tff(2221,plain,
% 1.03/0.98 ((~hskp5) | c3_1(a131)),
% 1.03/0.98 inference(modus_ponens,[status(thm)],[2220, 2217])).
% 1.03/0.98 tff(2222,plain,
% 1.03/0.98 ((~hskp5) | c3_1(a131)),
% 1.03/0.98 inference(modus_ponens,[status(thm)],[2221, 2217])).
% 1.03/0.98 tff(2223,plain,
% 1.03/0.98 ((~hskp5) | c3_1(a131)),
% 1.03/0.98 inference(modus_ponens,[status(thm)],[2222, 2217])).
% 1.03/0.98 tff(2224,plain,
% 1.03/0.98 ((~hskp5) | c3_1(a131)),
% 1.03/0.98 inference(modus_ponens,[status(thm)],[2223, 2217])).
% 1.03/0.98 tff(2225,plain,
% 1.03/0.98 ((~hskp5) | c3_1(a131)),
% 1.03/0.98 inference(modus_ponens,[status(thm)],[2224, 2217])).
% 1.03/0.98 tff(2226,plain,
% 1.03/0.98 ((~hskp5) | c3_1(a131)),
% 1.03/0.98 inference(modus_ponens,[status(thm)],[2225, 2217])).
% 1.03/0.98 tff(2227,plain,
% 1.03/0.98 (c3_1(a131)),
% 1.03/0.98 inference(unit_resolution,[status(thm)],[2226, 2208])).
% 1.03/0.98 tff(2228,plain,
% 1.03/0.98 (((~hskp5) | c1_1(a131)) <=> ((~hskp5) | c1_1(a131))),
% 1.03/0.98 inference(rewrite,[status(thm)],[])).
% 1.03/0.98 tff(2229,axiom,((~hskp5) | c1_1(a131)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause75')).
% 1.03/0.98 tff(2230,plain,
% 1.03/0.98 ((~hskp5) | c1_1(a131)),
% 1.03/0.98 inference(modus_ponens,[status(thm)],[2229, 2228])).
% 1.03/0.98 tff(2231,plain,
% 1.03/0.98 ((~hskp5) | c1_1(a131)),
% 1.03/0.98 inference(modus_ponens,[status(thm)],[2230, 2228])).
% 1.03/0.98 tff(2232,plain,
% 1.03/0.98 ((~hskp5) | c1_1(a131)),
% 1.03/0.98 inference(modus_ponens,[status(thm)],[2231, 2228])).
% 1.03/0.98 tff(2233,plain,
% 1.03/0.98 ((~hskp5) | c1_1(a131)),
% 1.03/0.98 inference(modus_ponens,[status(thm)],[2232, 2228])).
% 1.03/0.98 tff(2234,plain,
% 1.03/0.98 ((~hskp5) | c1_1(a131)),
% 1.03/0.98 inference(modus_ponens,[status(thm)],[2233, 2228])).
% 1.03/0.98 tff(2235,plain,
% 1.03/0.98 ((~hskp5) | c1_1(a131)),
% 1.03/0.98 inference(modus_ponens,[status(thm)],[2234, 2228])).
% 1.03/0.98 tff(2236,plain,
% 1.03/0.98 ((~hskp5) | c1_1(a131)),
% 1.03/0.98 inference(modus_ponens,[status(thm)],[2235, 2228])).
% 1.03/0.98 tff(2237,plain,
% 1.03/0.98 ((~hskp5) | c1_1(a131)),
% 1.03/0.98 inference(modus_ponens,[status(thm)],[2236, 2228])).
% 1.03/0.98 tff(2238,plain,
% 1.03/0.98 (c1_1(a131)),
% 1.03/0.98 inference(unit_resolution,[status(thm)],[2237, 2208])).
% 1.03/0.98 tff(2239,assumption,(c3_1(a137)), introduced(assumption)).
% 1.03/0.98 tff(2240,assumption,(c2_1(a137)), introduced(assumption)).
% 1.03/0.98 tff(2241,plain,
% 1.03/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c1_1(a133) | c2_1(a133) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131)) | (~c2_1(a137)) | (~c3_1(a137)) | c0_1(a137) | (~c3_1(a133)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a133) | c2_1(a133) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131)) | (~c2_1(a137)) | (~c3_1(a137)) | c0_1(a137) | (~c3_1(a133)))),
% 1.03/0.98 inference(rewrite,[status(thm)],[])).
% 1.03/0.98 tff(2242,plain,
% 1.03/0.98 (((~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131)) | c1_1(a133) | c2_1(a133) | (~c3_1(a133)) | c0_1(a137) | (~c2_1(a137)) | (~c3_1(a137))) <=> (c1_1(a133) | c2_1(a133) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131)) | (~c2_1(a137)) | (~c3_1(a137)) | c0_1(a137) | (~c3_1(a133)))),
% 1.03/0.98 inference(rewrite,[status(thm)],[])).
% 1.03/0.98 tff(2243,plain,
% 1.03/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131)) | c1_1(a133) | c2_1(a133) | (~c3_1(a133)) | c0_1(a137) | (~c2_1(a137)) | (~c3_1(a137)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c1_1(a133) | c2_1(a133) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131)) | (~c2_1(a137)) | (~c3_1(a137)) | c0_1(a137) | (~c3_1(a133))))),
% 1.03/0.98 inference(monotonicity,[status(thm)],[2242])).
% 1.03/0.98 tff(2244,plain,
% 1.03/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131)) | c1_1(a133) | c2_1(a133) | (~c3_1(a133)) | c0_1(a137) | (~c2_1(a137)) | (~c3_1(a137)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a133) | c2_1(a133) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131)) | (~c2_1(a137)) | (~c3_1(a137)) | c0_1(a137) | (~c3_1(a133)))),
% 1.03/0.98 inference(transitivity,[status(thm)],[2243, 2241])).
% 1.03/0.98 tff(2245,plain,
% 1.03/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131)) | c1_1(a133) | c2_1(a133) | (~c3_1(a133)) | c0_1(a137) | (~c2_1(a137)) | (~c3_1(a137)))),
% 1.03/0.98 inference(quant_inst,[status(thm)],[])).
% 1.03/0.98 tff(2246,plain,
% 1.03/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a133) | c2_1(a133) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131)) | (~c2_1(a137)) | (~c3_1(a137)) | c0_1(a137) | (~c3_1(a133))),
% 1.03/0.98 inference(modus_ponens,[status(thm)],[2245, 2244])).
% 1.03/0.98 tff(2247,plain,
% 1.03/0.98 (~c3_1(a133)),
% 1.03/0.98 inference(unit_resolution,[status(thm)],[2246, 187, 2240, 2239, 2238, 2227, 2216, 2215, 2214, 229, 2188])).
% 1.03/0.98 tff(2248,assumption,(~c0_1(a133)), introduced(assumption)).
% 1.03/0.98 tff(2249,plain,
% 1.03/0.98 (^[U: $i] : refl((hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 1.03/0.98 inference(bind,[status(th)],[])).
% 1.03/0.98 tff(2250,plain,
% 1.03/0.98 (![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.03/0.98 inference(quant_intro,[status(thm)],[2249])).
% 1.03/0.98 tff(2251,plain,
% 1.03/0.98 (![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.03/0.98 inference(rewrite,[status(thm)],[])).
% 1.03/0.98 tff(2252,plain,
% 1.03/0.98 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp4) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp4))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp4) <=> (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp4) | hskp24) <=> ((hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp24))), rewrite(((hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp24) <=> (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp4) | hskp24) <=> (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 1.03/0.98 inference(bind,[status(th)],[])).
% 1.03/0.98 tff(2253,plain,
% 1.03/0.98 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp4) | hskp24) <=> ![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.03/0.98 inference(quant_intro,[status(thm)],[2252])).
% 1.03/0.98 tff(2254,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp4) | hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause153')).
% 1.03/0.98 tff(2255,plain,
% 1.03/0.98 (![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.03/0.98 inference(modus_ponens,[status(thm)],[2254, 2253])).
% 1.03/0.98 tff(2256,plain,
% 1.03/0.98 (![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.03/0.98 inference(modus_ponens,[status(thm)],[2255, 2251])).
% 1.03/0.98 tff(2257,plain,(
% 1.03/0.98 ![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.03/0.98 inference(skolemize,[status(sab)],[2256])).
% 1.03/0.98 tff(2258,plain,
% 1.03/0.98 (![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.03/0.98 inference(modus_ponens,[status(thm)],[2257, 2250])).
% 1.03/0.98 tff(2259,plain,
% 1.03/0.98 (((~![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp4 | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131)))) <=> ((~![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp4 | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131)))),
% 1.03/0.98 inference(rewrite,[status(thm)],[])).
% 1.03/0.98 tff(2260,plain,
% 1.03/0.98 ((hskp24 | hskp4 | (~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131))) <=> (hskp24 | hskp4 | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131)))),
% 1.03/0.98 inference(rewrite,[status(thm)],[])).
% 1.03/0.98 tff(2261,plain,
% 1.03/0.98 (((~![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp4 | (~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131)))) <=> ((~![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp4 | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131))))),
% 1.03/0.98 inference(monotonicity,[status(thm)],[2260])).
% 1.03/0.98 tff(2262,plain,
% 1.03/0.98 (((~![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp4 | (~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131)))) <=> ((~![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp4 | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131)))),
% 1.03/0.98 inference(transitivity,[status(thm)],[2261, 2259])).
% 1.03/0.98 tff(2263,plain,
% 1.03/0.98 ((~![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp4 | (~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131)))),
% 1.03/0.98 inference(quant_inst,[status(thm)],[])).
% 1.03/0.98 tff(2264,plain,
% 1.03/0.98 ((~![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp4 | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131))),
% 1.03/0.98 inference(modus_ponens,[status(thm)],[2263, 2262])).
% 1.03/0.98 tff(2265,plain,
% 1.03/0.98 (hskp24),
% 1.03/0.98 inference(unit_resolution,[status(thm)],[2264, 187, 2190, 2238, 2227, 2214, 2258])).
% 1.03/0.98 tff(2266,plain,
% 1.03/0.98 (((~hskp24) | (~c2_1(a183))) <=> ((~hskp24) | (~c2_1(a183)))),
% 1.03/0.98 inference(rewrite,[status(thm)],[])).
% 1.03/0.98 tff(2267,plain,
% 1.03/0.98 (((~c2_1(a183)) | (~hskp24)) <=> ((~hskp24) | (~c2_1(a183)))),
% 1.03/0.98 inference(rewrite,[status(thm)],[])).
% 1.03/0.98 tff(2268,axiom,((~c2_1(a183)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause89')).
% 1.03/0.99 tff(2269,plain,
% 1.03/0.99 ((~hskp24) | (~c2_1(a183))),
% 1.03/0.99 inference(modus_ponens,[status(thm)],[2268, 2267])).
% 1.03/0.99 tff(2270,plain,
% 1.03/0.99 ((~hskp24) | (~c2_1(a183))),
% 1.03/0.99 inference(modus_ponens,[status(thm)],[2269, 2266])).
% 1.03/0.99 tff(2271,plain,
% 1.03/0.99 (~c2_1(a183)),
% 1.03/0.99 inference(unit_resolution,[status(thm)],[2270, 2265])).
% 1.03/0.99 tff(2272,plain,
% 1.03/0.99 (((~hskp24) | (~c1_1(a183))) <=> ((~hskp24) | (~c1_1(a183)))),
% 1.03/0.99 inference(rewrite,[status(thm)],[])).
% 1.03/0.99 tff(2273,plain,
% 1.03/0.99 (((~c1_1(a183)) | (~hskp24)) <=> ((~hskp24) | (~c1_1(a183)))),
% 1.03/0.99 inference(rewrite,[status(thm)],[])).
% 1.03/0.99 tff(2274,axiom,((~c1_1(a183)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause88')).
% 1.03/0.99 tff(2275,plain,
% 1.03/0.99 ((~hskp24) | (~c1_1(a183))),
% 1.03/0.99 inference(modus_ponens,[status(thm)],[2274, 2273])).
% 1.03/0.99 tff(2276,plain,
% 1.03/0.99 ((~hskp24) | (~c1_1(a183))),
% 1.03/0.99 inference(modus_ponens,[status(thm)],[2275, 2272])).
% 1.03/0.99 tff(2277,plain,
% 1.03/0.99 (~c1_1(a183)),
% 1.03/0.99 inference(unit_resolution,[status(thm)],[2276, 2265])).
% 1.03/0.99 tff(2278,plain,
% 1.03/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a183) | c2_1(a183) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | c3_1(a133) | (~c0_1(a183)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a183) | c2_1(a183) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | c3_1(a133) | (~c0_1(a183)))),
% 1.03/0.99 inference(rewrite,[status(thm)],[])).
% 1.03/0.99 tff(2279,plain,
% 1.03/0.99 (((~ndr1_0) | c1_1(a183) | c2_1(a183) | (~c0_1(a183)) | c3_1(a133) | c1_1(a133) | c0_1(a133) | c2_1(a133) | c1_1(a133) | c0_1(a133)) <=> (c1_1(a183) | c2_1(a183) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | c3_1(a133) | (~c0_1(a183)))),
% 1.03/0.99 inference(rewrite,[status(thm)],[])).
% 1.03/0.99 tff(2280,plain,
% 1.03/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a183) | c2_1(a183) | (~c0_1(a183)) | c3_1(a133) | c1_1(a133) | c0_1(a133) | c2_1(a133) | c1_1(a133) | c0_1(a133))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a183) | c2_1(a183) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | c3_1(a133) | (~c0_1(a183))))),
% 1.03/0.99 inference(monotonicity,[status(thm)],[2279])).
% 1.03/0.99 tff(2281,plain,
% 1.03/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a183) | c2_1(a183) | (~c0_1(a183)) | c3_1(a133) | c1_1(a133) | c0_1(a133) | c2_1(a133) | c1_1(a133) | c0_1(a133))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a183) | c2_1(a183) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | c3_1(a133) | (~c0_1(a183)))),
% 1.03/0.99 inference(transitivity,[status(thm)],[2280, 2278])).
% 1.03/0.99 tff(2282,plain,
% 1.03/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a183) | c2_1(a183) | (~c0_1(a183)) | c3_1(a133) | c1_1(a133) | c0_1(a133) | c2_1(a133) | c1_1(a133) | c0_1(a133))),
% 1.03/0.99 inference(quant_inst,[status(thm)],[])).
