TSTP Solution File: SYN455-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN455-1 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 23:55:32 EDT 2022
% Result : Unsatisfiable 1.88s 1.44s
% Output : Proof 2.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN455-1 : TPTP v8.1.0. Released v2.1.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n019.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Sep 5 03:55:50 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 1.88/1.44 % SZS status Unsatisfiable
% 1.88/1.44 % SZS output start Proof
% 1.88/1.44 tff(c1_1_type, type, (
% 1.88/1.44 c1_1: $i > $o)).
% 1.88/1.44 tff(c2_1_type, type, (
% 1.88/1.44 c2_1: $i > $o)).
% 1.88/1.44 tff(c3_1_type, type, (
% 1.88/1.44 c3_1: $i > $o)).
% 1.88/1.44 tff(ndr1_0_type, type, (
% 1.88/1.44 ndr1_0: $o)).
% 1.88/1.44 tff(a908_type, type, (
% 1.88/1.44 a908: $i)).
% 1.88/1.44 tff(hskp7_type, type, (
% 1.88/1.44 hskp7: $o)).
% 1.88/1.44 tff(a924_type, type, (
% 1.88/1.44 a924: $i)).
% 1.88/1.44 tff(c0_1_type, type, (
% 1.88/1.44 c0_1: $i > $o)).
% 1.88/1.44 tff(hskp13_type, type, (
% 1.88/1.44 hskp13: $o)).
% 1.88/1.44 tff(hskp15_type, type, (
% 1.88/1.44 hskp15: $o)).
% 1.88/1.44 tff(a900_type, type, (
% 1.88/1.44 a900: $i)).
% 1.88/1.44 tff(hskp27_type, type, (
% 1.88/1.44 hskp27: $o)).
% 1.88/1.44 tff(hskp10_type, type, (
% 1.88/1.44 hskp10: $o)).
% 1.88/1.44 tff(a912_type, type, (
% 1.88/1.44 a912: $i)).
% 1.88/1.44 tff(a906_type, type, (
% 1.88/1.44 a906: $i)).
% 1.88/1.44 tff(a946_type, type, (
% 1.88/1.44 a946: $i)).
% 1.88/1.44 tff(a917_type, type, (
% 1.88/1.44 a917: $i)).
% 1.88/1.44 tff(hskp12_type, type, (
% 1.88/1.44 hskp12: $o)).
% 1.88/1.44 tff(hskp5_type, type, (
% 1.88/1.44 hskp5: $o)).
% 1.88/1.44 tff(a902_type, type, (
% 1.88/1.44 a902: $i)).
% 1.88/1.44 tff(hskp1_type, type, (
% 1.88/1.44 hskp1: $o)).
% 1.88/1.44 tff(a914_type, type, (
% 1.88/1.44 a914: $i)).
% 1.88/1.44 tff(a916_type, type, (
% 1.88/1.44 a916: $i)).
% 1.88/1.44 tff(hskp28_type, type, (
% 1.88/1.44 hskp28: $o)).
% 1.88/1.44 tff(hskp11_type, type, (
% 1.88/1.44 hskp11: $o)).
% 1.88/1.44 tff(hskp26_type, type, (
% 1.88/1.44 hskp26: $o)).
% 1.88/1.44 tff(hskp21_type, type, (
% 1.88/1.44 hskp21: $o)).
% 1.88/1.44 tff(a907_type, type, (
% 1.88/1.44 a907: $i)).
% 1.88/1.44 tff(hskp6_type, type, (
% 1.88/1.44 hskp6: $o)).
% 1.88/1.44 tff(a921_type, type, (
% 1.88/1.44 a921: $i)).
% 1.88/1.44 tff(a903_type, type, (
% 1.88/1.44 a903: $i)).
% 1.88/1.44 tff(hskp2_type, type, (
% 1.88/1.44 hskp2: $o)).
% 1.88/1.44 tff(a936_type, type, (
% 1.88/1.44 a936: $i)).
% 1.88/1.44 tff(hskp17_type, type, (
% 1.88/1.44 hskp17: $o)).
% 1.88/1.44 tff(hskp14_type, type, (
% 1.88/1.44 hskp14: $o)).
% 1.88/1.44 tff(a923_type, type, (
% 1.88/1.44 a923: $i)).
% 1.88/1.44 tff(a901_type, type, (
% 1.88/1.44 a901: $i)).
% 1.88/1.44 tff(hskp0_type, type, (
% 1.88/1.44 hskp0: $o)).
% 1.88/1.44 tff(a910_type, type, (
% 1.88/1.44 a910: $i)).
% 1.88/1.44 tff(hskp9_type, type, (
% 1.88/1.44 hskp9: $o)).
% 1.88/1.44 tff(a942_type, type, (
% 1.88/1.44 a942: $i)).
% 1.88/1.44 tff(hskp30_type, type, (
% 1.88/1.44 hskp30: $o)).
% 1.88/1.44 tff(a937_type, type, (
% 1.88/1.44 a937: $i)).
% 1.88/1.44 tff(hskp18_type, type, (
% 1.88/1.44 hskp18: $o)).
% 1.88/1.44 tff(a939_type, type, (
% 1.88/1.44 a939: $i)).
% 1.88/1.44 tff(hskp20_type, type, (
% 1.88/1.44 hskp20: $o)).
% 1.88/1.44 tff(a960_type, type, (
% 1.88/1.44 a960: $i)).
% 1.88/1.44 tff(hskp25_type, type, (
% 1.88/1.44 hskp25: $o)).
% 1.88/1.44 tff(a979_type, type, (
% 1.88/1.44 a979: $i)).
% 1.88/1.44 tff(a926_type, type, (
% 1.88/1.44 a926: $i)).
% 1.88/1.44 tff(hskp16_type, type, (
% 1.88/1.44 hskp16: $o)).
% 1.88/1.44 tff(hskp4_type, type, (
% 1.88/1.44 hskp4: $o)).
% 1.88/1.44 tff(a905_type, type, (
% 1.88/1.44 a905: $i)).
% 1.88/1.44 tff(a954_type, type, (
% 1.88/1.44 a954: $i)).
% 1.88/1.44 tff(hskp23_type, type, (
% 1.88/1.44 hskp23: $o)).
% 1.88/1.44 tff(a909_type, type, (
% 1.88/1.44 a909: $i)).
% 1.88/1.44 tff(hskp8_type, type, (
% 1.88/1.44 hskp8: $o)).
% 1.88/1.44 tff(1,plain,
% 1.88/1.44 (^[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))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))))),
% 1.88/1.44 inference(bind,[status(th)],[])).
% 1.88/1.44 tff(2,plain,
% 1.88/1.44 (![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.88/1.44 inference(quant_intro,[status(thm)],[1])).
% 1.88/1.44 tff(3,plain,
% 1.88/1.44 (![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.88/1.44 inference(rewrite,[status(thm)],[])).
% 1.88/1.44 tff(4,plain,
% 1.88/1.44 (^[V: $i, U: $i] : 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(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | 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))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_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)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | 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)))))),
% 1.88/1.44 inference(bind,[status(th)],[])).
% 1.88/1.44 tff(5,plain,
% 1.88/1.44 (![V: $i, U: $i] : (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.88/1.44 inference(quant_intro,[status(thm)],[4])).
% 1.88/1.44 tff(6,axiom,(![V: $i, U: $i] : (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause163')).
% 1.88/1.44 tff(7,plain,
% 1.88/1.44 (![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.88/1.44 inference(modus_ponens,[status(thm)],[6, 5])).
% 1.88/1.44 tff(8,plain,
% 1.88/1.44 (![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.88/1.44 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.88/1.44 tff(9,plain,(
% 1.88/1.44 ![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.88/1.44 inference(skolemize,[status(sab)],[8])).
% 1.88/1.44 tff(10,plain,
% 1.88/1.44 (![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.88/1.44 inference(modus_ponens,[status(thm)],[9, 2])).
% 1.88/1.44 tff(11,plain,
% 1.88/1.44 (^[U: $i] : refl((hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))),
% 1.88/1.44 inference(bind,[status(th)],[])).
% 1.88/1.44 tff(12,plain,
% 1.88/1.44 (![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.88/1.44 inference(quant_intro,[status(thm)],[11])).
% 1.88/1.44 tff(13,plain,
% 1.88/1.44 (![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.88/1.44 inference(rewrite,[status(thm)],[])).
% 1.88/1.44 tff(14,plain,
% 1.88/1.44 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp7) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp7))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp7) <=> (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp7) | hskp13) <=> ((hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp13))), rewrite(((hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp13) <=> (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp7) | hskp13) <=> (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))))),
% 1.88/1.44 inference(bind,[status(th)],[])).
% 1.88/1.44 tff(15,plain,
% 1.88/1.44 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp7) | hskp13) <=> ![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.88/1.44 inference(quant_intro,[status(thm)],[14])).
% 1.88/1.44 tff(16,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp7) | hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause148')).
% 1.88/1.44 tff(17,plain,
% 1.88/1.44 (![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.88/1.44 inference(modus_ponens,[status(thm)],[16, 15])).
% 1.88/1.44 tff(18,plain,
% 1.88/1.44 (![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.88/1.44 inference(modus_ponens,[status(thm)],[17, 13])).
% 1.88/1.44 tff(19,plain,(
% 1.88/1.44 ![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.88/1.44 inference(skolemize,[status(sab)],[18])).
% 1.88/1.44 tff(20,plain,
% 1.88/1.44 (![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.88/1.44 inference(modus_ponens,[status(thm)],[19, 12])).
% 1.88/1.44 tff(21,assumption,(~hskp7), introduced(assumption)).
% 1.88/1.44 tff(22,plain,
% 1.88/1.44 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W))))),
% 1.88/1.44 inference(bind,[status(th)],[])).
% 1.88/1.44 tff(23,plain,
% 1.88/1.44 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.88/1.44 inference(quant_intro,[status(thm)],[22])).
% 1.88/1.44 tff(24,plain,
% 1.88/1.44 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.88/1.44 inference(rewrite,[status(thm)],[])).
% 1.88/1.44 tff(25,plain,
% 1.88/1.44 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) | c2_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))))),
% 1.88/1.44 inference(bind,[status(th)],[])).
% 1.88/1.44 tff(26,plain,
% 1.88/1.44 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.88/1.44 inference(quant_intro,[status(thm)],[25])).
% 1.88/1.44 tff(27,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c3_1(V)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause184')).
% 1.88/1.44 tff(28,plain,
% 1.88/1.44 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.88/1.44 inference(modus_ponens,[status(thm)],[27, 26])).
% 1.88/1.44 tff(29,plain,
% 1.88/1.44 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.88/1.44 inference(modus_ponens,[status(thm)],[28, 24])).
% 1.88/1.44 tff(30,plain,(
% 1.88/1.44 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.88/1.44 inference(skolemize,[status(sab)],[29])).
% 1.88/1.44 tff(31,plain,
% 1.88/1.44 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.88/1.44 inference(modus_ponens,[status(thm)],[30, 23])).
% 1.88/1.44 tff(32,assumption,(~hskp12), introduced(assumption)).
% 1.88/1.44 tff(33,plain,
% 1.88/1.44 (^[V: $i, U: $i] : refl((hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 1.88/1.44 inference(bind,[status(th)],[])).
% 1.88/1.44 tff(34,plain,
% 1.88/1.44 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.88/1.44 inference(quant_intro,[status(thm)],[33])).
% 1.88/1.44 tff(35,plain,
% 1.88/1.44 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.88/1.44 inference(rewrite,[status(thm)],[])).
% 1.88/1.44 tff(36,plain,
% 1.88/1.44 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_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)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_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)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp27) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp27))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 1.88/1.44 inference(bind,[status(th)],[])).
% 1.88/1.44 tff(37,plain,
% 1.88/1.44 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp27) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.88/1.44 inference(quant_intro,[status(thm)],[36])).
% 1.88/1.44 tff(38,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause166')).
% 1.88/1.45 tff(39,plain,
% 1.88/1.45 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[38, 37])).
% 1.88/1.45 tff(40,plain,
% 1.88/1.45 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[39, 35])).
% 1.88/1.45 tff(41,plain,(
% 1.88/1.45 ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.88/1.45 inference(skolemize,[status(sab)],[40])).
% 1.88/1.45 tff(42,plain,
% 1.88/1.45 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[41, 34])).
% 1.88/1.45 tff(43,assumption,(~hskp5), introduced(assumption)).
% 1.88/1.45 tff(44,plain,
% 1.88/1.45 (^[U: $i] : refl((hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))),
% 1.88/1.45 inference(bind,[status(th)],[])).
% 1.88/1.45 tff(45,plain,
% 1.88/1.45 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.88/1.45 inference(quant_intro,[status(thm)],[44])).
% 1.88/1.45 tff(46,plain,
% 1.88/1.45 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(47,plain,
% 1.88/1.45 (^[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)) | hskp11) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp11))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp11) <=> (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp11) <=> (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp11) | hskp12) <=> ((hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp12))), rewrite(((hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp12) <=> (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp11) | hskp12) <=> (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))))),
% 1.88/1.45 inference(bind,[status(th)],[])).
% 1.88/1.45 tff(48,plain,
% 1.88/1.45 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp11) | hskp12) <=> ![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.88/1.45 inference(quant_intro,[status(thm)],[47])).
% 1.88/1.45 tff(49,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp11) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause158')).
% 1.88/1.45 tff(50,plain,
% 1.88/1.45 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[49, 48])).
% 1.88/1.45 tff(51,plain,
% 1.88/1.45 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[50, 46])).
% 1.88/1.45 tff(52,plain,(
% 1.88/1.45 ![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.88/1.45 inference(skolemize,[status(sab)],[51])).
% 1.88/1.45 tff(53,plain,
% 1.88/1.45 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[52, 45])).
% 1.88/1.45 tff(54,plain,
% 1.88/1.45 (^[U: $i] : refl((hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 1.88/1.45 inference(bind,[status(th)],[])).
% 1.88/1.45 tff(55,plain,
% 1.88/1.45 (![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.88/1.45 inference(quant_intro,[status(thm)],[54])).
% 1.88/1.45 tff(56,plain,
% 1.88/1.45 (![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(57,plain,
% 1.88/1.45 (^[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) | hskp7) <=> ((hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp7))), rewrite(((hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp7) <=> (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp7) <=> (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 1.88/1.45 inference(bind,[status(th)],[])).
% 1.88/1.45 tff(58,plain,
% 1.88/1.45 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp7) <=> ![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.88/1.45 inference(quant_intro,[status(thm)],[57])).
% 1.88/1.45 tff(59,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause151')).
% 1.88/1.45 tff(60,plain,
% 1.88/1.45 (![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[59, 58])).
% 1.88/1.45 tff(61,plain,
% 1.88/1.45 (![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[60, 56])).
% 1.88/1.45 tff(62,plain,(
% 1.88/1.45 ![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.88/1.45 inference(skolemize,[status(sab)],[61])).
% 1.88/1.45 tff(63,plain,
% 1.88/1.45 (![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[62, 55])).
% 1.88/1.45 tff(64,assumption,(hskp11), introduced(assumption)).
% 1.88/1.45 tff(65,plain,
% 1.88/1.45 (((~hskp11) | (~c2_1(a914))) <=> ((~hskp11) | (~c2_1(a914)))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(66,plain,
% 1.88/1.45 (((~c2_1(a914)) | (~hskp11)) <=> ((~hskp11) | (~c2_1(a914)))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(67,axiom,((~c2_1(a914)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause108')).
% 1.88/1.45 tff(68,plain,
% 1.88/1.45 ((~hskp11) | (~c2_1(a914))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[67, 66])).
% 1.88/1.45 tff(69,plain,
% 1.88/1.45 ((~hskp11) | (~c2_1(a914))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[68, 65])).
% 1.88/1.45 tff(70,plain,
% 1.88/1.45 (~c2_1(a914)),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[69, 64])).
% 1.88/1.45 tff(71,plain,
% 1.88/1.45 (((~hskp11) | c3_1(a914)) <=> ((~hskp11) | c3_1(a914))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(72,axiom,((~hskp11) | c3_1(a914)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause67')).
% 1.88/1.45 tff(73,plain,
% 1.88/1.45 ((~hskp11) | c3_1(a914)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[72, 71])).
% 1.88/1.45 tff(74,plain,
% 1.88/1.45 ((~hskp11) | c3_1(a914)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[73, 71])).
% 1.88/1.45 tff(75,plain,
% 1.88/1.45 ((~hskp11) | c3_1(a914)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[74, 71])).
% 1.88/1.45 tff(76,plain,
% 1.88/1.45 ((~hskp11) | c3_1(a914)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[75, 71])).
% 1.88/1.45 tff(77,plain,
% 1.88/1.45 ((~hskp11) | c3_1(a914)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[76, 71])).
% 1.88/1.45 tff(78,plain,
% 1.88/1.45 ((~hskp11) | c3_1(a914)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[77, 71])).
% 1.88/1.45 tff(79,plain,
% 1.88/1.45 ((~hskp11) | c3_1(a914)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[78, 71])).
% 1.88/1.45 tff(80,plain,
% 1.88/1.45 ((~hskp11) | c3_1(a914)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[79, 71])).
% 1.88/1.45 tff(81,plain,
% 1.88/1.45 (c3_1(a914)),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[80, 64])).
% 1.88/1.45 tff(82,plain,
% 1.88/1.45 (((~hskp11) | c0_1(a914)) <=> ((~hskp11) | c0_1(a914))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(83,axiom,((~hskp11) | c0_1(a914)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause66')).
% 1.88/1.45 tff(84,plain,
% 1.88/1.45 ((~hskp11) | c0_1(a914)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[83, 82])).
% 1.88/1.45 tff(85,plain,
% 1.88/1.45 ((~hskp11) | c0_1(a914)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[84, 82])).
% 1.88/1.45 tff(86,plain,
% 1.88/1.45 ((~hskp11) | c0_1(a914)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[85, 82])).
% 1.88/1.45 tff(87,plain,
% 1.88/1.45 ((~hskp11) | c0_1(a914)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[86, 82])).
% 1.88/1.45 tff(88,plain,
% 1.88/1.45 ((~hskp11) | c0_1(a914)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[87, 82])).
% 1.88/1.45 tff(89,plain,
% 1.88/1.45 ((~hskp11) | c0_1(a914)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[88, 82])).
% 1.88/1.45 tff(90,plain,
% 1.88/1.45 ((~hskp11) | c0_1(a914)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[89, 82])).
% 1.88/1.45 tff(91,plain,
% 1.88/1.45 ((~hskp11) | c0_1(a914)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[90, 82])).
% 1.88/1.45 tff(92,plain,
% 1.88/1.45 (c0_1(a914)),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[91, 64])).
% 1.88/1.45 tff(93,assumption,(~ndr1_0), introduced(assumption)).
% 1.88/1.45 tff(94,plain,
% 1.88/1.45 ((ndr1_0 | (~hskp5)) <=> (ndr1_0 | (~hskp5))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(95,plain,
% 1.88/1.45 (((~hskp5) | ndr1_0) <=> (ndr1_0 | (~hskp5))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(96,axiom,((~hskp5) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause26')).
% 1.88/1.45 tff(97,plain,
% 1.88/1.45 (ndr1_0 | (~hskp5)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[96, 95])).
% 1.88/1.45 tff(98,plain,
% 1.88/1.45 (ndr1_0 | (~hskp5)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[97, 94])).
% 1.88/1.45 tff(99,plain,
% 1.88/1.45 (~hskp5),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[98, 93])).
% 1.88/1.45 tff(100,plain,
% 1.88/1.45 ((ndr1_0 | (~hskp26)) <=> (ndr1_0 | (~hskp26))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(101,plain,
% 1.88/1.45 (((~hskp26) | ndr1_0) <=> (ndr1_0 | (~hskp26))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(102,axiom,((~hskp26) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause5')).
% 1.88/1.45 tff(103,plain,
% 1.88/1.45 (ndr1_0 | (~hskp26)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[102, 101])).
% 1.88/1.45 tff(104,plain,
% 1.88/1.45 (ndr1_0 | (~hskp26)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[103, 100])).
% 1.88/1.45 tff(105,plain,
% 1.88/1.45 (~hskp26),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[104, 93])).
% 1.88/1.45 tff(106,plain,
% 1.88/1.45 ((ndr1_0 | (~hskp21)) <=> (ndr1_0 | (~hskp21))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(107,plain,
% 1.88/1.45 (((~hskp21) | ndr1_0) <=> (ndr1_0 | (~hskp21))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(108,axiom,((~hskp21) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause10')).
% 1.88/1.45 tff(109,plain,
% 1.88/1.45 (ndr1_0 | (~hskp21)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[108, 107])).
% 1.88/1.45 tff(110,plain,
% 1.88/1.45 (ndr1_0 | (~hskp21)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[109, 106])).
% 1.88/1.45 tff(111,plain,
% 1.88/1.45 (~hskp21),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[110, 93])).
% 1.88/1.45 tff(112,plain,
% 1.88/1.45 ((hskp26 | hskp21 | hskp5) <=> (hskp26 | hskp21 | hskp5)),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(113,plain,
% 1.88/1.45 (((hskp26 | hskp5) | hskp21) <=> (hskp26 | hskp21 | hskp5)),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(114,axiom,((hskp26 | hskp5) | hskp21), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause32')).
% 1.88/1.45 tff(115,plain,
% 1.88/1.45 (hskp26 | hskp21 | hskp5),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[114, 113])).
% 1.88/1.45 tff(116,plain,
% 1.88/1.45 (hskp26 | hskp21 | hskp5),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[115, 112])).
% 1.88/1.45 tff(117,plain,
% 1.88/1.45 (hskp26 | hskp21 | hskp5),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[116, 112])).
% 1.88/1.45 tff(118,plain,
% 1.88/1.45 (hskp26 | hskp21 | hskp5),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[117, 112])).
% 1.88/1.45 tff(119,plain,
% 1.88/1.45 (hskp26 | hskp21 | hskp5),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[118, 112])).
% 1.88/1.45 tff(120,plain,
% 1.88/1.45 (hskp26 | hskp21 | hskp5),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[119, 112])).
% 1.88/1.45 tff(121,plain,
% 1.88/1.45 (hskp26 | hskp21 | hskp5),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[120, 112])).
% 1.88/1.45 tff(122,plain,
% 1.88/1.45 (hskp26 | hskp21 | hskp5),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[121, 112])).
% 1.88/1.45 tff(123,plain,
% 1.88/1.45 ($false),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[122, 111, 105, 99])).
% 1.88/1.45 tff(124,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 1.88/1.45 tff(125,plain,
% 1.88/1.45 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp5 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914)))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp7 | hskp5 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914)))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(126,plain,
% 1.88/1.45 ((hskp7 | hskp5 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c0_1(a914))) <=> (hskp7 | hskp5 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914)))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(127,plain,
% 1.88/1.45 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp5 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c0_1(a914)))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp5 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914))))),
% 1.88/1.45 inference(monotonicity,[status(thm)],[126])).
% 1.88/1.45 tff(128,plain,
% 1.88/1.45 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp5 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c0_1(a914)))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp7 | hskp5 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914)))),
% 1.88/1.45 inference(transitivity,[status(thm)],[127, 125])).
% 1.88/1.45 tff(129,plain,
% 1.88/1.45 ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp5 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c0_1(a914)))),
% 1.88/1.45 inference(quant_inst,[status(thm)],[])).
% 1.88/1.45 tff(130,plain,
% 1.88/1.45 ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp7 | hskp5 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[129, 128])).
% 1.88/1.45 tff(131,plain,
% 1.88/1.45 ($false),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[130, 124, 21, 43, 92, 81, 70, 63])).
% 1.88/1.45 tff(132,plain,((~hskp11) | hskp7 | hskp5), inference(lemma,lemma(discharge,[]))).
% 1.88/1.45 tff(133,plain,
% 1.88/1.45 (~hskp11),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[132, 21, 43])).
% 1.88/1.45 tff(134,assumption,(hskp27), introduced(assumption)).
% 1.88/1.45 tff(135,plain,
% 1.88/1.45 (((~hskp27) | c3_1(a900)) <=> ((~hskp27) | c3_1(a900))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(136,axiom,((~hskp27) | c3_1(a900)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause46')).
% 1.88/1.45 tff(137,plain,
% 1.88/1.45 ((~hskp27) | c3_1(a900)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[136, 135])).
% 1.88/1.45 tff(138,plain,
% 1.88/1.45 ((~hskp27) | c3_1(a900)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[137, 135])).
% 1.88/1.45 tff(139,plain,
% 1.88/1.45 ((~hskp27) | c3_1(a900)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[138, 135])).
% 1.88/1.45 tff(140,plain,
% 1.88/1.45 ((~hskp27) | c3_1(a900)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[139, 135])).
% 1.88/1.45 tff(141,plain,
% 1.88/1.45 ((~hskp27) | c3_1(a900)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[140, 135])).
% 1.88/1.45 tff(142,plain,
% 1.88/1.45 ((~hskp27) | c3_1(a900)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[141, 135])).
% 1.88/1.45 tff(143,plain,
% 1.88/1.45 ((~hskp27) | c3_1(a900)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[142, 135])).
% 1.88/1.45 tff(144,plain,
% 1.88/1.45 ((~hskp27) | c3_1(a900)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[143, 135])).
% 1.88/1.45 tff(145,plain,
% 1.88/1.45 (c3_1(a900)),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[144, 134])).
% 1.88/1.45 tff(146,plain,
% 1.88/1.45 (((~hskp27) | c2_1(a900)) <=> ((~hskp27) | c2_1(a900))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(147,axiom,((~hskp27) | c2_1(a900)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause45')).
% 1.88/1.45 tff(148,plain,
% 1.88/1.45 ((~hskp27) | c2_1(a900)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[147, 146])).
% 1.88/1.45 tff(149,plain,
% 1.88/1.45 ((~hskp27) | c2_1(a900)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[148, 146])).
% 1.88/1.45 tff(150,plain,
% 1.88/1.45 ((~hskp27) | c2_1(a900)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[149, 146])).
% 1.88/1.45 tff(151,plain,
% 1.88/1.45 ((~hskp27) | c2_1(a900)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[150, 146])).
% 1.88/1.45 tff(152,plain,
% 1.88/1.45 ((~hskp27) | c2_1(a900)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[151, 146])).
% 1.88/1.45 tff(153,plain,
% 1.88/1.45 ((~hskp27) | c2_1(a900)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[152, 146])).
% 1.88/1.45 tff(154,plain,
% 1.88/1.45 ((~hskp27) | c2_1(a900)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[153, 146])).
% 1.88/1.45 tff(155,plain,
% 1.88/1.45 ((~hskp27) | c2_1(a900)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[154, 146])).
% 1.88/1.45 tff(156,plain,
% 1.88/1.45 (c2_1(a900)),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[155, 134])).
% 1.88/1.45 tff(157,plain,
% 1.88/1.45 (((~hskp27) | c1_1(a900)) <=> ((~hskp27) | c1_1(a900))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(158,axiom,((~hskp27) | c1_1(a900)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause44')).
% 1.88/1.45 tff(159,plain,
% 1.88/1.45 ((~hskp27) | c1_1(a900)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[158, 157])).
% 1.88/1.45 tff(160,plain,
% 1.88/1.45 ((~hskp27) | c1_1(a900)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[159, 157])).
% 1.88/1.45 tff(161,plain,
% 1.88/1.45 ((~hskp27) | c1_1(a900)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[160, 157])).
% 1.88/1.45 tff(162,plain,
% 1.88/1.45 ((~hskp27) | c1_1(a900)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[161, 157])).
% 1.88/1.45 tff(163,plain,
% 1.88/1.45 ((~hskp27) | c1_1(a900)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[162, 157])).
% 1.88/1.45 tff(164,plain,
% 1.88/1.45 ((~hskp27) | c1_1(a900)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[163, 157])).
% 1.88/1.45 tff(165,plain,
% 1.88/1.45 ((~hskp27) | c1_1(a900)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[164, 157])).
% 1.88/1.45 tff(166,plain,
% 1.88/1.45 ((~hskp27) | c1_1(a900)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[165, 157])).
% 1.88/1.45 tff(167,plain,
% 1.88/1.45 (c1_1(a900)),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[166, 134])).
% 1.88/1.45 tff(168,assumption,(~hskp11), introduced(assumption)).
% 1.88/1.45 tff(169,plain,
% 1.88/1.45 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | (~ndr1_0) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900)))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(170,plain,
% 1.88/1.45 ((hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c1_1(a900))) <=> (hskp12 | hskp11 | (~ndr1_0) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900)))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(171,plain,
% 1.88/1.45 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c1_1(a900)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900))))),
% 1.88/1.45 inference(monotonicity,[status(thm)],[170])).
% 1.88/1.45 tff(172,plain,
% 1.88/1.45 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c1_1(a900)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | (~ndr1_0) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900)))),
% 1.88/1.45 inference(transitivity,[status(thm)],[171, 169])).
% 1.88/1.45 tff(173,plain,
% 1.88/1.45 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c1_1(a900)))),
% 1.88/1.45 inference(quant_inst,[status(thm)],[])).
% 1.88/1.45 tff(174,plain,
% 1.88/1.45 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | (~ndr1_0) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[173, 172])).
% 1.88/1.45 tff(175,plain,
% 1.88/1.45 ($false),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[174, 124, 32, 168, 167, 156, 145, 53])).
% 1.88/1.45 tff(176,plain,((~hskp27) | hskp12 | hskp11), inference(lemma,lemma(discharge,[]))).
% 1.88/1.45 tff(177,plain,
% 1.88/1.45 (~hskp27),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[176, 133, 32])).
% 1.88/1.45 tff(178,plain,
% 1.88/1.45 (^[U: $i] : refl((hskp27 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> (hskp27 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))),
% 1.88/1.45 inference(bind,[status(th)],[])).
% 1.88/1.45 tff(179,plain,
% 1.88/1.45 (![U: $i] : (hskp27 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp27 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.88/1.45 inference(quant_intro,[status(thm)],[178])).
% 1.88/1.45 tff(180,plain,
% 1.88/1.45 (![U: $i] : (hskp27 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp27 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(181,plain,
% 1.88/1.45 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp27))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) | hskp10) <=> ((hskp27 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp10))), rewrite(((hskp27 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp10) <=> (hskp27 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) | hskp10) <=> (hskp27 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))))),
% 1.88/1.45 inference(bind,[status(th)],[])).
% 1.88/1.45 tff(182,plain,
% 1.88/1.45 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) | hskp10) <=> ![U: $i] : (hskp27 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.88/1.45 inference(quant_intro,[status(thm)],[181])).
% 1.88/1.45 tff(183,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause129')).
% 1.88/1.45 tff(184,plain,
% 1.88/1.45 (![U: $i] : (hskp27 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[183, 182])).
% 1.88/1.45 tff(185,plain,
% 1.88/1.45 (![U: $i] : (hskp27 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[184, 180])).
% 1.88/1.45 tff(186,plain,(
% 1.88/1.45 ![U: $i] : (hskp27 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.88/1.45 inference(skolemize,[status(sab)],[185])).
% 1.88/1.45 tff(187,plain,
% 1.88/1.45 (![U: $i] : (hskp27 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[186, 179])).
% 1.88/1.45 tff(188,plain,
% 1.88/1.45 (^[V: $i, U: $i] : refl((hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))))),
% 1.88/1.45 inference(bind,[status(th)],[])).
% 1.88/1.45 tff(189,plain,
% 1.88/1.45 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.88/1.45 inference(quant_intro,[status(thm)],[188])).
% 1.88/1.45 tff(190,plain,
% 1.88/1.45 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(191,plain,
% 1.88/1.45 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp21) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) | hskp21))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) | hskp21) <=> (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp21) <=> (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))))),
% 1.88/1.45 inference(bind,[status(th)],[])).
% 1.88/1.45 tff(192,plain,
% 1.88/1.45 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp21) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.88/1.45 inference(quant_intro,[status(thm)],[191])).
% 1.88/1.45 tff(193,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause167')).
% 1.88/1.45 tff(194,plain,
% 1.88/1.45 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[193, 192])).
% 1.88/1.45 tff(195,plain,
% 1.88/1.45 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[194, 190])).
% 1.88/1.45 tff(196,plain,(
% 1.88/1.45 ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.88/1.45 inference(skolemize,[status(sab)],[195])).
% 1.88/1.45 tff(197,plain,
% 1.88/1.45 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[196, 189])).
% 1.88/1.45 tff(198,assumption,(~hskp21), introduced(assumption)).
% 1.88/1.45 tff(199,plain,
% 1.88/1.45 (^[U: $i] : refl((hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))),
% 1.88/1.45 inference(bind,[status(th)],[])).
% 1.88/1.45 tff(200,plain,
% 1.88/1.45 (![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.88/1.45 inference(quant_intro,[status(thm)],[199])).
% 1.88/1.45 tff(201,plain,
% 1.88/1.45 (![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(202,plain,
% 1.88/1.45 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp28) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp28))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp28) | hskp12) <=> ((hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp12))), rewrite(((hskp28 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp12) <=> (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp28) | hskp12) <=> (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))))),
% 1.88/1.45 inference(bind,[status(th)],[])).
% 1.88/1.45 tff(203,plain,
% 1.88/1.45 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp28) | hskp12) <=> ![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.88/1.45 inference(quant_intro,[status(thm)],[202])).
% 1.88/1.45 tff(204,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp28) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause135')).
% 1.88/1.45 tff(205,plain,
% 1.88/1.45 (![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[204, 203])).
% 1.88/1.45 tff(206,plain,
% 1.88/1.45 (![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[205, 201])).
% 1.88/1.45 tff(207,plain,(
% 1.88/1.45 ![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.88/1.45 inference(skolemize,[status(sab)],[206])).
% 1.88/1.45 tff(208,plain,
% 1.88/1.45 (![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[207, 200])).
% 1.88/1.45 tff(209,plain,
% 1.88/1.45 ((hskp21 | hskp13 | hskp12) <=> (hskp21 | hskp13 | hskp12)),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(210,plain,
% 1.88/1.45 (((hskp12 | hskp13) | hskp21) <=> (hskp21 | hskp13 | hskp12)),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(211,axiom,((hskp12 | hskp13) | hskp21), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause34')).
% 1.88/1.45 tff(212,plain,
% 1.88/1.45 (hskp21 | hskp13 | hskp12),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[211, 210])).
% 1.88/1.45 tff(213,plain,
% 1.88/1.45 (hskp21 | hskp13 | hskp12),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[212, 209])).
% 1.88/1.45 tff(214,plain,
% 1.88/1.45 (hskp21 | hskp13 | hskp12),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[213, 209])).
% 1.88/1.45 tff(215,plain,
% 1.88/1.45 (hskp21 | hskp13 | hskp12),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[214, 209])).
% 1.88/1.45 tff(216,plain,
% 1.88/1.45 (hskp21 | hskp13 | hskp12),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[215, 209])).
% 1.88/1.45 tff(217,plain,
% 1.88/1.45 (hskp21 | hskp13 | hskp12),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[216, 209])).
% 1.88/1.45 tff(218,plain,
% 1.88/1.45 (hskp21 | hskp13 | hskp12),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[217, 209])).
% 1.88/1.45 tff(219,plain,
% 1.88/1.45 (hskp21 | hskp13 | hskp12),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[218, 209])).
% 1.88/1.45 tff(220,plain,
% 1.88/1.45 (hskp13),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[219, 32, 198])).
% 1.88/1.45 tff(221,plain,
% 1.88/1.45 (((~hskp13) | (~c3_1(a921))) <=> ((~hskp13) | (~c3_1(a921)))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(222,plain,
% 1.88/1.45 (((~c3_1(a921)) | (~hskp13)) <=> ((~hskp13) | (~c3_1(a921)))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(223,axiom,((~c3_1(a921)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause106')).
% 1.88/1.45 tff(224,plain,
% 1.88/1.45 ((~hskp13) | (~c3_1(a921))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[223, 222])).
% 1.88/1.45 tff(225,plain,
% 1.88/1.45 ((~hskp13) | (~c3_1(a921))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[224, 221])).
% 1.88/1.45 tff(226,plain,
% 1.88/1.45 (~c3_1(a921)),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[225, 220])).
% 1.88/1.45 tff(227,plain,
% 1.88/1.45 (((~hskp13) | (~c0_1(a921))) <=> ((~hskp13) | (~c0_1(a921)))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(228,plain,
% 1.88/1.45 (((~c0_1(a921)) | (~hskp13)) <=> ((~hskp13) | (~c0_1(a921)))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(229,axiom,((~c0_1(a921)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause105')).
% 1.88/1.45 tff(230,plain,
% 1.88/1.45 ((~hskp13) | (~c0_1(a921))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[229, 228])).
% 1.88/1.45 tff(231,plain,
% 1.88/1.45 ((~hskp13) | (~c0_1(a921))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[230, 227])).
% 1.88/1.45 tff(232,plain,
% 1.88/1.45 (~c0_1(a921)),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[231, 220])).
% 1.88/1.45 tff(233,plain,
% 1.88/1.45 (((~hskp13) | c2_1(a921)) <=> ((~hskp13) | c2_1(a921))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(234,axiom,((~hskp13) | c2_1(a921)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause63')).
% 1.88/1.45 tff(235,plain,
% 1.88/1.45 ((~hskp13) | c2_1(a921)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[234, 233])).
% 1.88/1.45 tff(236,plain,
% 1.88/1.45 ((~hskp13) | c2_1(a921)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[235, 233])).
% 1.88/1.45 tff(237,plain,
% 1.88/1.45 ((~hskp13) | c2_1(a921)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[236, 233])).
% 1.88/1.45 tff(238,plain,
% 1.88/1.45 ((~hskp13) | c2_1(a921)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[237, 233])).
% 1.88/1.45 tff(239,plain,
% 1.88/1.45 ((~hskp13) | c2_1(a921)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[238, 233])).
% 1.88/1.45 tff(240,plain,
% 1.88/1.45 ((~hskp13) | c2_1(a921)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[239, 233])).
% 1.88/1.45 tff(241,plain,
% 1.88/1.45 ((~hskp13) | c2_1(a921)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[240, 233])).
% 1.88/1.45 tff(242,plain,
% 1.88/1.45 ((~hskp13) | c2_1(a921)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[241, 233])).
% 1.88/1.45 tff(243,plain,
% 1.88/1.45 (c2_1(a921)),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[242, 220])).
% 1.88/1.45 tff(244,plain,
% 1.88/1.45 (((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp28 | hskp12 | c0_1(a921) | c3_1(a921) | (~ndr1_0) | (~c2_1(a921)))) <=> ((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp28 | hskp12 | c0_1(a921) | c3_1(a921) | (~ndr1_0) | (~c2_1(a921)))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(245,plain,
% 1.88/1.45 ((hskp28 | hskp12 | (~ndr1_0) | c0_1(a921) | c3_1(a921) | (~c2_1(a921))) <=> (hskp28 | hskp12 | c0_1(a921) | c3_1(a921) | (~ndr1_0) | (~c2_1(a921)))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(246,plain,
% 1.88/1.45 (((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp28 | hskp12 | (~ndr1_0) | c0_1(a921) | c3_1(a921) | (~c2_1(a921)))) <=> ((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp28 | hskp12 | c0_1(a921) | c3_1(a921) | (~ndr1_0) | (~c2_1(a921))))),
% 1.88/1.45 inference(monotonicity,[status(thm)],[245])).
% 1.88/1.45 tff(247,plain,
% 1.88/1.46 (((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp28 | hskp12 | (~ndr1_0) | c0_1(a921) | c3_1(a921) | (~c2_1(a921)))) <=> ((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp28 | hskp12 | c0_1(a921) | c3_1(a921) | (~ndr1_0) | (~c2_1(a921)))),
% 1.88/1.46 inference(transitivity,[status(thm)],[246, 244])).
% 1.88/1.46 tff(248,plain,
% 1.88/1.46 ((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp28 | hskp12 | (~ndr1_0) | c0_1(a921) | c3_1(a921) | (~c2_1(a921)))),
% 1.88/1.46 inference(quant_inst,[status(thm)],[])).
% 1.88/1.46 tff(249,plain,
% 1.88/1.46 ((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp28 | hskp12 | c0_1(a921) | c3_1(a921) | (~ndr1_0) | (~c2_1(a921))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[248, 247])).
% 1.88/1.46 tff(250,plain,
% 1.88/1.46 (hskp28),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[249, 124, 32, 243, 232, 226, 208])).
% 1.88/1.46 tff(251,plain,
% 1.88/1.46 (((~hskp28) | c0_1(a916)) <=> ((~hskp28) | c0_1(a916))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(252,axiom,((~hskp28) | c0_1(a916)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause41')).
% 1.88/1.46 tff(253,plain,
% 1.88/1.46 ((~hskp28) | c0_1(a916)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[252, 251])).
% 1.88/1.46 tff(254,plain,
% 1.88/1.46 ((~hskp28) | c0_1(a916)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[253, 251])).
% 1.88/1.46 tff(255,plain,
% 1.88/1.46 ((~hskp28) | c0_1(a916)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[254, 251])).
% 1.88/1.46 tff(256,plain,
% 1.88/1.46 ((~hskp28) | c0_1(a916)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[255, 251])).
% 1.88/1.46 tff(257,plain,
% 1.88/1.46 ((~hskp28) | c0_1(a916)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[256, 251])).
% 1.88/1.46 tff(258,plain,
% 1.88/1.46 ((~hskp28) | c0_1(a916)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[257, 251])).
% 1.88/1.46 tff(259,plain,
% 1.88/1.46 ((~hskp28) | c0_1(a916)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[258, 251])).
% 1.88/1.46 tff(260,plain,
% 1.88/1.46 ((~hskp28) | c0_1(a916)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[259, 251])).
% 1.88/1.46 tff(261,plain,
% 1.88/1.46 (c0_1(a916)),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[260, 250])).
% 1.88/1.46 tff(262,plain,
% 1.88/1.46 (((~hskp28) | c3_1(a916)) <=> ((~hskp28) | c3_1(a916))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(263,axiom,((~hskp28) | c3_1(a916)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause43')).
% 1.88/1.46 tff(264,plain,
% 1.88/1.46 ((~hskp28) | c3_1(a916)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[263, 262])).
% 1.88/1.46 tff(265,plain,
% 1.88/1.46 ((~hskp28) | c3_1(a916)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[264, 262])).
% 1.88/1.46 tff(266,plain,
% 1.88/1.46 ((~hskp28) | c3_1(a916)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[265, 262])).
% 1.88/1.46 tff(267,plain,
% 1.88/1.46 ((~hskp28) | c3_1(a916)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[266, 262])).
% 1.88/1.46 tff(268,plain,
% 1.88/1.46 ((~hskp28) | c3_1(a916)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[267, 262])).
% 1.88/1.46 tff(269,plain,
% 1.88/1.46 ((~hskp28) | c3_1(a916)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[268, 262])).
% 1.88/1.46 tff(270,plain,
% 1.88/1.46 ((~hskp28) | c3_1(a916)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[269, 262])).
% 1.88/1.46 tff(271,plain,
% 1.88/1.46 ((~hskp28) | c3_1(a916)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[270, 262])).
% 1.88/1.46 tff(272,plain,
% 1.88/1.46 (c3_1(a916)),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[271, 250])).
% 1.88/1.46 tff(273,plain,
% 1.88/1.46 (((~hskp28) | c1_1(a916)) <=> ((~hskp28) | c1_1(a916))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(274,axiom,((~hskp28) | c1_1(a916)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause42')).
% 1.88/1.46 tff(275,plain,
% 1.88/1.46 ((~hskp28) | c1_1(a916)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[274, 273])).
% 1.88/1.46 tff(276,plain,
% 1.88/1.46 ((~hskp28) | c1_1(a916)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[275, 273])).
% 1.88/1.46 tff(277,plain,
% 1.88/1.46 ((~hskp28) | c1_1(a916)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[276, 273])).
% 1.88/1.46 tff(278,plain,
% 1.88/1.46 ((~hskp28) | c1_1(a916)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[277, 273])).
% 1.88/1.46 tff(279,plain,
% 1.88/1.46 ((~hskp28) | c1_1(a916)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[278, 273])).
% 1.88/1.46 tff(280,plain,
% 1.88/1.46 ((~hskp28) | c1_1(a916)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[279, 273])).
% 1.88/1.46 tff(281,plain,
% 1.88/1.46 ((~hskp28) | c1_1(a916)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[280, 273])).
% 1.88/1.46 tff(282,plain,
% 1.88/1.46 ((~hskp28) | c1_1(a916)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[281, 273])).
% 1.88/1.46 tff(283,plain,
% 1.88/1.46 (c1_1(a916)),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[282, 250])).
% 1.88/1.46 tff(284,assumption,(hskp5), introduced(assumption)).
% 1.88/1.46 tff(285,plain,
% 1.88/1.46 (((~hskp5) | c2_1(a906)) <=> ((~hskp5) | c2_1(a906))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(286,axiom,((~hskp5) | c2_1(a906)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause76')).
% 1.88/1.46 tff(287,plain,
% 1.88/1.46 ((~hskp5) | c2_1(a906)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[286, 285])).
% 1.88/1.46 tff(288,plain,
% 1.88/1.46 ((~hskp5) | c2_1(a906)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[287, 285])).
% 1.88/1.46 tff(289,plain,
% 1.88/1.46 ((~hskp5) | c2_1(a906)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[288, 285])).
% 1.88/1.46 tff(290,plain,
% 1.88/1.46 ((~hskp5) | c2_1(a906)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[289, 285])).
% 1.88/1.46 tff(291,plain,
% 1.88/1.46 ((~hskp5) | c2_1(a906)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[290, 285])).
% 1.88/1.46 tff(292,plain,
% 1.88/1.46 ((~hskp5) | c2_1(a906)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[291, 285])).
% 1.88/1.46 tff(293,plain,
% 1.88/1.46 ((~hskp5) | c2_1(a906)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[292, 285])).
% 1.88/1.46 tff(294,plain,
% 1.88/1.46 ((~hskp5) | c2_1(a906)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[293, 285])).
% 1.88/1.46 tff(295,plain,
% 1.88/1.46 (c2_1(a906)),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[294, 284])).
% 1.88/1.46 tff(296,plain,
% 1.88/1.46 (((~hskp5) | (~c3_1(a906))) <=> ((~hskp5) | (~c3_1(a906)))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(297,plain,
% 1.88/1.46 (((~c3_1(a906)) | (~hskp5)) <=> ((~hskp5) | (~c3_1(a906)))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(298,axiom,((~c3_1(a906)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause117')).
% 1.88/1.46 tff(299,plain,
% 1.88/1.46 ((~hskp5) | (~c3_1(a906))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[298, 297])).
% 1.88/1.46 tff(300,plain,
% 1.88/1.46 ((~hskp5) | (~c3_1(a906))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[299, 296])).
% 1.88/1.46 tff(301,plain,
% 1.88/1.46 (~c3_1(a906)),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[300, 284])).
% 1.88/1.46 tff(302,plain,
% 1.88/1.46 (((~hskp5) | c0_1(a906)) <=> ((~hskp5) | c0_1(a906))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(303,axiom,((~hskp5) | c0_1(a906)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause75')).
% 1.88/1.46 tff(304,plain,
% 1.88/1.46 ((~hskp5) | c0_1(a906)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[303, 302])).
% 1.88/1.46 tff(305,plain,
% 1.88/1.46 ((~hskp5) | c0_1(a906)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[304, 302])).
% 1.88/1.46 tff(306,plain,
% 1.88/1.46 ((~hskp5) | c0_1(a906)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[305, 302])).
% 1.88/1.46 tff(307,plain,
% 1.88/1.46 ((~hskp5) | c0_1(a906)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[306, 302])).
% 1.88/1.46 tff(308,plain,
% 1.88/1.46 ((~hskp5) | c0_1(a906)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[307, 302])).
% 1.88/1.46 tff(309,plain,
% 1.88/1.46 ((~hskp5) | c0_1(a906)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[308, 302])).
% 1.88/1.46 tff(310,plain,
% 1.88/1.46 ((~hskp5) | c0_1(a906)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[309, 302])).
% 1.88/1.46 tff(311,plain,
% 1.88/1.46 ((~hskp5) | c0_1(a906)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[310, 302])).
% 1.88/1.46 tff(312,plain,
% 1.88/1.46 (c0_1(a906)),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[311, 284])).
% 1.88/1.46 tff(313,plain,
% 1.88/1.46 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)))),
% 1.88/1.46 inference(bind,[status(th)],[])).
% 1.88/1.46 tff(314,plain,
% 1.88/1.46 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.88/1.46 inference(quant_intro,[status(thm)],[313])).
% 1.88/1.46 tff(315,plain,
% 1.88/1.46 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(316,plain,
% 1.88/1.46 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))))),
% 1.88/1.46 inference(bind,[status(th)],[])).
% 1.88/1.46 tff(317,plain,
% 1.88/1.46 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.88/1.46 inference(quant_intro,[status(thm)],[316])).
% 1.88/1.46 tff(318,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause180')).
% 1.88/1.46 tff(319,plain,
% 1.88/1.46 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[318, 317])).
% 1.88/1.46 tff(320,plain,
% 1.88/1.46 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[319, 315])).
% 1.88/1.46 tff(321,plain,(
% 1.88/1.46 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.88/1.46 inference(skolemize,[status(sab)],[320])).
% 1.88/1.46 tff(322,plain,
% 1.88/1.46 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[321, 314])).
% 1.88/1.46 tff(323,assumption,(c0_1(a906)), introduced(assumption)).
% 1.88/1.46 tff(324,assumption,(c2_1(a906)), introduced(assumption)).
% 1.88/1.46 tff(325,assumption,(~c3_1(a906)), introduced(assumption)).
% 1.88/1.46 tff(326,assumption,(~hskp10), introduced(assumption)).
% 1.88/1.46 tff(327,assumption,(hskp12), introduced(assumption)).
% 1.88/1.46 tff(328,plain,
% 1.88/1.46 (((~hskp12) | (~c2_1(a917))) <=> ((~hskp12) | (~c2_1(a917)))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(329,plain,
% 1.88/1.46 (((~c2_1(a917)) | (~hskp12)) <=> ((~hskp12) | (~c2_1(a917)))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(330,axiom,((~c2_1(a917)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause107')).
% 1.88/1.46 tff(331,plain,
% 1.88/1.46 ((~hskp12) | (~c2_1(a917))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[330, 329])).
% 1.88/1.46 tff(332,plain,
% 1.88/1.46 ((~hskp12) | (~c2_1(a917))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[331, 328])).
% 1.88/1.46 tff(333,plain,
% 1.88/1.46 (~c2_1(a917)),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[332, 327])).
% 1.88/1.46 tff(334,plain,
% 1.88/1.46 (((~hskp12) | c1_1(a917)) <=> ((~hskp12) | c1_1(a917))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(335,axiom,((~hskp12) | c1_1(a917)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause64')).
% 1.88/1.46 tff(336,plain,
% 1.88/1.46 ((~hskp12) | c1_1(a917)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[335, 334])).
% 1.88/1.46 tff(337,plain,
% 1.88/1.46 ((~hskp12) | c1_1(a917)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[336, 334])).
% 1.88/1.46 tff(338,plain,
% 1.88/1.46 ((~hskp12) | c1_1(a917)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[337, 334])).
% 1.88/1.46 tff(339,plain,
% 1.88/1.46 ((~hskp12) | c1_1(a917)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[338, 334])).
% 1.88/1.46 tff(340,plain,
% 1.88/1.46 ((~hskp12) | c1_1(a917)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[339, 334])).
% 1.88/1.46 tff(341,plain,
% 1.88/1.46 ((~hskp12) | c1_1(a917)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[340, 334])).
% 1.88/1.46 tff(342,plain,
% 1.88/1.46 ((~hskp12) | c1_1(a917)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[341, 334])).
% 1.88/1.46 tff(343,plain,
% 1.88/1.46 ((~hskp12) | c1_1(a917)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[342, 334])).
% 1.88/1.46 tff(344,plain,
% 1.88/1.46 (c1_1(a917)),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[343, 327])).
% 1.88/1.46 tff(345,plain,
% 1.88/1.46 (((~hskp12) | c3_1(a917)) <=> ((~hskp12) | c3_1(a917))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(346,axiom,((~hskp12) | c3_1(a917)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause65')).
% 1.88/1.46 tff(347,plain,
% 1.88/1.46 ((~hskp12) | c3_1(a917)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[346, 345])).
% 1.88/1.46 tff(348,plain,
% 1.88/1.46 ((~hskp12) | c3_1(a917)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[347, 345])).
% 1.88/1.46 tff(349,plain,
% 1.88/1.46 ((~hskp12) | c3_1(a917)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[348, 345])).
% 1.88/1.46 tff(350,plain,
% 1.88/1.46 ((~hskp12) | c3_1(a917)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[349, 345])).
% 1.88/1.46 tff(351,plain,
% 1.88/1.46 ((~hskp12) | c3_1(a917)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[350, 345])).
% 1.88/1.46 tff(352,plain,
% 1.88/1.46 ((~hskp12) | c3_1(a917)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[351, 345])).
% 1.88/1.46 tff(353,plain,
% 1.88/1.46 ((~hskp12) | c3_1(a917)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[352, 345])).
% 1.88/1.46 tff(354,plain,
% 1.88/1.46 ((~hskp12) | c3_1(a917)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[353, 345])).
% 1.88/1.46 tff(355,plain,
% 1.88/1.46 (c3_1(a917)),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[354, 327])).
% 1.88/1.46 tff(356,plain,
% 1.88/1.46 (^[U: $i] : refl((hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 1.88/1.46 inference(bind,[status(th)],[])).
% 1.88/1.46 tff(357,plain,
% 1.88/1.46 (![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.88/1.46 inference(quant_intro,[status(thm)],[356])).
% 1.88/1.46 tff(358,plain,
% 1.88/1.46 (![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(359,plain,
% 1.88/1.46 (^[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)) | hskp10) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp10))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp10) | hskp21) <=> ((hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp21))), rewrite(((hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp21) <=> (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp10) | hskp21) <=> (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 1.88/1.46 inference(bind,[status(th)],[])).
% 1.88/1.46 tff(360,plain,
% 1.88/1.46 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp10) | hskp21) <=> ![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.88/1.46 inference(quant_intro,[status(thm)],[359])).
% 1.88/1.46 tff(361,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp10) | hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause153')).
% 1.88/1.46 tff(362,plain,
% 1.88/1.46 (![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[361, 360])).
% 1.88/1.46 tff(363,plain,
% 1.88/1.46 (![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[362, 358])).
% 1.88/1.46 tff(364,plain,(
% 1.88/1.46 ![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.88/1.46 inference(skolemize,[status(sab)],[363])).
% 1.88/1.46 tff(365,plain,
% 1.88/1.46 (![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[364, 357])).
% 1.88/1.46 tff(366,assumption,(~c2_1(a917)), introduced(assumption)).
% 1.88/1.46 tff(367,plain,
% 1.88/1.46 (((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917)))) <=> ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp10 | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917)))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(368,plain,
% 1.88/1.46 ((hskp21 | hskp10 | (~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917))) <=> (hskp21 | hskp10 | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917)))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(369,plain,
% 1.88/1.46 (((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | (~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)))) <=> ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917))))),
% 1.88/1.46 inference(monotonicity,[status(thm)],[368])).
% 1.88/1.46 tff(370,plain,
% 1.88/1.46 (((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | (~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)))) <=> ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp10 | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917)))),
% 1.88/1.46 inference(transitivity,[status(thm)],[369, 367])).
% 1.88/1.46 tff(371,plain,
% 1.88/1.46 ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | (~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)))),
% 1.88/1.46 inference(quant_inst,[status(thm)],[])).
% 1.88/1.46 tff(372,plain,
% 1.88/1.46 ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp10 | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[371, 370])).
% 1.88/1.46 tff(373,plain,
% 1.88/1.46 (hskp10 | (~c3_1(a917)) | (~c1_1(a917))),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[372, 124, 198, 366, 365])).
% 1.88/1.46 tff(374,plain,
% 1.88/1.46 ($false),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[373, 355, 344, 326])).
% 1.88/1.46 tff(375,plain,((~hskp12) | hskp10 | hskp21 | c2_1(a917)), inference(lemma,lemma(discharge,[]))).
% 1.88/1.46 tff(376,plain,
% 1.88/1.46 ($false),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[375, 333, 327, 198, 326])).
% 1.88/1.46 tff(377,plain,((~hskp12) | hskp21 | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.88/1.46 tff(378,plain,
% 1.88/1.46 (~hskp12),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[377, 326, 198])).
% 1.88/1.46 tff(379,plain,
% 1.88/1.46 (((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | (~ndr1_0) | c2_1(a916) | (~c3_1(a916)) | (~c1_1(a916)))) <=> ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp10 | (~ndr1_0) | c2_1(a916) | (~c3_1(a916)) | (~c1_1(a916)))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(380,plain,
% 1.88/1.46 ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | (~ndr1_0) | c2_1(a916) | (~c3_1(a916)) | (~c1_1(a916)))),
% 1.88/1.46 inference(quant_inst,[status(thm)],[])).
% 1.88/1.46 tff(381,plain,
% 1.88/1.46 ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp10 | (~ndr1_0) | c2_1(a916) | (~c3_1(a916)) | (~c1_1(a916))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[380, 379])).
% 1.88/1.46 tff(382,plain,
% 1.88/1.46 (hskp10 | c2_1(a916)),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[381, 124, 198, 283, 272, 365])).
% 1.88/1.46 tff(383,plain,
% 1.88/1.46 (c2_1(a916)),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[382, 326])).
% 1.88/1.46 tff(384,plain,
% 1.88/1.46 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | (~c3_1(a916)) | (~c2_1(a916)) | (~c1_1(a916)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | (~ndr1_0) | (~c3_1(a916)) | (~c2_1(a916)) | (~c1_1(a916)))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(385,plain,
% 1.88/1.46 ((hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a916)) | (~c3_1(a916)) | (~c1_1(a916))) <=> (hskp12 | hskp11 | (~ndr1_0) | (~c3_1(a916)) | (~c2_1(a916)) | (~c1_1(a916)))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(386,plain,
% 1.88/1.46 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a916)) | (~c3_1(a916)) | (~c1_1(a916)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | (~c3_1(a916)) | (~c2_1(a916)) | (~c1_1(a916))))),
% 1.88/1.46 inference(monotonicity,[status(thm)],[385])).
% 1.88/1.46 tff(387,plain,
% 1.88/1.46 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a916)) | (~c3_1(a916)) | (~c1_1(a916)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | (~ndr1_0) | (~c3_1(a916)) | (~c2_1(a916)) | (~c1_1(a916)))),
% 1.88/1.46 inference(transitivity,[status(thm)],[386, 384])).
% 1.88/1.46 tff(388,plain,
% 1.88/1.46 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a916)) | (~c3_1(a916)) | (~c1_1(a916)))),
% 1.88/1.46 inference(quant_inst,[status(thm)],[])).
% 1.88/1.46 tff(389,plain,
% 1.88/1.46 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | (~ndr1_0) | (~c3_1(a916)) | (~c2_1(a916)) | (~c1_1(a916))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[388, 387])).
% 1.88/1.46 tff(390,plain,
% 1.88/1.46 (hskp11 | (~c2_1(a916))),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[389, 124, 32, 283, 272, 53])).
% 1.88/1.46 tff(391,plain,
% 1.88/1.46 (hskp11),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[390, 383])).
% 1.88/1.46 tff(392,plain,
% 1.88/1.46 (c0_1(a914)),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[91, 391])).
% 1.88/1.46 tff(393,plain,
% 1.88/1.46 (c3_1(a914)),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[80, 391])).
% 1.88/1.46 tff(394,plain,
% 1.88/1.46 (~c2_1(a914)),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[69, 391])).
% 1.88/1.46 tff(395,plain,
% 1.88/1.46 (((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c1_1(a914)))) <=> ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp10 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c1_1(a914)))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(396,plain,
% 1.88/1.46 ((hskp21 | hskp10 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914))) <=> (hskp21 | hskp10 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c1_1(a914)))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(397,plain,
% 1.88/1.46 (((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)))) <=> ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c1_1(a914))))),
% 1.88/1.46 inference(monotonicity,[status(thm)],[396])).
% 1.88/1.46 tff(398,plain,
% 1.88/1.46 (((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)))) <=> ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp10 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c1_1(a914)))),
% 1.88/1.46 inference(transitivity,[status(thm)],[397, 395])).
% 1.88/1.46 tff(399,plain,
% 1.88/1.46 ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)))),
% 1.88/1.46 inference(quant_inst,[status(thm)],[])).
% 1.88/1.46 tff(400,plain,
% 1.88/1.46 ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp10 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c1_1(a914))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[399, 398])).
% 1.88/1.46 tff(401,plain,
% 1.88/1.46 (~c1_1(a914)),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[400, 124, 198, 326, 393, 394, 365])).
% 1.88/1.46 tff(402,assumption,(hskp6), introduced(assumption)).
% 1.88/1.46 tff(403,plain,
% 1.88/1.46 (((~hskp6) | (~c2_1(a907))) <=> ((~hskp6) | (~c2_1(a907)))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(404,plain,
% 1.88/1.46 (((~c2_1(a907)) | (~hskp6)) <=> ((~hskp6) | (~c2_1(a907)))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(405,axiom,((~c2_1(a907)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause116')).
% 1.88/1.46 tff(406,plain,
% 1.88/1.46 ((~hskp6) | (~c2_1(a907))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[405, 404])).
% 1.88/1.46 tff(407,plain,
% 1.88/1.46 ((~hskp6) | (~c2_1(a907))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[406, 403])).
% 1.88/1.46 tff(408,plain,
% 1.88/1.46 (~c2_1(a907)),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[407, 402])).
% 1.88/1.46 tff(409,plain,
% 1.88/1.46 (((~hskp6) | c1_1(a907)) <=> ((~hskp6) | c1_1(a907))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(410,axiom,((~hskp6) | c1_1(a907)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause74')).
% 1.88/1.46 tff(411,plain,
% 1.88/1.46 ((~hskp6) | c1_1(a907)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[410, 409])).
% 1.88/1.46 tff(412,plain,
% 1.88/1.46 ((~hskp6) | c1_1(a907)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[411, 409])).
% 1.88/1.46 tff(413,plain,
% 1.88/1.46 ((~hskp6) | c1_1(a907)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[412, 409])).
% 1.88/1.46 tff(414,plain,
% 1.88/1.46 ((~hskp6) | c1_1(a907)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[413, 409])).
% 1.88/1.46 tff(415,plain,
% 1.88/1.46 ((~hskp6) | c1_1(a907)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[414, 409])).
% 1.88/1.46 tff(416,plain,
% 1.88/1.46 ((~hskp6) | c1_1(a907)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[415, 409])).
% 1.88/1.46 tff(417,plain,
% 1.88/1.46 ((~hskp6) | c1_1(a907)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[416, 409])).
% 1.88/1.46 tff(418,plain,
% 1.88/1.46 ((~hskp6) | c1_1(a907)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[417, 409])).
% 1.88/1.46 tff(419,plain,
% 1.88/1.46 (c1_1(a907)),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[418, 402])).
% 1.88/1.46 tff(420,plain,
% 1.88/1.46 (((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | c2_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)))) <=> ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp10 | c2_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(421,plain,
% 1.88/1.46 ((hskp21 | hskp10 | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907))) <=> (hskp21 | hskp10 | c2_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(422,plain,
% 1.88/1.46 (((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907)))) <=> ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | c2_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907))))),
% 1.88/1.46 inference(monotonicity,[status(thm)],[421])).
% 1.88/1.46 tff(423,plain,
% 1.88/1.46 (((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907)))) <=> ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp10 | c2_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)))),
% 1.88/1.46 inference(transitivity,[status(thm)],[422, 420])).
% 1.88/1.46 tff(424,plain,
% 1.88/1.46 ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907)))),
% 1.88/1.46 inference(quant_inst,[status(thm)],[])).
% 1.88/1.46 tff(425,plain,
% 1.88/1.46 ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp10 | c2_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[424, 423])).
% 1.88/1.46 tff(426,plain,
% 1.88/1.46 (~c3_1(a907)),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[425, 124, 198, 326, 419, 408, 365])).
% 1.88/1.46 tff(427,assumption,(~c1_1(a914)), introduced(assumption)).
% 1.88/1.46 tff(428,assumption,(c3_1(a914)), introduced(assumption)).
% 1.88/1.46 tff(429,assumption,(c0_1(a914)), introduced(assumption)).
% 1.88/1.46 tff(430,plain,
% 1.88/1.46 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c1_1(a907)) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c1_1(a907)) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(431,plain,
% 1.88/1.46 ((hskp21 | (~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c1_1(a907)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914))) <=> (hskp21 | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c1_1(a907)) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(432,plain,
% 1.88/1.46 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c1_1(a907)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c1_1(a907)) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914))))),
% 1.88/1.46 inference(monotonicity,[status(thm)],[431])).
% 1.88/1.46 tff(433,plain,
% 1.88/1.46 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c1_1(a907)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c1_1(a907)) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)))),
% 1.88/1.46 inference(transitivity,[status(thm)],[432, 430])).
% 1.88/1.46 tff(434,plain,
% 1.88/1.46 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c1_1(a907)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914)))),
% 1.88/1.46 inference(quant_inst,[status(thm)],[])).
% 1.88/1.46 tff(435,plain,
% 1.88/1.46 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c1_1(a907)) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[434, 433])).
% 1.88/1.46 tff(436,plain,
% 1.88/1.46 ($false),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[435, 124, 198, 429, 428, 419, 408, 197, 427, 426])).
% 1.88/1.46 tff(437,plain,((~hskp6) | hskp21 | (~c0_1(a914)) | (~c3_1(a914)) | c1_1(a914) | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.88/1.46 tff(438,plain,
% 1.88/1.46 (~hskp6),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[437, 401, 198, 393, 392, 326])).
% 1.88/1.46 tff(439,plain,
% 1.88/1.46 (^[U: $i] : refl((hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))),
% 1.88/1.46 inference(bind,[status(th)],[])).
% 1.88/1.46 tff(440,plain,
% 1.88/1.46 (![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.88/1.46 inference(quant_intro,[status(thm)],[439])).
% 1.88/1.46 tff(441,plain,
% 1.88/1.46 (![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(442,plain,
% 1.88/1.46 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp12) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp12))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp12) <=> (hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp12) | hskp17) <=> ((hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp17))), rewrite(((hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp17) <=> (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp12) | hskp17) <=> (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))))),
% 1.91/1.47 inference(bind,[status(th)],[])).
% 1.91/1.47 tff(443,plain,
% 1.91/1.47 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp12) | hskp17) <=> ![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.91/1.47 inference(quant_intro,[status(thm)],[442])).
% 1.91/1.47 tff(444,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp12) | hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause137')).
% 1.91/1.47 tff(445,plain,
% 1.91/1.47 (![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.91/1.47 inference(modus_ponens,[status(thm)],[444, 443])).
% 1.91/1.47 tff(446,plain,
% 1.91/1.47 (![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.91/1.47 inference(modus_ponens,[status(thm)],[445, 441])).
% 1.91/1.47 tff(447,plain,(
% 1.91/1.47 ![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.91/1.47 inference(skolemize,[status(sab)],[446])).
% 1.91/1.47 tff(448,plain,
% 1.91/1.47 (![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.91/1.47 inference(modus_ponens,[status(thm)],[447, 440])).
% 1.91/1.47 tff(449,plain,
% 1.91/1.47 (((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | c2_1(a914) | (~ndr1_0) | c1_1(a914) | (~c0_1(a914)))) <=> ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp17 | hskp12 | c2_1(a914) | (~ndr1_0) | c1_1(a914) | (~c0_1(a914)))),
% 1.91/1.47 inference(rewrite,[status(thm)],[])).
% 1.91/1.47 tff(450,plain,
% 1.91/1.47 ((hskp17 | hskp12 | (~ndr1_0) | c2_1(a914) | c1_1(a914) | (~c0_1(a914))) <=> (hskp17 | hskp12 | c2_1(a914) | (~ndr1_0) | c1_1(a914) | (~c0_1(a914)))),
% 1.91/1.47 inference(rewrite,[status(thm)],[])).
% 1.91/1.47 tff(451,plain,
% 1.91/1.47 (((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | (~ndr1_0) | c2_1(a914) | c1_1(a914) | (~c0_1(a914)))) <=> ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | c2_1(a914) | (~ndr1_0) | c1_1(a914) | (~c0_1(a914))))),
% 1.91/1.47 inference(monotonicity,[status(thm)],[450])).
% 1.91/1.47 tff(452,plain,
% 1.91/1.47 (((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | (~ndr1_0) | c2_1(a914) | c1_1(a914) | (~c0_1(a914)))) <=> ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp17 | hskp12 | c2_1(a914) | (~ndr1_0) | c1_1(a914) | (~c0_1(a914)))),
% 1.91/1.47 inference(transitivity,[status(thm)],[451, 449])).
% 1.91/1.47 tff(453,plain,
% 1.91/1.47 ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | (~ndr1_0) | c2_1(a914) | c1_1(a914) | (~c0_1(a914)))),
% 1.91/1.47 inference(quant_inst,[status(thm)],[])).
% 1.91/1.47 tff(454,plain,
% 1.91/1.47 ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp17 | hskp12 | c2_1(a914) | (~ndr1_0) | c1_1(a914) | (~c0_1(a914))),
% 1.91/1.47 inference(modus_ponens,[status(thm)],[453, 452])).
% 1.91/1.47 tff(455,plain,
% 1.91/1.47 (hskp17),
% 1.91/1.47 inference(unit_resolution,[status(thm)],[454, 124, 32, 392, 394, 448, 401])).
% 1.91/1.47 tff(456,plain,
% 1.91/1.47 (((~hskp17) | (~c3_1(a936))) <=> ((~hskp17) | (~c3_1(a936)))),
% 1.91/1.47 inference(rewrite,[status(thm)],[])).
% 1.91/1.47 tff(457,plain,
% 1.91/1.47 (((~c3_1(a936)) | (~hskp17)) <=> ((~hskp17) | (~c3_1(a936)))),
% 1.91/1.47 inference(rewrite,[status(thm)],[])).
% 1.91/1.47 tff(458,axiom,((~c3_1(a936)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause99')).
% 1.91/1.47 tff(459,plain,
% 1.91/1.47 ((~hskp17) | (~c3_1(a936))),
% 1.91/1.47 inference(modus_ponens,[status(thm)],[458, 457])).
% 1.91/1.47 tff(460,plain,
% 1.91/1.47 ((~hskp17) | (~c3_1(a936))),
% 1.91/1.47 inference(modus_ponens,[status(thm)],[459, 456])).
% 1.91/1.47 tff(461,plain,
% 1.91/1.47 (~c3_1(a936)),
% 1.91/1.47 inference(unit_resolution,[status(thm)],[460, 455])).
% 1.91/1.47 tff(462,assumption,(hskp7), introduced(assumption)).
% 1.91/1.47 tff(463,plain,
% 1.91/1.47 (((~hskp7) | (~c3_1(a908))) <=> ((~hskp7) | (~c3_1(a908)))),
% 1.91/1.47 inference(rewrite,[status(thm)],[])).
% 1.91/1.47 tff(464,plain,
% 1.91/1.47 (((~c3_1(a908)) | (~hskp7)) <=> ((~hskp7) | (~c3_1(a908)))),
% 1.91/1.47 inference(rewrite,[status(thm)],[])).
% 1.91/1.47 tff(465,axiom,((~c3_1(a908)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause115')).
% 1.91/1.47 tff(466,plain,
% 1.91/1.47 ((~hskp7) | (~c3_1(a908))),
% 1.91/1.47 inference(modus_ponens,[status(thm)],[465, 464])).
% 1.91/1.47 tff(467,plain,
% 1.91/1.47 ((~hskp7) | (~c3_1(a908))),
% 1.91/1.47 inference(modus_ponens,[status(thm)],[466, 463])).
% 1.91/1.47 tff(468,plain,
% 1.91/1.47 (~c3_1(a908)),
% 1.91/1.47 inference(unit_resolution,[status(thm)],[467, 462])).
% 1.91/1.47 tff(469,plain,
% 1.91/1.47 (((~hskp7) | (~c2_1(a908))) <=> ((~hskp7) | (~c2_1(a908)))),
% 1.91/1.47 inference(rewrite,[status(thm)],[])).
% 1.91/1.47 tff(470,plain,
% 1.91/1.47 (((~c2_1(a908)) | (~hskp7)) <=> ((~hskp7) | (~c2_1(a908)))),
% 1.91/1.47 inference(rewrite,[status(thm)],[])).
% 1.91/1.47 tff(471,axiom,((~c2_1(a908)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause114')).
% 1.91/1.47 tff(472,plain,
% 1.91/1.47 ((~hskp7) | (~c2_1(a908))),
% 1.91/1.47 inference(modus_ponens,[status(thm)],[471, 470])).
% 1.91/1.47 tff(473,plain,
% 1.91/1.47 ((~hskp7) | (~c2_1(a908))),
% 1.91/1.47 inference(modus_ponens,[status(thm)],[472, 469])).
% 1.91/1.47 tff(474,plain,
% 1.91/1.47 (~c2_1(a908)),
% 1.91/1.47 inference(unit_resolution,[status(thm)],[473, 462])).
% 1.91/1.47 tff(475,plain,
% 1.91/1.47 (((~hskp7) | c1_1(a908)) <=> ((~hskp7) | c1_1(a908))),
% 1.91/1.47 inference(rewrite,[status(thm)],[])).
% 1.91/1.47 tff(476,axiom,((~hskp7) | c1_1(a908)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause72')).
% 1.91/1.47 tff(477,plain,
% 1.91/1.47 ((~hskp7) | c1_1(a908)),
% 1.91/1.47 inference(modus_ponens,[status(thm)],[476, 475])).
% 1.91/1.47 tff(478,plain,
% 1.91/1.47 ((~hskp7) | c1_1(a908)),
% 1.91/1.47 inference(modus_ponens,[status(thm)],[477, 475])).
% 1.91/1.47 tff(479,plain,
% 1.91/1.47 ((~hskp7) | c1_1(a908)),
% 1.91/1.47 inference(modus_ponens,[status(thm)],[478, 475])).
% 1.91/1.47 tff(480,plain,
% 1.91/1.47 ((~hskp7) | c1_1(a908)),
% 1.91/1.47 inference(modus_ponens,[status(thm)],[479, 475])).
% 1.91/1.47 tff(481,plain,
% 1.91/1.47 ((~hskp7) | c1_1(a908)),
% 1.91/1.47 inference(modus_ponens,[status(thm)],[480, 475])).
% 1.91/1.47 tff(482,plain,
% 1.91/1.47 ((~hskp7) | c1_1(a908)),
% 1.91/1.47 inference(modus_ponens,[status(thm)],[481, 475])).
% 1.91/1.47 tff(483,plain,
% 1.91/1.47 ((~hskp7) | c1_1(a908)),
% 1.91/1.47 inference(modus_ponens,[status(thm)],[482, 475])).