% 1.03/0.99 tff(2283,plain,
% 1.03/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a183) | c2_1(a183) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | c3_1(a133) | (~c0_1(a183))),
% 1.03/0.99 inference(modus_ponens,[status(thm)],[2282, 2281])).
% 1.03/0.99 tff(2284,plain,
% 1.03/0.99 (~c0_1(a183)),
% 1.03/0.99 inference(unit_resolution,[status(thm)],[2283, 187, 2277, 2271, 2248, 2216, 2215, 493, 2247])).
% 1.03/0.99 tff(2285,plain,
% 1.03/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a183) | c2_1(a183) | c2_1(a159) | c0_1(a133) | c1_1(a133) | (~ndr1_0) | c3_1(a133) | c1_1(a159) | (~c0_1(a159)) | c0_1(a183))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a183) | c2_1(a183) | c2_1(a159) | c0_1(a133) | c1_1(a133) | (~ndr1_0) | c3_1(a133) | c1_1(a159) | (~c0_1(a159)) | c0_1(a183))),
% 1.03/0.99 inference(rewrite,[status(thm)],[])).
% 1.03/0.99 tff(2286,plain,
% 1.03/0.99 (((~ndr1_0) | c1_1(a159) | c2_1(a159) | (~c0_1(a159)) | c3_1(a133) | c1_1(a133) | c0_1(a133) | c2_1(a183) | c1_1(a183) | c0_1(a183)) <=> (c1_1(a183) | c2_1(a183) | c2_1(a159) | c0_1(a133) | c1_1(a133) | (~ndr1_0) | c3_1(a133) | c1_1(a159) | (~c0_1(a159)) | c0_1(a183))),
% 1.03/0.99 inference(rewrite,[status(thm)],[])).
% 1.03/0.99 tff(2287,plain,
% 1.03/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a159) | c2_1(a159) | (~c0_1(a159)) | c3_1(a133) | c1_1(a133) | c0_1(a133) | c2_1(a183) | c1_1(a183) | c0_1(a183))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a183) | c2_1(a183) | c2_1(a159) | c0_1(a133) | c1_1(a133) | (~ndr1_0) | c3_1(a133) | c1_1(a159) | (~c0_1(a159)) | c0_1(a183)))),
% 1.03/0.99 inference(monotonicity,[status(thm)],[2286])).
% 1.03/0.99 tff(2288,plain,
% 1.03/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a159) | c2_1(a159) | (~c0_1(a159)) | c3_1(a133) | c1_1(a133) | c0_1(a133) | c2_1(a183) | c1_1(a183) | c0_1(a183))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a183) | c2_1(a183) | c2_1(a159) | c0_1(a133) | c1_1(a133) | (~ndr1_0) | c3_1(a133) | c1_1(a159) | (~c0_1(a159)) | c0_1(a183))),
% 1.03/0.99 inference(transitivity,[status(thm)],[2287, 2285])).
% 1.03/0.99 tff(2289,plain,
% 1.03/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a159) | c2_1(a159) | (~c0_1(a159)) | c3_1(a133) | c1_1(a133) | c0_1(a133) | c2_1(a183) | c1_1(a183) | c0_1(a183))),
% 1.03/0.99 inference(quant_inst,[status(thm)],[])).
% 1.03/0.99 tff(2290,plain,
% 1.03/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a183) | c2_1(a183) | c2_1(a159) | c0_1(a133) | c1_1(a133) | (~ndr1_0) | c3_1(a133) | c1_1(a159) | (~c0_1(a159)) | c0_1(a183)),
% 1.03/0.99 inference(modus_ponens,[status(thm)],[2289, 2288])).
% 1.03/0.99 tff(2291,plain,
% 1.03/0.99 ($false),
% 1.03/0.99 inference(unit_resolution,[status(thm)],[2290, 187, 1941, 2277, 2271, 1930, 2248, 2216, 493, 2189, 2247, 2284])).
% 1.03/0.99 tff(2292,plain,(hskp4 | c0_1(a133) | c1_1(a133) | c1_1(a159) | c2_1(a133) | (~c2_1(a137)) | (~c3_1(a137)) | c0_1(a137)), inference(lemma,lemma(discharge,[]))).
% 1.03/0.99 tff(2293,plain,
% 1.03/0.99 (hskp4),
% 1.03/0.99 inference(unit_resolution,[status(thm)],[2292, 2187, 2186, 1982, 2185, 2162, 2161, 2176])).
% 1.03/0.99 tff(2294,assumption,(hskp4), introduced(assumption)).
% 1.03/0.99 tff(2295,plain,
% 1.03/0.99 (((~hskp4) | (~c3_1(a130))) <=> ((~hskp4) | (~c3_1(a130)))),
% 1.03/0.99 inference(rewrite,[status(thm)],[])).
% 1.03/0.99 tff(2296,plain,
% 1.03/0.99 (((~c3_1(a130)) | (~hskp4)) <=> ((~hskp4) | (~c3_1(a130)))),
% 1.03/0.99 inference(rewrite,[status(thm)],[])).
% 1.03/0.99 tff(2297,axiom,((~c3_1(a130)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause122')).
% 1.03/0.99 tff(2298,plain,
% 1.03/0.99 ((~hskp4) | (~c3_1(a130))),
% 1.03/0.99 inference(modus_ponens,[status(thm)],[2297, 2296])).
% 1.03/0.99 tff(2299,plain,
% 1.03/0.99 ((~hskp4) | (~c3_1(a130))),
% 1.03/0.99 inference(modus_ponens,[status(thm)],[2298, 2295])).
% 1.03/0.99 tff(2300,plain,
% 1.03/0.99 (~c3_1(a130)),
% 1.03/0.99 inference(unit_resolution,[status(thm)],[2299, 2294])).
% 1.03/0.99 tff(2301,plain,
% 1.03/0.99 (((~hskp4) | c2_1(a130)) <=> ((~hskp4) | c2_1(a130))),
% 1.03/0.99 inference(rewrite,[status(thm)],[])).
% 1.03/0.99 tff(2302,axiom,((~hskp4) | c2_1(a130)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause78')).
% 1.03/0.99 tff(2303,plain,
% 1.03/0.99 ((~hskp4) | c2_1(a130)),
% 1.03/0.99 inference(modus_ponens,[status(thm)],[2302, 2301])).
% 1.03/0.99 tff(2304,plain,
% 1.03/0.99 ((~hskp4) | c2_1(a130)),
% 1.03/0.99 inference(modus_ponens,[status(thm)],[2303, 2301])).
% 1.03/0.99 tff(2305,plain,
% 1.03/0.99 ((~hskp4) | c2_1(a130)),
% 1.03/0.99 inference(modus_ponens,[status(thm)],[2304, 2301])).
% 1.03/0.99 tff(2306,plain,
% 1.03/0.99 ((~hskp4) | c2_1(a130)),
% 1.03/0.99 inference(modus_ponens,[status(thm)],[2305, 2301])).
% 1.03/0.99 tff(2307,plain,
% 1.03/0.99 ((~hskp4) | c2_1(a130)),
% 1.03/0.99 inference(modus_ponens,[status(thm)],[2306, 2301])).
% 1.03/0.99 tff(2308,plain,
% 1.03/0.99 ((~hskp4) | c2_1(a130)),
% 1.03/0.99 inference(modus_ponens,[status(thm)],[2307, 2301])).
% 1.03/0.99 tff(2309,plain,
% 1.03/0.99 ((~hskp4) | c2_1(a130)),
% 1.03/0.99 inference(modus_ponens,[status(thm)],[2308, 2301])).
% 1.03/0.99 tff(2310,plain,
% 1.03/0.99 ((~hskp4) | c2_1(a130)),
% 1.03/0.99 inference(modus_ponens,[status(thm)],[2309, 2301])).
% 1.03/0.99 tff(2311,plain,
% 1.03/0.99 (c2_1(a130)),
% 1.03/0.99 inference(unit_resolution,[status(thm)],[2310, 2294])).
% 1.03/0.99 tff(2312,assumption,(c1_1(a137)), introduced(assumption)).
% 1.03/0.99 tff(2313,plain,
% 1.03/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a159) | c3_1(a159) | c3_1(a130) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c0_1(a130) | (~c2_1(a130)) | c1_1(a159))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a159) | c3_1(a159) | c3_1(a130) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c0_1(a130) | (~c2_1(a130)) | c1_1(a159))),
% 1.03/0.99 inference(rewrite,[status(thm)],[])).
% 1.03/0.99 tff(2314,plain,
% 1.03/0.99 (((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a130) | c0_1(a130) | (~c2_1(a130)) | c2_1(a159) | c1_1(a159) | c3_1(a159)) <=> (c2_1(a159) | c3_1(a159) | c3_1(a130) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c0_1(a130) | (~c2_1(a130)) | c1_1(a159))),
% 1.03/0.99 inference(rewrite,[status(thm)],[])).
% 1.03/0.99 tff(2315,plain,
% 1.03/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a130) | c0_1(a130) | (~c2_1(a130)) | c2_1(a159) | c1_1(a159) | c3_1(a159))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a159) | c3_1(a159) | c3_1(a130) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c0_1(a130) | (~c2_1(a130)) | c1_1(a159)))),
% 1.03/0.99 inference(monotonicity,[status(thm)],[2314])).
% 1.03/0.99 tff(2316,plain,
% 1.03/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a130) | c0_1(a130) | (~c2_1(a130)) | c2_1(a159) | c1_1(a159) | c3_1(a159))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a159) | c3_1(a159) | c3_1(a130) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c0_1(a130) | (~c2_1(a130)) | c1_1(a159))),
% 1.03/0.99 inference(transitivity,[status(thm)],[2315, 2313])).
% 1.03/0.99 tff(2317,plain,
% 1.03/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a130) | c0_1(a130) | (~c2_1(a130)) | c2_1(a159) | c1_1(a159) | c3_1(a159))),
% 1.03/0.99 inference(quant_inst,[status(thm)],[])).
% 1.03/0.99 tff(2318,plain,
% 1.03/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a159) | c3_1(a159) | c3_1(a130) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c0_1(a130) | (~c2_1(a130)) | c1_1(a159)),
% 1.03/0.99 inference(modus_ponens,[status(thm)],[2317, 2316])).
% 1.03/0.99 tff(2319,plain,
% 1.03/0.99 (c0_1(a130)),
% 1.03/0.99 inference(unit_resolution,[status(thm)],[2318, 187, 2312, 2240, 2239, 2311, 1930, 1924, 2300, 1176, 2189])).
% 1.03/0.99 tff(2320,plain,
% 1.03/0.99 (((~hskp4) | c1_1(a130)) <=> ((~hskp4) | c1_1(a130))),
% 1.03/0.99 inference(rewrite,[status(thm)],[])).
% 1.03/0.99 tff(2321,axiom,((~hskp4) | c1_1(a130)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause77')).
% 1.03/0.99 tff(2322,plain,
% 1.03/0.99 ((~hskp4) | c1_1(a130)),
% 1.03/0.99 inference(modus_ponens,[status(thm)],[2321, 2320])).
% 1.03/0.99 tff(2323,plain,
% 1.03/0.99 ((~hskp4) | c1_1(a130)),
% 1.03/0.99 inference(modus_ponens,[status(thm)],[2322, 2320])).
% 1.03/0.99 tff(2324,plain,
% 1.03/0.99 ((~hskp4) | c1_1(a130)),
% 1.03/0.99 inference(modus_ponens,[status(thm)],[2323, 2320])).
% 1.03/0.99 tff(2325,plain,
% 1.03/0.99 ((~hskp4) | c1_1(a130)),
% 1.03/0.99 inference(modus_ponens,[status(thm)],[2324, 2320])).
% 1.03/0.99 tff(2326,plain,
% 1.03/0.99 ((~hskp4) | c1_1(a130)),
% 1.03/0.99 inference(modus_ponens,[status(thm)],[2325, 2320])).
% 1.03/0.99 tff(2327,plain,
% 1.03/0.99 ((~hskp4) | c1_1(a130)),
% 1.03/0.99 inference(modus_ponens,[status(thm)],[2326, 2320])).
% 1.03/0.99 tff(2328,plain,
% 1.03/0.99 ((~hskp4) | c1_1(a130)),
% 1.03/0.99 inference(modus_ponens,[status(thm)],[2327, 2320])).
% 1.03/0.99 tff(2329,plain,
% 1.03/0.99 ((~hskp4) | c1_1(a130)),
% 1.03/0.99 inference(modus_ponens,[status(thm)],[2328, 2320])).
% 1.03/0.99 tff(2330,plain,
% 1.03/0.99 (c1_1(a130)),
% 1.03/0.99 inference(unit_resolution,[status(thm)],[2329, 2294])).
% 1.03/0.99 tff(2331,plain,
% 1.03/0.99 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | c3_1(a130) | (~ndr1_0) | (~c1_1(a130)) | (~c0_1(a130)) | (~c2_1(a130)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | c3_1(a130) | (~ndr1_0) | (~c1_1(a130)) | (~c0_1(a130)) | (~c2_1(a130)))),
% 1.03/0.99 inference(rewrite,[status(thm)],[])).
% 1.03/0.99 tff(2332,plain,
% 1.03/0.99 ((hskp13 | (~ndr1_0) | (~c2_1(a130)) | (~c1_1(a130)) | (~c0_1(a130)) | c3_1(a130) | (~c1_1(a130)) | (~c0_1(a130))) <=> (hskp13 | c3_1(a130) | (~ndr1_0) | (~c1_1(a130)) | (~c0_1(a130)) | (~c2_1(a130)))),
% 1.03/0.99 inference(rewrite,[status(thm)],[])).
% 1.03/0.99 tff(2333,plain,
% 1.03/0.99 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a130)) | (~c1_1(a130)) | (~c0_1(a130)) | c3_1(a130) | (~c1_1(a130)) | (~c0_1(a130)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | c3_1(a130) | (~ndr1_0) | (~c1_1(a130)) | (~c0_1(a130)) | (~c2_1(a130))))),
% 1.03/0.99 inference(monotonicity,[status(thm)],[2332])).
% 1.03/0.99 tff(2334,plain,
% 1.03/0.99 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a130)) | (~c1_1(a130)) | (~c0_1(a130)) | c3_1(a130) | (~c1_1(a130)) | (~c0_1(a130)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | c3_1(a130) | (~ndr1_0) | (~c1_1(a130)) | (~c0_1(a130)) | (~c2_1(a130)))),
% 1.03/0.99 inference(transitivity,[status(thm)],[2333, 2331])).
% 1.03/0.99 tff(2335,plain,
% 1.03/0.99 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a130)) | (~c1_1(a130)) | (~c0_1(a130)) | c3_1(a130) | (~c1_1(a130)) | (~c0_1(a130)))),
% 1.03/0.99 inference(quant_inst,[status(thm)],[])).
% 1.03/0.99 tff(2336,plain,
% 1.03/0.99 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | c3_1(a130) | (~ndr1_0) | (~c1_1(a130)) | (~c0_1(a130)) | (~c2_1(a130))),
% 1.03/0.99 inference(modus_ponens,[status(thm)],[2335, 2334])).
% 1.03/0.99 tff(2337,plain,
% 1.03/0.99 ($false),
% 1.03/0.99 inference(unit_resolution,[status(thm)],[2336, 187, 11, 2330, 2311, 2300, 21, 2319])).
% 1.03/0.99 tff(2338,plain,((~hskp4) | hskp13 | (~c1_1(a137)) | (~c2_1(a137)) | (~c3_1(a137)) | c1_1(a159)), inference(lemma,lemma(discharge,[]))).
% 1.03/0.99 tff(2339,plain,
% 1.03/0.99 (hskp13),
% 1.03/0.99 inference(unit_resolution,[status(thm)],[2338, 2293, 1982, 2162, 2161, 2177])).
% 1.03/0.99 tff(2340,plain,
% 1.03/0.99 (~c3_1(a144)),
% 1.03/0.99 inference(unit_resolution,[status(thm)],[991, 2339])).
% 1.03/0.99 tff(2341,plain,
% 1.03/0.99 (~c0_1(a144)),
% 1.03/0.99 inference(unit_resolution,[status(thm)],[1015, 2339])).
% 1.03/0.99 tff(2342,plain,
% 1.03/0.99 (c2_1(a144)),
% 1.03/0.99 inference(unit_resolution,[status(thm)],[1002, 2339])).
% 1.03/0.99 tff(2343,plain,
% 1.03/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a159) | c3_1(a159) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a144)) | c1_1(a159))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a159) | c3_1(a159) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a144)) | c1_1(a159))),
% 1.03/0.99 inference(rewrite,[status(thm)],[])).
% 1.03/0.99 tff(2344,plain,
% 1.03/0.99 (((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a159) | c1_1(a159) | c3_1(a159)) <=> (c2_1(a159) | c3_1(a159) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a144)) | c1_1(a159))),
% 1.03/0.99 inference(rewrite,[status(thm)],[])).
% 1.03/0.99 tff(2345,plain,
% 1.03/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a159) | c1_1(a159) | c3_1(a159))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a159) | c3_1(a159) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a144)) | c1_1(a159)))),
% 1.03/0.99 inference(monotonicity,[status(thm)],[2344])).
% 1.03/0.99 tff(2346,plain,
% 1.03/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a159) | c1_1(a159) | c3_1(a159))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a159) | c3_1(a159) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a144)) | c1_1(a159))),
% 1.03/0.99 inference(transitivity,[status(thm)],[2345, 2343])).
% 1.03/0.99 tff(2347,plain,
% 1.03/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a159) | c1_1(a159) | c3_1(a159))),
% 1.03/0.99 inference(quant_inst,[status(thm)],[])).
% 1.03/0.99 tff(2348,plain,
% 1.03/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a159) | c3_1(a159) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a144)) | c1_1(a159)),
% 1.03/0.99 inference(modus_ponens,[status(thm)],[2347, 2346])).
% 1.03/0.99 tff(2349,plain,
% 1.03/0.99 (c1_1(a159)),
% 1.03/0.99 inference(unit_resolution,[status(thm)],[2348, 187, 2312, 2240, 2239, 1605, 1930, 1924, 1604, 1603, 1176])).
% 1.03/0.99 tff(2350,assumption,(hskp11), introduced(assumption)).
% 1.03/0.99 tff(2351,plain,
% 1.03/0.99 (~c3_1(a139)),
% 1.03/0.99 inference(unit_resolution,[status(thm)],[1506, 2350])).
% 1.03/0.99 tff(2352,plain,
% 1.03/0.99 (~c1_1(a139)),
% 1.03/0.99 inference(unit_resolution,[status(thm)],[1512, 2350])).
% 1.03/0.99 tff(2353,plain,
% 1.03/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a159) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a139)) | (~c1_1(a159)) | (~c0_1(a159)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a159) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a139)) | (~c1_1(a159)) | (~c0_1(a159)))),
% 1.03/0.99 inference(rewrite,[status(thm)],[])).
% 1.03/0.99 tff(2354,plain,
% 1.03/0.99 (((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a159) | (~c1_1(a159)) | (~c0_1(a159)) | c1_1(a139) | c3_1(a139) | (~c2_1(a139))) <=> (c2_1(a159) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a139)) | (~c1_1(a159)) | (~c0_1(a159)))),
% 1.03/0.99 inference(rewrite,[status(thm)],[])).
% 1.03/0.99 tff(2355,plain,
% 1.03/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a159) | (~c1_1(a159)) | (~c0_1(a159)) | c1_1(a139) | c3_1(a139) | (~c2_1(a139)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a159) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a139)) | (~c1_1(a159)) | (~c0_1(a159))))),
% 1.03/0.99 inference(monotonicity,[status(thm)],[2354])).
% 1.03/0.99 tff(2356,plain,
% 1.03/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a159) | (~c1_1(a159)) | (~c0_1(a159)) | c1_1(a139) | c3_1(a139) | (~c2_1(a139)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a159) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a139)) | (~c1_1(a159)) | (~c0_1(a159)))),
% 1.03/0.99 inference(transitivity,[status(thm)],[2355, 2353])).
% 1.03/0.99 tff(2357,plain,
% 1.03/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a159) | (~c1_1(a159)) | (~c0_1(a159)) | c1_1(a139) | c3_1(a139) | (~c2_1(a139)))),
% 1.03/0.99 inference(quant_inst,[status(thm)],[])).
% 1.03/0.99 tff(2358,plain,
% 1.03/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a159) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a139)) | (~c1_1(a159)) | (~c0_1(a159))),
% 1.03/0.99 inference(modus_ponens,[status(thm)],[2357, 2356])).
% 1.03/0.99 tff(2359,plain,
% 1.03/0.99 (~c2_1(a139)),
% 1.03/0.99 inference(unit_resolution,[status(thm)],[2358, 187, 2312, 2240, 2239, 1941, 1930, 2352, 2351, 94, 2349])).
% 1.03/0.99 tff(2360,plain,
% 1.03/0.99 ($false),
% 1.03/0.99 inference(unit_resolution,[status(thm)],[1916, 187, 2312, 2240, 2239, 1605, 1604, 1603, 2352, 2351, 1176, 2359])).
% 1.03/0.99 tff(2361,plain,((~hskp11) | (~c1_1(a137)) | (~c2_1(a137)) | (~c3_1(a137)) | (~c2_1(a144)) | c0_1(a144) | c3_1(a144)), inference(lemma,lemma(discharge,[]))).
% 1.03/0.99 tff(2362,plain,
% 1.03/0.99 (~hskp11),
% 1.03/0.99 inference(unit_resolution,[status(thm)],[2361, 2342, 2162, 2161, 2177, 2341, 2340])).
% 1.03/0.99 tff(2363,plain,
% 1.03/0.99 (hskp11 | hskp10 | (~c1_1(a128))),
% 1.03/0.99 inference(unit_resolution,[status(thm)],[1743, 187, 2125, 2124, 1478])).
% 1.03/0.99 tff(2364,plain,
% 1.03/0.99 (hskp10),
% 1.03/0.99 inference(unit_resolution,[status(thm)],[2363, 2362, 2142])).
% 1.03/0.99 tff(2365,plain,
% 1.03/0.99 (~c1_1(a138)),
% 1.03/0.99 inference(unit_resolution,[status(thm)],[101, 2364])).
% 1.03/0.99 tff(2366,plain,
% 1.03/0.99 (c3_1(a138)),
% 1.03/0.99 inference(unit_resolution,[status(thm)],[112, 2364])).
% 1.03/0.99 tff(2367,plain,
% 1.03/0.99 (c0_1(a138)),
% 1.03/0.99 inference(unit_resolution,[status(thm)],[123, 2364])).
% 1.03/0.99 tff(2368,plain,
% 1.03/0.99 ($false),
% 1.03/0.99 inference(unit_resolution,[status(thm)],[379, 187, 2367, 2366, 2365, 2187, 2186, 2185, 2125, 2124, 2123, 279])).
% 1.03/0.99 tff(2369,plain,(hskp15), inference(lemma,lemma(discharge,[]))).
% 1.03/0.99 tff(2370,plain,
% 1.03/0.99 (~c1_1(a149)),
% 1.03/0.99 inference(unit_resolution,[status(thm)],[564, 2369])).
% 1.03/0.99 tff(2371,plain,
% 1.03/0.99 (~c2_1(a149)),
% 1.03/0.99 inference(unit_resolution,[status(thm)],[558, 2369])).
% 1.03/0.99 tff(2372,assumption,(~c3_1(a149)), introduced(assumption)).
% 1.03/0.99 tff(2373,plain,
% 1.03/0.99 (~hskp15),
% 1.03/0.99 inference(unit_resolution,[status(thm)],[267, 2372])).
% 1.03/0.99 tff(2374,plain,
% 1.03/0.99 (~c1_1(a159)),
% 1.03/0.99 inference(unit_resolution,[status(thm)],[1981, 2373])).
% 1.03/0.99 tff(2375,plain,
% 1.03/0.99 (c1_1(a128)),
% 1.03/0.99 inference(unit_resolution,[status(thm)],[2141, 187, 1941, 1930, 2125, 2124, 2123, 493, 2374])).
% 1.03/0.99 tff(2376,plain,
% 1.03/0.99 (hskp27),
% 1.03/0.99 inference(unit_resolution,[status(thm)],[2159, 2375, 2373])).
% 1.03/0.99 tff(2377,plain,
% 1.03/0.99 (c3_1(a137)),
% 1.03/0.99 inference(unit_resolution,[status(thm)],[1221, 2376])).
% 1.03/0.99 tff(2378,plain,
% 1.03/0.99 (c2_1(a137)),
% 1.03/0.99 inference(unit_resolution,[status(thm)],[1232, 2376])).
% 1.03/0.99 tff(2379,plain,
% 1.03/0.99 (c1_1(a137)),
% 1.03/0.99 inference(unit_resolution,[status(thm)],[1243, 2376])).
% 1.03/0.99 tff(2380,plain,
% 1.03/0.99 (~hskp16),
% 1.03/0.99 inference(unit_resolution,[status(thm)],[2168, 2373])).
% 1.03/0.99 tff(2381,plain,
% 1.03/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a149) | c2_1(a159) | c1_1(a149) | c2_1(a149) | (~ndr1_0) | c0_1(a149) | c1_1(a159) | (~c0_1(a159)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a149) | c2_1(a159) | c1_1(a149) | c2_1(a149) | (~ndr1_0) | c0_1(a149) | c1_1(a159) | (~c0_1(a159)))),
% 1.03/0.99 inference(rewrite,[status(thm)],[])).
% 1.03/0.99 tff(2382,plain,
% 1.03/0.99 (((~ndr1_0) | c1_1(a159) | c2_1(a159) | (~c0_1(a159)) | c3_1(a149) | c1_1(a149) | c0_1(a149) | c2_1(a149) | c1_1(a149) | c0_1(a149)) <=> (c3_1(a149) | c2_1(a159) | c1_1(a149) | c2_1(a149) | (~ndr1_0) | c0_1(a149) | c1_1(a159) | (~c0_1(a159)))),
% 1.03/0.99 inference(rewrite,[status(thm)],[])).
% 1.03/0.99 tff(2383,plain,
% 1.03/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a159) | c2_1(a159) | (~c0_1(a159)) | c3_1(a149) | c1_1(a149) | c0_1(a149) | c2_1(a149) | c1_1(a149) | c0_1(a149))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a149) | c2_1(a159) | c1_1(a149) | c2_1(a149) | (~ndr1_0) | c0_1(a149) | c1_1(a159) | (~c0_1(a159))))),
% 1.03/0.99 inference(monotonicity,[status(thm)],[2382])).
% 1.03/0.99 tff(2384,plain,
% 1.03/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a159) | c2_1(a159) | (~c0_1(a159)) | c3_1(a149) | c1_1(a149) | c0_1(a149) | c2_1(a149) | c1_1(a149) | c0_1(a149))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a149) | c2_1(a159) | c1_1(a149) | c2_1(a149) | (~ndr1_0) | c0_1(a149) | c1_1(a159) | (~c0_1(a159)))),
% 1.03/0.99 inference(transitivity,[status(thm)],[2383, 2381])).
% 1.03/0.99 tff(2385,plain,
% 1.03/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a159) | c2_1(a159) | (~c0_1(a159)) | c3_1(a149) | c1_1(a149) | c0_1(a149) | c2_1(a149) | c1_1(a149) | c0_1(a149))),
% 1.03/0.99 inference(quant_inst,[status(thm)],[])).
% 1.03/0.99 tff(2386,plain,
% 1.03/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a149) | c2_1(a159) | c1_1(a149) | c2_1(a149) | (~ndr1_0) | c0_1(a149) | c1_1(a159) | (~c0_1(a159))),
% 1.03/1.00 inference(modus_ponens,[status(thm)],[2385, 2384])).
% 1.03/1.00 tff(2387,plain,
% 1.03/1.00 (c0_1(a149)),
% 1.03/1.00 inference(unit_resolution,[status(thm)],[2386, 187, 1941, 2372, 1930, 635, 634, 493, 2374])).
% 1.03/1.00 tff(2388,plain,
% 1.03/1.00 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp16 | c1_1(a149) | c2_1(a149) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | (~c0_1(a149)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp16 | c1_1(a149) | c2_1(a149) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | (~c0_1(a149)))),
% 1.03/1.00 inference(rewrite,[status(thm)],[])).
% 1.03/1.00 tff(2389,plain,
% 1.03/1.00 ((hskp16 | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | c1_1(a149) | c2_1(a149) | (~c0_1(a149))) <=> (hskp16 | c1_1(a149) | c2_1(a149) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | (~c0_1(a149)))),
% 1.03/1.00 inference(rewrite,[status(thm)],[])).