% 1.91/1.47 tff(484,plain,
% 1.91/1.47 ((~hskp7) | c1_1(a908)),
% 1.91/1.47 inference(modus_ponens,[status(thm)],[483, 475])).
% 1.91/1.47 tff(485,plain,
% 1.91/1.47 (c1_1(a908)),
% 1.91/1.47 inference(unit_resolution,[status(thm)],[484, 462])).
% 1.91/1.47 tff(486,assumption,(c3_1(a916)), introduced(assumption)).
% 1.91/1.47 tff(487,assumption,(c1_1(a916)), introduced(assumption)).
% 1.91/1.47 tff(488,assumption,(c0_1(a916)), introduced(assumption)).
% 1.91/1.47 tff(489,plain,
% 1.91/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a908) | c3_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c1_1(a908)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a908) | c3_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c1_1(a908)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 1.91/1.47 inference(rewrite,[status(thm)],[])).
% 1.91/1.47 tff(490,plain,
% 1.91/1.47 (((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908))) <=> (c2_1(a908) | c3_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c1_1(a908)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 1.91/1.47 inference(rewrite,[status(thm)],[])).
% 1.91/1.47 tff(491,plain,
% 1.91/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a908) | c3_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c1_1(a908)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916))))),
% 1.91/1.47 inference(monotonicity,[status(thm)],[490])).
% 1.91/1.47 tff(492,plain,
% 1.91/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a908) | c3_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c1_1(a908)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 1.91/1.47 inference(transitivity,[status(thm)],[491, 489])).
% 1.91/1.47 tff(493,plain,
% 1.91/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))),
% 1.91/1.47 inference(quant_inst,[status(thm)],[])).
% 1.91/1.47 tff(494,plain,
% 1.91/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a908) | c3_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c1_1(a908)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916))),
% 1.91/1.47 inference(modus_ponens,[status(thm)],[493, 492])).
% 1.91/1.47 tff(495,plain,
% 1.91/1.47 ($false),
% 1.91/1.47 inference(unit_resolution,[status(thm)],[494, 124, 488, 487, 486, 485, 323, 324, 474, 468, 325, 31])).
% 1.91/1.47 tff(496,plain,((~hskp7) | (~c0_1(a916)) | (~c1_1(a916)) | (~c3_1(a916)) | (~c0_1(a906)) | (~c2_1(a906)) | c3_1(a906)), inference(lemma,lemma(discharge,[]))).
% 1.91/1.47 tff(497,plain,
% 1.91/1.47 (~hskp7),
% 1.91/1.47 inference(unit_resolution,[status(thm)],[496, 261, 283, 272, 323, 324, 325])).
% 1.91/1.47 tff(498,plain,
% 1.91/1.47 (((~hskp17) | (~c2_1(a936))) <=> ((~hskp17) | (~c2_1(a936)))),
% 1.91/1.47 inference(rewrite,[status(thm)],[])).
% 1.91/1.47 tff(499,plain,
% 1.91/1.47 (((~c2_1(a936)) | (~hskp17)) <=> ((~hskp17) | (~c2_1(a936)))),
% 1.91/1.47 inference(rewrite,[status(thm)],[])).
% 1.91/1.47 tff(500,axiom,((~c2_1(a936)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause98')).
% 1.91/1.47 tff(501,plain,
% 1.91/1.47 ((~hskp17) | (~c2_1(a936))),
% 1.91/1.47 inference(modus_ponens,[status(thm)],[500, 499])).
% 1.91/1.47 tff(502,plain,
% 1.91/1.47 ((~hskp17) | (~c2_1(a936))),
% 1.91/1.47 inference(modus_ponens,[status(thm)],[501, 498])).
% 1.91/1.47 tff(503,plain,
% 1.91/1.47 (~c2_1(a936)),
% 1.91/1.47 inference(unit_resolution,[status(thm)],[502, 455])).
% 1.91/1.47 tff(504,plain,
% 1.91/1.47 (((~hskp17) | (~c1_1(a936))) <=> ((~hskp17) | (~c1_1(a936)))),
% 1.91/1.47 inference(rewrite,[status(thm)],[])).
% 1.91/1.47 tff(505,plain,
% 1.91/1.47 (((~c1_1(a936)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a936)))),
% 1.91/1.47 inference(rewrite,[status(thm)],[])).
% 1.91/1.47 tff(506,axiom,((~c1_1(a936)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause97')).
% 1.91/1.47 tff(507,plain,
% 1.91/1.47 ((~hskp17) | (~c1_1(a936))),
% 1.91/1.47 inference(modus_ponens,[status(thm)],[506, 505])).
% 1.91/1.47 tff(508,plain,
% 1.91/1.47 ((~hskp17) | (~c1_1(a936))),
% 1.91/1.47 inference(modus_ponens,[status(thm)],[507, 504])).
% 1.91/1.47 tff(509,plain,
% 1.91/1.47 (~c1_1(a936)),
% 1.91/1.47 inference(unit_resolution,[status(thm)],[508, 455])).
% 1.91/1.47 tff(510,assumption,(~c0_1(a936)), introduced(assumption)).
% 1.91/1.47 tff(511,plain,
% 1.91/1.47 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)))),
% 1.91/1.47 inference(bind,[status(th)],[])).
% 1.91/1.47 tff(512,plain,
% 1.91/1.47 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.91/1.47 inference(quant_intro,[status(thm)],[511])).
% 1.91/1.47 tff(513,plain,
% 1.91/1.47 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.91/1.47 inference(rewrite,[status(thm)],[])).
% 1.91/1.47 tff(514,plain,
% 1.91/1.47 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))))),
% 1.91/1.47 inference(bind,[status(th)],[])).
% 1.91/1.47 tff(515,plain,
% 1.91/1.47 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.91/1.47 inference(quant_intro,[status(thm)],[514])).
% 1.91/1.47 tff(516,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause182')).
% 1.91/1.47 tff(517,plain,
% 1.91/1.47 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.91/1.47 inference(modus_ponens,[status(thm)],[516, 515])).
% 1.91/1.47 tff(518,plain,
% 1.91/1.47 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.91/1.47 inference(modus_ponens,[status(thm)],[517, 513])).
% 1.91/1.47 tff(519,plain,(
% 1.91/1.47 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.91/1.47 inference(skolemize,[status(sab)],[518])).
% 1.91/1.47 tff(520,plain,
% 1.91/1.47 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.91/1.47 inference(modus_ponens,[status(thm)],[519, 512])).
% 1.91/1.47 tff(521,assumption,(~c2_1(a936)), introduced(assumption)).
% 1.91/1.47 tff(522,assumption,(~c1_1(a936)), introduced(assumption)).
% 1.91/1.47 tff(523,plain,
% 1.91/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a936) | c2_1(a936) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c0_1(a936))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a936) | c2_1(a936) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c0_1(a936))),
% 1.91/1.47 inference(rewrite,[status(thm)],[])).
% 1.91/1.47 tff(524,plain,
% 1.91/1.47 (((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a936) | c0_1(a936) | c2_1(a936)) <=> (c1_1(a936) | c2_1(a936) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c0_1(a936))),
% 1.91/1.47 inference(rewrite,[status(thm)],[])).
% 1.91/1.47 tff(525,plain,
% 1.91/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a936) | c0_1(a936) | c2_1(a936))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a936) | c2_1(a936) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c0_1(a936)))),
% 1.91/1.47 inference(monotonicity,[status(thm)],[524])).
% 1.91/1.47 tff(526,plain,
% 1.91/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a936) | c0_1(a936) | c2_1(a936))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a936) | c2_1(a936) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c0_1(a936))),
% 1.91/1.47 inference(transitivity,[status(thm)],[525, 523])).
% 1.91/1.47 tff(527,plain,
% 1.91/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a936) | c0_1(a936) | c2_1(a936))),
% 1.91/1.47 inference(quant_inst,[status(thm)],[])).
% 1.91/1.47 tff(528,plain,
% 1.91/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a936) | c2_1(a936) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c0_1(a936)),
% 1.91/1.47 inference(modus_ponens,[status(thm)],[527, 526])).
% 1.91/1.47 tff(529,plain,
% 1.91/1.47 ((~c1_1(a906)) | c0_1(a936)),
% 1.91/1.47 inference(unit_resolution,[status(thm)],[528, 124, 323, 324, 522, 521, 325, 520])).
% 1.91/1.47 tff(530,plain,
% 1.91/1.47 (~c1_1(a906)),
% 1.91/1.47 inference(unit_resolution,[status(thm)],[529, 510])).
% 1.91/1.47 tff(531,plain,
% 1.91/1.47 (^[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)) | 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)) | c1_1(W) | c0_1(W) | c2_1(W)))),
% 1.91/1.47 inference(bind,[status(th)],[])).
% 1.91/1.47 tff(532,plain,
% 1.91/1.47 (![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)) | c1_1(W) | c0_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)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.91/1.47 inference(quant_intro,[status(thm)],[531])).
% 1.91/1.47 tff(533,plain,
% 1.91/1.47 (![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)) | c1_1(W) | c0_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)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.91/1.47 inference(rewrite,[status(thm)],[])).
% 1.91/1.47 tff(534,plain,
% 1.91/1.47 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_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)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_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)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_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)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_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)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_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)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_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)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_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)) | c1_1(W) | c0_1(W) | c2_1(W))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_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))))),
% 1.91/1.47 inference(bind,[status(th)],[])).
% 1.91/1.47 tff(535,plain,
% 1.91/1.47 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_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)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.91/1.47 inference(quant_intro,[status(thm)],[534])).
% 1.91/1.47 tff(536,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause179')).
% 1.91/1.47 tff(537,plain,
% 1.91/1.47 (![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)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.91/1.47 inference(modus_ponens,[status(thm)],[536, 535])).
% 1.91/1.47 tff(538,plain,
% 1.91/1.47 (![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)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.91/1.47 inference(modus_ponens,[status(thm)],[537, 533])).
% 1.91/1.47 tff(539,plain,(
% 1.91/1.47 ![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)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.91/1.47 inference(skolemize,[status(sab)],[538])).
% 1.91/1.47 tff(540,plain,
% 1.91/1.47 (![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)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.91/1.47 inference(modus_ponens,[status(thm)],[539, 532])).
% 1.91/1.47 tff(541,assumption,(~c3_1(a921)), introduced(assumption)).
% 1.91/1.47 tff(542,assumption,(~c0_1(a921)), introduced(assumption)).
% 1.91/1.47 tff(543,assumption,(c2_1(a921)), introduced(assumption)).
% 1.91/1.47 tff(544,plain,
% 1.91/1.47 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a936) | c2_1(a936) | c0_1(a921) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921)) | c0_1(a936))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a936) | c2_1(a936) | c0_1(a921) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921)) | c0_1(a936))),
% 1.91/1.47 inference(rewrite,[status(thm)],[])).
% 1.91/1.47 tff(545,plain,
% 1.91/1.47 (((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a936) | c0_1(a936) | c2_1(a936)) <=> (c1_1(a936) | c2_1(a936) | c0_1(a921) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921)) | c0_1(a936))),
% 1.91/1.47 inference(rewrite,[status(thm)],[])).
% 1.91/1.47 tff(546,plain,
% 1.91/1.47 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a936) | c0_1(a936) | c2_1(a936))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a936) | c2_1(a936) | c0_1(a921) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921)) | c0_1(a936)))),
% 1.91/1.47 inference(monotonicity,[status(thm)],[545])).
% 1.91/1.47 tff(547,plain,
% 1.91/1.47 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a936) | c0_1(a936) | c2_1(a936))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a936) | c2_1(a936) | c0_1(a921) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921)) | c0_1(a936))),
% 1.91/1.47 inference(transitivity,[status(thm)],[546, 544])).
% 1.91/1.47 tff(548,plain,
% 1.91/1.47 ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a936) | c0_1(a936) | c2_1(a936))),
% 1.91/1.47 inference(quant_inst,[status(thm)],[])).
% 1.91/1.47 tff(549,plain,
% 1.91/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a936) | c2_1(a936) | c0_1(a921) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921)) | c0_1(a936)),
% 1.91/1.47 inference(modus_ponens,[status(thm)],[548, 547])).
% 1.91/1.47 tff(550,plain,
% 1.91/1.47 ($false),
% 1.91/1.47 inference(unit_resolution,[status(thm)],[549, 124, 543, 323, 522, 521, 542, 541, 325, 540, 530, 510])).
% 1.91/1.47 tff(551,plain,(c0_1(a936) | (~c2_1(a921)) | (~c0_1(a906)) | c1_1(a936) | c2_1(a936) | c0_1(a921) | c3_1(a921) | c3_1(a906) | (~c2_1(a906))), inference(lemma,lemma(discharge,[]))).
% 1.91/1.47 tff(552,plain,
% 1.91/1.47 (c0_1(a936)),
% 1.91/1.47 inference(unit_resolution,[status(thm)],[551, 509, 323, 243, 503, 232, 226, 325, 324])).
% 1.91/1.47 tff(553,assumption,(c0_1(a936)), introduced(assumption)).
% 1.91/1.47 tff(554,assumption,(~hskp6), introduced(assumption)).
% 1.91/1.47 tff(555,plain,
% 1.91/1.47 (^[U: $i] : refl((hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))),
% 1.91/1.47 inference(bind,[status(th)],[])).
% 1.91/1.47 tff(556,plain,
% 1.91/1.47 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.91/1.47 inference(quant_intro,[status(thm)],[555])).
% 1.91/1.47 tff(557,plain,
% 1.91/1.47 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.91/1.47 inference(rewrite,[status(thm)],[])).
% 1.91/1.47 tff(558,plain,
% 1.91/1.47 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp6))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp6) <=> (hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp7) <=> ((hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp7))), rewrite(((hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp7) <=> (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp7) <=> (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))))),
% 1.91/1.47 inference(bind,[status(th)],[])).
% 1.91/1.47 tff(559,plain,
% 1.91/1.47 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp7) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.91/1.47 inference(quant_intro,[status(thm)],[558])).
% 1.91/1.47 tff(560,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause133')).
% 1.91/1.47 tff(561,plain,
% 1.91/1.47 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.91/1.47 inference(modus_ponens,[status(thm)],[560, 559])).
% 1.91/1.47 tff(562,plain,
% 1.91/1.47 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.91/1.47 inference(modus_ponens,[status(thm)],[561, 557])).
% 1.91/1.47 tff(563,plain,(
% 1.91/1.47 ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.91/1.47 inference(skolemize,[status(sab)],[562])).
% 1.91/1.47 tff(564,plain,
% 1.91/1.47 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.91/1.47 inference(modus_ponens,[status(thm)],[563, 556])).
% 1.91/1.47 tff(565,assumption,(hskp14), introduced(assumption)).
% 1.91/1.47 tff(566,plain,
% 1.91/1.47 (((~hskp14) | (~c1_1(a923))) <=> ((~hskp14) | (~c1_1(a923)))),
% 1.91/1.47 inference(rewrite,[status(thm)],[])).
% 1.91/1.47 tff(567,plain,
% 1.91/1.47 (((~c1_1(a923)) | (~hskp14)) <=> ((~hskp14) | (~c1_1(a923)))),
% 1.91/1.47 inference(rewrite,[status(thm)],[])).
% 1.91/1.47 tff(568,axiom,((~c1_1(a923)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause104')).
% 1.91/1.47 tff(569,plain,
% 1.91/1.47 ((~hskp14) | (~c1_1(a923))),
% 1.91/1.47 inference(modus_ponens,[status(thm)],[568, 567])).
% 1.91/1.47 tff(570,plain,
% 1.91/1.47 ((~hskp14) | (~c1_1(a923))),
% 1.91/1.47 inference(modus_ponens,[status(thm)],[569, 566])).
% 1.91/1.47 tff(571,plain,
% 1.91/1.47 (~c1_1(a923)),
% 1.91/1.47 inference(unit_resolution,[status(thm)],[570, 565])).
% 1.91/1.47 tff(572,plain,
% 1.91/1.47 (((~hskp14) | (~c0_1(a923))) <=> ((~hskp14) | (~c0_1(a923)))),
% 1.91/1.47 inference(rewrite,[status(thm)],[])).
% 1.91/1.47 tff(573,plain,
% 1.91/1.47 (((~c0_1(a923)) | (~hskp14)) <=> ((~hskp14) | (~c0_1(a923)))),
% 1.91/1.47 inference(rewrite,[status(thm)],[])).
% 1.91/1.47 tff(574,axiom,((~c0_1(a923)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause103')).
% 1.91/1.47 tff(575,plain,
% 1.91/1.47 ((~hskp14) | (~c0_1(a923))),
% 1.91/1.47 inference(modus_ponens,[status(thm)],[574, 573])).
% 1.91/1.47 tff(576,plain,
% 1.91/1.47 ((~hskp14) | (~c0_1(a923))),
% 1.91/1.47 inference(modus_ponens,[status(thm)],[575, 572])).
% 1.91/1.47 tff(577,plain,
% 1.91/1.47 (~c0_1(a923)),
% 1.91/1.47 inference(unit_resolution,[status(thm)],[576, 565])).
% 1.91/1.47 tff(578,plain,
% 1.91/1.47 (((~hskp14) | c3_1(a923)) <=> ((~hskp14) | c3_1(a923))),
% 1.91/1.47 inference(rewrite,[status(thm)],[])).
% 1.91/1.47 tff(579,axiom,((~hskp14) | c3_1(a923)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause62')).
% 1.91/1.47 tff(580,plain,
% 1.91/1.47 ((~hskp14) | c3_1(a923)),
% 1.91/1.47 inference(modus_ponens,[status(thm)],[579, 578])).
% 1.91/1.47 tff(581,plain,
% 1.91/1.47 ((~hskp14) | c3_1(a923)),
% 1.91/1.47 inference(modus_ponens,[status(thm)],[580, 578])).
% 1.91/1.47 tff(582,plain,
% 1.91/1.47 ((~hskp14) | c3_1(a923)),
% 1.91/1.47 inference(modus_ponens,[status(thm)],[581, 578])).
% 1.91/1.47 tff(583,plain,
% 1.91/1.47 ((~hskp14) | c3_1(a923)),
% 1.91/1.47 inference(modus_ponens,[status(thm)],[582, 578])).
% 1.91/1.47 tff(584,plain,
% 1.91/1.47 ((~hskp14) | c3_1(a923)),
% 1.91/1.47 inference(modus_ponens,[status(thm)],[583, 578])).
% 1.91/1.47 tff(585,plain,
% 1.91/1.47 ((~hskp14) | c3_1(a923)),
% 1.91/1.47 inference(modus_ponens,[status(thm)],[584, 578])).
% 1.91/1.48 tff(586,plain,
% 1.91/1.48 ((~hskp14) | c3_1(a923)),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[585, 578])).
% 1.91/1.48 tff(587,plain,
% 1.91/1.48 ((~hskp14) | c3_1(a923)),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[586, 578])).
% 1.91/1.48 tff(588,plain,
% 1.91/1.48 (c3_1(a923)),
% 1.91/1.48 inference(unit_resolution,[status(thm)],[587, 565])).
% 1.91/1.48 tff(589,plain,
% 1.91/1.48 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | c0_1(a923) | c1_1(a923) | (~ndr1_0) | (~c3_1(a923)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c0_1(a923) | c1_1(a923) | (~ndr1_0) | (~c3_1(a923)))),
% 1.91/1.48 inference(rewrite,[status(thm)],[])).
% 1.91/1.48 tff(590,plain,
% 1.91/1.48 ((hskp7 | hskp6 | (~ndr1_0) | c1_1(a923) | c0_1(a923) | (~c3_1(a923))) <=> (hskp7 | hskp6 | c0_1(a923) | c1_1(a923) | (~ndr1_0) | (~c3_1(a923)))),
% 1.91/1.48 inference(rewrite,[status(thm)],[])).
% 1.91/1.48 tff(591,plain,
% 1.91/1.48 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a923) | c0_1(a923) | (~c3_1(a923)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | c0_1(a923) | c1_1(a923) | (~ndr1_0) | (~c3_1(a923))))),
% 1.91/1.48 inference(monotonicity,[status(thm)],[590])).
% 1.91/1.48 tff(592,plain,
% 1.91/1.48 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a923) | c0_1(a923) | (~c3_1(a923)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c0_1(a923) | c1_1(a923) | (~ndr1_0) | (~c3_1(a923)))),
% 1.91/1.48 inference(transitivity,[status(thm)],[591, 589])).
% 1.91/1.48 tff(593,plain,
% 1.91/1.48 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a923) | c0_1(a923) | (~c3_1(a923)))),
% 1.91/1.48 inference(quant_inst,[status(thm)],[])).
% 1.91/1.48 tff(594,plain,
% 1.91/1.48 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c0_1(a923) | c1_1(a923) | (~ndr1_0) | (~c3_1(a923))),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[593, 592])).
% 1.91/1.48 tff(595,plain,
% 1.91/1.48 ($false),
% 1.91/1.48 inference(unit_resolution,[status(thm)],[594, 124, 21, 554, 588, 577, 571, 564])).
% 1.91/1.48 tff(596,plain,((~hskp14) | hskp7 | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.91/1.48 tff(597,plain,
% 1.91/1.48 (~hskp14),
% 1.91/1.48 inference(unit_resolution,[status(thm)],[596, 554, 21])).
% 1.91/1.48 tff(598,plain,
% 1.91/1.48 (^[U: $i] : refl((hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))),
% 1.91/1.48 inference(bind,[status(th)],[])).
% 1.91/1.48 tff(599,plain,
% 1.91/1.48 (![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.91/1.48 inference(quant_intro,[status(thm)],[598])).
% 1.91/1.48 tff(600,plain,
% 1.91/1.48 (![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.91/1.48 inference(rewrite,[status(thm)],[])).
% 1.91/1.48 tff(601,plain,
% 1.91/1.48 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp6) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp6))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp14) <=> ((hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp14))), rewrite(((hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp14) <=> (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp14) <=> (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))))),
% 1.91/1.48 inference(bind,[status(th)],[])).
% 1.91/1.48 tff(602,plain,
% 1.91/1.48 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp14) <=> ![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.91/1.48 inference(quant_intro,[status(thm)],[601])).
% 1.91/1.48 tff(603,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause142')).
% 1.91/1.48 tff(604,plain,
% 1.91/1.48 (![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[603, 602])).
% 1.91/1.48 tff(605,plain,
% 1.91/1.48 (![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[604, 600])).
% 1.91/1.48 tff(606,plain,(
% 1.91/1.48 ![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.91/1.48 inference(skolemize,[status(sab)],[605])).
% 1.91/1.48 tff(607,plain,
% 1.91/1.48 (![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[606, 599])).
% 1.91/1.48 tff(608,assumption,(~c3_1(a936)), introduced(assumption)).
% 1.91/1.48 tff(609,plain,
% 1.91/1.48 (((~![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp14 | hskp6 | c2_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936)))) <=> ((~![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp14 | hskp6 | c2_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936)))),
% 1.91/1.48 inference(rewrite,[status(thm)],[])).
% 1.91/1.48 tff(610,plain,
% 1.91/1.48 ((hskp14 | hskp6 | (~ndr1_0) | c2_1(a936) | c3_1(a936) | (~c0_1(a936))) <=> (hskp14 | hskp6 | c2_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936)))),
% 1.91/1.48 inference(rewrite,[status(thm)],[])).
% 1.91/1.48 tff(611,plain,
% 1.91/1.48 (((~![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp14 | hskp6 | (~ndr1_0) | c2_1(a936) | c3_1(a936) | (~c0_1(a936)))) <=> ((~![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp14 | hskp6 | c2_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936))))),
% 1.91/1.48 inference(monotonicity,[status(thm)],[610])).
% 1.91/1.48 tff(612,plain,
% 1.91/1.48 (((~![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp14 | hskp6 | (~ndr1_0) | c2_1(a936) | c3_1(a936) | (~c0_1(a936)))) <=> ((~![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp14 | hskp6 | c2_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936)))),
% 1.91/1.48 inference(transitivity,[status(thm)],[611, 609])).
% 1.91/1.48 tff(613,plain,
% 1.91/1.48 ((~![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp14 | hskp6 | (~ndr1_0) | c2_1(a936) | c3_1(a936) | (~c0_1(a936)))),
% 1.91/1.48 inference(quant_inst,[status(thm)],[])).
% 1.91/1.48 tff(614,plain,
% 1.91/1.48 ((~![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp14 | hskp6 | c2_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936))),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[613, 612])).
% 1.91/1.48 tff(615,plain,
% 1.91/1.48 (hskp14 | hskp6 | (~c0_1(a936))),
% 1.91/1.48 inference(unit_resolution,[status(thm)],[614, 124, 521, 608, 607])).
% 1.91/1.48 tff(616,plain,
% 1.91/1.48 ($false),
% 1.91/1.48 inference(unit_resolution,[status(thm)],[615, 597, 554, 553])).
% 1.91/1.48 tff(617,plain,(hskp6 | (~c0_1(a936)) | c2_1(a936) | c3_1(a936) | hskp7), inference(lemma,lemma(discharge,[]))).
% 1.91/1.48 tff(618,plain,
% 1.91/1.48 ($false),
% 1.91/1.48 inference(unit_resolution,[status(thm)],[617, 552, 503, 497, 461, 438])).
% 1.91/1.48 tff(619,plain,(hskp10 | (~c0_1(a906)) | c3_1(a906) | (~c2_1(a906)) | hskp21 | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.91/1.48 tff(620,plain,
% 1.91/1.48 ($false),
% 1.91/1.48 inference(unit_resolution,[status(thm)],[619, 378, 326, 325, 324, 198, 323])).
% 1.91/1.48 tff(621,plain,(hskp10 | c3_1(a906) | (~c2_1(a906)) | hskp21 | (~c0_1(a906))), inference(lemma,lemma(discharge,[]))).
% 1.91/1.48 tff(622,plain,
% 1.91/1.48 (hskp10),
% 1.91/1.48 inference(unit_resolution,[status(thm)],[621, 325, 324, 198, 323])).
% 1.91/1.48 tff(623,plain,
% 1.91/1.48 (((~hskp10) | (~c0_1(a912))) <=> ((~hskp10) | (~c0_1(a912)))),
% 1.91/1.48 inference(rewrite,[status(thm)],[])).
% 1.91/1.48 tff(624,plain,
% 1.91/1.48 (((~c0_1(a912)) | (~hskp10)) <=> ((~hskp10) | (~c0_1(a912)))),
% 1.91/1.48 inference(rewrite,[status(thm)],[])).
% 1.91/1.48 tff(625,axiom,((~c0_1(a912)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause109')).
% 1.91/1.48 tff(626,plain,
% 1.91/1.48 ((~hskp10) | (~c0_1(a912))),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[625, 624])).
% 1.91/1.48 tff(627,plain,
% 1.91/1.48 ((~hskp10) | (~c0_1(a912))),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[626, 623])).
% 1.91/1.48 tff(628,plain,
% 1.91/1.48 (~c0_1(a912)),
% 1.91/1.48 inference(unit_resolution,[status(thm)],[627, 622])).
% 1.91/1.48 tff(629,plain,
% 1.91/1.48 (^[U: $i] : refl((hskp2 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp2 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))),
% 1.91/1.48 inference(bind,[status(th)],[])).
% 1.91/1.48 tff(630,plain,
% 1.91/1.48 (![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.91/1.48 inference(quant_intro,[status(thm)],[629])).
% 1.91/1.48 tff(631,plain,
% 1.91/1.48 (![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.91/1.48 inference(rewrite,[status(thm)],[])).
% 1.91/1.48 tff(632,plain,
% 1.91/1.48 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp2) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp2))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp2) <=> (hskp2 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp2) | hskp0) <=> ((hskp2 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp0))), rewrite(((hskp2 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp0) <=> (hskp2 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp2) | hskp0) <=> (hskp2 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))))),
% 1.91/1.48 inference(bind,[status(th)],[])).
% 1.91/1.48 tff(633,plain,
% 1.91/1.48 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp2) | hskp0) <=> ![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.91/1.48 inference(quant_intro,[status(thm)],[632])).
% 1.91/1.48 tff(634,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp2) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause136')).
% 1.91/1.48 tff(635,plain,
% 1.91/1.48 (![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[634, 633])).
% 1.91/1.48 tff(636,plain,
% 1.91/1.48 (![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[635, 631])).
% 1.91/1.48 tff(637,plain,(
% 1.91/1.48 ![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.91/1.48 inference(skolemize,[status(sab)],[636])).
% 1.91/1.48 tff(638,plain,
% 1.91/1.48 (![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[637, 630])).
% 1.91/1.48 tff(639,assumption,(~hskp2), introduced(assumption)).
% 1.91/1.48 tff(640,plain,
% 1.91/1.48 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp0 | c0_1(a921) | c3_1(a921) | (~ndr1_0) | (~c2_1(a921)))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp2 | hskp0 | c0_1(a921) | c3_1(a921) | (~ndr1_0) | (~c2_1(a921)))),
% 1.91/1.48 inference(rewrite,[status(thm)],[])).
% 1.91/1.48 tff(641,plain,
% 1.91/1.48 ((hskp2 | hskp0 | (~ndr1_0) | c0_1(a921) | c3_1(a921) | (~c2_1(a921))) <=> (hskp2 | hskp0 | c0_1(a921) | c3_1(a921) | (~ndr1_0) | (~c2_1(a921)))),
% 1.91/1.48 inference(rewrite,[status(thm)],[])).
% 1.91/1.48 tff(642,plain,
% 1.91/1.48 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp0 | (~ndr1_0) | c0_1(a921) | c3_1(a921) | (~c2_1(a921)))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp0 | c0_1(a921) | c3_1(a921) | (~ndr1_0) | (~c2_1(a921))))),
% 1.91/1.48 inference(monotonicity,[status(thm)],[641])).
% 1.91/1.48 tff(643,plain,
% 1.91/1.48 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp0 | (~ndr1_0) | c0_1(a921) | c3_1(a921) | (~c2_1(a921)))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp2 | hskp0 | c0_1(a921) | c3_1(a921) | (~ndr1_0) | (~c2_1(a921)))),
% 1.91/1.48 inference(transitivity,[status(thm)],[642, 640])).
% 1.91/1.48 tff(644,plain,
% 1.91/1.48 ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp2 | hskp0 | (~ndr1_0) | c0_1(a921) | c3_1(a921) | (~c2_1(a921)))),
% 1.91/1.48 inference(quant_inst,[status(thm)],[])).
% 1.91/1.48 tff(645,plain,
% 1.91/1.48 ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp2 | hskp0 | c0_1(a921) | c3_1(a921) | (~ndr1_0) | (~c2_1(a921))),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[644, 643])).
% 1.91/1.48 tff(646,plain,
% 1.91/1.48 (hskp0),
% 1.91/1.48 inference(unit_resolution,[status(thm)],[645, 124, 639, 243, 232, 226, 638])).
% 1.91/1.48 tff(647,plain,
% 1.91/1.48 (((~hskp0) | (~c3_1(a901))) <=> ((~hskp0) | (~c3_1(a901)))),
% 1.91/1.48 inference(rewrite,[status(thm)],[])).
% 1.91/1.48 tff(648,plain,
% 1.91/1.48 (((~c3_1(a901)) | (~hskp0)) <=> ((~hskp0) | (~c3_1(a901)))),
% 1.91/1.48 inference(rewrite,[status(thm)],[])).
% 1.91/1.48 tff(649,axiom,((~c3_1(a901)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause127')).
% 1.91/1.48 tff(650,plain,
% 1.91/1.48 ((~hskp0) | (~c3_1(a901))),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[649, 648])).
% 1.91/1.48 tff(651,plain,
% 1.91/1.48 ((~hskp0) | (~c3_1(a901))),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[650, 647])).
% 1.91/1.48 tff(652,plain,
% 1.91/1.48 (~c3_1(a901)),
% 1.91/1.48 inference(unit_resolution,[status(thm)],[651, 646])).
% 1.91/1.48 tff(653,plain,
% 1.91/1.48 (((~hskp0) | (~c1_1(a901))) <=> ((~hskp0) | (~c1_1(a901)))),
% 1.91/1.48 inference(rewrite,[status(thm)],[])).
% 1.91/1.48 tff(654,plain,
% 1.91/1.48 (((~c1_1(a901)) | (~hskp0)) <=> ((~hskp0) | (~c1_1(a901)))),
% 1.91/1.48 inference(rewrite,[status(thm)],[])).
% 1.91/1.48 tff(655,axiom,((~c1_1(a901)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause126')).
% 1.91/1.48 tff(656,plain,
% 1.91/1.48 ((~hskp0) | (~c1_1(a901))),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[655, 654])).
% 1.91/1.48 tff(657,plain,
% 1.91/1.48 ((~hskp0) | (~c1_1(a901))),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[656, 653])).
% 1.91/1.48 tff(658,plain,
% 1.91/1.48 (~c1_1(a901)),
% 1.91/1.48 inference(unit_resolution,[status(thm)],[657, 646])).
% 1.91/1.48 tff(659,plain,
% 1.91/1.48 (((~hskp0) | (~c0_1(a901))) <=> ((~hskp0) | (~c0_1(a901)))),
% 1.91/1.48 inference(rewrite,[status(thm)],[])).
% 1.91/1.48 tff(660,plain,
% 1.91/1.48 (((~c0_1(a901)) | (~hskp0)) <=> ((~hskp0) | (~c0_1(a901)))),
% 1.91/1.48 inference(rewrite,[status(thm)],[])).
% 1.91/1.48 tff(661,axiom,((~c0_1(a901)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause125')).
% 1.91/1.48 tff(662,plain,
% 1.91/1.48 ((~hskp0) | (~c0_1(a901))),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[661, 660])).
% 1.91/1.48 tff(663,plain,
% 1.91/1.48 ((~hskp0) | (~c0_1(a901))),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[662, 659])).
% 1.91/1.48 tff(664,plain,
% 1.91/1.48 (~c0_1(a901)),
% 1.91/1.48 inference(unit_resolution,[status(thm)],[663, 646])).
% 1.91/1.48 tff(665,assumption,(~c0_1(a912)), introduced(assumption)).
% 1.91/1.48 tff(666,plain,
% 1.91/1.48 (hskp10),
% 1.91/1.48 inference(unit_resolution,[status(thm)],[619, 32, 325, 324, 198, 323])).
% 1.91/1.48 tff(667,plain,
% 1.91/1.48 (((~hskp10) | c2_1(a912)) <=> ((~hskp10) | c2_1(a912))),
% 1.91/1.48 inference(rewrite,[status(thm)],[])).
% 1.91/1.48 tff(668,axiom,((~hskp10) | c2_1(a912)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause69')).
% 1.91/1.48 tff(669,plain,
% 1.91/1.48 ((~hskp10) | c2_1(a912)),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[668, 667])).
% 1.91/1.48 tff(670,plain,
% 1.91/1.48 ((~hskp10) | c2_1(a912)),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[669, 667])).
% 1.91/1.48 tff(671,plain,
% 1.91/1.48 ((~hskp10) | c2_1(a912)),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[670, 667])).
% 1.91/1.48 tff(672,plain,
% 1.91/1.48 ((~hskp10) | c2_1(a912)),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[671, 667])).
% 1.91/1.48 tff(673,plain,
% 1.91/1.48 ((~hskp10) | c2_1(a912)),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[672, 667])).
% 1.91/1.48 tff(674,plain,
% 1.91/1.48 ((~hskp10) | c2_1(a912)),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[673, 667])).
% 1.91/1.48 tff(675,plain,
% 1.91/1.48 ((~hskp10) | c2_1(a912)),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[674, 667])).
% 1.91/1.48 tff(676,plain,
% 1.91/1.48 ((~hskp10) | c2_1(a912)),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[675, 667])).
% 1.91/1.48 tff(677,plain,
% 1.91/1.48 (c2_1(a912)),
% 1.91/1.48 inference(unit_resolution,[status(thm)],[676, 666])).
% 1.91/1.48 tff(678,plain,
% 1.91/1.48 (((~hskp10) | c1_1(a912)) <=> ((~hskp10) | c1_1(a912))),
% 1.91/1.48 inference(rewrite,[status(thm)],[])).
% 1.91/1.48 tff(679,axiom,((~hskp10) | c1_1(a912)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause68')).
% 1.91/1.48 tff(680,plain,
% 1.91/1.48 ((~hskp10) | c1_1(a912)),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[679, 678])).
% 1.91/1.48 tff(681,plain,
% 1.91/1.48 ((~hskp10) | c1_1(a912)),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[680, 678])).
% 1.91/1.48 tff(682,plain,
% 1.91/1.48 ((~hskp10) | c1_1(a912)),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[681, 678])).
% 1.91/1.48 tff(683,plain,
% 1.91/1.48 ((~hskp10) | c1_1(a912)),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[682, 678])).
% 1.91/1.48 tff(684,plain,
% 1.91/1.48 ((~hskp10) | c1_1(a912)),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[683, 678])).
% 1.91/1.48 tff(685,plain,
% 1.91/1.48 ((~hskp10) | c1_1(a912)),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[684, 678])).
% 1.91/1.48 tff(686,plain,
% 1.91/1.48 ((~hskp10) | c1_1(a912)),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[685, 678])).
% 1.91/1.48 tff(687,plain,
% 1.91/1.48 ((~hskp10) | c1_1(a912)),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[686, 678])).
% 1.91/1.48 tff(688,plain,
% 1.91/1.48 (c1_1(a912)),
% 1.91/1.48 inference(unit_resolution,[status(thm)],[687, 666])).
% 1.91/1.48 tff(689,assumption,(c2_1(a912)), introduced(assumption)).
% 1.91/1.48 tff(690,assumption,(c1_1(a912)), introduced(assumption)).
% 1.91/1.48 tff(691,plain,
% 1.91/1.48 (^[U: $i] : refl((hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))),
% 1.91/1.48 inference(bind,[status(th)],[])).
% 1.91/1.48 tff(692,plain,
% 1.91/1.48 (![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.91/1.48 inference(quant_intro,[status(thm)],[691])).
% 1.91/1.48 tff(693,plain,
% 1.91/1.48 (![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.91/1.48 inference(rewrite,[status(thm)],[])).
% 1.91/1.48 tff(694,plain,
% 1.91/1.48 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp7) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp7))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp7) <=> (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp7) | hskp14) <=> ((hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp14))), rewrite(((hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp14) <=> (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp7) | hskp14) <=> (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))))),
% 1.91/1.48 inference(bind,[status(th)],[])).
% 1.91/1.48 tff(695,plain,
% 1.91/1.48 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp7) | hskp14) <=> ![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.91/1.48 inference(quant_intro,[status(thm)],[694])).
% 1.91/1.48 tff(696,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp7) | hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause146')).
% 1.91/1.48 tff(697,plain,
% 1.91/1.48 (![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[696, 695])).
% 1.91/1.48 tff(698,plain,
% 1.91/1.48 (![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[697, 693])).
% 1.91/1.48 tff(699,plain,(
% 1.91/1.48 ![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.91/1.48 inference(skolemize,[status(sab)],[698])).
% 1.91/1.48 tff(700,plain,
% 1.91/1.48 (![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[699, 692])).
% 1.91/1.48 tff(701,plain,
% 1.91/1.48 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp14 | hskp7 | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)))),
% 1.91/1.48 inference(rewrite,[status(thm)],[])).
% 1.91/1.48 tff(702,plain,
% 1.91/1.48 ((hskp14 | hskp7 | (~ndr1_0) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912))) <=> (hskp14 | hskp7 | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)))),
% 1.91/1.48 inference(rewrite,[status(thm)],[])).
% 1.91/1.48 tff(703,plain,
% 1.91/1.48 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912))))),
% 1.91/1.48 inference(monotonicity,[status(thm)],[702])).
% 1.91/1.48 tff(704,plain,
% 1.91/1.48 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp14 | hskp7 | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)))),
% 1.91/1.48 inference(transitivity,[status(thm)],[703, 701])).
% 1.91/1.48 tff(705,plain,
% 1.91/1.48 ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))),
% 1.91/1.48 inference(quant_inst,[status(thm)],[])).
% 1.91/1.48 tff(706,plain,
% 1.91/1.48 ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp14 | hskp7 | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912))),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[705, 704])).
% 1.91/1.48 tff(707,plain,
% 1.91/1.48 (hskp14 | hskp7 | (~c2_1(a912)) | (~c1_1(a912))),
% 1.91/1.48 inference(unit_resolution,[status(thm)],[706, 124, 665, 700])).
% 1.91/1.48 tff(708,plain,
% 1.91/1.48 (hskp14),
% 1.91/1.48 inference(unit_resolution,[status(thm)],[707, 21, 690, 689])).
% 1.91/1.48 tff(709,plain,
% 1.91/1.48 (~c1_1(a923)),
% 1.91/1.48 inference(unit_resolution,[status(thm)],[570, 708])).
% 1.91/1.48 tff(710,plain,
% 1.91/1.48 (~c0_1(a923)),
% 1.91/1.48 inference(unit_resolution,[status(thm)],[576, 708])).
% 1.91/1.48 tff(711,plain,
% 1.91/1.48 (c3_1(a923)),
% 1.91/1.48 inference(unit_resolution,[status(thm)],[587, 708])).
% 1.91/1.48 tff(712,plain,
% 1.91/1.48 ($false),
% 1.91/1.48 inference(unit_resolution,[status(thm)],[594, 124, 21, 554, 711, 710, 709, 564])).
% 1.91/1.48 tff(713,plain,(hskp7 | hskp6 | (~c1_1(a912)) | (~c2_1(a912)) | c0_1(a912)), inference(lemma,lemma(discharge,[]))).
% 1.91/1.48 tff(714,plain,
% 1.91/1.48 (hskp6),
% 1.91/1.48 inference(unit_resolution,[status(thm)],[713, 688, 497, 677, 665])).
% 1.91/1.48 tff(715,plain,
% 1.91/1.48 (~c2_1(a907)),
% 1.91/1.48 inference(unit_resolution,[status(thm)],[407, 714])).
% 1.91/1.48 tff(716,plain,
% 1.91/1.48 (((~hskp6) | c0_1(a907)) <=> ((~hskp6) | c0_1(a907))),
% 1.91/1.48 inference(rewrite,[status(thm)],[])).
% 1.91/1.48 tff(717,axiom,((~hskp6) | c0_1(a907)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause73')).
% 1.91/1.48 tff(718,plain,
% 1.91/1.48 ((~hskp6) | c0_1(a907)),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[717, 716])).
% 1.91/1.48 tff(719,plain,
% 1.91/1.48 ((~hskp6) | c0_1(a907)),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[718, 716])).
% 1.91/1.48 tff(720,plain,
% 1.91/1.48 ((~hskp6) | c0_1(a907)),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[719, 716])).
% 1.91/1.48 tff(721,plain,
% 1.91/1.48 ((~hskp6) | c0_1(a907)),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[720, 716])).
% 1.91/1.48 tff(722,plain,
% 1.91/1.48 ((~hskp6) | c0_1(a907)),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[721, 716])).
% 1.91/1.48 tff(723,plain,
% 1.91/1.48 ((~hskp6) | c0_1(a907)),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[722, 716])).
% 1.91/1.48 tff(724,plain,
% 1.91/1.48 ((~hskp6) | c0_1(a907)),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[723, 716])).
% 1.91/1.48 tff(725,plain,
% 1.91/1.48 ((~hskp6) | c0_1(a907)),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[724, 716])).
% 1.91/1.48 tff(726,plain,
% 1.91/1.48 (c0_1(a907)),
% 1.91/1.48 inference(unit_resolution,[status(thm)],[725, 714])).
% 1.91/1.48 tff(727,plain,
% 1.91/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a912) | c2_1(a907) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a912) | c2_1(a907) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c2_1(a912)) | (~c1_1(a912)))),
% 1.91/1.48 inference(rewrite,[status(thm)],[])).
% 1.91/1.48 tff(728,plain,
% 1.91/1.48 (((~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c0_1(a907)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a901) | c1_1(a901) | c0_1(a901)) <=> (c0_1(a912) | c2_1(a907) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c2_1(a912)) | (~c1_1(a912)))),
% 1.91/1.48 inference(rewrite,[status(thm)],[])).
% 1.91/1.48 tff(729,plain,
% 1.91/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c0_1(a907)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a901) | c1_1(a901) | c0_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a912) | c2_1(a907) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c2_1(a912)) | (~c1_1(a912))))),
% 1.91/1.48 inference(monotonicity,[status(thm)],[728])).
% 1.91/1.48 tff(730,plain,
% 1.91/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c0_1(a907)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a901) | c1_1(a901) | c0_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a912) | c2_1(a907) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c2_1(a912)) | (~c1_1(a912)))),
% 1.91/1.48 inference(transitivity,[status(thm)],[729, 727])).
% 1.91/1.48 tff(731,plain,
% 1.91/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c0_1(a907)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a901) | c1_1(a901) | c0_1(a901))),
% 1.91/1.48 inference(quant_inst,[status(thm)],[])).
% 1.91/1.48 tff(732,plain,
% 1.91/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a912) | c2_1(a907) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c2_1(a912)) | (~c1_1(a912))),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[731, 730])).
% 1.91/1.48 tff(733,plain,
% 1.91/1.48 (c3_1(a907)),
% 1.91/1.48 inference(unit_resolution,[status(thm)],[732, 124, 688, 677, 726, 665, 715, 664, 658, 652, 322])).
% 1.91/1.48 tff(734,plain,
% 1.91/1.48 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))))),
% 1.91/1.48 inference(bind,[status(th)],[])).
% 1.91/1.48 tff(735,plain,
% 1.91/1.48 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.91/1.48 inference(quant_intro,[status(thm)],[734])).
% 1.91/1.48 tff(736,plain,
% 1.91/1.48 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.91/1.48 inference(rewrite,[status(thm)],[])).
% 1.91/1.48 tff(737,plain,
% 1.91/1.48 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(W)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(W))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))))),
% 1.91/1.49 inference(bind,[status(th)],[])).
% 1.91/1.49 tff(738,plain,
% 1.91/1.49 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.91/1.49 inference(quant_intro,[status(thm)],[737])).
% 1.91/1.49 tff(739,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause183')).
% 1.91/1.49 tff(740,plain,
% 1.91/1.49 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[739, 738])).
% 1.91/1.49 tff(741,plain,
% 1.91/1.49 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[740, 736])).
% 1.91/1.49 tff(742,plain,(
% 1.91/1.49 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.91/1.49 inference(skolemize,[status(sab)],[741])).
% 1.91/1.49 tff(743,plain,
% 1.91/1.49 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[742, 735])).
% 1.91/1.49 tff(744,plain,
% 1.91/1.49 (c1_1(a907)),
% 1.91/1.49 inference(unit_resolution,[status(thm)],[418, 714])).
% 1.91/1.49 tff(745,plain,
% 1.91/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a921) | c0_1(a912) | c2_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921) | (~c2_1(a921)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a921) | c0_1(a912) | c2_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921) | (~c2_1(a921)))),
% 1.91/1.49 inference(rewrite,[status(thm)],[])).
% 1.91/1.49 tff(746,plain,
% 1.91/1.49 (((~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907)) | c3_1(a921) | c1_1(a921) | (~c2_1(a921)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912))) <=> (c3_1(a921) | c0_1(a912) | c2_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921) | (~c2_1(a921)))),
% 1.91/1.49 inference(rewrite,[status(thm)],[])).
% 1.91/1.49 tff(747,plain,
% 1.91/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907)) | c3_1(a921) | c1_1(a921) | (~c2_1(a921)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a921) | c0_1(a912) | c2_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921) | (~c2_1(a921))))),
% 1.91/1.49 inference(monotonicity,[status(thm)],[746])).
% 1.91/1.49 tff(748,plain,
% 1.91/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907)) | c3_1(a921) | c1_1(a921) | (~c2_1(a921)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a921) | c0_1(a912) | c2_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921) | (~c2_1(a921)))),
% 1.91/1.49 inference(transitivity,[status(thm)],[747, 745])).
% 1.91/1.49 tff(749,plain,
% 1.91/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907)) | c3_1(a921) | c1_1(a921) | (~c2_1(a921)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))),
% 1.91/1.49 inference(quant_inst,[status(thm)],[])).
% 1.91/1.49 tff(750,plain,
% 1.91/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a921) | c0_1(a912) | c2_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921) | (~c2_1(a921))),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[749, 748])).
% 1.91/1.49 tff(751,plain,
% 1.91/1.49 ((~c3_1(a907)) | c1_1(a921)),
% 1.91/1.49 inference(unit_resolution,[status(thm)],[750, 124, 243, 688, 677, 744, 226, 665, 715, 743])).
% 1.91/1.49 tff(752,plain,
% 1.91/1.49 (c1_1(a921)),
% 1.91/1.49 inference(unit_resolution,[status(thm)],[751, 733])).
% 1.91/1.49 tff(753,plain,
% 1.91/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a912) | c2_1(a907) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a912) | c2_1(a907) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a912)) | (~c1_1(a912)))),
% 1.91/1.49 inference(rewrite,[status(thm)],[])).
% 1.91/1.49 tff(754,plain,
% 1.91/1.49 (((~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907)) | c3_1(a901) | c1_1(a901) | (~c2_1(a901)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912))) <=> (c0_1(a912) | c2_1(a907) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a912)) | (~c1_1(a912)))),
% 1.91/1.49 inference(rewrite,[status(thm)],[])).
% 1.91/1.49 tff(755,plain,
% 1.91/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907)) | c3_1(a901) | c1_1(a901) | (~c2_1(a901)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a912) | c2_1(a907) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a912)) | (~c1_1(a912))))),
% 1.91/1.49 inference(monotonicity,[status(thm)],[754])).
% 1.91/1.49 tff(756,plain,
% 1.91/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907)) | c3_1(a901) | c1_1(a901) | (~c2_1(a901)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a912) | c2_1(a907) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a912)) | (~c1_1(a912)))),
% 1.91/1.49 inference(transitivity,[status(thm)],[755, 753])).
% 1.91/1.49 tff(757,plain,
% 1.91/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907)) | c3_1(a901) | c1_1(a901) | (~c2_1(a901)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))),
% 1.91/1.49 inference(quant_inst,[status(thm)],[])).
% 1.91/1.49 tff(758,plain,
% 1.91/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a912) | c2_1(a907) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a912)) | (~c1_1(a912))),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[757, 756])).
% 1.91/1.49 tff(759,plain,
% 1.91/1.49 ((~c2_1(a901)) | (~c3_1(a907))),
% 1.91/1.49 inference(unit_resolution,[status(thm)],[758, 124, 688, 677, 744, 665, 715, 658, 652, 743])).
% 1.91/1.49 tff(760,plain,
% 1.91/1.49 (~c2_1(a901)),
% 1.91/1.49 inference(unit_resolution,[status(thm)],[759, 733])).
% 1.91/1.49 tff(761,plain,
% 1.91/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a921) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c3_1(a921) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921)))),
% 1.91/1.49 inference(rewrite,[status(thm)],[])).
% 1.91/1.49 tff(762,plain,
% 1.91/1.49 (((~ndr1_0) | c3_1(a921) | (~c2_1(a921)) | (~c1_1(a921)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a901) | c0_1(a901) | c2_1(a901)) <=> (c3_1(a921) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921)))),
% 1.91/1.49 inference(rewrite,[status(thm)],[])).
% 1.91/1.49 tff(763,plain,
% 1.91/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a921) | (~c2_1(a921)) | (~c1_1(a921)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a901) | c0_1(a901) | c2_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a921) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921))))),
% 1.91/1.49 inference(monotonicity,[status(thm)],[762])).
% 1.91/1.49 tff(764,plain,
% 1.91/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a921) | (~c2_1(a921)) | (~c1_1(a921)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a901) | c0_1(a901) | c2_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c3_1(a921) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921)))),
% 1.91/1.49 inference(transitivity,[status(thm)],[763, 761])).
% 1.91/1.49 tff(765,plain,
% 1.91/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a921) | (~c2_1(a921)) | (~c1_1(a921)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a901) | c0_1(a901) | c2_1(a901))),
% 1.91/1.49 inference(quant_inst,[status(thm)],[])).
% 1.91/1.49 tff(766,plain,
% 1.91/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c3_1(a921) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921))),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[765, 764])).
% 1.91/1.49 tff(767,plain,
% 1.91/1.49 (c2_1(a901) | (~c1_1(a921))),
% 1.91/1.49 inference(unit_resolution,[status(thm)],[766, 124, 243, 323, 324, 226, 325, 664, 658, 520])).
% 1.91/1.49 tff(768,plain,
% 1.91/1.49 ($false),
% 1.91/1.49 inference(unit_resolution,[status(thm)],[767, 760, 752])).
% 1.91/1.49 tff(769,plain,(hskp12 | (~c0_1(a906)) | (~c2_1(a906)) | c3_1(a906) | c0_1(a912) | hskp21 | hskp2), inference(lemma,lemma(discharge,[]))).
% 1.91/1.49 tff(770,plain,
% 1.91/1.49 (hskp2),
% 1.91/1.49 inference(unit_resolution,[status(thm)],[769, 32, 324, 325, 323, 198, 628])).
% 1.91/1.49 tff(771,plain,
% 1.91/1.49 (((~hskp2) | (~c3_1(a903))) <=> ((~hskp2) | (~c3_1(a903)))),
% 1.91/1.49 inference(rewrite,[status(thm)],[])).
% 1.91/1.49 tff(772,plain,
% 1.91/1.49 (((~c3_1(a903)) | (~hskp2)) <=> ((~hskp2) | (~c3_1(a903)))),
% 1.91/1.49 inference(rewrite,[status(thm)],[])).
% 1.91/1.49 tff(773,axiom,((~c3_1(a903)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause123')).
% 1.91/1.49 tff(774,plain,
% 1.91/1.49 ((~hskp2) | (~c3_1(a903))),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[773, 772])).
% 1.91/1.49 tff(775,plain,
% 1.91/1.49 ((~hskp2) | (~c3_1(a903))),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[774, 771])).
% 1.91/1.49 tff(776,plain,
% 1.91/1.49 (~c3_1(a903)),
% 1.91/1.49 inference(unit_resolution,[status(thm)],[775, 770])).
% 1.91/1.49 tff(777,plain,
% 1.91/1.49 (((~hskp2) | (~c2_1(a903))) <=> ((~hskp2) | (~c2_1(a903)))),
% 1.91/1.49 inference(rewrite,[status(thm)],[])).
% 1.91/1.49 tff(778,plain,
% 1.91/1.49 (((~c2_1(a903)) | (~hskp2)) <=> ((~hskp2) | (~c2_1(a903)))),
% 1.91/1.49 inference(rewrite,[status(thm)],[])).
% 1.91/1.49 tff(779,axiom,((~c2_1(a903)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause122')).
% 1.91/1.49 tff(780,plain,
% 1.91/1.49 ((~hskp2) | (~c2_1(a903))),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[779, 778])).
% 1.91/1.49 tff(781,plain,
% 1.91/1.49 ((~hskp2) | (~c2_1(a903))),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[780, 777])).
% 1.91/1.49 tff(782,plain,
% 1.91/1.49 (~c2_1(a903)),
% 1.91/1.49 inference(unit_resolution,[status(thm)],[781, 770])).
% 1.91/1.49 tff(783,plain,
% 1.91/1.49 (((~hskp2) | c0_1(a903)) <=> ((~hskp2) | c0_1(a903))),
% 1.91/1.49 inference(rewrite,[status(thm)],[])).
% 1.91/1.49 tff(784,axiom,((~hskp2) | c0_1(a903)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause79')).
% 1.91/1.49 tff(785,plain,
% 1.91/1.49 ((~hskp2) | c0_1(a903)),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[784, 783])).
% 1.91/1.49 tff(786,plain,
% 1.91/1.49 ((~hskp2) | c0_1(a903)),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[785, 783])).
% 1.91/1.49 tff(787,plain,
% 1.91/1.49 ((~hskp2) | c0_1(a903)),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[786, 783])).
% 1.91/1.49 tff(788,plain,
% 1.91/1.49 ((~hskp2) | c0_1(a903)),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[787, 783])).
% 1.91/1.49 tff(789,plain,
% 1.91/1.49 ((~hskp2) | c0_1(a903)),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[788, 783])).
% 1.91/1.49 tff(790,plain,
% 1.91/1.49 ((~hskp2) | c0_1(a903)),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[789, 783])).
% 1.91/1.49 tff(791,plain,
% 1.91/1.49 ((~hskp2) | c0_1(a903)),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[790, 783])).
% 1.91/1.49 tff(792,plain,
% 1.91/1.49 ((~hskp2) | c0_1(a903)),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[791, 783])).
% 1.91/1.49 tff(793,plain,
% 1.91/1.49 (c0_1(a903)),
% 1.91/1.49 inference(unit_resolution,[status(thm)],[792, 770])).
% 1.91/1.49 tff(794,plain,
% 1.91/1.49 (c2_1(a912)),
% 1.91/1.49 inference(unit_resolution,[status(thm)],[676, 622])).
% 1.91/1.49 tff(795,plain,
% 1.91/1.49 (c1_1(a912)),
% 1.91/1.49 inference(unit_resolution,[status(thm)],[687, 622])).
% 1.91/1.49 tff(796,plain,
% 1.91/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a921) | c3_1(a921) | c0_1(a912) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c0_1(a903)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a921) | c3_1(a921) | c0_1(a912) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c0_1(a903)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921))),
% 1.91/1.49 inference(rewrite,[status(thm)],[])).
% 1.91/1.49 tff(797,plain,
% 1.91/1.49 (((~ndr1_0) | c2_1(a903) | c3_1(a903) | (~c0_1(a903)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a921) | c1_1(a921) | c0_1(a921)) <=> (c0_1(a921) | c3_1(a921) | c0_1(a912) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c0_1(a903)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921))),
% 1.91/1.49 inference(rewrite,[status(thm)],[])).
% 1.91/1.49 tff(798,plain,
% 1.91/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a903) | c3_1(a903) | (~c0_1(a903)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a921) | c1_1(a921) | c0_1(a921))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a921) | c3_1(a921) | c0_1(a912) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c0_1(a903)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921)))),
% 1.91/1.49 inference(monotonicity,[status(thm)],[797])).
% 1.91/1.49 tff(799,plain,
% 1.91/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a903) | c3_1(a903) | (~c0_1(a903)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a921) | c1_1(a921) | c0_1(a921))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a921) | c3_1(a921) | c0_1(a912) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c0_1(a903)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921))),
% 1.91/1.49 inference(transitivity,[status(thm)],[798, 796])).
% 1.91/1.49 tff(800,plain,
% 1.91/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a903) | c3_1(a903) | (~c0_1(a903)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a921) | c1_1(a921) | c0_1(a921))),
% 1.91/1.49 inference(quant_inst,[status(thm)],[])).
% 1.91/1.49 tff(801,plain,
% 1.91/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a921) | c3_1(a921) | c0_1(a912) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c0_1(a903)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921)),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[800, 799])).
% 1.91/1.49 tff(802,plain,
% 1.91/1.49 (c1_1(a921)),
% 1.91/1.49 inference(unit_resolution,[status(thm)],[801, 124, 795, 794, 793, 232, 226, 628, 782, 776, 322])).
% 1.91/1.49 tff(803,plain,
% 1.91/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c3_1(a906) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c1_1(a903)) | (~c2_1(a906)) | (~c0_1(a906)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a906) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c1_1(a903)) | (~c2_1(a906)) | (~c0_1(a906)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 1.91/1.49 inference(rewrite,[status(thm)],[])).
% 1.91/1.49 tff(804,plain,
% 1.91/1.49 (((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a903) | c2_1(a903) | (~c1_1(a903))) <=> (c3_1(a906) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c1_1(a903)) | (~c2_1(a906)) | (~c0_1(a906)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 1.91/1.49 inference(rewrite,[status(thm)],[])).
% 1.91/1.49 tff(805,plain,
% 1.91/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a903) | c2_1(a903) | (~c1_1(a903)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c3_1(a906) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c1_1(a903)) | (~c2_1(a906)) | (~c0_1(a906)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916))))),
% 1.91/1.49 inference(monotonicity,[status(thm)],[804])).
% 1.91/1.49 tff(806,plain,
% 1.91/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a903) | c2_1(a903) | (~c1_1(a903)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a906) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c1_1(a903)) | (~c2_1(a906)) | (~c0_1(a906)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 1.91/1.49 inference(transitivity,[status(thm)],[805, 803])).
% 1.91/1.49 tff(807,plain,
% 1.91/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a903) | c2_1(a903) | (~c1_1(a903)))),
% 1.91/1.49 inference(quant_inst,[status(thm)],[])).
% 1.91/1.49 tff(808,plain,
% 1.91/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a906) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c1_1(a903)) | (~c2_1(a906)) | (~c0_1(a906)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916))),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[807, 806])).
% 1.91/1.49 tff(809,plain,
% 1.91/1.49 (~c1_1(a903)),
% 1.91/1.49 inference(unit_resolution,[status(thm)],[808, 124, 261, 283, 272, 323, 324, 325, 782, 776, 31])).
% 1.91/1.49 tff(810,plain,
% 1.91/1.49 (((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a903)))) <=> ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp17 | hskp12 | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a903)))),
% 1.91/1.49 inference(rewrite,[status(thm)],[])).
% 1.91/1.49 tff(811,plain,
% 1.91/1.49 ((hskp17 | hskp12 | (~ndr1_0) | c2_1(a903) | c1_1(a903) | (~c0_1(a903))) <=> (hskp17 | hskp12 | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a903)))),
% 1.91/1.49 inference(rewrite,[status(thm)],[])).
% 1.91/1.49 tff(812,plain,
% 1.91/1.49 (((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | (~ndr1_0) | c2_1(a903) | c1_1(a903) | (~c0_1(a903)))) <=> ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a903))))),
% 1.91/1.49 inference(monotonicity,[status(thm)],[811])).
% 1.91/1.49 tff(813,plain,
% 1.91/1.49 (((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | (~ndr1_0) | c2_1(a903) | c1_1(a903) | (~c0_1(a903)))) <=> ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp17 | hskp12 | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a903)))),
% 1.91/1.49 inference(transitivity,[status(thm)],[812, 810])).
% 1.91/1.49 tff(814,plain,
% 1.91/1.49 ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | (~ndr1_0) | c2_1(a903) | c1_1(a903) | (~c0_1(a903)))),
% 1.91/1.49 inference(quant_inst,[status(thm)],[])).
% 1.91/1.49 tff(815,plain,
% 1.91/1.49 ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp17 | hskp12 | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a903))),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[814, 813])).
% 1.91/1.49 tff(816,plain,
% 1.91/1.49 (hskp17 | c1_1(a903)),
% 1.91/1.49 inference(unit_resolution,[status(thm)],[815, 124, 32, 793, 782, 448])).
% 1.91/1.49 tff(817,plain,
% 1.91/1.49 (hskp17),
% 1.91/1.49 inference(unit_resolution,[status(thm)],[816, 809])).
% 1.91/1.49 tff(818,plain,
% 1.91/1.49 (~c2_1(a936)),
% 1.91/1.49 inference(unit_resolution,[status(thm)],[502, 817])).
% 1.91/1.49 tff(819,plain,
% 1.91/1.49 (^[U: $i] : refl((hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) <=> (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))))),
% 1.91/1.49 inference(bind,[status(th)],[])).
% 1.91/1.49 tff(820,plain,
% 1.91/1.49 (![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.91/1.49 inference(quant_intro,[status(thm)],[819])).
% 1.91/1.49 tff(821,plain,
% 1.91/1.49 (![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.91/1.49 inference(rewrite,[status(thm)],[])).
% 1.91/1.49 tff(822,plain,
% 1.91/1.49 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp30) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp30))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp30) <=> (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp30) <=> (hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp30) | hskp7) <=> ((hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp7))), rewrite(((hskp30 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp7) <=> (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp30) | hskp7) <=> (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))))),
% 1.91/1.49 inference(bind,[status(th)],[])).
% 1.91/1.49 tff(823,plain,
% 1.91/1.49 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp30) | hskp7) <=> ![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.91/1.49 inference(quant_intro,[status(thm)],[822])).
% 1.91/1.49 tff(824,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp30) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause140')).
% 1.91/1.49 tff(825,plain,
% 1.91/1.49 (![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[824, 823])).
% 1.91/1.49 tff(826,plain,
% 1.91/1.49 (![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[825, 821])).
% 1.91/1.49 tff(827,plain,(
% 1.91/1.49 ![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.91/1.49 inference(skolemize,[status(sab)],[826])).
% 1.91/1.49 tff(828,plain,
% 1.91/1.49 (![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[827, 820])).
% 1.91/1.49 tff(829,plain,
% 1.91/1.49 (((~![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp30 | hskp7 | c3_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a903)))) <=> ((~![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp30 | hskp7 | c3_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a903)))),
% 1.91/1.49 inference(rewrite,[status(thm)],[])).
% 1.91/1.49 tff(830,plain,
% 1.91/1.49 ((hskp30 | hskp7 | (~ndr1_0) | c1_1(a903) | c3_1(a903) | (~c0_1(a903))) <=> (hskp30 | hskp7 | c3_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a903)))),
% 1.91/1.49 inference(rewrite,[status(thm)],[])).
% 1.91/1.49 tff(831,plain,
% 1.91/1.49 (((~![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp30 | hskp7 | (~ndr1_0) | c1_1(a903) | c3_1(a903) | (~c0_1(a903)))) <=> ((~![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp30 | hskp7 | c3_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a903))))),
% 1.91/1.49 inference(monotonicity,[status(thm)],[830])).
% 1.91/1.49 tff(832,plain,
% 1.91/1.49 (((~![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp30 | hskp7 | (~ndr1_0) | c1_1(a903) | c3_1(a903) | (~c0_1(a903)))) <=> ((~![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp30 | hskp7 | c3_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a903)))),
% 1.91/1.49 inference(transitivity,[status(thm)],[831, 829])).
% 1.91/1.49 tff(833,plain,
% 1.91/1.49 ((~![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp30 | hskp7 | (~ndr1_0) | c1_1(a903) | c3_1(a903) | (~c0_1(a903)))),
% 1.91/1.49 inference(quant_inst,[status(thm)],[])).
% 1.91/1.49 tff(834,plain,
% 1.91/1.49 ((~![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp30 | hskp7 | c3_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a903))),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[833, 832])).
% 1.91/1.49 tff(835,plain,
% 1.91/1.49 (hskp30 | hskp7 | c1_1(a903)),
% 1.91/1.49 inference(unit_resolution,[status(thm)],[834, 124, 793, 776, 828])).
% 1.91/1.49 tff(836,plain,
% 1.91/1.49 (hskp30),
% 1.91/1.49 inference(unit_resolution,[status(thm)],[835, 809, 497])).
% 1.91/1.49 tff(837,plain,
% 1.91/1.49 (((~hskp30) | c2_1(a942)) <=> ((~hskp30) | c2_1(a942))),
% 1.91/1.49 inference(rewrite,[status(thm)],[])).
% 1.91/1.49 tff(838,axiom,((~hskp30) | c2_1(a942)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause37')).
% 1.91/1.49 tff(839,plain,
% 1.91/1.49 ((~hskp30) | c2_1(a942)),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[838, 837])).
% 1.91/1.49 tff(840,plain,
% 1.91/1.49 ((~hskp30) | c2_1(a942)),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[839, 837])).
% 1.91/1.49 tff(841,plain,
% 1.91/1.49 ((~hskp30) | c2_1(a942)),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[840, 837])).
% 1.91/1.49 tff(842,plain,
% 1.91/1.49 ((~hskp30) | c2_1(a942)),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[841, 837])).
% 1.91/1.49 tff(843,plain,
% 1.91/1.49 ((~hskp30) | c2_1(a942)),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[842, 837])).
% 1.91/1.49 tff(844,plain,
% 1.91/1.49 ((~hskp30) | c2_1(a942)),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[843, 837])).
% 1.91/1.49 tff(845,plain,
% 1.91/1.49 ((~hskp30) | c2_1(a942)),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[844, 837])).
% 1.91/1.49 tff(846,plain,
% 1.91/1.49 ((~hskp30) | c2_1(a942)),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[845, 837])).
% 1.91/1.49 tff(847,plain,
% 1.91/1.49 (c2_1(a942)),
% 1.91/1.49 inference(unit_resolution,[status(thm)],[846, 836])).
% 1.91/1.49 tff(848,plain,
% 1.91/1.49 (~c1_1(a936)),
% 1.91/1.49 inference(unit_resolution,[status(thm)],[508, 817])).
% 1.91/1.49 tff(849,plain,
% 1.91/1.49 (((~hskp30) | c1_1(a942)) <=> ((~hskp30) | c1_1(a942))),
% 1.91/1.49 inference(rewrite,[status(thm)],[])).
% 1.91/1.49 tff(850,axiom,((~hskp30) | c1_1(a942)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause36')).
% 1.91/1.49 tff(851,plain,
% 1.91/1.49 ((~hskp30) | c1_1(a942)),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[850, 849])).
% 1.91/1.49 tff(852,plain,
% 1.91/1.49 ((~hskp30) | c1_1(a942)),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[851, 849])).
% 1.91/1.49 tff(853,plain,
% 1.91/1.49 ((~hskp30) | c1_1(a942)),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[852, 849])).
% 1.91/1.49 tff(854,plain,
% 1.91/1.49 ((~hskp30) | c1_1(a942)),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[853, 849])).
% 1.91/1.49 tff(855,plain,
% 1.91/1.49 ((~hskp30) | c1_1(a942)),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[854, 849])).
% 1.91/1.49 tff(856,plain,
% 1.91/1.49 ((~hskp30) | c1_1(a942)),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[855, 849])).
% 1.91/1.49 tff(857,plain,
% 1.91/1.49 ((~hskp30) | c1_1(a942)),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[856, 849])).
% 1.91/1.49 tff(858,plain,
% 1.91/1.49 ((~hskp30) | c1_1(a942)),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[857, 849])).
% 1.91/1.49 tff(859,plain,
% 1.91/1.49 (c1_1(a942)),
% 1.91/1.49 inference(unit_resolution,[status(thm)],[858, 836])).
% 1.91/1.49 tff(860,plain,
% 1.91/1.49 (((~hskp30) | c0_1(a942)) <=> ((~hskp30) | c0_1(a942))),
% 1.91/1.49 inference(rewrite,[status(thm)],[])).
% 1.91/1.49 tff(861,axiom,((~hskp30) | c0_1(a942)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause35')).
% 1.91/1.49 tff(862,plain,
% 1.91/1.49 ((~hskp30) | c0_1(a942)),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[861, 860])).
% 1.91/1.49 tff(863,plain,
% 1.91/1.49 ((~hskp30) | c0_1(a942)),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[862, 860])).
% 1.91/1.49 tff(864,plain,
% 1.91/1.49 ((~hskp30) | c0_1(a942)),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[863, 860])).
% 1.91/1.49 tff(865,plain,
% 1.91/1.49 ((~hskp30) | c0_1(a942)),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[864, 860])).
% 1.91/1.49 tff(866,plain,
% 1.91/1.49 ((~hskp30) | c0_1(a942)),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[865, 860])).
% 1.91/1.49 tff(867,plain,
% 1.91/1.49 ((~hskp30) | c0_1(a942)),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[866, 860])).
% 1.91/1.49 tff(868,plain,
% 1.91/1.49 ((~hskp30) | c0_1(a942)),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[867, 860])).
% 1.91/1.49 tff(869,plain,
% 1.91/1.49 ((~hskp30) | c0_1(a942)),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[868, 860])).
% 1.91/1.49 tff(870,plain,
% 1.91/1.49 (c0_1(a942)),
% 1.91/1.49 inference(unit_resolution,[status(thm)],[869, 836])).
% 1.91/1.49 tff(871,plain,
% 1.91/1.49 (c0_1(a936)),
% 1.91/1.49 inference(unit_resolution,[status(thm)],[551, 848, 323, 226, 818, 232, 243, 325, 324])).
% 1.91/1.49 tff(872,plain,
% 1.91/1.49 (~c3_1(a936)),
% 1.91/1.49 inference(unit_resolution,[status(thm)],[460, 817])).
% 1.91/1.49 tff(873,plain,
% 1.91/1.49 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))),
% 1.91/1.50 inference(bind,[status(th)],[])).
% 1.91/1.50 tff(874,plain,
% 1.91/1.50 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.91/1.50 inference(quant_intro,[status(thm)],[873])).
% 1.91/1.50 tff(875,plain,
% 1.91/1.50 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.91/1.50 inference(rewrite,[status(thm)],[])).
% 1.91/1.50 tff(876,plain,
% 1.91/1.50 (^[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)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp9) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp9))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))))),
% 1.91/1.50 inference(bind,[status(th)],[])).
% 1.91/1.50 tff(877,plain,
% 1.91/1.50 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.91/1.50 inference(quant_intro,[status(thm)],[876])).
% 1.91/1.50 tff(878,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause172')).
% 1.91/1.50 tff(879,plain,
% 1.91/1.50 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.91/1.50 inference(modus_ponens,[status(thm)],[878, 877])).
% 1.91/1.50 tff(880,plain,
% 1.91/1.50 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.91/1.50 inference(modus_ponens,[status(thm)],[879, 875])).
% 1.91/1.50 tff(881,plain,(
% 1.91/1.50 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.91/1.50 inference(skolemize,[status(sab)],[880])).
% 1.91/1.50 tff(882,plain,
% 1.91/1.50 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.91/1.50 inference(modus_ponens,[status(thm)],[881, 874])).
% 1.91/1.50 tff(883,assumption,(~c1_1(a903)), introduced(assumption)).
% 1.91/1.50 tff(884,assumption,(~c2_1(a903)), introduced(assumption)).
% 1.91/1.50 tff(885,assumption,(~hskp9), introduced(assumption)).
% 1.91/1.50 tff(886,plain,
% 1.91/1.50 (^[U: $i] : refl((hskp27 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> (hskp27 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))),
% 1.91/1.50 inference(bind,[status(th)],[])).
% 1.91/1.50 tff(887,plain,
% 1.91/1.50 (![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> ![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.91/1.50 inference(quant_intro,[status(thm)],[886])).
% 1.91/1.50 tff(888,plain,
% 1.91/1.50 (![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> ![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.91/1.50 inference(rewrite,[status(thm)],[])).
% 1.91/1.50 tff(889,plain,
% 1.91/1.50 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U)))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp27))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) | hskp9) <=> ((hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp9))), rewrite(((hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp9) <=> (hskp27 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) | hskp9) <=> (hskp27 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))))),
% 1.91/1.50 inference(bind,[status(th)],[])).
% 1.91/1.50 tff(890,plain,
% 1.91/1.50 (![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) | hskp9) <=> ![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.91/1.50 inference(quant_intro,[status(thm)],[889])).
% 1.91/1.50 tff(891,axiom,(![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause131')).
% 1.91/1.50 tff(892,plain,
% 1.91/1.50 (![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.91/1.50 inference(modus_ponens,[status(thm)],[891, 890])).