% 1.03/1.00 tff(2390,plain,
% 1.03/1.00 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | c1_1(a149) | c2_1(a149) | (~c0_1(a149)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp16 | c1_1(a149) | c2_1(a149) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | (~c0_1(a149))))),
% 1.03/1.00 inference(monotonicity,[status(thm)],[2389])).
% 1.03/1.00 tff(2391,plain,
% 1.03/1.00 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | c1_1(a149) | c2_1(a149) | (~c0_1(a149)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp16 | c1_1(a149) | c2_1(a149) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | (~c0_1(a149)))),
% 1.03/1.00 inference(transitivity,[status(thm)],[2390, 2388])).
% 1.03/1.00 tff(2392,plain,
% 1.03/1.00 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | c1_1(a149) | c2_1(a149) | (~c0_1(a149)))),
% 1.03/1.00 inference(quant_inst,[status(thm)],[])).
% 1.03/1.00 tff(2393,plain,
% 1.03/1.00 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp16 | c1_1(a149) | c2_1(a149) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | (~c0_1(a149))),
% 1.03/1.00 inference(modus_ponens,[status(thm)],[2392, 2391])).
% 1.03/1.00 tff(2394,plain,
% 1.03/1.00 (hskp16 | (~c0_1(a137))),
% 1.03/1.00 inference(unit_resolution,[status(thm)],[2393, 187, 2378, 2377, 635, 634, 2135, 2387])).
% 1.03/1.00 tff(2395,plain,
% 1.03/1.00 (~c0_1(a137)),
% 1.03/1.00 inference(unit_resolution,[status(thm)],[2394, 2380])).
% 1.03/1.00 tff(2396,plain,
% 1.03/1.00 (hskp6),
% 1.03/1.00 inference(unit_resolution,[status(thm)],[2183, 187, 2379, 2377, 2125, 2123, 336, 2375, 2395])).
% 1.03/1.00 tff(2397,plain,
% 1.03/1.00 (~c2_1(a133)),
% 1.03/1.00 inference(unit_resolution,[status(thm)],[360, 2396])).
% 1.03/1.00 tff(2398,plain,
% 1.03/1.00 (~c1_1(a133)),
% 1.03/1.00 inference(unit_resolution,[status(thm)],[366, 2396])).
% 1.03/1.00 tff(2399,plain,
% 1.03/1.00 (~c0_1(a133)),
% 1.03/1.00 inference(unit_resolution,[status(thm)],[372, 2396])).
% 1.03/1.00 tff(2400,plain,
% 1.03/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a183) | c2_1(a183) | c1_1(a149) | c2_1(a149) | c0_1(a133) | c1_1(a133) | (~ndr1_0) | c3_1(a133) | (~c0_1(a149)) | c0_1(a183))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a183) | c2_1(a183) | c1_1(a149) | c2_1(a149) | c0_1(a133) | c1_1(a133) | (~ndr1_0) | c3_1(a133) | (~c0_1(a149)) | c0_1(a183))),
% 1.03/1.00 inference(rewrite,[status(thm)],[])).
% 1.03/1.00 tff(2401,plain,
% 1.03/1.00 (((~ndr1_0) | c1_1(a149) | c2_1(a149) | (~c0_1(a149)) | c3_1(a133) | c1_1(a133) | c0_1(a133) | c2_1(a183) | c1_1(a183) | c0_1(a183)) <=> (c1_1(a183) | c2_1(a183) | c1_1(a149) | c2_1(a149) | c0_1(a133) | c1_1(a133) | (~ndr1_0) | c3_1(a133) | (~c0_1(a149)) | c0_1(a183))),
% 1.03/1.00 inference(rewrite,[status(thm)],[])).
% 1.03/1.00 tff(2402,plain,
% 1.03/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | c2_1(a149) | (~c0_1(a149)) | c3_1(a133) | c1_1(a133) | c0_1(a133) | c2_1(a183) | c1_1(a183) | c0_1(a183))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a183) | c2_1(a183) | c1_1(a149) | c2_1(a149) | c0_1(a133) | c1_1(a133) | (~ndr1_0) | c3_1(a133) | (~c0_1(a149)) | c0_1(a183)))),
% 1.03/1.00 inference(monotonicity,[status(thm)],[2401])).
% 1.03/1.00 tff(2403,plain,
% 1.03/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | c2_1(a149) | (~c0_1(a149)) | c3_1(a133) | c1_1(a133) | c0_1(a133) | c2_1(a183) | c1_1(a183) | c0_1(a183))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a183) | c2_1(a183) | c1_1(a149) | c2_1(a149) | c0_1(a133) | c1_1(a133) | (~ndr1_0) | c3_1(a133) | (~c0_1(a149)) | c0_1(a183))),
% 1.03/1.00 inference(transitivity,[status(thm)],[2402, 2400])).
% 1.03/1.00 tff(2404,plain,
% 1.03/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | c2_1(a149) | (~c0_1(a149)) | c3_1(a133) | c1_1(a133) | c0_1(a133) | c2_1(a183) | c1_1(a183) | c0_1(a183))),
% 1.03/1.00 inference(quant_inst,[status(thm)],[])).
% 1.03/1.00 tff(2405,plain,
% 1.03/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a183) | c2_1(a183) | c1_1(a149) | c2_1(a149) | c0_1(a133) | c1_1(a133) | (~ndr1_0) | c3_1(a133) | (~c0_1(a149)) | c0_1(a183)),
% 1.03/1.00 inference(modus_ponens,[status(thm)],[2404, 2403])).
% 1.03/1.00 tff(2406,plain,
% 1.03/1.00 ($false),
% 1.03/1.00 inference(unit_resolution,[status(thm)],[2405, 187, 2277, 2271, 635, 634, 2248, 2216, 493, 780, 2247, 2284])).
% 1.03/1.00 tff(2407,plain,(hskp4 | c1_1(a149) | c2_1(a149) | c0_1(a133) | c1_1(a133) | (~c0_1(a149)) | c2_1(a133) | (~c2_1(a137)) | (~c3_1(a137)) | c0_1(a137) | c1_1(a159)), inference(lemma,lemma(discharge,[]))).
% 1.03/1.00 tff(2408,plain,
% 1.03/1.00 (hskp4),
% 1.03/1.00 inference(unit_resolution,[status(thm)],[2407, 2399, 634, 635, 2398, 2387, 2397, 2378, 2377, 2395, 2374])).
% 1.03/1.00 tff(2409,plain,
% 1.03/1.00 (hskp13),
% 1.03/1.00 inference(unit_resolution,[status(thm)],[2338, 2408, 2379, 2378, 2377, 2374])).
% 1.03/1.00 tff(2410,plain,
% 1.03/1.00 (~c3_1(a144)),
% 1.03/1.00 inference(unit_resolution,[status(thm)],[991, 2409])).
% 1.03/1.00 tff(2411,plain,
% 1.03/1.00 (~c0_1(a144)),
% 1.03/1.00 inference(unit_resolution,[status(thm)],[1015, 2409])).
% 1.03/1.00 tff(2412,plain,
% 1.03/1.00 (c2_1(a144)),
% 1.03/1.00 inference(unit_resolution,[status(thm)],[1002, 2409])).
% 1.03/1.00 tff(2413,plain,
% 1.03/1.00 ($false),
% 1.03/1.00 inference(unit_resolution,[status(thm)],[2348, 187, 2379, 2378, 2377, 2412, 1930, 1924, 2411, 2410, 1176, 2374])).
% 1.03/1.00 tff(2414,plain,(c3_1(a149) | c2_1(a149) | c1_1(a149)), inference(lemma,lemma(discharge,[]))).
% 1.03/1.00 tff(2415,plain,
% 1.03/1.00 (c3_1(a149)),
% 1.03/1.00 inference(unit_resolution,[status(thm)],[2414, 635, 634])).
% 1.03/1.00 tff(2416,plain,
% 1.03/1.00 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c2_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | c0_1(a149))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c2_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | c0_1(a149))),
% 1.03/1.00 inference(rewrite,[status(thm)],[])).
% 1.03/1.00 tff(2417,plain,
% 1.03/1.00 ((hskp9 | (~ndr1_0) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)) | c3_1(a128) | c0_1(a128) | c2_1(a128)) <=> (hskp9 | c2_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | c0_1(a149))),
% 1.03/1.00 inference(rewrite,[status(thm)],[])).
% 1.03/1.00 tff(2418,plain,
% 1.03/1.00 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)) | c3_1(a128) | c0_1(a128) | c2_1(a128))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c2_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | c0_1(a149)))),
% 1.03/1.00 inference(monotonicity,[status(thm)],[2417])).
% 1.03/1.00 tff(2419,plain,
% 1.03/1.00 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)) | c3_1(a128) | c0_1(a128) | c2_1(a128))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c2_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | c0_1(a149))),
% 1.03/1.00 inference(transitivity,[status(thm)],[2418, 2416])).
% 1.03/1.00 tff(2420,plain,
% 1.03/1.00 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)) | c3_1(a128) | c0_1(a128) | c2_1(a128))),
% 1.03/1.00 inference(quant_inst,[status(thm)],[])).
% 1.03/1.00 tff(2421,plain,
% 1.03/1.00 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c2_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | c0_1(a149)),
% 1.03/1.00 inference(modus_ponens,[status(thm)],[2420, 2419])).
% 1.03/1.00 tff(2422,plain,
% 1.03/1.00 (hskp9),
% 1.03/1.00 inference(unit_resolution,[status(thm)],[2421, 187, 2415, 634, 2125, 2124, 2123, 31, 1403])).
% 1.03/1.00 tff(2423,plain,
% 1.03/1.00 (~c3_1(a136)),
% 1.03/1.00 inference(unit_resolution,[status(thm)],[810, 2422])).
% 1.03/1.00 tff(2424,plain,
% 1.03/1.00 (c2_1(a136)),
% 1.03/1.00 inference(unit_resolution,[status(thm)],[821, 2422])).
% 1.03/1.00 tff(2425,plain,
% 1.03/1.00 (c0_1(a136)),
% 1.03/1.00 inference(unit_resolution,[status(thm)],[840, 2422])).
% 1.03/1.00 tff(2426,plain,
% 1.03/1.00 (~c1_1(a136)),
% 1.03/1.00 inference(unit_resolution,[status(thm)],[1436, 187, 11, 2425, 2424, 2423, 21])).
% 1.03/1.00 tff(2427,plain,
% 1.03/1.00 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | c2_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | c0_1(a149))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c2_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | c0_1(a149))),
% 1.03/1.00 inference(rewrite,[status(thm)],[])).
% 1.03/1.00 tff(2428,plain,
% 1.03/1.00 ((hskp27 | (~ndr1_0) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)) | c3_1(a128) | c0_1(a128) | c2_1(a128)) <=> (hskp27 | c2_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | c0_1(a149))),
% 1.03/1.00 inference(rewrite,[status(thm)],[])).
% 1.03/1.00 tff(2429,plain,
% 1.03/1.00 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)) | c3_1(a128) | c0_1(a128) | c2_1(a128))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | c2_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | c0_1(a149)))),
% 1.03/1.00 inference(monotonicity,[status(thm)],[2428])).
% 1.03/1.00 tff(2430,plain,
% 1.03/1.00 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)) | c3_1(a128) | c0_1(a128) | c2_1(a128))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c2_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | c0_1(a149))),
% 1.03/1.00 inference(transitivity,[status(thm)],[2429, 2427])).
% 1.03/1.00 tff(2431,plain,
% 1.03/1.00 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)) | c3_1(a128) | c0_1(a128) | c2_1(a128))),
% 1.03/1.00 inference(quant_inst,[status(thm)],[])).
% 1.03/1.00 tff(2432,plain,
% 1.03/1.00 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c2_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | c0_1(a149)),
% 1.03/1.00 inference(modus_ponens,[status(thm)],[2431, 2430])).
% 1.03/1.00 tff(2433,plain,
% 1.03/1.00 (hskp27),
% 1.03/1.00 inference(unit_resolution,[status(thm)],[2432, 187, 2415, 634, 2125, 2124, 2123, 1203, 1403])).
% 1.03/1.00 tff(2434,plain,
% 1.03/1.00 (c3_1(a137)),
% 1.03/1.00 inference(unit_resolution,[status(thm)],[1221, 2433])).
% 1.03/1.00 tff(2435,plain,
% 1.03/1.00 (c2_1(a137)),
% 1.03/1.00 inference(unit_resolution,[status(thm)],[1232, 2433])).
% 1.03/1.00 tff(2436,plain,
% 1.03/1.00 (c1_1(a137)),
% 1.03/1.00 inference(unit_resolution,[status(thm)],[1243, 2433])).
% 1.03/1.00 tff(2437,plain,
% 1.03/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a159) | c3_1(a136) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c1_1(a136) | (~c2_1(a136)) | (~c1_1(a159)) | (~c0_1(a159)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a159) | c3_1(a136) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c1_1(a136) | (~c2_1(a136)) | (~c1_1(a159)) | (~c0_1(a159)))),
% 1.03/1.00 inference(rewrite,[status(thm)],[])).
% 1.03/1.00 tff(2438,plain,
% 1.03/1.00 (((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a159) | (~c1_1(a159)) | (~c0_1(a159)) | c1_1(a136) | c3_1(a136) | (~c2_1(a136))) <=> (c2_1(a159) | c3_1(a136) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c1_1(a136) | (~c2_1(a136)) | (~c1_1(a159)) | (~c0_1(a159)))),
% 1.03/1.00 inference(rewrite,[status(thm)],[])).
% 1.03/1.00 tff(2439,plain,
% 1.03/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a159) | (~c1_1(a159)) | (~c0_1(a159)) | c1_1(a136) | c3_1(a136) | (~c2_1(a136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a159) | c3_1(a136) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c1_1(a136) | (~c2_1(a136)) | (~c1_1(a159)) | (~c0_1(a159))))),
% 1.03/1.00 inference(monotonicity,[status(thm)],[2438])).
% 1.03/1.00 tff(2440,plain,
% 1.03/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a159) | (~c1_1(a159)) | (~c0_1(a159)) | c1_1(a136) | c3_1(a136) | (~c2_1(a136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a159) | c3_1(a136) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c1_1(a136) | (~c2_1(a136)) | (~c1_1(a159)) | (~c0_1(a159)))),
% 1.03/1.00 inference(transitivity,[status(thm)],[2439, 2437])).
% 1.03/1.00 tff(2441,plain,
% 1.03/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a159) | (~c1_1(a159)) | (~c0_1(a159)) | c1_1(a136) | c3_1(a136) | (~c2_1(a136)))),
% 1.03/1.00 inference(quant_inst,[status(thm)],[])).
% 1.03/1.00 tff(2442,plain,
% 1.03/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a159) | c3_1(a136) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c1_1(a136) | (~c2_1(a136)) | (~c1_1(a159)) | (~c0_1(a159))),
% 1.03/1.00 inference(modus_ponens,[status(thm)],[2441, 2440])).
% 1.03/1.00 tff(2443,plain,
% 1.03/1.00 (~c1_1(a159)),
% 1.03/1.00 inference(unit_resolution,[status(thm)],[2442, 187, 2436, 2435, 2434, 1941, 2424, 1930, 2423, 94, 2426])).
% 1.03/1.00 tff(2444,plain,
% 1.03/1.00 (~hskp4),
% 1.03/1.00 inference(unit_resolution,[status(thm)],[2338, 2443, 11, 2435, 2434, 2436])).
% 1.03/1.00 tff(2445,plain,
% 1.03/1.00 (hskp5),
% 1.03/1.00 inference(unit_resolution,[status(thm)],[2207, 2444, 2443])).
% 1.03/1.00 tff(2446,assumption,(hskp5), introduced(assumption)).
% 1.03/1.00 tff(2447,plain,
% 1.03/1.00 (~c2_1(a131)),
% 1.03/1.00 inference(unit_resolution,[status(thm)],[2213, 2446])).
% 1.03/1.00 tff(2448,plain,
% 1.03/1.00 (c3_1(a131)),
% 1.03/1.00 inference(unit_resolution,[status(thm)],[2226, 2446])).
% 1.03/1.00 tff(2449,plain,
% 1.03/1.00 (c1_1(a131)),
% 1.03/1.00 inference(unit_resolution,[status(thm)],[2237, 2446])).
% 1.03/1.00 tff(2450,plain,
% 1.03/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c3_1(a136) | c2_1(a131) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131)) | (~c1_1(a128)) | c1_1(a136) | (~c2_1(a136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c3_1(a136) | c2_1(a131) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131)) | (~c1_1(a128)) | c1_1(a136) | (~c2_1(a136)))),
% 1.03/1.00 inference(rewrite,[status(thm)],[])).
% 1.03/1.00 tff(2451,plain,
% 1.03/1.00 (((~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131)) | c3_1(a128) | c2_1(a128) | (~c1_1(a128)) | c1_1(a136) | c3_1(a136) | (~c2_1(a136))) <=> (c3_1(a136) | c2_1(a131) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131)) | (~c1_1(a128)) | c1_1(a136) | (~c2_1(a136)))),
% 1.03/1.00 inference(rewrite,[status(thm)],[])).
% 1.03/1.00 tff(2452,plain,
% 1.03/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131)) | c3_1(a128) | c2_1(a128) | (~c1_1(a128)) | c1_1(a136) | c3_1(a136) | (~c2_1(a136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c3_1(a136) | c2_1(a131) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131)) | (~c1_1(a128)) | c1_1(a136) | (~c2_1(a136))))),
% 1.03/1.00 inference(monotonicity,[status(thm)],[2451])).
% 1.03/1.00 tff(2453,plain,
% 1.03/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131)) | c3_1(a128) | c2_1(a128) | (~c1_1(a128)) | c1_1(a136) | c3_1(a136) | (~c2_1(a136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c3_1(a136) | c2_1(a131) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131)) | (~c1_1(a128)) | c1_1(a136) | (~c2_1(a136)))),
% 1.03/1.00 inference(transitivity,[status(thm)],[2452, 2450])).
% 1.03/1.00 tff(2454,plain,
% 1.03/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131)) | c3_1(a128) | c2_1(a128) | (~c1_1(a128)) | c1_1(a136) | c3_1(a136) | (~c2_1(a136)))),
% 1.03/1.00 inference(quant_inst,[status(thm)],[])).
% 1.03/1.00 tff(2455,plain,
% 1.03/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c3_1(a136) | c2_1(a131) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131)) | (~c1_1(a128)) | c1_1(a136) | (~c2_1(a136))),
% 1.03/1.00 inference(modus_ponens,[status(thm)],[2454, 2453])).
% 1.03/1.00 tff(2456,plain,
% 1.03/1.00 ($false),
% 1.03/1.00 inference(unit_resolution,[status(thm)],[2455, 187, 1125, 2449, 2448, 1137, 2447, 2124, 2123, 10, 667, 1124])).
% 1.03/1.00 tff(2457,plain,((~hskp5) | (~c2_1(a136)) | c3_1(a136) | (~c1_1(a128)) | c1_1(a136)), inference(lemma,lemma(discharge,[]))).
% 1.03/1.00 tff(2458,plain,
% 1.03/1.00 (~c1_1(a128)),
% 1.03/1.00 inference(unit_resolution,[status(thm)],[2457, 2445, 2423, 2426, 2424])).
% 1.03/1.00 tff(2459,plain,
% 1.03/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a159) | c1_1(a149) | c2_1(a149) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | c0_1(a149) | c1_1(a159) | (~c0_1(a159)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a159) | c1_1(a149) | c2_1(a149) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | c0_1(a149) | c1_1(a159) | (~c0_1(a159)))),
% 1.09/1.00 inference(rewrite,[status(thm)],[])).
% 1.09/1.00 tff(2460,plain,
% 1.09/1.00 (((~ndr1_0) | c1_1(a159) | c2_1(a159) | (~c0_1(a159)) | c3_1(a128) | c1_1(a128) | c0_1(a128) | c2_1(a149) | c1_1(a149) | c0_1(a149)) <=> (c2_1(a159) | c1_1(a149) | c2_1(a149) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | c0_1(a149) | c1_1(a159) | (~c0_1(a159)))),
% 1.09/1.00 inference(rewrite,[status(thm)],[])).
% 1.09/1.00 tff(2461,plain,
% 1.09/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a159) | c2_1(a159) | (~c0_1(a159)) | c3_1(a128) | c1_1(a128) | c0_1(a128) | c2_1(a149) | c1_1(a149) | c0_1(a149))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a159) | c1_1(a149) | c2_1(a149) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | c0_1(a149) | c1_1(a159) | (~c0_1(a159))))),
% 1.09/1.00 inference(monotonicity,[status(thm)],[2460])).
% 1.09/1.00 tff(2462,plain,
% 1.09/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a159) | c2_1(a159) | (~c0_1(a159)) | c3_1(a128) | c1_1(a128) | c0_1(a128) | c2_1(a149) | c1_1(a149) | c0_1(a149))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a159) | c1_1(a149) | c2_1(a149) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | c0_1(a149) | c1_1(a159) | (~c0_1(a159)))),
% 1.09/1.00 inference(transitivity,[status(thm)],[2461, 2459])).
% 1.09/1.00 tff(2463,plain,
% 1.09/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a159) | c2_1(a159) | (~c0_1(a159)) | c3_1(a128) | c1_1(a128) | c0_1(a128) | c2_1(a149) | c1_1(a149) | c0_1(a149))),
% 1.09/1.00 inference(quant_inst,[status(thm)],[])).
% 1.09/1.00 tff(2464,plain,
% 1.09/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a159) | c1_1(a149) | c2_1(a149) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | c0_1(a149) | c1_1(a159) | (~c0_1(a159))),
% 1.09/1.00 inference(modus_ponens,[status(thm)],[2463, 2462])).
% 1.09/1.00 tff(2465,plain,
% 1.09/1.00 ($false),
% 1.09/1.00 inference(unit_resolution,[status(thm)],[2464, 187, 1941, 1930, 635, 634, 2125, 2123, 493, 2458, 1403, 2443])).
% 1.09/1.00 tff(2466,plain,(c0_1(a149) | c1_1(a149) | c2_1(a149) | hskp13), inference(lemma,lemma(discharge,[]))).
% 1.09/1.00 tff(2467,plain,
% 1.09/1.00 (c0_1(a149)),
% 1.09/1.00 inference(unit_resolution,[status(thm)],[2466, 11, 634, 635])).
% 1.09/1.00 tff(2468,plain,
% 1.09/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a149) | c2_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c0_1(a149)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c2_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c0_1(a149)))),
% 1.09/1.00 inference(rewrite,[status(thm)],[])).
% 1.09/1.00 tff(2469,plain,
% 1.09/1.00 (((~ndr1_0) | c1_1(a149) | c2_1(a149) | (~c0_1(a149)) | c3_1(a128) | c1_1(a128) | c0_1(a128) | c2_1(a128) | c1_1(a128) | c0_1(a128)) <=> (c1_1(a149) | c2_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c0_1(a149)))),
% 1.09/1.00 inference(rewrite,[status(thm)],[])).
% 1.09/1.00 tff(2470,plain,
% 1.09/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | c2_1(a149) | (~c0_1(a149)) | c3_1(a128) | c1_1(a128) | c0_1(a128) | c2_1(a128) | c1_1(a128) | c0_1(a128))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a149) | c2_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c0_1(a149))))),
% 1.09/1.00 inference(monotonicity,[status(thm)],[2469])).
% 1.09/1.00 tff(2471,plain,
% 1.09/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | c2_1(a149) | (~c0_1(a149)) | c3_1(a128) | c1_1(a128) | c0_1(a128) | c2_1(a128) | c1_1(a128) | c0_1(a128))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c2_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c0_1(a149)))),
% 1.09/1.00 inference(transitivity,[status(thm)],[2470, 2468])).
% 1.09/1.00 tff(2472,plain,
% 1.09/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | c2_1(a149) | (~c0_1(a149)) | c3_1(a128) | c1_1(a128) | c0_1(a128) | c2_1(a128) | c1_1(a128) | c0_1(a128))),
% 1.09/1.00 inference(quant_inst,[status(thm)],[])).
% 1.09/1.00 tff(2473,plain,
% 1.09/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c2_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c0_1(a149))),
% 1.09/1.00 inference(modus_ponens,[status(thm)],[2472, 2471])).
% 1.09/1.00 tff(2474,plain,
% 1.09/1.00 (c1_1(a128) | (~c0_1(a149))),
% 1.09/1.00 inference(unit_resolution,[status(thm)],[2473, 187, 635, 634, 2125, 2124, 2123, 493])).
% 1.09/1.00 tff(2475,plain,
% 1.09/1.00 (c1_1(a128)),
% 1.09/1.00 inference(unit_resolution,[status(thm)],[2474, 2467])).
% 1.09/1.00 tff(2476,plain,
% 1.09/1.00 (hskp16 | (~c3_1(a149)) | (~c0_1(a149))),
% 1.09/1.00 inference(unit_resolution,[status(thm)],[1392, 187, 53, 635, 144])).
% 1.09/1.00 tff(2477,plain,
% 1.09/1.00 (hskp16),
% 1.09/1.00 inference(unit_resolution,[status(thm)],[2476, 2467, 2415])).
% 1.09/1.00 tff(2478,plain,
% 1.09/1.00 (~c2_1(a151)),
% 1.09/1.00 inference(unit_resolution,[status(thm)],[200, 2477])).
% 1.09/1.00 tff(2479,plain,
% 1.09/1.00 (hskp17 | (~c3_1(a149)) | (~c0_1(a149))),
% 1.09/1.00 inference(unit_resolution,[status(thm)],[2006, 187, 1941, 1930, 1924, 634, 290])).
% 1.09/1.00 tff(2480,plain,
% 1.09/1.00 (hskp17),
% 1.09/1.00 inference(unit_resolution,[status(thm)],[2479, 2467, 2415])).
% 1.09/1.00 tff(2481,plain,
% 1.09/1.00 (~c3_1(a158)),
% 1.09/1.00 inference(unit_resolution,[status(thm)],[441, 2480])).
% 1.09/1.00 tff(2482,plain,
% 1.09/1.00 (~c2_1(a158)),
% 1.09/1.00 inference(unit_resolution,[status(thm)],[447, 2480])).
% 1.09/1.00 tff(2483,plain,
% 1.09/1.00 (c1_1(a158)),
% 1.09/1.00 inference(unit_resolution,[status(thm)],[458, 2480])).
% 1.09/1.00 tff(2484,plain,
% 1.09/1.00 (c1_1(a151)),
% 1.09/1.00 inference(unit_resolution,[status(thm)],[211, 2477])).
% 1.09/1.00 tff(2485,plain,
% 1.09/1.00 (c0_1(a151)),
% 1.09/1.00 inference(unit_resolution,[status(thm)],[249, 2477])).
% 1.09/1.00 tff(2486,assumption,(~hskp6), introduced(assumption)).
% 1.09/1.00 tff(2487,plain,
% 1.09/1.00 (hskp9),
% 1.09/1.00 inference(unit_resolution,[status(thm)],[804, 2486, 53])).
% 1.09/1.00 tff(2488,plain,
% 1.09/1.00 (~c3_1(a136)),
% 1.09/1.00 inference(unit_resolution,[status(thm)],[810, 2487])).
% 1.09/1.00 tff(2489,plain,
% 1.09/1.00 (c2_1(a136)),
% 1.09/1.00 inference(unit_resolution,[status(thm)],[821, 2487])).
% 1.09/1.00 tff(2490,plain,
% 1.09/1.00 (c0_1(a136)),
% 1.09/1.00 inference(unit_resolution,[status(thm)],[840, 2487])).
% 1.09/1.00 tff(2491,plain,
% 1.09/1.00 (~c1_1(a136)),
% 1.09/1.00 inference(unit_resolution,[status(thm)],[1436, 187, 11, 2490, 2489, 2488, 21])).
% 1.09/1.00 tff(2492,plain,
% 1.09/1.00 (~hskp5),
% 1.09/1.00 inference(unit_resolution,[status(thm)],[2457, 2491, 667, 2488, 2489])).
% 1.09/1.00 tff(2493,plain,
% 1.09/1.00 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp5 | hskp4 | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c0_1(a136)))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp5 | hskp4 | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c0_1(a136)))),
% 1.09/1.00 inference(rewrite,[status(thm)],[])).
% 1.09/1.00 tff(2494,plain,
% 1.09/1.00 ((hskp5 | hskp4 | (~ndr1_0) | c3_1(a136) | c1_1(a136) | (~c0_1(a136))) <=> (hskp5 | hskp4 | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c0_1(a136)))),
% 1.09/1.01 inference(rewrite,[status(thm)],[])).