% 1.91/1.50 tff(893,plain,
% 1.91/1.50 (![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.91/1.50 inference(modus_ponens,[status(thm)],[892, 888])).
% 1.91/1.50 tff(894,plain,(
% 1.91/1.50 ![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.91/1.50 inference(skolemize,[status(sab)],[893])).
% 1.91/1.50 tff(895,plain,
% 1.91/1.50 (![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.91/1.50 inference(modus_ponens,[status(thm)],[894, 887])).
% 1.91/1.50 tff(896,assumption,(~c3_1(a903)), introduced(assumption)).
% 1.91/1.50 tff(897,plain,
% 1.91/1.50 (((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp9 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903))) <=> ((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp27 | hskp9 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903))),
% 1.91/1.50 inference(rewrite,[status(thm)],[])).
% 1.91/1.50 tff(898,plain,
% 1.91/1.50 ((hskp27 | hskp9 | (~ndr1_0) | c2_1(a903) | c1_1(a903) | c3_1(a903)) <=> (hskp27 | hskp9 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903))),
% 1.91/1.50 inference(rewrite,[status(thm)],[])).
% 1.91/1.50 tff(899,plain,
% 1.91/1.50 (((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp9 | (~ndr1_0) | c2_1(a903) | c1_1(a903) | c3_1(a903))) <=> ((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp9 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903)))),
% 1.91/1.50 inference(monotonicity,[status(thm)],[898])).
% 1.91/1.50 tff(900,plain,
% 1.91/1.50 (((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp9 | (~ndr1_0) | c2_1(a903) | c1_1(a903) | c3_1(a903))) <=> ((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp27 | hskp9 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903))),
% 1.91/1.50 inference(transitivity,[status(thm)],[899, 897])).
% 1.91/1.50 tff(901,plain,
% 1.91/1.50 ((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp9 | (~ndr1_0) | c2_1(a903) | c1_1(a903) | c3_1(a903))),
% 1.91/1.50 inference(quant_inst,[status(thm)],[])).
% 1.91/1.50 tff(902,plain,
% 1.91/1.50 ((~![U: $i] : (hskp27 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp27 | hskp9 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903)),
% 1.91/1.50 inference(modus_ponens,[status(thm)],[901, 900])).
% 1.91/1.50 tff(903,plain,
% 1.91/1.50 (hskp27 | hskp9 | c2_1(a903) | c1_1(a903)),
% 1.91/1.50 inference(unit_resolution,[status(thm)],[902, 124, 896, 895])).
% 1.91/1.50 tff(904,plain,
% 1.91/1.50 (hskp27),
% 1.91/1.50 inference(unit_resolution,[status(thm)],[903, 885, 884, 883])).
% 1.91/1.50 tff(905,plain,
% 1.91/1.50 (c3_1(a900)),
% 1.91/1.50 inference(unit_resolution,[status(thm)],[144, 904])).
% 1.91/1.50 tff(906,plain,
% 1.91/1.50 (c2_1(a900)),
% 1.91/1.50 inference(unit_resolution,[status(thm)],[155, 904])).
% 1.91/1.50 tff(907,plain,
% 1.91/1.50 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c1_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936)) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c1_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936)) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)))),
% 1.91/1.50 inference(rewrite,[status(thm)],[])).
% 1.91/1.50 tff(908,plain,
% 1.91/1.50 ((hskp9 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c3_1(a936) | c1_1(a936) | (~c0_1(a936))) <=> (hskp9 | c1_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936)) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)))),
% 1.91/1.50 inference(rewrite,[status(thm)],[])).
% 1.91/1.50 tff(909,plain,
% 1.91/1.50 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c3_1(a936) | c1_1(a936) | (~c0_1(a936)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c1_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936)) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900))))),
% 1.91/1.50 inference(monotonicity,[status(thm)],[908])).
% 1.91/1.50 tff(910,plain,
% 1.91/1.50 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c3_1(a936) | c1_1(a936) | (~c0_1(a936)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c1_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936)) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)))),
% 1.91/1.50 inference(transitivity,[status(thm)],[909, 907])).
% 1.91/1.50 tff(911,plain,
% 1.91/1.50 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c3_1(a936) | c1_1(a936) | (~c0_1(a936)))),
% 1.91/1.50 inference(quant_inst,[status(thm)],[])).
% 1.91/1.50 tff(912,plain,
% 1.91/1.50 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c1_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936)) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900))),
% 1.91/1.50 inference(modus_ponens,[status(thm)],[911, 910])).
% 1.91/1.50 tff(913,plain,
% 1.91/1.50 (~c0_1(a900)),
% 1.91/1.50 inference(unit_resolution,[status(thm)],[912, 124, 885, 906, 905, 522, 608, 882, 553])).
% 1.91/1.50 tff(914,assumption,(c2_1(a942)), introduced(assumption)).
% 1.91/1.50 tff(915,assumption,(c0_1(a942)), introduced(assumption)).
% 1.91/1.50 tff(916,plain,
% 1.91/1.50 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c1_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936)) | (~c0_1(a942)) | (~c2_1(a942)) | (~c3_1(a942)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c1_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936)) | (~c0_1(a942)) | (~c2_1(a942)) | (~c3_1(a942)))),
% 1.91/1.50 inference(rewrite,[status(thm)],[])).
% 1.91/1.50 tff(917,plain,
% 1.91/1.50 ((hskp9 | (~ndr1_0) | (~c2_1(a942)) | (~c3_1(a942)) | (~c0_1(a942)) | c3_1(a936) | c1_1(a936) | (~c0_1(a936))) <=> (hskp9 | c1_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936)) | (~c0_1(a942)) | (~c2_1(a942)) | (~c3_1(a942)))),
% 1.91/1.50 inference(rewrite,[status(thm)],[])).
% 1.91/1.50 tff(918,plain,
% 1.91/1.50 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a942)) | (~c3_1(a942)) | (~c0_1(a942)) | c3_1(a936) | c1_1(a936) | (~c0_1(a936)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c1_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936)) | (~c0_1(a942)) | (~c2_1(a942)) | (~c3_1(a942))))),
% 1.91/1.50 inference(monotonicity,[status(thm)],[917])).
% 1.91/1.50 tff(919,plain,
% 1.91/1.50 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a942)) | (~c3_1(a942)) | (~c0_1(a942)) | c3_1(a936) | c1_1(a936) | (~c0_1(a936)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c1_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936)) | (~c0_1(a942)) | (~c2_1(a942)) | (~c3_1(a942)))),
% 1.91/1.50 inference(transitivity,[status(thm)],[918, 916])).
% 1.91/1.50 tff(920,plain,
% 1.91/1.50 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a942)) | (~c3_1(a942)) | (~c0_1(a942)) | c3_1(a936) | c1_1(a936) | (~c0_1(a936)))),
% 1.91/1.50 inference(quant_inst,[status(thm)],[])).
% 1.91/1.50 tff(921,plain,
% 1.91/1.50 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c1_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936)) | (~c0_1(a942)) | (~c2_1(a942)) | (~c3_1(a942))),
% 1.91/1.50 inference(modus_ponens,[status(thm)],[920, 919])).
% 1.91/1.50 tff(922,plain,
% 1.91/1.50 (hskp9 | (~c3_1(a942))),
% 1.91/1.50 inference(unit_resolution,[status(thm)],[921, 124, 915, 914, 522, 608, 882, 553])).
% 1.91/1.50 tff(923,plain,
% 1.91/1.50 (~c3_1(a942)),
% 1.91/1.50 inference(unit_resolution,[status(thm)],[922, 885])).
% 1.91/1.50 tff(924,plain,
% 1.91/1.50 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))))),
% 1.91/1.50 inference(bind,[status(th)],[])).
% 1.91/1.50 tff(925,plain,
% 1.91/1.50 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.91/1.50 inference(quant_intro,[status(thm)],[924])).
% 1.91/1.50 tff(926,plain,
% 1.91/1.50 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.91/1.50 inference(rewrite,[status(thm)],[])).
% 1.91/1.50 tff(927,plain,
% 1.91/1.50 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp0) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) | hskp0))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))))),
% 1.91/1.50 inference(bind,[status(th)],[])).
% 1.91/1.50 tff(928,plain,
% 1.91/1.50 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.91/1.50 inference(quant_intro,[status(thm)],[927])).
% 1.91/1.50 tff(929,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause169')).
% 1.91/1.50 tff(930,plain,
% 1.91/1.50 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.91/1.50 inference(modus_ponens,[status(thm)],[929, 928])).
% 1.91/1.50 tff(931,plain,
% 1.91/1.50 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.91/1.50 inference(modus_ponens,[status(thm)],[930, 926])).
% 1.91/1.50 tff(932,plain,(
% 1.91/1.50 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.91/1.50 inference(skolemize,[status(sab)],[931])).
% 1.91/1.50 tff(933,plain,
% 1.91/1.50 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.91/1.50 inference(modus_ponens,[status(thm)],[932, 925])).
% 1.91/1.50 tff(934,assumption,(c1_1(a942)), introduced(assumption)).
% 1.91/1.50 tff(935,plain,
% 1.91/1.50 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp0 | c2_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936)) | (~c0_1(a942)) | c3_1(a942) | (~c1_1(a942)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp0 | c2_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936)) | (~c0_1(a942)) | c3_1(a942) | (~c1_1(a942)))),
% 1.91/1.50 inference(rewrite,[status(thm)],[])).
% 1.91/1.50 tff(936,plain,
% 1.91/1.50 ((hskp0 | (~ndr1_0) | c3_1(a942) | (~c1_1(a942)) | (~c0_1(a942)) | c3_1(a936) | c2_1(a936) | (~c0_1(a936))) <=> (hskp0 | c2_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936)) | (~c0_1(a942)) | c3_1(a942) | (~c1_1(a942)))),
% 1.91/1.50 inference(rewrite,[status(thm)],[])).
% 1.91/1.50 tff(937,plain,
% 1.91/1.50 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a942) | (~c1_1(a942)) | (~c0_1(a942)) | c3_1(a936) | c2_1(a936) | (~c0_1(a936)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp0 | c2_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936)) | (~c0_1(a942)) | c3_1(a942) | (~c1_1(a942))))),
% 1.91/1.50 inference(monotonicity,[status(thm)],[936])).
% 1.91/1.50 tff(938,plain,
% 1.91/1.50 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a942) | (~c1_1(a942)) | (~c0_1(a942)) | c3_1(a936) | c2_1(a936) | (~c0_1(a936)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp0 | c2_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936)) | (~c0_1(a942)) | c3_1(a942) | (~c1_1(a942)))),
% 1.91/1.50 inference(transitivity,[status(thm)],[937, 935])).
% 1.91/1.50 tff(939,plain,
% 1.91/1.50 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a942) | (~c1_1(a942)) | (~c0_1(a942)) | c3_1(a936) | c2_1(a936) | (~c0_1(a936)))),
% 1.91/1.50 inference(quant_inst,[status(thm)],[])).
% 1.91/1.50 tff(940,plain,
% 1.91/1.50 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp0 | c2_1(a936) | c3_1(a936) | (~ndr1_0) | (~c0_1(a936)) | (~c0_1(a942)) | c3_1(a942) | (~c1_1(a942))),
% 1.91/1.50 inference(modus_ponens,[status(thm)],[939, 938])).
% 1.91/1.50 tff(941,plain,
% 1.91/1.50 (hskp0),
% 1.91/1.50 inference(unit_resolution,[status(thm)],[940, 124, 915, 934, 521, 608, 933, 923, 553])).
% 1.91/1.50 tff(942,plain,
% 1.91/1.50 (~c3_1(a901)),
% 1.91/1.50 inference(unit_resolution,[status(thm)],[651, 941])).
% 1.91/1.50 tff(943,plain,
% 1.91/1.50 (~c1_1(a901)),
% 1.91/1.50 inference(unit_resolution,[status(thm)],[657, 941])).
% 1.91/1.50 tff(944,plain,
% 1.91/1.50 (~c0_1(a901)),
% 1.91/1.50 inference(unit_resolution,[status(thm)],[663, 941])).
% 1.91/1.50 tff(945,plain,
% 1.91/1.50 (c1_1(a900)),
% 1.91/1.50 inference(unit_resolution,[status(thm)],[166, 904])).
% 1.91/1.50 tff(946,plain,
% 1.91/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a936) | c3_1(a936) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c0_1(a936)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a936) | c3_1(a936) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c0_1(a936)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900))),
% 1.91/1.50 inference(rewrite,[status(thm)],[])).
% 1.91/1.50 tff(947,plain,
% 1.91/1.50 (((~ndr1_0) | c2_1(a936) | c3_1(a936) | (~c0_1(a936)) | c0_1(a900) | (~c1_1(a900)) | (~c2_1(a900)) | c3_1(a901) | c1_1(a901) | c0_1(a901)) <=> (c2_1(a936) | c3_1(a936) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c0_1(a936)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900))),
% 1.91/1.50 inference(rewrite,[status(thm)],[])).
% 1.91/1.50 tff(948,plain,
% 1.91/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a936) | c3_1(a936) | (~c0_1(a936)) | c0_1(a900) | (~c1_1(a900)) | (~c2_1(a900)) | c3_1(a901) | c1_1(a901) | c0_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a936) | c3_1(a936) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c0_1(a936)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900)))),
% 1.91/1.50 inference(monotonicity,[status(thm)],[947])).
% 1.91/1.50 tff(949,plain,
% 1.91/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a936) | c3_1(a936) | (~c0_1(a936)) | c0_1(a900) | (~c1_1(a900)) | (~c2_1(a900)) | c3_1(a901) | c1_1(a901) | c0_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a936) | c3_1(a936) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c0_1(a936)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900))),
% 1.91/1.50 inference(transitivity,[status(thm)],[948, 946])).
% 1.91/1.50 tff(950,plain,
% 1.91/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a936) | c3_1(a936) | (~c0_1(a936)) | c0_1(a900) | (~c1_1(a900)) | (~c2_1(a900)) | c3_1(a901) | c1_1(a901) | c0_1(a901))),
% 1.91/1.50 inference(quant_inst,[status(thm)],[])).
% 1.91/1.50 tff(951,plain,
% 1.91/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a936) | c3_1(a936) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c0_1(a936)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900)),
% 1.91/1.50 inference(modus_ponens,[status(thm)],[950, 949])).
% 1.91/1.50 tff(952,plain,
% 1.91/1.50 ($false),
% 1.91/1.50 inference(unit_resolution,[status(thm)],[951, 124, 945, 906, 521, 608, 944, 943, 942, 322, 553, 913])).
% 1.91/1.50 tff(953,plain,(hskp9 | c2_1(a936) | c3_1(a936) | (~c0_1(a936)) | (~c0_1(a942)) | (~c1_1(a942)) | c1_1(a936) | (~c2_1(a942)) | c2_1(a903) | c1_1(a903) | c3_1(a903)), inference(lemma,lemma(discharge,[]))).
% 1.91/1.50 tff(954,plain,
% 1.91/1.50 (hskp9),
% 1.91/1.50 inference(unit_resolution,[status(thm)],[953, 872, 776, 871, 870, 859, 848, 847, 782, 809, 818])).
% 1.91/1.50 tff(955,plain,
% 1.91/1.50 (((~hskp9) | (~c3_1(a910))) <=> ((~hskp9) | (~c3_1(a910)))),
% 1.91/1.50 inference(rewrite,[status(thm)],[])).
% 1.91/1.50 tff(956,plain,
% 1.91/1.50 (((~c3_1(a910)) | (~hskp9)) <=> ((~hskp9) | (~c3_1(a910)))),
% 1.91/1.50 inference(rewrite,[status(thm)],[])).
% 1.91/1.50 tff(957,axiom,((~c3_1(a910)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause111')).
% 1.91/1.50 tff(958,plain,
% 1.91/1.50 ((~hskp9) | (~c3_1(a910))),
% 1.91/1.50 inference(modus_ponens,[status(thm)],[957, 956])).
% 1.91/1.50 tff(959,plain,
% 1.91/1.50 ((~hskp9) | (~c3_1(a910))),
% 1.91/1.50 inference(modus_ponens,[status(thm)],[958, 955])).
% 1.91/1.50 tff(960,plain,
% 1.91/1.50 (~c3_1(a910)),
% 1.91/1.50 inference(unit_resolution,[status(thm)],[959, 954])).
% 1.91/1.50 tff(961,plain,
% 1.91/1.50 (((~hskp9) | (~c1_1(a910))) <=> ((~hskp9) | (~c1_1(a910)))),
% 1.91/1.50 inference(rewrite,[status(thm)],[])).
% 1.91/1.50 tff(962,plain,
% 1.91/1.50 (((~c1_1(a910)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a910)))),
% 1.91/1.50 inference(rewrite,[status(thm)],[])).
% 1.91/1.50 tff(963,axiom,((~c1_1(a910)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause110')).
% 1.91/1.50 tff(964,plain,
% 1.91/1.50 ((~hskp9) | (~c1_1(a910))),
% 1.91/1.50 inference(modus_ponens,[status(thm)],[963, 962])).
% 1.91/1.50 tff(965,plain,
% 1.91/1.50 ((~hskp9) | (~c1_1(a910))),
% 1.91/1.50 inference(modus_ponens,[status(thm)],[964, 961])).
% 1.91/1.50 tff(966,plain,
% 1.91/1.50 (~c1_1(a910)),
% 1.91/1.50 inference(unit_resolution,[status(thm)],[965, 954])).
% 1.91/1.50 tff(967,plain,
% 1.91/1.50 (^[U: $i] : refl((hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))),
% 1.91/1.50 inference(bind,[status(th)],[])).
% 1.91/1.50 tff(968,plain,
% 1.91/1.50 (![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> ![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.91/1.50 inference(quant_intro,[status(thm)],[967])).
% 1.91/1.50 tff(969,plain,
% 1.91/1.50 (![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> ![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.91/1.50 inference(rewrite,[status(thm)],[])).
% 1.91/1.50 tff(970,plain,
% 1.91/1.50 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U)))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp11) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp11))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp11) <=> (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp11) <=> (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp11) | hskp27) <=> ((hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp27))), rewrite(((hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp27) <=> (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp11) | hskp27) <=> (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))))),
% 1.91/1.50 inference(bind,[status(th)],[])).
% 1.91/1.50 tff(971,plain,
% 1.91/1.50 (![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp11) | hskp27) <=> ![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.91/1.50 inference(quant_intro,[status(thm)],[970])).
% 1.91/1.50 tff(972,axiom,(![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp11) | hskp27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause130')).
% 1.91/1.50 tff(973,plain,
% 1.91/1.50 (![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.91/1.50 inference(modus_ponens,[status(thm)],[972, 971])).
% 1.91/1.50 tff(974,plain,
% 1.91/1.50 (![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.91/1.50 inference(modus_ponens,[status(thm)],[973, 969])).
% 1.91/1.50 tff(975,plain,(
% 1.91/1.50 ![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.91/1.50 inference(skolemize,[status(sab)],[974])).
% 1.91/1.50 tff(976,plain,
% 1.91/1.50 (![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.91/1.50 inference(modus_ponens,[status(thm)],[975, 968])).
% 1.91/1.50 tff(977,plain,
% 1.91/1.50 (((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp11 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903))) <=> ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp27 | hskp11 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903))),
% 1.91/1.50 inference(rewrite,[status(thm)],[])).
% 1.91/1.50 tff(978,plain,
% 1.91/1.50 ((hskp27 | hskp11 | (~ndr1_0) | c2_1(a903) | c1_1(a903) | c3_1(a903)) <=> (hskp27 | hskp11 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903))),
% 1.91/1.50 inference(rewrite,[status(thm)],[])).
% 1.91/1.50 tff(979,plain,
% 1.91/1.50 (((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp11 | (~ndr1_0) | c2_1(a903) | c1_1(a903) | c3_1(a903))) <=> ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp11 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903)))),
% 1.91/1.50 inference(monotonicity,[status(thm)],[978])).
% 1.91/1.50 tff(980,plain,
% 1.91/1.50 (((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp11 | (~ndr1_0) | c2_1(a903) | c1_1(a903) | c3_1(a903))) <=> ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp27 | hskp11 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903))),
% 1.91/1.50 inference(transitivity,[status(thm)],[979, 977])).
% 1.91/1.50 tff(981,plain,
% 1.91/1.50 ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp11 | (~ndr1_0) | c2_1(a903) | c1_1(a903) | c3_1(a903))),
% 1.91/1.50 inference(quant_inst,[status(thm)],[])).
% 1.91/1.50 tff(982,plain,
% 1.91/1.50 ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp27 | hskp11 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903)),
% 1.91/1.50 inference(modus_ponens,[status(thm)],[981, 980])).
% 1.91/1.51 tff(983,plain,
% 1.91/1.51 (hskp27 | hskp11 | c2_1(a903) | c1_1(a903)),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[982, 124, 896, 976])).
% 1.91/1.51 tff(984,plain,
% 1.91/1.51 (hskp27),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[983, 168, 884, 883])).
% 1.91/1.51 tff(985,plain,
% 1.91/1.51 (c3_1(a900)),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[144, 984])).
% 1.91/1.51 tff(986,plain,
% 1.91/1.51 (c2_1(a900)),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[155, 984])).
% 1.91/1.51 tff(987,plain,
% 1.91/1.51 (c1_1(a900)),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[166, 984])).
% 1.91/1.51 tff(988,plain,
% 1.91/1.51 ($false),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[174, 124, 32, 168, 987, 986, 985, 53])).
% 1.91/1.51 tff(989,plain,(hskp11 | hskp12 | c2_1(a903) | c1_1(a903) | c3_1(a903)), inference(lemma,lemma(discharge,[]))).
% 1.91/1.51 tff(990,plain,
% 1.91/1.51 (c1_1(a903)),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[989, 32, 884, 168, 896])).
% 1.91/1.51 tff(991,plain,
% 1.91/1.51 (hskp28 | hskp12 | c3_1(a921) | (~c2_1(a921))),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[249, 124, 542, 208])).
% 1.91/1.51 tff(992,plain,
% 1.91/1.51 (hskp28),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[991, 32, 543, 541])).
% 1.91/1.51 tff(993,plain,
% 1.91/1.51 (c3_1(a916)),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[271, 992])).
% 1.91/1.51 tff(994,plain,
% 1.91/1.51 (c1_1(a916)),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[282, 992])).
% 1.91/1.51 tff(995,plain,
% 1.91/1.51 (c0_1(a916)),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[260, 992])).
% 1.91/1.51 tff(996,plain,
% 1.91/1.51 ($false),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[808, 124, 995, 994, 993, 323, 324, 325, 884, 896, 31, 990])).
% 1.91/1.51 tff(997,plain,(hskp12 | (~c0_1(a906)) | (~c2_1(a906)) | c3_1(a906) | c2_1(a903) | c3_1(a903) | (~c2_1(a921)) | c3_1(a921) | c0_1(a921) | hskp11), inference(lemma,lemma(discharge,[]))).
% 1.91/1.51 tff(998,plain,
% 1.91/1.51 (hskp11),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[997, 782, 324, 325, 232, 776, 323, 226, 32, 243])).
% 1.91/1.51 tff(999,plain,
% 1.91/1.51 (~c2_1(a914)),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[69, 998])).
% 1.91/1.51 tff(1000,plain,
% 1.91/1.51 (((~hskp9) | c2_1(a910)) <=> ((~hskp9) | c2_1(a910))),
% 1.91/1.51 inference(rewrite,[status(thm)],[])).
% 1.91/1.51 tff(1001,axiom,((~hskp9) | c2_1(a910)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause70')).
% 1.91/1.51 tff(1002,plain,
% 1.91/1.51 ((~hskp9) | c2_1(a910)),
% 1.91/1.51 inference(modus_ponens,[status(thm)],[1001, 1000])).
% 1.91/1.51 tff(1003,plain,
% 1.91/1.51 ((~hskp9) | c2_1(a910)),
% 1.91/1.51 inference(modus_ponens,[status(thm)],[1002, 1000])).
% 1.91/1.51 tff(1004,plain,
% 1.91/1.51 ((~hskp9) | c2_1(a910)),
% 1.91/1.51 inference(modus_ponens,[status(thm)],[1003, 1000])).
% 1.91/1.51 tff(1005,plain,
% 1.91/1.51 ((~hskp9) | c2_1(a910)),
% 1.91/1.51 inference(modus_ponens,[status(thm)],[1004, 1000])).
% 1.91/1.51 tff(1006,plain,
% 1.91/1.51 ((~hskp9) | c2_1(a910)),
% 1.91/1.51 inference(modus_ponens,[status(thm)],[1005, 1000])).
% 1.91/1.51 tff(1007,plain,
% 1.91/1.51 ((~hskp9) | c2_1(a910)),
% 1.91/1.51 inference(modus_ponens,[status(thm)],[1006, 1000])).
% 1.91/1.51 tff(1008,plain,
% 1.91/1.51 ((~hskp9) | c2_1(a910)),
% 1.91/1.51 inference(modus_ponens,[status(thm)],[1007, 1000])).
% 1.91/1.51 tff(1009,plain,
% 1.91/1.51 ((~hskp9) | c2_1(a910)),
% 1.91/1.51 inference(modus_ponens,[status(thm)],[1008, 1000])).
% 1.91/1.51 tff(1010,plain,
% 1.91/1.51 (c2_1(a910)),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[1009, 954])).
% 1.91/1.51 tff(1011,plain,
% 1.91/1.51 (c3_1(a914)),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[80, 998])).
% 1.91/1.51 tff(1012,plain,
% 1.91/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a921) | c2_1(a914) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | (~c2_1(a910)) | (~c3_1(a914)) | (~c1_1(a914)) | (~c2_1(a921)) | (~c1_1(a921)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a921) | c2_1(a914) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | (~c2_1(a910)) | (~c3_1(a914)) | (~c1_1(a914)) | (~c2_1(a921)) | (~c1_1(a921)))),
% 1.91/1.51 inference(rewrite,[status(thm)],[])).
% 1.91/1.51 tff(1013,plain,
% 1.91/1.51 (((~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)) | c3_1(a910) | c1_1(a910) | (~c2_1(a910)) | c0_1(a921) | (~c2_1(a921)) | (~c1_1(a921))) <=> (c0_1(a921) | c2_1(a914) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | (~c2_1(a910)) | (~c3_1(a914)) | (~c1_1(a914)) | (~c2_1(a921)) | (~c1_1(a921)))),
% 1.91/1.51 inference(rewrite,[status(thm)],[])).
% 1.91/1.51 tff(1014,plain,
% 1.91/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)) | c3_1(a910) | c1_1(a910) | (~c2_1(a910)) | c0_1(a921) | (~c2_1(a921)) | (~c1_1(a921)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a921) | c2_1(a914) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | (~c2_1(a910)) | (~c3_1(a914)) | (~c1_1(a914)) | (~c2_1(a921)) | (~c1_1(a921))))),
% 1.91/1.51 inference(monotonicity,[status(thm)],[1013])).
% 1.91/1.51 tff(1015,plain,
% 1.91/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)) | c3_1(a910) | c1_1(a910) | (~c2_1(a910)) | c0_1(a921) | (~c2_1(a921)) | (~c1_1(a921)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a921) | c2_1(a914) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | (~c2_1(a910)) | (~c3_1(a914)) | (~c1_1(a914)) | (~c2_1(a921)) | (~c1_1(a921)))),
% 1.91/1.51 inference(transitivity,[status(thm)],[1014, 1012])).
% 1.91/1.51 tff(1016,plain,
% 1.91/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)) | c3_1(a910) | c1_1(a910) | (~c2_1(a910)) | c0_1(a921) | (~c2_1(a921)) | (~c1_1(a921)))),
% 1.91/1.51 inference(quant_inst,[status(thm)],[])).
% 1.91/1.51 tff(1017,plain,
% 1.91/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a921) | c2_1(a914) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | (~c2_1(a910)) | (~c3_1(a914)) | (~c1_1(a914)) | (~c2_1(a921)) | (~c1_1(a921))),
% 1.91/1.51 inference(modus_ponens,[status(thm)],[1016, 1015])).
% 1.91/1.51 tff(1018,plain,
% 1.91/1.51 (~c1_1(a914)),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[1017, 124, 243, 1011, 1010, 232, 999, 966, 960, 743, 802])).
% 1.91/1.51 tff(1019,plain,
% 1.91/1.51 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))))),
% 1.91/1.51 inference(bind,[status(th)],[])).
% 1.91/1.51 tff(1020,plain,
% 1.91/1.51 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.91/1.51 inference(quant_intro,[status(thm)],[1019])).
% 1.91/1.51 tff(1021,plain,
% 1.91/1.51 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.91/1.51 inference(rewrite,[status(thm)],[])).
% 1.91/1.51 tff(1022,plain,
% 1.91/1.51 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp1) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) | hskp1))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V))) | hskp1) <=> (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))))),
% 1.91/1.51 inference(bind,[status(th)],[])).
% 1.91/1.51 tff(1023,plain,
% 1.91/1.51 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.91/1.51 inference(quant_intro,[status(thm)],[1022])).
% 1.91/1.51 tff(1024,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause178')).
% 1.91/1.51 tff(1025,plain,
% 1.91/1.51 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.91/1.51 inference(modus_ponens,[status(thm)],[1024, 1023])).
% 1.91/1.51 tff(1026,plain,
% 1.91/1.51 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.91/1.51 inference(modus_ponens,[status(thm)],[1025, 1021])).
% 1.91/1.51 tff(1027,plain,(
% 1.91/1.51 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.91/1.51 inference(skolemize,[status(sab)],[1026])).
% 1.91/1.51 tff(1028,plain,
% 1.91/1.51 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.91/1.51 inference(modus_ponens,[status(thm)],[1027, 1020])).
% 1.91/1.51 tff(1029,plain,
% 1.91/1.51 (c0_1(a914)),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[91, 998])).
% 1.91/1.51 tff(1030,assumption,(~c1_1(a902)), introduced(assumption)).
% 1.91/1.51 tff(1031,plain,
% 1.91/1.51 (hskp10),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[377, 327, 198])).
% 1.91/1.51 tff(1032,plain,
% 1.91/1.51 (c2_1(a912)),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[676, 1031])).
% 1.91/1.51 tff(1033,plain,
% 1.91/1.51 (c1_1(a912)),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[687, 1031])).
% 1.91/1.51 tff(1034,plain,
% 1.91/1.51 (hskp7),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[713, 1033, 554, 1032, 665])).
% 1.91/1.51 tff(1035,plain,
% 1.91/1.51 (~c3_1(a908)),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[467, 1034])).
% 1.91/1.51 tff(1036,plain,
% 1.91/1.51 (~c2_1(a908)),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[473, 1034])).
% 1.91/1.51 tff(1037,plain,
% 1.91/1.51 (c1_1(a908)),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[484, 1034])).
% 1.91/1.51 tff(1038,plain,
% 1.91/1.51 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (c2_1(a917) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a917)) | (~c1_1(a917)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | c2_1(a917) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a917)) | (~c1_1(a917)))),
% 1.91/1.51 inference(rewrite,[status(thm)],[])).
% 1.91/1.51 tff(1039,plain,
% 1.91/1.51 (((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908))) <=> (c2_1(a917) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a917)) | (~c1_1(a917)))),
% 1.91/1.51 inference(rewrite,[status(thm)],[])).
% 1.91/1.51 tff(1040,plain,
% 1.91/1.51 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (c2_1(a917) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a917)) | (~c1_1(a917))))),
% 1.91/1.51 inference(monotonicity,[status(thm)],[1039])).
% 1.91/1.51 tff(1041,plain,
% 1.91/1.51 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | c2_1(a917) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a917)) | (~c1_1(a917)))),
% 1.91/1.51 inference(transitivity,[status(thm)],[1040, 1038])).
% 1.91/1.51 tff(1042,plain,
% 1.91/1.51 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))),
% 1.91/1.51 inference(quant_inst,[status(thm)],[])).
% 1.91/1.51 tff(1043,plain,
% 1.91/1.51 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | c2_1(a917) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a917)) | (~c1_1(a917))),
% 1.91/1.51 inference(modus_ponens,[status(thm)],[1042, 1041])).
% 1.91/1.51 tff(1044,plain,
% 1.91/1.51 ($false),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[1043, 124, 344, 355, 1037, 333, 1036, 1035, 10])).
% 1.91/1.51 tff(1045,plain,((~hskp12) | hskp6 | c0_1(a912) | hskp21), inference(lemma,lemma(discharge,[]))).
% 1.91/1.51 tff(1046,plain,
% 1.91/1.51 (~hskp12),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[1045, 665, 554, 198])).
% 1.91/1.51 tff(1047,plain,
% 1.91/1.51 (hskp13),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[219, 1046, 198])).
% 1.91/1.51 tff(1048,plain,
% 1.91/1.51 (hskp11),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[997, 232, 324, 325, 884, 896, 323, 541, 32, 243])).
% 1.91/1.51 tff(1049,plain,
% 1.91/1.51 (~c2_1(a914)),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[69, 1048])).
% 1.91/1.51 tff(1050,plain,
% 1.91/1.51 (hskp28 | hskp12 | c0_1(a921) | (~c2_1(a921))),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[249, 124, 541, 208])).
% 1.91/1.51 tff(1051,plain,
% 1.91/1.51 (hskp28),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[1050, 243, 32, 232])).
% 1.91/1.51 tff(1052,plain,
% 1.91/1.51 (c3_1(a916)),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[271, 1051])).
% 1.91/1.51 tff(1053,plain,
% 1.91/1.51 (c1_1(a916)),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[282, 1051])).
% 1.91/1.51 tff(1054,plain,
% 1.91/1.51 (c0_1(a916)),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[260, 1051])).
% 1.91/1.51 tff(1055,assumption,(~c1_1(a912)), introduced(assumption)).
% 1.91/1.51 tff(1056,plain,
% 1.91/1.51 (~hskp10),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[687, 1055])).
% 1.91/1.51 tff(1057,plain,
% 1.91/1.51 (c3_1(a914)),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[80, 1048])).
% 1.91/1.51 tff(1058,plain,
% 1.91/1.51 (hskp10 | (~c1_1(a914))),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[400, 124, 198, 1057, 1049, 365])).
% 1.91/1.51 tff(1059,plain,
% 1.91/1.51 (~c1_1(a914)),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[1058, 1056])).
% 1.91/1.51 tff(1060,plain,
% 1.91/1.51 (c0_1(a914)),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[91, 1048])).
% 1.91/1.51 tff(1061,plain,
% 1.91/1.51 (hskp17 | c1_1(a914)),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[454, 124, 32, 1060, 1049, 448])).
% 1.91/1.51 tff(1062,plain,
% 1.91/1.51 (hskp17),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[1061, 1059])).
% 1.91/1.51 tff(1063,plain,
% 1.91/1.51 (~c3_1(a936)),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[460, 1062])).
% 1.91/1.51 tff(1064,plain,
% 1.91/1.51 (~c2_1(a936)),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[502, 1062])).
% 1.91/1.51 tff(1065,plain,
% 1.91/1.51 (~c1_1(a936)),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[508, 1062])).
% 1.91/1.51 tff(1066,plain,
% 1.91/1.51 (~c1_1(a903)),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[808, 124, 1054, 1053, 1052, 323, 324, 325, 884, 896, 31])).
% 1.91/1.51 tff(1067,plain,
% 1.91/1.51 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | c1_1(a912) | c0_1(a912) | (~ndr1_0) | (~c3_1(a912)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c1_1(a912) | c0_1(a912) | (~ndr1_0) | (~c3_1(a912)))),
% 1.91/1.51 inference(rewrite,[status(thm)],[])).
% 1.91/1.51 tff(1068,plain,
% 1.91/1.51 ((hskp7 | hskp6 | (~ndr1_0) | c1_1(a912) | c0_1(a912) | (~c3_1(a912))) <=> (hskp7 | hskp6 | c1_1(a912) | c0_1(a912) | (~ndr1_0) | (~c3_1(a912)))),
% 1.91/1.51 inference(rewrite,[status(thm)],[])).
% 1.91/1.51 tff(1069,plain,
% 1.91/1.51 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a912) | c0_1(a912) | (~c3_1(a912)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | c1_1(a912) | c0_1(a912) | (~ndr1_0) | (~c3_1(a912))))),
% 1.91/1.51 inference(monotonicity,[status(thm)],[1068])).
% 1.91/1.51 tff(1070,plain,
% 1.91/1.51 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a912) | c0_1(a912) | (~c3_1(a912)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c1_1(a912) | c0_1(a912) | (~ndr1_0) | (~c3_1(a912)))),
% 1.91/1.51 inference(transitivity,[status(thm)],[1069, 1067])).
% 1.91/1.51 tff(1071,plain,
% 1.91/1.51 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a912) | c0_1(a912) | (~c3_1(a912)))),
% 1.91/1.51 inference(quant_inst,[status(thm)],[])).
% 1.91/1.51 tff(1072,plain,
% 1.91/1.51 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c1_1(a912) | c0_1(a912) | (~ndr1_0) | (~c3_1(a912))),
% 1.91/1.51 inference(modus_ponens,[status(thm)],[1071, 1070])).
% 1.91/1.51 tff(1073,plain,
% 1.91/1.51 (hskp7 | c1_1(a912) | (~c3_1(a912))),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[1072, 124, 554, 665, 564])).
% 1.91/1.51 tff(1074,plain,
% 1.91/1.51 (~c3_1(a912)),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[1073, 21, 1055])).
% 1.91/1.51 tff(1075,assumption,(c0_1(a903)), introduced(assumption)).
% 1.91/1.51 tff(1076,plain,
% 1.91/1.51 (((~![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp14 | hskp6 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c0_1(a903)))) <=> ((~![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp14 | hskp6 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c0_1(a903)))),
% 1.91/1.51 inference(rewrite,[status(thm)],[])).
% 1.91/1.51 tff(1077,plain,
% 1.91/1.51 ((hskp14 | hskp6 | (~ndr1_0) | c2_1(a903) | c3_1(a903) | (~c0_1(a903))) <=> (hskp14 | hskp6 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c0_1(a903)))),
% 1.91/1.51 inference(rewrite,[status(thm)],[])).
% 1.91/1.51 tff(1078,plain,
% 1.91/1.51 (((~![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp14 | hskp6 | (~ndr1_0) | c2_1(a903) | c3_1(a903) | (~c0_1(a903)))) <=> ((~![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp14 | hskp6 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c0_1(a903))))),
% 1.91/1.51 inference(monotonicity,[status(thm)],[1077])).
% 1.91/1.51 tff(1079,plain,
% 1.91/1.51 (((~![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp14 | hskp6 | (~ndr1_0) | c2_1(a903) | c3_1(a903) | (~c0_1(a903)))) <=> ((~![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp14 | hskp6 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c0_1(a903)))),
% 1.91/1.51 inference(transitivity,[status(thm)],[1078, 1076])).
% 1.91/1.51 tff(1080,plain,
% 1.91/1.51 ((~![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp14 | hskp6 | (~ndr1_0) | c2_1(a903) | c3_1(a903) | (~c0_1(a903)))),
% 1.91/1.51 inference(quant_inst,[status(thm)],[])).
% 1.91/1.51 tff(1081,plain,
% 1.91/1.51 ((~![U: $i] : (hskp14 | hskp6 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp14 | hskp6 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c0_1(a903))),
% 1.91/1.51 inference(modus_ponens,[status(thm)],[1080, 1079])).
% 1.91/1.51 tff(1082,plain,
% 1.91/1.51 (hskp14 | hskp6 | c2_1(a903) | (~c0_1(a903))),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[1081, 124, 896, 607])).
% 1.91/1.51 tff(1083,plain,
% 1.91/1.51 (hskp14),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[1082, 554, 1075, 884])).
% 1.91/1.51 tff(1084,plain,
% 1.91/1.51 (~c1_1(a923)),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[570, 1083])).
% 1.91/1.51 tff(1085,plain,
% 1.91/1.51 (~c0_1(a923)),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[576, 1083])).
% 1.91/1.51 tff(1086,plain,
% 1.91/1.51 (c3_1(a923)),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[587, 1083])).
% 1.91/1.51 tff(1087,plain,
% 1.91/1.51 ($false),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[594, 124, 21, 554, 1086, 1085, 1084, 564])).
% 1.91/1.51 tff(1088,plain,(hskp6 | hskp7 | (~c0_1(a903)) | c2_1(a903) | c3_1(a903)), inference(lemma,lemma(discharge,[]))).
% 1.91/1.51 tff(1089,plain,
% 1.91/1.51 (~c0_1(a903)),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[1088, 21, 554, 884, 896])).
% 1.91/1.51 tff(1090,plain,
% 1.91/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a903) | c3_1(a921) | c3_1(a906) | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a903) | c3_1(a921) | c3_1(a906) | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921)))),
% 1.91/1.51 inference(rewrite,[status(thm)],[])).
% 1.91/1.51 tff(1091,plain,
% 1.91/1.51 (((~ndr1_0) | c3_1(a921) | (~c2_1(a921)) | (~c1_1(a921)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a903) | c0_1(a903) | c2_1(a903)) <=> (c0_1(a903) | c3_1(a921) | c3_1(a906) | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921)))),
% 1.91/1.51 inference(rewrite,[status(thm)],[])).
% 1.91/1.51 tff(1092,plain,
% 1.91/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a921) | (~c2_1(a921)) | (~c1_1(a921)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a903) | c0_1(a903) | c2_1(a903))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a903) | c3_1(a921) | c3_1(a906) | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921))))),
% 1.91/1.51 inference(monotonicity,[status(thm)],[1091])).
% 1.91/1.51 tff(1093,plain,
% 1.91/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a921) | (~c2_1(a921)) | (~c1_1(a921)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a903) | c0_1(a903) | c2_1(a903))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a903) | c3_1(a921) | c3_1(a906) | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921)))),
% 1.91/1.51 inference(transitivity,[status(thm)],[1092, 1090])).
% 1.91/1.51 tff(1094,plain,
% 1.91/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a921) | (~c2_1(a921)) | (~c1_1(a921)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a903) | c0_1(a903) | c2_1(a903))),
% 1.91/1.51 inference(quant_inst,[status(thm)],[])).
% 1.91/1.51 tff(1095,plain,
% 1.91/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a903) | c3_1(a921) | c3_1(a906) | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921))),
% 1.91/1.51 inference(modus_ponens,[status(thm)],[1094, 1093])).
% 1.91/1.51 tff(1096,plain,
% 1.91/1.51 (c0_1(a903) | (~c1_1(a921))),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[1095, 124, 543, 323, 324, 541, 325, 884, 520, 883])).
% 1.91/1.51 tff(1097,plain,
% 1.91/1.51 (~c1_1(a921)),
% 1.91/1.51 inference(unit_resolution,[status(thm)],[1096, 1089])).
% 1.91/1.51 tff(1098,plain,
% 1.91/1.51 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W)))),
% 1.91/1.51 inference(bind,[status(th)],[])).
% 1.91/1.51 tff(1099,plain,
% 1.91/1.51 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.91/1.51 inference(quant_intro,[status(thm)],[1098])).
% 1.91/1.51 tff(1100,plain,
% 1.91/1.51 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.91/1.51 inference(rewrite,[status(thm)],[])).
% 1.91/1.51 tff(1101,plain,
% 1.91/1.51 (^[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)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | 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)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V)) | 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)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | 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)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c0_1(W))), (((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c0_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))))),
% 1.91/1.51 inference(bind,[status(th)],[])).
% 1.91/1.51 tff(1102,plain,
% 1.91/1.51 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.91/1.51 inference(quant_intro,[status(thm)],[1101])).
% 1.91/1.51 tff(1103,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause176')).
% 1.91/1.51 tff(1104,plain,
% 1.91/1.51 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.91/1.51 inference(modus_ponens,[status(thm)],[1103, 1102])).
% 1.91/1.51 tff(1105,plain,
% 1.91/1.51 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.91/1.51 inference(modus_ponens,[status(thm)],[1104, 1100])).
% 1.91/1.51 tff(1106,plain,(
% 1.91/1.51 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.91/1.51 inference(skolemize,[status(sab)],[1105])).
% 1.91/1.51 tff(1107,plain,
% 1.91/1.51 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))),
% 1.91/1.51 inference(modus_ponens,[status(thm)],[1106, 1099])).
% 1.91/1.51 tff(1108,plain,
% 1.91/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a903) | c2_1(a936) | c3_1(a936) | c0_1(a921) | c3_1(a921) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a921) | (~c0_1(a936)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a903) | c2_1(a936) | c3_1(a936) | c0_1(a921) | c3_1(a921) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a921) | (~c0_1(a936)))),
% 1.91/1.51 inference(rewrite,[status(thm)],[])).
% 1.91/1.51 tff(1109,plain,
% 1.91/1.51 (((~ndr1_0) | c2_1(a936) | c3_1(a936) | (~c0_1(a936)) | c3_1(a903) | c2_1(a903) | c0_1(a903) | c3_1(a921) | c1_1(a921) | c0_1(a921)) <=> (c0_1(a903) | c2_1(a936) | c3_1(a936) | c0_1(a921) | c3_1(a921) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a921) | (~c0_1(a936)))),
% 1.91/1.51 inference(rewrite,[status(thm)],[])).
% 1.91/1.51 tff(1110,plain,
% 1.91/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a936) | c3_1(a936) | (~c0_1(a936)) | c3_1(a903) | c2_1(a903) | c0_1(a903) | c3_1(a921) | c1_1(a921) | c0_1(a921))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a903) | c2_1(a936) | c3_1(a936) | c0_1(a921) | c3_1(a921) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a921) | (~c0_1(a936))))),
% 1.91/1.51 inference(monotonicity,[status(thm)],[1109])).
% 1.91/1.51 tff(1111,plain,
% 1.91/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a936) | c3_1(a936) | (~c0_1(a936)) | c3_1(a903) | c2_1(a903) | c0_1(a903) | c3_1(a921) | c1_1(a921) | c0_1(a921))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a903) | c2_1(a936) | c3_1(a936) | c0_1(a921) | c3_1(a921) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a921) | (~c0_1(a936)))),
% 1.91/1.52 inference(transitivity,[status(thm)],[1110, 1108])).
% 1.91/1.52 tff(1112,plain,
% 1.91/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a936) | c3_1(a936) | (~c0_1(a936)) | c3_1(a903) | c2_1(a903) | c0_1(a903) | c3_1(a921) | c1_1(a921) | c0_1(a921))),
% 1.91/1.52 inference(quant_inst,[status(thm)],[])).
% 1.91/1.52 tff(1113,plain,
% 1.91/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a903) | c2_1(a936) | c3_1(a936) | c0_1(a921) | c3_1(a921) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a921) | (~c0_1(a936))),
% 1.91/1.52 inference(modus_ponens,[status(thm)],[1112, 1111])).
% 1.91/1.52 tff(1114,plain,
% 1.91/1.52 (c0_1(a903) | c1_1(a921) | (~c0_1(a936))),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[1113, 124, 521, 608, 542, 541, 884, 896, 1107])).
% 1.91/1.52 tff(1115,plain,
% 1.91/1.52 (~c0_1(a936)),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[1114, 1089, 1097])).
% 1.91/1.52 tff(1116,plain,
% 1.91/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a903) | c3_1(a906) | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a903) | c3_1(a906) | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)))),
% 1.91/1.52 inference(rewrite,[status(thm)],[])).
% 1.91/1.52 tff(1117,plain,
% 1.91/1.52 (((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a903) | c0_1(a903) | c2_1(a903)) <=> (c0_1(a903) | c3_1(a906) | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)))),
% 1.91/1.52 inference(rewrite,[status(thm)],[])).
% 1.91/1.52 tff(1118,plain,
% 1.91/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a903) | c0_1(a903) | c2_1(a903))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a903) | c3_1(a906) | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906))))),
% 1.91/1.52 inference(monotonicity,[status(thm)],[1117])).
% 1.91/1.52 tff(1119,plain,
% 1.91/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a903) | c0_1(a903) | c2_1(a903))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a903) | c3_1(a906) | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)))),
% 1.91/1.52 inference(transitivity,[status(thm)],[1118, 1116])).
% 1.91/1.52 tff(1120,plain,
% 1.91/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a903) | c0_1(a903) | c2_1(a903))),
% 1.91/1.52 inference(quant_inst,[status(thm)],[])).
% 1.91/1.52 tff(1121,plain,
% 1.91/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a903) | c3_1(a906) | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906))),
% 1.91/1.52 inference(modus_ponens,[status(thm)],[1120, 1119])).
% 1.91/1.52 tff(1122,plain,
% 1.91/1.52 (c0_1(a903) | (~c1_1(a906))),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[1121, 124, 323, 324, 325, 884, 520, 883])).
% 1.91/1.52 tff(1123,plain,
% 1.91/1.52 (~c1_1(a906)),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[1122, 1089])).
% 1.91/1.52 tff(1124,assumption,(~c2_1(a912)), introduced(assumption)).
% 1.91/1.52 tff(1125,plain,
% 1.91/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a912) | c2_1(a912) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)))),
% 1.91/1.52 inference(rewrite,[status(thm)],[])).
% 1.91/1.52 tff(1126,plain,
% 1.91/1.52 (((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a912) | c0_1(a912) | c2_1(a912)) <=> (c1_1(a912) | c2_1(a912) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)))),
% 1.91/1.52 inference(rewrite,[status(thm)],[])).
% 1.91/1.52 tff(1127,plain,
% 1.91/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a912) | c0_1(a912) | c2_1(a912))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a912) | c2_1(a912) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906))))),
% 1.91/1.52 inference(monotonicity,[status(thm)],[1126])).
% 1.91/1.52 tff(1128,plain,
% 1.91/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a912) | c0_1(a912) | c2_1(a912))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)))),
% 1.91/1.52 inference(transitivity,[status(thm)],[1127, 1125])).
% 1.91/1.52 tff(1129,plain,
% 1.91/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a912) | c0_1(a912) | c2_1(a912))),
% 1.91/1.52 inference(quant_inst,[status(thm)],[])).
% 1.91/1.52 tff(1130,plain,
% 1.91/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906))),
% 1.91/1.52 inference(modus_ponens,[status(thm)],[1129, 1128])).
% 1.91/1.52 tff(1131,plain,
% 1.91/1.52 (c2_1(a912) | (~c1_1(a906))),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[1130, 124, 1055, 323, 324, 665, 325, 520])).
% 1.91/1.52 tff(1132,plain,
% 1.91/1.52 (~c1_1(a906)),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[1131, 1124])).
% 1.91/1.52 tff(1133,plain,
% 1.91/1.52 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a912) | c2_1(a912) | c0_1(a921) | c3_1(a921) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921)))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c0_1(a921) | c3_1(a921) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921)))),
% 1.91/1.52 inference(rewrite,[status(thm)],[])).
% 1.91/1.52 tff(1134,plain,
% 1.91/1.52 (((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a912) | c0_1(a912) | c2_1(a912)) <=> (c1_1(a912) | c2_1(a912) | c0_1(a921) | c3_1(a921) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921)))),
% 1.91/1.52 inference(rewrite,[status(thm)],[])).
% 1.91/1.52 tff(1135,plain,
% 1.91/1.52 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a912) | c0_1(a912) | c2_1(a912))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a912) | c2_1(a912) | c0_1(a921) | c3_1(a921) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921))))),
% 1.91/1.52 inference(monotonicity,[status(thm)],[1134])).
% 1.91/1.52 tff(1136,plain,
% 1.91/1.52 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a912) | c0_1(a912) | c2_1(a912))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c0_1(a921) | c3_1(a921) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921)))),
% 1.91/1.52 inference(transitivity,[status(thm)],[1135, 1133])).
% 1.91/1.52 tff(1137,plain,
% 1.91/1.52 ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a912) | c0_1(a912) | c2_1(a912))),
% 1.91/1.52 inference(quant_inst,[status(thm)],[])).
% 1.91/1.52 tff(1138,plain,
% 1.91/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c0_1(a921) | c3_1(a921) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921))),
% 1.91/1.52 inference(modus_ponens,[status(thm)],[1137, 1136])).
% 1.91/1.52 tff(1139,plain,
% 1.91/1.52 ($false),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[1138, 124, 543, 1055, 1124, 323, 542, 541, 665, 325, 540, 1132])).
% 1.91/1.52 tff(1140,plain,(c2_1(a912) | (~c2_1(a921)) | c1_1(a912) | (~c0_1(a906)) | c0_1(a921) | c3_1(a921) | c0_1(a912) | c3_1(a906) | (~c2_1(a906))), inference(lemma,lemma(discharge,[]))).
% 1.91/1.52 tff(1141,plain,
% 1.91/1.52 (c2_1(a912)),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[1140, 1055, 543, 323, 542, 541, 665, 325, 324])).
% 1.91/1.52 tff(1142,plain,
% 1.91/1.52 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a936) | c2_1(a936) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912) | c0_1(a936))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a936) | c2_1(a936) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912) | c0_1(a936))),
% 1.91/1.52 inference(rewrite,[status(thm)],[])).
% 1.91/1.52 tff(1143,plain,
% 1.91/1.52 (((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a936) | c0_1(a936) | c2_1(a936)) <=> (c1_1(a936) | c2_1(a936) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912) | c0_1(a936))),
% 1.91/1.52 inference(rewrite,[status(thm)],[])).
% 1.91/1.52 tff(1144,plain,
% 1.91/1.52 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a936) | c0_1(a936) | c2_1(a936))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a936) | c2_1(a936) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912) | c0_1(a936)))),
% 1.91/1.52 inference(monotonicity,[status(thm)],[1143])).
% 1.91/1.52 tff(1145,plain,
% 1.91/1.52 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a936) | c0_1(a936) | c2_1(a936))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a936) | c2_1(a936) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912) | c0_1(a936))),
% 1.91/1.52 inference(transitivity,[status(thm)],[1144, 1142])).
% 1.91/1.52 tff(1146,plain,
% 1.91/1.52 ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a936) | c0_1(a936) | c2_1(a936))),
% 1.91/1.52 inference(quant_inst,[status(thm)],[])).
% 1.91/1.52 tff(1147,plain,
% 1.91/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a936) | c2_1(a936) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912) | c0_1(a936)),
% 1.91/1.52 inference(modus_ponens,[status(thm)],[1146, 1145])).
% 1.91/1.52 tff(1148,plain,
% 1.91/1.52 ($false),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[1147, 124, 1141, 323, 522, 521, 665, 325, 540, 1123, 1115, 1074])).
% 1.91/1.52 tff(1149,plain,(hskp7 | (~c0_1(a906)) | c1_1(a936) | c2_1(a936) | c0_1(a912) | c3_1(a906) | c3_1(a936) | c0_1(a921) | c3_1(a921) | c2_1(a903) | c3_1(a903) | (~c2_1(a906)) | c1_1(a903) | (~c2_1(a921)) | c1_1(a912) | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.91/1.52 tff(1150,plain,
% 1.91/1.52 (hskp7),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[1149, 1065, 323, 1064, 665, 325, 1063, 232, 541, 884, 896, 324, 1066, 243, 1055, 554])).
% 1.91/1.52 tff(1151,plain,
% 1.91/1.52 (~c2_1(a908)),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[473, 1150])).
% 1.91/1.52 tff(1152,plain,
% 1.91/1.52 (~c3_1(a908)),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[467, 1150])).
% 1.91/1.52 tff(1153,assumption,(~c2_1(a908)), introduced(assumption)).
% 1.91/1.52 tff(1154,assumption,(~c3_1(a908)), introduced(assumption)).
% 1.91/1.52 tff(1155,plain,
% 1.91/1.52 (c2_1(a908) | (~c1_1(a908))),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[494, 124, 488, 487, 486, 323, 324, 1154, 325, 31])).
% 1.91/1.52 tff(1156,plain,
% 1.91/1.52 (~c1_1(a908)),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[1155, 1153])).
% 1.91/1.52 tff(1157,plain,
% 1.91/1.52 (~hskp7),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[484, 1156])).
% 1.91/1.52 tff(1158,plain,
% 1.91/1.52 (~c3_1(a912)),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[1073, 1157, 1055])).
% 1.91/1.52 tff(1159,plain,
% 1.91/1.52 (~c0_1(a903)),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[1088, 1157, 554, 884, 896])).
% 1.91/1.52 tff(1160,plain,
% 1.91/1.52 (~c1_1(a903)),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[808, 124, 488, 487, 486, 323, 324, 325, 884, 896, 31])).
% 1.91/1.52 tff(1161,plain,
% 1.91/1.52 (c0_1(a903) | (~c1_1(a921))),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[1095, 124, 543, 323, 324, 541, 325, 884, 520, 1160])).
% 1.91/1.52 tff(1162,plain,
% 1.91/1.52 (~c1_1(a921)),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[1161, 1159])).
% 1.91/1.52 tff(1163,plain,
% 1.91/1.52 (~c0_1(a936)),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[1114, 1159, 1162])).
% 1.91/1.52 tff(1164,plain,
% 1.91/1.52 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a908) | c1_1(a936) | c2_1(a936) | c0_1(a912) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908)) | (~c2_1(a912)) | c3_1(a912) | c0_1(a936))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a908) | c1_1(a936) | c2_1(a936) | c0_1(a912) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908)) | (~c2_1(a912)) | c3_1(a912) | c0_1(a936))),
% 1.91/1.52 inference(rewrite,[status(thm)],[])).
% 1.91/1.52 tff(1165,plain,
% 1.91/1.52 (((~ndr1_0) | c1_1(a908) | c3_1(a908) | (~c0_1(a908)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a936) | c0_1(a936) | c2_1(a936)) <=> (c1_1(a908) | c1_1(a936) | c2_1(a936) | c0_1(a912) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908)) | (~c2_1(a912)) | c3_1(a912) | c0_1(a936))),
% 1.91/1.52 inference(rewrite,[status(thm)],[])).
% 1.91/1.52 tff(1166,plain,
% 1.91/1.52 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a908) | c3_1(a908) | (~c0_1(a908)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a936) | c0_1(a936) | c2_1(a936))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a908) | c1_1(a936) | c2_1(a936) | c0_1(a912) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908)) | (~c2_1(a912)) | c3_1(a912) | c0_1(a936)))),
% 1.91/1.52 inference(monotonicity,[status(thm)],[1165])).
% 1.91/1.52 tff(1167,plain,
% 1.91/1.52 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a908) | c3_1(a908) | (~c0_1(a908)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a936) | c0_1(a936) | c2_1(a936))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a908) | c1_1(a936) | c2_1(a936) | c0_1(a912) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908)) | (~c2_1(a912)) | c3_1(a912) | c0_1(a936))),
% 1.91/1.52 inference(transitivity,[status(thm)],[1166, 1164])).
% 1.91/1.52 tff(1168,plain,
% 1.91/1.52 ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a908) | c3_1(a908) | (~c0_1(a908)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a936) | c0_1(a936) | c2_1(a936))),
% 1.91/1.52 inference(quant_inst,[status(thm)],[])).
% 1.91/1.52 tff(1169,plain,
% 1.91/1.52 ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a908) | c1_1(a936) | c2_1(a936) | c0_1(a912) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908)) | (~c2_1(a912)) | c3_1(a912) | c0_1(a936)),
% 1.91/1.52 inference(modus_ponens,[status(thm)],[1168, 1167])).
% 1.91/1.52 tff(1170,plain,
% 1.91/1.52 (~c0_1(a908)),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[1169, 124, 1141, 1156, 522, 521, 665, 1154, 540, 1163, 1158])).
% 1.91/1.52 tff(1171,plain,
% 1.91/1.52 (c0_1(a903) | (~c1_1(a906))),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[1121, 124, 323, 324, 325, 884, 520, 1160])).
% 1.91/1.52 tff(1172,plain,
% 1.91/1.52 (~c1_1(a906)),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[1171, 1159])).
% 1.91/1.52 tff(1173,plain,
% 1.91/1.52 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a908) | c0_1(a912) | c2_1(a908) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | c0_1(a908) | (~c2_1(a912)) | c3_1(a912))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a908) | c0_1(a912) | c2_1(a908) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | c0_1(a908) | (~c2_1(a912)) | c3_1(a912))),
% 1.91/1.52 inference(rewrite,[status(thm)],[])).
% 1.91/1.52 tff(1174,plain,
% 1.91/1.52 (((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a908) | c0_1(a908) | c2_1(a908)) <=> (c1_1(a908) | c0_1(a912) | c2_1(a908) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | c0_1(a908) | (~c2_1(a912)) | c3_1(a912))),
% 1.91/1.52 inference(rewrite,[status(thm)],[])).
% 1.91/1.52 tff(1175,plain,
% 1.91/1.52 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a908) | c0_1(a908) | c2_1(a908))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a908) | c0_1(a912) | c2_1(a908) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | c0_1(a908) | (~c2_1(a912)) | c3_1(a912)))),
% 1.91/1.52 inference(monotonicity,[status(thm)],[1174])).
% 1.91/1.52 tff(1176,plain,
% 1.91/1.52 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a908) | c0_1(a908) | c2_1(a908))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a908) | c0_1(a912) | c2_1(a908) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | c0_1(a908) | (~c2_1(a912)) | c3_1(a912))),
% 1.91/1.52 inference(transitivity,[status(thm)],[1175, 1173])).
% 1.91/1.52 tff(1177,plain,
% 1.91/1.52 ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a908) | c0_1(a908) | c2_1(a908))),
% 1.91/1.52 inference(quant_inst,[status(thm)],[])).
% 1.91/1.52 tff(1178,plain,
% 1.91/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a908) | c0_1(a912) | c2_1(a908) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | c0_1(a908) | (~c2_1(a912)) | c3_1(a912)),
% 1.91/1.52 inference(modus_ponens,[status(thm)],[1177, 1176])).
% 1.91/1.52 tff(1179,plain,
% 1.91/1.52 ($false),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[1178, 124, 1141, 1156, 323, 665, 1153, 325, 540, 1172, 1170, 1158])).
% 1.91/1.52 tff(1180,plain,(c2_1(a908) | (~c0_1(a906)) | c0_1(a912) | c3_1(a906) | c1_1(a936) | c2_1(a936) | c3_1(a908) | c3_1(a936) | c0_1(a921) | c3_1(a921) | c2_1(a903) | c3_1(a903) | (~c2_1(a906)) | (~c2_1(a921)) | c1_1(a912) | hskp6 | (~c0_1(a916)) | (~c1_1(a916)) | (~c3_1(a916))), inference(lemma,lemma(discharge,[]))).
% 1.91/1.52 tff(1181,plain,
% 1.91/1.52 ($false),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[1180, 1152, 1151, 665, 325, 1065, 1064, 323, 1063, 232, 541, 884, 896, 324, 243, 1055, 554, 1054, 1053, 1052])).
% 1.91/1.52 tff(1182,plain,(c1_1(a912) | c0_1(a912) | c3_1(a906) | (~c0_1(a906)) | c3_1(a921) | c2_1(a903) | c3_1(a903) | (~c2_1(a906)) | hskp6 | hskp12 | hskp21), inference(lemma,lemma(discharge,[]))).
% 1.91/1.52 tff(1183,plain,
% 1.91/1.52 (c1_1(a912)),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[1182, 32, 325, 323, 541, 884, 896, 324, 554, 665, 198])).
% 1.91/1.52 tff(1184,plain,
% 1.91/1.52 (~hskp10),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[676, 1124])).
% 1.91/1.52 tff(1185,plain,
% 1.91/1.52 (((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | c2_1(a912) | (~ndr1_0) | (~c1_1(a912)) | (~c3_1(a912)))) <=> ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp10 | c2_1(a912) | (~ndr1_0) | (~c1_1(a912)) | (~c3_1(a912)))),
% 1.91/1.52 inference(rewrite,[status(thm)],[])).
% 1.91/1.52 tff(1186,plain,
% 1.91/1.52 ((hskp21 | hskp10 | (~ndr1_0) | c2_1(a912) | (~c3_1(a912)) | (~c1_1(a912))) <=> (hskp21 | hskp10 | c2_1(a912) | (~ndr1_0) | (~c1_1(a912)) | (~c3_1(a912)))),
% 1.91/1.52 inference(rewrite,[status(thm)],[])).
% 1.91/1.52 tff(1187,plain,
% 1.91/1.52 (((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | (~ndr1_0) | c2_1(a912) | (~c3_1(a912)) | (~c1_1(a912)))) <=> ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | c2_1(a912) | (~ndr1_0) | (~c1_1(a912)) | (~c3_1(a912))))),
% 1.91/1.52 inference(monotonicity,[status(thm)],[1186])).
% 1.91/1.52 tff(1188,plain,
% 1.91/1.52 (((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | (~ndr1_0) | c2_1(a912) | (~c3_1(a912)) | (~c1_1(a912)))) <=> ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp10 | c2_1(a912) | (~ndr1_0) | (~c1_1(a912)) | (~c3_1(a912)))),
% 1.91/1.52 inference(transitivity,[status(thm)],[1187, 1185])).
% 1.91/1.52 tff(1189,plain,
% 1.91/1.52 ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | (~ndr1_0) | c2_1(a912) | (~c3_1(a912)) | (~c1_1(a912)))),
% 1.91/1.52 inference(quant_inst,[status(thm)],[])).
% 1.91/1.52 tff(1190,plain,
% 1.91/1.52 ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp10 | c2_1(a912) | (~ndr1_0) | (~c1_1(a912)) | (~c3_1(a912))),
% 1.91/1.52 inference(modus_ponens,[status(thm)],[1189, 1188])).
% 1.91/1.52 tff(1191,plain,
% 1.91/1.52 (hskp10 | c2_1(a912) | (~c3_1(a912))),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[1190, 124, 198, 690, 365])).
% 1.91/1.52 tff(1192,plain,
% 1.91/1.52 (~c3_1(a912)),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[1191, 1184, 1124])).
% 1.91/1.52 tff(1193,assumption,(~c2_1(a914)), introduced(assumption)).
% 1.91/1.52 tff(1194,plain,
% 1.91/1.52 (hskp10 | (~c1_1(a914))),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[400, 124, 198, 428, 1193, 365])).
% 1.91/1.52 tff(1195,plain,
% 1.91/1.52 (~c1_1(a914)),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[1194, 1184])).
% 1.91/1.52 tff(1196,plain,
% 1.91/1.52 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | c2_1(a912) | (~ndr1_0) | (~c1_1(a912)) | c3_1(a912) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c2_1(a912) | (~ndr1_0) | (~c1_1(a912)) | c3_1(a912) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)))),
% 1.91/1.52 inference(rewrite,[status(thm)],[])).
% 1.91/1.52 tff(1197,plain,
% 1.91/1.52 ((hskp21 | (~ndr1_0) | c2_1(a912) | c3_1(a912) | (~c1_1(a912)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914))) <=> (hskp21 | c2_1(a912) | (~ndr1_0) | (~c1_1(a912)) | c3_1(a912) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)))),
% 1.91/1.52 inference(rewrite,[status(thm)],[])).
% 1.91/1.52 tff(1198,plain,
% 1.91/1.52 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a912) | c3_1(a912) | (~c1_1(a912)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | c2_1(a912) | (~ndr1_0) | (~c1_1(a912)) | c3_1(a912) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914))))),
% 1.91/1.52 inference(monotonicity,[status(thm)],[1197])).
% 1.91/1.52 tff(1199,plain,
% 1.91/1.52 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a912) | c3_1(a912) | (~c1_1(a912)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c2_1(a912) | (~ndr1_0) | (~c1_1(a912)) | c3_1(a912) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)))),
% 1.91/1.52 inference(transitivity,[status(thm)],[1198, 1196])).
% 1.91/1.52 tff(1200,plain,
% 1.91/1.52 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a912) | c3_1(a912) | (~c1_1(a912)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914)))),
% 1.91/1.52 inference(quant_inst,[status(thm)],[])).
% 1.91/1.52 tff(1201,plain,
% 1.91/1.52 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c2_1(a912) | (~ndr1_0) | (~c1_1(a912)) | c3_1(a912) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914))),
% 1.91/1.52 inference(modus_ponens,[status(thm)],[1200, 1199])).
% 1.91/1.52 tff(1202,plain,
% 1.91/1.52 ($false),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[1201, 124, 198, 429, 428, 690, 1124, 197, 1195, 1192])).
% 1.91/1.52 tff(1203,plain,(c2_1(a912) | hskp21 | (~c0_1(a914)) | (~c3_1(a914)) | (~c1_1(a912)) | c2_1(a914)), inference(lemma,lemma(discharge,[]))).
% 1.91/1.52 tff(1204,plain,
% 1.91/1.52 (c2_1(a912)),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[1203, 1060, 198, 1057, 1183, 1049])).
% 1.91/1.52 tff(1205,plain,
% 1.91/1.52 (hskp7),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[713, 1183, 554, 1204, 665])).
% 1.91/1.52 tff(1206,plain,
% 1.91/1.52 (~c3_1(a908)),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[467, 1205])).
% 1.91/1.52 tff(1207,plain,
% 1.91/1.52 (~c2_1(a908)),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[473, 1205])).
% 1.91/1.52 tff(1208,plain,
% 1.91/1.52 (c1_1(a908)),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[484, 1205])).
% 1.91/1.52 tff(1209,plain,
% 1.91/1.52 ($false),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[494, 124, 1054, 1053, 1052, 1208, 323, 324, 1207, 1206, 325, 31])).
% 1.91/1.52 tff(1210,plain,(hskp12 | (~c0_1(a906)) | (~c2_1(a906)) | c3_1(a906) | hskp6 | c0_1(a912) | hskp21 | c3_1(a921) | c2_1(a903) | c3_1(a903)), inference(lemma,lemma(discharge,[]))).
% 1.91/1.52 tff(1211,plain,
% 1.91/1.52 (c3_1(a921)),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[1210, 1046, 324, 325, 554, 665, 198, 323, 884, 896])).
% 1.91/1.52 tff(1212,plain,
% 1.91/1.52 ($false),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[225, 1211, 1047])).
% 1.91/1.52 tff(1213,plain,(c0_1(a912) | (~c2_1(a906)) | c3_1(a906) | hskp6 | hskp21 | (~c0_1(a906)) | c2_1(a903) | c3_1(a903)), inference(lemma,lemma(discharge,[]))).
% 1.91/1.52 tff(1214,plain,
% 1.91/1.52 (c0_1(a912)),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[1213, 554, 325, 324, 198, 323, 884, 896])).
% 1.91/1.52 tff(1215,plain,
% 1.91/1.52 (~hskp10),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[627, 1214])).
% 1.91/1.52 tff(1216,plain,
% 1.91/1.52 (~hskp12),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[377, 1215, 198])).
% 1.91/1.52 tff(1217,plain,
% 1.91/1.52 (hskp13),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[219, 1216, 198])).
% 1.91/1.52 tff(1218,plain,
% 1.91/1.52 (c2_1(a921)),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[242, 1217])).
% 1.91/1.52 tff(1219,plain,
% 1.91/1.52 (~c0_1(a921)),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[231, 1217])).
% 1.91/1.52 tff(1220,plain,
% 1.91/1.52 (~c3_1(a921)),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[225, 1217])).
% 1.91/1.52 tff(1221,plain,
% 1.91/1.52 (hskp11),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[997, 1220, 324, 325, 884, 896, 323, 1216, 1219, 1218])).
% 1.91/1.52 tff(1222,plain,
% 1.91/1.52 (~c2_1(a914)),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[69, 1221])).
% 1.91/1.52 tff(1223,plain,
% 1.91/1.52 (c3_1(a914)),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[80, 1221])).
% 1.91/1.52 tff(1224,plain,
% 1.91/1.52 (~c1_1(a914)),
% 1.91/1.52 inference(unit_resolution,[status(thm)],[400, 124, 198, 1215, 1223, 1222, 365])).
% 1.91/1.52 tff(1225,plain,
% 1.91/1.52 (^[V: $i, U: $i] : refl((hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 1.91/1.52 inference(bind,[status(th)],[])).
% 1.91/1.52 tff(1226,plain,
% 1.91/1.52 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.91/1.52 inference(quant_intro,[status(thm)],[1225])).
% 1.91/1.52 tff(1227,plain,
% 1.91/1.52 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.91/1.52 inference(rewrite,[status(thm)],[])).
% 1.91/1.52 tff(1228,plain,
% 1.91/1.52 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp15) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp15))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp15) <=> (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp15) <=> (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 1.91/1.53 inference(bind,[status(th)],[])).
% 1.91/1.53 tff(1229,plain,
% 1.91/1.53 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp15) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.91/1.53 inference(quant_intro,[status(thm)],[1228])).
% 1.91/1.53 tff(1230,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause171')).
% 1.91/1.53 tff(1231,plain,
% 1.91/1.53 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.91/1.53 inference(modus_ponens,[status(thm)],[1230, 1229])).
% 1.91/1.53 tff(1232,plain,
% 1.91/1.53 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.91/1.53 inference(modus_ponens,[status(thm)],[1231, 1227])).
% 1.91/1.53 tff(1233,plain,(
% 1.91/1.53 ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.91/1.53 inference(skolemize,[status(sab)],[1232])).
% 1.91/1.53 tff(1234,plain,
% 1.91/1.53 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.91/1.53 inference(modus_ponens,[status(thm)],[1233, 1226])).
% 1.91/1.53 tff(1235,plain,
% 1.91/1.53 (c0_1(a914)),
% 1.91/1.53 inference(unit_resolution,[status(thm)],[91, 1221])).
% 1.91/1.53 tff(1236,plain,
% 1.91/1.53 (hskp28),
% 1.91/1.53 inference(unit_resolution,[status(thm)],[249, 124, 1216, 1218, 1219, 1220, 208])).
% 1.91/1.53 tff(1237,plain,
% 1.91/1.53 (c3_1(a916)),
% 1.91/1.53 inference(unit_resolution,[status(thm)],[271, 1236])).
% 1.91/1.53 tff(1238,plain,
% 1.91/1.53 (c1_1(a916)),
% 1.91/1.53 inference(unit_resolution,[status(thm)],[282, 1236])).
% 1.91/1.53 tff(1239,plain,
% 1.91/1.53 (c0_1(a916)),
% 1.91/1.53 inference(unit_resolution,[status(thm)],[260, 1236])).
% 1.91/1.53 tff(1240,plain,
% 1.91/1.53 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | c2_1(a914) | (~ndr1_0) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp15 | c2_1(a914) | (~ndr1_0) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 1.91/1.53 inference(rewrite,[status(thm)],[])).
% 1.91/1.53 tff(1241,plain,
% 1.91/1.53 ((hskp15 | (~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c2_1(a914) | c1_1(a914) | (~c0_1(a914))) <=> (hskp15 | c2_1(a914) | (~ndr1_0) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 1.91/1.53 inference(rewrite,[status(thm)],[])).
% 1.91/1.53 tff(1242,plain,
% 1.91/1.53 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c2_1(a914) | c1_1(a914) | (~c0_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | c2_1(a914) | (~ndr1_0) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916))))),
% 1.97/1.53 inference(monotonicity,[status(thm)],[1241])).
% 1.97/1.53 tff(1243,plain,
% 1.97/1.53 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c2_1(a914) | c1_1(a914) | (~c0_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp15 | c2_1(a914) | (~ndr1_0) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 1.97/1.53 inference(transitivity,[status(thm)],[1242, 1240])).