% 1.09/1.01 tff(2495,plain,
% 1.09/1.01 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp5 | hskp4 | (~ndr1_0) | c3_1(a136) | c1_1(a136) | (~c0_1(a136)))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp5 | hskp4 | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c0_1(a136))))),
% 1.09/1.01 inference(monotonicity,[status(thm)],[2494])).
% 1.09/1.01 tff(2496,plain,
% 1.09/1.01 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp5 | hskp4 | (~ndr1_0) | c3_1(a136) | c1_1(a136) | (~c0_1(a136)))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp5 | hskp4 | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c0_1(a136)))),
% 1.09/1.01 inference(transitivity,[status(thm)],[2495, 2493])).
% 1.09/1.01 tff(2497,plain,
% 1.09/1.01 ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp5 | hskp4 | (~ndr1_0) | c3_1(a136) | c1_1(a136) | (~c0_1(a136)))),
% 1.09/1.01 inference(quant_inst,[status(thm)],[])).
% 1.09/1.01 tff(2498,plain,
% 1.09/1.01 ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp5 | hskp4 | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c0_1(a136))),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2497, 2496])).
% 1.09/1.01 tff(2499,plain,
% 1.09/1.01 (hskp5 | hskp4 | c1_1(a136)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2498, 187, 2490, 2488, 2200])).
% 1.09/1.01 tff(2500,plain,
% 1.09/1.01 (hskp4),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2499, 2492, 2491])).
% 1.09/1.01 tff(2501,plain,
% 1.09/1.01 (~c3_1(a130)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2299, 2500])).
% 1.09/1.01 tff(2502,plain,
% 1.09/1.01 (c2_1(a130)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2310, 2500])).
% 1.09/1.01 tff(2503,plain,
% 1.09/1.01 (c1_1(a130)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2329, 2500])).
% 1.09/1.01 tff(2504,plain,
% 1.09/1.01 (~c0_1(a130)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2336, 187, 11, 2503, 2502, 2501, 21])).
% 1.09/1.01 tff(2505,assumption,(~c3_1(a158)), introduced(assumption)).
% 1.09/1.01 tff(2506,assumption,(~c2_1(a158)), introduced(assumption)).
% 1.09/1.01 tff(2507,assumption,(c1_1(a158)), introduced(assumption)).
% 1.09/1.01 tff(2508,plain,
% 1.09/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a158) | c3_1(a158) | c2_1(a151) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a151)) | (~c1_1(a151)) | (~c1_1(a158)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a158) | c3_1(a158) | c2_1(a151) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a151)) | (~c1_1(a151)) | (~c1_1(a158)))),
% 1.09/1.01 inference(rewrite,[status(thm)],[])).
% 1.09/1.01 tff(2509,plain,
% 1.09/1.01 (((~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c1_1(a151)) | c3_1(a158) | c2_1(a158) | (~c1_1(a158)) | c1_1(a136) | c3_1(a136) | (~c2_1(a136))) <=> (c2_1(a158) | c3_1(a158) | c2_1(a151) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a151)) | (~c1_1(a151)) | (~c1_1(a158)))),
% 1.09/1.01 inference(rewrite,[status(thm)],[])).
% 1.09/1.01 tff(2510,plain,
% 1.09/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c1_1(a151)) | c3_1(a158) | c2_1(a158) | (~c1_1(a158)) | c1_1(a136) | c3_1(a136) | (~c2_1(a136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a158) | c3_1(a158) | c2_1(a151) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a151)) | (~c1_1(a151)) | (~c1_1(a158))))),
% 1.09/1.01 inference(monotonicity,[status(thm)],[2509])).
% 1.09/1.01 tff(2511,plain,
% 1.09/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c1_1(a151)) | c3_1(a158) | c2_1(a158) | (~c1_1(a158)) | c1_1(a136) | c3_1(a136) | (~c2_1(a136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a158) | c3_1(a158) | c2_1(a151) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a151)) | (~c1_1(a151)) | (~c1_1(a158)))),
% 1.09/1.01 inference(transitivity,[status(thm)],[2510, 2508])).
% 1.09/1.01 tff(2512,plain,
% 1.09/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c1_1(a151)) | c3_1(a158) | c2_1(a158) | (~c1_1(a158)) | c1_1(a136) | c3_1(a136) | (~c2_1(a136)))),
% 1.09/1.01 inference(quant_inst,[status(thm)],[])).
% 1.09/1.01 tff(2513,plain,
% 1.09/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a158) | c3_1(a158) | c2_1(a151) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a151)) | (~c1_1(a151)) | (~c1_1(a158))),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2512, 2511])).
% 1.09/1.01 tff(2514,plain,
% 1.09/1.01 (~c3_1(a151)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2513, 187, 2507, 649, 2489, 2506, 2505, 636, 2488, 10, 2491])).
% 1.09/1.01 tff(2515,assumption,(c0_1(a151)), introduced(assumption)).
% 1.09/1.01 tff(2516,plain,
% 1.09/1.01 (((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | c3_1(a151) | (~c1_1(a151)) | (~c0_1(a151)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp12 | (~ndr1_0) | c3_1(a151) | (~c1_1(a151)) | (~c0_1(a151)))),
% 1.09/1.01 inference(rewrite,[status(thm)],[])).
% 1.09/1.01 tff(2517,plain,
% 1.09/1.01 ((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | c3_1(a151) | (~c1_1(a151)) | (~c0_1(a151)))),
% 1.09/1.01 inference(quant_inst,[status(thm)],[])).
% 1.09/1.01 tff(2518,plain,
% 1.09/1.01 ((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp12 | (~ndr1_0) | c3_1(a151) | (~c1_1(a151)) | (~c0_1(a151))),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2517, 2516])).
% 1.09/1.01 tff(2519,plain,
% 1.09/1.01 (hskp12 | c3_1(a151)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2518, 187, 2515, 649, 239])).
% 1.09/1.01 tff(2520,plain,
% 1.09/1.01 (hskp12),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2519, 2514])).
% 1.09/1.01 tff(2521,plain,
% 1.09/1.01 (~c0_1(a140)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[632, 2520])).
% 1.09/1.01 tff(2522,plain,
% 1.09/1.01 (c3_1(a140)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[646, 2520])).
% 1.09/1.01 tff(2523,plain,
% 1.09/1.01 (c1_1(a140)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[861, 2520])).
% 1.09/1.01 tff(2524,plain,
% 1.09/1.01 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a140) | c3_1(a130) | (~ndr1_0) | (~c1_1(a130)) | c0_1(a130) | (~c3_1(a140)) | (~c1_1(a140)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a140) | c3_1(a130) | (~ndr1_0) | (~c1_1(a130)) | c0_1(a130) | (~c3_1(a140)) | (~c1_1(a140)))),
% 1.09/1.01 inference(rewrite,[status(thm)],[])).
% 1.09/1.01 tff(2525,plain,
% 1.09/1.01 ((hskp6 | (~ndr1_0) | c0_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | c3_1(a130) | c0_1(a130) | (~c1_1(a130))) <=> (hskp6 | c0_1(a140) | c3_1(a130) | (~ndr1_0) | (~c1_1(a130)) | c0_1(a130) | (~c3_1(a140)) | (~c1_1(a140)))),
% 1.09/1.01 inference(rewrite,[status(thm)],[])).
% 1.09/1.01 tff(2526,plain,
% 1.09/1.01 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | c3_1(a130) | c0_1(a130) | (~c1_1(a130)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a140) | c3_1(a130) | (~ndr1_0) | (~c1_1(a130)) | c0_1(a130) | (~c3_1(a140)) | (~c1_1(a140))))),
% 1.09/1.01 inference(monotonicity,[status(thm)],[2525])).
% 1.09/1.01 tff(2527,plain,
% 1.09/1.01 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | c3_1(a130) | c0_1(a130) | (~c1_1(a130)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a140) | c3_1(a130) | (~ndr1_0) | (~c1_1(a130)) | c0_1(a130) | (~c3_1(a140)) | (~c1_1(a140)))),
% 1.09/1.01 inference(transitivity,[status(thm)],[2526, 2524])).
% 1.09/1.01 tff(2528,plain,
% 1.09/1.01 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | c3_1(a130) | c0_1(a130) | (~c1_1(a130)))),
% 1.09/1.01 inference(quant_inst,[status(thm)],[])).
% 1.09/1.01 tff(2529,plain,
% 1.09/1.01 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a140) | c3_1(a130) | (~ndr1_0) | (~c1_1(a130)) | c0_1(a130) | (~c3_1(a140)) | (~c1_1(a140))),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2528, 2527])).
% 1.09/1.01 tff(2530,plain,
% 1.09/1.01 ($false),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2529, 187, 2486, 2523, 2522, 2503, 2521, 2501, 336, 2504])).
% 1.09/1.01 tff(2531,plain,(hskp6 | (~c0_1(a151)) | (~c1_1(a151)) | hskp13 | (~c1_1(a158)) | c2_1(a158) | c3_1(a158) | c2_1(a151) | (~c1_1(a128)) | hskp21), inference(lemma,lemma(discharge,[]))).
% 1.09/1.01 tff(2532,plain,
% 1.09/1.01 (hskp6),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2531, 2485, 2484, 11, 2483, 2482, 2481, 2478, 2475, 53])).
% 1.09/1.01 tff(2533,plain,
% 1.09/1.01 (~c2_1(a133)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[360, 2532])).
% 1.09/1.01 tff(2534,plain,
% 1.09/1.01 (~c1_1(a133)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[366, 2532])).
% 1.09/1.01 tff(2535,plain,
% 1.09/1.01 (~c0_1(a133)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[372, 2532])).
% 1.09/1.01 tff(2536,plain,
% 1.09/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a149) | c0_1(a133) | c1_1(a133) | c2_1(a133) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c0_1(a133) | c1_1(a133) | c2_1(a133) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)))),
% 1.09/1.01 inference(rewrite,[status(thm)],[])).
% 1.09/1.01 tff(2537,plain,
% 1.09/1.01 (((~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a133) | c1_1(a133) | c0_1(a133)) <=> (c1_1(a149) | c0_1(a133) | c1_1(a133) | c2_1(a133) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)))),
% 1.09/1.01 inference(rewrite,[status(thm)],[])).
% 1.09/1.01 tff(2538,plain,
% 1.09/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a133) | c1_1(a133) | c0_1(a133))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a149) | c0_1(a133) | c1_1(a133) | c2_1(a133) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149))))),
% 1.09/1.01 inference(monotonicity,[status(thm)],[2537])).
% 1.09/1.01 tff(2539,plain,
% 1.09/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a133) | c1_1(a133) | c0_1(a133))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c0_1(a133) | c1_1(a133) | c2_1(a133) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)))),
% 1.09/1.01 inference(transitivity,[status(thm)],[2538, 2536])).
% 1.09/1.01 tff(2540,plain,
% 1.09/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a133) | c1_1(a133) | c0_1(a133))),
% 1.09/1.01 inference(quant_inst,[status(thm)],[])).
% 1.09/1.01 tff(2541,plain,
% 1.09/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c0_1(a133) | c1_1(a133) | c2_1(a133) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149))),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2540, 2539])).
% 1.09/1.01 tff(2542,plain,
% 1.09/1.01 ($false),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2541, 187, 2415, 635, 2535, 2534, 2533, 2125, 2124, 2123, 279, 2467])).
% 1.09/1.01 tff(2543,plain,(hskp13 | c1_1(a149) | hskp21 | c2_1(a149)), inference(lemma,lemma(discharge,[]))).
% 1.09/1.01 tff(2544,plain,
% 1.09/1.01 (hskp13),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2543, 635, 53, 634])).
% 1.09/1.01 tff(2545,plain,
% 1.09/1.01 (~c3_1(a144)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[991, 2544])).
% 1.09/1.01 tff(2546,plain,
% 1.09/1.01 (~c0_1(a144)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[1015, 2544])).
% 1.09/1.01 tff(2547,plain,
% 1.09/1.01 (c2_1(a144)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[1002, 2544])).
% 1.09/1.01 tff(2548,plain,
% 1.09/1.01 (c1_1(a128)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[1617, 2433, 1604, 1603, 2124, 2123, 1605])).
% 1.09/1.01 tff(2549,plain,
% 1.09/1.01 (~hskp11),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2361, 2436, 2435, 2434, 1605, 1604, 1603])).
% 1.09/1.01 tff(2550,plain,
% 1.09/1.01 (hskp10),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2363, 2549, 2548])).
% 1.09/1.01 tff(2551,plain,
% 1.09/1.01 (~c1_1(a138)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[101, 2550])).
% 1.09/1.01 tff(2552,plain,
% 1.09/1.01 (c3_1(a138)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[112, 2550])).
% 1.09/1.01 tff(2553,plain,
% 1.09/1.01 (c0_1(a138)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[123, 2550])).
% 1.09/1.01 tff(2554,plain,
% 1.09/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a149) | c2_1(a149) | c1_1(a138) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c0_1(a149))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c2_1(a149) | c1_1(a138) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c0_1(a149))),
% 1.09/1.01 inference(rewrite,[status(thm)],[])).
% 1.09/1.01 tff(2555,plain,
% 1.09/1.01 (((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a149) | c1_1(a149) | c0_1(a149)) <=> (c1_1(a149) | c2_1(a149) | c1_1(a138) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c0_1(a149))),
% 1.09/1.01 inference(rewrite,[status(thm)],[])).
% 1.09/1.01 tff(2556,plain,
% 1.09/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a149) | c1_1(a149) | c0_1(a149))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a149) | c2_1(a149) | c1_1(a138) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c0_1(a149)))),
% 1.09/1.01 inference(monotonicity,[status(thm)],[2555])).
% 1.09/1.01 tff(2557,plain,
% 1.09/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a149) | c1_1(a149) | c0_1(a149))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c2_1(a149) | c1_1(a138) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c0_1(a149))),
% 1.09/1.01 inference(transitivity,[status(thm)],[2556, 2554])).
% 1.09/1.01 tff(2558,plain,
% 1.09/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a149) | c1_1(a149) | c0_1(a149))),
% 1.09/1.01 inference(quant_inst,[status(thm)],[])).
% 1.09/1.01 tff(2559,plain,
% 1.09/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c2_1(a149) | c1_1(a138) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c0_1(a149)),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2558, 2557])).
% 1.09/1.01 tff(2560,plain,
% 1.09/1.01 ($false),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2559, 187, 2553, 2552, 635, 634, 2551, 2125, 2124, 2123, 279, 1403])).
% 1.09/1.01 tff(2561,plain,(c0_1(a149) | c1_1(a149) | c2_1(a149) | (~c2_1(a144)) | c0_1(a144) | c3_1(a144)), inference(lemma,lemma(discharge,[]))).
% 1.09/1.01 tff(2562,plain,
% 1.09/1.01 (c0_1(a149)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2561, 635, 634, 2547, 2546, 2545])).
% 1.09/1.01 tff(2563,plain,
% 1.09/1.01 (hskp16),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2476, 2562, 2415])).
% 1.09/1.01 tff(2564,plain,
% 1.09/1.01 (c0_1(a151)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[249, 2563])).
% 1.09/1.01 tff(2565,plain,
% 1.09/1.01 (~c2_1(a151)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[200, 2563])).
% 1.09/1.01 tff(2566,plain,
% 1.09/1.01 (hskp17),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2479, 2562, 2415])).
% 1.09/1.01 tff(2567,plain,
% 1.09/1.01 (~c3_1(a158)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[441, 2566])).
% 1.09/1.01 tff(2568,plain,
% 1.09/1.01 (~c2_1(a158)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[447, 2566])).
% 1.09/1.01 tff(2569,plain,
% 1.09/1.01 (c1_1(a158)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[458, 2566])).
% 1.09/1.01 tff(2570,plain,
% 1.09/1.01 (c1_1(a151)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[211, 2563])).
% 1.09/1.01 tff(2571,plain,
% 1.09/1.01 (c1_1(a128)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2474, 2562])).
% 1.09/1.01 tff(2572,assumption,(~hskp12), introduced(assumption)).
% 1.09/1.01 tff(2573,plain,
% 1.09/1.01 (hskp12 | (~c1_1(a136))),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[847, 187, 1126, 1137, 239])).
% 1.09/1.01 tff(2574,plain,
% 1.09/1.01 (~c1_1(a136)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2573, 2572])).
% 1.09/1.01 tff(2575,plain,
% 1.09/1.01 (c3_1(a151)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2519, 2572])).
% 1.09/1.01 tff(2576,plain,
% 1.09/1.01 ($false),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2513, 187, 2507, 649, 1125, 2506, 2505, 636, 1137, 10, 2575, 2574])).
% 1.09/1.01 tff(2577,plain,(hskp12 | (~c1_1(a158)) | (~c1_1(a151)) | (~c2_1(a136)) | c2_1(a158) | c3_1(a158) | c2_1(a151) | c3_1(a136) | (~c0_1(a136)) | (~c0_1(a151))), inference(lemma,lemma(discharge,[]))).
% 1.09/1.01 tff(2578,plain,
% 1.09/1.01 (hskp12),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2577, 2489, 649, 2507, 2506, 2505, 636, 2488, 2490, 2515])).
% 1.09/1.01 tff(2579,plain,
% 1.09/1.01 (~c0_1(a140)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[632, 2578])).
% 1.09/1.01 tff(2580,plain,
% 1.09/1.01 (c3_1(a140)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[646, 2578])).
% 1.09/1.01 tff(2581,plain,
% 1.09/1.01 (c1_1(a140)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[861, 2578])).
% 1.09/1.01 tff(2582,plain,
% 1.09/1.01 ($false),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[868, 187, 2486, 2581, 2580, 2579, 2125, 2123, 336, 667])).
% 1.09/1.01 tff(2583,plain,(hskp6 | (~c1_1(a128)) | (~c1_1(a151)) | (~c1_1(a158)) | c2_1(a158) | c3_1(a158) | c2_1(a151) | (~c0_1(a151)) | hskp21), inference(lemma,lemma(discharge,[]))).
% 1.09/1.01 tff(2584,plain,
% 1.09/1.01 (hskp6),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2583, 2571, 2570, 2569, 2568, 2567, 2565, 2564, 53])).
% 1.09/1.01 tff(2585,plain,
% 1.09/1.01 (~c2_1(a133)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[360, 2584])).
% 1.09/1.01 tff(2586,plain,
% 1.09/1.01 (~c1_1(a133)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[366, 2584])).
% 1.09/1.01 tff(2587,plain,
% 1.09/1.01 (~c0_1(a133)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[372, 2584])).
% 1.09/1.01 tff(2588,plain,
% 1.09/1.01 ($false),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2541, 187, 2415, 635, 2587, 2586, 2585, 2125, 2124, 2123, 279, 2562])).
% 1.09/1.01 tff(2589,plain,(c1_1(a149) | hskp21 | c2_1(a149)), inference(lemma,lemma(discharge,[]))).
% 1.09/1.01 tff(2590,plain,
% 1.09/1.01 (hskp21),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2589, 2371, 2370])).
% 1.09/1.01 tff(2591,plain,
% 1.09/1.01 (~c2_1(a170)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[312, 2590])).
% 1.09/1.01 tff(2592,plain,
% 1.09/1.01 (~c0_1(a170)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[318, 2590])).
% 1.09/1.01 tff(2593,plain,
% 1.09/1.01 (c3_1(a170)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[346, 2590])).
% 1.09/1.01 tff(2594,plain,
% 1.09/1.01 (hskp9),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[1768, 187, 2593, 2592, 2591, 2125, 2124, 2123, 31])).
% 1.09/1.01 tff(2595,plain,
% 1.09/1.01 (~c3_1(a136)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[810, 2594])).
% 1.09/1.01 tff(2596,plain,
% 1.09/1.01 (c2_1(a136)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[821, 2594])).
% 1.09/1.01 tff(2597,plain,
% 1.09/1.01 (c0_1(a136)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[840, 2594])).
% 1.09/1.01 tff(2598,plain,
% 1.09/1.01 (hskp13 | (~c1_1(a136))),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[1436, 187, 2597, 2596, 2595, 21])).
% 1.09/1.01 tff(2599,plain,
% 1.09/1.01 (~c1_1(a136)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2598, 11])).
% 1.09/1.01 tff(2600,plain,
% 1.09/1.01 (c0_1(a149) | hskp13),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2466, 2371, 2370])).
% 1.09/1.01 tff(2601,plain,
% 1.09/1.01 (c0_1(a149)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2600, 11])).
% 1.09/1.01 tff(2602,plain,
% 1.09/1.01 (c3_1(a149)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[267, 2369])).
% 1.09/1.01 tff(2603,plain,
% 1.09/1.01 (c1_1(a128) | (~c0_1(a149))),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[1680, 187, 2602, 2370, 2125, 2124, 2123, 279])).
% 1.09/1.01 tff(2604,plain,
% 1.09/1.01 (c1_1(a128)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2603, 2601])).
% 1.09/1.01 tff(2605,plain,
% 1.09/1.01 ((~hskp5) | (~c1_1(a128)) | c1_1(a136)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2457, 2595, 2596])).
% 1.09/1.01 tff(2606,plain,
% 1.09/1.01 (~hskp5),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2605, 2604, 2599])).
% 1.09/1.01 tff(2607,plain,
% 1.09/1.01 (hskp5 | hskp4 | c1_1(a136)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2498, 187, 2597, 2595, 2200])).
% 1.09/1.01 tff(2608,plain,
% 1.09/1.01 (hskp4),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2607, 2606, 2599])).
% 1.09/1.01 tff(2609,plain,
% 1.09/1.01 (hskp27),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[1899, 187, 2593, 2592, 2591, 2125, 2124, 2123, 1203])).
% 1.09/1.01 tff(2610,plain,
% 1.09/1.01 (c1_1(a137)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[1243, 2609])).
% 1.09/1.01 tff(2611,plain,
% 1.09/1.01 (c3_1(a137)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[1221, 2609])).
% 1.09/1.01 tff(2612,plain,
% 1.09/1.01 (c2_1(a137)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[1232, 2609])).
% 1.09/1.01 tff(2613,plain,
% 1.09/1.01 ((~hskp4) | hskp13 | c1_1(a159)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2338, 2612, 2611, 2610])).
% 1.09/1.01 tff(2614,plain,
% 1.09/1.01 (c1_1(a159)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2613, 2608, 11])).
% 1.09/1.01 tff(2615,plain,
% 1.09/1.01 ($false),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2442, 187, 2610, 2612, 2611, 1941, 2596, 1930, 2595, 94, 2599, 2614])).
% 1.09/1.01 tff(2616,plain,(hskp13), inference(lemma,lemma(discharge,[]))).
% 1.09/1.01 tff(2617,plain,
% 1.09/1.01 (~c3_1(a144)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[991, 2616])).
% 1.09/1.01 tff(2618,plain,
% 1.09/1.01 (~c0_1(a144)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[1015, 2616])).
% 1.09/1.01 tff(2619,plain,
% 1.09/1.01 (c2_1(a144)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[1002, 2616])).
% 1.09/1.01 tff(2620,plain,
% 1.09/1.01 (c0_1(a149) | (~c2_1(a144)) | c0_1(a144) | c3_1(a144)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2561, 2371, 2370])).
% 1.09/1.01 tff(2621,plain,
% 1.09/1.01 (c0_1(a149)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2620, 2619, 2618, 2617])).
% 1.09/1.01 tff(2622,assumption,(hskp24), introduced(assumption)).
% 1.09/1.01 tff(2623,plain,
% 1.09/1.01 (((~hskp24) | (~c3_1(a183))) <=> ((~hskp24) | (~c3_1(a183)))),
% 1.09/1.01 inference(rewrite,[status(thm)],[])).
% 1.09/1.01 tff(2624,plain,
% 1.09/1.01 (((~c3_1(a183)) | (~hskp24)) <=> ((~hskp24) | (~c3_1(a183)))),
% 1.09/1.01 inference(rewrite,[status(thm)],[])).
% 1.09/1.01 tff(2625,axiom,((~c3_1(a183)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause90')).
% 1.09/1.01 tff(2626,plain,
% 1.09/1.01 ((~hskp24) | (~c3_1(a183))),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2625, 2624])).
% 1.09/1.01 tff(2627,plain,
% 1.09/1.01 ((~hskp24) | (~c3_1(a183))),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2626, 2623])).
% 1.09/1.01 tff(2628,plain,
% 1.09/1.01 (~c3_1(a183)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2627, 2622])).
% 1.09/1.01 tff(2629,plain,
% 1.09/1.01 (~c2_1(a183)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2270, 2622])).
% 1.09/1.01 tff(2630,plain,
% 1.09/1.01 (~c1_1(a183)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2276, 2622])).
% 1.09/1.01 tff(2631,plain,
% 1.09/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a183) | c2_1(a183) | c3_1(a183) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a144)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a183) | c2_1(a183) | c3_1(a183) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a144)))),
% 1.09/1.01 inference(rewrite,[status(thm)],[])).
% 1.09/1.01 tff(2632,plain,
% 1.09/1.01 (((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a183) | c1_1(a183) | c3_1(a183)) <=> (c1_1(a183) | c2_1(a183) | c3_1(a183) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a144)))),
% 1.09/1.01 inference(rewrite,[status(thm)],[])).
% 1.09/1.01 tff(2633,plain,
% 1.09/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a183) | c1_1(a183) | c3_1(a183))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a183) | c2_1(a183) | c3_1(a183) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a144))))),
% 1.09/1.01 inference(monotonicity,[status(thm)],[2632])).
% 1.09/1.01 tff(2634,plain,
% 1.09/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a183) | c1_1(a183) | c3_1(a183))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a183) | c2_1(a183) | c3_1(a183) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a144)))),
% 1.09/1.01 inference(transitivity,[status(thm)],[2633, 2631])).
% 1.09/1.01 tff(2635,plain,
% 1.09/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a183) | c1_1(a183) | c3_1(a183))),
% 1.09/1.01 inference(quant_inst,[status(thm)],[])).
% 1.09/1.01 tff(2636,plain,
% 1.09/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a183) | c2_1(a183) | c3_1(a183) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a144))),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2635, 2634])).
% 1.09/1.01 tff(2637,plain,
% 1.09/1.01 ($false),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2636, 187, 2312, 2240, 2239, 1605, 2630, 2629, 2628, 1604, 1603, 1176])).
% 1.09/1.01 tff(2638,plain,((~hskp24) | (~c1_1(a137)) | (~c2_1(a137)) | (~c3_1(a137)) | (~c2_1(a144)) | c0_1(a144) | c3_1(a144)), inference(lemma,lemma(discharge,[]))).
% 1.09/1.01 tff(2639,plain,
% 1.09/1.01 ((~hskp24) | (~c2_1(a144)) | c0_1(a144) | c3_1(a144)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2638, 2612, 2611, 2610])).
% 1.09/1.01 tff(2640,plain,
% 1.09/1.01 (~hskp24),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2639, 2618, 2619, 2617])).
% 1.09/1.01 tff(2641,plain,
% 1.09/1.01 (^[U: $i] : refl((hskp24 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp24 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 1.09/1.01 inference(bind,[status(th)],[])).
% 1.09/1.01 tff(2642,plain,
% 1.09/1.01 (![U: $i] : (hskp24 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.09/1.01 inference(quant_intro,[status(thm)],[2641])).
% 1.09/1.01 tff(2643,plain,
% 1.09/1.01 (![U: $i] : (hskp24 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.09/1.01 inference(rewrite,[status(thm)],[])).
% 1.09/1.02 tff(2644,plain,
% 1.09/1.02 (^[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)) | hskp5) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp5))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp24) <=> ((hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp24))), rewrite(((hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp24) <=> (hskp24 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp24) <=> (hskp24 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 1.09/1.02 inference(bind,[status(th)],[])).
% 1.09/1.02 tff(2645,plain,
% 1.09/1.02 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp24) <=> ![U: $i] : (hskp24 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.09/1.02 inference(quant_intro,[status(thm)],[2644])).
% 1.09/1.02 tff(2646,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause152')).
% 1.09/1.02 tff(2647,plain,
% 1.09/1.02 (![U: $i] : (hskp24 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2646, 2645])).
% 1.09/1.02 tff(2648,plain,
% 1.09/1.02 (![U: $i] : (hskp24 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2647, 2643])).
% 1.09/1.02 tff(2649,plain,(
% 1.09/1.02 ![U: $i] : (hskp24 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.09/1.02 inference(skolemize,[status(sab)],[2648])).
% 1.09/1.02 tff(2650,plain,
% 1.09/1.02 (![U: $i] : (hskp24 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2649, 2642])).