% 1.97/1.53 tff(1244,plain,
% 1.97/1.53 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c2_1(a914) | c1_1(a914) | (~c0_1(a914)))),
% 1.97/1.53 inference(quant_inst,[status(thm)],[])).
% 1.97/1.53 tff(1245,plain,
% 1.97/1.53 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp15 | c2_1(a914) | (~ndr1_0) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916))),
% 1.97/1.53 inference(modus_ponens,[status(thm)],[1244, 1243])).
% 1.97/1.53 tff(1246,plain,
% 1.97/1.53 (hskp15),
% 1.97/1.53 inference(unit_resolution,[status(thm)],[1245, 124, 1239, 1238, 1237, 1235, 1222, 1234, 1224])).
% 1.97/1.53 tff(1247,plain,
% 1.97/1.53 (((~hskp15) | (~c1_1(a924))) <=> ((~hskp15) | (~c1_1(a924)))),
% 1.97/1.53 inference(rewrite,[status(thm)],[])).
% 1.97/1.53 tff(1248,plain,
% 1.97/1.53 (((~c1_1(a924)) | (~hskp15)) <=> ((~hskp15) | (~c1_1(a924)))),
% 1.97/1.53 inference(rewrite,[status(thm)],[])).
% 1.97/1.53 tff(1249,axiom,((~c1_1(a924)) | (~hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause102')).
% 1.97/1.53 tff(1250,plain,
% 1.97/1.53 ((~hskp15) | (~c1_1(a924))),
% 1.97/1.53 inference(modus_ponens,[status(thm)],[1249, 1248])).
% 1.97/1.53 tff(1251,plain,
% 1.97/1.53 ((~hskp15) | (~c1_1(a924))),
% 1.97/1.53 inference(modus_ponens,[status(thm)],[1250, 1247])).
% 1.97/1.53 tff(1252,plain,
% 1.97/1.53 (~c1_1(a924)),
% 1.97/1.53 inference(unit_resolution,[status(thm)],[1251, 1246])).
% 1.97/1.53 tff(1253,plain,
% 1.97/1.53 (hskp17 | c1_1(a914)),
% 1.97/1.53 inference(unit_resolution,[status(thm)],[454, 124, 1216, 1235, 1222, 448])).
% 1.97/1.53 tff(1254,plain,
% 1.97/1.53 (hskp17),
% 1.97/1.53 inference(unit_resolution,[status(thm)],[1253, 1224])).
% 1.97/1.53 tff(1255,plain,
% 1.97/1.53 (~c3_1(a936)),
% 1.97/1.53 inference(unit_resolution,[status(thm)],[460, 1254])).
% 1.97/1.53 tff(1256,plain,
% 1.97/1.53 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c1_1(a903)) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c1_1(a903)) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)))),
% 1.97/1.53 inference(rewrite,[status(thm)],[])).
% 1.97/1.53 tff(1257,plain,
% 1.97/1.53 ((hskp21 | (~ndr1_0) | c2_1(a903) | c3_1(a903) | (~c1_1(a903)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914))) <=> (hskp21 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c1_1(a903)) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)))),
% 1.97/1.53 inference(rewrite,[status(thm)],[])).
% 1.97/1.53 tff(1258,plain,
% 1.97/1.53 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a903) | c3_1(a903) | (~c1_1(a903)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c1_1(a903)) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914))))),
% 1.97/1.53 inference(monotonicity,[status(thm)],[1257])).
% 1.97/1.53 tff(1259,plain,
% 1.97/1.53 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a903) | c3_1(a903) | (~c1_1(a903)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c1_1(a903)) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)))),
% 1.97/1.53 inference(transitivity,[status(thm)],[1258, 1256])).
% 1.97/1.53 tff(1260,plain,
% 1.97/1.53 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a903) | c3_1(a903) | (~c1_1(a903)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914)))),
% 1.97/1.53 inference(quant_inst,[status(thm)],[])).
% 1.97/1.53 tff(1261,plain,
% 1.97/1.53 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c1_1(a903)) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914))),
% 1.97/1.53 inference(modus_ponens,[status(thm)],[1260, 1259])).
% 1.97/1.53 tff(1262,plain,
% 1.97/1.53 (~c1_1(a903)),
% 1.97/1.53 inference(unit_resolution,[status(thm)],[1261, 124, 198, 1235, 1223, 884, 896, 197, 1224])).
% 1.97/1.53 tff(1263,plain,
% 1.97/1.53 (((~hskp15) | (~c0_1(a924))) <=> ((~hskp15) | (~c0_1(a924)))),
% 1.97/1.53 inference(rewrite,[status(thm)],[])).
% 1.97/1.53 tff(1264,plain,
% 1.97/1.53 (((~c0_1(a924)) | (~hskp15)) <=> ((~hskp15) | (~c0_1(a924)))),
% 1.97/1.53 inference(rewrite,[status(thm)],[])).
% 1.97/1.53 tff(1265,axiom,((~c0_1(a924)) | (~hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause101')).
% 1.97/1.53 tff(1266,plain,
% 1.97/1.53 ((~hskp15) | (~c0_1(a924))),
% 1.97/1.53 inference(modus_ponens,[status(thm)],[1265, 1264])).
% 1.97/1.53 tff(1267,plain,
% 1.97/1.53 ((~hskp15) | (~c0_1(a924))),
% 1.97/1.53 inference(modus_ponens,[status(thm)],[1266, 1263])).
% 1.97/1.53 tff(1268,plain,
% 1.97/1.53 (~c0_1(a924)),
% 1.97/1.53 inference(unit_resolution,[status(thm)],[1267, 1246])).
% 1.97/1.53 tff(1269,plain,
% 1.97/1.53 (~c2_1(a936)),
% 1.97/1.53 inference(unit_resolution,[status(thm)],[502, 1254])).
% 1.97/1.53 tff(1270,plain,
% 1.97/1.53 (~c1_1(a936)),
% 1.97/1.53 inference(unit_resolution,[status(thm)],[508, 1254])).
% 1.97/1.53 tff(1271,plain,
% 1.97/1.53 (((~hskp15) | c2_1(a924)) <=> ((~hskp15) | c2_1(a924))),
% 1.97/1.53 inference(rewrite,[status(thm)],[])).
% 1.97/1.53 tff(1272,axiom,((~hskp15) | c2_1(a924)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause61')).
% 1.97/1.53 tff(1273,plain,
% 1.97/1.53 ((~hskp15) | c2_1(a924)),
% 1.97/1.53 inference(modus_ponens,[status(thm)],[1272, 1271])).
% 1.97/1.53 tff(1274,plain,
% 1.97/1.53 ((~hskp15) | c2_1(a924)),
% 1.97/1.53 inference(modus_ponens,[status(thm)],[1273, 1271])).
% 1.97/1.53 tff(1275,plain,
% 1.97/1.53 ((~hskp15) | c2_1(a924)),
% 1.97/1.53 inference(modus_ponens,[status(thm)],[1274, 1271])).
% 1.97/1.53 tff(1276,plain,
% 1.97/1.53 ((~hskp15) | c2_1(a924)),
% 1.97/1.53 inference(modus_ponens,[status(thm)],[1275, 1271])).
% 1.97/1.53 tff(1277,plain,
% 1.97/1.53 ((~hskp15) | c2_1(a924)),
% 1.97/1.53 inference(modus_ponens,[status(thm)],[1276, 1271])).
% 1.97/1.53 tff(1278,plain,
% 1.97/1.53 ((~hskp15) | c2_1(a924)),
% 1.97/1.53 inference(modus_ponens,[status(thm)],[1277, 1271])).
% 1.97/1.53 tff(1279,plain,
% 1.97/1.53 ((~hskp15) | c2_1(a924)),
% 1.97/1.53 inference(modus_ponens,[status(thm)],[1278, 1271])).
% 1.97/1.53 tff(1280,plain,
% 1.97/1.53 ((~hskp15) | c2_1(a924)),
% 1.97/1.53 inference(modus_ponens,[status(thm)],[1279, 1271])).
% 1.97/1.53 tff(1281,plain,
% 1.97/1.53 (c2_1(a924)),
% 1.97/1.53 inference(unit_resolution,[status(thm)],[1280, 1246])).
% 1.97/1.53 tff(1282,assumption,(~c1_1(a924)), introduced(assumption)).
% 1.97/1.53 tff(1283,assumption,(~c0_1(a924)), introduced(assumption)).
% 1.97/1.53 tff(1284,plain,
% 1.97/1.53 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | c0_1(a924) | c1_1(a924) | (~ndr1_0) | (~c3_1(a924)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c0_1(a924) | c1_1(a924) | (~ndr1_0) | (~c3_1(a924)))),
% 1.97/1.53 inference(rewrite,[status(thm)],[])).
% 1.97/1.53 tff(1285,plain,
% 1.97/1.53 ((hskp7 | hskp6 | (~ndr1_0) | c1_1(a924) | c0_1(a924) | (~c3_1(a924))) <=> (hskp7 | hskp6 | c0_1(a924) | c1_1(a924) | (~ndr1_0) | (~c3_1(a924)))),
% 1.97/1.53 inference(rewrite,[status(thm)],[])).
% 1.97/1.53 tff(1286,plain,
% 1.97/1.53 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a924) | c0_1(a924) | (~c3_1(a924)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | c0_1(a924) | c1_1(a924) | (~ndr1_0) | (~c3_1(a924))))),
% 1.97/1.53 inference(monotonicity,[status(thm)],[1285])).
% 1.97/1.53 tff(1287,plain,
% 1.97/1.53 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a924) | c0_1(a924) | (~c3_1(a924)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c0_1(a924) | c1_1(a924) | (~ndr1_0) | (~c3_1(a924)))),
% 1.97/1.53 inference(transitivity,[status(thm)],[1286, 1284])).
% 1.97/1.53 tff(1288,plain,
% 1.97/1.53 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a924) | c0_1(a924) | (~c3_1(a924)))),
% 1.97/1.53 inference(quant_inst,[status(thm)],[])).
% 1.97/1.53 tff(1289,plain,
% 1.97/1.53 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c0_1(a924) | c1_1(a924) | (~ndr1_0) | (~c3_1(a924))),
% 1.97/1.53 inference(modus_ponens,[status(thm)],[1288, 1287])).
% 1.97/1.53 tff(1290,plain,
% 1.97/1.53 (hskp7 | (~c3_1(a924))),
% 1.97/1.53 inference(unit_resolution,[status(thm)],[1289, 124, 554, 1283, 1282, 564])).
% 1.97/1.53 tff(1291,plain,
% 1.97/1.53 (~c3_1(a924)),
% 1.97/1.53 inference(unit_resolution,[status(thm)],[1290, 21])).
% 1.97/1.53 tff(1292,plain,
% 1.97/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a903) | c2_1(a936) | c3_1(a936) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a936)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a903) | c2_1(a936) | c3_1(a936) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a936)))),
% 1.97/1.53 inference(rewrite,[status(thm)],[])).
% 1.97/1.53 tff(1293,plain,
% 1.97/1.53 (((~ndr1_0) | c2_1(a936) | c3_1(a936) | (~c0_1(a936)) | c3_1(a903) | c2_1(a903) | c0_1(a903) | c3_1(a903) | c1_1(a903) | c0_1(a903)) <=> (c0_1(a903) | c2_1(a936) | c3_1(a936) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a936)))),
% 1.97/1.53 inference(rewrite,[status(thm)],[])).
% 1.97/1.53 tff(1294,plain,
% 1.97/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a936) | c3_1(a936) | (~c0_1(a936)) | c3_1(a903) | c2_1(a903) | c0_1(a903) | c3_1(a903) | c1_1(a903) | c0_1(a903))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a903) | c2_1(a936) | c3_1(a936) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a936))))),
% 1.97/1.53 inference(monotonicity,[status(thm)],[1293])).
% 1.97/1.53 tff(1295,plain,
% 1.97/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a936) | c3_1(a936) | (~c0_1(a936)) | c3_1(a903) | c2_1(a903) | c0_1(a903) | c3_1(a903) | c1_1(a903) | c0_1(a903))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a903) | c2_1(a936) | c3_1(a936) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a936)))),
% 1.97/1.53 inference(transitivity,[status(thm)],[1294, 1292])).
% 1.97/1.53 tff(1296,plain,
% 1.97/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a936) | c3_1(a936) | (~c0_1(a936)) | c3_1(a903) | c2_1(a903) | c0_1(a903) | c3_1(a903) | c1_1(a903) | c0_1(a903))),
% 1.97/1.53 inference(quant_inst,[status(thm)],[])).
% 1.97/1.53 tff(1297,plain,
% 1.97/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a903) | c2_1(a936) | c3_1(a936) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a936))),
% 1.97/1.53 inference(modus_ponens,[status(thm)],[1296, 1295])).
% 1.97/1.53 tff(1298,plain,
% 1.97/1.53 (c0_1(a903) | (~c0_1(a936))),
% 1.97/1.53 inference(unit_resolution,[status(thm)],[1297, 124, 521, 608, 884, 896, 1107, 883])).
% 1.97/1.53 tff(1299,plain,
% 1.97/1.53 (~c0_1(a936)),
% 1.97/1.53 inference(unit_resolution,[status(thm)],[1298, 1089])).
% 1.97/1.53 tff(1300,assumption,(c2_1(a924)), introduced(assumption)).
% 1.97/1.53 tff(1301,plain,
% 1.97/1.53 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a936) | c2_1(a936) | c0_1(a924) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | c3_1(a924) | (~c2_1(a924)) | c0_1(a936))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a936) | c2_1(a936) | c0_1(a924) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | c3_1(a924) | (~c2_1(a924)) | c0_1(a936))),
% 1.97/1.53 inference(rewrite,[status(thm)],[])).
% 1.97/1.53 tff(1302,plain,
% 1.97/1.53 (((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a924) | c0_1(a924) | (~c2_1(a924)) | c1_1(a936) | c0_1(a936) | c2_1(a936)) <=> (c1_1(a936) | c2_1(a936) | c0_1(a924) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | c3_1(a924) | (~c2_1(a924)) | c0_1(a936))),
% 1.97/1.53 inference(rewrite,[status(thm)],[])).
% 1.97/1.53 tff(1303,plain,
% 1.97/1.53 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a924) | c0_1(a924) | (~c2_1(a924)) | c1_1(a936) | c0_1(a936) | c2_1(a936))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a936) | c2_1(a936) | c0_1(a924) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | c3_1(a924) | (~c2_1(a924)) | c0_1(a936)))),
% 1.97/1.53 inference(monotonicity,[status(thm)],[1302])).
% 1.97/1.53 tff(1304,plain,
% 1.97/1.53 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a924) | c0_1(a924) | (~c2_1(a924)) | c1_1(a936) | c0_1(a936) | c2_1(a936))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a936) | c2_1(a936) | c0_1(a924) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | c3_1(a924) | (~c2_1(a924)) | c0_1(a936))),
% 1.97/1.53 inference(transitivity,[status(thm)],[1303, 1301])).
% 1.97/1.53 tff(1305,plain,
% 1.97/1.53 ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a924) | c0_1(a924) | (~c2_1(a924)) | c1_1(a936) | c0_1(a936) | c2_1(a936))),
% 1.97/1.53 inference(quant_inst,[status(thm)],[])).
% 1.97/1.53 tff(1306,plain,
% 1.97/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a936) | c2_1(a936) | c0_1(a924) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | c3_1(a924) | (~c2_1(a924)) | c0_1(a936)),
% 1.97/1.53 inference(modus_ponens,[status(thm)],[1305, 1304])).
% 1.97/1.53 tff(1307,plain,
% 1.97/1.53 ($false),
% 1.97/1.53 inference(unit_resolution,[status(thm)],[1306, 124, 1300, 323, 522, 521, 1283, 325, 540, 1123, 1299, 1291])).
% 1.97/1.53 tff(1308,plain,(hskp7 | (~c2_1(a924)) | (~c0_1(a906)) | c1_1(a936) | c2_1(a936) | c0_1(a924) | c3_1(a906) | (~c2_1(a906)) | c2_1(a903) | c1_1(a903) | c3_1(a936) | c3_1(a903) | hskp6 | c1_1(a924)), inference(lemma,lemma(discharge,[]))).
% 1.97/1.53 tff(1309,plain,
% 1.97/1.53 (hskp7),
% 1.97/1.53 inference(unit_resolution,[status(thm)],[1308, 1281, 323, 1270, 1269, 1268, 325, 324, 884, 1262, 1255, 896, 554, 1252])).
% 1.97/1.53 tff(1310,plain,
% 1.97/1.53 (~c3_1(a908)),
% 1.97/1.53 inference(unit_resolution,[status(thm)],[467, 1309])).
% 1.97/1.53 tff(1311,plain,
% 1.97/1.53 (~c2_1(a908)),
% 1.97/1.53 inference(unit_resolution,[status(thm)],[473, 1309])).
% 1.97/1.53 tff(1312,plain,
% 1.97/1.53 (c1_1(a908)),
% 1.97/1.53 inference(unit_resolution,[status(thm)],[484, 1309])).
% 1.97/1.53 tff(1313,plain,
% 1.97/1.53 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)))),
% 1.97/1.53 inference(rewrite,[status(thm)],[])).
% 1.97/1.53 tff(1314,plain,
% 1.97/1.53 ((hskp21 | (~ndr1_0) | c2_1(a908) | c3_1(a908) | (~c1_1(a908)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914))) <=> (hskp21 | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)))),
% 1.97/1.53 inference(rewrite,[status(thm)],[])).
% 1.97/1.53 tff(1315,plain,
% 1.97/1.53 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a908) | c3_1(a908) | (~c1_1(a908)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914))))),
% 1.97/1.53 inference(monotonicity,[status(thm)],[1314])).
% 1.97/1.53 tff(1316,plain,
% 1.97/1.53 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a908) | c3_1(a908) | (~c1_1(a908)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)))),
% 1.97/1.53 inference(transitivity,[status(thm)],[1315, 1313])).
% 1.97/1.53 tff(1317,plain,
% 1.97/1.53 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a908) | c3_1(a908) | (~c1_1(a908)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914)))),
% 1.97/1.53 inference(quant_inst,[status(thm)],[])).
% 1.97/1.53 tff(1318,plain,
% 1.97/1.53 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914))),
% 1.97/1.53 inference(modus_ponens,[status(thm)],[1317, 1316])).
% 1.97/1.53 tff(1319,plain,
% 1.97/1.53 ($false),
% 1.97/1.53 inference(unit_resolution,[status(thm)],[1318, 124, 198, 1235, 1223, 1312, 1311, 1310, 197, 1224])).
% 1.97/1.53 tff(1320,plain,(hskp6 | hskp21 | (~c0_1(a906)) | c3_1(a906) | (~c2_1(a906)) | c2_1(a903) | c3_1(a903)), inference(lemma,lemma(discharge,[]))).
% 1.97/1.53 tff(1321,plain,
% 1.97/1.53 (hskp6),
% 1.97/1.53 inference(unit_resolution,[status(thm)],[1320, 884, 323, 325, 324, 198, 896])).
% 1.97/1.53 tff(1322,plain,
% 1.97/1.53 (~c2_1(a907)),
% 1.97/1.53 inference(unit_resolution,[status(thm)],[407, 1321])).
% 1.97/1.53 tff(1323,assumption,(~hskp13), introduced(assumption)).
% 1.97/1.53 tff(1324,plain,
% 1.97/1.53 (hskp12),
% 1.97/1.53 inference(unit_resolution,[status(thm)],[219, 1323, 198])).
% 1.97/1.53 tff(1325,plain,
% 1.97/1.53 (hskp10),
% 1.97/1.53 inference(unit_resolution,[status(thm)],[377, 1324, 198])).
% 1.97/1.53 tff(1326,plain,
% 1.97/1.53 (~c0_1(a912)),
% 1.97/1.53 inference(unit_resolution,[status(thm)],[627, 1325])).
% 1.97/1.53 tff(1327,plain,
% 1.97/1.53 (c2_1(a912)),
% 1.97/1.53 inference(unit_resolution,[status(thm)],[676, 1325])).
% 1.97/1.53 tff(1328,plain,
% 1.97/1.53 (((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c3_1(a912)))) <=> ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp13 | hskp7 | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c3_1(a912)))),
% 1.97/1.53 inference(rewrite,[status(thm)],[])).
% 1.97/1.53 tff(1329,plain,
% 1.97/1.53 ((hskp13 | hskp7 | (~ndr1_0) | c0_1(a912) | (~c2_1(a912)) | (~c3_1(a912))) <=> (hskp13 | hskp7 | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c3_1(a912)))),
% 1.97/1.53 inference(rewrite,[status(thm)],[])).
% 1.97/1.53 tff(1330,plain,
% 1.97/1.53 (((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | (~ndr1_0) | c0_1(a912) | (~c2_1(a912)) | (~c3_1(a912)))) <=> ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c3_1(a912))))),
% 1.97/1.53 inference(monotonicity,[status(thm)],[1329])).
% 1.97/1.53 tff(1331,plain,
% 1.97/1.53 (((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | (~ndr1_0) | c0_1(a912) | (~c2_1(a912)) | (~c3_1(a912)))) <=> ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp13 | hskp7 | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c3_1(a912)))),
% 1.97/1.53 inference(transitivity,[status(thm)],[1330, 1328])).
% 1.97/1.53 tff(1332,plain,
% 1.97/1.53 ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | (~ndr1_0) | c0_1(a912) | (~c2_1(a912)) | (~c3_1(a912)))),
% 1.97/1.53 inference(quant_inst,[status(thm)],[])).
% 1.97/1.53 tff(1333,plain,
% 1.97/1.53 ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp13 | hskp7 | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c3_1(a912))),
% 1.97/1.53 inference(modus_ponens,[status(thm)],[1332, 1331])).
% 1.97/1.53 tff(1334,plain,
% 1.97/1.53 (~c3_1(a912)),
% 1.97/1.53 inference(unit_resolution,[status(thm)],[1333, 124, 1323, 21, 1327, 1326, 20])).
% 1.97/1.53 tff(1335,plain,
% 1.97/1.53 (~c2_1(a917)),
% 1.97/1.53 inference(unit_resolution,[status(thm)],[332, 1324])).
% 1.97/1.53 tff(1336,plain,
% 1.97/1.53 (c3_1(a917)),
% 1.97/1.53 inference(unit_resolution,[status(thm)],[354, 1324])).
% 1.97/1.53 tff(1337,plain,
% 1.97/1.53 (c1_1(a917)),
% 1.97/1.53 inference(unit_resolution,[status(thm)],[343, 1324])).
% 1.97/1.53 tff(1338,plain,
% 1.97/1.53 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (c2_1(a917) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c1_1(a903)) | (~c3_1(a917)) | (~c1_1(a917)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | c2_1(a917) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c1_1(a903)) | (~c3_1(a917)) | (~c1_1(a917)))),
% 1.97/1.53 inference(rewrite,[status(thm)],[])).
% 1.97/1.53 tff(1339,plain,
% 1.97/1.53 (((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a903) | c2_1(a903) | (~c1_1(a903))) <=> (c2_1(a917) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c1_1(a903)) | (~c3_1(a917)) | (~c1_1(a917)))),
% 1.97/1.53 inference(rewrite,[status(thm)],[])).
% 1.97/1.53 tff(1340,plain,
% 1.97/1.53 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a903) | c2_1(a903) | (~c1_1(a903)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (c2_1(a917) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c1_1(a903)) | (~c3_1(a917)) | (~c1_1(a917))))),
% 1.97/1.53 inference(monotonicity,[status(thm)],[1339])).
% 1.97/1.53 tff(1341,plain,
% 1.97/1.53 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a903) | c2_1(a903) | (~c1_1(a903)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | c2_1(a917) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c1_1(a903)) | (~c3_1(a917)) | (~c1_1(a917)))),
% 1.97/1.53 inference(transitivity,[status(thm)],[1340, 1338])).
% 1.97/1.53 tff(1342,plain,
% 1.97/1.53 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a903) | c2_1(a903) | (~c1_1(a903)))),
% 1.97/1.53 inference(quant_inst,[status(thm)],[])).
% 1.97/1.53 tff(1343,plain,
% 1.97/1.53 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | c2_1(a917) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c1_1(a903)) | (~c3_1(a917)) | (~c1_1(a917))),
% 1.97/1.53 inference(modus_ponens,[status(thm)],[1342, 1341])).
% 1.97/1.53 tff(1344,plain,
% 1.97/1.53 (~c1_1(a903)),
% 1.97/1.53 inference(unit_resolution,[status(thm)],[1343, 124, 1337, 1336, 1335, 884, 896, 10])).
% 1.97/1.53 tff(1345,plain,
% 1.97/1.53 (c1_1(a912)),
% 1.97/1.53 inference(unit_resolution,[status(thm)],[687, 1325])).
% 1.97/1.53 tff(1346,plain,
% 1.97/1.53 (hskp14),
% 1.97/1.53 inference(unit_resolution,[status(thm)],[706, 124, 21, 1345, 1327, 1326, 700])).
% 1.97/1.53 tff(1347,plain,
% 1.97/1.53 (~c1_1(a923)),
% 1.97/1.53 inference(unit_resolution,[status(thm)],[570, 1346])).
% 1.97/1.53 tff(1348,plain,
% 1.97/1.53 (~c0_1(a923)),
% 1.97/1.53 inference(unit_resolution,[status(thm)],[576, 1346])).
% 1.97/1.53 tff(1349,plain,
% 1.97/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a917) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | c1_1(a906) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a917)) | (~c1_1(a917)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a917) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | c1_1(a906) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a917)) | (~c1_1(a917)))),
% 1.97/1.54 inference(rewrite,[status(thm)],[])).
% 1.97/1.54 tff(1350,plain,
% 1.97/1.54 (((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a906) | c1_1(a906) | (~c2_1(a906)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912))) <=> (c2_1(a917) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | c1_1(a906) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a917)) | (~c1_1(a917)))),
% 1.97/1.54 inference(rewrite,[status(thm)],[])).
% 1.97/1.54 tff(1351,plain,
% 1.97/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a906) | c1_1(a906) | (~c2_1(a906)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a917) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | c1_1(a906) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a917)) | (~c1_1(a917))))),
% 1.97/1.54 inference(monotonicity,[status(thm)],[1350])).
% 1.97/1.54 tff(1352,plain,
% 1.97/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a906) | c1_1(a906) | (~c2_1(a906)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a917) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | c1_1(a906) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a917)) | (~c1_1(a917)))),
% 1.97/1.54 inference(transitivity,[status(thm)],[1351, 1349])).
% 1.97/1.54 tff(1353,plain,
% 1.97/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a906) | c1_1(a906) | (~c2_1(a906)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))),
% 1.97/1.54 inference(quant_inst,[status(thm)],[])).
% 1.97/1.54 tff(1354,plain,
% 1.97/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a917) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | c1_1(a906) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a917)) | (~c1_1(a917))),
% 1.97/1.54 inference(modus_ponens,[status(thm)],[1353, 1352])).
% 1.97/1.54 tff(1355,plain,
% 1.97/1.54 (c1_1(a906)),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[1354, 124, 1337, 1336, 1345, 1327, 324, 1335, 1326, 325, 743])).
% 1.97/1.54 tff(1356,plain,
% 1.97/1.54 (c0_1(a903)),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[1121, 124, 323, 324, 325, 884, 520, 1355, 1344])).
% 1.97/1.54 tff(1357,plain,
% 1.97/1.54 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a923) | c1_1(a923) | c0_1(a912) | c3_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a903)) | (~c2_1(a912)) | c3_1(a912) | c2_1(a923))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a923) | c1_1(a923) | c0_1(a912) | c3_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a903)) | (~c2_1(a912)) | c3_1(a912) | c2_1(a923))),
% 1.97/1.54 inference(rewrite,[status(thm)],[])).
% 1.97/1.54 tff(1358,plain,
% 1.97/1.54 (((~ndr1_0) | c1_1(a903) | c3_1(a903) | (~c0_1(a903)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a923) | c0_1(a923) | c2_1(a923)) <=> (c0_1(a923) | c1_1(a923) | c0_1(a912) | c3_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a903)) | (~c2_1(a912)) | c3_1(a912) | c2_1(a923))),
% 1.97/1.54 inference(rewrite,[status(thm)],[])).
% 1.97/1.54 tff(1359,plain,
% 1.97/1.54 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a903) | c3_1(a903) | (~c0_1(a903)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a923) | c0_1(a923) | c2_1(a923))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a923) | c1_1(a923) | c0_1(a912) | c3_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a903)) | (~c2_1(a912)) | c3_1(a912) | c2_1(a923)))),
% 1.97/1.54 inference(monotonicity,[status(thm)],[1358])).
% 1.97/1.54 tff(1360,plain,
% 1.97/1.54 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a903) | c3_1(a903) | (~c0_1(a903)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a923) | c0_1(a923) | c2_1(a923))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a923) | c1_1(a923) | c0_1(a912) | c3_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a903)) | (~c2_1(a912)) | c3_1(a912) | c2_1(a923))),
% 1.97/1.54 inference(transitivity,[status(thm)],[1359, 1357])).
% 1.97/1.54 tff(1361,plain,
% 1.97/1.54 ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a903) | c3_1(a903) | (~c0_1(a903)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a923) | c0_1(a923) | c2_1(a923))),
% 1.97/1.54 inference(quant_inst,[status(thm)],[])).
% 1.97/1.54 tff(1362,plain,
% 1.97/1.54 ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a923) | c1_1(a923) | c0_1(a912) | c3_1(a903) | (~ndr1_0) | c1_1(a903) | (~c0_1(a903)) | (~c2_1(a912)) | c3_1(a912) | c2_1(a923)),
% 1.97/1.54 inference(modus_ponens,[status(thm)],[1361, 1360])).
% 1.97/1.54 tff(1363,plain,
% 1.97/1.54 (c2_1(a923)),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[1362, 124, 1327, 1356, 1348, 1347, 1326, 896, 540, 1344, 1334])).
% 1.97/1.54 tff(1364,plain,
% 1.97/1.54 (c3_1(a923)),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[587, 1346])).
% 1.97/1.54 tff(1365,plain,
% 1.97/1.54 (((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | c0_1(a923) | (~ndr1_0) | (~c2_1(a923)) | (~c3_1(a923)))) <=> ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp13 | hskp7 | c0_1(a923) | (~ndr1_0) | (~c2_1(a923)) | (~c3_1(a923)))),
% 1.97/1.54 inference(rewrite,[status(thm)],[])).
% 1.97/1.54 tff(1366,plain,
% 1.97/1.54 ((hskp13 | hskp7 | (~ndr1_0) | c0_1(a923) | (~c2_1(a923)) | (~c3_1(a923))) <=> (hskp13 | hskp7 | c0_1(a923) | (~ndr1_0) | (~c2_1(a923)) | (~c3_1(a923)))),
% 1.97/1.54 inference(rewrite,[status(thm)],[])).
% 1.97/1.54 tff(1367,plain,
% 1.97/1.54 (((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | (~ndr1_0) | c0_1(a923) | (~c2_1(a923)) | (~c3_1(a923)))) <=> ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | c0_1(a923) | (~ndr1_0) | (~c2_1(a923)) | (~c3_1(a923))))),
% 1.97/1.54 inference(monotonicity,[status(thm)],[1366])).
% 1.97/1.54 tff(1368,plain,
% 1.97/1.54 (((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | (~ndr1_0) | c0_1(a923) | (~c2_1(a923)) | (~c3_1(a923)))) <=> ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp13 | hskp7 | c0_1(a923) | (~ndr1_0) | (~c2_1(a923)) | (~c3_1(a923)))),
% 1.97/1.54 inference(transitivity,[status(thm)],[1367, 1365])).
% 1.97/1.54 tff(1369,plain,
% 1.97/1.54 ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | (~ndr1_0) | c0_1(a923) | (~c2_1(a923)) | (~c3_1(a923)))),
% 1.97/1.54 inference(quant_inst,[status(thm)],[])).
% 1.97/1.54 tff(1370,plain,
% 1.97/1.54 ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp13 | hskp7 | c0_1(a923) | (~ndr1_0) | (~c2_1(a923)) | (~c3_1(a923))),
% 1.97/1.54 inference(modus_ponens,[status(thm)],[1369, 1368])).
% 1.97/1.54 tff(1371,plain,
% 1.97/1.54 ($false),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[1370, 124, 1323, 21, 1364, 1348, 20, 1363])).
% 1.97/1.54 tff(1372,plain,(hskp13 | hskp7 | c3_1(a903) | (~c0_1(a906)) | (~c2_1(a906)) | c3_1(a906) | c2_1(a903) | hskp21), inference(lemma,lemma(discharge,[]))).
% 1.97/1.54 tff(1373,plain,
% 1.97/1.54 (hskp13),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[1372, 21, 896, 323, 324, 325, 884, 198])).
% 1.97/1.54 tff(1374,plain,
% 1.97/1.54 (c2_1(a921)),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[242, 1373])).
% 1.97/1.54 tff(1375,plain,
% 1.97/1.54 (~c0_1(a921)),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[231, 1373])).
% 1.97/1.54 tff(1376,plain,
% 1.97/1.54 (~c3_1(a921)),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[225, 1373])).
% 1.97/1.54 tff(1377,plain,
% 1.97/1.54 (hskp11),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[997, 32, 324, 325, 884, 896, 323, 1376, 1375, 1374])).
% 1.97/1.54 tff(1378,plain,
% 1.97/1.54 (~c2_1(a914)),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[69, 1377])).
% 1.97/1.54 tff(1379,plain,
% 1.97/1.54 (hskp28 | hskp12),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[249, 124, 1374, 1375, 1376, 208])).
% 1.97/1.54 tff(1380,plain,
% 1.97/1.54 (hskp28),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[1379, 32])).
% 1.97/1.54 tff(1381,plain,
% 1.97/1.54 (c3_1(a916)),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[271, 1380])).
% 1.97/1.54 tff(1382,plain,
% 1.97/1.54 (c1_1(a916)),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[282, 1380])).
% 1.97/1.54 tff(1383,plain,
% 1.97/1.54 (c0_1(a916)),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[260, 1380])).
% 1.97/1.54 tff(1384,plain,
% 1.97/1.54 (~c1_1(a903)),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[808, 124, 1383, 1382, 1381, 323, 324, 325, 884, 896, 31])).
% 1.97/1.54 tff(1385,plain,
% 1.97/1.54 (c0_1(a914)),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[91, 1377])).
% 1.97/1.54 tff(1386,assumption,(~c2_1(a907)), introduced(assumption)).
% 1.97/1.54 tff(1387,plain,
% 1.97/1.54 (c3_1(a914)),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[80, 1377])).
% 1.97/1.54 tff(1388,plain,
% 1.97/1.54 (hskp11),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[989, 883, 884, 32, 896])).
% 1.97/1.54 tff(1389,plain,
% 1.97/1.54 (c0_1(a914)),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[91, 1388])).
% 1.97/1.54 tff(1390,plain,
% 1.97/1.54 (c3_1(a914)),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[80, 1388])).
% 1.97/1.54 tff(1391,plain,
% 1.97/1.54 (hskp10 | (~c3_1(a914)) | (~c1_1(a914))),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[400, 124, 198, 1193, 365])).
% 1.97/1.54 tff(1392,plain,
% 1.97/1.54 (~c1_1(a914)),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[1391, 326, 1390])).
% 1.97/1.54 tff(1393,plain,
% 1.97/1.54 (hskp17 | hskp12 | c1_1(a914) | (~c0_1(a914))),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[454, 124, 1193, 448])).
% 1.97/1.54 tff(1394,plain,
% 1.97/1.54 (hskp17),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[1393, 1392, 32, 1389])).
% 1.97/1.54 tff(1395,plain,
% 1.97/1.54 (~c2_1(a936)),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[502, 1394])).
% 1.97/1.54 tff(1396,plain,
% 1.97/1.54 (~c1_1(a936)),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[508, 1394])).
% 1.97/1.54 tff(1397,assumption,(~hskp18), introduced(assumption)).
% 1.97/1.54 tff(1398,plain,
% 1.97/1.54 (^[U: $i] : refl((hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))),
% 1.97/1.54 inference(bind,[status(th)],[])).
% 1.97/1.54 tff(1399,plain,
% 1.97/1.54 (![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.97/1.54 inference(quant_intro,[status(thm)],[1398])).
% 1.97/1.54 tff(1400,plain,
% 1.97/1.54 (![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.97/1.54 inference(rewrite,[status(thm)],[])).
% 1.97/1.54 tff(1401,plain,
% 1.97/1.54 (^[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)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp20) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp20))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp20) | hskp18) <=> ((hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp18))), rewrite(((hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp18) <=> (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp20) | hskp18) <=> (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))))),
% 1.97/1.54 inference(bind,[status(th)],[])).
% 1.97/1.54 tff(1402,plain,
% 1.97/1.54 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp20) | hskp18) <=> ![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.97/1.54 inference(quant_intro,[status(thm)],[1401])).
% 1.97/1.54 tff(1403,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp20) | hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause139')).
% 1.97/1.54 tff(1404,plain,
% 1.97/1.54 (![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.97/1.54 inference(modus_ponens,[status(thm)],[1403, 1402])).
% 1.97/1.54 tff(1405,plain,
% 1.97/1.54 (![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.97/1.54 inference(modus_ponens,[status(thm)],[1404, 1400])).
% 1.97/1.54 tff(1406,plain,(
% 1.97/1.54 ![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.97/1.54 inference(skolemize,[status(sab)],[1405])).
% 1.97/1.54 tff(1407,plain,
% 1.97/1.54 (![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.97/1.54 inference(modus_ponens,[status(thm)],[1406, 1399])).
% 1.97/1.54 tff(1408,plain,
% 1.97/1.54 (((~![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp20 | hskp18 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914))) <=> ((~![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp20 | hskp18 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914))),
% 1.97/1.54 inference(rewrite,[status(thm)],[])).
% 1.97/1.54 tff(1409,plain,
% 1.97/1.54 ((hskp20 | hskp18 | (~ndr1_0) | c2_1(a914) | c1_1(a914) | (~c3_1(a914))) <=> (hskp20 | hskp18 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914))),
% 1.97/1.54 inference(rewrite,[status(thm)],[])).
% 1.97/1.54 tff(1410,plain,
% 1.97/1.54 (((~![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp20 | hskp18 | (~ndr1_0) | c2_1(a914) | c1_1(a914) | (~c3_1(a914)))) <=> ((~![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp20 | hskp18 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914)))),
% 1.97/1.54 inference(monotonicity,[status(thm)],[1409])).
% 1.97/1.54 tff(1411,plain,
% 1.97/1.54 (((~![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp20 | hskp18 | (~ndr1_0) | c2_1(a914) | c1_1(a914) | (~c3_1(a914)))) <=> ((~![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp20 | hskp18 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914))),
% 1.97/1.54 inference(transitivity,[status(thm)],[1410, 1408])).
% 1.97/1.54 tff(1412,plain,
% 1.97/1.54 ((~![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp20 | hskp18 | (~ndr1_0) | c2_1(a914) | c1_1(a914) | (~c3_1(a914)))),
% 1.97/1.54 inference(quant_inst,[status(thm)],[])).
% 1.97/1.54 tff(1413,plain,
% 1.97/1.54 ((~![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp20 | hskp18 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914)),
% 1.97/1.54 inference(modus_ponens,[status(thm)],[1412, 1411])).
% 1.97/1.54 tff(1414,plain,
% 1.97/1.54 (hskp20 | hskp18 | (~c3_1(a914)) | c1_1(a914)),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[1413, 124, 1193, 1407])).
% 1.97/1.54 tff(1415,plain,
% 1.97/1.54 (hskp20),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[1414, 1392, 1397, 1390])).
% 1.97/1.54 tff(1416,plain,
% 1.97/1.54 (((~hskp20) | (~c3_1(a939))) <=> ((~hskp20) | (~c3_1(a939)))),
% 1.97/1.54 inference(rewrite,[status(thm)],[])).
% 1.97/1.54 tff(1417,plain,
% 1.97/1.54 (((~c3_1(a939)) | (~hskp20)) <=> ((~hskp20) | (~c3_1(a939)))),
% 1.97/1.54 inference(rewrite,[status(thm)],[])).
% 1.97/1.54 tff(1418,axiom,((~c3_1(a939)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause93')).
% 1.97/1.54 tff(1419,plain,
% 1.97/1.54 ((~hskp20) | (~c3_1(a939))),
% 1.97/1.54 inference(modus_ponens,[status(thm)],[1418, 1417])).
% 1.97/1.54 tff(1420,plain,
% 1.97/1.54 ((~hskp20) | (~c3_1(a939))),
% 1.97/1.54 inference(modus_ponens,[status(thm)],[1419, 1416])).
% 1.97/1.54 tff(1421,plain,
% 1.97/1.54 (~c3_1(a939)),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[1420, 1415])).
% 1.97/1.54 tff(1422,plain,
% 1.97/1.54 (((~hskp20) | (~c1_1(a939))) <=> ((~hskp20) | (~c1_1(a939)))),
% 1.97/1.54 inference(rewrite,[status(thm)],[])).
% 1.97/1.54 tff(1423,plain,
% 1.97/1.54 (((~c1_1(a939)) | (~hskp20)) <=> ((~hskp20) | (~c1_1(a939)))),
% 1.97/1.54 inference(rewrite,[status(thm)],[])).
% 1.97/1.54 tff(1424,axiom,((~c1_1(a939)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause92')).
% 1.97/1.54 tff(1425,plain,
% 1.97/1.54 ((~hskp20) | (~c1_1(a939))),
% 1.97/1.54 inference(modus_ponens,[status(thm)],[1424, 1423])).
% 1.97/1.54 tff(1426,plain,
% 1.97/1.54 ((~hskp20) | (~c1_1(a939))),
% 1.97/1.54 inference(modus_ponens,[status(thm)],[1425, 1422])).
% 1.97/1.54 tff(1427,plain,
% 1.97/1.54 (~c1_1(a939)),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[1426, 1415])).
% 1.97/1.54 tff(1428,plain,
% 1.97/1.54 (((~hskp20) | c0_1(a939)) <=> ((~hskp20) | c0_1(a939))),
% 1.97/1.54 inference(rewrite,[status(thm)],[])).
% 1.97/1.54 tff(1429,axiom,((~hskp20) | c0_1(a939)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause55')).
% 1.97/1.54 tff(1430,plain,
% 1.97/1.54 ((~hskp20) | c0_1(a939)),
% 1.97/1.54 inference(modus_ponens,[status(thm)],[1429, 1428])).
% 1.97/1.54 tff(1431,plain,
% 1.97/1.54 ((~hskp20) | c0_1(a939)),
% 1.97/1.54 inference(modus_ponens,[status(thm)],[1430, 1428])).
% 1.97/1.54 tff(1432,plain,
% 1.97/1.54 ((~hskp20) | c0_1(a939)),
% 1.97/1.54 inference(modus_ponens,[status(thm)],[1431, 1428])).
% 1.97/1.54 tff(1433,plain,
% 1.97/1.54 ((~hskp20) | c0_1(a939)),
% 1.97/1.54 inference(modus_ponens,[status(thm)],[1432, 1428])).
% 1.97/1.54 tff(1434,plain,
% 1.97/1.54 ((~hskp20) | c0_1(a939)),
% 1.97/1.54 inference(modus_ponens,[status(thm)],[1433, 1428])).
% 1.97/1.54 tff(1435,plain,
% 1.97/1.54 ((~hskp20) | c0_1(a939)),
% 1.97/1.54 inference(modus_ponens,[status(thm)],[1434, 1428])).
% 1.97/1.54 tff(1436,plain,
% 1.97/1.54 ((~hskp20) | c0_1(a939)),
% 1.97/1.54 inference(modus_ponens,[status(thm)],[1435, 1428])).
% 1.97/1.54 tff(1437,plain,
% 1.97/1.54 ((~hskp20) | c0_1(a939)),
% 1.97/1.54 inference(modus_ponens,[status(thm)],[1436, 1428])).
% 1.97/1.54 tff(1438,plain,
% 1.97/1.54 (c0_1(a939)),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[1437, 1415])).
% 1.97/1.54 tff(1439,plain,
% 1.97/1.54 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a939) | c3_1(a939) | c1_1(a936) | c2_1(a936) | c0_1(a921) | c3_1(a921) | (~ndr1_0) | (~c2_1(a921)) | c0_1(a936) | (~c0_1(a939)))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a939) | c3_1(a939) | c1_1(a936) | c2_1(a936) | c0_1(a921) | c3_1(a921) | (~ndr1_0) | (~c2_1(a921)) | c0_1(a936) | (~c0_1(a939)))),
% 1.97/1.54 inference(rewrite,[status(thm)],[])).
% 1.97/1.54 tff(1440,plain,
% 1.97/1.54 (((~ndr1_0) | c1_1(a939) | c3_1(a939) | (~c0_1(a939)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a936) | c0_1(a936) | c2_1(a936)) <=> (c1_1(a939) | c3_1(a939) | c1_1(a936) | c2_1(a936) | c0_1(a921) | c3_1(a921) | (~ndr1_0) | (~c2_1(a921)) | c0_1(a936) | (~c0_1(a939)))),
% 1.97/1.54 inference(rewrite,[status(thm)],[])).
% 1.97/1.54 tff(1441,plain,
% 1.97/1.54 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a939) | c3_1(a939) | (~c0_1(a939)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a936) | c0_1(a936) | c2_1(a936))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a939) | c3_1(a939) | c1_1(a936) | c2_1(a936) | c0_1(a921) | c3_1(a921) | (~ndr1_0) | (~c2_1(a921)) | c0_1(a936) | (~c0_1(a939))))),
% 1.97/1.54 inference(monotonicity,[status(thm)],[1440])).
% 1.97/1.54 tff(1442,plain,
% 1.97/1.54 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a939) | c3_1(a939) | (~c0_1(a939)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a936) | c0_1(a936) | c2_1(a936))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a939) | c3_1(a939) | c1_1(a936) | c2_1(a936) | c0_1(a921) | c3_1(a921) | (~ndr1_0) | (~c2_1(a921)) | c0_1(a936) | (~c0_1(a939)))),
% 1.97/1.54 inference(transitivity,[status(thm)],[1441, 1439])).
% 1.97/1.54 tff(1443,plain,
% 1.97/1.54 ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a939) | c3_1(a939) | (~c0_1(a939)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a936) | c0_1(a936) | c2_1(a936))),
% 1.97/1.54 inference(quant_inst,[status(thm)],[])).
% 1.97/1.54 tff(1444,plain,
% 1.97/1.54 ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a939) | c3_1(a939) | c1_1(a936) | c2_1(a936) | c0_1(a921) | c3_1(a921) | (~ndr1_0) | (~c2_1(a921)) | c0_1(a936) | (~c0_1(a939))),
% 1.97/1.54 inference(modus_ponens,[status(thm)],[1443, 1442])).
% 1.97/1.54 tff(1445,plain,
% 1.97/1.54 (c0_1(a936)),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[1444, 124, 1438, 543, 1427, 1421, 1396, 1395, 542, 541, 540])).
% 1.97/1.54 tff(1446,plain,
% 1.97/1.54 (~c3_1(a936)),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[460, 1394])).
% 1.97/1.54 tff(1447,plain,
% 1.97/1.54 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a903) | c1_1(a936) | c3_1(a936) | c0_1(a921) | c3_1(a921) | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c2_1(a921)) | (~c0_1(a936)))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a903) | c1_1(a936) | c3_1(a936) | c0_1(a921) | c3_1(a921) | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c2_1(a921)) | (~c0_1(a936)))),
% 1.97/1.54 inference(rewrite,[status(thm)],[])).
% 1.97/1.54 tff(1448,plain,
% 1.97/1.54 (((~ndr1_0) | c1_1(a936) | c3_1(a936) | (~c0_1(a936)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a903) | c0_1(a903) | c2_1(a903)) <=> (c0_1(a903) | c1_1(a936) | c3_1(a936) | c0_1(a921) | c3_1(a921) | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c2_1(a921)) | (~c0_1(a936)))),
% 1.97/1.54 inference(rewrite,[status(thm)],[])).
% 1.97/1.54 tff(1449,plain,
% 1.97/1.54 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a936) | c3_1(a936) | (~c0_1(a936)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a903) | c0_1(a903) | c2_1(a903))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a903) | c1_1(a936) | c3_1(a936) | c0_1(a921) | c3_1(a921) | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c2_1(a921)) | (~c0_1(a936))))),
% 1.97/1.54 inference(monotonicity,[status(thm)],[1448])).
% 1.97/1.54 tff(1450,plain,
% 1.97/1.54 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a936) | c3_1(a936) | (~c0_1(a936)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a903) | c0_1(a903) | c2_1(a903))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a903) | c1_1(a936) | c3_1(a936) | c0_1(a921) | c3_1(a921) | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c2_1(a921)) | (~c0_1(a936)))),
% 1.97/1.54 inference(transitivity,[status(thm)],[1449, 1447])).
% 1.97/1.54 tff(1451,plain,
% 1.97/1.54 ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a936) | c3_1(a936) | (~c0_1(a936)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a903) | c0_1(a903) | c2_1(a903))),
% 1.97/1.54 inference(quant_inst,[status(thm)],[])).
% 1.97/1.54 tff(1452,plain,
% 1.97/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a903) | c1_1(a936) | c3_1(a936) | c0_1(a921) | c3_1(a921) | c2_1(a903) | (~ndr1_0) | c1_1(a903) | (~c2_1(a921)) | (~c0_1(a936))),
% 1.97/1.54 inference(modus_ponens,[status(thm)],[1451, 1450])).
% 1.97/1.54 tff(1453,plain,
% 1.97/1.54 (c0_1(a903)),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[1452, 124, 543, 1396, 1446, 542, 541, 884, 540, 883, 1445])).
% 1.97/1.54 tff(1454,plain,
% 1.97/1.54 (hskp6),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[1088, 1453, 21, 884, 896])).
% 1.97/1.54 tff(1455,plain,
% 1.97/1.54 (c1_1(a907)),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[418, 1454])).
% 1.97/1.54 tff(1456,plain,
% 1.97/1.54 (hskp10 | (~c3_1(a907)) | (~c1_1(a907))),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[425, 124, 198, 1386, 365])).
% 1.97/1.54 tff(1457,plain,
% 1.97/1.54 (~c3_1(a907)),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[1456, 1455, 326])).
% 1.97/1.54 tff(1458,plain,
% 1.97/1.54 (c3_1(a907) | (~c1_1(a907))),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[435, 124, 198, 1389, 1390, 1386, 197, 1392])).
% 1.97/1.54 tff(1459,plain,
% 1.97/1.54 ($false),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[1458, 1457, 1455])).
% 1.97/1.54 tff(1460,plain,(hskp10 | hskp21 | c2_1(a907) | hskp7 | c2_1(a903) | c3_1(a903) | (~c2_1(a921)) | c0_1(a921) | c3_1(a921) | c1_1(a903) | hskp18 | c2_1(a914) | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.97/1.54 tff(1461,plain,
% 1.97/1.54 (hskp18),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[1460, 326, 1386, 198, 884, 896, 883, 542, 541, 243, 21, 1193, 32])).
% 1.97/1.54 tff(1462,plain,
% 1.97/1.54 (((~hskp18) | c1_1(a937)) <=> ((~hskp18) | c1_1(a937))),
% 1.97/1.54 inference(rewrite,[status(thm)],[])).
% 1.97/1.54 tff(1463,axiom,((~hskp18) | c1_1(a937)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause58')).
% 1.97/1.54 tff(1464,plain,
% 1.97/1.54 ((~hskp18) | c1_1(a937)),
% 1.97/1.54 inference(modus_ponens,[status(thm)],[1463, 1462])).
% 1.97/1.54 tff(1465,plain,
% 1.97/1.54 ((~hskp18) | c1_1(a937)),
% 1.97/1.54 inference(modus_ponens,[status(thm)],[1464, 1462])).
% 1.97/1.54 tff(1466,plain,
% 1.97/1.54 ((~hskp18) | c1_1(a937)),
% 1.97/1.54 inference(modus_ponens,[status(thm)],[1465, 1462])).
% 1.97/1.54 tff(1467,plain,
% 1.97/1.54 ((~hskp18) | c1_1(a937)),
% 1.97/1.54 inference(modus_ponens,[status(thm)],[1466, 1462])).
% 1.97/1.54 tff(1468,plain,
% 1.97/1.54 ((~hskp18) | c1_1(a937)),
% 1.97/1.54 inference(modus_ponens,[status(thm)],[1467, 1462])).
% 1.97/1.54 tff(1469,plain,
% 1.97/1.54 ((~hskp18) | c1_1(a937)),
% 1.97/1.54 inference(modus_ponens,[status(thm)],[1468, 1462])).
% 1.97/1.54 tff(1470,plain,
% 1.97/1.54 ((~hskp18) | c1_1(a937)),
% 1.97/1.54 inference(modus_ponens,[status(thm)],[1469, 1462])).
% 1.97/1.54 tff(1471,plain,
% 1.97/1.54 ((~hskp18) | c1_1(a937)),
% 1.97/1.54 inference(modus_ponens,[status(thm)],[1470, 1462])).
% 1.97/1.54 tff(1472,plain,
% 1.97/1.54 (c1_1(a937)),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[1471, 1461])).
% 1.97/1.54 tff(1473,plain,
% 1.97/1.54 (((~hskp18) | (~c2_1(a937))) <=> ((~hskp18) | (~c2_1(a937)))),
% 1.97/1.54 inference(rewrite,[status(thm)],[])).
% 1.97/1.54 tff(1474,plain,
% 1.97/1.54 (((~c2_1(a937)) | (~hskp18)) <=> ((~hskp18) | (~c2_1(a937)))),
% 1.97/1.54 inference(rewrite,[status(thm)],[])).
% 1.97/1.54 tff(1475,axiom,((~c2_1(a937)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause96')).
% 1.97/1.54 tff(1476,plain,
% 1.97/1.54 ((~hskp18) | (~c2_1(a937))),
% 1.97/1.54 inference(modus_ponens,[status(thm)],[1475, 1474])).
% 1.97/1.54 tff(1477,plain,
% 1.97/1.54 ((~hskp18) | (~c2_1(a937))),
% 1.97/1.54 inference(modus_ponens,[status(thm)],[1476, 1473])).
% 1.97/1.54 tff(1478,plain,
% 1.97/1.54 (~c2_1(a937)),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[1477, 1461])).
% 1.97/1.54 tff(1479,assumption,(~c2_1(a937)), introduced(assumption)).
% 1.97/1.54 tff(1480,assumption,(c1_1(a937)), introduced(assumption)).
% 1.97/1.54 tff(1481,plain,
% 1.97/1.54 (~c1_1(a914)),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[1391, 326, 428])).
% 1.97/1.54 tff(1482,plain,
% 1.97/1.54 (((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | c2_1(a937) | (~ndr1_0) | (~c3_1(a937)) | (~c1_1(a937)))) <=> ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp10 | c2_1(a937) | (~ndr1_0) | (~c3_1(a937)) | (~c1_1(a937)))),
% 1.97/1.54 inference(rewrite,[status(thm)],[])).
% 1.97/1.54 tff(1483,plain,
% 1.97/1.54 ((hskp21 | hskp10 | (~ndr1_0) | c2_1(a937) | (~c3_1(a937)) | (~c1_1(a937))) <=> (hskp21 | hskp10 | c2_1(a937) | (~ndr1_0) | (~c3_1(a937)) | (~c1_1(a937)))),
% 1.97/1.54 inference(rewrite,[status(thm)],[])).
% 1.97/1.54 tff(1484,plain,
% 1.97/1.54 (((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | (~ndr1_0) | c2_1(a937) | (~c3_1(a937)) | (~c1_1(a937)))) <=> ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | c2_1(a937) | (~ndr1_0) | (~c3_1(a937)) | (~c1_1(a937))))),
% 1.97/1.54 inference(monotonicity,[status(thm)],[1483])).
% 1.97/1.54 tff(1485,plain,
% 1.97/1.54 (((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | (~ndr1_0) | c2_1(a937) | (~c3_1(a937)) | (~c1_1(a937)))) <=> ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp10 | c2_1(a937) | (~ndr1_0) | (~c3_1(a937)) | (~c1_1(a937)))),
% 1.97/1.54 inference(transitivity,[status(thm)],[1484, 1482])).
% 1.97/1.54 tff(1486,plain,
% 1.97/1.54 ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp10 | (~ndr1_0) | c2_1(a937) | (~c3_1(a937)) | (~c1_1(a937)))),
% 1.97/1.54 inference(quant_inst,[status(thm)],[])).
% 1.97/1.54 tff(1487,plain,
% 1.97/1.54 ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp10 | c2_1(a937) | (~ndr1_0) | (~c3_1(a937)) | (~c1_1(a937))),
% 1.97/1.54 inference(modus_ponens,[status(thm)],[1486, 1485])).
% 1.97/1.54 tff(1488,plain,
% 1.97/1.54 (hskp10 | (~c3_1(a937)) | (~c1_1(a937))),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[1487, 124, 198, 1479, 365])).
% 1.97/1.54 tff(1489,plain,
% 1.97/1.54 (~c3_1(a937)),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[1488, 1480, 326])).
% 1.97/1.54 tff(1490,plain,
% 1.97/1.54 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | c2_1(a937) | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)) | c3_1(a937) | (~c1_1(a937)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c2_1(a937) | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)) | c3_1(a937) | (~c1_1(a937)))),
% 1.97/1.54 inference(rewrite,[status(thm)],[])).
% 1.97/1.54 tff(1491,plain,
% 1.97/1.54 ((hskp21 | (~ndr1_0) | c2_1(a937) | c3_1(a937) | (~c1_1(a937)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914))) <=> (hskp21 | c2_1(a937) | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)) | c3_1(a937) | (~c1_1(a937)))),
% 1.97/1.54 inference(rewrite,[status(thm)],[])).
% 1.97/1.54 tff(1492,plain,
% 1.97/1.54 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a937) | c3_1(a937) | (~c1_1(a937)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | c2_1(a937) | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)) | c3_1(a937) | (~c1_1(a937))))),
% 1.97/1.54 inference(monotonicity,[status(thm)],[1491])).
% 1.97/1.54 tff(1493,plain,
% 1.97/1.54 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a937) | c3_1(a937) | (~c1_1(a937)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c2_1(a937) | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)) | c3_1(a937) | (~c1_1(a937)))),
% 1.97/1.54 inference(transitivity,[status(thm)],[1492, 1490])).
% 1.97/1.54 tff(1494,plain,
% 1.97/1.54 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a937) | c3_1(a937) | (~c1_1(a937)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914)))),
% 1.97/1.54 inference(quant_inst,[status(thm)],[])).
% 1.97/1.54 tff(1495,plain,
% 1.97/1.54 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c2_1(a937) | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)) | c3_1(a937) | (~c1_1(a937))),
% 1.97/1.54 inference(modus_ponens,[status(thm)],[1494, 1493])).
% 1.97/1.54 tff(1496,plain,
% 1.97/1.54 (c3_1(a937) | (~c1_1(a937))),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[1495, 124, 198, 429, 428, 1479, 197, 427])).
% 1.97/1.54 tff(1497,plain,
% 1.97/1.54 ($false),
% 1.97/1.54 inference(unit_resolution,[status(thm)],[1496, 1489, 1480])).
% 1.97/1.54 tff(1498,plain,((~c1_1(a937)) | hskp21 | (~c0_1(a914)) | (~c3_1(a914)) | c2_1(a937) | c1_1(a914) | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.97/1.55 tff(1499,plain,
% 1.97/1.55 ($false),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[1498, 1481, 326, 198, 1480, 1479, 429, 428])).
% 1.97/1.55 tff(1500,plain,(hskp10 | hskp21 | (~c1_1(a937)) | c2_1(a937) | (~c0_1(a914)) | (~c3_1(a914)) | c2_1(a914)), inference(lemma,lemma(discharge,[]))).
% 1.97/1.55 tff(1501,plain,
% 1.97/1.55 ($false),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[1500, 1478, 1472, 198, 326, 429, 428, 1193])).
% 1.97/1.55 tff(1502,plain,(hskp10 | hskp21 | (~c0_1(a914)) | (~c3_1(a914)) | c2_1(a914) | c2_1(a907) | c2_1(a903) | c3_1(a903) | c1_1(a903) | c0_1(a921) | c3_1(a921) | hskp7 | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.97/1.55 tff(1503,plain,
% 1.97/1.55 (hskp10),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[1502, 1384, 198, 1387, 1378, 1386, 884, 896, 1385, 1375, 1376, 21, 32])).
% 1.97/1.55 tff(1504,plain,
% 1.97/1.55 (~c0_1(a912)),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[627, 1503])).
% 1.97/1.55 tff(1505,plain,
% 1.97/1.55 (c2_1(a912)),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[676, 1503])).
% 1.97/1.55 tff(1506,plain,
% 1.97/1.55 (c1_1(a912)),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[687, 1503])).
% 1.97/1.55 tff(1507,plain,
% 1.97/1.55 (hskp14),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[706, 124, 21, 1506, 1505, 1504, 700])).
% 1.97/1.55 tff(1508,plain,
% 1.97/1.55 (~c1_1(a923)),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[570, 1507])).
% 1.97/1.55 tff(1509,plain,
% 1.97/1.55 (~c0_1(a923)),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[576, 1507])).
% 1.97/1.55 tff(1510,plain,
% 1.97/1.55 (c3_1(a923)),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[587, 1507])).
% 1.97/1.55 tff(1511,plain,
% 1.97/1.55 (hskp6),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[594, 124, 21, 1510, 1509, 1508, 564])).
% 1.97/1.55 tff(1512,plain,
% 1.97/1.55 (c0_1(a907)),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[725, 1511])).
% 1.97/1.55 tff(1513,plain,
% 1.97/1.55 (c1_1(a907)),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[418, 1511])).
% 1.97/1.55 tff(1514,assumption,(c1_1(a907)), introduced(assumption)).
% 1.97/1.55 tff(1515,assumption,(c0_1(a907)), introduced(assumption)).
% 1.97/1.55 tff(1516,assumption,(~c0_1(a903)), introduced(assumption)).
% 1.97/1.55 tff(1517,plain,
% 1.97/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a903) | c2_1(a907) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903) | c3_1(a907) | (~c0_1(a907)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a903) | c2_1(a907) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903) | c3_1(a907) | (~c0_1(a907)))),
% 1.97/1.55 inference(rewrite,[status(thm)],[])).
% 1.97/1.55 tff(1518,plain,
% 1.97/1.55 (((~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c0_1(a907)) | c3_1(a903) | c2_1(a903) | c0_1(a903) | c3_1(a903) | c1_1(a903) | c0_1(a903)) <=> (c0_1(a903) | c2_1(a907) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903) | c3_1(a907) | (~c0_1(a907)))),
% 1.97/1.55 inference(rewrite,[status(thm)],[])).
% 1.97/1.55 tff(1519,plain,
% 1.97/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c0_1(a907)) | c3_1(a903) | c2_1(a903) | c0_1(a903) | c3_1(a903) | c1_1(a903) | c0_1(a903))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a903) | c2_1(a907) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903) | c3_1(a907) | (~c0_1(a907))))),
% 1.97/1.55 inference(monotonicity,[status(thm)],[1518])).
% 1.97/1.55 tff(1520,plain,
% 1.97/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c0_1(a907)) | c3_1(a903) | c2_1(a903) | c0_1(a903) | c3_1(a903) | c1_1(a903) | c0_1(a903))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a903) | c2_1(a907) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903) | c3_1(a907) | (~c0_1(a907)))),
% 1.97/1.55 inference(transitivity,[status(thm)],[1519, 1517])).
% 1.97/1.55 tff(1521,plain,
% 1.97/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c0_1(a907)) | c3_1(a903) | c2_1(a903) | c0_1(a903) | c3_1(a903) | c1_1(a903) | c0_1(a903))),
% 1.97/1.55 inference(quant_inst,[status(thm)],[])).
% 1.97/1.55 tff(1522,plain,
% 1.97/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a903) | c2_1(a907) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | c1_1(a903) | c3_1(a907) | (~c0_1(a907))),
% 1.97/1.55 inference(modus_ponens,[status(thm)],[1521, 1520])).
% 1.97/1.55 tff(1523,plain,
% 1.97/1.55 (c0_1(a903) | c1_1(a903) | c3_1(a907) | (~c0_1(a907))),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[1522, 124, 1386, 884, 896, 1107])).
% 1.97/1.55 tff(1524,plain,
% 1.97/1.55 (c3_1(a907)),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[1523, 1516, 883, 1515])).
% 1.97/1.55 tff(1525,plain,
% 1.97/1.55 (~c1_1(a921)),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[1096, 1516])).
% 1.97/1.55 tff(1526,plain,
% 1.97/1.55 ((~c3_1(a907)) | (~c1_1(a907)) | c1_1(a921)),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[750, 124, 543, 690, 689, 541, 665, 1386, 743])).
% 1.97/1.55 tff(1527,plain,
% 1.97/1.55 ($false),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[1526, 1525, 1524, 1514])).
% 1.97/1.55 tff(1528,plain,(c0_1(a903) | (~c1_1(a907)) | (~c2_1(a921)) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a921) | c0_1(a912) | c2_1(a907) | (~c0_1(a906)) | (~c2_1(a906)) | c3_1(a906) | c2_1(a903) | c1_1(a903) | (~c0_1(a907)) | c3_1(a903)), inference(lemma,lemma(discharge,[]))).
% 1.97/1.55 tff(1529,plain,
% 1.97/1.55 (c0_1(a903)),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[1528, 1513, 1374, 1506, 1505, 1376, 1504, 1386, 323, 324, 325, 884, 1384, 1512, 896])).
% 1.97/1.55 tff(1530,plain,
% 1.97/1.55 (hskp17 | hskp12 | c1_1(a903) | (~c0_1(a903))),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[815, 124, 884, 448])).
% 1.97/1.55 tff(1531,plain,
% 1.97/1.55 (hskp17),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[1530, 1529, 32, 1384])).
% 1.97/1.55 tff(1532,plain,
% 1.97/1.55 (~c2_1(a936)),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[502, 1531])).
% 1.97/1.55 tff(1533,plain,
% 1.97/1.55 (hskp30 | hskp7 | c1_1(a903) | (~c0_1(a903))),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[834, 124, 896, 828])).
% 1.97/1.55 tff(1534,plain,
% 1.97/1.55 (hskp30),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[1533, 1529, 21, 1384])).
% 1.97/1.55 tff(1535,plain,
% 1.97/1.55 (c2_1(a942)),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[846, 1534])).
% 1.97/1.55 tff(1536,plain,
% 1.97/1.55 (~c1_1(a936)),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[508, 1531])).
% 1.97/1.55 tff(1537,plain,
% 1.97/1.55 (c1_1(a942)),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[858, 1534])).
% 1.97/1.55 tff(1538,plain,
% 1.97/1.55 (c0_1(a942)),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[869, 1534])).
% 1.97/1.55 tff(1539,plain,
% 1.97/1.55 (~c3_1(a936)),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[460, 1531])).
% 1.97/1.55 tff(1540,plain,
% 1.97/1.55 ((~c0_1(a903)) | c1_1(a921)),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[801, 124, 1506, 1505, 1375, 1376, 1504, 884, 896, 322])).
% 1.97/1.55 tff(1541,plain,
% 1.97/1.55 (c1_1(a921)),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[1540, 1529])).
% 1.97/1.55 tff(1542,plain,
% 1.97/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a936) | c2_1(a936) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921)) | c0_1(a936))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a936) | c2_1(a936) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921)) | c0_1(a936))),
% 1.97/1.55 inference(rewrite,[status(thm)],[])).
% 1.97/1.55 tff(1543,plain,
% 1.97/1.55 (((~ndr1_0) | c3_1(a921) | (~c2_1(a921)) | (~c1_1(a921)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a936) | c0_1(a936) | c2_1(a936)) <=> (c1_1(a936) | c2_1(a936) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921)) | c0_1(a936))),
% 1.97/1.55 inference(rewrite,[status(thm)],[])).
% 1.97/1.55 tff(1544,plain,
% 1.97/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a921) | (~c2_1(a921)) | (~c1_1(a921)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a936) | c0_1(a936) | c2_1(a936))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a936) | c2_1(a936) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921)) | c0_1(a936)))),
% 1.97/1.55 inference(monotonicity,[status(thm)],[1543])).
% 1.97/1.55 tff(1545,plain,
% 1.97/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a921) | (~c2_1(a921)) | (~c1_1(a921)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a936) | c0_1(a936) | c2_1(a936))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a936) | c2_1(a936) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921)) | c0_1(a936))),
% 1.97/1.55 inference(transitivity,[status(thm)],[1544, 1542])).
% 1.97/1.55 tff(1546,plain,
% 1.97/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a921) | (~c2_1(a921)) | (~c1_1(a921)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a936) | c0_1(a936) | c2_1(a936))),
% 1.97/1.55 inference(quant_inst,[status(thm)],[])).
% 1.97/1.55 tff(1547,plain,
% 1.97/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a936) | c2_1(a936) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921)) | c0_1(a936)),
% 1.97/1.55 inference(modus_ponens,[status(thm)],[1546, 1545])).
% 1.97/1.55 tff(1548,plain,
% 1.97/1.55 (c0_1(a936)),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[1547, 124, 1374, 323, 324, 1536, 1532, 1376, 325, 520, 1541])).
% 1.97/1.55 tff(1549,plain,
% 1.97/1.55 (hskp9),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[953, 1548, 1384, 1539, 1538, 1537, 1536, 1535, 884, 1532, 896])).
% 1.97/1.55 tff(1550,plain,
% 1.97/1.55 (~c3_1(a910)),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[959, 1549])).
% 1.97/1.55 tff(1551,plain,
% 1.97/1.55 (~c1_1(a910)),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[965, 1549])).
% 1.97/1.55 tff(1552,plain,
% 1.97/1.55 (c2_1(a910)),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[1009, 1549])).
% 1.97/1.55 tff(1553,plain,
% 1.97/1.55 (~c1_1(a914)),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[1017, 124, 1374, 1387, 1552, 1375, 1378, 1551, 1550, 743, 1541])).
% 1.97/1.55 tff(1554,plain,
% 1.97/1.55 (c3_1(a907)),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[435, 124, 198, 429, 428, 1514, 1386, 197, 427])).
% 1.97/1.55 tff(1555,plain,
% 1.97/1.55 ((~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921) | (~c2_1(a921))),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[750, 124, 541, 665, 1386, 743])).
% 1.97/1.55 tff(1556,plain,
% 1.97/1.55 (c1_1(a921)),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[1555, 1554, 543, 689, 690, 1514])).
% 1.97/1.55 tff(1557,plain,
% 1.97/1.55 (hskp17),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[1393, 427, 32, 429])).
% 1.97/1.55 tff(1558,plain,
% 1.97/1.55 (~c2_1(a936)),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[502, 1557])).
% 1.97/1.55 tff(1559,plain,
% 1.97/1.55 (~c1_1(a936)),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[508, 1557])).
% 1.97/1.55 tff(1560,plain,
% 1.97/1.55 (hskp20),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[1414, 427, 1397, 428])).
% 1.97/1.55 tff(1561,plain,
% 1.97/1.55 (~c3_1(a939)),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[1420, 1560])).
% 1.97/1.55 tff(1562,plain,
% 1.97/1.55 (~c1_1(a939)),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[1426, 1560])).
% 1.97/1.55 tff(1563,plain,
% 1.97/1.55 (c0_1(a939)),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[1437, 1560])).
% 1.97/1.55 tff(1564,plain,
% 1.97/1.55 (c0_1(a936)),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[1444, 124, 1563, 543, 1562, 1561, 1559, 1558, 542, 541, 540])).
% 1.97/1.55 tff(1565,assumption,(~c3_1(a910)), introduced(assumption)).
% 1.97/1.55 tff(1566,assumption,(~c1_1(a910)), introduced(assumption)).
% 1.97/1.55 tff(1567,plain,
% 1.97/1.55 (~c3_1(a936)),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[460, 1557])).
% 1.97/1.55 tff(1568,plain,
% 1.97/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a936) | c3_1(a936) | c0_1(a912) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | c0_1(a910) | (~c2_1(a912)) | (~c1_1(a912)) | (~c0_1(a936)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a936) | c3_1(a936) | c0_1(a912) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | c0_1(a910) | (~c2_1(a912)) | (~c1_1(a912)) | (~c0_1(a936)))),
% 1.97/1.55 inference(rewrite,[status(thm)],[])).
% 1.97/1.55 tff(1569,plain,
% 1.97/1.55 (((~ndr1_0) | c2_1(a936) | c3_1(a936) | (~c0_1(a936)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a910) | c1_1(a910) | c0_1(a910)) <=> (c2_1(a936) | c3_1(a936) | c0_1(a912) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | c0_1(a910) | (~c2_1(a912)) | (~c1_1(a912)) | (~c0_1(a936)))),
% 1.97/1.55 inference(rewrite,[status(thm)],[])).
% 1.97/1.55 tff(1570,plain,
% 1.97/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a936) | c3_1(a936) | (~c0_1(a936)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a910) | c1_1(a910) | c0_1(a910))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a936) | c3_1(a936) | c0_1(a912) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | c0_1(a910) | (~c2_1(a912)) | (~c1_1(a912)) | (~c0_1(a936))))),
% 1.97/1.55 inference(monotonicity,[status(thm)],[1569])).
% 1.97/1.55 tff(1571,plain,
% 1.97/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a936) | c3_1(a936) | (~c0_1(a936)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a910) | c1_1(a910) | c0_1(a910))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a936) | c3_1(a936) | c0_1(a912) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | c0_1(a910) | (~c2_1(a912)) | (~c1_1(a912)) | (~c0_1(a936)))),
% 1.97/1.55 inference(transitivity,[status(thm)],[1570, 1568])).
% 1.97/1.55 tff(1572,plain,
% 1.97/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a936) | c3_1(a936) | (~c0_1(a936)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a910) | c1_1(a910) | c0_1(a910))),
% 1.97/1.55 inference(quant_inst,[status(thm)],[])).
% 1.97/1.55 tff(1573,plain,
% 1.97/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a936) | c3_1(a936) | c0_1(a912) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | c0_1(a910) | (~c2_1(a912)) | (~c1_1(a912)) | (~c0_1(a936))),
% 1.97/1.55 inference(modus_ponens,[status(thm)],[1572, 1571])).
% 1.97/1.55 tff(1574,plain,
% 1.97/1.55 (c0_1(a910) | (~c0_1(a936))),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[1573, 124, 690, 689, 1558, 1567, 665, 1566, 1565, 322])).
% 1.97/1.55 tff(1575,plain,
% 1.97/1.55 (c0_1(a910)),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[1574, 1564])).
% 1.97/1.55 tff(1576,plain,
% 1.97/1.55 (hskp28),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[1050, 32, 543, 542])).
% 1.97/1.55 tff(1577,plain,
% 1.97/1.55 (c3_1(a916)),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[271, 1576])).
% 1.97/1.55 tff(1578,plain,
% 1.97/1.55 (c1_1(a916)),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[282, 1576])).
% 1.97/1.55 tff(1579,plain,
% 1.97/1.55 (c0_1(a916)),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[260, 1576])).
% 1.97/1.55 tff(1580,plain,
% 1.97/1.55 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp1 | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 1.97/1.55 inference(rewrite,[status(thm)],[])).
% 1.97/1.55 tff(1581,plain,
% 1.97/1.55 ((hskp1 | (~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914))) <=> (hskp1 | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 1.97/1.55 inference(rewrite,[status(thm)],[])).
% 1.97/1.55 tff(1582,plain,
% 1.97/1.55 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916))))),
% 1.97/1.55 inference(monotonicity,[status(thm)],[1581])).
% 1.97/1.55 tff(1583,plain,
% 1.97/1.55 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp1 | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 1.97/1.55 inference(transitivity,[status(thm)],[1582, 1580])).
% 1.97/1.55 tff(1584,plain,
% 1.97/1.55 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a914)))),
% 1.97/1.55 inference(quant_inst,[status(thm)],[])).
% 1.97/1.55 tff(1585,plain,
% 1.97/1.55 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp1 | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916))),
% 1.97/1.55 inference(modus_ponens,[status(thm)],[1584, 1583])).
% 1.97/1.55 tff(1586,plain,
% 1.97/1.55 (hskp1),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[1585, 124, 1579, 1578, 1577, 429, 428, 1028, 427])).
% 1.97/1.55 tff(1587,plain,
% 1.97/1.55 (((~hskp1) | c2_1(a902)) <=> ((~hskp1) | c2_1(a902))),
% 1.97/1.55 inference(rewrite,[status(thm)],[])).
% 1.97/1.55 tff(1588,axiom,((~hskp1) | c2_1(a902)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause81')).
% 1.97/1.55 tff(1589,plain,
% 1.97/1.55 ((~hskp1) | c2_1(a902)),
% 1.97/1.55 inference(modus_ponens,[status(thm)],[1588, 1587])).
% 1.97/1.55 tff(1590,plain,
% 1.97/1.55 ((~hskp1) | c2_1(a902)),
% 1.97/1.55 inference(modus_ponens,[status(thm)],[1589, 1587])).
% 1.97/1.55 tff(1591,plain,
% 1.97/1.55 ((~hskp1) | c2_1(a902)),
% 1.97/1.55 inference(modus_ponens,[status(thm)],[1590, 1587])).
% 1.97/1.55 tff(1592,plain,
% 1.97/1.55 ((~hskp1) | c2_1(a902)),
% 1.97/1.55 inference(modus_ponens,[status(thm)],[1591, 1587])).
% 1.97/1.55 tff(1593,plain,
% 1.97/1.55 ((~hskp1) | c2_1(a902)),
% 1.97/1.55 inference(modus_ponens,[status(thm)],[1592, 1587])).
% 1.97/1.55 tff(1594,plain,
% 1.97/1.55 ((~hskp1) | c2_1(a902)),
% 1.97/1.55 inference(modus_ponens,[status(thm)],[1593, 1587])).
% 1.97/1.55 tff(1595,plain,
% 1.97/1.55 ((~hskp1) | c2_1(a902)),
% 1.97/1.55 inference(modus_ponens,[status(thm)],[1594, 1587])).
% 1.97/1.55 tff(1596,plain,
% 1.97/1.55 ((~hskp1) | c2_1(a902)),
% 1.97/1.55 inference(modus_ponens,[status(thm)],[1595, 1587])).
% 1.97/1.55 tff(1597,plain,
% 1.97/1.55 (c2_1(a902)),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[1596, 1586])).
% 1.97/1.55 tff(1598,plain,
% 1.97/1.55 (((~hskp1) | c0_1(a902)) <=> ((~hskp1) | c0_1(a902))),
% 1.97/1.55 inference(rewrite,[status(thm)],[])).
% 1.97/1.55 tff(1599,axiom,((~hskp1) | c0_1(a902)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause80')).
% 1.97/1.55 tff(1600,plain,
% 1.97/1.55 ((~hskp1) | c0_1(a902)),
% 1.97/1.55 inference(modus_ponens,[status(thm)],[1599, 1598])).
% 1.97/1.55 tff(1601,plain,
% 1.97/1.55 ((~hskp1) | c0_1(a902)),
% 1.97/1.55 inference(modus_ponens,[status(thm)],[1600, 1598])).
% 1.97/1.55 tff(1602,plain,
% 1.97/1.55 ((~hskp1) | c0_1(a902)),
% 1.97/1.55 inference(modus_ponens,[status(thm)],[1601, 1598])).
% 1.97/1.55 tff(1603,plain,
% 1.97/1.55 ((~hskp1) | c0_1(a902)),
% 1.97/1.55 inference(modus_ponens,[status(thm)],[1602, 1598])).
% 1.97/1.55 tff(1604,plain,
% 1.97/1.55 ((~hskp1) | c0_1(a902)),
% 1.97/1.55 inference(modus_ponens,[status(thm)],[1603, 1598])).
% 1.97/1.55 tff(1605,plain,
% 1.97/1.55 ((~hskp1) | c0_1(a902)),
% 1.97/1.55 inference(modus_ponens,[status(thm)],[1604, 1598])).
% 1.97/1.55 tff(1606,plain,
% 1.97/1.55 ((~hskp1) | c0_1(a902)),
% 1.97/1.55 inference(modus_ponens,[status(thm)],[1605, 1598])).
% 1.97/1.55 tff(1607,plain,
% 1.97/1.55 ((~hskp1) | c0_1(a902)),
% 1.97/1.55 inference(modus_ponens,[status(thm)],[1606, 1598])).
% 1.97/1.55 tff(1608,plain,
% 1.97/1.55 (c0_1(a902)),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[1607, 1586])).
% 1.97/1.55 tff(1609,plain,
% 1.97/1.55 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 1.97/1.55 inference(bind,[status(th)],[])).
% 1.97/1.55 tff(1610,plain,
% 1.97/1.55 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.97/1.55 inference(quant_intro,[status(thm)],[1609])).
% 1.97/1.55 tff(1611,plain,
% 1.97/1.55 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.97/1.55 inference(rewrite,[status(thm)],[])).
% 1.97/1.55 tff(1612,plain,
% 1.97/1.55 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp0) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp0))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 1.97/1.55 inference(bind,[status(th)],[])).
% 1.97/1.55 tff(1613,plain,
% 1.97/1.55 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.97/1.55 inference(quant_intro,[status(thm)],[1612])).
% 1.97/1.55 tff(1614,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause173')).
% 1.97/1.55 tff(1615,plain,
% 1.97/1.55 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.97/1.55 inference(modus_ponens,[status(thm)],[1614, 1613])).
% 1.97/1.55 tff(1616,plain,
% 1.97/1.55 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.97/1.55 inference(modus_ponens,[status(thm)],[1615, 1611])).
% 1.97/1.55 tff(1617,plain,(
% 1.97/1.55 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.97/1.55 inference(skolemize,[status(sab)],[1616])).
% 1.97/1.55 tff(1618,plain,
% 1.97/1.55 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.97/1.55 inference(modus_ponens,[status(thm)],[1617, 1610])).
% 1.97/1.55 tff(1619,plain,
% 1.97/1.55 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | c2_1(a907) | c1_1(a902) | (~ndr1_0) | (~c0_1(a902)) | (~c2_1(a902)) | (~c0_1(a907)) | (~c1_1(a907)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a907) | c1_1(a902) | (~ndr1_0) | (~c0_1(a902)) | (~c2_1(a902)) | (~c0_1(a907)) | (~c1_1(a907)))),
% 1.97/1.55 inference(rewrite,[status(thm)],[])).
% 1.97/1.55 tff(1620,plain,
% 1.97/1.55 ((hskp0 | (~ndr1_0) | c2_1(a907) | (~c1_1(a907)) | (~c0_1(a907)) | c1_1(a902) | (~c2_1(a902)) | (~c0_1(a902))) <=> (hskp0 | c2_1(a907) | c1_1(a902) | (~ndr1_0) | (~c0_1(a902)) | (~c2_1(a902)) | (~c0_1(a907)) | (~c1_1(a907)))),
% 1.97/1.55 inference(rewrite,[status(thm)],[])).
% 1.97/1.55 tff(1621,plain,
% 1.97/1.55 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a907) | (~c1_1(a907)) | (~c0_1(a907)) | c1_1(a902) | (~c2_1(a902)) | (~c0_1(a902)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | c2_1(a907) | c1_1(a902) | (~ndr1_0) | (~c0_1(a902)) | (~c2_1(a902)) | (~c0_1(a907)) | (~c1_1(a907))))),
% 1.97/1.55 inference(monotonicity,[status(thm)],[1620])).
% 1.97/1.55 tff(1622,plain,
% 1.97/1.55 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a907) | (~c1_1(a907)) | (~c0_1(a907)) | c1_1(a902) | (~c2_1(a902)) | (~c0_1(a902)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a907) | c1_1(a902) | (~ndr1_0) | (~c0_1(a902)) | (~c2_1(a902)) | (~c0_1(a907)) | (~c1_1(a907)))),
% 1.97/1.55 inference(transitivity,[status(thm)],[1621, 1619])).
% 1.97/1.55 tff(1623,plain,
% 1.97/1.55 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c2_1(a907) | (~c1_1(a907)) | (~c0_1(a907)) | c1_1(a902) | (~c2_1(a902)) | (~c0_1(a902)))),
% 1.97/1.55 inference(quant_inst,[status(thm)],[])).
% 1.97/1.55 tff(1624,plain,
% 1.97/1.55 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c2_1(a907) | c1_1(a902) | (~ndr1_0) | (~c0_1(a902)) | (~c2_1(a902)) | (~c0_1(a907)) | (~c1_1(a907))),
% 1.97/1.55 inference(modus_ponens,[status(thm)],[1623, 1622])).
% 1.97/1.55 tff(1625,plain,
% 1.97/1.55 (hskp0 | (~c0_1(a902)) | (~c2_1(a902)) | (~c0_1(a907)) | (~c1_1(a907))),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[1624, 124, 1386, 1030, 1618])).
% 1.97/1.55 tff(1626,plain,
% 1.97/1.55 (hskp0),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[1625, 1608, 1514, 1515, 1597])).
% 1.97/1.55 tff(1627,plain,
% 1.97/1.55 (~c3_1(a901)),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[651, 1626])).
% 1.97/1.55 tff(1628,plain,
% 1.97/1.55 (~c1_1(a901)),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[657, 1626])).
% 1.97/1.55 tff(1629,plain,
% 1.97/1.55 (~c0_1(a901)),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[663, 1626])).
% 1.97/1.55 tff(1630,plain,
% 1.97/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a912) | c1_1(a910) | c3_1(a910) | c2_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a910)) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a912) | c1_1(a910) | c3_1(a910) | c2_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a910)) | (~c2_1(a912)) | (~c1_1(a912)))),
% 1.97/1.55 inference(rewrite,[status(thm)],[])).
% 1.97/1.55 tff(1631,plain,
% 1.97/1.55 (((~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907)) | c3_1(a910) | c1_1(a910) | (~c2_1(a910)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912))) <=> (c0_1(a912) | c1_1(a910) | c3_1(a910) | c2_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a910)) | (~c2_1(a912)) | (~c1_1(a912)))),
% 1.97/1.55 inference(rewrite,[status(thm)],[])).
% 1.97/1.55 tff(1632,plain,
% 1.97/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907)) | c3_1(a910) | c1_1(a910) | (~c2_1(a910)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a912) | c1_1(a910) | c3_1(a910) | c2_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a910)) | (~c2_1(a912)) | (~c1_1(a912))))),
% 1.97/1.55 inference(monotonicity,[status(thm)],[1631])).
% 1.97/1.55 tff(1633,plain,
% 1.97/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907)) | c3_1(a910) | c1_1(a910) | (~c2_1(a910)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a912) | c1_1(a910) | c3_1(a910) | c2_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a910)) | (~c2_1(a912)) | (~c1_1(a912)))),
% 1.97/1.55 inference(transitivity,[status(thm)],[1632, 1630])).
% 1.97/1.55 tff(1634,plain,
% 1.97/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907)) | c3_1(a910) | c1_1(a910) | (~c2_1(a910)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))),
% 1.97/1.55 inference(quant_inst,[status(thm)],[])).
% 1.97/1.55 tff(1635,plain,
% 1.97/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a912) | c1_1(a910) | c3_1(a910) | c2_1(a907) | (~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a910)) | (~c2_1(a912)) | (~c1_1(a912))),
% 1.97/1.55 inference(modus_ponens,[status(thm)],[1634, 1633])).
% 1.97/1.55 tff(1636,plain,
% 1.97/1.55 ((~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a910)) | (~c2_1(a912)) | (~c1_1(a912))),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[1635, 124, 665, 1566, 1565, 1386, 743])).
% 1.97/1.55 tff(1637,plain,
% 1.97/1.55 (~c2_1(a910)),
% 1.97/1.55 inference(unit_resolution,[status(thm)],[1636, 1554, 689, 690, 1514])).
% 1.97/1.55 tff(1638,plain,
% 1.97/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a910) | c0_1(a921) | c3_1(a910) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c0_1(a910)) | (~c2_1(a921)) | (~c1_1(a921)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a910) | c0_1(a921) | c3_1(a910) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c0_1(a910)) | (~c2_1(a921)) | (~c1_1(a921)))),
% 1.97/1.55 inference(rewrite,[status(thm)],[])).
% 1.97/1.55 tff(1639,plain,
% 1.97/1.55 (((~ndr1_0) | c2_1(a910) | c3_1(a910) | (~c0_1(a910)) | c0_1(a921) | (~c1_1(a921)) | (~c2_1(a921)) | c3_1(a901) | c1_1(a901) | c0_1(a901)) <=> (c2_1(a910) | c0_1(a921) | c3_1(a910) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c0_1(a910)) | (~c2_1(a921)) | (~c1_1(a921)))),
% 1.97/1.56 inference(rewrite,[status(thm)],[])).
% 1.97/1.56 tff(1640,plain,
% 1.97/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a910) | c3_1(a910) | (~c0_1(a910)) | c0_1(a921) | (~c1_1(a921)) | (~c2_1(a921)) | c3_1(a901) | c1_1(a901) | c0_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a910) | c0_1(a921) | c3_1(a910) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c0_1(a910)) | (~c2_1(a921)) | (~c1_1(a921))))),
% 1.97/1.56 inference(monotonicity,[status(thm)],[1639])).
% 1.97/1.56 tff(1641,plain,
% 1.97/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a910) | c3_1(a910) | (~c0_1(a910)) | c0_1(a921) | (~c1_1(a921)) | (~c2_1(a921)) | c3_1(a901) | c1_1(a901) | c0_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a910) | c0_1(a921) | c3_1(a910) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c0_1(a910)) | (~c2_1(a921)) | (~c1_1(a921)))),
% 1.97/1.56 inference(transitivity,[status(thm)],[1640, 1638])).
% 1.97/1.56 tff(1642,plain,
% 1.97/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a910) | c3_1(a910) | (~c0_1(a910)) | c0_1(a921) | (~c1_1(a921)) | (~c2_1(a921)) | c3_1(a901) | c1_1(a901) | c0_1(a901))),
% 1.97/1.56 inference(quant_inst,[status(thm)],[])).
% 1.97/1.56 tff(1643,plain,
% 1.97/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a910) | c0_1(a921) | c3_1(a910) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c0_1(a910)) | (~c2_1(a921)) | (~c1_1(a921))),
% 1.97/1.56 inference(modus_ponens,[status(thm)],[1642, 1641])).
% 1.97/1.56 tff(1644,plain,
% 1.97/1.56 ($false),
% 1.97/1.56 inference(unit_resolution,[status(thm)],[1643, 124, 543, 1637, 542, 1565, 1629, 1628, 1627, 322, 1575, 1556])).
% 1.97/1.56 tff(1645,plain,(c1_1(a914) | (~c2_1(a921)) | c0_1(a921) | c3_1(a910) | (~c1_1(a907)) | (~c0_1(a907)) | c2_1(a907) | c1_1(a902) | (~c1_1(a912)) | (~c2_1(a912)) | c0_1(a912) | c1_1(a910) | c3_1(a921) | hskp21 | (~c0_1(a914)) | (~c3_1(a914)) | hskp18 | c2_1(a914) | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.97/1.56 tff(1646,plain,
% 1.97/1.56 (hskp18),
% 1.97/1.56 inference(unit_resolution,[status(thm)],[1645, 1553, 1375, 32, 1513, 1512, 1386, 1030, 1506, 1505, 1504, 1551, 1376, 198, 1385, 1387, 1550, 1378, 1374])).
% 1.97/1.56 tff(1647,plain,
% 1.97/1.56 (c1_1(a937)),
% 1.97/1.56 inference(unit_resolution,[status(thm)],[1471, 1646])).
% 1.97/1.56 tff(1648,plain,
% 1.97/1.56 (((~hskp18) | (~c0_1(a937))) <=> ((~hskp18) | (~c0_1(a937)))),
% 1.97/1.56 inference(rewrite,[status(thm)],[])).
% 1.97/1.56 tff(1649,plain,
% 1.97/1.56 (((~c0_1(a937)) | (~hskp18)) <=> ((~hskp18) | (~c0_1(a937)))),
% 1.97/1.56 inference(rewrite,[status(thm)],[])).
% 1.97/1.56 tff(1650,axiom,((~c0_1(a937)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause95')).
% 1.97/1.56 tff(1651,plain,
% 1.97/1.56 ((~hskp18) | (~c0_1(a937))),
% 1.97/1.56 inference(modus_ponens,[status(thm)],[1650, 1649])).
% 1.97/1.56 tff(1652,plain,
% 1.97/1.56 ((~hskp18) | (~c0_1(a937))),
% 1.97/1.56 inference(modus_ponens,[status(thm)],[1651, 1648])).
% 1.97/1.56 tff(1653,plain,
% 1.97/1.56 (~c0_1(a937)),
% 1.97/1.56 inference(unit_resolution,[status(thm)],[1652, 1646])).
% 1.97/1.56 tff(1654,plain,
% 1.97/1.56 (~c2_1(a937)),
% 1.97/1.56 inference(unit_resolution,[status(thm)],[1477, 1646])).
% 1.97/1.56 tff(1655,plain,
% 1.97/1.56 (c3_1(a937)),
% 1.97/1.56 inference(unit_resolution,[status(thm)],[1495, 124, 198, 1480, 429, 428, 1479, 197, 427])).
% 1.97/1.56 tff(1656,plain,
% 1.97/1.56 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)))),
% 1.97/1.56 inference(bind,[status(th)],[])).
% 1.97/1.56 tff(1657,plain,
% 1.97/1.56 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.97/1.56 inference(quant_intro,[status(thm)],[1656])).
% 1.97/1.56 tff(1658,plain,
% 1.97/1.56 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 1.97/1.56 inference(rewrite,[status(thm)],[])).
% 1.97/1.56 tff(1659,plain,
% 1.97/1.56 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))))),
% 2.00/1.56 inference(bind,[status(th)],[])).
% 2.00/1.56 tff(1660,plain,
% 2.00/1.56 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 2.00/1.56 inference(quant_intro,[status(thm)],[1659])).
% 2.00/1.56 tff(1661,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause181')).
% 2.00/1.56 tff(1662,plain,
% 2.00/1.56 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 2.00/1.56 inference(modus_ponens,[status(thm)],[1661, 1660])).
% 2.00/1.56 tff(1663,plain,
% 2.00/1.56 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 2.00/1.56 inference(modus_ponens,[status(thm)],[1662, 1658])).
% 2.00/1.56 tff(1664,plain,(
% 2.00/1.56 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 2.00/1.56 inference(skolemize,[status(sab)],[1663])).
% 2.00/1.56 tff(1665,plain,
% 2.00/1.56 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 2.00/1.56 inference(modus_ponens,[status(thm)],[1664, 1657])).
% 2.00/1.56 tff(1666,plain,
% 2.00/1.56 (hskp1),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[1585, 124, 488, 487, 486, 429, 428, 1028, 427])).
% 2.00/1.56 tff(1667,plain,
% 2.00/1.56 (c2_1(a902)),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[1596, 1666])).
% 2.00/1.56 tff(1668,plain,
% 2.00/1.56 (c0_1(a902)),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[1607, 1666])).
% 2.00/1.56 tff(1669,plain,
% 2.00/1.56 (hskp0),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[1625, 1668, 1514, 1515, 1667])).
% 2.00/1.56 tff(1670,plain,
% 2.00/1.56 (~c1_1(a901)),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[657, 1669])).
% 2.00/1.56 tff(1671,plain,
% 2.00/1.56 (~c0_1(a901)),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[663, 1669])).
% 2.00/1.56 tff(1672,assumption,(~c0_1(a937)), introduced(assumption)).
% 2.00/1.56 tff(1673,plain,
% 2.00/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a937) | c2_1(a937) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c0_1(a907)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c3_1(a937)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a937) | c2_1(a937) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c0_1(a907)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c3_1(a937)))),
% 2.00/1.56 inference(rewrite,[status(thm)],[])).
% 2.00/1.56 tff(1674,plain,
% 2.00/1.56 (((~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c0_1(a907)) | c2_1(a937) | c0_1(a937) | (~c3_1(a937)) | c1_1(a901) | c0_1(a901) | c2_1(a901)) <=> (c0_1(a937) | c2_1(a937) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c0_1(a907)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c3_1(a937)))),
% 2.00/1.56 inference(rewrite,[status(thm)],[])).
% 2.00/1.56 tff(1675,plain,
% 2.00/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c0_1(a907)) | c2_1(a937) | c0_1(a937) | (~c3_1(a937)) | c1_1(a901) | c0_1(a901) | c2_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a937) | c2_1(a937) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c0_1(a907)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c3_1(a937))))),
% 2.00/1.56 inference(monotonicity,[status(thm)],[1674])).
% 2.00/1.56 tff(1676,plain,
% 2.00/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c0_1(a907)) | c2_1(a937) | c0_1(a937) | (~c3_1(a937)) | c1_1(a901) | c0_1(a901) | c2_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a937) | c2_1(a937) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c0_1(a907)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c3_1(a937)))),
% 2.00/1.56 inference(transitivity,[status(thm)],[1675, 1673])).
% 2.00/1.56 tff(1677,plain,
% 2.00/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c0_1(a907)) | c2_1(a937) | c0_1(a937) | (~c3_1(a937)) | c1_1(a901) | c0_1(a901) | c2_1(a901))),
% 2.00/1.56 inference(quant_inst,[status(thm)],[])).
% 2.00/1.56 tff(1678,plain,
% 2.00/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a937) | c2_1(a937) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c0_1(a907)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c3_1(a937))),
% 2.00/1.56 inference(modus_ponens,[status(thm)],[1677, 1676])).
% 2.00/1.56 tff(1679,plain,
% 2.00/1.56 (c2_1(a901)),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[1678, 124, 1515, 1514, 1672, 1479, 1671, 1670, 1665, 1554, 1655])).
% 2.00/1.56 tff(1680,plain,
% 2.00/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a937) | c3_1(a921) | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921) | (~c2_1(a921)) | (~c3_1(a937)) | (~c1_1(a937)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a937) | c3_1(a921) | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921) | (~c2_1(a921)) | (~c3_1(a937)) | (~c1_1(a937)))),
% 2.00/1.56 inference(rewrite,[status(thm)],[])).
% 2.00/1.56 tff(1681,plain,
% 2.00/1.56 (((~ndr1_0) | c2_1(a937) | (~c3_1(a937)) | (~c1_1(a937)) | c3_1(a921) | c1_1(a921) | (~c2_1(a921)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912))) <=> (c2_1(a937) | c3_1(a921) | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921) | (~c2_1(a921)) | (~c3_1(a937)) | (~c1_1(a937)))),
% 2.00/1.56 inference(rewrite,[status(thm)],[])).
% 2.00/1.56 tff(1682,plain,
% 2.00/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a937) | (~c3_1(a937)) | (~c1_1(a937)) | c3_1(a921) | c1_1(a921) | (~c2_1(a921)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a937) | c3_1(a921) | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921) | (~c2_1(a921)) | (~c3_1(a937)) | (~c1_1(a937))))),
% 2.00/1.56 inference(monotonicity,[status(thm)],[1681])).
% 2.00/1.56 tff(1683,plain,
% 2.00/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a937) | (~c3_1(a937)) | (~c1_1(a937)) | c3_1(a921) | c1_1(a921) | (~c2_1(a921)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a937) | c3_1(a921) | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921) | (~c2_1(a921)) | (~c3_1(a937)) | (~c1_1(a937)))),
% 2.00/1.56 inference(transitivity,[status(thm)],[1682, 1680])).
% 2.00/1.56 tff(1684,plain,
% 2.00/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a937) | (~c3_1(a937)) | (~c1_1(a937)) | c3_1(a921) | c1_1(a921) | (~c2_1(a921)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))),
% 2.00/1.56 inference(quant_inst,[status(thm)],[])).
% 2.00/1.56 tff(1685,plain,
% 2.00/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a937) | c3_1(a921) | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921) | (~c2_1(a921)) | (~c3_1(a937)) | (~c1_1(a937))),
% 2.00/1.56 inference(modus_ponens,[status(thm)],[1684, 1683])).
% 2.00/1.56 tff(1686,plain,
% 2.00/1.56 ((~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921) | (~c2_1(a921)) | (~c3_1(a937)) | (~c1_1(a937))),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[1685, 124, 1479, 541, 665, 743])).
% 2.00/1.56 tff(1687,plain,
% 2.00/1.56 (c1_1(a921)),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[1686, 1655, 689, 690, 543, 1480])).
% 2.00/1.56 tff(1688,plain,
% 2.00/1.56 (~c3_1(a901)),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[651, 1669])).
% 2.00/1.56 tff(1689,plain,
% 2.00/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a937) | c0_1(a921) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c2_1(a921)) | (~c1_1(a921)) | (~c3_1(a937)) | (~c1_1(a937)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a937) | c0_1(a921) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c2_1(a921)) | (~c1_1(a921)) | (~c3_1(a937)) | (~c1_1(a937)))),
% 2.00/1.56 inference(rewrite,[status(thm)],[])).
% 2.00/1.56 tff(1690,plain,
% 2.00/1.56 (((~ndr1_0) | c2_1(a937) | (~c3_1(a937)) | (~c1_1(a937)) | c3_1(a901) | c1_1(a901) | (~c2_1(a901)) | c0_1(a921) | (~c2_1(a921)) | (~c1_1(a921))) <=> (c2_1(a937) | c0_1(a921) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c2_1(a921)) | (~c1_1(a921)) | (~c3_1(a937)) | (~c1_1(a937)))),
% 2.00/1.56 inference(rewrite,[status(thm)],[])).
% 2.00/1.56 tff(1691,plain,
% 2.00/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a937) | (~c3_1(a937)) | (~c1_1(a937)) | c3_1(a901) | c1_1(a901) | (~c2_1(a901)) | c0_1(a921) | (~c2_1(a921)) | (~c1_1(a921)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a937) | c0_1(a921) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c2_1(a921)) | (~c1_1(a921)) | (~c3_1(a937)) | (~c1_1(a937))))),
% 2.00/1.56 inference(monotonicity,[status(thm)],[1690])).
% 2.00/1.56 tff(1692,plain,
% 2.00/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a937) | (~c3_1(a937)) | (~c1_1(a937)) | c3_1(a901) | c1_1(a901) | (~c2_1(a901)) | c0_1(a921) | (~c2_1(a921)) | (~c1_1(a921)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a937) | c0_1(a921) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c2_1(a921)) | (~c1_1(a921)) | (~c3_1(a937)) | (~c1_1(a937)))),
% 2.00/1.56 inference(transitivity,[status(thm)],[1691, 1689])).
% 2.00/1.56 tff(1693,plain,
% 2.00/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a937) | (~c3_1(a937)) | (~c1_1(a937)) | c3_1(a901) | c1_1(a901) | (~c2_1(a901)) | c0_1(a921) | (~c2_1(a921)) | (~c1_1(a921)))),
% 2.00/1.56 inference(quant_inst,[status(thm)],[])).
% 2.00/1.56 tff(1694,plain,
% 2.00/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a937) | c0_1(a921) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c2_1(a921)) | (~c1_1(a921)) | (~c3_1(a937)) | (~c1_1(a937))),
% 2.00/1.56 inference(modus_ponens,[status(thm)],[1693, 1692])).
% 2.00/1.56 tff(1695,plain,
% 2.00/1.56 ($false),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[1694, 124, 1480, 543, 1479, 542, 1670, 1688, 743, 1687, 1655, 1679])).
% 2.00/1.56 tff(1696,plain,(c1_1(a914) | (~c1_1(a937)) | (~c2_1(a921)) | c2_1(a937) | c0_1(a921) | (~c0_1(a907)) | (~c1_1(a907)) | c0_1(a937) | c2_1(a907) | c1_1(a902) | (~c2_1(a912)) | (~c1_1(a912)) | c3_1(a921) | c0_1(a912) | hskp21 | (~c0_1(a914)) | (~c3_1(a914)) | (~c0_1(a916)) | (~c1_1(a916)) | (~c3_1(a916))), inference(lemma,lemma(discharge,[]))).
% 2.00/1.56 tff(1697,plain,
% 2.00/1.56 ($false),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[1696, 1654, 1653, 1374, 1381, 1375, 1512, 1513, 1553, 1386, 1030, 1505, 1506, 1376, 1504, 198, 1385, 1387, 1383, 1382, 1647])).
% 2.00/1.56 tff(1698,plain,(hskp12 | c2_1(a907) | c1_1(a902) | hskp21 | c2_1(a903) | c3_1(a903) | (~c0_1(a906)) | (~c2_1(a906)) | c3_1(a906) | hskp7), inference(lemma,lemma(discharge,[]))).
% 2.00/1.56 tff(1699,plain,
% 2.00/1.56 (hskp7),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[1698, 32, 1030, 198, 884, 896, 323, 324, 325, 1322])).
% 2.00/1.56 tff(1700,plain,
% 2.00/1.56 (~c3_1(a908)),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[467, 1699])).
% 2.00/1.56 tff(1701,plain,
% 2.00/1.56 (~c2_1(a908)),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[473, 1699])).
% 2.00/1.56 tff(1702,plain,
% 2.00/1.56 (hskp13),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[219, 378, 198])).
% 2.00/1.56 tff(1703,plain,
% 2.00/1.56 (~c0_1(a921)),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[231, 1702])).
% 2.00/1.56 tff(1704,plain,
% 2.00/1.56 (~c3_1(a921)),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[225, 1702])).
% 2.00/1.56 tff(1705,plain,
% 2.00/1.56 (hskp11),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[997, 243, 324, 325, 884, 896, 323, 541, 542, 32])).
% 2.00/1.56 tff(1706,plain,
% 2.00/1.56 (~c2_1(a914)),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[69, 1705])).
% 2.00/1.56 tff(1707,plain,
% 2.00/1.56 (c3_1(a914)),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[80, 1705])).
% 2.00/1.56 tff(1708,plain,
% 2.00/1.56 (~c1_1(a914)),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[400, 124, 198, 326, 1707, 1706, 365])).
% 2.00/1.56 tff(1709,plain,
% 2.00/1.56 (c0_1(a914)),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[91, 1705])).
% 2.00/1.56 tff(1710,plain,
% 2.00/1.56 (hskp28),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[1050, 243, 32, 542])).
% 2.00/1.56 tff(1711,plain,
% 2.00/1.56 (c3_1(a916)),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[271, 1710])).
% 2.00/1.56 tff(1712,plain,
% 2.00/1.56 (c1_1(a916)),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[282, 1710])).
% 2.00/1.56 tff(1713,plain,
% 2.00/1.56 (c0_1(a916)),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[260, 1710])).
% 2.00/1.56 tff(1714,plain,
% 2.00/1.56 (~c1_1(a908)),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[494, 124, 1713, 1712, 1711, 323, 324, 1153, 1154, 325, 31])).
% 2.00/1.56 tff(1715,plain,
% 2.00/1.56 (~hskp7),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[484, 1714])).
% 2.00/1.56 tff(1716,plain,
% 2.00/1.56 (~c1_1(a903)),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[808, 124, 1713, 1712, 1711, 323, 324, 325, 884, 896, 31])).
% 2.00/1.56 tff(1717,plain,
% 2.00/1.56 (hskp18),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[1460, 1716, 1386, 198, 884, 896, 326, 542, 541, 243, 1715, 1706, 32])).
% 2.00/1.56 tff(1718,plain,
% 2.00/1.56 (c1_1(a937)),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[1471, 1717])).
% 2.00/1.56 tff(1719,plain,
% 2.00/1.56 (~c2_1(a937)),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[1477, 1717])).
% 2.00/1.56 tff(1720,plain,
% 2.00/1.56 ($false),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[1498, 1719, 1718, 326, 1707, 1709, 1708, 198])).
% 2.00/1.56 tff(1721,plain,(hskp12 | hskp10 | hskp21 | c2_1(a907) | c2_1(a903) | c3_1(a903) | c0_1(a921) | c3_1(a921) | (~c0_1(a906)) | (~c2_1(a906)) | c3_1(a906) | c2_1(a908) | c3_1(a908)), inference(lemma,lemma(discharge,[]))).
% 2.00/1.56 tff(1722,plain,
% 2.00/1.56 ($false),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[1721, 1704, 1703, 198, 1386, 884, 896, 326, 378, 323, 324, 325, 1153, 1154])).
% 2.00/1.56 tff(1723,plain,(hskp10 | hskp21 | c2_1(a907) | c2_1(a903) | c3_1(a903) | (~c0_1(a906)) | (~c2_1(a906)) | c3_1(a906) | c2_1(a908) | c3_1(a908)), inference(lemma,lemma(discharge,[]))).
% 2.00/1.56 tff(1724,plain,
% 2.00/1.56 (hskp10),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[1723, 1153, 1386, 884, 896, 323, 324, 325, 198, 1154])).
% 2.00/1.56 tff(1725,plain,
% 2.00/1.56 (~c0_1(a912)),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[627, 1724])).
% 2.00/1.56 tff(1726,plain,
% 2.00/1.56 (c2_1(a912)),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[676, 1724])).
% 2.00/1.56 tff(1727,plain,
% 2.00/1.56 (c1_1(a912)),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[687, 1724])).
% 2.00/1.56 tff(1728,assumption,(~c1_1(a908)), introduced(assumption)).
% 2.00/1.56 tff(1729,plain,
% 2.00/1.56 (~hskp7),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[484, 1728])).
% 2.00/1.56 tff(1730,plain,
% 2.00/1.56 (hskp14 | hskp7),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[706, 124, 690, 689, 665, 700])).
% 2.00/1.56 tff(1731,plain,
% 2.00/1.56 (hskp14),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[1730, 1729])).
% 2.00/1.56 tff(1732,plain,
% 2.00/1.56 (~c1_1(a923)),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[570, 1731])).
% 2.00/1.56 tff(1733,plain,
% 2.00/1.56 (~c0_1(a923)),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[576, 1731])).
% 2.00/1.56 tff(1734,plain,
% 2.00/1.56 (c3_1(a923)),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[587, 1731])).
% 2.00/1.56 tff(1735,plain,
% 2.00/1.56 (hskp6),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[594, 124, 1729, 1734, 1733, 1732, 564])).
% 2.00/1.56 tff(1736,plain,
% 2.00/1.56 (c1_1(a907)),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[418, 1735])).
% 2.00/1.56 tff(1737,plain,
% 2.00/1.56 (c0_1(a907)),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[725, 1735])).
% 2.00/1.56 tff(1738,assumption,(~c0_1(a908)), introduced(assumption)).
% 2.00/1.56 tff(1739,plain,
% 2.00/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a908) | c2_1(a908) | c3_1(a908) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | c0_1(a908))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a908) | c2_1(a908) | c3_1(a908) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | c0_1(a908))),
% 2.00/1.56 inference(rewrite,[status(thm)],[])).
% 2.00/1.56 tff(1740,plain,
% 2.00/1.56 (((~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c0_1(a907)) | c3_1(a908) | c2_1(a908) | c0_1(a908) | c3_1(a908) | c1_1(a908) | c0_1(a908)) <=> (c1_1(a908) | c2_1(a908) | c3_1(a908) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | c0_1(a908))),
% 2.00/1.56 inference(rewrite,[status(thm)],[])).
% 2.00/1.56 tff(1741,plain,
% 2.00/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c0_1(a907)) | c3_1(a908) | c2_1(a908) | c0_1(a908) | c3_1(a908) | c1_1(a908) | c0_1(a908))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a908) | c2_1(a908) | c3_1(a908) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | c0_1(a908)))),
% 2.00/1.56 inference(monotonicity,[status(thm)],[1740])).
% 2.00/1.56 tff(1742,plain,
% 2.00/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c0_1(a907)) | c3_1(a908) | c2_1(a908) | c0_1(a908) | c3_1(a908) | c1_1(a908) | c0_1(a908))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a908) | c2_1(a908) | c3_1(a908) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | c0_1(a908))),
% 2.00/1.56 inference(transitivity,[status(thm)],[1741, 1739])).
% 2.00/1.56 tff(1743,plain,
% 2.00/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c0_1(a907)) | c3_1(a908) | c2_1(a908) | c0_1(a908) | c3_1(a908) | c1_1(a908) | c0_1(a908))),
% 2.00/1.56 inference(quant_inst,[status(thm)],[])).
% 2.00/1.56 tff(1744,plain,
% 2.00/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a908) | c2_1(a908) | c3_1(a908) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | c0_1(a908)),
% 2.00/1.56 inference(modus_ponens,[status(thm)],[1743, 1742])).
% 2.00/1.56 tff(1745,plain,
% 2.00/1.56 (c1_1(a908) | c2_1(a908) | c3_1(a907) | (~c0_1(a907)) | c0_1(a908)),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[1744, 124, 1154, 1386, 1107])).
% 2.00/1.56 tff(1746,plain,
% 2.00/1.56 (c3_1(a907)),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[1745, 1738, 1153, 1728, 1737])).
% 2.00/1.56 tff(1747,plain,
% 2.00/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a908) | c3_1(a921) | c2_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | c0_1(a908) | (~c2_1(a921)) | (~c1_1(a921)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a908) | c3_1(a921) | c2_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | c0_1(a908) | (~c2_1(a921)) | (~c1_1(a921)))),
% 2.00/1.56 inference(rewrite,[status(thm)],[])).
% 2.00/1.56 tff(1748,plain,
% 2.00/1.56 (((~ndr1_0) | c3_1(a921) | (~c2_1(a921)) | (~c1_1(a921)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a908) | c0_1(a908) | c2_1(a908)) <=> (c1_1(a908) | c3_1(a921) | c2_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | c0_1(a908) | (~c2_1(a921)) | (~c1_1(a921)))),
% 2.00/1.56 inference(rewrite,[status(thm)],[])).
% 2.00/1.56 tff(1749,plain,
% 2.00/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a921) | (~c2_1(a921)) | (~c1_1(a921)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a908) | c0_1(a908) | c2_1(a908))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a908) | c3_1(a921) | c2_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | c0_1(a908) | (~c2_1(a921)) | (~c1_1(a921))))),
% 2.00/1.56 inference(monotonicity,[status(thm)],[1748])).
% 2.00/1.56 tff(1750,plain,
% 2.00/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a921) | (~c2_1(a921)) | (~c1_1(a921)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a908) | c0_1(a908) | c2_1(a908))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a908) | c3_1(a921) | c2_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | c0_1(a908) | (~c2_1(a921)) | (~c1_1(a921)))),
% 2.00/1.56 inference(transitivity,[status(thm)],[1749, 1747])).
% 2.00/1.56 tff(1751,plain,
% 2.00/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a921) | (~c2_1(a921)) | (~c1_1(a921)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a908) | c0_1(a908) | c2_1(a908))),
% 2.00/1.56 inference(quant_inst,[status(thm)],[])).
% 2.00/1.56 tff(1752,plain,
% 2.00/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a908) | c3_1(a921) | c2_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | c0_1(a908) | (~c2_1(a921)) | (~c1_1(a921))),
% 2.00/1.56 inference(modus_ponens,[status(thm)],[1751, 1750])).
% 2.00/1.56 tff(1753,plain,
% 2.00/1.56 (c0_1(a908) | (~c1_1(a921))),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[1752, 124, 543, 1728, 323, 324, 541, 1153, 325, 520])).
% 2.00/1.56 tff(1754,plain,
% 2.00/1.56 (~c1_1(a921)),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[1753, 1738])).
% 2.00/1.56 tff(1755,plain,
% 2.00/1.56 ((~c3_1(a907)) | (~c1_1(a907)) | c1_1(a921) | (~c2_1(a921))),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[750, 124, 690, 689, 541, 665, 1386, 743])).
% 2.00/1.56 tff(1756,plain,
% 2.00/1.56 ($false),
% 2.00/1.56 inference(unit_resolution,[status(thm)],[1755, 1754, 1746, 543, 1736])).
% 2.00/1.56 tff(1757,plain,(c0_1(a908) | (~c2_1(a921)) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a921) | c0_1(a912) | c2_1(a907) | c1_1(a908) | (~c0_1(a906)) | (~c2_1(a906)) | c2_1(a908) | c3_1(a906) | c3_1(a908)), inference(lemma,lemma(discharge,[]))).
% 2.00/1.57 tff(1758,plain,
% 2.00/1.57 (c0_1(a908)),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[1757, 243, 1727, 1726, 541, 1725, 1386, 1714, 323, 324, 1153, 325, 1154])).
% 2.00/1.57 tff(1759,plain,
% 2.00/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a921) | c3_1(a921) | c0_1(a912) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a921) | c3_1(a921) | c0_1(a912) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921))),
% 2.00/1.57 inference(rewrite,[status(thm)],[])).
% 2.00/1.57 tff(1760,plain,
% 2.00/1.57 (((~ndr1_0) | c2_1(a908) | c3_1(a908) | (~c0_1(a908)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a921) | c1_1(a921) | c0_1(a921)) <=> (c0_1(a921) | c3_1(a921) | c0_1(a912) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921))),
% 2.00/1.57 inference(rewrite,[status(thm)],[])).
% 2.00/1.57 tff(1761,plain,
% 2.00/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a908) | c3_1(a908) | (~c0_1(a908)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a921) | c1_1(a921) | c0_1(a921))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a921) | c3_1(a921) | c0_1(a912) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921)))),
% 2.00/1.57 inference(monotonicity,[status(thm)],[1760])).
% 2.00/1.57 tff(1762,plain,
% 2.00/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a908) | c3_1(a908) | (~c0_1(a908)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a921) | c1_1(a921) | c0_1(a921))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a921) | c3_1(a921) | c0_1(a912) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921))),
% 2.00/1.57 inference(transitivity,[status(thm)],[1761, 1759])).
% 2.00/1.57 tff(1763,plain,
% 2.00/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a908) | c3_1(a908) | (~c0_1(a908)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a921) | c1_1(a921) | c0_1(a921))),
% 2.00/1.57 inference(quant_inst,[status(thm)],[])).
% 2.00/1.57 tff(1764,plain,
% 2.00/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a921) | c3_1(a921) | c0_1(a912) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a921)),
% 2.00/1.57 inference(modus_ponens,[status(thm)],[1763, 1762])).
% 2.00/1.57 tff(1765,plain,
% 2.00/1.57 (c0_1(a921) | (~c0_1(a908)) | c1_1(a921)),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[1764, 124, 1727, 1726, 541, 1725, 1153, 1154, 322])).
% 2.00/1.57 tff(1766,plain,
% 2.00/1.57 (c1_1(a921)),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[1765, 1758, 542])).
% 2.00/1.57 tff(1767,plain,
% 2.00/1.57 (((~![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp30 | hskp7 | c1_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908)))) <=> ((~![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp30 | hskp7 | c1_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908)))),
% 2.00/1.57 inference(rewrite,[status(thm)],[])).
% 2.00/1.57 tff(1768,plain,
% 2.00/1.57 ((hskp30 | hskp7 | (~ndr1_0) | c1_1(a908) | c3_1(a908) | (~c0_1(a908))) <=> (hskp30 | hskp7 | c1_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908)))),
% 2.00/1.57 inference(rewrite,[status(thm)],[])).
% 2.00/1.57 tff(1769,plain,
% 2.00/1.57 (((~![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp30 | hskp7 | (~ndr1_0) | c1_1(a908) | c3_1(a908) | (~c0_1(a908)))) <=> ((~![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp30 | hskp7 | c1_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908))))),
% 2.00/1.57 inference(monotonicity,[status(thm)],[1768])).
% 2.00/1.57 tff(1770,plain,
% 2.00/1.57 (((~![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp30 | hskp7 | (~ndr1_0) | c1_1(a908) | c3_1(a908) | (~c0_1(a908)))) <=> ((~![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp30 | hskp7 | c1_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908)))),
% 2.00/1.57 inference(transitivity,[status(thm)],[1769, 1767])).
% 2.00/1.57 tff(1771,plain,
% 2.00/1.57 ((~![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp30 | hskp7 | (~ndr1_0) | c1_1(a908) | c3_1(a908) | (~c0_1(a908)))),
% 2.00/1.57 inference(quant_inst,[status(thm)],[])).
% 2.00/1.57 tff(1772,plain,
% 2.00/1.57 ((~![U: $i] : (hskp30 | hskp7 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp30 | hskp7 | c1_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908))),
% 2.00/1.57 inference(modus_ponens,[status(thm)],[1771, 1770])).
% 2.00/1.57 tff(1773,plain,
% 2.00/1.57 (hskp30 | hskp7 | c1_1(a908) | (~c0_1(a908))),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[1772, 124, 1154, 828])).
% 2.00/1.57 tff(1774,plain,
% 2.00/1.57 (hskp30),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[1773, 1758, 1714, 1715])).
% 2.00/1.57 tff(1775,plain,
% 2.00/1.57 (c2_1(a942)),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[846, 1774])).
% 2.00/1.57 tff(1776,plain,
% 2.00/1.57 (((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | c1_1(a908) | c2_1(a908) | (~ndr1_0) | (~c0_1(a908)))) <=> ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp17 | hskp12 | c1_1(a908) | c2_1(a908) | (~ndr1_0) | (~c0_1(a908)))),
% 2.00/1.57 inference(rewrite,[status(thm)],[])).
% 2.00/1.57 tff(1777,plain,
% 2.00/1.57 ((hskp17 | hskp12 | (~ndr1_0) | c2_1(a908) | c1_1(a908) | (~c0_1(a908))) <=> (hskp17 | hskp12 | c1_1(a908) | c2_1(a908) | (~ndr1_0) | (~c0_1(a908)))),
% 2.00/1.57 inference(rewrite,[status(thm)],[])).
% 2.00/1.57 tff(1778,plain,
% 2.00/1.57 (((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | (~ndr1_0) | c2_1(a908) | c1_1(a908) | (~c0_1(a908)))) <=> ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | c1_1(a908) | c2_1(a908) | (~ndr1_0) | (~c0_1(a908))))),
% 2.00/1.57 inference(monotonicity,[status(thm)],[1777])).
% 2.00/1.57 tff(1779,plain,
% 2.00/1.57 (((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | (~ndr1_0) | c2_1(a908) | c1_1(a908) | (~c0_1(a908)))) <=> ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp17 | hskp12 | c1_1(a908) | c2_1(a908) | (~ndr1_0) | (~c0_1(a908)))),
% 2.00/1.57 inference(transitivity,[status(thm)],[1778, 1776])).
% 2.00/1.57 tff(1780,plain,
% 2.00/1.57 ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp17 | hskp12 | (~ndr1_0) | c2_1(a908) | c1_1(a908) | (~c0_1(a908)))),
% 2.00/1.57 inference(quant_inst,[status(thm)],[])).
% 2.00/1.57 tff(1781,plain,
% 2.00/1.57 ((~![U: $i] : (hskp17 | hskp12 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp17 | hskp12 | c1_1(a908) | c2_1(a908) | (~ndr1_0) | (~c0_1(a908))),
% 2.00/1.57 inference(modus_ponens,[status(thm)],[1780, 1779])).
% 2.00/1.57 tff(1782,plain,
% 2.00/1.57 (hskp17 | hskp12 | c1_1(a908) | (~c0_1(a908))),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[1781, 124, 1153, 448])).
% 2.00/1.57 tff(1783,plain,
% 2.00/1.57 (hskp17),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[1782, 1758, 32, 1714])).
% 2.00/1.57 tff(1784,plain,
% 2.00/1.57 (~c1_1(a936)),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[508, 1783])).
% 2.00/1.57 tff(1785,plain,
% 2.00/1.57 (c1_1(a942)),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[858, 1774])).
% 2.00/1.57 tff(1786,plain,
% 2.00/1.57 (c0_1(a942)),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[869, 1774])).
% 2.00/1.57 tff(1787,plain,
% 2.00/1.57 (~c2_1(a936)),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[502, 1783])).
% 2.00/1.57 tff(1788,plain,
% 2.00/1.57 (c0_1(a936)),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[1547, 124, 243, 323, 324, 1784, 1787, 541, 325, 520, 1766])).
% 2.00/1.57 tff(1789,plain,
% 2.00/1.57 (~c3_1(a936)),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[460, 1783])).
% 2.00/1.57 tff(1790,plain,
% 2.00/1.57 (hskp9),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[953, 1787, 1789, 1788, 1786, 1785, 1784, 1775, 884, 1716, 896])).
% 2.00/1.57 tff(1791,plain,
% 2.00/1.57 (~c3_1(a910)),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[959, 1790])).
% 2.00/1.57 tff(1792,plain,
% 2.00/1.57 (~c1_1(a910)),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[965, 1790])).
% 2.00/1.57 tff(1793,plain,
% 2.00/1.57 (~c1_1(a903)),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[808, 124, 1579, 1578, 1577, 323, 324, 325, 884, 896, 31])).
% 2.00/1.57 tff(1794,plain,
% 2.00/1.57 (~c1_1(a908)),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[494, 124, 1579, 1578, 1577, 323, 324, 1153, 1154, 325, 31])).
% 2.00/1.57 tff(1795,plain,
% 2.00/1.57 (~hskp7),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[484, 1794])).
% 2.00/1.57 tff(1796,plain,
% 2.00/1.57 (hskp10),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[1460, 1795, 1386, 198, 884, 896, 543, 542, 541, 1793, 1397, 1193, 32])).
% 2.00/1.57 tff(1797,plain,
% 2.00/1.57 (c1_1(a912)),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[687, 1796])).
% 2.00/1.57 tff(1798,plain,
% 2.00/1.57 (c2_1(a912)),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[676, 1796])).
% 2.00/1.57 tff(1799,plain,
% 2.00/1.57 (hskp11),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[989, 1793, 884, 32, 896])).
% 2.00/1.57 tff(1800,plain,
% 2.00/1.57 (c3_1(a914)),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[80, 1799])).
% 2.00/1.57 tff(1801,plain,
% 2.00/1.57 (c0_1(a914)),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[91, 1799])).
% 2.00/1.57 tff(1802,plain,
% 2.00/1.57 (hskp14),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[707, 1795, 689, 690])).
% 2.00/1.57 tff(1803,plain,
% 2.00/1.57 (~c1_1(a923)),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[570, 1802])).
% 2.00/1.57 tff(1804,plain,
% 2.00/1.57 (~c0_1(a923)),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[576, 1802])).
% 2.00/1.57 tff(1805,plain,
% 2.00/1.57 (c3_1(a923)),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[587, 1802])).
% 2.00/1.57 tff(1806,plain,
% 2.00/1.57 (hskp6),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[594, 124, 1795, 1805, 1804, 1803, 564])).
% 2.00/1.57 tff(1807,plain,
% 2.00/1.57 (c0_1(a907)),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[725, 1806])).
% 2.00/1.57 tff(1808,plain,
% 2.00/1.57 (c1_1(a907)),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[418, 1806])).
% 2.00/1.57 tff(1809,plain,
% 2.00/1.57 (c1_1(a914)),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[1645, 1808, 542, 1565, 543, 1807, 1386, 1030, 690, 689, 665, 1566, 541, 198, 1801, 1800, 1397, 1193, 32])).
% 2.00/1.57 tff(1810,plain,
% 2.00/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a921) | c2_1(a914) | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a914)) | (~c1_1(a914)) | c1_1(a921) | (~c2_1(a921)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a921) | c2_1(a914) | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a914)) | (~c1_1(a914)) | c1_1(a921) | (~c2_1(a921)))),
% 2.00/1.57 inference(rewrite,[status(thm)],[])).
% 2.00/1.57 tff(1811,plain,
% 2.00/1.57 (((~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)) | c3_1(a921) | c1_1(a921) | (~c2_1(a921)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912))) <=> (c3_1(a921) | c2_1(a914) | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a914)) | (~c1_1(a914)) | c1_1(a921) | (~c2_1(a921)))),
% 2.00/1.57 inference(rewrite,[status(thm)],[])).
% 2.00/1.57 tff(1812,plain,
% 2.00/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)) | c3_1(a921) | c1_1(a921) | (~c2_1(a921)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a921) | c2_1(a914) | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a914)) | (~c1_1(a914)) | c1_1(a921) | (~c2_1(a921))))),
% 2.00/1.57 inference(monotonicity,[status(thm)],[1811])).
% 2.00/1.57 tff(1813,plain,
% 2.00/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)) | c3_1(a921) | c1_1(a921) | (~c2_1(a921)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a921) | c2_1(a914) | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a914)) | (~c1_1(a914)) | c1_1(a921) | (~c2_1(a921)))),
% 2.00/1.57 inference(transitivity,[status(thm)],[1812, 1810])).
% 2.00/1.57 tff(1814,plain,
% 2.00/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)) | c3_1(a921) | c1_1(a921) | (~c2_1(a921)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))),
% 2.00/1.57 inference(quant_inst,[status(thm)],[])).
% 2.00/1.57 tff(1815,plain,
% 2.00/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a921) | c2_1(a914) | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a914)) | (~c1_1(a914)) | c1_1(a921) | (~c2_1(a921))),
% 2.00/1.57 inference(modus_ponens,[status(thm)],[1814, 1813])).
% 2.00/1.57 tff(1816,plain,
% 2.00/1.57 ((~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a914)) | (~c1_1(a914)) | c1_1(a921) | (~c2_1(a921))),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[1815, 124, 541, 1193, 665, 743])).
% 2.00/1.57 tff(1817,plain,
% 2.00/1.57 (c1_1(a921)),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[1816, 1809, 543, 689, 690, 1800])).
% 2.00/1.57 tff(1818,plain,
% 2.00/1.57 (c0_1(a908) | (~c1_1(a921))),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[1752, 124, 543, 1794, 323, 324, 541, 1153, 325, 520])).
% 2.00/1.57 tff(1819,plain,
% 2.00/1.57 (c0_1(a908)),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[1818, 1817])).
% 2.00/1.57 tff(1820,plain,
% 2.00/1.57 ((~c2_1(a910)) | (~c3_1(a914)) | (~c1_1(a914)) | (~c2_1(a921)) | (~c1_1(a921))),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[1017, 124, 542, 1193, 1566, 1565, 743])).
% 2.00/1.57 tff(1821,plain,
% 2.00/1.57 (~c2_1(a910)),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[1820, 1809, 543, 1800, 1817])).
% 2.00/1.57 tff(1822,plain,
% 2.00/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a910) | c1_1(a910) | c3_1(a910) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908)) | c0_1(a910))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a910) | c1_1(a910) | c3_1(a910) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908)) | c0_1(a910))),
% 2.00/1.57 inference(rewrite,[status(thm)],[])).
% 2.00/1.57 tff(1823,plain,
% 2.00/1.57 (((~ndr1_0) | c2_1(a908) | c3_1(a908) | (~c0_1(a908)) | c3_1(a910) | c2_1(a910) | c0_1(a910) | c3_1(a910) | c1_1(a910) | c0_1(a910)) <=> (c2_1(a910) | c1_1(a910) | c3_1(a910) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908)) | c0_1(a910))),
% 2.00/1.57 inference(rewrite,[status(thm)],[])).
% 2.00/1.57 tff(1824,plain,
% 2.00/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a908) | c3_1(a908) | (~c0_1(a908)) | c3_1(a910) | c2_1(a910) | c0_1(a910) | c3_1(a910) | c1_1(a910) | c0_1(a910))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a910) | c1_1(a910) | c3_1(a910) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908)) | c0_1(a910)))),
% 2.00/1.57 inference(monotonicity,[status(thm)],[1823])).
% 2.00/1.57 tff(1825,plain,
% 2.00/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a908) | c3_1(a908) | (~c0_1(a908)) | c3_1(a910) | c2_1(a910) | c0_1(a910) | c3_1(a910) | c1_1(a910) | c0_1(a910))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a910) | c1_1(a910) | c3_1(a910) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908)) | c0_1(a910))),
% 2.00/1.57 inference(transitivity,[status(thm)],[1824, 1822])).
% 2.00/1.57 tff(1826,plain,
% 2.00/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a908) | c3_1(a908) | (~c0_1(a908)) | c3_1(a910) | c2_1(a910) | c0_1(a910) | c3_1(a910) | c1_1(a910) | c0_1(a910))),
% 2.00/1.57 inference(quant_inst,[status(thm)],[])).
% 2.00/1.57 tff(1827,plain,
% 2.00/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a910) | c1_1(a910) | c3_1(a910) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a908)) | c0_1(a910)),
% 2.00/1.57 inference(modus_ponens,[status(thm)],[1826, 1825])).
% 2.00/1.57 tff(1828,plain,
% 2.00/1.57 (c2_1(a910) | c1_1(a910) | (~c0_1(a908)) | c0_1(a910)),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[1827, 124, 1565, 1153, 1154, 1107])).
% 2.00/1.57 tff(1829,plain,
% 2.00/1.57 (c0_1(a910)),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[1828, 1821, 1566, 1819])).
% 2.00/1.57 tff(1830,plain,
% 2.00/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a914) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | c1_1(a906) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a914)) | (~c1_1(a914)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a914) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | c1_1(a906) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a914)) | (~c1_1(a914)))),
% 2.00/1.57 inference(rewrite,[status(thm)],[])).
% 2.00/1.57 tff(1831,plain,
% 2.00/1.57 (((~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)) | c3_1(a906) | c1_1(a906) | (~c2_1(a906)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912))) <=> (c2_1(a914) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | c1_1(a906) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a914)) | (~c1_1(a914)))),
% 2.00/1.57 inference(rewrite,[status(thm)],[])).
% 2.00/1.57 tff(1832,plain,
% 2.00/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)) | c3_1(a906) | c1_1(a906) | (~c2_1(a906)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a914) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | c1_1(a906) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a914)) | (~c1_1(a914))))),
% 2.00/1.57 inference(monotonicity,[status(thm)],[1831])).
% 2.00/1.57 tff(1833,plain,
% 2.00/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)) | c3_1(a906) | c1_1(a906) | (~c2_1(a906)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a914) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | c1_1(a906) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a914)) | (~c1_1(a914)))),
% 2.00/1.57 inference(transitivity,[status(thm)],[1832, 1830])).
% 2.00/1.57 tff(1834,plain,
% 2.00/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)) | c3_1(a906) | c1_1(a906) | (~c2_1(a906)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))),
% 2.00/1.57 inference(quant_inst,[status(thm)],[])).
% 2.00/1.57 tff(1835,plain,
% 2.00/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a914) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | c1_1(a906) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a914)) | (~c1_1(a914))),
% 2.00/1.57 inference(modus_ponens,[status(thm)],[1834, 1833])).
% 2.00/1.57 tff(1836,plain,
% 2.00/1.57 (c1_1(a906) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a914)) | (~c1_1(a914))),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[1835, 124, 324, 1193, 665, 325, 743])).
% 2.00/1.57 tff(1837,plain,
% 2.00/1.57 (c1_1(a906)),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[1836, 1809, 689, 1800, 690])).
% 2.00/1.57 tff(1838,plain,
% 2.00/1.57 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp0 | c2_1(a910) | c3_1(a910) | c3_1(a906) | (~ndr1_0) | (~c1_1(a906)) | (~c0_1(a906)) | (~c0_1(a910)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp0 | c2_1(a910) | c3_1(a910) | c3_1(a906) | (~ndr1_0) | (~c1_1(a906)) | (~c0_1(a906)) | (~c0_1(a910)))),
% 2.00/1.57 inference(rewrite,[status(thm)],[])).
% 2.00/1.57 tff(1839,plain,
% 2.00/1.57 ((hskp0 | (~ndr1_0) | c3_1(a906) | (~c1_1(a906)) | (~c0_1(a906)) | c3_1(a910) | c2_1(a910) | (~c0_1(a910))) <=> (hskp0 | c2_1(a910) | c3_1(a910) | c3_1(a906) | (~ndr1_0) | (~c1_1(a906)) | (~c0_1(a906)) | (~c0_1(a910)))),
% 2.00/1.57 inference(rewrite,[status(thm)],[])).
% 2.00/1.57 tff(1840,plain,
% 2.00/1.57 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a906) | (~c1_1(a906)) | (~c0_1(a906)) | c3_1(a910) | c2_1(a910) | (~c0_1(a910)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp0 | c2_1(a910) | c3_1(a910) | c3_1(a906) | (~ndr1_0) | (~c1_1(a906)) | (~c0_1(a906)) | (~c0_1(a910))))),
% 2.00/1.57 inference(monotonicity,[status(thm)],[1839])).
% 2.00/1.57 tff(1841,plain,
% 2.00/1.57 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a906) | (~c1_1(a906)) | (~c0_1(a906)) | c3_1(a910) | c2_1(a910) | (~c0_1(a910)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp0 | c2_1(a910) | c3_1(a910) | c3_1(a906) | (~ndr1_0) | (~c1_1(a906)) | (~c0_1(a906)) | (~c0_1(a910)))),
% 2.00/1.57 inference(transitivity,[status(thm)],[1840, 1838])).
% 2.00/1.57 tff(1842,plain,
% 2.00/1.57 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a906) | (~c1_1(a906)) | (~c0_1(a906)) | c3_1(a910) | c2_1(a910) | (~c0_1(a910)))),
% 2.00/1.57 inference(quant_inst,[status(thm)],[])).
% 2.00/1.57 tff(1843,plain,
% 2.00/1.57 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp0 | c2_1(a910) | c3_1(a910) | c3_1(a906) | (~ndr1_0) | (~c1_1(a906)) | (~c0_1(a906)) | (~c0_1(a910))),
% 2.00/1.57 inference(modus_ponens,[status(thm)],[1842, 1841])).
% 2.00/1.57 tff(1844,plain,
% 2.00/1.57 (hskp0 | c2_1(a910) | (~c1_1(a906)) | (~c0_1(a910))),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[1843, 124, 323, 1565, 325, 933])).
% 2.00/1.57 tff(1845,plain,
% 2.00/1.57 (hskp0),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[1844, 1821, 1837, 1829])).
% 2.00/1.57 tff(1846,plain,
% 2.00/1.57 (~c3_1(a901)),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[651, 1845])).
% 2.00/1.57 tff(1847,plain,
% 2.00/1.57 (~c1_1(a901)),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[657, 1845])).
% 2.00/1.57 tff(1848,plain,
% 2.00/1.57 (~c0_1(a901)),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[663, 1845])).
% 2.00/1.57 tff(1849,plain,
% 2.00/1.57 ($false),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[1643, 124, 543, 1821, 542, 1565, 1848, 1847, 1846, 322, 1829, 1817])).
% 2.00/1.57 tff(1850,plain,(hskp12 | (~c2_1(a921)) | c0_1(a921) | c3_1(a910) | (~c0_1(a906)) | c3_1(a906) | c1_1(a910) | c2_1(a908) | c3_1(a908) | (~c2_1(a906)) | c3_1(a921) | (~c2_1(a912)) | (~c1_1(a912)) | c2_1(a914) | c0_1(a912) | c2_1(a907) | c1_1(a902) | hskp21 | hskp18 | c2_1(a903) | c3_1(a903)), inference(lemma,lemma(discharge,[]))).
% 2.00/1.57 tff(1851,plain,
% 2.00/1.57 ($false),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[1850, 1798, 1797, 542, 1565, 323, 325, 1566, 1153, 1154, 324, 541, 1397, 32, 1193, 665, 1386, 1030, 198, 543, 884, 896])).
% 2.00/1.57 tff(1852,plain,(hskp12 | c0_1(a921) | c3_1(a910) | (~c0_1(a906)) | c3_1(a906) | c1_1(a910) | c2_1(a908) | c3_1(a908) | (~c2_1(a906)) | c3_1(a921) | hskp18 | c2_1(a914) | c0_1(a912) | c2_1(a907) | c1_1(a902) | hskp21 | (~c2_1(a921)) | c2_1(a903) | c3_1(a903)), inference(lemma,lemma(discharge,[]))).
% 2.00/1.57 tff(1853,plain,
% 2.00/1.57 (hskp18),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[1852, 1791, 1725, 323, 325, 1792, 1153, 1154, 324, 541, 542, 32, 1706, 1386, 1030, 198, 243, 884, 896])).
% 2.00/1.57 tff(1854,plain,
% 2.00/1.57 (~c2_1(a937)),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[1477, 1853])).
% 2.00/1.57 tff(1855,plain,
% 2.00/1.57 (c2_1(a910)),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[1009, 1790])).
% 2.00/1.57 tff(1856,plain,
% 2.00/1.57 (c1_1(a937)),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[1471, 1853])).
% 2.00/1.57 tff(1857,plain,
% 2.00/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a937) | c0_1(a921) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | (~c2_1(a910)) | (~c2_1(a921)) | (~c1_1(a921)) | (~c3_1(a937)) | (~c1_1(a937)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a937) | c0_1(a921) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | (~c2_1(a910)) | (~c2_1(a921)) | (~c1_1(a921)) | (~c3_1(a937)) | (~c1_1(a937)))),
% 2.00/1.57 inference(rewrite,[status(thm)],[])).
% 2.00/1.57 tff(1858,plain,
% 2.00/1.57 (((~ndr1_0) | c2_1(a937) | (~c3_1(a937)) | (~c1_1(a937)) | c3_1(a910) | c1_1(a910) | (~c2_1(a910)) | c0_1(a921) | (~c2_1(a921)) | (~c1_1(a921))) <=> (c2_1(a937) | c0_1(a921) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | (~c2_1(a910)) | (~c2_1(a921)) | (~c1_1(a921)) | (~c3_1(a937)) | (~c1_1(a937)))),
% 2.00/1.57 inference(rewrite,[status(thm)],[])).
% 2.00/1.57 tff(1859,plain,
% 2.00/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a937) | (~c3_1(a937)) | (~c1_1(a937)) | c3_1(a910) | c1_1(a910) | (~c2_1(a910)) | c0_1(a921) | (~c2_1(a921)) | (~c1_1(a921)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a937) | c0_1(a921) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | (~c2_1(a910)) | (~c2_1(a921)) | (~c1_1(a921)) | (~c3_1(a937)) | (~c1_1(a937))))),
% 2.00/1.57 inference(monotonicity,[status(thm)],[1858])).
% 2.00/1.57 tff(1860,plain,
% 2.00/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a937) | (~c3_1(a937)) | (~c1_1(a937)) | c3_1(a910) | c1_1(a910) | (~c2_1(a910)) | c0_1(a921) | (~c2_1(a921)) | (~c1_1(a921)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a937) | c0_1(a921) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | (~c2_1(a910)) | (~c2_1(a921)) | (~c1_1(a921)) | (~c3_1(a937)) | (~c1_1(a937)))),
% 2.00/1.57 inference(transitivity,[status(thm)],[1859, 1857])).
% 2.00/1.57 tff(1861,plain,
% 2.00/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a937) | (~c3_1(a937)) | (~c1_1(a937)) | c3_1(a910) | c1_1(a910) | (~c2_1(a910)) | c0_1(a921) | (~c2_1(a921)) | (~c1_1(a921)))),
% 2.00/1.57 inference(quant_inst,[status(thm)],[])).
% 2.00/1.57 tff(1862,plain,
% 2.00/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a937) | c0_1(a921) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | (~c2_1(a910)) | (~c2_1(a921)) | (~c1_1(a921)) | (~c3_1(a937)) | (~c1_1(a937))),
% 2.00/1.57 inference(modus_ponens,[status(thm)],[1861, 1860])).
% 2.00/1.57 tff(1863,plain,
% 2.00/1.57 (~c3_1(a937)),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[1862, 124, 1856, 243, 1855, 1854, 542, 1792, 1791, 743, 1766])).
% 2.00/1.57 tff(1864,plain,
% 2.00/1.57 (hskp14 | hskp7),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[706, 124, 1727, 1726, 1725, 700])).
% 2.00/1.57 tff(1865,plain,
% 2.00/1.57 (hskp14),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[1864, 1715])).
% 2.00/1.57 tff(1866,plain,
% 2.00/1.57 (~c1_1(a923)),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[570, 1865])).
% 2.00/1.57 tff(1867,plain,
% 2.00/1.57 (~c0_1(a923)),
% 2.00/1.57 inference(unit_resolution,[status(thm)],[576, 1865])).
% 2.00/1.58 tff(1868,plain,
% 2.00/1.58 (c3_1(a923)),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[587, 1865])).
% 2.00/1.58 tff(1869,plain,
% 2.00/1.58 (hskp6),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[594, 124, 1715, 1868, 1867, 1866, 564])).
% 2.00/1.58 tff(1870,plain,
% 2.00/1.58 (c1_1(a907)),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[418, 1869])).
% 2.00/1.58 tff(1871,plain,
% 2.00/1.58 (c0_1(a907)),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[725, 1869])).
% 2.00/1.58 tff(1872,plain,
% 2.00/1.58 (~c0_1(a937)),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[1652, 1853])).
% 2.00/1.58 tff(1873,plain,
% 2.00/1.58 (c1_1(a914)),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[1696, 1872, 243, 1711, 542, 1871, 1870, 1854, 1386, 1030, 1726, 1727, 541, 1725, 198, 1709, 1707, 1713, 1712, 1856])).
% 2.00/1.58 tff(1874,plain,
% 2.00/1.58 (^[U: $i] : refl((hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 2.00/1.58 inference(bind,[status(th)],[])).
% 2.00/1.58 tff(1875,plain,
% 2.00/1.58 (![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.00/1.58 inference(quant_intro,[status(thm)],[1874])).
% 2.00/1.58 tff(1876,plain,
% 2.00/1.58 (![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.00/1.58 inference(rewrite,[status(thm)],[])).
% 2.00/1.58 tff(1877,plain,
% 2.00/1.58 (^[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)) | hskp25) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp25))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp25) <=> (hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) <=> (hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) | hskp21) <=> ((hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp21))), rewrite(((hskp25 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp21) <=> (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) | hskp21) <=> (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 2.00/1.58 inference(bind,[status(th)],[])).
% 2.00/1.58 tff(1878,plain,
% 2.00/1.58 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) | hskp21) <=> ![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.00/1.58 inference(quant_intro,[status(thm)],[1877])).
% 2.00/1.58 tff(1879,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) | hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause152')).
% 2.00/1.58 tff(1880,plain,
% 2.00/1.58 (![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.00/1.58 inference(modus_ponens,[status(thm)],[1879, 1878])).
% 2.00/1.58 tff(1881,plain,
% 2.00/1.58 (![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.00/1.58 inference(modus_ponens,[status(thm)],[1880, 1876])).
% 2.00/1.58 tff(1882,plain,(
% 2.00/1.58 ![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.00/1.58 inference(skolemize,[status(sab)],[1881])).
% 2.00/1.58 tff(1883,plain,
% 2.00/1.58 (![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 2.00/1.58 inference(modus_ponens,[status(thm)],[1882, 1875])).
% 2.00/1.58 tff(1884,plain,
% 2.00/1.58 (((~![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp25 | hskp21 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c1_1(a914)))) <=> ((~![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp25 | hskp21 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c1_1(a914)))),
% 2.00/1.58 inference(rewrite,[status(thm)],[])).
% 2.00/1.58 tff(1885,plain,
% 2.00/1.58 ((hskp25 | hskp21 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914))) <=> (hskp25 | hskp21 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c1_1(a914)))),
% 2.00/1.58 inference(rewrite,[status(thm)],[])).
% 2.00/1.58 tff(1886,plain,
% 2.00/1.58 (((~![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp25 | hskp21 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)))) <=> ((~![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp25 | hskp21 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c1_1(a914))))),
% 2.00/1.58 inference(monotonicity,[status(thm)],[1885])).
% 2.00/1.58 tff(1887,plain,
% 2.00/1.58 (((~![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp25 | hskp21 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)))) <=> ((~![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp25 | hskp21 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c1_1(a914)))),
% 2.00/1.58 inference(transitivity,[status(thm)],[1886, 1884])).
% 2.00/1.58 tff(1888,plain,
% 2.00/1.58 ((~![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp25 | hskp21 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)))),
% 2.00/1.58 inference(quant_inst,[status(thm)],[])).
% 2.00/1.58 tff(1889,plain,
% 2.00/1.58 ((~![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp25 | hskp21 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c1_1(a914))),
% 2.00/1.58 inference(modus_ponens,[status(thm)],[1888, 1887])).
% 2.00/1.58 tff(1890,plain,
% 2.00/1.58 (hskp25 | (~c1_1(a914))),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[1889, 124, 198, 1707, 1706, 1883])).
% 2.00/1.58 tff(1891,plain,
% 2.00/1.58 (hskp25),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[1890, 1873])).
% 2.00/1.58 tff(1892,plain,
% 2.00/1.58 (((~hskp25) | (~c1_1(a960))) <=> ((~hskp25) | (~c1_1(a960)))),
% 2.00/1.58 inference(rewrite,[status(thm)],[])).
% 2.00/1.58 tff(1893,plain,
% 2.00/1.58 (((~c1_1(a960)) | (~hskp25)) <=> ((~hskp25) | (~c1_1(a960)))),
% 2.00/1.58 inference(rewrite,[status(thm)],[])).
% 2.00/1.58 tff(1894,axiom,((~c1_1(a960)) | (~hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause83')).
% 2.00/1.58 tff(1895,plain,
% 2.00/1.58 ((~hskp25) | (~c1_1(a960))),
% 2.00/1.58 inference(modus_ponens,[status(thm)],[1894, 1893])).
% 2.00/1.58 tff(1896,plain,
% 2.00/1.58 ((~hskp25) | (~c1_1(a960))),
% 2.00/1.58 inference(modus_ponens,[status(thm)],[1895, 1892])).
% 2.00/1.58 tff(1897,plain,
% 2.00/1.58 (~c1_1(a960)),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[1896, 1891])).
% 2.00/1.58 tff(1898,plain,
% 2.00/1.58 (((~hskp25) | c3_1(a960)) <=> ((~hskp25) | c3_1(a960))),
% 2.00/1.58 inference(rewrite,[status(thm)],[])).