% 1.09/1.02 tff(2651,plain,
% 1.09/1.02 (((~![U: $i] : (hskp24 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp5 | c2_1(a149) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)))) <=> ((~![U: $i] : (hskp24 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp24 | hskp5 | c2_1(a149) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)))),
% 1.09/1.02 inference(rewrite,[status(thm)],[])).
% 1.09/1.02 tff(2652,plain,
% 1.09/1.02 ((hskp24 | hskp5 | (~ndr1_0) | c2_1(a149) | (~c3_1(a149)) | (~c0_1(a149))) <=> (hskp24 | hskp5 | c2_1(a149) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)))),
% 1.09/1.02 inference(rewrite,[status(thm)],[])).
% 1.09/1.02 tff(2653,plain,
% 1.09/1.02 (((~![U: $i] : (hskp24 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp5 | (~ndr1_0) | c2_1(a149) | (~c3_1(a149)) | (~c0_1(a149)))) <=> ((~![U: $i] : (hskp24 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp5 | c2_1(a149) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149))))),
% 1.09/1.02 inference(monotonicity,[status(thm)],[2652])).
% 1.09/1.02 tff(2654,plain,
% 1.09/1.02 (((~![U: $i] : (hskp24 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp5 | (~ndr1_0) | c2_1(a149) | (~c3_1(a149)) | (~c0_1(a149)))) <=> ((~![U: $i] : (hskp24 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp24 | hskp5 | c2_1(a149) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)))),
% 1.09/1.02 inference(transitivity,[status(thm)],[2653, 2651])).
% 1.09/1.02 tff(2655,plain,
% 1.09/1.02 ((~![U: $i] : (hskp24 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp5 | (~ndr1_0) | c2_1(a149) | (~c3_1(a149)) | (~c0_1(a149)))),
% 1.09/1.02 inference(quant_inst,[status(thm)],[])).
% 1.09/1.02 tff(2656,plain,
% 1.09/1.02 ((~![U: $i] : (hskp24 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp24 | hskp5 | c2_1(a149) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149))),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2655, 2654])).
% 1.09/1.02 tff(2657,plain,
% 1.09/1.02 (hskp24 | hskp5 | (~c0_1(a149))),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[2656, 187, 2602, 2371, 2650])).
% 1.09/1.02 tff(2658,plain,
% 1.09/1.02 (hskp5),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[2657, 2640, 2621])).
% 1.09/1.02 tff(2659,plain,
% 1.09/1.02 (~c2_1(a131)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[2213, 2658])).
% 1.09/1.02 tff(2660,plain,
% 1.09/1.02 (hskp17 | (~c0_1(a149))),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[2006, 187, 1941, 2602, 1930, 1924, 2371, 290])).
% 1.09/1.02 tff(2661,plain,
% 1.09/1.02 (hskp17),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[2660, 2621])).
% 1.09/1.02 tff(2662,plain,
% 1.09/1.02 (~c3_1(a158)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[441, 2661])).
% 1.09/1.02 tff(2663,plain,
% 1.09/1.02 (~c2_1(a158)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[447, 2661])).
% 1.09/1.02 tff(2664,plain,
% 1.09/1.02 ((~c2_1(a144)) | c0_1(a144) | c3_1(a144) | c1_1(a128)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[1617, 2609, 2124, 2123])).
% 1.09/1.02 tff(2665,plain,
% 1.09/1.02 (c1_1(a128)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[2664, 2618, 2617, 2619])).
% 1.09/1.02 tff(2666,plain,
% 1.09/1.02 (c1_1(a136)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[2605, 2658, 2665])).
% 1.09/1.02 tff(2667,plain,
% 1.09/1.02 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp22 | c2_1(a149) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)) | (~c3_1(a149)) | (~c0_1(a149)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp22 | c2_1(a149) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)) | (~c3_1(a149)) | (~c0_1(a149)))),
% 1.09/1.02 inference(rewrite,[status(thm)],[])).
% 1.09/1.02 tff(2668,plain,
% 1.09/1.02 ((hskp22 | (~ndr1_0) | (~c2_1(a136)) | (~c1_1(a136)) | (~c0_1(a136)) | c2_1(a149) | (~c3_1(a149)) | (~c0_1(a149))) <=> (hskp22 | c2_1(a149) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)) | (~c3_1(a149)) | (~c0_1(a149)))),
% 1.09/1.02 inference(rewrite,[status(thm)],[])).
% 1.09/1.02 tff(2669,plain,
% 1.09/1.02 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | (~c2_1(a136)) | (~c1_1(a136)) | (~c0_1(a136)) | c2_1(a149) | (~c3_1(a149)) | (~c0_1(a149)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp22 | c2_1(a149) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)) | (~c3_1(a149)) | (~c0_1(a149))))),
% 1.09/1.02 inference(monotonicity,[status(thm)],[2668])).
% 1.09/1.02 tff(2670,plain,
% 1.09/1.02 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | (~c2_1(a136)) | (~c1_1(a136)) | (~c0_1(a136)) | c2_1(a149) | (~c3_1(a149)) | (~c0_1(a149)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp22 | c2_1(a149) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)) | (~c3_1(a149)) | (~c0_1(a149)))),
% 1.09/1.02 inference(transitivity,[status(thm)],[2669, 2667])).
% 1.09/1.02 tff(2671,plain,
% 1.09/1.02 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | (~c2_1(a136)) | (~c1_1(a136)) | (~c0_1(a136)) | c2_1(a149) | (~c3_1(a149)) | (~c0_1(a149)))),
% 1.09/1.02 inference(quant_inst,[status(thm)],[])).
% 1.09/1.02 tff(2672,plain,
% 1.09/1.02 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp22 | c2_1(a149) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)) | (~c3_1(a149)) | (~c0_1(a149))),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2671, 2670])).
% 1.09/1.02 tff(2673,plain,
% 1.09/1.02 (hskp22 | (~c1_1(a136)) | (~c0_1(a149))),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[2672, 187, 2602, 2597, 2596, 2371, 1042])).
% 1.09/1.02 tff(2674,plain,
% 1.09/1.02 (hskp22),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[2673, 2666, 2621])).
% 1.09/1.02 tff(2675,plain,
% 1.09/1.02 (~c1_1(a179)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[1055, 2674])).
% 1.09/1.02 tff(2676,plain,
% 1.09/1.02 (c3_1(a131)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[2226, 2658])).
% 1.09/1.02 tff(2677,plain,
% 1.09/1.02 (c1_1(a131)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[2237, 2658])).
% 1.09/1.02 tff(2678,plain,
% 1.09/1.02 (c1_1(a158)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[458, 2661])).
% 1.09/1.02 tff(2679,plain,
% 1.09/1.02 (c2_1(a179)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[1066, 2674])).
% 1.09/1.02 tff(2680,plain,
% 1.09/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c1_1(a179) | c2_1(a158) | c3_1(a158) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131)) | (~c1_1(a158)) | c3_1(a179) | (~c2_1(a179)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a179) | c2_1(a158) | c3_1(a158) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131)) | (~c1_1(a158)) | c3_1(a179) | (~c2_1(a179)))),
% 1.09/1.02 inference(rewrite,[status(thm)],[])).
% 1.09/1.02 tff(2681,plain,
% 1.09/1.02 (((~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131)) | c3_1(a158) | c2_1(a158) | (~c1_1(a158)) | c1_1(a179) | c3_1(a179) | (~c2_1(a179))) <=> (c1_1(a179) | c2_1(a158) | c3_1(a158) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131)) | (~c1_1(a158)) | c3_1(a179) | (~c2_1(a179)))),
% 1.09/1.02 inference(rewrite,[status(thm)],[])).
% 1.09/1.02 tff(2682,plain,
% 1.09/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131)) | c3_1(a158) | c2_1(a158) | (~c1_1(a158)) | c1_1(a179) | c3_1(a179) | (~c2_1(a179)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c1_1(a179) | c2_1(a158) | c3_1(a158) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131)) | (~c1_1(a158)) | c3_1(a179) | (~c2_1(a179))))),
% 1.09/1.02 inference(monotonicity,[status(thm)],[2681])).
% 1.09/1.02 tff(2683,plain,
% 1.09/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131)) | c3_1(a158) | c2_1(a158) | (~c1_1(a158)) | c1_1(a179) | c3_1(a179) | (~c2_1(a179)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a179) | c2_1(a158) | c3_1(a158) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131)) | (~c1_1(a158)) | c3_1(a179) | (~c2_1(a179)))),
% 1.09/1.02 inference(transitivity,[status(thm)],[2682, 2680])).
% 1.09/1.02 tff(2684,plain,
% 1.09/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131)) | c3_1(a158) | c2_1(a158) | (~c1_1(a158)) | c1_1(a179) | c3_1(a179) | (~c2_1(a179)))),
% 1.09/1.02 inference(quant_inst,[status(thm)],[])).
% 1.09/1.02 tff(2685,plain,
% 1.09/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a179) | c2_1(a158) | c3_1(a158) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131)) | (~c1_1(a158)) | c3_1(a179) | (~c2_1(a179))),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2684, 2683])).
% 1.09/1.02 tff(2686,plain,
% 1.09/1.02 (c3_1(a179)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[2685, 187, 2679, 2678, 2677, 2676, 2675, 2663, 2662, 2659, 10])).
% 1.09/1.02 tff(2687,plain,
% 1.09/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a170) | c2_1(a170) | c1_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)) | c1_1(a170))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a170) | c2_1(a170) | c1_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)) | c1_1(a170))),
% 1.09/1.02 inference(rewrite,[status(thm)],[])).
% 1.09/1.02 tff(2688,plain,
% 1.09/1.02 (((~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a170) | c1_1(a170) | c0_1(a170)) <=> (c0_1(a170) | c2_1(a170) | c1_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)) | c1_1(a170))),
% 1.09/1.02 inference(rewrite,[status(thm)],[])).
% 1.09/1.02 tff(2689,plain,
% 1.09/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a170) | c1_1(a170) | c0_1(a170))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a170) | c2_1(a170) | c1_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)) | c1_1(a170)))),
% 1.09/1.02 inference(monotonicity,[status(thm)],[2688])).
% 1.09/1.02 tff(2690,plain,
% 1.09/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a170) | c1_1(a170) | c0_1(a170))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a170) | c2_1(a170) | c1_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)) | c1_1(a170))),
% 1.09/1.02 inference(transitivity,[status(thm)],[2689, 2687])).
% 1.09/1.02 tff(2691,plain,
% 1.09/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a170) | c1_1(a170) | c0_1(a170))),
% 1.09/1.02 inference(quant_inst,[status(thm)],[])).
% 1.09/1.02 tff(2692,plain,
% 1.09/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a170) | c2_1(a170) | c1_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)) | c1_1(a170)),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2691, 2690])).
% 1.09/1.02 tff(2693,plain,
% 1.09/1.02 ((~c0_1(a149)) | c1_1(a170)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[2692, 187, 2602, 2592, 2591, 2370, 2125, 2124, 2123, 279])).
% 1.09/1.02 tff(2694,plain,
% 1.09/1.02 (c1_1(a170)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[2693, 2621])).
% 1.09/1.02 tff(2695,plain,
% 1.09/1.02 (hskp6 | (~c1_1(a128)) | (~c1_1(a170))),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[353, 187, 2593, 2592, 2125, 2123, 336])).
% 1.09/1.02 tff(2696,plain,
% 1.09/1.02 (hskp6),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[2695, 2665, 2694])).
% 1.09/1.02 tff(2697,plain,
% 1.09/1.02 (~c2_1(a133)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[360, 2696])).
% 1.09/1.02 tff(2698,plain,
% 1.09/1.02 (~c1_1(a133)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[366, 2696])).
% 1.09/1.02 tff(2699,plain,
% 1.09/1.02 (~c0_1(a133)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[372, 2696])).
% 1.09/1.02 tff(2700,plain,
% 1.09/1.02 (c0_1(a179)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[1077, 2674])).
% 1.09/1.02 tff(2701,plain,
% 1.09/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a179) | c0_1(a133) | c1_1(a133) | c2_1(a133) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a179)) | (~c0_1(a179)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a179) | c0_1(a133) | c1_1(a133) | c2_1(a133) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a179)) | (~c0_1(a179)))),
% 1.09/1.02 inference(rewrite,[status(thm)],[])).
% 1.09/1.02 tff(2702,plain,
% 1.09/1.02 (((~ndr1_0) | c1_1(a179) | (~c3_1(a179)) | (~c0_1(a179)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a133) | c1_1(a133) | c0_1(a133)) <=> (c1_1(a179) | c0_1(a133) | c1_1(a133) | c2_1(a133) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a179)) | (~c0_1(a179)))),
% 1.09/1.03 inference(rewrite,[status(thm)],[])).
% 1.09/1.03 tff(2703,plain,
% 1.09/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a179) | (~c3_1(a179)) | (~c0_1(a179)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a133) | c1_1(a133) | c0_1(a133))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a179) | c0_1(a133) | c1_1(a133) | c2_1(a133) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a179)) | (~c0_1(a179))))),
% 1.09/1.03 inference(monotonicity,[status(thm)],[2702])).
% 1.09/1.03 tff(2704,plain,
% 1.09/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a179) | (~c3_1(a179)) | (~c0_1(a179)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a133) | c1_1(a133) | c0_1(a133))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a179) | c0_1(a133) | c1_1(a133) | c2_1(a133) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a179)) | (~c0_1(a179)))),
% 1.09/1.03 inference(transitivity,[status(thm)],[2703, 2701])).
% 1.09/1.03 tff(2705,plain,
% 1.09/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a179) | (~c3_1(a179)) | (~c0_1(a179)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a133) | c1_1(a133) | c0_1(a133))),
% 1.09/1.03 inference(quant_inst,[status(thm)],[])).
% 1.09/1.03 tff(2706,plain,
% 1.09/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a179) | c0_1(a133) | c1_1(a133) | c2_1(a133) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a179)) | (~c0_1(a179))),
% 1.09/1.03 inference(modus_ponens,[status(thm)],[2705, 2704])).
% 1.09/1.03 tff(2707,plain,
% 1.09/1.03 ($false),
% 1.09/1.03 inference(unit_resolution,[status(thm)],[2706, 187, 2700, 2675, 2699, 2698, 2697, 2125, 2124, 2123, 279, 2686])).
% 1.09/1.03 % SZS output end Proof
%------------------------------------------------------------------------------