% 2.00/1.58 tff(1899,axiom,((~hskp25) | c3_1(a960)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause50')).
% 2.00/1.58 tff(1900,plain,
% 2.00/1.58 ((~hskp25) | c3_1(a960)),
% 2.00/1.58 inference(modus_ponens,[status(thm)],[1899, 1898])).
% 2.00/1.58 tff(1901,plain,
% 2.00/1.58 ((~hskp25) | c3_1(a960)),
% 2.00/1.58 inference(modus_ponens,[status(thm)],[1900, 1898])).
% 2.00/1.58 tff(1902,plain,
% 2.00/1.58 ((~hskp25) | c3_1(a960)),
% 2.00/1.58 inference(modus_ponens,[status(thm)],[1901, 1898])).
% 2.00/1.58 tff(1903,plain,
% 2.00/1.58 ((~hskp25) | c3_1(a960)),
% 2.00/1.58 inference(modus_ponens,[status(thm)],[1902, 1898])).
% 2.00/1.58 tff(1904,plain,
% 2.00/1.58 ((~hskp25) | c3_1(a960)),
% 2.00/1.58 inference(modus_ponens,[status(thm)],[1903, 1898])).
% 2.00/1.58 tff(1905,plain,
% 2.00/1.58 ((~hskp25) | c3_1(a960)),
% 2.00/1.58 inference(modus_ponens,[status(thm)],[1904, 1898])).
% 2.00/1.58 tff(1906,plain,
% 2.00/1.58 ((~hskp25) | c3_1(a960)),
% 2.00/1.58 inference(modus_ponens,[status(thm)],[1905, 1898])).
% 2.00/1.58 tff(1907,plain,
% 2.00/1.58 ((~hskp25) | c3_1(a960)),
% 2.00/1.58 inference(modus_ponens,[status(thm)],[1906, 1898])).
% 2.00/1.58 tff(1908,plain,
% 2.00/1.58 (c3_1(a960)),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[1907, 1891])).
% 2.00/1.58 tff(1909,plain,
% 2.00/1.58 (((~hskp25) | c0_1(a960)) <=> ((~hskp25) | c0_1(a960))),
% 2.00/1.58 inference(rewrite,[status(thm)],[])).
% 2.00/1.58 tff(1910,axiom,((~hskp25) | c0_1(a960)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause49')).
% 2.00/1.58 tff(1911,plain,
% 2.00/1.58 ((~hskp25) | c0_1(a960)),
% 2.00/1.58 inference(modus_ponens,[status(thm)],[1910, 1909])).
% 2.00/1.58 tff(1912,plain,
% 2.00/1.58 ((~hskp25) | c0_1(a960)),
% 2.00/1.58 inference(modus_ponens,[status(thm)],[1911, 1909])).
% 2.00/1.58 tff(1913,plain,
% 2.00/1.58 ((~hskp25) | c0_1(a960)),
% 2.00/1.58 inference(modus_ponens,[status(thm)],[1912, 1909])).
% 2.00/1.58 tff(1914,plain,
% 2.00/1.58 ((~hskp25) | c0_1(a960)),
% 2.00/1.58 inference(modus_ponens,[status(thm)],[1913, 1909])).
% 2.00/1.58 tff(1915,plain,
% 2.00/1.58 ((~hskp25) | c0_1(a960)),
% 2.00/1.58 inference(modus_ponens,[status(thm)],[1914, 1909])).
% 2.00/1.58 tff(1916,plain,
% 2.00/1.58 ((~hskp25) | c0_1(a960)),
% 2.00/1.58 inference(modus_ponens,[status(thm)],[1915, 1909])).
% 2.00/1.58 tff(1917,plain,
% 2.00/1.58 ((~hskp25) | c0_1(a960)),
% 2.00/1.58 inference(modus_ponens,[status(thm)],[1916, 1909])).
% 2.00/1.58 tff(1918,plain,
% 2.00/1.58 ((~hskp25) | c0_1(a960)),
% 2.00/1.58 inference(modus_ponens,[status(thm)],[1917, 1909])).
% 2.00/1.58 tff(1919,plain,
% 2.00/1.58 (c0_1(a960)),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[1918, 1891])).
% 2.00/1.58 tff(1920,plain,
% 2.00/1.58 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | c1_1(a960) | c2_1(a937) | (~ndr1_0) | c3_1(a937) | (~c1_1(a937)) | (~c0_1(a960)) | (~c3_1(a960)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c1_1(a960) | c2_1(a937) | (~ndr1_0) | c3_1(a937) | (~c1_1(a937)) | (~c0_1(a960)) | (~c3_1(a960)))),
% 2.00/1.58 inference(rewrite,[status(thm)],[])).
% 2.00/1.58 tff(1921,plain,
% 2.00/1.58 ((hskp21 | (~ndr1_0) | c2_1(a937) | c3_1(a937) | (~c1_1(a937)) | c1_1(a960) | (~c0_1(a960)) | (~c3_1(a960))) <=> (hskp21 | c1_1(a960) | c2_1(a937) | (~ndr1_0) | c3_1(a937) | (~c1_1(a937)) | (~c0_1(a960)) | (~c3_1(a960)))),
% 2.00/1.58 inference(rewrite,[status(thm)],[])).
% 2.00/1.58 tff(1922,plain,
% 2.00/1.58 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a937) | c3_1(a937) | (~c1_1(a937)) | c1_1(a960) | (~c0_1(a960)) | (~c3_1(a960)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | c1_1(a960) | c2_1(a937) | (~ndr1_0) | c3_1(a937) | (~c1_1(a937)) | (~c0_1(a960)) | (~c3_1(a960))))),
% 2.00/1.58 inference(monotonicity,[status(thm)],[1921])).
% 2.00/1.58 tff(1923,plain,
% 2.00/1.58 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a937) | c3_1(a937) | (~c1_1(a937)) | c1_1(a960) | (~c0_1(a960)) | (~c3_1(a960)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c1_1(a960) | c2_1(a937) | (~ndr1_0) | c3_1(a937) | (~c1_1(a937)) | (~c0_1(a960)) | (~c3_1(a960)))),
% 2.00/1.58 inference(transitivity,[status(thm)],[1922, 1920])).
% 2.00/1.58 tff(1924,plain,
% 2.00/1.58 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a937) | c3_1(a937) | (~c1_1(a937)) | c1_1(a960) | (~c0_1(a960)) | (~c3_1(a960)))),
% 2.00/1.58 inference(quant_inst,[status(thm)],[])).
% 2.00/1.58 tff(1925,plain,
% 2.00/1.58 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c1_1(a960) | c2_1(a937) | (~ndr1_0) | c3_1(a937) | (~c1_1(a937)) | (~c0_1(a960)) | (~c3_1(a960))),
% 2.00/1.58 inference(modus_ponens,[status(thm)],[1924, 1923])).
% 2.00/1.58 tff(1926,plain,
% 2.00/1.58 ($false),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[1925, 124, 198, 1919, 1908, 1856, 1897, 1854, 197, 1863])).
% 2.00/1.58 tff(1927,plain,(hskp12 | hskp21 | c0_1(a921) | c2_1(a907) | c1_1(a902) | c3_1(a921) | (~c0_1(a906)) | c3_1(a906) | c2_1(a908) | c3_1(a908) | (~c2_1(a906)) | c2_1(a903) | c3_1(a903)), inference(lemma,lemma(discharge,[]))).
% 2.00/1.58 tff(1928,plain,
% 2.00/1.58 (hskp12),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[1927, 542, 198, 1386, 1030, 541, 323, 325, 1153, 1154, 324, 884, 896])).
% 2.00/1.58 tff(1929,plain,
% 2.00/1.58 (~c2_1(a917)),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[332, 1928])).
% 2.00/1.58 tff(1930,plain,
% 2.00/1.58 (c3_1(a917)),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[354, 1928])).
% 2.00/1.58 tff(1931,plain,
% 2.00/1.58 (c1_1(a917)),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[343, 1928])).
% 2.00/1.58 tff(1932,plain,
% 2.00/1.58 (c1_1(a906)),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[1354, 124, 1931, 1930, 1727, 1726, 324, 1929, 1725, 325, 743])).
% 2.00/1.58 tff(1933,plain,
% 2.00/1.58 (~c1_1(a908)),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[1043, 124, 1931, 1930, 1929, 1153, 1154, 10])).
% 2.00/1.58 tff(1934,plain,
% 2.00/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a908) | c2_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c0_1(a908))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a908) | c2_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c0_1(a908))),
% 2.00/1.58 inference(rewrite,[status(thm)],[])).
% 2.00/1.58 tff(1935,plain,
% 2.00/1.58 (((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a908) | c0_1(a908) | c2_1(a908)) <=> (c1_1(a908) | c2_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c0_1(a908))),
% 2.00/1.58 inference(rewrite,[status(thm)],[])).
% 2.00/1.58 tff(1936,plain,
% 2.00/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a908) | c0_1(a908) | c2_1(a908))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a908) | c2_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c0_1(a908)))),
% 2.00/1.58 inference(monotonicity,[status(thm)],[1935])).
% 2.00/1.58 tff(1937,plain,
% 2.00/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a908) | c0_1(a908) | c2_1(a908))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a908) | c2_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c0_1(a908))),
% 2.00/1.58 inference(transitivity,[status(thm)],[1936, 1934])).
% 2.00/1.58 tff(1938,plain,
% 2.00/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a908) | c0_1(a908) | c2_1(a908))),
% 2.00/1.58 inference(quant_inst,[status(thm)],[])).
% 2.00/1.58 tff(1939,plain,
% 2.00/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a908) | c2_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c0_1(a908)),
% 2.00/1.58 inference(modus_ponens,[status(thm)],[1938, 1937])).
% 2.00/1.58 tff(1940,plain,
% 2.00/1.58 (c0_1(a908)),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[1939, 124, 1933, 323, 324, 1153, 325, 520, 1932])).
% 2.00/1.58 tff(1941,plain,
% 2.00/1.58 (c1_1(a921)),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[1765, 1940, 542])).
% 2.00/1.58 tff(1942,plain,
% 2.00/1.58 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp0 | c2_1(a908) | c3_1(a908) | c3_1(a906) | (~ndr1_0) | (~c1_1(a906)) | (~c0_1(a906)) | (~c0_1(a908)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp0 | c2_1(a908) | c3_1(a908) | c3_1(a906) | (~ndr1_0) | (~c1_1(a906)) | (~c0_1(a906)) | (~c0_1(a908)))),
% 2.00/1.58 inference(rewrite,[status(thm)],[])).
% 2.00/1.58 tff(1943,plain,
% 2.00/1.58 ((hskp0 | (~ndr1_0) | c3_1(a906) | (~c1_1(a906)) | (~c0_1(a906)) | c3_1(a908) | c2_1(a908) | (~c0_1(a908))) <=> (hskp0 | c2_1(a908) | c3_1(a908) | c3_1(a906) | (~ndr1_0) | (~c1_1(a906)) | (~c0_1(a906)) | (~c0_1(a908)))),
% 2.00/1.58 inference(rewrite,[status(thm)],[])).
% 2.00/1.58 tff(1944,plain,
% 2.00/1.58 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a906) | (~c1_1(a906)) | (~c0_1(a906)) | c3_1(a908) | c2_1(a908) | (~c0_1(a908)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp0 | c2_1(a908) | c3_1(a908) | c3_1(a906) | (~ndr1_0) | (~c1_1(a906)) | (~c0_1(a906)) | (~c0_1(a908))))),
% 2.00/1.58 inference(monotonicity,[status(thm)],[1943])).
% 2.00/1.58 tff(1945,plain,
% 2.00/1.58 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a906) | (~c1_1(a906)) | (~c0_1(a906)) | c3_1(a908) | c2_1(a908) | (~c0_1(a908)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp0 | c2_1(a908) | c3_1(a908) | c3_1(a906) | (~ndr1_0) | (~c1_1(a906)) | (~c0_1(a906)) | (~c0_1(a908)))),
% 2.00/1.58 inference(transitivity,[status(thm)],[1944, 1942])).
% 2.00/1.58 tff(1946,plain,
% 2.00/1.58 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a906) | (~c1_1(a906)) | (~c0_1(a906)) | c3_1(a908) | c2_1(a908) | (~c0_1(a908)))),
% 2.00/1.58 inference(quant_inst,[status(thm)],[])).
% 2.00/1.58 tff(1947,plain,
% 2.00/1.58 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp0 | c2_1(a908) | c3_1(a908) | c3_1(a906) | (~ndr1_0) | (~c1_1(a906)) | (~c0_1(a906)) | (~c0_1(a908))),
% 2.00/1.58 inference(modus_ponens,[status(thm)],[1946, 1945])).
% 2.00/1.58 tff(1948,plain,
% 2.00/1.58 (hskp0 | c2_1(a908) | (~c1_1(a906)) | (~c0_1(a908))),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[1947, 124, 323, 1154, 325, 933])).
% 2.00/1.58 tff(1949,plain,
% 2.00/1.58 (hskp0),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[1948, 1940, 1153, 1932])).
% 2.00/1.58 tff(1950,plain,
% 2.00/1.58 (~c1_1(a901)),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[657, 1949])).
% 2.00/1.58 tff(1951,plain,
% 2.00/1.58 (~c0_1(a901)),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[663, 1949])).
% 2.00/1.58 tff(1952,plain,
% 2.00/1.58 (~hskp7),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[484, 1933])).
% 2.00/1.58 tff(1953,plain,
% 2.00/1.58 (hskp14),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[1864, 1952])).
% 2.00/1.58 tff(1954,plain,
% 2.00/1.58 (~c1_1(a923)),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[570, 1953])).
% 2.00/1.58 tff(1955,plain,
% 2.00/1.58 (~c0_1(a923)),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[576, 1953])).
% 2.00/1.58 tff(1956,plain,
% 2.00/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a923) | c1_1(a923) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c2_1(a923))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a923) | c1_1(a923) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c2_1(a923))),
% 2.00/1.58 inference(rewrite,[status(thm)],[])).
% 2.00/1.58 tff(1957,plain,
% 2.00/1.58 (((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a923) | c0_1(a923) | c2_1(a923)) <=> (c0_1(a923) | c1_1(a923) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c2_1(a923))),
% 2.00/1.58 inference(rewrite,[status(thm)],[])).
% 2.00/1.58 tff(1958,plain,
% 2.00/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a923) | c0_1(a923) | c2_1(a923))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a923) | c1_1(a923) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c2_1(a923)))),
% 2.00/1.58 inference(monotonicity,[status(thm)],[1957])).
% 2.00/1.58 tff(1959,plain,
% 2.00/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a923) | c0_1(a923) | c2_1(a923))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a923) | c1_1(a923) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c2_1(a923))),
% 2.00/1.58 inference(transitivity,[status(thm)],[1958, 1956])).
% 2.00/1.58 tff(1960,plain,
% 2.00/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a923) | c0_1(a923) | c2_1(a923))),
% 2.00/1.58 inference(quant_inst,[status(thm)],[])).
% 2.00/1.58 tff(1961,plain,
% 2.00/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a923) | c1_1(a923) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c2_1(a923)),
% 2.00/1.58 inference(modus_ponens,[status(thm)],[1960, 1959])).
% 2.00/1.58 tff(1962,plain,
% 2.00/1.58 (c2_1(a923)),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[1961, 124, 323, 324, 1955, 1954, 325, 520, 1932])).
% 2.00/1.58 tff(1963,plain,
% 2.00/1.58 (c3_1(a923)),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[587, 1953])).
% 2.00/1.58 tff(1964,plain,
% 2.00/1.58 (hskp13),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[1370, 124, 1952, 1963, 1955, 20, 1962])).
% 2.00/1.58 tff(1965,plain,
% 2.00/1.58 (c2_1(a921)),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[242, 1964])).
% 2.00/1.58 tff(1966,plain,
% 2.00/1.58 (c2_1(a901)),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[766, 124, 1965, 323, 324, 541, 325, 1951, 1950, 520, 1941])).
% 2.00/1.58 tff(1967,plain,
% 2.00/1.58 (~c3_1(a901)),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[651, 1949])).
% 2.00/1.58 tff(1968,plain,
% 2.00/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a921) | c2_1(a917) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c3_1(a917)) | (~c1_1(a917)) | (~c2_1(a921)) | (~c1_1(a921)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a921) | c2_1(a917) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c3_1(a917)) | (~c1_1(a917)) | (~c2_1(a921)) | (~c1_1(a921)))),
% 2.00/1.58 inference(rewrite,[status(thm)],[])).
% 2.00/1.58 tff(1969,plain,
% 2.00/1.58 (((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a901) | c1_1(a901) | (~c2_1(a901)) | c0_1(a921) | (~c2_1(a921)) | (~c1_1(a921))) <=> (c0_1(a921) | c2_1(a917) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c3_1(a917)) | (~c1_1(a917)) | (~c2_1(a921)) | (~c1_1(a921)))),
% 2.00/1.58 inference(rewrite,[status(thm)],[])).
% 2.00/1.58 tff(1970,plain,
% 2.00/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a901) | c1_1(a901) | (~c2_1(a901)) | c0_1(a921) | (~c2_1(a921)) | (~c1_1(a921)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a921) | c2_1(a917) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c3_1(a917)) | (~c1_1(a917)) | (~c2_1(a921)) | (~c1_1(a921))))),
% 2.00/1.58 inference(monotonicity,[status(thm)],[1969])).
% 2.00/1.58 tff(1971,plain,
% 2.00/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a901) | c1_1(a901) | (~c2_1(a901)) | c0_1(a921) | (~c2_1(a921)) | (~c1_1(a921)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a921) | c2_1(a917) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c3_1(a917)) | (~c1_1(a917)) | (~c2_1(a921)) | (~c1_1(a921)))),
% 2.00/1.58 inference(transitivity,[status(thm)],[1970, 1968])).
% 2.00/1.58 tff(1972,plain,
% 2.00/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a901) | c1_1(a901) | (~c2_1(a901)) | c0_1(a921) | (~c2_1(a921)) | (~c1_1(a921)))),
% 2.00/1.58 inference(quant_inst,[status(thm)],[])).
% 2.00/1.58 tff(1973,plain,
% 2.00/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a921) | c2_1(a917) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c3_1(a917)) | (~c1_1(a917)) | (~c2_1(a921)) | (~c1_1(a921))),
% 2.00/1.58 inference(modus_ponens,[status(thm)],[1972, 1971])).
% 2.00/1.58 tff(1974,plain,
% 2.00/1.58 ($false),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[1973, 124, 1965, 1931, 1930, 542, 1929, 1950, 1967, 743, 1941, 1966])).
% 2.00/1.58 tff(1975,plain,(c0_1(a921) | (~c0_1(a906)) | (~c2_1(a906)) | c3_1(a921) | c3_1(a906) | c2_1(a908) | c3_1(a908) | hskp21 | c2_1(a907) | c1_1(a902) | c2_1(a903) | c3_1(a903)), inference(lemma,lemma(discharge,[]))).
% 2.00/1.58 tff(1976,plain,
% 2.00/1.58 ($false),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[1975, 1701, 232, 324, 323, 325, 1322, 541, 198, 1700, 1030, 884, 896])).
% 2.00/1.58 tff(1977,plain,(hskp12 | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a906) | c3_1(a921) | hskp21 | c1_1(a902) | c2_1(a903) | c3_1(a903)), inference(lemma,lemma(discharge,[]))).
% 2.00/1.58 tff(1978,plain,
% 2.00/1.58 (c3_1(a921)),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[1977, 32, 323, 325, 324, 198, 1030, 884, 896])).
% 2.00/1.58 tff(1979,plain,
% 2.00/1.58 ($false),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[225, 1978, 220])).
% 2.00/1.58 tff(1980,plain,(hskp12 | (~c0_1(a906)) | c3_1(a906) | (~c2_1(a906)) | hskp21 | c1_1(a902) | c2_1(a903) | c3_1(a903)), inference(lemma,lemma(discharge,[]))).
% 2.00/1.58 tff(1981,plain,
% 2.00/1.58 (c1_1(a902)),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[1980, 782, 325, 324, 198, 32, 323, 776])).
% 2.00/1.58 tff(1982,plain,
% 2.00/1.58 (((~hskp1) | (~c1_1(a902))) <=> ((~hskp1) | (~c1_1(a902)))),
% 2.00/1.58 inference(rewrite,[status(thm)],[])).
% 2.00/1.58 tff(1983,plain,
% 2.00/1.58 (((~c1_1(a902)) | (~hskp1)) <=> ((~hskp1) | (~c1_1(a902)))),
% 2.00/1.58 inference(rewrite,[status(thm)],[])).
% 2.00/1.58 tff(1984,axiom,((~c1_1(a902)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause124')).
% 2.00/1.58 tff(1985,plain,
% 2.00/1.58 ((~hskp1) | (~c1_1(a902))),
% 2.00/1.58 inference(modus_ponens,[status(thm)],[1984, 1983])).
% 2.00/1.58 tff(1986,plain,
% 2.00/1.58 ((~hskp1) | (~c1_1(a902))),
% 2.00/1.58 inference(modus_ponens,[status(thm)],[1985, 1982])).
% 2.00/1.58 tff(1987,plain,
% 2.00/1.58 (~hskp1),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[1986, 1981])).
% 2.00/1.58 tff(1988,plain,
% 2.00/1.58 ($false),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[1585, 124, 1987, 261, 283, 272, 1029, 1011, 1028, 1018])).
% 2.00/1.58 tff(1989,plain,(hskp12 | (~c0_1(a906)) | c3_1(a906) | (~c2_1(a906)) | hskp21), inference(lemma,lemma(discharge,[]))).
% 2.00/1.58 tff(1990,plain,
% 2.00/1.58 (hskp12),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[1989, 312, 301, 295, 198])).
% 2.00/1.58 tff(1991,plain,
% 2.00/1.58 (hskp10),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[621, 301, 295, 198, 312])).
% 2.00/1.58 tff(1992,plain,
% 2.00/1.58 (~c0_1(a912)),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[627, 1991])).
% 2.00/1.58 tff(1993,plain,
% 2.00/1.58 (hskp6),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[1045, 1990, 1992, 198])).
% 2.00/1.58 tff(1994,plain,
% 2.00/1.58 (~c2_1(a907)),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[407, 1993])).
% 2.00/1.58 tff(1995,plain,
% 2.00/1.58 (~c2_1(a917)),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[332, 1990])).
% 2.00/1.58 tff(1996,plain,
% 2.00/1.58 (c3_1(a917)),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[354, 1990])).
% 2.00/1.58 tff(1997,plain,
% 2.00/1.58 (c1_1(a917)),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[343, 1990])).
% 2.00/1.58 tff(1998,plain,
% 2.00/1.58 (((~![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp25 | hskp21 | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917)))) <=> ((~![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp25 | hskp21 | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917)))),
% 2.00/1.58 inference(rewrite,[status(thm)],[])).
% 2.00/1.58 tff(1999,plain,
% 2.00/1.58 ((hskp25 | hskp21 | (~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917))) <=> (hskp25 | hskp21 | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917)))),
% 2.00/1.58 inference(rewrite,[status(thm)],[])).
% 2.00/1.58 tff(2000,plain,
% 2.00/1.58 (((~![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp25 | hskp21 | (~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)))) <=> ((~![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp25 | hskp21 | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917))))),
% 2.00/1.58 inference(monotonicity,[status(thm)],[1999])).
% 2.00/1.58 tff(2001,plain,
% 2.00/1.58 (((~![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp25 | hskp21 | (~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)))) <=> ((~![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp25 | hskp21 | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917)))),
% 2.00/1.58 inference(transitivity,[status(thm)],[2000, 1998])).
% 2.00/1.58 tff(2002,plain,
% 2.00/1.58 ((~![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp25 | hskp21 | (~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)))),
% 2.00/1.58 inference(quant_inst,[status(thm)],[])).
% 2.00/1.58 tff(2003,plain,
% 2.00/1.58 ((~![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp25 | hskp21 | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917))),
% 2.00/1.58 inference(modus_ponens,[status(thm)],[2002, 2001])).
% 2.00/1.58 tff(2004,plain,
% 2.00/1.58 (hskp25),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[2003, 124, 198, 1997, 1996, 1995, 1883])).
% 2.00/1.58 tff(2005,plain,
% 2.00/1.58 (~c1_1(a960)),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[1896, 2004])).
% 2.00/1.58 tff(2006,plain,
% 2.00/1.58 (c1_1(a907)),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[418, 1993])).
% 2.00/1.58 tff(2007,plain,
% 2.00/1.58 (c3_1(a960)),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[1907, 2004])).
% 2.00/1.58 tff(2008,plain,
% 2.00/1.58 (c0_1(a960)),
% 2.00/1.58 inference(unit_resolution,[status(thm)],[1918, 2004])).
% 2.00/1.58 tff(2009,plain,
% 2.00/1.58 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | c1_1(a960) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c1_1(a907)) | (~c0_1(a960)) | (~c3_1(a960)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c1_1(a960) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c1_1(a907)) | (~c0_1(a960)) | (~c3_1(a960)))),
% 2.00/1.58 inference(rewrite,[status(thm)],[])).
% 2.00/1.58 tff(2010,plain,
% 2.00/1.58 ((hskp21 | (~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c1_1(a907)) | c1_1(a960) | (~c0_1(a960)) | (~c3_1(a960))) <=> (hskp21 | c1_1(a960) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c1_1(a907)) | (~c0_1(a960)) | (~c3_1(a960)))),
% 2.00/1.58 inference(rewrite,[status(thm)],[])).
% 2.00/1.58 tff(2011,plain,
% 2.00/1.58 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c1_1(a907)) | c1_1(a960) | (~c0_1(a960)) | (~c3_1(a960)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | c1_1(a960) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c1_1(a907)) | (~c0_1(a960)) | (~c3_1(a960))))),
% 2.00/1.58 inference(monotonicity,[status(thm)],[2010])).
% 2.00/1.58 tff(2012,plain,
% 2.00/1.58 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c1_1(a907)) | c1_1(a960) | (~c0_1(a960)) | (~c3_1(a960)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c1_1(a960) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c1_1(a907)) | (~c0_1(a960)) | (~c3_1(a960)))),
% 2.00/1.58 inference(transitivity,[status(thm)],[2011, 2009])).
% 2.00/1.58 tff(2013,plain,
% 2.00/1.58 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c1_1(a907)) | c1_1(a960) | (~c0_1(a960)) | (~c3_1(a960)))),
% 2.00/1.58 inference(quant_inst,[status(thm)],[])).
% 2.00/1.58 tff(2014,plain,
% 2.00/1.58 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c1_1(a960) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c1_1(a907)) | (~c0_1(a960)) | (~c3_1(a960))),
% 2.00/1.59 inference(modus_ponens,[status(thm)],[2013, 2012])).
% 2.00/1.59 tff(2015,plain,
% 2.00/1.59 (c3_1(a907)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[2014, 124, 198, 2008, 2007, 2006, 2005, 1994, 197])).
% 2.00/1.59 tff(2016,plain,
% 2.00/1.59 (c0_1(a907)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[725, 1993])).
% 2.00/1.59 tff(2017,plain,
% 2.00/1.59 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp1 | c1_1(a960) | (~ndr1_0) | (~c0_1(a907)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c0_1(a960)) | (~c3_1(a960)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp1 | c1_1(a960) | (~ndr1_0) | (~c0_1(a907)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c0_1(a960)) | (~c3_1(a960)))),
% 2.00/1.59 inference(rewrite,[status(thm)],[])).
% 2.00/1.59 tff(2018,plain,
% 2.00/1.59 ((hskp1 | (~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c0_1(a907)) | c1_1(a960) | (~c0_1(a960)) | (~c3_1(a960))) <=> (hskp1 | c1_1(a960) | (~ndr1_0) | (~c0_1(a907)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c0_1(a960)) | (~c3_1(a960)))),
% 2.00/1.59 inference(rewrite,[status(thm)],[])).
% 2.00/1.59 tff(2019,plain,
% 2.00/1.59 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c0_1(a907)) | c1_1(a960) | (~c0_1(a960)) | (~c3_1(a960)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp1 | c1_1(a960) | (~ndr1_0) | (~c0_1(a907)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c0_1(a960)) | (~c3_1(a960))))),
% 2.00/1.59 inference(monotonicity,[status(thm)],[2018])).
% 2.00/1.59 tff(2020,plain,
% 2.00/1.59 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c0_1(a907)) | c1_1(a960) | (~c0_1(a960)) | (~c3_1(a960)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp1 | c1_1(a960) | (~ndr1_0) | (~c0_1(a907)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c0_1(a960)) | (~c3_1(a960)))),
% 2.00/1.59 inference(transitivity,[status(thm)],[2019, 2017])).
% 2.00/1.59 tff(2021,plain,
% 2.00/1.59 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c0_1(a907)) | c1_1(a960) | (~c0_1(a960)) | (~c3_1(a960)))),
% 2.00/1.59 inference(quant_inst,[status(thm)],[])).
% 2.00/1.59 tff(2022,plain,
% 2.00/1.59 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp1 | c1_1(a960) | (~ndr1_0) | (~c0_1(a907)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c0_1(a960)) | (~c3_1(a960))),
% 2.00/1.59 inference(modus_ponens,[status(thm)],[2021, 2020])).
% 2.00/1.59 tff(2023,plain,
% 2.00/1.59 (hskp1),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[2022, 124, 2008, 2007, 2016, 2006, 2005, 1028, 2015])).
% 2.00/1.59 tff(2024,plain,
% 2.00/1.59 (~c1_1(a902)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[1986, 2023])).
% 2.00/1.59 tff(2025,plain,
% 2.00/1.59 (hskp12),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[769, 665, 324, 325, 323, 198, 639])).
% 2.00/1.59 tff(2026,plain,
% 2.00/1.59 (~c2_1(a917)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[332, 2025])).
% 2.00/1.59 tff(2027,plain,
% 2.00/1.59 (hskp10),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[377, 2025, 198])).
% 2.00/1.59 tff(2028,plain,
% 2.00/1.59 (c2_1(a912)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[676, 2027])).
% 2.00/1.59 tff(2029,plain,
% 2.00/1.59 (c1_1(a912)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[687, 2027])).
% 2.00/1.59 tff(2030,plain,
% 2.00/1.59 (c3_1(a917)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[354, 2025])).
% 2.00/1.59 tff(2031,plain,
% 2.00/1.59 (c1_1(a917)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[343, 2025])).
% 2.00/1.59 tff(2032,plain,
% 2.00/1.59 (c1_1(a906)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[1354, 124, 2031, 2030, 2029, 2028, 324, 2026, 665, 325, 743])).
% 2.00/1.59 tff(2033,plain,
% 2.00/1.59 (^[U: $i] : refl((hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 2.00/1.59 inference(bind,[status(th)],[])).
% 2.00/1.59 tff(2034,plain,
% 2.00/1.59 (![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.00/1.59 inference(quant_intro,[status(thm)],[2033])).
% 2.00/1.59 tff(2035,plain,
% 2.00/1.59 (![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.00/1.59 inference(rewrite,[status(thm)],[])).
% 2.00/1.59 tff(2036,plain,
% 2.00/1.59 (^[U: $i] : 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)) | hskp28) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp28))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 2.00/1.59 inference(bind,[status(th)],[])).
% 2.00/1.59 tff(2037,plain,
% 2.00/1.59 (![U: $i] : (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp28) <=> ![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.00/1.59 inference(quant_intro,[status(thm)],[2036])).
% 2.00/1.59 tff(2038,axiom,(![U: $i] : (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause141')).
% 2.00/1.59 tff(2039,plain,
% 2.00/1.59 (![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.00/1.59 inference(modus_ponens,[status(thm)],[2038, 2037])).
% 2.00/1.59 tff(2040,plain,
% 2.00/1.59 (![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.00/1.59 inference(modus_ponens,[status(thm)],[2039, 2035])).
% 2.00/1.59 tff(2041,plain,(
% 2.00/1.59 ![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.00/1.59 inference(skolemize,[status(sab)],[2040])).
% 2.00/1.59 tff(2042,plain,
% 2.00/1.59 (![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.00/1.59 inference(modus_ponens,[status(thm)],[2041, 2034])).
% 2.00/1.59 tff(2043,plain,
% 2.00/1.59 (hskp25),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[2003, 124, 198, 2031, 2030, 2026, 1883])).
% 2.00/1.59 tff(2044,plain,
% 2.00/1.59 (~c1_1(a960)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[1896, 2043])).
% 2.00/1.59 tff(2045,plain,
% 2.00/1.59 (c3_1(a960)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[1907, 2043])).
% 2.00/1.59 tff(2046,plain,
% 2.00/1.59 (c0_1(a960)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[1918, 2043])).
% 2.00/1.59 tff(2047,plain,
% 2.00/1.59 (((~![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | c1_1(a960) | (~ndr1_0) | (~c0_1(a960)) | (~c3_1(a960)))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | c1_1(a960) | (~ndr1_0) | (~c0_1(a960)) | (~c3_1(a960)))),
% 2.00/1.59 inference(rewrite,[status(thm)],[])).
% 2.00/1.59 tff(2048,plain,
% 2.00/1.59 ((hskp28 | (~ndr1_0) | c1_1(a960) | (~c3_1(a960)) | (~c0_1(a960))) <=> (hskp28 | c1_1(a960) | (~ndr1_0) | (~c0_1(a960)) | (~c3_1(a960)))),
% 2.00/1.59 inference(rewrite,[status(thm)],[])).
% 2.00/1.59 tff(2049,plain,
% 2.00/1.59 (((~![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | (~ndr1_0) | c1_1(a960) | (~c3_1(a960)) | (~c0_1(a960)))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | c1_1(a960) | (~ndr1_0) | (~c0_1(a960)) | (~c3_1(a960))))),
% 2.00/1.59 inference(monotonicity,[status(thm)],[2048])).
% 2.00/1.59 tff(2050,plain,
% 2.00/1.59 (((~![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | (~ndr1_0) | c1_1(a960) | (~c3_1(a960)) | (~c0_1(a960)))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | c1_1(a960) | (~ndr1_0) | (~c0_1(a960)) | (~c3_1(a960)))),
% 2.00/1.59 inference(transitivity,[status(thm)],[2049, 2047])).
% 2.00/1.59 tff(2051,plain,
% 2.00/1.59 ((~![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | (~ndr1_0) | c1_1(a960) | (~c3_1(a960)) | (~c0_1(a960)))),
% 2.00/1.59 inference(quant_inst,[status(thm)],[])).
% 2.00/1.59 tff(2052,plain,
% 2.00/1.59 ((~![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | c1_1(a960) | (~ndr1_0) | (~c0_1(a960)) | (~c3_1(a960))),
% 2.00/1.59 inference(modus_ponens,[status(thm)],[2051, 2050])).
% 2.00/1.59 tff(2053,plain,
% 2.00/1.59 (hskp28),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[2052, 124, 2046, 2045, 2044, 2042])).
% 2.00/1.59 tff(2054,plain,
% 2.00/1.59 (c3_1(a916)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[271, 2053])).
% 2.00/1.59 tff(2055,plain,
% 2.00/1.59 (c1_1(a916)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[282, 2053])).
% 2.00/1.59 tff(2056,plain,
% 2.00/1.59 (c0_1(a916)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[260, 2053])).
% 2.00/1.59 tff(2057,plain,
% 2.00/1.59 (~hskp7),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[496, 2056, 2055, 2054, 323, 324, 325])).
% 2.00/1.59 tff(2058,plain,
% 2.00/1.59 (hskp14),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[707, 2057, 2029, 2028])).
% 2.00/1.59 tff(2059,plain,
% 2.00/1.59 (~c1_1(a923)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[570, 2058])).
% 2.00/1.59 tff(2060,plain,
% 2.00/1.59 (~c0_1(a923)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[576, 2058])).
% 2.00/1.59 tff(2061,plain,
% 2.00/1.59 (c2_1(a923)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[1961, 124, 323, 324, 2060, 2059, 325, 520, 2032])).
% 2.00/1.59 tff(2062,plain,
% 2.00/1.59 (c3_1(a923)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[587, 2058])).
% 2.00/1.59 tff(2063,plain,
% 2.00/1.59 (hskp13 | (~c2_1(a923))),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[1370, 124, 2057, 2062, 2060, 20])).
% 2.00/1.59 tff(2064,plain,
% 2.00/1.59 (hskp13),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[2063, 2061])).
% 2.00/1.59 tff(2065,plain,
% 2.00/1.59 (~c3_1(a921)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[225, 2064])).
% 2.00/1.59 tff(2066,plain,
% 2.00/1.59 (c2_1(a921)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[242, 2064])).
% 2.00/1.59 tff(2067,plain,
% 2.00/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a921) | c2_1(a917) | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a917)) | (~c1_1(a917)) | c1_1(a921) | (~c2_1(a921)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a921) | c2_1(a917) | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a917)) | (~c1_1(a917)) | c1_1(a921) | (~c2_1(a921)))),
% 2.00/1.59 inference(rewrite,[status(thm)],[])).
% 2.00/1.59 tff(2068,plain,
% 2.00/1.59 (((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a921) | c1_1(a921) | (~c2_1(a921)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912))) <=> (c3_1(a921) | c2_1(a917) | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a917)) | (~c1_1(a917)) | c1_1(a921) | (~c2_1(a921)))),
% 2.00/1.59 inference(rewrite,[status(thm)],[])).
% 2.00/1.59 tff(2069,plain,
% 2.00/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a921) | c1_1(a921) | (~c2_1(a921)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a921) | c2_1(a917) | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a917)) | (~c1_1(a917)) | c1_1(a921) | (~c2_1(a921))))),
% 2.00/1.59 inference(monotonicity,[status(thm)],[2068])).
% 2.00/1.59 tff(2070,plain,
% 2.00/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a921) | c1_1(a921) | (~c2_1(a921)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a921) | c2_1(a917) | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a917)) | (~c1_1(a917)) | c1_1(a921) | (~c2_1(a921)))),
% 2.00/1.59 inference(transitivity,[status(thm)],[2069, 2067])).
% 2.00/1.59 tff(2071,plain,
% 2.00/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a921) | c1_1(a921) | (~c2_1(a921)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))),
% 2.00/1.59 inference(quant_inst,[status(thm)],[])).
% 2.00/1.59 tff(2072,plain,
% 2.00/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a921) | c2_1(a917) | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a917)) | (~c1_1(a917)) | c1_1(a921) | (~c2_1(a921))),
% 2.00/1.59 inference(modus_ponens,[status(thm)],[2071, 2070])).
% 2.00/1.59 tff(2073,plain,
% 2.00/1.59 (c1_1(a921)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[2072, 124, 2066, 2031, 2030, 2029, 2028, 2065, 2026, 665, 743])).
% 2.00/1.59 tff(2074,plain,
% 2.00/1.59 (hskp6),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[1045, 2025, 665, 198])).
% 2.00/1.59 tff(2075,plain,
% 2.00/1.59 (~c2_1(a907)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[407, 2074])).
% 2.00/1.59 tff(2076,plain,
% 2.00/1.59 (c1_1(a907)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[418, 2074])).
% 2.00/1.59 tff(2077,plain,
% 2.00/1.59 (c3_1(a907)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[2014, 124, 198, 2046, 2045, 2076, 2044, 2075, 197])).
% 2.00/1.59 tff(2078,plain,
% 2.00/1.59 (c0_1(a907)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[725, 2074])).
% 2.00/1.59 tff(2079,plain,
% 2.00/1.59 (hskp1),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[2022, 124, 2046, 2045, 2078, 2076, 2044, 1028, 2077])).
% 2.00/1.59 tff(2080,plain,
% 2.00/1.59 (c2_1(a902)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[1596, 2079])).
% 2.00/1.59 tff(2081,plain,
% 2.00/1.59 (c0_1(a902)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[1607, 2079])).
% 2.00/1.59 tff(2082,plain,
% 2.00/1.59 (hskp0 | (~c0_1(a902)) | (~c2_1(a902))),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[1624, 124, 2078, 2076, 2075, 1030, 1618])).
% 2.00/1.59 tff(2083,plain,
% 2.00/1.59 (hskp0),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[2082, 2081, 2080])).
% 2.00/1.59 tff(2084,plain,
% 2.00/1.59 (~c1_1(a901)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[657, 2083])).
% 2.00/1.59 tff(2085,plain,
% 2.00/1.59 (~c0_1(a901)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[663, 2083])).
% 2.00/1.59 tff(2086,plain,
% 2.00/1.59 (c2_1(a901)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[766, 124, 2066, 323, 324, 2065, 325, 2085, 2084, 520, 2073])).
% 2.00/1.59 tff(2087,plain,
% 2.00/1.59 (~c3_1(a901)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[651, 2083])).
% 2.00/1.59 tff(2088,plain,
% 2.00/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a917) | c0_1(a912) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a917)) | (~c1_1(a917)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a917) | c0_1(a912) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a917)) | (~c1_1(a917)))),
% 2.00/1.59 inference(rewrite,[status(thm)],[])).
% 2.00/1.59 tff(2089,plain,
% 2.00/1.59 (((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a901) | c1_1(a901) | (~c2_1(a901)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912))) <=> (c2_1(a917) | c0_1(a912) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a917)) | (~c1_1(a917)))),
% 2.00/1.59 inference(rewrite,[status(thm)],[])).
% 2.00/1.59 tff(2090,plain,
% 2.00/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a901) | c1_1(a901) | (~c2_1(a901)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a917) | c0_1(a912) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a917)) | (~c1_1(a917))))),
% 2.00/1.59 inference(monotonicity,[status(thm)],[2089])).
% 2.00/1.59 tff(2091,plain,
% 2.00/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a901) | c1_1(a901) | (~c2_1(a901)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a917) | c0_1(a912) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a917)) | (~c1_1(a917)))),
% 2.00/1.59 inference(transitivity,[status(thm)],[2090, 2088])).
% 2.00/1.59 tff(2092,plain,
% 2.00/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a901) | c1_1(a901) | (~c2_1(a901)) | c0_1(a912) | (~c2_1(a912)) | (~c1_1(a912)))),
% 2.00/1.59 inference(quant_inst,[status(thm)],[])).
% 2.00/1.59 tff(2093,plain,
% 2.00/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a917) | c0_1(a912) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a917)) | (~c1_1(a917))),
% 2.00/1.59 inference(modus_ponens,[status(thm)],[2092, 2091])).
% 2.00/1.59 tff(2094,plain,
% 2.00/1.59 ($false),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[2093, 124, 2031, 2030, 2029, 2028, 2026, 665, 2084, 2087, 743, 2086])).
% 2.00/1.59 tff(2095,plain,(c0_1(a912) | (~c0_1(a906)) | (~c2_1(a906)) | c3_1(a906) | c1_1(a902) | hskp21 | hskp2), inference(lemma,lemma(discharge,[]))).
% 2.00/1.59 tff(2096,plain,
% 2.00/1.59 (hskp2),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[2095, 2024, 295, 301, 1992, 198, 312])).
% 2.00/1.59 tff(2097,plain,
% 2.00/1.59 (~c2_1(a903)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[781, 2096])).
% 2.00/1.59 tff(2098,plain,
% 2.00/1.59 (~c3_1(a903)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[775, 2096])).
% 2.00/1.59 tff(2099,plain,
% 2.00/1.59 (c1_1(a906)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[1354, 124, 344, 355, 1033, 1032, 324, 333, 665, 325, 743])).
% 2.00/1.59 tff(2100,plain,
% 2.00/1.59 (~c1_1(a903)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[1343, 124, 344, 355, 333, 884, 896, 10])).
% 2.00/1.59 tff(2101,plain,
% 2.00/1.59 (c0_1(a903)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[1121, 124, 323, 324, 325, 884, 520, 2099, 2100])).
% 2.00/1.59 tff(2102,plain,
% 2.00/1.59 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp0 | c3_1(a906) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c0_1(a903)) | (~c1_1(a906)) | (~c0_1(a906)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp0 | c3_1(a906) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c0_1(a903)) | (~c1_1(a906)) | (~c0_1(a906)))),
% 2.00/1.59 inference(rewrite,[status(thm)],[])).
% 2.00/1.59 tff(2103,plain,
% 2.00/1.59 ((hskp0 | (~ndr1_0) | c3_1(a906) | (~c1_1(a906)) | (~c0_1(a906)) | c3_1(a903) | c2_1(a903) | (~c0_1(a903))) <=> (hskp0 | c3_1(a906) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c0_1(a903)) | (~c1_1(a906)) | (~c0_1(a906)))),
% 2.00/1.59 inference(rewrite,[status(thm)],[])).
% 2.00/1.59 tff(2104,plain,
% 2.00/1.59 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a906) | (~c1_1(a906)) | (~c0_1(a906)) | c3_1(a903) | c2_1(a903) | (~c0_1(a903)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp0 | c3_1(a906) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c0_1(a903)) | (~c1_1(a906)) | (~c0_1(a906))))),
% 2.00/1.59 inference(monotonicity,[status(thm)],[2103])).
% 2.00/1.59 tff(2105,plain,
% 2.00/1.59 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a906) | (~c1_1(a906)) | (~c0_1(a906)) | c3_1(a903) | c2_1(a903) | (~c0_1(a903)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp0 | c3_1(a906) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c0_1(a903)) | (~c1_1(a906)) | (~c0_1(a906)))),
% 2.00/1.59 inference(transitivity,[status(thm)],[2104, 2102])).
% 2.00/1.59 tff(2106,plain,
% 2.00/1.59 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a906) | (~c1_1(a906)) | (~c0_1(a906)) | c3_1(a903) | c2_1(a903) | (~c0_1(a903)))),
% 2.00/1.59 inference(quant_inst,[status(thm)],[])).
% 2.00/1.59 tff(2107,plain,
% 2.00/1.59 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp0 | c3_1(a906) | c2_1(a903) | c3_1(a903) | (~ndr1_0) | (~c0_1(a903)) | (~c1_1(a906)) | (~c0_1(a906))),
% 2.00/1.59 inference(modus_ponens,[status(thm)],[2106, 2105])).
% 2.00/1.59 tff(2108,plain,
% 2.00/1.59 (hskp0 | c2_1(a903) | (~c0_1(a903)) | (~c1_1(a906))),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[2107, 124, 323, 325, 896, 933])).
% 2.00/1.59 tff(2109,plain,
% 2.00/1.59 (hskp0),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[2108, 2101, 884, 2099])).
% 2.00/1.59 tff(2110,plain,
% 2.00/1.59 (~c3_1(a901)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[651, 2109])).
% 2.00/1.59 tff(2111,plain,
% 2.00/1.59 (~c1_1(a901)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[657, 2109])).
% 2.00/1.59 tff(2112,plain,
% 2.00/1.59 (~c0_1(a901)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[663, 2109])).
% 2.00/1.59 tff(2113,plain,
% 2.00/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a912) | c2_1(a903) | c3_1(a903) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c0_1(a903)) | (~c2_1(a912)) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a912) | c2_1(a903) | c3_1(a903) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c0_1(a903)) | (~c2_1(a912)) | (~c1_1(a912)))),
% 2.00/1.59 inference(rewrite,[status(thm)],[])).
% 2.00/1.59 tff(2114,plain,
% 2.00/1.59 (((~ndr1_0) | c2_1(a903) | c3_1(a903) | (~c0_1(a903)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a901) | c1_1(a901) | c0_1(a901)) <=> (c0_1(a912) | c2_1(a903) | c3_1(a903) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c0_1(a903)) | (~c2_1(a912)) | (~c1_1(a912)))),
% 2.00/1.59 inference(rewrite,[status(thm)],[])).
% 2.00/1.59 tff(2115,plain,
% 2.00/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a903) | c3_1(a903) | (~c0_1(a903)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a901) | c1_1(a901) | c0_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a912) | c2_1(a903) | c3_1(a903) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c0_1(a903)) | (~c2_1(a912)) | (~c1_1(a912))))),
% 2.00/1.59 inference(monotonicity,[status(thm)],[2114])).
% 2.00/1.59 tff(2116,plain,
% 2.00/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a903) | c3_1(a903) | (~c0_1(a903)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a901) | c1_1(a901) | c0_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a912) | c2_1(a903) | c3_1(a903) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c0_1(a903)) | (~c2_1(a912)) | (~c1_1(a912)))),
% 2.00/1.59 inference(transitivity,[status(thm)],[2115, 2113])).
% 2.00/1.59 tff(2117,plain,
% 2.00/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a903) | c3_1(a903) | (~c0_1(a903)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a901) | c1_1(a901) | c0_1(a901))),
% 2.00/1.59 inference(quant_inst,[status(thm)],[])).
% 2.00/1.59 tff(2118,plain,
% 2.00/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a912) | c2_1(a903) | c3_1(a903) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c0_1(a903)) | (~c2_1(a912)) | (~c1_1(a912))),
% 2.00/1.59 inference(modus_ponens,[status(thm)],[2117, 2116])).
% 2.00/1.59 tff(2119,plain,
% 2.00/1.59 ($false),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[2118, 124, 1033, 1032, 2101, 665, 884, 896, 2112, 2111, 2110, 322])).
% 2.00/1.59 tff(2120,plain,((~hskp12) | c0_1(a912) | c2_1(a903) | c3_1(a903) | (~c0_1(a906)) | c3_1(a906) | (~c2_1(a906)) | hskp21), inference(lemma,lemma(discharge,[]))).
% 2.00/1.59 tff(2121,plain,
% 2.00/1.59 ($false),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[2120, 2098, 2097, 1992, 1990, 312, 301, 295, 198])).
% 2.00/1.59 tff(2122,plain,((~hskp5) | hskp21), inference(lemma,lemma(discharge,[]))).
% 2.00/1.59 tff(2123,plain,
% 2.00/1.59 (~hskp5),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[2122, 198])).
% 2.00/1.59 tff(2124,plain,
% 2.00/1.59 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp5 | (~ndr1_0) | c2_1(a916) | (~c3_1(a916)) | (~c0_1(a916)))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp7 | hskp5 | (~ndr1_0) | c2_1(a916) | (~c3_1(a916)) | (~c0_1(a916)))),
% 2.00/1.59 inference(rewrite,[status(thm)],[])).
% 2.00/1.59 tff(2125,plain,
% 2.00/1.59 ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp5 | (~ndr1_0) | c2_1(a916) | (~c3_1(a916)) | (~c0_1(a916)))),
% 2.00/1.59 inference(quant_inst,[status(thm)],[])).
% 2.00/1.59 tff(2126,plain,
% 2.00/1.59 ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp7 | hskp5 | (~ndr1_0) | c2_1(a916) | (~c3_1(a916)) | (~c0_1(a916))),
% 2.00/1.59 inference(modus_ponens,[status(thm)],[2125, 2124])).
% 2.00/1.59 tff(2127,plain,
% 2.00/1.59 (hskp7 | c2_1(a916)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[2126, 124, 43, 488, 486, 63])).
% 2.00/1.59 tff(2128,plain,
% 2.00/1.59 (c2_1(a916)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[2127, 21])).
% 2.00/1.59 tff(2129,plain,
% 2.00/1.59 (hskp11 | (~c2_1(a916))),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[389, 124, 32, 487, 486, 53])).
% 2.00/1.59 tff(2130,plain,
% 2.00/1.59 (hskp11),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[2129, 2128])).
% 2.00/1.59 tff(2131,plain,
% 2.00/1.59 (~c2_1(a914)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[69, 2130])).
% 2.00/1.59 tff(2132,plain,
% 2.00/1.59 (c3_1(a914)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[80, 2130])).
% 2.00/1.59 tff(2133,plain,
% 2.00/1.59 (c0_1(a914)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[91, 2130])).
% 2.00/1.59 tff(2134,plain,
% 2.00/1.59 ($false),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[130, 124, 21, 43, 2133, 2132, 2131, 63])).
% 2.00/1.59 tff(2135,plain,(hskp7 | hskp5 | hskp12 | (~c1_1(a916)) | (~c3_1(a916)) | (~c0_1(a916))), inference(lemma,lemma(discharge,[]))).
% 2.00/1.59 tff(2136,plain,
% 2.00/1.59 (hskp7),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[2135, 32, 2123, 283, 272, 261])).
% 2.00/1.59 tff(2137,plain,
% 2.00/1.59 (~c3_1(a908)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[467, 2136])).
% 2.00/1.59 tff(2138,plain,
% 2.00/1.59 (~c2_1(a908)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[473, 2136])).
% 2.00/1.59 tff(2139,plain,
% 2.00/1.59 (hskp26),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[122, 2123, 198])).
% 2.00/1.59 tff(2140,plain,
% 2.00/1.59 (((~hskp26) | (~c3_1(a979))) <=> ((~hskp26) | (~c3_1(a979)))),
% 2.00/1.59 inference(rewrite,[status(thm)],[])).
% 2.00/1.59 tff(2141,plain,
% 2.00/1.59 (((~c3_1(a979)) | (~hskp26)) <=> ((~hskp26) | (~c3_1(a979)))),
% 2.00/1.59 inference(rewrite,[status(thm)],[])).
% 2.00/1.59 tff(2142,axiom,((~c3_1(a979)) | (~hskp26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause82')).
% 2.00/1.59 tff(2143,plain,
% 2.00/1.59 ((~hskp26) | (~c3_1(a979))),
% 2.00/1.59 inference(modus_ponens,[status(thm)],[2142, 2141])).
% 2.00/1.59 tff(2144,plain,
% 2.00/1.59 ((~hskp26) | (~c3_1(a979))),
% 2.00/1.59 inference(modus_ponens,[status(thm)],[2143, 2140])).
% 2.00/1.59 tff(2145,plain,
% 2.00/1.59 (~c3_1(a979)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[2144, 2139])).
% 2.00/1.59 tff(2146,plain,
% 2.00/1.59 (c1_1(a908)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[484, 2136])).
% 2.00/1.59 tff(2147,plain,
% 2.00/1.59 (((~hskp26) | c0_1(a979)) <=> ((~hskp26) | c0_1(a979))),
% 2.00/1.59 inference(rewrite,[status(thm)],[])).
% 2.00/1.59 tff(2148,axiom,((~hskp26) | c0_1(a979)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause47')).
% 2.00/1.59 tff(2149,plain,
% 2.00/1.59 ((~hskp26) | c0_1(a979)),
% 2.00/1.59 inference(modus_ponens,[status(thm)],[2148, 2147])).
% 2.00/1.59 tff(2150,plain,
% 2.00/1.59 ((~hskp26) | c0_1(a979)),
% 2.00/1.59 inference(modus_ponens,[status(thm)],[2149, 2147])).
% 2.00/1.59 tff(2151,plain,
% 2.00/1.59 ((~hskp26) | c0_1(a979)),
% 2.00/1.59 inference(modus_ponens,[status(thm)],[2150, 2147])).
% 2.00/1.59 tff(2152,plain,
% 2.00/1.59 ((~hskp26) | c0_1(a979)),
% 2.00/1.59 inference(modus_ponens,[status(thm)],[2151, 2147])).
% 2.00/1.59 tff(2153,plain,
% 2.00/1.59 ((~hskp26) | c0_1(a979)),
% 2.00/1.59 inference(modus_ponens,[status(thm)],[2152, 2147])).
% 2.00/1.59 tff(2154,plain,
% 2.00/1.59 ((~hskp26) | c0_1(a979)),
% 2.00/1.59 inference(modus_ponens,[status(thm)],[2153, 2147])).
% 2.00/1.59 tff(2155,plain,
% 2.00/1.59 ((~hskp26) | c0_1(a979)),
% 2.00/1.59 inference(modus_ponens,[status(thm)],[2154, 2147])).
% 2.00/1.59 tff(2156,plain,
% 2.00/1.59 ((~hskp26) | c0_1(a979)),
% 2.00/1.59 inference(modus_ponens,[status(thm)],[2155, 2147])).
% 2.00/1.59 tff(2157,plain,
% 2.00/1.59 (c0_1(a979)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[2156, 2139])).
% 2.00/1.59 tff(2158,plain,
% 2.00/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c3_1(a979) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)) | (~c2_1(a979)) | (~c0_1(a979)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a979) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)) | (~c2_1(a979)) | (~c0_1(a979)))),
% 2.00/1.59 inference(rewrite,[status(thm)],[])).
% 2.00/1.59 tff(2159,plain,
% 2.00/1.59 (((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a979) | (~c2_1(a979)) | (~c0_1(a979)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908))) <=> (c3_1(a979) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)) | (~c2_1(a979)) | (~c0_1(a979)))),
% 2.00/1.59 inference(rewrite,[status(thm)],[])).
% 2.00/1.59 tff(2160,plain,
% 2.00/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a979) | (~c2_1(a979)) | (~c0_1(a979)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c3_1(a979) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)) | (~c2_1(a979)) | (~c0_1(a979))))),
% 2.00/1.59 inference(monotonicity,[status(thm)],[2159])).
% 2.00/1.59 tff(2161,plain,
% 2.00/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a979) | (~c2_1(a979)) | (~c0_1(a979)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a979) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)) | (~c2_1(a979)) | (~c0_1(a979)))),
% 2.00/1.59 inference(transitivity,[status(thm)],[2160, 2158])).
% 2.00/1.59 tff(2162,plain,
% 2.00/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a979) | (~c2_1(a979)) | (~c0_1(a979)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))),
% 2.00/1.59 inference(quant_inst,[status(thm)],[])).
% 2.00/1.59 tff(2163,plain,
% 2.00/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a979) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)) | (~c2_1(a979)) | (~c0_1(a979))),
% 2.00/1.59 inference(modus_ponens,[status(thm)],[2162, 2161])).
% 2.00/1.59 tff(2164,plain,
% 2.00/1.59 (~c2_1(a979)),
% 2.00/1.59 inference(unit_resolution,[status(thm)],[2163, 124, 261, 283, 272, 2157, 2146, 2145, 2138, 2137, 31])).
% 2.00/1.59 tff(2165,assumption,(~c2_1(a979)), introduced(assumption)).
% 2.00/1.59 tff(2166,plain,
% 2.00/1.59 (((~hskp26) | c1_1(a979)) <=> ((~hskp26) | c1_1(a979))),
% 2.00/1.59 inference(rewrite,[status(thm)],[])).
% 2.00/1.59 tff(2167,axiom,((~hskp26) | c1_1(a979)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause48')).
% 2.00/1.60 tff(2168,plain,
% 2.00/1.60 ((~hskp26) | c1_1(a979)),
% 2.00/1.60 inference(modus_ponens,[status(thm)],[2167, 2166])).
% 2.00/1.60 tff(2169,plain,
% 2.00/1.60 ((~hskp26) | c1_1(a979)),
% 2.00/1.60 inference(modus_ponens,[status(thm)],[2168, 2166])).
% 2.00/1.60 tff(2170,plain,
% 2.00/1.60 ((~hskp26) | c1_1(a979)),
% 2.00/1.60 inference(modus_ponens,[status(thm)],[2169, 2166])).
% 2.00/1.60 tff(2171,plain,
% 2.00/1.60 ((~hskp26) | c1_1(a979)),
% 2.00/1.60 inference(modus_ponens,[status(thm)],[2170, 2166])).
% 2.00/1.60 tff(2172,plain,
% 2.00/1.60 ((~hskp26) | c1_1(a979)),
% 2.00/1.60 inference(modus_ponens,[status(thm)],[2171, 2166])).
% 2.00/1.60 tff(2173,plain,
% 2.00/1.60 ((~hskp26) | c1_1(a979)),
% 2.00/1.60 inference(modus_ponens,[status(thm)],[2172, 2166])).
% 2.00/1.60 tff(2174,plain,
% 2.00/1.60 ((~hskp26) | c1_1(a979)),
% 2.00/1.60 inference(modus_ponens,[status(thm)],[2173, 2166])).
% 2.00/1.60 tff(2175,plain,
% 2.00/1.60 ((~hskp26) | c1_1(a979)),
% 2.00/1.60 inference(modus_ponens,[status(thm)],[2174, 2166])).
% 2.00/1.60 tff(2176,plain,
% 2.00/1.60 (c1_1(a979)),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[2175, 2139])).
% 2.00/1.60 tff(2177,plain,
% 2.00/1.60 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (c3_1(a979) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c1_1(a914)) | c2_1(a979) | (~c1_1(a979)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | c3_1(a979) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c1_1(a914)) | c2_1(a979) | (~c1_1(a979)))),
% 2.00/1.60 inference(rewrite,[status(thm)],[])).
% 2.00/1.60 tff(2178,plain,
% 2.00/1.60 (((~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)) | c3_1(a979) | c2_1(a979) | (~c1_1(a979))) <=> (c3_1(a979) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c1_1(a914)) | c2_1(a979) | (~c1_1(a979)))),
% 2.00/1.60 inference(rewrite,[status(thm)],[])).
% 2.00/1.60 tff(2179,plain,
% 2.00/1.60 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | ((~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)) | c3_1(a979) | c2_1(a979) | (~c1_1(a979)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (c3_1(a979) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c1_1(a914)) | c2_1(a979) | (~c1_1(a979))))),
% 2.00/1.60 inference(monotonicity,[status(thm)],[2178])).
% 2.00/1.60 tff(2180,plain,
% 2.00/1.60 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | ((~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)) | c3_1(a979) | c2_1(a979) | (~c1_1(a979)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | c3_1(a979) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c1_1(a914)) | c2_1(a979) | (~c1_1(a979)))),
% 2.00/1.60 inference(transitivity,[status(thm)],[2179, 2177])).
% 2.00/1.60 tff(2181,plain,
% 2.00/1.60 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | ((~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)) | c3_1(a979) | c2_1(a979) | (~c1_1(a979)))),
% 2.00/1.60 inference(quant_inst,[status(thm)],[])).
% 2.00/1.60 tff(2182,plain,
% 2.00/1.60 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | c3_1(a979) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c1_1(a914)) | c2_1(a979) | (~c1_1(a979))),
% 2.00/1.60 inference(modus_ponens,[status(thm)],[2181, 2180])).
% 2.00/1.60 tff(2183,plain,
% 2.00/1.60 (~c1_1(a914)),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[2182, 124, 2176, 81, 2145, 70, 10, 2165])).
% 2.00/1.60 tff(2184,assumption,(c1_1(a908)), introduced(assumption)).
% 2.00/1.60 tff(2185,plain,
% 2.00/1.60 ($false),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[1318, 124, 198, 92, 81, 2184, 1153, 1154, 197, 2183])).
% 2.00/1.60 tff(2186,plain,((~hskp11) | hskp21 | (~c1_1(a908)) | c2_1(a908) | c3_1(a908) | c2_1(a979)), inference(lemma,lemma(discharge,[]))).
% 2.00/1.60 tff(2187,plain,
% 2.00/1.60 (~hskp11),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[2186, 2146, 198, 2138, 2137, 2164])).
% 2.00/1.60 tff(2188,plain,
% 2.00/1.60 (~c2_1(a916)),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[390, 2187])).
% 2.00/1.60 tff(2189,plain,
% 2.00/1.60 (((~![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp25 | hskp21 | (~ndr1_0) | c2_1(a916) | (~c3_1(a916)) | (~c1_1(a916)))) <=> ((~![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp25 | hskp21 | (~ndr1_0) | c2_1(a916) | (~c3_1(a916)) | (~c1_1(a916)))),
% 2.00/1.60 inference(rewrite,[status(thm)],[])).
% 2.00/1.60 tff(2190,plain,
% 2.00/1.60 ((~![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp25 | hskp21 | (~ndr1_0) | c2_1(a916) | (~c3_1(a916)) | (~c1_1(a916)))),
% 2.00/1.60 inference(quant_inst,[status(thm)],[])).
% 2.00/1.60 tff(2191,plain,
% 2.00/1.60 ((~![U: $i] : (hskp25 | hskp21 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp25 | hskp21 | (~ndr1_0) | c2_1(a916) | (~c3_1(a916)) | (~c1_1(a916))),
% 2.00/1.60 inference(modus_ponens,[status(thm)],[2190, 2189])).
% 2.00/1.60 tff(2192,plain,
% 2.00/1.60 (hskp25 | c2_1(a916)),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[2191, 124, 198, 283, 272, 1883])).
% 2.00/1.60 tff(2193,plain,
% 2.00/1.60 (hskp25),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[2192, 2188])).
% 2.00/1.60 tff(2194,plain,
% 2.00/1.60 (~c1_1(a960)),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[1896, 2193])).
% 2.00/1.60 tff(2195,plain,
% 2.00/1.60 (c3_1(a960)),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[1907, 2193])).
% 2.00/1.60 tff(2196,plain,
% 2.00/1.60 (c0_1(a960)),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[1918, 2193])).
% 2.00/1.60 tff(2197,plain,
% 2.00/1.60 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | c1_1(a960) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c0_1(a960)) | (~c3_1(a960)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c1_1(a960) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c0_1(a960)) | (~c3_1(a960)))),
% 2.00/1.60 inference(rewrite,[status(thm)],[])).
% 2.00/1.60 tff(2198,plain,
% 2.00/1.60 ((hskp21 | (~ndr1_0) | c2_1(a908) | c3_1(a908) | (~c1_1(a908)) | c1_1(a960) | (~c0_1(a960)) | (~c3_1(a960))) <=> (hskp21 | c1_1(a960) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c0_1(a960)) | (~c3_1(a960)))),
% 2.00/1.60 inference(rewrite,[status(thm)],[])).
% 2.00/1.60 tff(2199,plain,
% 2.00/1.60 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a908) | c3_1(a908) | (~c1_1(a908)) | c1_1(a960) | (~c0_1(a960)) | (~c3_1(a960)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | c1_1(a960) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c0_1(a960)) | (~c3_1(a960))))),
% 2.00/1.60 inference(monotonicity,[status(thm)],[2198])).
% 2.00/1.60 tff(2200,plain,
% 2.00/1.60 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a908) | c3_1(a908) | (~c1_1(a908)) | c1_1(a960) | (~c0_1(a960)) | (~c3_1(a960)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c1_1(a960) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c0_1(a960)) | (~c3_1(a960)))),
% 2.00/1.60 inference(transitivity,[status(thm)],[2199, 2197])).
% 2.00/1.60 tff(2201,plain,
% 2.00/1.60 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c2_1(a908) | c3_1(a908) | (~c1_1(a908)) | c1_1(a960) | (~c0_1(a960)) | (~c3_1(a960)))),
% 2.00/1.60 inference(quant_inst,[status(thm)],[])).
% 2.00/1.60 tff(2202,plain,
% 2.00/1.60 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp21 | c1_1(a960) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c0_1(a960)) | (~c3_1(a960))),
% 2.00/1.60 inference(modus_ponens,[status(thm)],[2201, 2200])).
% 2.00/1.60 tff(2203,plain,
% 2.00/1.60 ($false),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[2202, 124, 198, 2196, 2195, 2146, 2194, 2138, 2137, 197])).
% 2.00/1.60 tff(2204,plain,(hskp12 | hskp21), inference(lemma,lemma(discharge,[]))).
% 2.00/1.60 tff(2205,plain,
% 2.00/1.60 (hskp12),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[2204, 198])).
% 2.00/1.60 tff(2206,plain,
% 2.00/1.60 (hskp10),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[377, 2205, 198])).
% 2.00/1.60 tff(2207,plain,
% 2.00/1.60 (~c0_1(a912)),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[627, 2206])).
% 2.00/1.60 tff(2208,plain,
% 2.00/1.60 (hskp6),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[1045, 2207, 2205, 198])).
% 2.00/1.60 tff(2209,plain,
% 2.00/1.60 (~c2_1(a907)),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[407, 2208])).
% 2.00/1.60 tff(2210,plain,
% 2.00/1.60 (~c2_1(a917)),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[332, 2205])).
% 2.00/1.60 tff(2211,plain,
% 2.00/1.60 (c3_1(a917)),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[354, 2205])).
% 2.00/1.60 tff(2212,plain,
% 2.00/1.60 (c1_1(a917)),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[343, 2205])).
% 2.00/1.60 tff(2213,plain,
% 2.00/1.60 (hskp25),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[2003, 124, 198, 2212, 2211, 2210, 1883])).
% 2.00/1.60 tff(2214,plain,
% 2.00/1.60 (~c1_1(a960)),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[1896, 2213])).
% 2.00/1.60 tff(2215,plain,
% 2.00/1.60 (c1_1(a907)),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[418, 2208])).
% 2.00/1.60 tff(2216,plain,
% 2.00/1.60 (c3_1(a960)),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[1907, 2213])).
% 2.00/1.60 tff(2217,plain,
% 2.00/1.60 (c0_1(a960)),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[1918, 2213])).
% 2.00/1.60 tff(2218,plain,
% 2.00/1.60 (c3_1(a907)),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[2014, 124, 198, 2217, 2216, 2215, 2214, 2209, 197])).
% 2.00/1.60 tff(2219,plain,
% 2.00/1.60 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (c3_1(a979) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917)) | c2_1(a979) | (~c1_1(a979)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | c3_1(a979) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917)) | c2_1(a979) | (~c1_1(a979)))),
% 2.00/1.60 inference(rewrite,[status(thm)],[])).
% 2.00/1.60 tff(2220,plain,
% 2.00/1.60 (((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a979) | c2_1(a979) | (~c1_1(a979))) <=> (c3_1(a979) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917)) | c2_1(a979) | (~c1_1(a979)))),
% 2.00/1.60 inference(rewrite,[status(thm)],[])).
% 2.00/1.60 tff(2221,plain,
% 2.00/1.60 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a979) | c2_1(a979) | (~c1_1(a979)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (c3_1(a979) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917)) | c2_1(a979) | (~c1_1(a979))))),
% 2.00/1.60 inference(monotonicity,[status(thm)],[2220])).
% 2.00/1.60 tff(2222,plain,
% 2.00/1.60 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a979) | c2_1(a979) | (~c1_1(a979)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | c3_1(a979) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917)) | c2_1(a979) | (~c1_1(a979)))),
% 2.00/1.60 inference(transitivity,[status(thm)],[2221, 2219])).
% 2.00/1.60 tff(2223,plain,
% 2.00/1.60 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a979) | c2_1(a979) | (~c1_1(a979)))),
% 2.00/1.60 inference(quant_inst,[status(thm)],[])).
% 2.00/1.60 tff(2224,plain,
% 2.00/1.60 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | c3_1(a979) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917)) | c2_1(a979) | (~c1_1(a979))),
% 2.00/1.60 inference(modus_ponens,[status(thm)],[2223, 2222])).
% 2.00/1.60 tff(2225,plain,
% 2.00/1.60 (c2_1(a979)),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[2224, 124, 2176, 2212, 2211, 2145, 2210, 10])).
% 2.00/1.60 tff(2226,plain,
% 2.00/1.60 (c0_1(a907)),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[725, 2208])).
% 2.00/1.60 tff(2227,plain,
% 2.00/1.60 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp5 | c2_1(a907) | (~ndr1_0) | (~c0_1(a907)) | (~c3_1(a907)))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp7 | hskp5 | c2_1(a907) | (~ndr1_0) | (~c0_1(a907)) | (~c3_1(a907)))),
% 2.00/1.60 inference(rewrite,[status(thm)],[])).
% 2.00/1.60 tff(2228,plain,
% 2.00/1.60 ((hskp7 | hskp5 | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c0_1(a907))) <=> (hskp7 | hskp5 | c2_1(a907) | (~ndr1_0) | (~c0_1(a907)) | (~c3_1(a907)))),
% 2.00/1.60 inference(rewrite,[status(thm)],[])).
% 2.00/1.60 tff(2229,plain,
% 2.00/1.60 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp5 | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c0_1(a907)))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp5 | c2_1(a907) | (~ndr1_0) | (~c0_1(a907)) | (~c3_1(a907))))),
% 2.00/1.60 inference(monotonicity,[status(thm)],[2228])).
% 2.00/1.60 tff(2230,plain,
% 2.00/1.60 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp5 | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c0_1(a907)))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp7 | hskp5 | c2_1(a907) | (~ndr1_0) | (~c0_1(a907)) | (~c3_1(a907)))),
% 2.00/1.60 inference(transitivity,[status(thm)],[2229, 2227])).
% 2.00/1.60 tff(2231,plain,
% 2.00/1.60 ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp5 | (~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c0_1(a907)))),
% 2.00/1.60 inference(quant_inst,[status(thm)],[])).
% 2.00/1.60 tff(2232,plain,
% 2.00/1.60 ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp7 | hskp5 | c2_1(a907) | (~ndr1_0) | (~c0_1(a907)) | (~c3_1(a907))),
% 2.00/1.60 inference(modus_ponens,[status(thm)],[2231, 2230])).
% 2.00/1.60 tff(2233,plain,
% 2.00/1.60 (hskp7 | (~c3_1(a907))),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[2232, 124, 2123, 2226, 2209, 63])).
% 2.00/1.60 tff(2234,plain,
% 2.00/1.60 (hskp7),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[2233, 2218])).
% 2.00/1.60 tff(2235,plain,
% 2.00/1.60 (~c3_1(a908)),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[467, 2234])).
% 2.00/1.60 tff(2236,plain,
% 2.00/1.60 (~c2_1(a908)),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[473, 2234])).
% 2.00/1.60 tff(2237,plain,
% 2.00/1.60 (c1_1(a908)),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[484, 2234])).
% 2.00/1.60 tff(2238,plain,
% 2.00/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c3_1(a979) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a907)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c1_1(a908)) | (~c2_1(a979)) | (~c0_1(a979)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a979) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a907)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c1_1(a908)) | (~c2_1(a979)) | (~c0_1(a979)))),
% 2.00/1.60 inference(rewrite,[status(thm)],[])).
% 2.00/1.60 tff(2239,plain,
% 2.00/1.60 (((~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c0_1(a907)) | c3_1(a979) | (~c2_1(a979)) | (~c0_1(a979)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908))) <=> (c3_1(a979) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a907)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c1_1(a908)) | (~c2_1(a979)) | (~c0_1(a979)))),
% 2.00/1.60 inference(rewrite,[status(thm)],[])).
% 2.00/1.60 tff(2240,plain,
% 2.00/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c0_1(a907)) | c3_1(a979) | (~c2_1(a979)) | (~c0_1(a979)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c3_1(a979) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a907)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c1_1(a908)) | (~c2_1(a979)) | (~c0_1(a979))))),
% 2.00/1.60 inference(monotonicity,[status(thm)],[2239])).
% 2.00/1.60 tff(2241,plain,
% 2.00/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c0_1(a907)) | c3_1(a979) | (~c2_1(a979)) | (~c0_1(a979)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a979) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a907)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c1_1(a908)) | (~c2_1(a979)) | (~c0_1(a979)))),
% 2.00/1.60 inference(transitivity,[status(thm)],[2240, 2238])).
% 2.00/1.60 tff(2242,plain,
% 2.00/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a907)) | (~c1_1(a907)) | (~c0_1(a907)) | c3_1(a979) | (~c2_1(a979)) | (~c0_1(a979)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))),
% 2.00/1.60 inference(quant_inst,[status(thm)],[])).
% 2.00/1.60 tff(2243,plain,
% 2.00/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a979) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c0_1(a907)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c1_1(a908)) | (~c2_1(a979)) | (~c0_1(a979))),
% 2.00/1.60 inference(modus_ponens,[status(thm)],[2242, 2241])).
% 2.00/1.60 tff(2244,plain,
% 2.00/1.60 ($false),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[2243, 124, 2157, 2237, 2226, 2215, 2145, 2236, 2235, 31, 2225, 2218])).
% 2.00/1.60 tff(2245,plain,(hskp21), inference(lemma,lemma(discharge,[]))).
% 2.00/1.60 tff(2246,plain,
% 2.00/1.60 (((~hskp21) | (~c3_1(a946))) <=> ((~hskp21) | (~c3_1(a946)))),
% 2.00/1.60 inference(rewrite,[status(thm)],[])).
% 2.00/1.60 tff(2247,plain,
% 2.00/1.60 (((~c3_1(a946)) | (~hskp21)) <=> ((~hskp21) | (~c3_1(a946)))),
% 2.00/1.60 inference(rewrite,[status(thm)],[])).
% 2.00/1.60 tff(2248,axiom,((~c3_1(a946)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause91')).
% 2.00/1.60 tff(2249,plain,
% 2.00/1.60 ((~hskp21) | (~c3_1(a946))),
% 2.00/1.60 inference(modus_ponens,[status(thm)],[2248, 2247])).
% 2.00/1.60 tff(2250,plain,
% 2.00/1.60 ((~hskp21) | (~c3_1(a946))),
% 2.00/1.60 inference(modus_ponens,[status(thm)],[2249, 2246])).
% 2.00/1.60 tff(2251,plain,
% 2.00/1.60 (~c3_1(a946)),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[2250, 2245])).
% 2.00/1.60 tff(2252,plain,
% 2.00/1.60 (((~hskp21) | (~c2_1(a946))) <=> ((~hskp21) | (~c2_1(a946)))),
% 2.00/1.60 inference(rewrite,[status(thm)],[])).
% 2.00/1.60 tff(2253,plain,
% 2.00/1.60 (((~c2_1(a946)) | (~hskp21)) <=> ((~hskp21) | (~c2_1(a946)))),
% 2.00/1.60 inference(rewrite,[status(thm)],[])).
% 2.00/1.60 tff(2254,axiom,((~c2_1(a946)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause90')).
% 2.00/1.60 tff(2255,plain,
% 2.00/1.60 ((~hskp21) | (~c2_1(a946))),
% 2.00/1.60 inference(modus_ponens,[status(thm)],[2254, 2253])).
% 2.00/1.60 tff(2256,plain,
% 2.00/1.60 ((~hskp21) | (~c2_1(a946))),
% 2.00/1.60 inference(modus_ponens,[status(thm)],[2255, 2252])).
% 2.00/1.60 tff(2257,plain,
% 2.00/1.60 (~c2_1(a946)),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[2256, 2245])).
% 2.00/1.60 tff(2258,plain,
% 2.00/1.60 (((~hskp21) | (~c0_1(a946))) <=> ((~hskp21) | (~c0_1(a946)))),
% 2.00/1.60 inference(rewrite,[status(thm)],[])).
% 2.00/1.60 tff(2259,plain,
% 2.00/1.60 (((~c0_1(a946)) | (~hskp21)) <=> ((~hskp21) | (~c0_1(a946)))),
% 2.00/1.60 inference(rewrite,[status(thm)],[])).
% 2.00/1.60 tff(2260,axiom,((~c0_1(a946)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause89')).
% 2.00/1.60 tff(2261,plain,
% 2.00/1.60 ((~hskp21) | (~c0_1(a946))),
% 2.00/1.60 inference(modus_ponens,[status(thm)],[2260, 2259])).
% 2.00/1.60 tff(2262,plain,
% 2.00/1.60 ((~hskp21) | (~c0_1(a946))),
% 2.00/1.60 inference(modus_ponens,[status(thm)],[2261, 2258])).
% 2.00/1.60 tff(2263,plain,
% 2.00/1.60 (~c0_1(a946)),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[2262, 2245])).
% 2.00/1.60 tff(2264,plain,
% 2.00/1.60 (((~![U: $i] : (hskp27 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp27 | hskp10 | c0_1(a946) | c2_1(a946) | c3_1(a946) | (~ndr1_0))) <=> ((~![U: $i] : (hskp27 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp27 | hskp10 | c0_1(a946) | c2_1(a946) | c3_1(a946) | (~ndr1_0))),
% 2.00/1.60 inference(rewrite,[status(thm)],[])).
% 2.00/1.60 tff(2265,plain,
% 2.00/1.60 ((hskp27 | hskp10 | (~ndr1_0) | c2_1(a946) | c0_1(a946) | c3_1(a946)) <=> (hskp27 | hskp10 | c0_1(a946) | c2_1(a946) | c3_1(a946) | (~ndr1_0))),
% 2.00/1.60 inference(rewrite,[status(thm)],[])).
% 2.00/1.60 tff(2266,plain,
% 2.00/1.60 (((~![U: $i] : (hskp27 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp27 | hskp10 | (~ndr1_0) | c2_1(a946) | c0_1(a946) | c3_1(a946))) <=> ((~![U: $i] : (hskp27 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp27 | hskp10 | c0_1(a946) | c2_1(a946) | c3_1(a946) | (~ndr1_0)))),
% 2.00/1.60 inference(monotonicity,[status(thm)],[2265])).
% 2.00/1.60 tff(2267,plain,
% 2.00/1.60 (((~![U: $i] : (hskp27 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp27 | hskp10 | (~ndr1_0) | c2_1(a946) | c0_1(a946) | c3_1(a946))) <=> ((~![U: $i] : (hskp27 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp27 | hskp10 | c0_1(a946) | c2_1(a946) | c3_1(a946) | (~ndr1_0))),
% 2.00/1.60 inference(transitivity,[status(thm)],[2266, 2264])).
% 2.00/1.60 tff(2268,plain,
% 2.00/1.60 ((~![U: $i] : (hskp27 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp27 | hskp10 | (~ndr1_0) | c2_1(a946) | c0_1(a946) | c3_1(a946))),
% 2.00/1.60 inference(quant_inst,[status(thm)],[])).
% 2.00/1.60 tff(2269,plain,
% 2.00/1.60 ((~![U: $i] : (hskp27 | hskp10 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp27 | hskp10 | c0_1(a946) | c2_1(a946) | c3_1(a946) | (~ndr1_0)),
% 2.00/1.60 inference(modus_ponens,[status(thm)],[2268, 2267])).
% 2.00/1.60 tff(2270,plain,
% 2.00/1.60 (hskp27 | hskp10),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[2269, 124, 2263, 2257, 2251, 187])).
% 2.00/1.60 tff(2271,plain,
% 2.00/1.60 (hskp10),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[2270, 177])).
% 2.00/1.60 tff(2272,plain,
% 2.00/1.60 (c2_1(a912)),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[676, 2271])).
% 2.00/1.60 tff(2273,plain,
% 2.00/1.60 (c1_1(a912)),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[687, 2271])).
% 2.00/1.60 tff(2274,plain,
% 2.00/1.60 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a912)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a912)))),
% 2.00/1.60 inference(rewrite,[status(thm)],[])).
% 2.00/1.60 tff(2275,plain,
% 2.00/1.60 ((hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a912)) | (~c3_1(a912)) | (~c1_1(a912))) <=> (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a912)))),
% 2.00/1.60 inference(rewrite,[status(thm)],[])).
% 2.00/1.60 tff(2276,plain,
% 2.00/1.60 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a912)) | (~c3_1(a912)) | (~c1_1(a912)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a912))))),
% 2.00/1.60 inference(monotonicity,[status(thm)],[2275])).
% 2.00/1.60 tff(2277,plain,
% 2.00/1.60 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a912)) | (~c3_1(a912)) | (~c1_1(a912)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a912)))),
% 2.00/1.60 inference(transitivity,[status(thm)],[2276, 2274])).
% 2.00/1.60 tff(2278,plain,
% 2.00/1.60 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a912)) | (~c3_1(a912)) | (~c1_1(a912)))),
% 2.00/1.60 inference(quant_inst,[status(thm)],[])).
% 2.00/1.60 tff(2279,plain,
% 2.00/1.60 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a912)) | (~c1_1(a912)) | (~c3_1(a912))),
% 2.00/1.60 inference(modus_ponens,[status(thm)],[2278, 2277])).
% 2.00/1.60 tff(2280,plain,
% 2.00/1.60 (~c3_1(a912)),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[2279, 124, 32, 133, 2273, 2272, 53])).
% 2.00/1.60 tff(2281,plain,
% 2.00/1.60 (~c0_1(a912)),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[627, 2271])).
% 2.00/1.60 tff(2282,plain,
% 2.00/1.60 (((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp28 | hskp12 | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | c3_1(a912))) <=> ((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp28 | hskp12 | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | c3_1(a912))),
% 2.00/1.60 inference(rewrite,[status(thm)],[])).
% 2.00/1.60 tff(2283,plain,
% 2.00/1.60 ((hskp28 | hskp12 | (~ndr1_0) | c0_1(a912) | c3_1(a912) | (~c2_1(a912))) <=> (hskp28 | hskp12 | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | c3_1(a912))),
% 2.00/1.60 inference(rewrite,[status(thm)],[])).
% 2.00/1.60 tff(2284,plain,
% 2.00/1.60 (((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp28 | hskp12 | (~ndr1_0) | c0_1(a912) | c3_1(a912) | (~c2_1(a912)))) <=> ((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp28 | hskp12 | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | c3_1(a912)))),
% 2.00/1.60 inference(monotonicity,[status(thm)],[2283])).
% 2.00/1.60 tff(2285,plain,
% 2.00/1.60 (((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp28 | hskp12 | (~ndr1_0) | c0_1(a912) | c3_1(a912) | (~c2_1(a912)))) <=> ((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp28 | hskp12 | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | c3_1(a912))),
% 2.00/1.60 inference(transitivity,[status(thm)],[2284, 2282])).
% 2.00/1.60 tff(2286,plain,
% 2.00/1.60 ((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp28 | hskp12 | (~ndr1_0) | c0_1(a912) | c3_1(a912) | (~c2_1(a912)))),
% 2.00/1.60 inference(quant_inst,[status(thm)],[])).
% 2.00/1.60 tff(2287,plain,
% 2.00/1.60 ((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp28 | hskp12 | c0_1(a912) | (~ndr1_0) | (~c2_1(a912)) | c3_1(a912)),
% 2.00/1.60 inference(modus_ponens,[status(thm)],[2286, 2285])).
% 2.00/1.60 tff(2288,plain,
% 2.00/1.60 (hskp28),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[2287, 124, 32, 2272, 2281, 208, 2280])).
% 2.00/1.60 tff(2289,plain,
% 2.00/1.60 (c0_1(a916)),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[260, 2288])).
% 2.00/1.60 tff(2290,plain,
% 2.00/1.60 (c1_1(a916)),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[282, 2288])).
% 2.00/1.60 tff(2291,plain,
% 2.00/1.60 (c3_1(a916)),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[271, 2288])).
% 2.00/1.60 tff(2292,plain,
% 2.00/1.60 ($false),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[2135, 2291, 2290, 32, 43, 21, 2289])).
% 2.00/1.60 tff(2293,plain,(hskp7 | hskp12 | hskp5), inference(lemma,lemma(discharge,[]))).
% 2.00/1.60 tff(2294,plain,
% 2.00/1.60 (hskp7),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[2293, 43, 32])).
% 2.00/1.60 tff(2295,plain,
% 2.00/1.60 (~c3_1(a908)),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[467, 2294])).
% 2.00/1.60 tff(2296,plain,
% 2.00/1.60 (~c2_1(a908)),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[473, 2294])).
% 2.00/1.60 tff(2297,plain,
% 2.00/1.60 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))))),
% 2.00/1.60 inference(bind,[status(th)],[])).
% 2.00/1.60 tff(2298,plain,
% 2.00/1.60 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 2.00/1.60 inference(quant_intro,[status(thm)],[2297])).
% 2.00/1.60 tff(2299,plain,
% 2.00/1.60 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 2.00/1.60 inference(rewrite,[status(thm)],[])).
% 2.00/1.60 tff(2300,plain,
% 2.00/1.60 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_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)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) | hskp16) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) | hskp16))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))))),
% 2.00/1.60 inference(bind,[status(th)],[])).
% 2.00/1.60 tff(2301,plain,
% 2.00/1.60 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 2.00/1.60 inference(quant_intro,[status(thm)],[2300])).
% 2.00/1.60 tff(2302,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) | hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause174')).
% 2.00/1.60 tff(2303,plain,
% 2.00/1.60 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 2.00/1.60 inference(modus_ponens,[status(thm)],[2302, 2301])).
% 2.00/1.60 tff(2304,plain,
% 2.00/1.60 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 2.00/1.60 inference(modus_ponens,[status(thm)],[2303, 2299])).
% 2.00/1.60 tff(2305,plain,(
% 2.00/1.60 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 2.00/1.60 inference(skolemize,[status(sab)],[2304])).
% 2.00/1.60 tff(2306,plain,
% 2.00/1.60 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 2.00/1.60 inference(modus_ponens,[status(thm)],[2305, 2298])).
% 2.00/1.60 tff(2307,plain,
% 2.00/1.60 (c1_1(a908)),
% 2.00/1.60 inference(unit_resolution,[status(thm)],[484, 2294])).
% 2.00/1.60 tff(2308,plain,
% 2.00/1.60 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp16 | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900)))),
% 2.00/1.60 inference(rewrite,[status(thm)],[])).
% 2.00/1.60 tff(2309,plain,
% 2.00/1.60 ((hskp16 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c1_1(a900)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908))) <=> (hskp16 | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900)))),
% 2.00/1.60 inference(rewrite,[status(thm)],[])).
% 2.00/1.60 tff(2310,plain,
% 2.00/1.60 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c1_1(a900)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900))))),
% 2.00/1.60 inference(monotonicity,[status(thm)],[2309])).
% 2.00/1.60 tff(2311,plain,
% 2.00/1.60 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c1_1(a900)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp16 | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900)))),
% 2.00/1.61 inference(transitivity,[status(thm)],[2310, 2308])).
% 2.00/1.61 tff(2312,plain,
% 2.00/1.61 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c1_1(a900)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))),
% 2.00/1.61 inference(quant_inst,[status(thm)],[])).
% 2.00/1.61 tff(2313,plain,
% 2.00/1.61 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp16 | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900))),
% 2.00/1.61 inference(modus_ponens,[status(thm)],[2312, 2311])).
% 2.00/1.61 tff(2314,plain,
% 2.00/1.61 (hskp16),
% 2.00/1.61 inference(unit_resolution,[status(thm)],[2313, 124, 167, 156, 145, 2307, 2296, 2295, 2306])).
% 2.00/1.61 tff(2315,plain,
% 2.00/1.61 (((~hskp16) | (~c3_1(a926))) <=> ((~hskp16) | (~c3_1(a926)))),
% 2.00/1.61 inference(rewrite,[status(thm)],[])).
% 2.00/1.61 tff(2316,plain,
% 2.00/1.61 (((~c3_1(a926)) | (~hskp16)) <=> ((~hskp16) | (~c3_1(a926)))),
% 2.00/1.61 inference(rewrite,[status(thm)],[])).
% 2.00/1.61 tff(2317,axiom,((~c3_1(a926)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause100')).
% 2.00/1.61 tff(2318,plain,
% 2.00/1.61 ((~hskp16) | (~c3_1(a926))),
% 2.00/1.61 inference(modus_ponens,[status(thm)],[2317, 2316])).
% 2.00/1.61 tff(2319,plain,
% 2.00/1.61 ((~hskp16) | (~c3_1(a926))),
% 2.00/1.61 inference(modus_ponens,[status(thm)],[2318, 2315])).
% 2.00/1.61 tff(2320,plain,
% 2.00/1.61 (~c3_1(a926)),
% 2.00/1.61 inference(unit_resolution,[status(thm)],[2319, 2314])).
% 2.00/1.61 tff(2321,plain,
% 2.00/1.61 (((~hskp16) | c2_1(a926)) <=> ((~hskp16) | c2_1(a926))),
% 2.00/1.61 inference(rewrite,[status(thm)],[])).
% 2.00/1.61 tff(2322,axiom,((~hskp16) | c2_1(a926)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause60')).
% 2.00/1.61 tff(2323,plain,
% 2.00/1.61 ((~hskp16) | c2_1(a926)),
% 2.00/1.61 inference(modus_ponens,[status(thm)],[2322, 2321])).
% 2.00/1.61 tff(2324,plain,
% 2.00/1.61 ((~hskp16) | c2_1(a926)),
% 2.00/1.61 inference(modus_ponens,[status(thm)],[2323, 2321])).
% 2.00/1.61 tff(2325,plain,
% 2.00/1.61 ((~hskp16) | c2_1(a926)),
% 2.00/1.61 inference(modus_ponens,[status(thm)],[2324, 2321])).
% 2.00/1.61 tff(2326,plain,
% 2.00/1.61 ((~hskp16) | c2_1(a926)),
% 2.00/1.61 inference(modus_ponens,[status(thm)],[2325, 2321])).
% 2.00/1.61 tff(2327,plain,
% 2.00/1.61 ((~hskp16) | c2_1(a926)),
% 2.00/1.61 inference(modus_ponens,[status(thm)],[2326, 2321])).
% 2.00/1.61 tff(2328,plain,
% 2.00/1.61 ((~hskp16) | c2_1(a926)),
% 2.00/1.61 inference(modus_ponens,[status(thm)],[2327, 2321])).
% 2.00/1.61 tff(2329,plain,
% 2.00/1.61 ((~hskp16) | c2_1(a926)),
% 2.00/1.61 inference(modus_ponens,[status(thm)],[2328, 2321])).
% 2.00/1.61 tff(2330,plain,
% 2.00/1.61 ((~hskp16) | c2_1(a926)),
% 2.00/1.61 inference(modus_ponens,[status(thm)],[2329, 2321])).
% 2.00/1.61 tff(2331,plain,
% 2.00/1.61 (c2_1(a926)),
% 2.00/1.61 inference(unit_resolution,[status(thm)],[2330, 2314])).
% 2.00/1.61 tff(2332,plain,
% 2.00/1.61 (hskp11),
% 2.00/1.61 inference(unit_resolution,[status(thm)],[176, 134, 32])).
% 2.00/1.61 tff(2333,plain,
% 2.00/1.61 (~c2_1(a914)),
% 2.00/1.61 inference(unit_resolution,[status(thm)],[69, 2332])).
% 2.00/1.61 tff(2334,plain,
% 2.00/1.61 (c3_1(a914)),
% 2.00/1.61 inference(unit_resolution,[status(thm)],[80, 2332])).
% 2.00/1.61 tff(2335,plain,
% 2.00/1.61 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (c2_1(a914) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a914)) | (~c1_1(a914)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | c2_1(a914) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a914)) | (~c1_1(a914)))),
% 2.00/1.61 inference(rewrite,[status(thm)],[])).
% 2.00/1.61 tff(2336,plain,
% 2.00/1.61 (((~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908))) <=> (c2_1(a914) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a914)) | (~c1_1(a914)))),
% 2.00/1.61 inference(rewrite,[status(thm)],[])).
% 2.00/1.61 tff(2337,plain,
% 2.00/1.61 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | ((~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (c2_1(a914) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a914)) | (~c1_1(a914))))),
% 2.00/1.61 inference(monotonicity,[status(thm)],[2336])).
% 2.00/1.61 tff(2338,plain,
% 2.00/1.61 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | ((~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | c2_1(a914) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a914)) | (~c1_1(a914)))),
% 2.00/1.61 inference(transitivity,[status(thm)],[2337, 2335])).
% 2.00/1.61 tff(2339,plain,
% 2.00/1.61 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | ((~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c1_1(a914)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))),
% 2.00/1.61 inference(quant_inst,[status(thm)],[])).
% 2.00/1.61 tff(2340,plain,
% 2.00/1.61 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | c2_1(a914) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c3_1(a914)) | (~c1_1(a914))),
% 2.00/1.61 inference(modus_ponens,[status(thm)],[2339, 2338])).
% 2.00/1.61 tff(2341,plain,
% 2.00/1.61 (~c1_1(a914)),
% 2.00/1.61 inference(unit_resolution,[status(thm)],[2340, 124, 2334, 2307, 2333, 2296, 2295, 10])).
% 2.00/1.61 tff(2342,plain,
% 2.00/1.61 (c0_1(a914)),
% 2.00/1.61 inference(unit_resolution,[status(thm)],[91, 2332])).
% 2.00/1.61 tff(2343,plain,
% 2.00/1.61 (((~![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)))),
% 2.00/1.61 inference(rewrite,[status(thm)],[])).
% 2.00/1.61 tff(2344,plain,
% 2.00/1.61 ((hskp28 | (~ndr1_0) | c1_1(a914) | (~c3_1(a914)) | (~c0_1(a914))) <=> (hskp28 | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)))),
% 2.00/1.61 inference(rewrite,[status(thm)],[])).
% 2.00/1.61 tff(2345,plain,
% 2.00/1.61 (((~![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | (~ndr1_0) | c1_1(a914) | (~c3_1(a914)) | (~c0_1(a914)))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914))))),
% 2.00/1.61 inference(monotonicity,[status(thm)],[2344])).
% 2.00/1.61 tff(2346,plain,
% 2.00/1.61 (((~![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | (~ndr1_0) | c1_1(a914) | (~c3_1(a914)) | (~c0_1(a914)))) <=> ((~![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914)))),
% 2.00/1.61 inference(transitivity,[status(thm)],[2345, 2343])).
% 2.00/1.61 tff(2347,plain,
% 2.00/1.61 ((~![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | (~ndr1_0) | c1_1(a914) | (~c3_1(a914)) | (~c0_1(a914)))),
% 2.00/1.61 inference(quant_inst,[status(thm)],[])).
% 2.00/1.61 tff(2348,plain,
% 2.00/1.61 ((~![U: $i] : (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | (~ndr1_0) | (~c3_1(a914)) | c1_1(a914) | (~c0_1(a914))),
% 2.00/1.61 inference(modus_ponens,[status(thm)],[2347, 2346])).
% 2.00/1.61 tff(2349,plain,
% 2.00/1.61 (hskp28),
% 2.00/1.61 inference(unit_resolution,[status(thm)],[2348, 124, 2342, 2334, 2042, 2341])).
% 2.00/1.61 tff(2350,plain,
% 2.00/1.61 (c3_1(a916)),
% 2.00/1.61 inference(unit_resolution,[status(thm)],[271, 2349])).
% 2.00/1.61 tff(2351,plain,
% 2.00/1.61 (c1_1(a916)),
% 2.00/1.61 inference(unit_resolution,[status(thm)],[282, 2349])).
% 2.00/1.61 tff(2352,plain,
% 2.00/1.61 (c0_1(a916)),
% 2.00/1.61 inference(unit_resolution,[status(thm)],[260, 2349])).
% 2.00/1.61 tff(2353,plain,
% 2.00/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c3_1(a926) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c2_1(a926)) | (~c0_1(a926)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a926) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c2_1(a926)) | (~c0_1(a926)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 2.00/1.61 inference(rewrite,[status(thm)],[])).
% 2.00/1.61 tff(2354,plain,
% 2.00/1.61 (((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a926) | (~c2_1(a926)) | (~c0_1(a926)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908))) <=> (c3_1(a926) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c2_1(a926)) | (~c0_1(a926)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 2.00/1.61 inference(rewrite,[status(thm)],[])).
% 2.00/1.61 tff(2355,plain,
% 2.00/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a926) | (~c2_1(a926)) | (~c0_1(a926)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c3_1(a926) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c2_1(a926)) | (~c0_1(a926)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916))))),
% 2.00/1.61 inference(monotonicity,[status(thm)],[2354])).
% 2.00/1.61 tff(2356,plain,
% 2.00/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a926) | (~c2_1(a926)) | (~c0_1(a926)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a926) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c2_1(a926)) | (~c0_1(a926)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 2.00/1.61 inference(transitivity,[status(thm)],[2355, 2353])).
% 2.00/1.61 tff(2357,plain,
% 2.00/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a926) | (~c2_1(a926)) | (~c0_1(a926)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))),
% 2.00/1.61 inference(quant_inst,[status(thm)],[])).
% 2.00/1.61 tff(2358,plain,
% 2.00/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a926) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c2_1(a926)) | (~c0_1(a926)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916))),
% 2.00/1.61 inference(modus_ponens,[status(thm)],[2357, 2356])).
% 2.00/1.61 tff(2359,plain,
% 2.00/1.61 (~c0_1(a926)),
% 2.00/1.61 inference(unit_resolution,[status(thm)],[2358, 124, 2352, 2351, 2350, 2331, 2307, 2320, 2296, 2295, 31])).
% 2.00/1.61 tff(2360,plain,
% 2.00/1.61 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))),
% 2.00/1.61 inference(bind,[status(th)],[])).
% 2.00/1.61 tff(2361,plain,
% 2.00/1.61 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 2.00/1.61 inference(quant_intro,[status(thm)],[2360])).
% 2.00/1.61 tff(2362,plain,
% 2.00/1.61 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 2.00/1.61 inference(rewrite,[status(thm)],[])).
% 2.00/1.61 tff(2363,plain,
% 2.00/1.61 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | 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)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp9) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp9))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))))),
% 2.00/1.61 inference(bind,[status(th)],[])).
% 2.00/1.61 tff(2364,plain,
% 2.00/1.61 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 2.00/1.61 inference(quant_intro,[status(thm)],[2363])).
% 2.00/1.61 tff(2365,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause159')).
% 2.00/1.61 tff(2366,plain,
% 2.00/1.61 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 2.00/1.61 inference(modus_ponens,[status(thm)],[2365, 2364])).
% 2.00/1.61 tff(2367,plain,
% 2.00/1.61 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 2.00/1.61 inference(modus_ponens,[status(thm)],[2366, 2362])).
% 2.00/1.61 tff(2368,plain,(
% 2.00/1.61 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 2.00/1.61 inference(skolemize,[status(sab)],[2367])).
% 2.00/1.61 tff(2369,plain,
% 2.00/1.61 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 2.00/1.61 inference(modus_ponens,[status(thm)],[2368, 2361])).
% 2.00/1.61 tff(2370,plain,
% 2.00/1.61 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp9 | c0_1(a946) | c2_1(a946) | c3_1(a946) | c2_1(a914) | (~ndr1_0) | c1_1(a914) | (~c0_1(a914)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp9 | c0_1(a946) | c2_1(a946) | c3_1(a946) | c2_1(a914) | (~ndr1_0) | c1_1(a914) | (~c0_1(a914)))),
% 2.00/1.61 inference(rewrite,[status(thm)],[])).
% 2.00/1.61 tff(2371,plain,
% 2.00/1.61 ((hskp9 | (~ndr1_0) | c2_1(a914) | c1_1(a914) | (~c0_1(a914)) | c3_1(a946) | c2_1(a946) | c0_1(a946)) <=> (hskp9 | c0_1(a946) | c2_1(a946) | c3_1(a946) | c2_1(a914) | (~ndr1_0) | c1_1(a914) | (~c0_1(a914)))),
% 2.00/1.61 inference(rewrite,[status(thm)],[])).
% 2.00/1.61 tff(2372,plain,
% 2.00/1.61 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp9 | (~ndr1_0) | c2_1(a914) | c1_1(a914) | (~c0_1(a914)) | c3_1(a946) | c2_1(a946) | c0_1(a946))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp9 | c0_1(a946) | c2_1(a946) | c3_1(a946) | c2_1(a914) | (~ndr1_0) | c1_1(a914) | (~c0_1(a914))))),
% 2.00/1.61 inference(monotonicity,[status(thm)],[2371])).
% 2.00/1.61 tff(2373,plain,
% 2.00/1.61 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp9 | (~ndr1_0) | c2_1(a914) | c1_1(a914) | (~c0_1(a914)) | c3_1(a946) | c2_1(a946) | c0_1(a946))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp9 | c0_1(a946) | c2_1(a946) | c3_1(a946) | c2_1(a914) | (~ndr1_0) | c1_1(a914) | (~c0_1(a914)))),
% 2.00/1.61 inference(transitivity,[status(thm)],[2372, 2370])).
% 2.00/1.61 tff(2374,plain,
% 2.00/1.61 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp9 | (~ndr1_0) | c2_1(a914) | c1_1(a914) | (~c0_1(a914)) | c3_1(a946) | c2_1(a946) | c0_1(a946))),
% 2.00/1.61 inference(quant_inst,[status(thm)],[])).
% 2.00/1.61 tff(2375,plain,
% 2.00/1.61 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp9 | c0_1(a946) | c2_1(a946) | c3_1(a946) | c2_1(a914) | (~ndr1_0) | c1_1(a914) | (~c0_1(a914))),
% 2.00/1.61 inference(modus_ponens,[status(thm)],[2374, 2373])).
% 2.00/1.61 tff(2376,plain,
% 2.00/1.61 (hskp9),
% 2.00/1.61 inference(unit_resolution,[status(thm)],[2375, 124, 2342, 2263, 2257, 2251, 2333, 2369, 2341])).
% 2.00/1.61 tff(2377,plain,
% 2.00/1.61 (~c3_1(a910)),
% 2.00/1.61 inference(unit_resolution,[status(thm)],[959, 2376])).
% 2.00/1.61 tff(2378,plain,
% 2.00/1.61 (c2_1(a910)),
% 2.00/1.61 inference(unit_resolution,[status(thm)],[1009, 2376])).
% 2.00/1.61 tff(2379,plain,
% 2.00/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c3_1(a910) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c2_1(a910)) | (~c0_1(a910)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a910) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c2_1(a910)) | (~c0_1(a910)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 2.00/1.61 inference(rewrite,[status(thm)],[])).
% 2.00/1.61 tff(2380,plain,
% 2.00/1.61 (((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a910) | (~c2_1(a910)) | (~c0_1(a910)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908))) <=> (c3_1(a910) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c2_1(a910)) | (~c0_1(a910)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 2.00/1.61 inference(rewrite,[status(thm)],[])).
% 2.00/1.61 tff(2381,plain,
% 2.00/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a910) | (~c2_1(a910)) | (~c0_1(a910)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c3_1(a910) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c2_1(a910)) | (~c0_1(a910)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916))))),
% 2.00/1.61 inference(monotonicity,[status(thm)],[2380])).
% 2.00/1.61 tff(2382,plain,
% 2.00/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a910) | (~c2_1(a910)) | (~c0_1(a910)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a910) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c2_1(a910)) | (~c0_1(a910)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 2.00/1.61 inference(transitivity,[status(thm)],[2381, 2379])).
% 2.00/1.61 tff(2383,plain,
% 2.00/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a910) | (~c2_1(a910)) | (~c0_1(a910)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))),
% 2.00/1.61 inference(quant_inst,[status(thm)],[])).
% 2.00/1.61 tff(2384,plain,
% 2.00/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a910) | c2_1(a908) | c3_1(a908) | (~ndr1_0) | (~c1_1(a908)) | (~c2_1(a910)) | (~c0_1(a910)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916))),
% 2.00/1.61 inference(modus_ponens,[status(thm)],[2383, 2382])).
% 2.00/1.61 tff(2385,plain,
% 2.00/1.61 (~c0_1(a910)),
% 2.00/1.61 inference(unit_resolution,[status(thm)],[2384, 124, 2352, 2351, 2350, 2378, 2307, 2377, 2296, 2295, 31])).
% 2.00/1.61 tff(2386,plain,
% 2.00/1.61 (~c1_1(a910)),
% 2.00/1.61 inference(unit_resolution,[status(thm)],[965, 2376])).
% 2.00/1.61 tff(2387,plain,
% 2.00/1.61 (hskp17),
% 2.00/1.61 inference(unit_resolution,[status(thm)],[454, 124, 32, 2342, 2333, 448, 2341])).
% 2.00/1.61 tff(2388,plain,
% 2.00/1.61 (~c3_1(a936)),
% 2.00/1.61 inference(unit_resolution,[status(thm)],[460, 2387])).
% 2.00/1.61 tff(2389,plain,
% 2.00/1.61 (~c2_1(a936)),
% 2.00/1.61 inference(unit_resolution,[status(thm)],[502, 2387])).
% 2.00/1.61 tff(2390,plain,
% 2.00/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a946) | c2_1(a946) | c3_1(a946) | c2_1(a936) | c3_1(a936) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | c0_1(a910) | (~c0_1(a936)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a946) | c2_1(a946) | c3_1(a946) | c2_1(a936) | c3_1(a936) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | c0_1(a910) | (~c0_1(a936)))),
% 2.00/1.61 inference(rewrite,[status(thm)],[])).
% 2.00/1.61 tff(2391,plain,
% 2.00/1.61 (((~ndr1_0) | c2_1(a936) | c3_1(a936) | (~c0_1(a936)) | c3_1(a946) | c2_1(a946) | c0_1(a946) | c3_1(a910) | c1_1(a910) | c0_1(a910)) <=> (c0_1(a946) | c2_1(a946) | c3_1(a946) | c2_1(a936) | c3_1(a936) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | c0_1(a910) | (~c0_1(a936)))),
% 2.00/1.61 inference(rewrite,[status(thm)],[])).
% 2.00/1.61 tff(2392,plain,
% 2.00/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a936) | c3_1(a936) | (~c0_1(a936)) | c3_1(a946) | c2_1(a946) | c0_1(a946) | c3_1(a910) | c1_1(a910) | c0_1(a910))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a946) | c2_1(a946) | c3_1(a946) | c2_1(a936) | c3_1(a936) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | c0_1(a910) | (~c0_1(a936))))),
% 2.00/1.61 inference(monotonicity,[status(thm)],[2391])).
% 2.00/1.61 tff(2393,plain,
% 2.00/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a936) | c3_1(a936) | (~c0_1(a936)) | c3_1(a946) | c2_1(a946) | c0_1(a946) | c3_1(a910) | c1_1(a910) | c0_1(a910))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a946) | c2_1(a946) | c3_1(a946) | c2_1(a936) | c3_1(a936) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | c0_1(a910) | (~c0_1(a936)))),
% 2.00/1.61 inference(transitivity,[status(thm)],[2392, 2390])).
% 2.00/1.61 tff(2394,plain,
% 2.00/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a936) | c3_1(a936) | (~c0_1(a936)) | c3_1(a946) | c2_1(a946) | c0_1(a946) | c3_1(a910) | c1_1(a910) | c0_1(a910))),
% 2.00/1.61 inference(quant_inst,[status(thm)],[])).
% 2.00/1.61 tff(2395,plain,
% 2.00/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a946) | c2_1(a946) | c3_1(a946) | c2_1(a936) | c3_1(a936) | c1_1(a910) | c3_1(a910) | (~ndr1_0) | c0_1(a910) | (~c0_1(a936))),
% 2.00/1.61 inference(modus_ponens,[status(thm)],[2394, 2393])).
% 2.00/1.61 tff(2396,plain,
% 2.00/1.61 (c0_1(a910) | (~c0_1(a936))),
% 2.00/1.61 inference(unit_resolution,[status(thm)],[2395, 124, 2263, 2257, 2251, 2389, 2388, 2386, 2377, 1107])).
% 2.00/1.61 tff(2397,plain,
% 2.00/1.61 (~c0_1(a936)),
% 2.00/1.61 inference(unit_resolution,[status(thm)],[2396, 2385])).
% 2.00/1.61 tff(2398,plain,
% 2.00/1.61 (~c1_1(a936)),
% 2.00/1.61 inference(unit_resolution,[status(thm)],[508, 2387])).
% 2.00/1.61 tff(2399,plain,
% 2.00/1.61 (((~hskp16) | c1_1(a926)) <=> ((~hskp16) | c1_1(a926))),
% 2.00/1.61 inference(rewrite,[status(thm)],[])).
% 2.00/1.61 tff(2400,axiom,((~hskp16) | c1_1(a926)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause59')).
% 2.00/1.61 tff(2401,plain,
% 2.00/1.61 ((~hskp16) | c1_1(a926)),
% 2.00/1.61 inference(modus_ponens,[status(thm)],[2400, 2399])).
% 2.00/1.61 tff(2402,plain,
% 2.00/1.61 ((~hskp16) | c1_1(a926)),
% 2.00/1.61 inference(modus_ponens,[status(thm)],[2401, 2399])).
% 2.00/1.61 tff(2403,plain,
% 2.00/1.61 ((~hskp16) | c1_1(a926)),
% 2.00/1.61 inference(modus_ponens,[status(thm)],[2402, 2399])).
% 2.00/1.61 tff(2404,plain,
% 2.00/1.61 ((~hskp16) | c1_1(a926)),
% 2.00/1.61 inference(modus_ponens,[status(thm)],[2403, 2399])).
% 2.00/1.61 tff(2405,plain,
% 2.00/1.61 ((~hskp16) | c1_1(a926)),
% 2.00/1.61 inference(modus_ponens,[status(thm)],[2404, 2399])).
% 2.00/1.61 tff(2406,plain,
% 2.00/1.61 ((~hskp16) | c1_1(a926)),
% 2.00/1.61 inference(modus_ponens,[status(thm)],[2405, 2399])).
% 2.00/1.61 tff(2407,plain,
% 2.00/1.61 ((~hskp16) | c1_1(a926)),
% 2.00/1.61 inference(modus_ponens,[status(thm)],[2406, 2399])).
% 2.00/1.61 tff(2408,plain,
% 2.00/1.61 ((~hskp16) | c1_1(a926)),
% 2.00/1.61 inference(modus_ponens,[status(thm)],[2407, 2399])).
% 2.00/1.61 tff(2409,plain,
% 2.00/1.61 (c1_1(a926)),
% 2.00/1.61 inference(unit_resolution,[status(thm)],[2408, 2314])).
% 2.00/1.61 tff(2410,plain,
% 2.00/1.61 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))))),
% 2.00/1.61 inference(bind,[status(th)],[])).
% 2.00/1.61 tff(2411,plain,
% 2.00/1.61 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 2.00/1.61 inference(quant_intro,[status(thm)],[2410])).
% 2.00/1.61 tff(2412,plain,
% 2.00/1.61 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 2.00/1.61 inference(rewrite,[status(thm)],[])).
% 2.00/1.61 tff(2413,plain,
% 2.00/1.61 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp5) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) | hskp5))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))))),
% 2.00/1.61 inference(bind,[status(th)],[])).
% 2.00/1.61 tff(2414,plain,
% 2.00/1.61 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 2.00/1.61 inference(quant_intro,[status(thm)],[2413])).
% 2.00/1.61 tff(2415,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause170')).
% 2.00/1.61 tff(2416,plain,
% 2.00/1.61 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 2.00/1.61 inference(modus_ponens,[status(thm)],[2415, 2414])).
% 2.00/1.61 tff(2417,plain,
% 2.00/1.61 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 2.00/1.61 inference(modus_ponens,[status(thm)],[2416, 2412])).
% 2.00/1.61 tff(2418,plain,(
% 2.00/1.61 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 2.00/1.61 inference(skolemize,[status(sab)],[2417])).
% 2.00/1.61 tff(2419,plain,
% 2.00/1.61 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 2.00/1.61 inference(modus_ponens,[status(thm)],[2418, 2411])).
% 2.00/1.61 tff(2420,assumption,(hskp4), introduced(assumption)).
% 2.00/1.61 tff(2421,plain,
% 2.00/1.61 (((~hskp4) | (~c0_1(a905))) <=> ((~hskp4) | (~c0_1(a905)))),
% 2.00/1.61 inference(rewrite,[status(thm)],[])).
% 2.00/1.61 tff(2422,plain,
% 2.00/1.61 (((~c0_1(a905)) | (~hskp4)) <=> ((~hskp4) | (~c0_1(a905)))),
% 2.00/1.61 inference(rewrite,[status(thm)],[])).
% 2.00/1.61 tff(2423,axiom,((~c0_1(a905)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause118')).
% 2.00/1.61 tff(2424,plain,
% 2.00/1.61 ((~hskp4) | (~c0_1(a905))),
% 2.00/1.61 inference(modus_ponens,[status(thm)],[2423, 2422])).
% 2.00/1.61 tff(2425,plain,
% 2.00/1.61 ((~hskp4) | (~c0_1(a905))),
% 2.00/1.61 inference(modus_ponens,[status(thm)],[2424, 2421])).
% 2.00/1.61 tff(2426,plain,
% 2.00/1.61 (~c0_1(a905)),
% 2.00/1.61 inference(unit_resolution,[status(thm)],[2425, 2420])).
% 2.00/1.61 tff(2427,plain,
% 2.00/1.61 (((~hskp4) | c3_1(a905)) <=> ((~hskp4) | c3_1(a905))),
% 2.00/1.61 inference(rewrite,[status(thm)],[])).
% 2.00/1.61 tff(2428,axiom,((~hskp4) | c3_1(a905)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause77')).
% 2.00/1.61 tff(2429,plain,
% 2.00/1.61 ((~hskp4) | c3_1(a905)),
% 2.00/1.61 inference(modus_ponens,[status(thm)],[2428, 2427])).
% 2.00/1.61 tff(2430,plain,
% 2.00/1.61 ((~hskp4) | c3_1(a905)),
% 2.00/1.61 inference(modus_ponens,[status(thm)],[2429, 2427])).
% 2.00/1.61 tff(2431,plain,
% 2.00/1.61 ((~hskp4) | c3_1(a905)),
% 2.00/1.61 inference(modus_ponens,[status(thm)],[2430, 2427])).
% 2.00/1.61 tff(2432,plain,
% 2.00/1.61 ((~hskp4) | c3_1(a905)),
% 2.00/1.61 inference(modus_ponens,[status(thm)],[2431, 2427])).
% 2.00/1.61 tff(2433,plain,
% 2.00/1.61 ((~hskp4) | c3_1(a905)),
% 2.00/1.62 inference(modus_ponens,[status(thm)],[2432, 2427])).
% 2.00/1.62 tff(2434,plain,
% 2.00/1.62 ((~hskp4) | c3_1(a905)),
% 2.00/1.62 inference(modus_ponens,[status(thm)],[2433, 2427])).
% 2.00/1.62 tff(2435,plain,
% 2.00/1.62 ((~hskp4) | c3_1(a905)),
% 2.00/1.62 inference(modus_ponens,[status(thm)],[2434, 2427])).
% 2.00/1.62 tff(2436,plain,
% 2.00/1.62 ((~hskp4) | c3_1(a905)),
% 2.00/1.62 inference(modus_ponens,[status(thm)],[2435, 2427])).
% 2.00/1.62 tff(2437,plain,
% 2.00/1.62 (c3_1(a905)),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[2436, 2420])).
% 2.00/1.62 tff(2438,assumption,(c3_1(a900)), introduced(assumption)).
% 2.00/1.62 tff(2439,assumption,(c2_1(a900)), introduced(assumption)).
% 2.00/1.62 tff(2440,assumption,(c1_1(a900)), introduced(assumption)).
% 2.00/1.62 tff(2441,plain,
% 2.00/1.62 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a905) | (~ndr1_0) | (~c3_1(a905)) | c1_1(a905) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a905) | (~ndr1_0) | (~c3_1(a905)) | c1_1(a905) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900)))),
% 2.00/1.62 inference(rewrite,[status(thm)],[])).
% 2.00/1.62 tff(2442,plain,
% 2.00/1.62 ((hskp5 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c1_1(a900)) | c0_1(a905) | c1_1(a905) | (~c3_1(a905))) <=> (hskp5 | c0_1(a905) | (~ndr1_0) | (~c3_1(a905)) | c1_1(a905) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900)))),
% 2.00/1.62 inference(rewrite,[status(thm)],[])).
% 2.00/1.62 tff(2443,plain,
% 2.00/1.62 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c1_1(a900)) | c0_1(a905) | c1_1(a905) | (~c3_1(a905)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a905) | (~ndr1_0) | (~c3_1(a905)) | c1_1(a905) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900))))),
% 2.00/1.62 inference(monotonicity,[status(thm)],[2442])).
% 2.00/1.62 tff(2444,plain,
% 2.00/1.62 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c1_1(a900)) | c0_1(a905) | c1_1(a905) | (~c3_1(a905)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a905) | (~ndr1_0) | (~c3_1(a905)) | c1_1(a905) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900)))),
% 2.00/1.62 inference(transitivity,[status(thm)],[2443, 2441])).
% 2.00/1.62 tff(2445,plain,
% 2.00/1.62 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c1_1(a900)) | c0_1(a905) | c1_1(a905) | (~c3_1(a905)))),
% 2.00/1.62 inference(quant_inst,[status(thm)],[])).
% 2.00/1.62 tff(2446,plain,
% 2.00/1.62 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a905) | (~ndr1_0) | (~c3_1(a905)) | c1_1(a905) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900))),
% 2.00/1.62 inference(modus_ponens,[status(thm)],[2445, 2444])).
% 2.00/1.62 tff(2447,plain,
% 2.00/1.62 (c1_1(a905)),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[2446, 124, 43, 2440, 2439, 2438, 2437, 2426, 2419])).
% 2.00/1.62 tff(2448,assumption,(~c0_1(a926)), introduced(assumption)).
% 2.00/1.62 tff(2449,plain,
% 2.00/1.62 (((~hskp4) | (~c2_1(a905))) <=> ((~hskp4) | (~c2_1(a905)))),
% 2.00/1.62 inference(rewrite,[status(thm)],[])).
% 2.00/1.62 tff(2450,plain,
% 2.00/1.62 (((~c2_1(a905)) | (~hskp4)) <=> ((~hskp4) | (~c2_1(a905)))),
% 2.00/1.62 inference(rewrite,[status(thm)],[])).
% 2.00/1.62 tff(2451,axiom,((~c2_1(a905)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause119')).
% 2.00/1.62 tff(2452,plain,
% 2.00/1.62 ((~hskp4) | (~c2_1(a905))),
% 2.00/1.62 inference(modus_ponens,[status(thm)],[2451, 2450])).
% 2.00/1.62 tff(2453,plain,
% 2.00/1.62 ((~hskp4) | (~c2_1(a905))),
% 2.00/1.62 inference(modus_ponens,[status(thm)],[2452, 2449])).
% 2.00/1.62 tff(2454,plain,
% 2.00/1.62 (~c2_1(a905)),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[2453, 2420])).
% 2.00/1.62 tff(2455,assumption,(c2_1(a910)), introduced(assumption)).
% 2.00/1.62 tff(2456,assumption,(c2_1(a926)), introduced(assumption)).
% 2.00/1.62 tff(2457,assumption,(c1_1(a926)), introduced(assumption)).
% 2.00/1.62 tff(2458,plain,
% 2.00/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a910) | c3_1(a910) | c2_1(a905) | (~ndr1_0) | (~c3_1(a905)) | (~c1_1(a905)) | (~c2_1(a910)) | (~c2_1(a926)) | (~c1_1(a926)) | c0_1(a926))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a910) | c3_1(a910) | c2_1(a905) | (~ndr1_0) | (~c3_1(a905)) | (~c1_1(a905)) | (~c2_1(a910)) | (~c2_1(a926)) | (~c1_1(a926)) | c0_1(a926))),
% 2.00/1.62 inference(rewrite,[status(thm)],[])).
% 2.00/1.62 tff(2459,plain,
% 2.00/1.62 (((~ndr1_0) | c2_1(a905) | (~c3_1(a905)) | (~c1_1(a905)) | c3_1(a910) | c1_1(a910) | (~c2_1(a910)) | c0_1(a926) | (~c2_1(a926)) | (~c1_1(a926))) <=> (c1_1(a910) | c3_1(a910) | c2_1(a905) | (~ndr1_0) | (~c3_1(a905)) | (~c1_1(a905)) | (~c2_1(a910)) | (~c2_1(a926)) | (~c1_1(a926)) | c0_1(a926))),
% 2.00/1.62 inference(rewrite,[status(thm)],[])).
% 2.00/1.62 tff(2460,plain,
% 2.00/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a905) | (~c3_1(a905)) | (~c1_1(a905)) | c3_1(a910) | c1_1(a910) | (~c2_1(a910)) | c0_1(a926) | (~c2_1(a926)) | (~c1_1(a926)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a910) | c3_1(a910) | c2_1(a905) | (~ndr1_0) | (~c3_1(a905)) | (~c1_1(a905)) | (~c2_1(a910)) | (~c2_1(a926)) | (~c1_1(a926)) | c0_1(a926)))),
% 2.00/1.62 inference(monotonicity,[status(thm)],[2459])).
% 2.00/1.62 tff(2461,plain,
% 2.00/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a905) | (~c3_1(a905)) | (~c1_1(a905)) | c3_1(a910) | c1_1(a910) | (~c2_1(a910)) | c0_1(a926) | (~c2_1(a926)) | (~c1_1(a926)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a910) | c3_1(a910) | c2_1(a905) | (~ndr1_0) | (~c3_1(a905)) | (~c1_1(a905)) | (~c2_1(a910)) | (~c2_1(a926)) | (~c1_1(a926)) | c0_1(a926))),
% 2.00/1.62 inference(transitivity,[status(thm)],[2460, 2458])).
% 2.00/1.62 tff(2462,plain,
% 2.00/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a905) | (~c3_1(a905)) | (~c1_1(a905)) | c3_1(a910) | c1_1(a910) | (~c2_1(a910)) | c0_1(a926) | (~c2_1(a926)) | (~c1_1(a926)))),
% 2.00/1.62 inference(quant_inst,[status(thm)],[])).
% 2.00/1.62 tff(2463,plain,
% 2.00/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a910) | c3_1(a910) | c2_1(a905) | (~ndr1_0) | (~c3_1(a905)) | (~c1_1(a905)) | (~c2_1(a910)) | (~c2_1(a926)) | (~c1_1(a926)) | c0_1(a926)),
% 2.00/1.62 inference(modus_ponens,[status(thm)],[2462, 2461])).
% 2.00/1.62 tff(2464,plain,
% 2.00/1.62 ($false),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[2463, 124, 2457, 2456, 2455, 2437, 1566, 1565, 2454, 743, 2448, 2447])).
% 2.00/1.62 tff(2465,plain,((~hskp4) | (~c1_1(a926)) | (~c2_1(a926)) | (~c2_1(a910)) | c1_1(a910) | c3_1(a910) | c0_1(a926) | hskp5 | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900))), inference(lemma,lemma(discharge,[]))).
% 2.00/1.62 tff(2466,plain,
% 2.00/1.62 (~hskp4),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[2465, 2409, 2331, 2378, 2386, 2377, 2359, 43, 167, 156, 145])).
% 2.00/1.62 tff(2467,plain,
% 2.00/1.62 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a923) | c1_1(a923) | (~ndr1_0) | (~c3_1(a923)) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a923) | c1_1(a923) | (~ndr1_0) | (~c3_1(a923)) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900)))),
% 2.00/1.62 inference(rewrite,[status(thm)],[])).
% 2.00/1.62 tff(2468,plain,
% 2.00/1.62 ((hskp5 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c1_1(a900)) | c0_1(a923) | c1_1(a923) | (~c3_1(a923))) <=> (hskp5 | c0_1(a923) | c1_1(a923) | (~ndr1_0) | (~c3_1(a923)) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900)))),
% 2.00/1.62 inference(rewrite,[status(thm)],[])).
% 2.00/1.62 tff(2469,plain,
% 2.00/1.62 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c1_1(a900)) | c0_1(a923) | c1_1(a923) | (~c3_1(a923)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | c0_1(a923) | c1_1(a923) | (~ndr1_0) | (~c3_1(a923)) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900))))),
% 2.00/1.62 inference(monotonicity,[status(thm)],[2468])).
% 2.00/1.62 tff(2470,plain,
% 2.00/1.62 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c1_1(a900)) | c0_1(a923) | c1_1(a923) | (~c3_1(a923)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a923) | c1_1(a923) | (~ndr1_0) | (~c3_1(a923)) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900)))),
% 2.00/1.62 inference(transitivity,[status(thm)],[2469, 2467])).
% 2.00/1.62 tff(2471,plain,
% 2.00/1.62 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c1_1(a900)) | c0_1(a923) | c1_1(a923) | (~c3_1(a923)))),
% 2.00/1.62 inference(quant_inst,[status(thm)],[])).
% 2.00/1.62 tff(2472,plain,
% 2.00/1.62 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp5 | c0_1(a923) | c1_1(a923) | (~ndr1_0) | (~c3_1(a923)) | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900))),
% 2.00/1.62 inference(modus_ponens,[status(thm)],[2471, 2470])).
% 2.00/1.62 tff(2473,plain,
% 2.00/1.62 ($false),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[2472, 124, 43, 2440, 2439, 2438, 588, 577, 571, 2419])).
% 2.00/1.62 tff(2474,plain,((~hskp14) | hskp5 | (~c1_1(a900)) | (~c2_1(a900)) | (~c3_1(a900))), inference(lemma,lemma(discharge,[]))).
% 2.00/1.62 tff(2475,plain,
% 2.00/1.62 (~hskp14),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[2474, 167, 43, 156, 145])).
% 2.00/1.62 tff(2476,plain,
% 2.00/1.62 ((hskp20 | hskp14 | hskp4) <=> (hskp20 | hskp14 | hskp4)),
% 2.00/1.62 inference(rewrite,[status(thm)],[])).
% 2.00/1.62 tff(2477,plain,
% 2.00/1.62 (((hskp20 | hskp14) | hskp4) <=> (hskp20 | hskp14 | hskp4)),
% 2.00/1.62 inference(rewrite,[status(thm)],[])).
% 2.00/1.62 tff(2478,plain,
% 2.00/1.62 ((hskp20 | hskp14) <=> (hskp20 | hskp14)),
% 2.00/1.62 inference(rewrite,[status(thm)],[])).
% 2.00/1.62 tff(2479,plain,
% 2.00/1.62 (((hskp20 | hskp14) | hskp4) <=> ((hskp20 | hskp14) | hskp4)),
% 2.00/1.62 inference(monotonicity,[status(thm)],[2478])).
% 2.00/1.62 tff(2480,plain,
% 2.00/1.62 (((hskp20 | hskp14) | hskp4) <=> (hskp20 | hskp14 | hskp4)),
% 2.00/1.62 inference(transitivity,[status(thm)],[2479, 2477])).
% 2.00/1.62 tff(2481,axiom,((hskp20 | hskp14) | hskp4), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause33')).
% 2.00/1.62 tff(2482,plain,
% 2.00/1.62 (hskp20 | hskp14 | hskp4),
% 2.00/1.62 inference(modus_ponens,[status(thm)],[2481, 2480])).
% 2.00/1.62 tff(2483,plain,
% 2.00/1.62 (hskp20 | hskp14 | hskp4),
% 2.00/1.62 inference(modus_ponens,[status(thm)],[2482, 2476])).
% 2.00/1.62 tff(2484,plain,
% 2.00/1.62 (hskp20 | hskp14 | hskp4),
% 2.00/1.62 inference(modus_ponens,[status(thm)],[2483, 2476])).
% 2.00/1.62 tff(2485,plain,
% 2.00/1.62 (hskp20 | hskp14 | hskp4),
% 2.00/1.62 inference(modus_ponens,[status(thm)],[2484, 2476])).
% 2.00/1.62 tff(2486,plain,
% 2.00/1.62 (hskp20 | hskp14 | hskp4),
% 2.00/1.62 inference(modus_ponens,[status(thm)],[2485, 2476])).
% 2.00/1.62 tff(2487,plain,
% 2.00/1.62 (hskp20 | hskp14 | hskp4),
% 2.00/1.62 inference(modus_ponens,[status(thm)],[2486, 2476])).
% 2.00/1.62 tff(2488,plain,
% 2.00/1.62 (hskp20 | hskp14 | hskp4),
% 2.00/1.62 inference(modus_ponens,[status(thm)],[2487, 2476])).
% 2.00/1.62 tff(2489,plain,
% 2.00/1.62 (hskp20 | hskp14 | hskp4),
% 2.00/1.62 inference(modus_ponens,[status(thm)],[2488, 2476])).
% 2.00/1.62 tff(2490,plain,
% 2.00/1.62 (hskp20),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[2489, 2475, 2466])).
% 2.00/1.62 tff(2491,plain,
% 2.00/1.62 (~c3_1(a939)),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[1420, 2490])).
% 2.00/1.62 tff(2492,plain,
% 2.00/1.62 (~c1_1(a939)),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[1426, 2490])).
% 2.00/1.62 tff(2493,plain,
% 2.00/1.62 (c0_1(a939)),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[1437, 2490])).
% 2.00/1.62 tff(2494,plain,
% 2.00/1.62 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a939) | c3_1(a939) | c1_1(a936) | c2_1(a936) | c3_1(a926) | (~ndr1_0) | (~c2_1(a926)) | c0_1(a926) | c0_1(a936) | (~c0_1(a939)))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a939) | c3_1(a939) | c1_1(a936) | c2_1(a936) | c3_1(a926) | (~ndr1_0) | (~c2_1(a926)) | c0_1(a926) | c0_1(a936) | (~c0_1(a939)))),
% 2.00/1.62 inference(rewrite,[status(thm)],[])).
% 2.00/1.62 tff(2495,plain,
% 2.00/1.62 (((~ndr1_0) | c1_1(a939) | c3_1(a939) | (~c0_1(a939)) | c3_1(a926) | c0_1(a926) | (~c2_1(a926)) | c1_1(a936) | c0_1(a936) | c2_1(a936)) <=> (c1_1(a939) | c3_1(a939) | c1_1(a936) | c2_1(a936) | c3_1(a926) | (~ndr1_0) | (~c2_1(a926)) | c0_1(a926) | c0_1(a936) | (~c0_1(a939)))),
% 2.00/1.62 inference(rewrite,[status(thm)],[])).
% 2.00/1.62 tff(2496,plain,
% 2.00/1.62 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a939) | c3_1(a939) | (~c0_1(a939)) | c3_1(a926) | c0_1(a926) | (~c2_1(a926)) | c1_1(a936) | c0_1(a936) | c2_1(a936))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a939) | c3_1(a939) | c1_1(a936) | c2_1(a936) | c3_1(a926) | (~ndr1_0) | (~c2_1(a926)) | c0_1(a926) | c0_1(a936) | (~c0_1(a939))))),
% 2.00/1.62 inference(monotonicity,[status(thm)],[2495])).
% 2.00/1.62 tff(2497,plain,
% 2.00/1.62 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a939) | c3_1(a939) | (~c0_1(a939)) | c3_1(a926) | c0_1(a926) | (~c2_1(a926)) | c1_1(a936) | c0_1(a936) | c2_1(a936))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a939) | c3_1(a939) | c1_1(a936) | c2_1(a936) | c3_1(a926) | (~ndr1_0) | (~c2_1(a926)) | c0_1(a926) | c0_1(a936) | (~c0_1(a939)))),
% 2.00/1.62 inference(transitivity,[status(thm)],[2496, 2494])).
% 2.00/1.62 tff(2498,plain,
% 2.00/1.62 ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a939) | c3_1(a939) | (~c0_1(a939)) | c3_1(a926) | c0_1(a926) | (~c2_1(a926)) | c1_1(a936) | c0_1(a936) | c2_1(a936))),
% 2.00/1.62 inference(quant_inst,[status(thm)],[])).
% 2.00/1.62 tff(2499,plain,
% 2.00/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a939) | c3_1(a939) | c1_1(a936) | c2_1(a936) | c3_1(a926) | (~ndr1_0) | (~c2_1(a926)) | c0_1(a926) | c0_1(a936) | (~c0_1(a939))),
% 2.00/1.62 inference(modus_ponens,[status(thm)],[2498, 2497])).
% 2.00/1.62 tff(2500,plain,
% 2.00/1.62 ($false),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[2499, 124, 2493, 2331, 2492, 2491, 2398, 2389, 2320, 540, 2397, 2359])).
% 2.00/1.62 tff(2501,plain,((~hskp27) | hskp5 | hskp12), inference(lemma,lemma(discharge,[]))).
% 2.00/1.62 tff(2502,plain,
% 2.00/1.62 (~hskp27),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[2501, 43, 32])).
% 2.00/1.62 tff(2503,assumption,(~hskp27), introduced(assumption)).
% 2.00/1.62 tff(2504,plain,
% 2.00/1.62 (hskp10),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[2270, 2503])).
% 2.00/1.62 tff(2505,plain,
% 2.00/1.62 (c2_1(a912)),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[676, 2504])).
% 2.00/1.62 tff(2506,plain,
% 2.00/1.62 (c1_1(a912)),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[687, 2504])).
% 2.00/1.62 tff(2507,plain,
% 2.00/1.62 (hskp11 | (~c3_1(a912))),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[2279, 124, 32, 2506, 2505, 53])).
% 2.00/1.62 tff(2508,plain,
% 2.00/1.62 (~c3_1(a912)),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[2507, 168])).
% 2.00/1.62 tff(2509,plain,
% 2.00/1.62 (~c0_1(a912)),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[627, 2504])).
% 2.00/1.62 tff(2510,plain,
% 2.00/1.62 (hskp28 | c3_1(a912)),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[2287, 124, 32, 2505, 2509, 208])).
% 2.00/1.62 tff(2511,plain,
% 2.00/1.62 (hskp28),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[2510, 2508])).
% 2.00/1.62 tff(2512,plain,
% 2.00/1.62 (c3_1(a916)),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[271, 2511])).
% 2.00/1.62 tff(2513,plain,
% 2.00/1.62 (c1_1(a916)),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[282, 2511])).
% 2.00/1.62 tff(2514,plain,
% 2.00/1.62 (~c2_1(a916)),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[389, 124, 32, 168, 2513, 2512, 53])).
% 2.00/1.62 tff(2515,plain,
% 2.00/1.62 (((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp11 | c2_1(a946) | c3_1(a946) | (~ndr1_0) | c1_1(a946))) <=> ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp27 | hskp11 | c2_1(a946) | c3_1(a946) | (~ndr1_0) | c1_1(a946))),
% 2.00/1.62 inference(rewrite,[status(thm)],[])).
% 2.00/1.62 tff(2516,plain,
% 2.00/1.62 ((hskp27 | hskp11 | (~ndr1_0) | c2_1(a946) | c1_1(a946) | c3_1(a946)) <=> (hskp27 | hskp11 | c2_1(a946) | c3_1(a946) | (~ndr1_0) | c1_1(a946))),
% 2.00/1.62 inference(rewrite,[status(thm)],[])).
% 2.00/1.62 tff(2517,plain,
% 2.00/1.62 (((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp11 | (~ndr1_0) | c2_1(a946) | c1_1(a946) | c3_1(a946))) <=> ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp11 | c2_1(a946) | c3_1(a946) | (~ndr1_0) | c1_1(a946)))),
% 2.00/1.62 inference(monotonicity,[status(thm)],[2516])).
% 2.00/1.62 tff(2518,plain,
% 2.00/1.62 (((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp11 | (~ndr1_0) | c2_1(a946) | c1_1(a946) | c3_1(a946))) <=> ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp27 | hskp11 | c2_1(a946) | c3_1(a946) | (~ndr1_0) | c1_1(a946))),
% 2.00/1.62 inference(transitivity,[status(thm)],[2517, 2515])).
% 2.00/1.62 tff(2519,plain,
% 2.00/1.62 ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp27 | hskp11 | (~ndr1_0) | c2_1(a946) | c1_1(a946) | c3_1(a946))),
% 2.00/1.62 inference(quant_inst,[status(thm)],[])).
% 2.00/1.62 tff(2520,plain,
% 2.00/1.62 ((~![U: $i] : (hskp27 | hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp27 | hskp11 | c2_1(a946) | c3_1(a946) | (~ndr1_0) | c1_1(a946)),
% 2.00/1.62 inference(modus_ponens,[status(thm)],[2519, 2518])).
% 2.00/1.62 tff(2521,plain,
% 2.00/1.62 (hskp27 | hskp11 | c1_1(a946)),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[2520, 124, 2257, 2251, 976])).
% 2.00/1.62 tff(2522,plain,
% 2.00/1.62 (c1_1(a946)),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[2521, 168, 2503])).
% 2.00/1.62 tff(2523,plain,
% 2.00/1.62 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (c2_1(a946) | c3_1(a946) | (~ndr1_0) | c2_1(a916) | (~c3_1(a916)) | (~c1_1(a916)) | (~c1_1(a946)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | c2_1(a946) | c3_1(a946) | (~ndr1_0) | c2_1(a916) | (~c3_1(a916)) | (~c1_1(a916)) | (~c1_1(a946)))),
% 2.00/1.62 inference(rewrite,[status(thm)],[])).
% 2.00/1.62 tff(2524,plain,
% 2.00/1.62 (((~ndr1_0) | c2_1(a916) | (~c3_1(a916)) | (~c1_1(a916)) | c3_1(a946) | c2_1(a946) | (~c1_1(a946))) <=> (c2_1(a946) | c3_1(a946) | (~ndr1_0) | c2_1(a916) | (~c3_1(a916)) | (~c1_1(a916)) | (~c1_1(a946)))),
% 2.00/1.62 inference(rewrite,[status(thm)],[])).
% 2.00/1.62 tff(2525,plain,
% 2.00/1.62 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | ((~ndr1_0) | c2_1(a916) | (~c3_1(a916)) | (~c1_1(a916)) | c3_1(a946) | c2_1(a946) | (~c1_1(a946)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (c2_1(a946) | c3_1(a946) | (~ndr1_0) | c2_1(a916) | (~c3_1(a916)) | (~c1_1(a916)) | (~c1_1(a946))))),
% 2.00/1.62 inference(monotonicity,[status(thm)],[2524])).
% 2.00/1.62 tff(2526,plain,
% 2.00/1.62 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | ((~ndr1_0) | c2_1(a916) | (~c3_1(a916)) | (~c1_1(a916)) | c3_1(a946) | c2_1(a946) | (~c1_1(a946)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | c2_1(a946) | c3_1(a946) | (~ndr1_0) | c2_1(a916) | (~c3_1(a916)) | (~c1_1(a916)) | (~c1_1(a946)))),
% 2.00/1.62 inference(transitivity,[status(thm)],[2525, 2523])).
% 2.00/1.62 tff(2527,plain,
% 2.00/1.62 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | ((~ndr1_0) | c2_1(a916) | (~c3_1(a916)) | (~c1_1(a916)) | c3_1(a946) | c2_1(a946) | (~c1_1(a946)))),
% 2.00/1.62 inference(quant_inst,[status(thm)],[])).
% 2.00/1.62 tff(2528,plain,
% 2.00/1.62 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | c2_1(a946) | c3_1(a946) | (~ndr1_0) | c2_1(a916) | (~c3_1(a916)) | (~c1_1(a916)) | (~c1_1(a946))),
% 2.00/1.62 inference(modus_ponens,[status(thm)],[2527, 2526])).
% 2.00/1.62 tff(2529,plain,
% 2.00/1.62 ($false),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[2528, 124, 2513, 2512, 2257, 2251, 10, 2522, 2514])).
% 2.00/1.62 tff(2530,plain,(hskp11 | hskp12 | hskp27), inference(lemma,lemma(discharge,[]))).
% 2.00/1.62 tff(2531,plain,
% 2.00/1.62 (hskp11),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[2530, 2502, 32])).
% 2.00/1.62 tff(2532,plain,
% 2.00/1.62 (~c2_1(a914)),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[69, 2531])).
% 2.00/1.62 tff(2533,plain,
% 2.00/1.62 (c3_1(a914)),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[80, 2531])).
% 2.00/1.62 tff(2534,plain,
% 2.00/1.62 (~c1_1(a914)),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[2340, 124, 2533, 2307, 2532, 2296, 2295, 10])).
% 2.00/1.62 tff(2535,plain,
% 2.00/1.62 (c0_1(a914)),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[91, 2531])).
% 2.00/1.62 tff(2536,plain,
% 2.00/1.62 (hskp28 | c1_1(a914)),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[2348, 124, 2535, 2533, 2042])).
% 2.00/1.62 tff(2537,plain,
% 2.00/1.62 (hskp28),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[2536, 2534])).
% 2.00/1.62 tff(2538,plain,
% 2.00/1.62 (c3_1(a916)),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[271, 2537])).
% 2.00/1.62 tff(2539,plain,
% 2.00/1.62 (c1_1(a916)),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[282, 2537])).
% 2.00/1.62 tff(2540,plain,
% 2.00/1.62 (c0_1(a916)),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[260, 2537])).
% 2.00/1.62 tff(2541,plain,
% 2.00/1.62 (hskp1),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[1585, 124, 2540, 2539, 2538, 2535, 2533, 1028, 2534])).
% 2.00/1.62 tff(2542,plain,
% 2.00/1.62 (~c1_1(a902)),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[1986, 2541])).
% 2.00/1.62 tff(2543,plain,
% 2.00/1.62 (c2_1(a902)),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[1596, 2541])).
% 2.00/1.62 tff(2544,plain,
% 2.00/1.62 (c0_1(a902)),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[1607, 2541])).
% 2.00/1.62 tff(2545,plain,
% 2.00/1.62 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp27 | c2_1(a908) | c3_1(a908) | c1_1(a902) | (~ndr1_0) | (~c0_1(a902)) | (~c2_1(a902)) | (~c1_1(a908)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp27 | c2_1(a908) | c3_1(a908) | c1_1(a902) | (~ndr1_0) | (~c0_1(a902)) | (~c2_1(a902)) | (~c1_1(a908)))),
% 2.00/1.62 inference(rewrite,[status(thm)],[])).
% 2.00/1.62 tff(2546,plain,
% 2.00/1.62 ((hskp27 | (~ndr1_0) | c2_1(a908) | c3_1(a908) | (~c1_1(a908)) | c1_1(a902) | (~c2_1(a902)) | (~c0_1(a902))) <=> (hskp27 | c2_1(a908) | c3_1(a908) | c1_1(a902) | (~ndr1_0) | (~c0_1(a902)) | (~c2_1(a902)) | (~c1_1(a908)))),
% 2.00/1.62 inference(rewrite,[status(thm)],[])).
% 2.00/1.62 tff(2547,plain,
% 2.00/1.62 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a908) | c3_1(a908) | (~c1_1(a908)) | c1_1(a902) | (~c2_1(a902)) | (~c0_1(a902)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp27 | c2_1(a908) | c3_1(a908) | c1_1(a902) | (~ndr1_0) | (~c0_1(a902)) | (~c2_1(a902)) | (~c1_1(a908))))),
% 2.00/1.62 inference(monotonicity,[status(thm)],[2546])).
% 2.00/1.62 tff(2548,plain,
% 2.00/1.62 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a908) | c3_1(a908) | (~c1_1(a908)) | c1_1(a902) | (~c2_1(a902)) | (~c0_1(a902)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp27 | c2_1(a908) | c3_1(a908) | c1_1(a902) | (~ndr1_0) | (~c0_1(a902)) | (~c2_1(a902)) | (~c1_1(a908)))),
% 2.00/1.62 inference(transitivity,[status(thm)],[2547, 2545])).
% 2.00/1.62 tff(2549,plain,
% 2.00/1.62 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a908) | c3_1(a908) | (~c1_1(a908)) | c1_1(a902) | (~c2_1(a902)) | (~c0_1(a902)))),
% 2.00/1.62 inference(quant_inst,[status(thm)],[])).
% 2.00/1.62 tff(2550,plain,
% 2.00/1.62 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp27 | c2_1(a908) | c3_1(a908) | c1_1(a902) | (~ndr1_0) | (~c0_1(a902)) | (~c2_1(a902)) | (~c1_1(a908))),
% 2.00/1.62 inference(modus_ponens,[status(thm)],[2549, 2548])).
% 2.00/1.62 tff(2551,plain,
% 2.00/1.62 ($false),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[2550, 124, 2502, 2307, 2544, 2543, 2296, 2295, 2542, 42])).
% 2.00/1.62 tff(2552,plain,(hskp5 | hskp12), inference(lemma,lemma(discharge,[]))).
% 2.00/1.62 tff(2553,plain,
% 2.00/1.62 (hskp5),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[2552, 32])).
% 2.00/1.62 tff(2554,plain,
% 2.00/1.62 (~c3_1(a906)),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[300, 2553])).
% 2.00/1.62 tff(2555,plain,
% 2.00/1.62 (c2_1(a906)),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[294, 2553])).
% 2.00/1.62 tff(2556,plain,
% 2.00/1.62 (c0_1(a906)),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[311, 2553])).
% 2.00/1.62 tff(2557,plain,
% 2.00/1.62 (~hskp27),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[176, 168, 32])).
% 2.00/1.62 tff(2558,plain,
% 2.00/1.62 ($false),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[2530, 2557, 168, 32])).
% 2.00/1.62 tff(2559,plain,(hskp11 | hskp12), inference(lemma,lemma(discharge,[]))).
% 2.00/1.62 tff(2560,plain,
% 2.00/1.62 (hskp11),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[2559, 32])).
% 2.00/1.62 tff(2561,plain,
% 2.00/1.62 (~c2_1(a914)),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[69, 2560])).
% 2.00/1.62 tff(2562,plain,
% 2.00/1.62 (c3_1(a914)),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[80, 2560])).
% 2.00/1.62 tff(2563,plain,
% 2.00/1.62 (c0_1(a914)),
% 2.00/1.62 inference(unit_resolution,[status(thm)],[91, 2560])).
% 2.00/1.62 tff(2564,plain,
% 2.00/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a908) | c3_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c1_1(a908)) | (~c3_1(a914)) | (~c1_1(a914)) | (~c0_1(a914)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a908) | c3_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c1_1(a908)) | (~c3_1(a914)) | (~c1_1(a914)) | (~c0_1(a914)))),
% 2.00/1.62 inference(rewrite,[status(thm)],[])).
% 2.00/1.62 tff(2565,plain,
% 2.00/1.62 (((~ndr1_0) | (~c3_1(a914)) | (~c1_1(a914)) | (~c0_1(a914)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908))) <=> (c2_1(a908) | c3_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c1_1(a908)) | (~c3_1(a914)) | (~c1_1(a914)) | (~c0_1(a914)))),
% 2.00/1.62 inference(rewrite,[status(thm)],[])).
% 2.00/1.62 tff(2566,plain,
% 2.00/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a914)) | (~c1_1(a914)) | (~c0_1(a914)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a908) | c3_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c1_1(a908)) | (~c3_1(a914)) | (~c1_1(a914)) | (~c0_1(a914))))),
% 2.00/1.62 inference(monotonicity,[status(thm)],[2565])).
% 2.00/1.62 tff(2567,plain,
% 2.00/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a914)) | (~c1_1(a914)) | (~c0_1(a914)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a908) | c3_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c1_1(a908)) | (~c3_1(a914)) | (~c1_1(a914)) | (~c0_1(a914)))),
% 2.00/1.63 inference(transitivity,[status(thm)],[2566, 2564])).
% 2.00/1.63 tff(2568,plain,
% 2.00/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a914)) | (~c1_1(a914)) | (~c0_1(a914)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a908) | c2_1(a908) | (~c1_1(a908)))),
% 2.00/1.63 inference(quant_inst,[status(thm)],[])).
% 2.00/1.63 tff(2569,plain,
% 2.00/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a908) | c3_1(a908) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c1_1(a908)) | (~c3_1(a914)) | (~c1_1(a914)) | (~c0_1(a914))),
% 2.00/1.63 inference(modus_ponens,[status(thm)],[2568, 2567])).
% 2.00/1.63 tff(2570,plain,
% 2.00/1.63 (~c1_1(a914)),
% 2.00/1.63 inference(unit_resolution,[status(thm)],[2569, 124, 429, 428, 485, 323, 324, 474, 468, 325, 31])).
% 2.00/1.63 tff(2571,plain,
% 2.00/1.63 (hskp28 | c1_1(a914)),
% 2.00/1.63 inference(unit_resolution,[status(thm)],[2348, 124, 429, 428, 2042])).
% 2.00/1.63 tff(2572,plain,
% 2.00/1.63 (hskp28),
% 2.00/1.63 inference(unit_resolution,[status(thm)],[2571, 2570])).
% 2.00/1.63 tff(2573,plain,
% 2.00/1.63 (c1_1(a916)),
% 2.00/1.63 inference(unit_resolution,[status(thm)],[282, 2572])).
% 2.00/1.63 tff(2574,plain,
% 2.00/1.63 (c0_1(a916)),
% 2.00/1.63 inference(unit_resolution,[status(thm)],[260, 2572])).
% 2.00/1.63 tff(2575,plain,
% 2.00/1.63 (c3_1(a916)),
% 2.00/1.63 inference(unit_resolution,[status(thm)],[271, 2572])).
% 2.00/1.63 tff(2576,plain,
% 2.00/1.63 ($false),
% 2.00/1.63 inference(unit_resolution,[status(thm)],[496, 2575, 2574, 323, 324, 462, 2573, 325])).
% 2.00/1.63 tff(2577,plain,((~hskp7) | (~c0_1(a906)) | (~c2_1(a906)) | c3_1(a906) | (~c0_1(a914)) | (~c3_1(a914))), inference(lemma,lemma(discharge,[]))).
% 2.00/1.63 tff(2578,plain,
% 2.00/1.63 (~hskp7),
% 2.00/1.63 inference(unit_resolution,[status(thm)],[2577, 2556, 2555, 2554, 2563, 2562])).
% 2.00/1.63 tff(2579,assumption,(~hskp28), introduced(assumption)).
% 2.00/1.63 tff(2580,assumption,(hskp13), introduced(assumption)).
% 2.00/1.63 tff(2581,plain,
% 2.00/1.63 (~c3_1(a921)),
% 2.00/1.63 inference(unit_resolution,[status(thm)],[225, 2580])).
% 2.00/1.63 tff(2582,plain,
% 2.00/1.63 (c2_1(a921)),
% 2.00/1.63 inference(unit_resolution,[status(thm)],[242, 2580])).
% 2.00/1.63 tff(2583,plain,
% 2.00/1.63 (~c0_1(a921)),
% 2.00/1.63 inference(unit_resolution,[status(thm)],[231, 2580])).
% 2.00/1.63 tff(2584,plain,
% 2.00/1.63 ($false),
% 2.00/1.63 inference(unit_resolution,[status(thm)],[1140, 2583, 2582, 323, 665, 1055, 1124, 2581, 325, 324])).
% 2.00/1.63 tff(2585,plain,((~hskp13) | (~c0_1(a906)) | c0_1(a912) | c1_1(a912) | c2_1(a912) | c3_1(a906) | (~c2_1(a906))), inference(lemma,lemma(discharge,[]))).
% 2.00/1.63 tff(2586,plain,
% 2.00/1.63 (~hskp13),
% 2.00/1.63 inference(unit_resolution,[status(thm)],[2585, 1124, 665, 1055, 2556, 2554, 2555])).
% 2.00/1.63 tff(2587,plain,
% 2.00/1.63 (hskp27),
% 2.00/1.63 inference(unit_resolution,[status(thm)],[2270, 1056])).
% 2.00/1.63 tff(2588,plain,
% 2.00/1.63 (c3_1(a900)),
% 2.00/1.63 inference(unit_resolution,[status(thm)],[144, 2587])).
% 2.00/1.63 tff(2589,plain,
% 2.00/1.63 (c2_1(a900)),
% 2.00/1.63 inference(unit_resolution,[status(thm)],[155, 2587])).
% 2.00/1.63 tff(2590,plain,
% 2.00/1.63 (((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | c0_1(a900))) <=> ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp13 | hskp7 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | c0_1(a900))),
% 2.00/1.63 inference(rewrite,[status(thm)],[])).
% 2.00/1.63 tff(2591,plain,
% 2.00/1.63 ((hskp13 | hskp7 | (~ndr1_0) | c0_1(a900) | (~c2_1(a900)) | (~c3_1(a900))) <=> (hskp13 | hskp7 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | c0_1(a900))),
% 2.00/1.63 inference(rewrite,[status(thm)],[])).
% 2.00/1.63 tff(2592,plain,
% 2.00/1.63 (((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | (~ndr1_0) | c0_1(a900) | (~c2_1(a900)) | (~c3_1(a900)))) <=> ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | c0_1(a900)))),
% 2.00/1.63 inference(monotonicity,[status(thm)],[2591])).
% 2.00/1.63 tff(2593,plain,
% 2.00/1.63 (((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | (~ndr1_0) | c0_1(a900) | (~c2_1(a900)) | (~c3_1(a900)))) <=> ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp13 | hskp7 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | c0_1(a900))),
% 2.00/1.63 inference(transitivity,[status(thm)],[2592, 2590])).
% 2.00/1.63 tff(2594,plain,
% 2.00/1.63 ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | (~ndr1_0) | c0_1(a900) | (~c2_1(a900)) | (~c3_1(a900)))),
% 2.00/1.63 inference(quant_inst,[status(thm)],[])).
% 2.00/1.63 tff(2595,plain,
% 2.00/1.63 ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp13 | hskp7 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | c0_1(a900)),
% 2.00/1.63 inference(modus_ponens,[status(thm)],[2594, 2593])).
% 2.00/1.63 tff(2596,plain,
% 2.00/1.63 (hskp13 | c0_1(a900)),
% 2.00/1.63 inference(unit_resolution,[status(thm)],[2595, 124, 21, 2589, 2588, 20])).
% 2.00/1.63 tff(2597,plain,
% 2.00/1.63 (c0_1(a900)),
% 2.00/1.63 inference(unit_resolution,[status(thm)],[2596, 2586])).
% 2.00/1.63 tff(2598,assumption,(hskp15), introduced(assumption)).
% 2.00/1.63 tff(2599,plain,
% 2.00/1.63 (~c0_1(a924)),
% 2.00/1.63 inference(unit_resolution,[status(thm)],[1267, 2598])).
% 2.00/1.63 tff(2600,plain,
% 2.00/1.63 (c2_1(a924)),
% 2.00/1.63 inference(unit_resolution,[status(thm)],[1280, 2598])).
% 2.00/1.63 tff(2601,plain,
% 2.00/1.63 (((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | c0_1(a924) | (~ndr1_0) | (~c2_1(a924)) | (~c3_1(a924)))) <=> ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp13 | hskp7 | c0_1(a924) | (~ndr1_0) | (~c2_1(a924)) | (~c3_1(a924)))),
% 2.00/1.63 inference(rewrite,[status(thm)],[])).
% 2.00/1.63 tff(2602,plain,
% 2.00/1.63 ((hskp13 | hskp7 | (~ndr1_0) | c0_1(a924) | (~c2_1(a924)) | (~c3_1(a924))) <=> (hskp13 | hskp7 | c0_1(a924) | (~ndr1_0) | (~c2_1(a924)) | (~c3_1(a924)))),
% 2.00/1.63 inference(rewrite,[status(thm)],[])).
% 2.00/1.63 tff(2603,plain,
% 2.00/1.63 (((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | (~ndr1_0) | c0_1(a924) | (~c2_1(a924)) | (~c3_1(a924)))) <=> ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | c0_1(a924) | (~ndr1_0) | (~c2_1(a924)) | (~c3_1(a924))))),
% 2.00/1.63 inference(monotonicity,[status(thm)],[2602])).
% 2.00/1.63 tff(2604,plain,
% 2.00/1.63 (((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | (~ndr1_0) | c0_1(a924) | (~c2_1(a924)) | (~c3_1(a924)))) <=> ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp13 | hskp7 | c0_1(a924) | (~ndr1_0) | (~c2_1(a924)) | (~c3_1(a924)))),
% 2.00/1.63 inference(transitivity,[status(thm)],[2603, 2601])).
% 2.00/1.63 tff(2605,plain,
% 2.00/1.63 ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | (~ndr1_0) | c0_1(a924) | (~c2_1(a924)) | (~c3_1(a924)))),
% 2.00/1.63 inference(quant_inst,[status(thm)],[])).
% 2.00/1.63 tff(2606,plain,
% 2.00/1.63 ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp13 | hskp7 | c0_1(a924) | (~ndr1_0) | (~c2_1(a924)) | (~c3_1(a924))),
% 2.00/1.63 inference(modus_ponens,[status(thm)],[2605, 2604])).
% 2.00/1.63 tff(2607,plain,
% 2.00/1.63 (~c3_1(a924)),
% 2.00/1.63 inference(unit_resolution,[status(thm)],[2606, 124, 1323, 21, 2600, 2599, 20])).
% 2.00/1.63 tff(2608,plain,
% 2.00/1.63 (((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp28 | hskp12 | c0_1(a924) | (~ndr1_0) | c3_1(a924) | (~c2_1(a924)))) <=> ((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp28 | hskp12 | c0_1(a924) | (~ndr1_0) | c3_1(a924) | (~c2_1(a924)))),
% 2.00/1.63 inference(rewrite,[status(thm)],[])).
% 2.00/1.63 tff(2609,plain,
% 2.00/1.63 ((hskp28 | hskp12 | (~ndr1_0) | c0_1(a924) | c3_1(a924) | (~c2_1(a924))) <=> (hskp28 | hskp12 | c0_1(a924) | (~ndr1_0) | c3_1(a924) | (~c2_1(a924)))),
% 2.00/1.63 inference(rewrite,[status(thm)],[])).
% 2.00/1.63 tff(2610,plain,
% 2.00/1.63 (((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp28 | hskp12 | (~ndr1_0) | c0_1(a924) | c3_1(a924) | (~c2_1(a924)))) <=> ((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp28 | hskp12 | c0_1(a924) | (~ndr1_0) | c3_1(a924) | (~c2_1(a924))))),
% 2.00/1.63 inference(monotonicity,[status(thm)],[2609])).
% 2.00/1.63 tff(2611,plain,
% 2.00/1.63 (((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp28 | hskp12 | (~ndr1_0) | c0_1(a924) | c3_1(a924) | (~c2_1(a924)))) <=> ((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp28 | hskp12 | c0_1(a924) | (~ndr1_0) | c3_1(a924) | (~c2_1(a924)))),
% 2.00/1.63 inference(transitivity,[status(thm)],[2610, 2608])).
% 2.00/1.63 tff(2612,plain,
% 2.00/1.63 ((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp28 | hskp12 | (~ndr1_0) | c0_1(a924) | c3_1(a924) | (~c2_1(a924)))),
% 2.00/1.63 inference(quant_inst,[status(thm)],[])).
% 2.00/1.63 tff(2613,plain,
% 2.00/1.63 ((~![U: $i] : (hskp28 | hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp28 | hskp12 | c0_1(a924) | (~ndr1_0) | c3_1(a924) | (~c2_1(a924))),
% 2.00/1.63 inference(modus_ponens,[status(thm)],[2612, 2611])).
% 2.00/1.63 tff(2614,plain,
% 2.00/1.63 ($false),
% 2.00/1.63 inference(unit_resolution,[status(thm)],[2613, 124, 2579, 32, 2600, 2599, 208, 2607])).
% 2.00/1.63 tff(2615,plain,((~hskp15) | hskp28 | hskp12 | hskp13 | hskp7), inference(lemma,lemma(discharge,[]))).
% 2.00/1.63 tff(2616,plain,
% 2.00/1.63 (~hskp15),
% 2.00/1.63 inference(unit_resolution,[status(thm)],[2615, 2586, 32, 2579, 21])).
% 2.00/1.63 tff(2617,plain,
% 2.00/1.63 (^[U: $i] : refl((hskp23 | hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp23 | hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))),
% 2.00/1.63 inference(bind,[status(th)],[])).
% 2.00/1.63 tff(2618,plain,
% 2.00/1.63 (![U: $i] : (hskp23 | hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp23 | hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 2.00/1.63 inference(quant_intro,[status(thm)],[2617])).
% 2.00/1.63 tff(2619,plain,
% 2.00/1.63 (![U: $i] : (hskp23 | hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp23 | hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 2.00/1.63 inference(rewrite,[status(thm)],[])).
% 2.00/1.63 tff(2620,plain,
% 2.00/1.63 (^[U: $i] : 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)) | hskp23) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp23))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp23) <=> (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp23) <=> (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp23) | hskp15) <=> ((hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp15))), rewrite(((hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp15) <=> (hskp23 | hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp23) | hskp15) <=> (hskp23 | hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))))),
% 2.00/1.63 inference(bind,[status(th)],[])).
% 2.00/1.63 tff(2621,plain,
% 2.00/1.63 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp23) | hskp15) <=> ![U: $i] : (hskp23 | hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 2.00/1.63 inference(quant_intro,[status(thm)],[2620])).
% 2.00/1.63 tff(2622,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp23) | hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause157')).
% 2.00/1.63 tff(2623,plain,
% 2.00/1.63 (![U: $i] : (hskp23 | hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 2.00/1.63 inference(modus_ponens,[status(thm)],[2622, 2621])).
% 2.00/1.63 tff(2624,plain,
% 2.00/1.63 (![U: $i] : (hskp23 | hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 2.00/1.63 inference(modus_ponens,[status(thm)],[2623, 2619])).
% 2.00/1.63 tff(2625,plain,(
% 2.00/1.63 ![U: $i] : (hskp23 | hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 2.00/1.63 inference(skolemize,[status(sab)],[2624])).
% 2.00/1.63 tff(2626,plain,
% 2.00/1.63 (![U: $i] : (hskp23 | hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 2.00/1.63 inference(modus_ponens,[status(thm)],[2625, 2618])).
% 2.00/1.63 tff(2627,plain,
% 2.00/1.63 (((~![U: $i] : (hskp23 | hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | hskp15 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)))) <=> ((~![U: $i] : (hskp23 | hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | hskp15 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)))),
% 2.00/1.63 inference(rewrite,[status(thm)],[])).
% 2.00/1.63 tff(2628,plain,
% 2.00/1.63 ((~![U: $i] : (hskp23 | hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | hskp15 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)))),
% 2.00/1.63 inference(quant_inst,[status(thm)],[])).
% 2.00/1.63 tff(2629,plain,
% 2.00/1.63 ((~![U: $i] : (hskp23 | hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | hskp15 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900))),
% 2.00/1.63 inference(modus_ponens,[status(thm)],[2628, 2627])).
% 2.00/1.63 tff(2630,plain,
% 2.00/1.63 (hskp23 | hskp15 | (~c0_1(a900))),
% 2.00/1.63 inference(unit_resolution,[status(thm)],[2629, 124, 2589, 2588, 2626])).
% 2.00/1.63 tff(2631,plain,
% 2.00/1.63 (hskp23),
% 2.00/1.63 inference(unit_resolution,[status(thm)],[2630, 2616, 2597])).
% 2.00/1.63 tff(2632,plain,
% 2.00/1.63 (((~hskp23) | (~c0_1(a954))) <=> ((~hskp23) | (~c0_1(a954)))),
% 2.00/1.63 inference(rewrite,[status(thm)],[])).
% 2.00/1.63 tff(2633,plain,
% 2.00/1.63 (((~c0_1(a954)) | (~hskp23)) <=> ((~hskp23) | (~c0_1(a954)))),
% 2.00/1.63 inference(rewrite,[status(thm)],[])).
% 2.00/1.63 tff(2634,axiom,((~c0_1(a954)) | (~hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause87')).
% 2.00/1.63 tff(2635,plain,
% 2.00/1.63 ((~hskp23) | (~c0_1(a954))),
% 2.00/1.63 inference(modus_ponens,[status(thm)],[2634, 2633])).
% 2.00/1.63 tff(2636,plain,
% 2.00/1.63 ((~hskp23) | (~c0_1(a954))),
% 2.00/1.63 inference(modus_ponens,[status(thm)],[2635, 2632])).
% 2.00/1.63 tff(2637,plain,
% 2.00/1.63 (~c0_1(a954)),
% 2.00/1.63 inference(unit_resolution,[status(thm)],[2636, 2631])).
% 2.00/1.63 tff(2638,plain,
% 2.00/1.63 (((~hskp23) | c3_1(a954)) <=> ((~hskp23) | c3_1(a954))),
% 2.00/1.63 inference(rewrite,[status(thm)],[])).
% 2.00/1.63 tff(2639,axiom,((~hskp23) | c3_1(a954)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause52')).
% 2.00/1.63 tff(2640,plain,
% 2.00/1.63 ((~hskp23) | c3_1(a954)),
% 2.00/1.63 inference(modus_ponens,[status(thm)],[2639, 2638])).
% 2.00/1.63 tff(2641,plain,
% 2.00/1.63 ((~hskp23) | c3_1(a954)),
% 2.00/1.63 inference(modus_ponens,[status(thm)],[2640, 2638])).
% 2.00/1.63 tff(2642,plain,
% 2.00/1.63 ((~hskp23) | c3_1(a954)),
% 2.00/1.63 inference(modus_ponens,[status(thm)],[2641, 2638])).
% 2.00/1.63 tff(2643,plain,
% 2.00/1.63 ((~hskp23) | c3_1(a954)),
% 2.00/1.63 inference(modus_ponens,[status(thm)],[2642, 2638])).
% 2.00/1.63 tff(2644,plain,
% 2.00/1.63 ((~hskp23) | c3_1(a954)),
% 2.00/1.63 inference(modus_ponens,[status(thm)],[2643, 2638])).
% 2.00/1.63 tff(2645,plain,
% 2.00/1.63 ((~hskp23) | c3_1(a954)),
% 2.00/1.63 inference(modus_ponens,[status(thm)],[2644, 2638])).
% 2.00/1.63 tff(2646,plain,
% 2.00/1.63 ((~hskp23) | c3_1(a954)),
% 2.00/1.63 inference(modus_ponens,[status(thm)],[2645, 2638])).
% 2.00/1.63 tff(2647,plain,
% 2.00/1.63 ((~hskp23) | c3_1(a954)),
% 2.00/1.63 inference(modus_ponens,[status(thm)],[2646, 2638])).
% 2.00/1.63 tff(2648,plain,
% 2.00/1.63 (c3_1(a954)),
% 2.00/1.63 inference(unit_resolution,[status(thm)],[2647, 2631])).
% 2.00/1.63 tff(2649,plain,
% 2.00/1.63 (((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | c0_1(a954) | (~ndr1_0) | (~c2_1(a954)) | (~c3_1(a954)))) <=> ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp13 | hskp7 | c0_1(a954) | (~ndr1_0) | (~c2_1(a954)) | (~c3_1(a954)))),
% 2.00/1.63 inference(rewrite,[status(thm)],[])).
% 2.00/1.63 tff(2650,plain,
% 2.00/1.63 ((hskp13 | hskp7 | (~ndr1_0) | c0_1(a954) | (~c2_1(a954)) | (~c3_1(a954))) <=> (hskp13 | hskp7 | c0_1(a954) | (~ndr1_0) | (~c2_1(a954)) | (~c3_1(a954)))),
% 2.00/1.63 inference(rewrite,[status(thm)],[])).
% 2.00/1.63 tff(2651,plain,
% 2.00/1.63 (((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | (~ndr1_0) | c0_1(a954) | (~c2_1(a954)) | (~c3_1(a954)))) <=> ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | c0_1(a954) | (~ndr1_0) | (~c2_1(a954)) | (~c3_1(a954))))),
% 2.00/1.63 inference(monotonicity,[status(thm)],[2650])).
% 2.00/1.63 tff(2652,plain,
% 2.00/1.63 (((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | (~ndr1_0) | c0_1(a954) | (~c2_1(a954)) | (~c3_1(a954)))) <=> ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp13 | hskp7 | c0_1(a954) | (~ndr1_0) | (~c2_1(a954)) | (~c3_1(a954)))),
% 2.00/1.63 inference(transitivity,[status(thm)],[2651, 2649])).
% 2.00/1.63 tff(2653,plain,
% 2.00/1.63 ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp13 | hskp7 | (~ndr1_0) | c0_1(a954) | (~c2_1(a954)) | (~c3_1(a954)))),
% 2.00/1.63 inference(quant_inst,[status(thm)],[])).
% 2.00/1.63 tff(2654,plain,
% 2.00/1.63 ((~![U: $i] : (hskp13 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp13 | hskp7 | c0_1(a954) | (~ndr1_0) | (~c2_1(a954)) | (~c3_1(a954))),
% 2.00/1.63 inference(modus_ponens,[status(thm)],[2653, 2652])).
% 2.00/1.63 tff(2655,plain,
% 2.00/1.63 (~c2_1(a954)),
% 2.00/1.63 inference(unit_resolution,[status(thm)],[2654, 124, 2586, 21, 2648, 2637, 20])).
% 2.00/1.63 tff(2656,plain,
% 2.00/1.63 (c1_1(a900)),
% 2.00/1.63 inference(unit_resolution,[status(thm)],[166, 2587])).
% 2.00/1.63 tff(2657,plain,
% 2.00/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a912) | c2_1(a912) | c0_1(a954) | c0_1(a912) | (~ndr1_0) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c2_1(a954) | (~c3_1(a954)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c0_1(a954) | c0_1(a912) | (~ndr1_0) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c2_1(a954) | (~c3_1(a954)))),
% 2.00/1.63 inference(rewrite,[status(thm)],[])).
% 2.00/1.63 tff(2658,plain,
% 2.00/1.63 (((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a954) | c0_1(a954) | (~c3_1(a954)) | c1_1(a912) | c0_1(a912) | c2_1(a912)) <=> (c1_1(a912) | c2_1(a912) | c0_1(a954) | c0_1(a912) | (~ndr1_0) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c2_1(a954) | (~c3_1(a954)))),
% 2.00/1.63 inference(rewrite,[status(thm)],[])).
% 2.00/1.63 tff(2659,plain,
% 2.00/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a954) | c0_1(a954) | (~c3_1(a954)) | c1_1(a912) | c0_1(a912) | c2_1(a912))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a912) | c2_1(a912) | c0_1(a954) | c0_1(a912) | (~ndr1_0) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c2_1(a954) | (~c3_1(a954))))),
% 2.00/1.63 inference(monotonicity,[status(thm)],[2658])).
% 2.00/1.63 tff(2660,plain,
% 2.00/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a954) | c0_1(a954) | (~c3_1(a954)) | c1_1(a912) | c0_1(a912) | c2_1(a912))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c0_1(a954) | c0_1(a912) | (~ndr1_0) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c2_1(a954) | (~c3_1(a954)))),
% 2.00/1.63 inference(transitivity,[status(thm)],[2659, 2657])).
% 2.00/1.63 tff(2661,plain,
% 2.00/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a954) | c0_1(a954) | (~c3_1(a954)) | c1_1(a912) | c0_1(a912) | c2_1(a912))),
% 2.00/1.63 inference(quant_inst,[status(thm)],[])).
% 2.00/1.63 tff(2662,plain,
% 2.00/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c0_1(a954) | c0_1(a912) | (~ndr1_0) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c2_1(a954) | (~c3_1(a954))),
% 2.00/1.63 inference(modus_ponens,[status(thm)],[2661, 2660])).
% 2.00/1.63 tff(2663,plain,
% 2.00/1.63 ($false),
% 2.00/1.63 inference(unit_resolution,[status(thm)],[2662, 124, 2656, 2588, 2648, 1055, 1124, 2637, 665, 1665, 2597, 2655])).
% 2.00/1.63 tff(2664,plain,(c2_1(a912) | c1_1(a912) | c0_1(a912) | hskp7 | hskp12 | hskp28), inference(lemma,lemma(discharge,[]))).
% 2.00/1.63 tff(2665,plain,
% 2.00/1.63 (c2_1(a912)),
% 2.00/1.63 inference(unit_resolution,[status(thm)],[2664, 2579, 665, 21, 32, 1055])).
% 2.00/1.63 tff(2666,plain,
% 2.00/1.63 (hskp28 | (~c2_1(a912)) | c3_1(a912)),
% 2.00/1.63 inference(unit_resolution,[status(thm)],[2287, 124, 32, 665, 208])).
% 2.00/1.63 tff(2667,plain,
% 2.00/1.63 (c3_1(a912)),
% 2.00/1.63 inference(unit_resolution,[status(thm)],[2666, 2665, 2579])).
% 2.00/1.63 tff(2668,plain,
% 2.00/1.63 (hskp13 | hskp7 | (~c2_1(a912)) | (~c3_1(a912))),
% 2.00/1.63 inference(unit_resolution,[status(thm)],[1333, 124, 665, 20])).
% 2.00/1.63 tff(2669,plain,
% 2.00/1.63 (hskp13),
% 2.00/1.63 inference(unit_resolution,[status(thm)],[2668, 2665, 21, 2667])).
% 2.00/1.63 tff(2670,plain,
% 2.00/1.63 (~c3_1(a921)),
% 2.00/1.63 inference(unit_resolution,[status(thm)],[225, 2669])).
% 2.00/1.63 tff(2671,plain,
% 2.00/1.63 (~c0_1(a921)),
% 2.00/1.63 inference(unit_resolution,[status(thm)],[231, 2669])).
% 2.00/1.63 tff(2672,plain,
% 2.00/1.63 (c2_1(a921)),
% 2.00/1.63 inference(unit_resolution,[status(thm)],[242, 2669])).
% 2.00/1.63 tff(2673,plain,
% 2.00/1.63 ($false),
% 2.00/1.63 inference(unit_resolution,[status(thm)],[249, 124, 2579, 32, 2672, 2671, 2670, 208])).
% 2.00/1.63 tff(2674,plain,(hskp28 | hskp12 | hskp7 | c0_1(a912) | c1_1(a912)), inference(lemma,lemma(discharge,[]))).
% 2.00/1.63 tff(2675,plain,
% 2.00/1.63 (hskp28),
% 2.00/1.63 inference(unit_resolution,[status(thm)],[2674, 1055, 21, 665, 32])).
% 2.00/1.63 tff(2676,plain,
% 2.00/1.63 (c3_1(a916)),
% 2.00/1.63 inference(unit_resolution,[status(thm)],[271, 2675])).
% 2.00/1.63 tff(2677,plain,
% 2.00/1.63 (c1_1(a916)),
% 2.00/1.63 inference(unit_resolution,[status(thm)],[282, 2675])).
% 2.00/1.63 tff(2678,plain,
% 2.00/1.63 (c0_1(a916)),
% 2.00/1.63 inference(unit_resolution,[status(thm)],[260, 2675])).
% 2.00/1.63 tff(2679,plain,
% 2.00/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a946) | c3_1(a946) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)) | (~c1_1(a946)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a946) | c3_1(a946) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)) | (~c1_1(a946)))),
% 2.00/1.63 inference(rewrite,[status(thm)],[])).
% 2.00/1.63 tff(2680,plain,
% 2.00/1.63 (((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a946) | c2_1(a946) | (~c1_1(a946))) <=> (c2_1(a946) | c3_1(a946) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)) | (~c1_1(a946)))),
% 2.00/1.63 inference(rewrite,[status(thm)],[])).
% 2.00/1.63 tff(2681,plain,
% 2.00/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a946) | c2_1(a946) | (~c1_1(a946)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a946) | c3_1(a946) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)) | (~c1_1(a946))))),
% 2.00/1.63 inference(monotonicity,[status(thm)],[2680])).
% 2.00/1.63 tff(2682,plain,
% 2.00/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a946) | c2_1(a946) | (~c1_1(a946)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a946) | c3_1(a946) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)) | (~c1_1(a946)))),
% 2.00/1.63 inference(transitivity,[status(thm)],[2681, 2679])).
% 2.00/1.63 tff(2683,plain,
% 2.00/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a946) | c2_1(a946) | (~c1_1(a946)))),
% 2.00/1.63 inference(quant_inst,[status(thm)],[])).
% 2.00/1.63 tff(2684,plain,
% 2.00/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a946) | c3_1(a946) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)) | (~c1_1(a946))),
% 2.00/1.63 inference(modus_ponens,[status(thm)],[2683, 2682])).
% 2.00/1.63 tff(2685,plain,
% 2.00/1.63 (~c1_1(a946)),
% 2.00/1.63 inference(unit_resolution,[status(thm)],[2684, 124, 2678, 2677, 2676, 2556, 2555, 2257, 2251, 2554, 31])).
% 2.00/1.63 tff(2686,plain,
% 2.00/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a946) | c2_1(a946) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c1_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a946) | c2_1(a946) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c1_1(a946))),
% 2.00/1.63 inference(rewrite,[status(thm)],[])).
% 2.00/1.63 tff(2687,plain,
% 2.00/1.63 (((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a946) | c0_1(a946) | c2_1(a946)) <=> (c0_1(a946) | c2_1(a946) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c1_1(a946))),
% 2.00/1.63 inference(rewrite,[status(thm)],[])).
% 2.00/1.63 tff(2688,plain,
% 2.00/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a946) | c0_1(a946) | c2_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a946) | c2_1(a946) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c1_1(a946)))),
% 2.00/1.63 inference(monotonicity,[status(thm)],[2687])).
% 2.00/1.63 tff(2689,plain,
% 2.00/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a946) | c0_1(a946) | c2_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a946) | c2_1(a946) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c1_1(a946))),
% 2.00/1.63 inference(transitivity,[status(thm)],[2688, 2686])).
% 2.00/1.63 tff(2690,plain,
% 2.00/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a906) | (~c2_1(a906)) | (~c1_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a946) | c0_1(a946) | c2_1(a946))),
% 2.00/1.63 inference(quant_inst,[status(thm)],[])).
% 2.00/1.63 tff(2691,plain,
% 2.00/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a946) | c2_1(a946) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c1_1(a906)) | (~c0_1(a906)) | c1_1(a946)),
% 2.00/1.63 inference(modus_ponens,[status(thm)],[2690, 2689])).
% 2.00/1.63 tff(2692,plain,
% 2.00/1.63 (~c1_1(a906)),
% 2.00/1.63 inference(unit_resolution,[status(thm)],[2691, 124, 2556, 2555, 2263, 2257, 2554, 520, 2685])).
% 2.00/1.63 tff(2693,plain,
% 2.00/1.63 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V)) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V)))),
% 2.00/1.64 inference(bind,[status(th)],[])).
% 2.00/1.64 tff(2694,plain,
% 2.00/1.64 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))),
% 2.00/1.64 inference(quant_intro,[status(thm)],[2693])).
% 2.00/1.64 tff(2695,plain,
% 2.00/1.64 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))),
% 2.00/1.64 inference(rewrite,[status(thm)],[])).
% 2.00/1.64 tff(2696,plain,
% 2.00/1.64 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | 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)) | c0_1(V) | c1_1(V))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V)) | hskp0))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))))),
% 2.00/1.64 inference(bind,[status(th)],[])).
% 2.00/1.64 tff(2697,plain,
% 2.00/1.64 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))),
% 2.00/1.64 inference(quant_intro,[status(thm)],[2696])).
% 2.00/1.64 tff(2698,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause161')).
% 2.00/1.64 tff(2699,plain,
% 2.00/1.64 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))),
% 2.00/1.64 inference(modus_ponens,[status(thm)],[2698, 2697])).
% 2.00/1.64 tff(2700,plain,
% 2.00/1.64 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))),
% 2.00/1.64 inference(modus_ponens,[status(thm)],[2699, 2695])).
% 2.00/1.64 tff(2701,plain,(
% 2.00/1.64 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))),
% 2.00/1.64 inference(skolemize,[status(sab)],[2700])).
% 2.00/1.64 tff(2702,plain,
% 2.00/1.64 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))),
% 2.00/1.64 inference(modus_ponens,[status(thm)],[2701, 2694])).
% 2.00/1.64 tff(2703,plain,
% 2.00/1.64 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | c0_1(a946) | c2_1(a946) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914)) | c1_1(a946))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | hskp0 | c0_1(a946) | c2_1(a946) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914)) | c1_1(a946))),
% 2.00/1.64 inference(rewrite,[status(thm)],[])).
% 2.00/1.64 tff(2704,plain,
% 2.00/1.64 ((hskp0 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c0_1(a914)) | c2_1(a946) | c0_1(a946) | c1_1(a946)) <=> (hskp0 | c0_1(a946) | c2_1(a946) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914)) | c1_1(a946))),
% 2.00/1.64 inference(rewrite,[status(thm)],[])).
% 2.00/1.64 tff(2705,plain,
% 2.00/1.64 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c0_1(a914)) | c2_1(a946) | c0_1(a946) | c1_1(a946))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | c0_1(a946) | c2_1(a946) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914)) | c1_1(a946)))),
% 2.00/1.64 inference(monotonicity,[status(thm)],[2704])).
% 2.00/1.64 tff(2706,plain,
% 2.00/1.64 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c0_1(a914)) | c2_1(a946) | c0_1(a946) | c1_1(a946))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | hskp0 | c0_1(a946) | c2_1(a946) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914)) | c1_1(a946))),
% 2.00/1.64 inference(transitivity,[status(thm)],[2705, 2703])).
% 2.00/1.64 tff(2707,plain,
% 2.00/1.64 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c0_1(a914)) | c2_1(a946) | c0_1(a946) | c1_1(a946))),
% 2.00/1.64 inference(quant_inst,[status(thm)],[])).
% 2.00/1.64 tff(2708,plain,
% 2.00/1.64 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | hskp0 | c0_1(a946) | c2_1(a946) | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914)) | c1_1(a946)),
% 2.00/1.64 inference(modus_ponens,[status(thm)],[2707, 2706])).
% 2.00/1.64 tff(2709,plain,
% 2.00/1.64 (hskp0 | c1_1(a946)),
% 2.00/1.64 inference(unit_resolution,[status(thm)],[2708, 124, 2563, 2562, 2263, 2257, 2561, 2702])).
% 2.00/1.64 tff(2710,plain,
% 2.00/1.64 (hskp0),
% 2.00/1.64 inference(unit_resolution,[status(thm)],[2709, 2685])).
% 2.00/1.64 tff(2711,plain,
% 2.00/1.64 (~c3_1(a901)),
% 2.00/1.64 inference(unit_resolution,[status(thm)],[651, 2710])).
% 2.00/1.64 tff(2712,plain,
% 2.00/1.64 (~c0_1(a901)),
% 2.00/1.64 inference(unit_resolution,[status(thm)],[663, 2710])).
% 2.00/1.64 tff(2713,plain,
% 2.00/1.64 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a946) | c2_1(a946) | c3_1(a906) | c0_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | c1_1(a906) | (~c0_1(a906)) | c1_1(a946))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a946) | c2_1(a946) | c3_1(a906) | c0_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | c1_1(a906) | (~c0_1(a906)) | c1_1(a946))),
% 2.00/1.64 inference(rewrite,[status(thm)],[])).
% 2.00/1.64 tff(2714,plain,
% 2.00/1.64 (((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a901) | c0_1(a901) | (~c2_1(a901)) | c1_1(a946) | c0_1(a946) | c2_1(a946)) <=> (c0_1(a946) | c2_1(a946) | c3_1(a906) | c0_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | c1_1(a906) | (~c0_1(a906)) | c1_1(a946))),
% 2.00/1.64 inference(rewrite,[status(thm)],[])).
% 2.00/1.64 tff(2715,plain,
% 2.00/1.64 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a901) | c0_1(a901) | (~c2_1(a901)) | c1_1(a946) | c0_1(a946) | c2_1(a946))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a946) | c2_1(a946) | c3_1(a906) | c0_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | c1_1(a906) | (~c0_1(a906)) | c1_1(a946)))),
% 2.00/1.64 inference(monotonicity,[status(thm)],[2714])).
% 2.00/1.64 tff(2716,plain,
% 2.00/1.64 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a901) | c0_1(a901) | (~c2_1(a901)) | c1_1(a946) | c0_1(a946) | c2_1(a946))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a946) | c2_1(a946) | c3_1(a906) | c0_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | c1_1(a906) | (~c0_1(a906)) | c1_1(a946))),
% 2.00/1.64 inference(transitivity,[status(thm)],[2715, 2713])).
% 2.00/1.64 tff(2717,plain,
% 2.00/1.64 ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a901) | c0_1(a901) | (~c2_1(a901)) | c1_1(a946) | c0_1(a946) | c2_1(a946))),
% 2.00/1.64 inference(quant_inst,[status(thm)],[])).
% 2.00/1.64 tff(2718,plain,
% 2.00/1.64 ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a946) | c2_1(a946) | c3_1(a906) | c0_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | c1_1(a906) | (~c0_1(a906)) | c1_1(a946)),
% 2.00/1.64 inference(modus_ponens,[status(thm)],[2717, 2716])).
% 2.00/1.64 tff(2719,plain,
% 2.00/1.64 (~c2_1(a901)),
% 2.00/1.64 inference(unit_resolution,[status(thm)],[2718, 124, 2556, 2263, 2257, 2554, 2712, 2711, 540, 2685, 2692])).
% 2.00/1.64 tff(2720,plain,
% 2.00/1.64 (~c1_1(a901)),
% 2.00/1.64 inference(unit_resolution,[status(thm)],[657, 2710])).
% 2.00/1.64 tff(2721,plain,
% 2.00/1.64 (~hskp13),
% 2.00/1.64 inference(unit_resolution,[status(thm)],[2585, 1124, 665, 1055, 323, 325, 324])).
% 2.00/1.64 tff(2722,plain,
% 2.00/1.64 (c0_1(a900)),
% 2.00/1.64 inference(unit_resolution,[status(thm)],[2596, 1323])).
% 2.00/1.64 tff(2723,assumption,(~hskp14), introduced(assumption)).
% 2.00/1.64 tff(2724,assumption,(hskp23), introduced(assumption)).
% 2.00/1.64 tff(2725,plain,
% 2.00/1.64 (~c0_1(a954)),
% 2.00/1.64 inference(unit_resolution,[status(thm)],[2636, 2724])).
% 2.00/1.64 tff(2726,plain,
% 2.00/1.64 (((~hskp23) | c1_1(a954)) <=> ((~hskp23) | c1_1(a954))),
% 2.00/1.64 inference(rewrite,[status(thm)],[])).
% 2.00/1.64 tff(2727,axiom,((~hskp23) | c1_1(a954)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause51')).
% 2.00/1.64 tff(2728,plain,
% 2.00/1.64 ((~hskp23) | c1_1(a954)),
% 2.00/1.64 inference(modus_ponens,[status(thm)],[2727, 2726])).
% 2.00/1.64 tff(2729,plain,
% 2.00/1.64 ((~hskp23) | c1_1(a954)),
% 2.00/1.64 inference(modus_ponens,[status(thm)],[2728, 2726])).
% 2.00/1.64 tff(2730,plain,
% 2.00/1.64 ((~hskp23) | c1_1(a954)),
% 2.00/1.64 inference(modus_ponens,[status(thm)],[2729, 2726])).
% 2.00/1.64 tff(2731,plain,
% 2.00/1.64 ((~hskp23) | c1_1(a954)),
% 2.00/1.64 inference(modus_ponens,[status(thm)],[2730, 2726])).
% 2.00/1.64 tff(2732,plain,
% 2.00/1.64 ((~hskp23) | c1_1(a954)),
% 2.00/1.64 inference(modus_ponens,[status(thm)],[2731, 2726])).
% 2.00/1.64 tff(2733,plain,
% 2.00/1.64 ((~hskp23) | c1_1(a954)),
% 2.00/1.64 inference(modus_ponens,[status(thm)],[2732, 2726])).
% 2.00/1.64 tff(2734,plain,
% 2.00/1.64 ((~hskp23) | c1_1(a954)),
% 2.00/1.64 inference(modus_ponens,[status(thm)],[2733, 2726])).
% 2.00/1.64 tff(2735,plain,
% 2.00/1.64 ((~hskp23) | c1_1(a954)),
% 2.00/1.64 inference(modus_ponens,[status(thm)],[2734, 2726])).
% 2.00/1.64 tff(2736,plain,
% 2.00/1.64 (c1_1(a954)),
% 2.00/1.64 inference(unit_resolution,[status(thm)],[2735, 2724])).
% 2.00/1.64 tff(2737,plain,
% 2.00/1.64 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | c0_1(a954) | (~ndr1_0) | (~c2_1(a954)) | (~c1_1(a954)))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp14 | hskp7 | c0_1(a954) | (~ndr1_0) | (~c2_1(a954)) | (~c1_1(a954)))),
% 2.00/1.64 inference(rewrite,[status(thm)],[])).
% 2.00/1.64 tff(2738,plain,
% 2.00/1.64 ((hskp14 | hskp7 | (~ndr1_0) | c0_1(a954) | (~c2_1(a954)) | (~c1_1(a954))) <=> (hskp14 | hskp7 | c0_1(a954) | (~ndr1_0) | (~c2_1(a954)) | (~c1_1(a954)))),
% 2.00/1.64 inference(rewrite,[status(thm)],[])).
% 2.00/1.64 tff(2739,plain,
% 2.00/1.64 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c0_1(a954) | (~c2_1(a954)) | (~c1_1(a954)))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | c0_1(a954) | (~ndr1_0) | (~c2_1(a954)) | (~c1_1(a954))))),
% 2.00/1.64 inference(monotonicity,[status(thm)],[2738])).
% 2.00/1.64 tff(2740,plain,
% 2.00/1.64 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c0_1(a954) | (~c2_1(a954)) | (~c1_1(a954)))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp14 | hskp7 | c0_1(a954) | (~ndr1_0) | (~c2_1(a954)) | (~c1_1(a954)))),
% 2.00/1.64 inference(transitivity,[status(thm)],[2739, 2737])).
% 2.00/1.64 tff(2741,plain,
% 2.00/1.64 ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c0_1(a954) | (~c2_1(a954)) | (~c1_1(a954)))),
% 2.00/1.64 inference(quant_inst,[status(thm)],[])).
% 2.00/1.64 tff(2742,plain,
% 2.00/1.64 ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp14 | hskp7 | c0_1(a954) | (~ndr1_0) | (~c2_1(a954)) | (~c1_1(a954))),
% 2.00/1.64 inference(modus_ponens,[status(thm)],[2741, 2740])).
% 2.00/1.64 tff(2743,plain,
% 2.00/1.64 (~c2_1(a954)),
% 2.00/1.64 inference(unit_resolution,[status(thm)],[2742, 124, 2723, 21, 2736, 2725, 700])).
% 2.00/1.64 tff(2744,plain,
% 2.00/1.64 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp14 | hskp7 | (~ndr1_0) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900))),
% 2.00/1.64 inference(rewrite,[status(thm)],[])).
% 2.00/1.64 tff(2745,plain,
% 2.00/1.64 ((hskp14 | hskp7 | (~ndr1_0) | c0_1(a900) | (~c2_1(a900)) | (~c1_1(a900))) <=> (hskp14 | hskp7 | (~ndr1_0) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900))),
% 2.00/1.64 inference(rewrite,[status(thm)],[])).
% 2.00/1.64 tff(2746,plain,
% 2.00/1.64 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c0_1(a900) | (~c2_1(a900)) | (~c1_1(a900)))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900)))),
% 2.00/1.64 inference(monotonicity,[status(thm)],[2745])).
% 2.00/1.64 tff(2747,plain,
% 2.00/1.64 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c0_1(a900) | (~c2_1(a900)) | (~c1_1(a900)))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp14 | hskp7 | (~ndr1_0) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900))),
% 2.00/1.64 inference(transitivity,[status(thm)],[2746, 2744])).
% 2.00/1.64 tff(2748,plain,
% 2.00/1.64 ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c0_1(a900) | (~c2_1(a900)) | (~c1_1(a900)))),
% 2.00/1.64 inference(quant_inst,[status(thm)],[])).
% 2.00/1.64 tff(2749,plain,
% 2.00/1.64 ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp14 | hskp7 | (~ndr1_0) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900)),
% 2.00/1.64 inference(modus_ponens,[status(thm)],[2748, 2747])).
% 2.00/1.64 tff(2750,plain,
% 2.00/1.64 (hskp14 | c0_1(a900)),
% 2.00/1.64 inference(unit_resolution,[status(thm)],[2749, 124, 21, 2656, 2589, 700])).
% 2.00/1.64 tff(2751,plain,
% 2.00/1.64 (c0_1(a900)),
% 2.00/1.64 inference(unit_resolution,[status(thm)],[2750, 2723])).
% 2.00/1.64 tff(2752,plain,
% 2.00/1.64 (c3_1(a954)),
% 2.00/1.64 inference(unit_resolution,[status(thm)],[2647, 2724])).
% 2.00/1.64 tff(2753,plain,
% 2.00/1.64 ($false),
% 2.00/1.64 inference(unit_resolution,[status(thm)],[2662, 124, 2656, 2588, 2752, 1055, 1124, 2725, 665, 1665, 2751, 2743])).
% 2.00/1.64 tff(2754,plain,((~hskp23) | c1_1(a912) | c2_1(a912) | c0_1(a912) | hskp14 | hskp7), inference(lemma,lemma(discharge,[]))).
% 2.00/1.64 tff(2755,plain,
% 2.00/1.64 (~hskp23),
% 2.00/1.64 inference(unit_resolution,[status(thm)],[2754, 2723, 1124, 665, 1055, 21])).
% 2.08/1.64 tff(2756,plain,
% 2.08/1.64 (hskp15),
% 2.08/1.64 inference(unit_resolution,[status(thm)],[2630, 2755, 2722])).
% 2.08/1.64 tff(2757,plain,
% 2.08/1.64 (~c0_1(a924)),
% 2.08/1.64 inference(unit_resolution,[status(thm)],[1267, 2756])).
% 2.08/1.64 tff(2758,plain,
% 2.08/1.64 (c2_1(a924)),
% 2.08/1.64 inference(unit_resolution,[status(thm)],[1280, 2756])).
% 2.08/1.64 tff(2759,plain,
% 2.08/1.64 (~c3_1(a924)),
% 2.08/1.64 inference(unit_resolution,[status(thm)],[2606, 124, 1323, 21, 2758, 2757, 20])).
% 2.08/1.64 tff(2760,assumption,(c0_1(a900)), introduced(assumption)).
% 2.08/1.64 tff(2761,plain,
% 2.08/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a912) | c2_1(a912) | c0_1(a912) | c0_1(a905) | c2_1(a905) | (~ndr1_0) | (~c3_1(a905)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c0_1(a912) | c0_1(a905) | c2_1(a905) | (~ndr1_0) | (~c3_1(a905)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)))),
% 2.08/1.64 inference(rewrite,[status(thm)],[])).
% 2.08/1.64 tff(2762,plain,
% 2.08/1.64 (((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a905) | c0_1(a905) | (~c3_1(a905)) | c1_1(a912) | c0_1(a912) | c2_1(a912)) <=> (c1_1(a912) | c2_1(a912) | c0_1(a912) | c0_1(a905) | c2_1(a905) | (~ndr1_0) | (~c3_1(a905)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)))),
% 2.08/1.64 inference(rewrite,[status(thm)],[])).
% 2.08/1.64 tff(2763,plain,
% 2.08/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a905) | c0_1(a905) | (~c3_1(a905)) | c1_1(a912) | c0_1(a912) | c2_1(a912))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a912) | c2_1(a912) | c0_1(a912) | c0_1(a905) | c2_1(a905) | (~ndr1_0) | (~c3_1(a905)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900))))),
% 2.08/1.64 inference(monotonicity,[status(thm)],[2762])).
% 2.08/1.64 tff(2764,plain,
% 2.08/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a905) | c0_1(a905) | (~c3_1(a905)) | c1_1(a912) | c0_1(a912) | c2_1(a912))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c0_1(a912) | c0_1(a905) | c2_1(a905) | (~ndr1_0) | (~c3_1(a905)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)))),
% 2.08/1.64 inference(transitivity,[status(thm)],[2763, 2761])).
% 2.08/1.64 tff(2765,plain,
% 2.08/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a905) | c0_1(a905) | (~c3_1(a905)) | c1_1(a912) | c0_1(a912) | c2_1(a912))),
% 2.08/1.64 inference(quant_inst,[status(thm)],[])).
% 2.08/1.64 tff(2766,plain,
% 2.08/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c0_1(a912) | c0_1(a905) | c2_1(a905) | (~ndr1_0) | (~c3_1(a905)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900))),
% 2.08/1.64 inference(modus_ponens,[status(thm)],[2765, 2764])).
% 2.08/1.64 tff(2767,plain,
% 2.08/1.64 ($false),
% 2.08/1.64 inference(unit_resolution,[status(thm)],[2766, 124, 2656, 2588, 1055, 1124, 2437, 665, 2426, 2454, 1665, 2760])).
% 2.08/1.64 tff(2768,plain,((~hskp4) | c1_1(a912) | c2_1(a912) | c0_1(a912) | (~c0_1(a900))), inference(lemma,lemma(discharge,[]))).
% 2.08/1.64 tff(2769,plain,
% 2.08/1.64 (~hskp4),
% 2.08/1.64 inference(unit_resolution,[status(thm)],[2768, 2722, 1124, 665, 1055])).
% 2.08/1.64 tff(2770,plain,
% 2.08/1.64 (hskp20),
% 2.08/1.64 inference(unit_resolution,[status(thm)],[2489, 2723, 2769])).
% 2.08/1.64 tff(2771,plain,
% 2.08/1.64 (~c3_1(a939)),
% 2.08/1.64 inference(unit_resolution,[status(thm)],[1420, 2770])).
% 2.08/1.64 tff(2772,plain,
% 2.08/1.64 (~c1_1(a939)),
% 2.08/1.64 inference(unit_resolution,[status(thm)],[1426, 2770])).
% 2.08/1.64 tff(2773,plain,
% 2.08/1.64 (c0_1(a939)),
% 2.08/1.64 inference(unit_resolution,[status(thm)],[1437, 2770])).
% 2.08/1.64 tff(2774,plain,
% 2.08/1.64 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a912) | c2_1(a912) | c1_1(a939) | c3_1(a939) | c0_1(a924) | c0_1(a912) | (~ndr1_0) | c3_1(a924) | (~c2_1(a924)) | (~c0_1(a939)))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c1_1(a939) | c3_1(a939) | c0_1(a924) | c0_1(a912) | (~ndr1_0) | c3_1(a924) | (~c2_1(a924)) | (~c0_1(a939)))),
% 2.08/1.64 inference(rewrite,[status(thm)],[])).
% 2.08/1.64 tff(2775,plain,
% 2.08/1.64 (((~ndr1_0) | c1_1(a939) | c3_1(a939) | (~c0_1(a939)) | c3_1(a924) | c0_1(a924) | (~c2_1(a924)) | c1_1(a912) | c0_1(a912) | c2_1(a912)) <=> (c1_1(a912) | c2_1(a912) | c1_1(a939) | c3_1(a939) | c0_1(a924) | c0_1(a912) | (~ndr1_0) | c3_1(a924) | (~c2_1(a924)) | (~c0_1(a939)))),
% 2.08/1.64 inference(rewrite,[status(thm)],[])).
% 2.08/1.64 tff(2776,plain,
% 2.08/1.64 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a939) | c3_1(a939) | (~c0_1(a939)) | c3_1(a924) | c0_1(a924) | (~c2_1(a924)) | c1_1(a912) | c0_1(a912) | c2_1(a912))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a912) | c2_1(a912) | c1_1(a939) | c3_1(a939) | c0_1(a924) | c0_1(a912) | (~ndr1_0) | c3_1(a924) | (~c2_1(a924)) | (~c0_1(a939))))),
% 2.08/1.64 inference(monotonicity,[status(thm)],[2775])).
% 2.08/1.64 tff(2777,plain,
% 2.08/1.64 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a939) | c3_1(a939) | (~c0_1(a939)) | c3_1(a924) | c0_1(a924) | (~c2_1(a924)) | c1_1(a912) | c0_1(a912) | c2_1(a912))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c1_1(a939) | c3_1(a939) | c0_1(a924) | c0_1(a912) | (~ndr1_0) | c3_1(a924) | (~c2_1(a924)) | (~c0_1(a939)))),
% 2.08/1.64 inference(transitivity,[status(thm)],[2776, 2774])).
% 2.08/1.64 tff(2778,plain,
% 2.08/1.64 ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a939) | c3_1(a939) | (~c0_1(a939)) | c3_1(a924) | c0_1(a924) | (~c2_1(a924)) | c1_1(a912) | c0_1(a912) | c2_1(a912))),
% 2.08/1.64 inference(quant_inst,[status(thm)],[])).
% 2.08/1.64 tff(2779,plain,
% 2.08/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c1_1(a939) | c3_1(a939) | c0_1(a924) | c0_1(a912) | (~ndr1_0) | c3_1(a924) | (~c2_1(a924)) | (~c0_1(a939))),
% 2.08/1.64 inference(modus_ponens,[status(thm)],[2778, 2777])).
% 2.08/1.64 tff(2780,plain,
% 2.08/1.64 ($false),
% 2.08/1.64 inference(unit_resolution,[status(thm)],[2779, 124, 2773, 2758, 1055, 1124, 2772, 2771, 2757, 665, 540, 2759])).
% 2.08/1.64 tff(2781,plain,(hskp14 | c1_1(a912) | c2_1(a912) | c0_1(a912) | hskp13 | hskp7), inference(lemma,lemma(discharge,[]))).
% 2.08/1.64 tff(2782,plain,
% 2.08/1.64 (hskp14),
% 2.08/1.64 inference(unit_resolution,[status(thm)],[2781, 1124, 1055, 665, 2721, 21])).
% 2.08/1.64 tff(2783,plain,
% 2.08/1.64 (~c0_1(a923)),
% 2.08/1.64 inference(unit_resolution,[status(thm)],[576, 2782])).
% 2.08/1.64 tff(2784,plain,
% 2.08/1.64 (c3_1(a923)),
% 2.08/1.64 inference(unit_resolution,[status(thm)],[587, 2782])).
% 2.08/1.64 tff(2785,plain,
% 2.08/1.64 (~c2_1(a923)),
% 2.08/1.64 inference(unit_resolution,[status(thm)],[1370, 124, 2721, 21, 2784, 2783, 20])).
% 2.08/1.64 tff(2786,plain,
% 2.08/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a912) | c2_1(a912) | c0_1(a923) | c0_1(a912) | (~ndr1_0) | c2_1(a923) | (~c3_1(a923)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c0_1(a923) | c0_1(a912) | (~ndr1_0) | c2_1(a923) | (~c3_1(a923)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 2.08/1.64 inference(rewrite,[status(thm)],[])).
% 2.08/1.64 tff(2787,plain,
% 2.08/1.64 (((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c2_1(a923) | c0_1(a923) | (~c3_1(a923)) | c1_1(a912) | c0_1(a912) | c2_1(a912)) <=> (c1_1(a912) | c2_1(a912) | c0_1(a923) | c0_1(a912) | (~ndr1_0) | c2_1(a923) | (~c3_1(a923)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 2.08/1.64 inference(rewrite,[status(thm)],[])).
% 2.08/1.64 tff(2788,plain,
% 2.08/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c2_1(a923) | c0_1(a923) | (~c3_1(a923)) | c1_1(a912) | c0_1(a912) | c2_1(a912))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a912) | c2_1(a912) | c0_1(a923) | c0_1(a912) | (~ndr1_0) | c2_1(a923) | (~c3_1(a923)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916))))),
% 2.08/1.64 inference(monotonicity,[status(thm)],[2787])).
% 2.08/1.64 tff(2789,plain,
% 2.08/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c2_1(a923) | c0_1(a923) | (~c3_1(a923)) | c1_1(a912) | c0_1(a912) | c2_1(a912))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c0_1(a923) | c0_1(a912) | (~ndr1_0) | c2_1(a923) | (~c3_1(a923)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 2.08/1.64 inference(transitivity,[status(thm)],[2788, 2786])).
% 2.08/1.64 tff(2790,plain,
% 2.08/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c2_1(a923) | c0_1(a923) | (~c3_1(a923)) | c1_1(a912) | c0_1(a912) | c2_1(a912))),
% 2.08/1.64 inference(quant_inst,[status(thm)],[])).
% 2.08/1.64 tff(2791,plain,
% 2.08/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c0_1(a923) | c0_1(a912) | (~ndr1_0) | c2_1(a923) | (~c3_1(a923)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916))),
% 2.08/1.64 inference(modus_ponens,[status(thm)],[2790, 2789])).
% 2.08/1.64 tff(2792,plain,
% 2.08/1.64 ($false),
% 2.08/1.64 inference(unit_resolution,[status(thm)],[2791, 124, 488, 487, 486, 2784, 1055, 1124, 2783, 665, 1665, 2785])).
% 2.08/1.64 tff(2793,plain,(c2_1(a912) | (~c0_1(a916)) | (~c1_1(a916)) | (~c3_1(a916)) | c1_1(a912) | c0_1(a912) | hskp7 | (~c0_1(a906)) | c3_1(a906) | (~c2_1(a906))), inference(lemma,lemma(discharge,[]))).
% 2.08/1.64 tff(2794,plain,
% 2.08/1.64 (c2_1(a912)),
% 2.08/1.64 inference(unit_resolution,[status(thm)],[2793, 2678, 2677, 2676, 1055, 665, 21, 2556, 2554, 2555])).
% 2.08/1.64 tff(2795,assumption,(~c2_1(a901)), introduced(assumption)).
% 2.08/1.64 tff(2796,assumption,(~c3_1(a912)), introduced(assumption)).
% 2.08/1.64 tff(2797,assumption,(~c1_1(a906)), introduced(assumption)).
% 2.08/1.64 tff(2798,assumption,(~c1_1(a901)), introduced(assumption)).
% 2.08/1.64 tff(2799,assumption,(~c0_1(a901)), introduced(assumption)).
% 2.08/1.64 tff(2800,plain,
% 2.08/1.64 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a912) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a912) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912))),
% 2.08/1.64 inference(rewrite,[status(thm)],[])).
% 2.08/1.64 tff(2801,plain,
% 2.08/1.64 (((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a901) | c0_1(a901) | c2_1(a901)) <=> (c0_1(a912) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912))),
% 2.08/1.65 inference(rewrite,[status(thm)],[])).
% 2.08/1.65 tff(2802,plain,
% 2.08/1.65 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a901) | c0_1(a901) | c2_1(a901))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a912) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912)))),
% 2.08/1.65 inference(monotonicity,[status(thm)],[2801])).
% 2.08/1.65 tff(2803,plain,
% 2.08/1.65 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a901) | c0_1(a901) | c2_1(a901))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a912) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912))),
% 2.08/1.65 inference(transitivity,[status(thm)],[2802, 2800])).
% 2.08/1.65 tff(2804,plain,
% 2.08/1.65 ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a901) | c0_1(a901) | c2_1(a901))),
% 2.08/1.65 inference(quant_inst,[status(thm)],[])).
% 2.08/1.65 tff(2805,plain,
% 2.08/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a912) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912)),
% 2.08/1.65 inference(modus_ponens,[status(thm)],[2804, 2803])).
% 2.08/1.65 tff(2806,plain,
% 2.08/1.65 ($false),
% 2.08/1.65 inference(unit_resolution,[status(thm)],[2805, 124, 689, 323, 665, 325, 2799, 2798, 540, 2797, 2796, 2795])).
% 2.08/1.65 tff(2807,plain,(c3_1(a912) | (~c2_1(a912)) | (~c0_1(a906)) | c0_1(a912) | c3_1(a906) | c0_1(a901) | c1_1(a901) | c1_1(a906) | c2_1(a901)), inference(lemma,lemma(discharge,[]))).
% 2.08/1.65 tff(2808,plain,
% 2.08/1.65 (c3_1(a912)),
% 2.08/1.65 inference(unit_resolution,[status(thm)],[2807, 2794, 2556, 665, 2554, 2712, 2720, 2692, 2719])).
% 2.08/1.65 tff(2809,plain,
% 2.08/1.65 (hskp13),
% 2.08/1.65 inference(unit_resolution,[status(thm)],[2668, 2808, 21, 2794])).
% 2.08/1.65 tff(2810,plain,
% 2.08/1.65 (~c3_1(a921)),
% 2.08/1.65 inference(unit_resolution,[status(thm)],[225, 2809])).
% 2.08/1.65 tff(2811,plain,
% 2.08/1.65 (~c0_1(a921)),
% 2.08/1.65 inference(unit_resolution,[status(thm)],[231, 2809])).
% 2.08/1.65 tff(2812,plain,
% 2.08/1.65 (c2_1(a921)),
% 2.08/1.65 inference(unit_resolution,[status(thm)],[242, 2809])).
% 2.08/1.65 tff(2813,plain,
% 2.08/1.65 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a921) | c3_1(a921) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921)))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a921) | c3_1(a921) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921)))),
% 2.08/1.65 inference(rewrite,[status(thm)],[])).
% 2.08/1.65 tff(2814,plain,
% 2.08/1.65 (((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a901) | c0_1(a901) | c2_1(a901)) <=> (c0_1(a921) | c3_1(a921) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921)))),
% 2.08/1.65 inference(rewrite,[status(thm)],[])).
% 2.08/1.65 tff(2815,plain,
% 2.08/1.65 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a901) | c0_1(a901) | c2_1(a901))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a921) | c3_1(a921) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921))))),
% 2.08/1.65 inference(monotonicity,[status(thm)],[2814])).
% 2.08/1.65 tff(2816,plain,
% 2.08/1.65 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a901) | c0_1(a901) | c2_1(a901))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a921) | c3_1(a921) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921)))),
% 2.08/1.65 inference(transitivity,[status(thm)],[2815, 2813])).
% 2.08/1.65 tff(2817,plain,
% 2.08/1.65 ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a901) | c0_1(a901) | c2_1(a901))),
% 2.08/1.65 inference(quant_inst,[status(thm)],[])).
% 2.08/1.65 tff(2818,plain,
% 2.08/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a921) | c3_1(a921) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921))),
% 2.08/1.65 inference(modus_ponens,[status(thm)],[2817, 2816])).
% 2.08/1.65 tff(2819,plain,
% 2.08/1.65 ($false),
% 2.08/1.65 inference(unit_resolution,[status(thm)],[2818, 124, 2812, 2556, 2811, 2810, 2554, 2712, 2720, 540, 2692, 2719])).
% 2.08/1.65 tff(2820,plain,(c1_1(a912) | hskp7 | c0_1(a912) | hskp12), inference(lemma,lemma(discharge,[]))).
% 2.08/1.65 tff(2821,plain,
% 2.08/1.65 (c1_1(a912)),
% 2.08/1.65 inference(unit_resolution,[status(thm)],[2820, 21, 665, 32])).
% 2.08/1.65 tff(2822,plain,
% 2.08/1.65 (hskp27),
% 2.08/1.65 inference(unit_resolution,[status(thm)],[2270, 1184])).
% 2.08/1.65 tff(2823,plain,
% 2.08/1.65 (c3_1(a900)),
% 2.08/1.65 inference(unit_resolution,[status(thm)],[144, 2822])).
% 2.08/1.65 tff(2824,plain,
% 2.08/1.65 (c1_1(a900)),
% 2.08/1.65 inference(unit_resolution,[status(thm)],[166, 2822])).
% 2.08/1.65 tff(2825,plain,
% 2.08/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a946) | c3_1(a946) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | (~c1_1(a946)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a946) | c3_1(a946) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | (~c1_1(a946)))),
% 2.08/1.65 inference(rewrite,[status(thm)],[])).
% 2.08/1.65 tff(2826,plain,
% 2.08/1.65 (((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a946) | c2_1(a946) | (~c1_1(a946))) <=> (c2_1(a946) | c3_1(a946) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | (~c1_1(a946)))),
% 2.08/1.65 inference(rewrite,[status(thm)],[])).
% 2.08/1.65 tff(2827,plain,
% 2.08/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a946) | c2_1(a946) | (~c1_1(a946)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a946) | c3_1(a946) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | (~c1_1(a946))))),
% 2.08/1.65 inference(monotonicity,[status(thm)],[2826])).
% 2.08/1.65 tff(2828,plain,
% 2.08/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a946) | c2_1(a946) | (~c1_1(a946)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a946) | c3_1(a946) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | (~c1_1(a946)))),
% 2.08/1.65 inference(transitivity,[status(thm)],[2827, 2825])).
% 2.08/1.65 tff(2829,plain,
% 2.08/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a946) | c2_1(a946) | (~c1_1(a946)))),
% 2.08/1.65 inference(quant_inst,[status(thm)],[])).
% 2.08/1.65 tff(2830,plain,
% 2.08/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a946) | c3_1(a946) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | (~c1_1(a946))),
% 2.08/1.65 inference(modus_ponens,[status(thm)],[2829, 2828])).
% 2.08/1.65 tff(2831,plain,
% 2.08/1.65 ((~c0_1(a900)) | (~c1_1(a946))),
% 2.08/1.65 inference(unit_resolution,[status(thm)],[2830, 124, 2824, 2823, 323, 324, 2257, 2251, 325, 31])).
% 2.08/1.65 tff(2832,plain,
% 2.08/1.65 (~c1_1(a946)),
% 2.08/1.65 inference(unit_resolution,[status(thm)],[2831, 2760])).
% 2.08/1.65 tff(2833,plain,
% 2.08/1.65 (~c1_1(a906)),
% 2.08/1.65 inference(unit_resolution,[status(thm)],[2691, 124, 323, 324, 2263, 2257, 325, 520, 2832])).
% 2.08/1.65 tff(2834,plain,
% 2.08/1.65 (c2_1(a900)),
% 2.08/1.65 inference(unit_resolution,[status(thm)],[155, 2822])).
% 2.08/1.65 tff(2835,plain,
% 2.08/1.65 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)))),
% 2.08/1.65 inference(rewrite,[status(thm)],[])).
% 2.08/1.65 tff(2836,plain,
% 2.08/1.65 ((hskp9 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c3_1(a906) | c1_1(a906) | (~c0_1(a906))) <=> (hskp9 | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)))),
% 2.08/1.65 inference(rewrite,[status(thm)],[])).
% 2.08/1.65 tff(2837,plain,
% 2.08/1.65 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c3_1(a906) | c1_1(a906) | (~c0_1(a906)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900))))),
% 2.08/1.65 inference(monotonicity,[status(thm)],[2836])).
% 2.08/1.65 tff(2838,plain,
% 2.08/1.65 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c3_1(a906) | c1_1(a906) | (~c0_1(a906)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)))),
% 2.08/1.65 inference(transitivity,[status(thm)],[2837, 2835])).
% 2.08/1.65 tff(2839,plain,
% 2.08/1.65 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c3_1(a906) | c1_1(a906) | (~c0_1(a906)))),
% 2.08/1.65 inference(quant_inst,[status(thm)],[])).
% 2.08/1.65 tff(2840,plain,
% 2.08/1.65 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a900)) | (~c3_1(a900)) | (~c0_1(a900))),
% 2.08/1.65 inference(modus_ponens,[status(thm)],[2839, 2838])).
% 2.08/1.65 tff(2841,plain,
% 2.08/1.65 (hskp9 | c1_1(a906) | (~c0_1(a900))),
% 2.08/1.65 inference(unit_resolution,[status(thm)],[2840, 124, 2834, 2823, 323, 325, 882])).
% 2.08/1.65 tff(2842,plain,
% 2.08/1.65 (hskp9),
% 2.08/1.65 inference(unit_resolution,[status(thm)],[2841, 2833, 2760])).
% 2.08/1.65 tff(2843,plain,
% 2.08/1.65 (~c3_1(a910)),
% 2.08/1.65 inference(unit_resolution,[status(thm)],[959, 2842])).
% 2.08/1.65 tff(2844,plain,
% 2.08/1.65 (c2_1(a910)),
% 2.08/1.65 inference(unit_resolution,[status(thm)],[1009, 2842])).
% 2.08/1.65 tff(2845,plain,
% 2.08/1.65 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a946) | c2_1(a946) | c3_1(a910) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a910)) | c0_1(a910) | c1_1(a946))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a946) | c2_1(a946) | c3_1(a910) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a910)) | c0_1(a910) | c1_1(a946))),
% 2.08/1.65 inference(rewrite,[status(thm)],[])).
% 2.08/1.65 tff(2846,plain,
% 2.08/1.65 (((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a910) | c0_1(a910) | (~c2_1(a910)) | c1_1(a946) | c0_1(a946) | c2_1(a946)) <=> (c0_1(a946) | c2_1(a946) | c3_1(a910) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a910)) | c0_1(a910) | c1_1(a946))),
% 2.08/1.65 inference(rewrite,[status(thm)],[])).
% 2.08/1.65 tff(2847,plain,
% 2.08/1.65 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a910) | c0_1(a910) | (~c2_1(a910)) | c1_1(a946) | c0_1(a946) | c2_1(a946))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a946) | c2_1(a946) | c3_1(a910) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a910)) | c0_1(a910) | c1_1(a946)))),
% 2.08/1.65 inference(monotonicity,[status(thm)],[2846])).
% 2.08/1.65 tff(2848,plain,
% 2.08/1.65 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a910) | c0_1(a910) | (~c2_1(a910)) | c1_1(a946) | c0_1(a946) | c2_1(a946))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a946) | c2_1(a946) | c3_1(a910) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a910)) | c0_1(a910) | c1_1(a946))),
% 2.08/1.65 inference(transitivity,[status(thm)],[2847, 2845])).
% 2.08/1.65 tff(2849,plain,
% 2.08/1.65 ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a910) | c0_1(a910) | (~c2_1(a910)) | c1_1(a946) | c0_1(a946) | c2_1(a946))),
% 2.08/1.65 inference(quant_inst,[status(thm)],[])).
% 2.08/1.65 tff(2850,plain,
% 2.08/1.65 ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a946) | c2_1(a946) | c3_1(a910) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a910)) | c0_1(a910) | c1_1(a946)),
% 2.08/1.65 inference(modus_ponens,[status(thm)],[2849, 2848])).
% 2.08/1.65 tff(2851,plain,
% 2.08/1.65 (c0_1(a910)),
% 2.08/1.65 inference(unit_resolution,[status(thm)],[2850, 124, 2844, 323, 2263, 2257, 2843, 325, 540, 2832, 2833])).
% 2.08/1.65 tff(2852,plain,
% 2.08/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a912) | c0_1(a946) | c2_1(a946) | c0_1(a912) | (~ndr1_0) | (~c3_1(a912)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c1_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c2_1(a912) | c0_1(a946) | c2_1(a946) | c0_1(a912) | (~ndr1_0) | (~c3_1(a912)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c1_1(a946))),
% 2.08/1.65 inference(rewrite,[status(thm)],[])).
% 2.08/1.65 tff(2853,plain,
% 2.08/1.65 (((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a912) | c0_1(a912) | (~c3_1(a912)) | c1_1(a946) | c0_1(a946) | c2_1(a946)) <=> (c2_1(a912) | c0_1(a946) | c2_1(a946) | c0_1(a912) | (~ndr1_0) | (~c3_1(a912)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c1_1(a946))),
% 2.08/1.65 inference(rewrite,[status(thm)],[])).
% 2.08/1.65 tff(2854,plain,
% 2.08/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a912) | c0_1(a912) | (~c3_1(a912)) | c1_1(a946) | c0_1(a946) | c2_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a912) | c0_1(a946) | c2_1(a946) | c0_1(a912) | (~ndr1_0) | (~c3_1(a912)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c1_1(a946)))),
% 2.08/1.65 inference(monotonicity,[status(thm)],[2853])).
% 2.08/1.65 tff(2855,plain,
% 2.08/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a912) | c0_1(a912) | (~c3_1(a912)) | c1_1(a946) | c0_1(a946) | c2_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c2_1(a912) | c0_1(a946) | c2_1(a946) | c0_1(a912) | (~ndr1_0) | (~c3_1(a912)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c1_1(a946))),
% 2.08/1.65 inference(transitivity,[status(thm)],[2854, 2852])).
% 2.08/1.65 tff(2856,plain,
% 2.08/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a912) | c0_1(a912) | (~c3_1(a912)) | c1_1(a946) | c0_1(a946) | c2_1(a946))),
% 2.08/1.65 inference(quant_inst,[status(thm)],[])).
% 2.08/1.65 tff(2857,plain,
% 2.08/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c2_1(a912) | c0_1(a946) | c2_1(a946) | c0_1(a912) | (~ndr1_0) | (~c3_1(a912)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c1_1(a946)),
% 2.08/1.65 inference(modus_ponens,[status(thm)],[2856, 2855])).
% 2.08/1.65 tff(2858,plain,
% 2.08/1.65 (~c3_1(a912)),
% 2.08/1.65 inference(unit_resolution,[status(thm)],[2857, 124, 2824, 2823, 1124, 2263, 2257, 665, 1665, 2832, 2760])).
% 2.08/1.65 tff(2859,plain,
% 2.08/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a912) | c3_1(a910) | (~ndr1_0) | (~c2_1(a910)) | (~c0_1(a910)) | (~c1_1(a912)) | c3_1(a912) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a912) | c3_1(a910) | (~ndr1_0) | (~c2_1(a910)) | (~c0_1(a910)) | (~c1_1(a912)) | c3_1(a912) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)))),
% 2.08/1.65 inference(rewrite,[status(thm)],[])).
% 2.08/1.65 tff(2860,plain,
% 2.08/1.65 (((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c3_1(a910) | (~c2_1(a910)) | (~c0_1(a910)) | c3_1(a912) | c2_1(a912) | (~c1_1(a912))) <=> (c2_1(a912) | c3_1(a910) | (~ndr1_0) | (~c2_1(a910)) | (~c0_1(a910)) | (~c1_1(a912)) | c3_1(a912) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)))),
% 2.08/1.65 inference(rewrite,[status(thm)],[])).
% 2.08/1.65 tff(2861,plain,
% 2.08/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c3_1(a910) | (~c2_1(a910)) | (~c0_1(a910)) | c3_1(a912) | c2_1(a912) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a912) | c3_1(a910) | (~ndr1_0) | (~c2_1(a910)) | (~c0_1(a910)) | (~c1_1(a912)) | c3_1(a912) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900))))),
% 2.08/1.65 inference(monotonicity,[status(thm)],[2860])).
% 2.08/1.65 tff(2862,plain,
% 2.08/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c3_1(a910) | (~c2_1(a910)) | (~c0_1(a910)) | c3_1(a912) | c2_1(a912) | (~c1_1(a912)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a912) | c3_1(a910) | (~ndr1_0) | (~c2_1(a910)) | (~c0_1(a910)) | (~c1_1(a912)) | c3_1(a912) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)))),
% 2.08/1.65 inference(transitivity,[status(thm)],[2861, 2859])).
% 2.08/1.65 tff(2863,plain,
% 2.08/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c3_1(a910) | (~c2_1(a910)) | (~c0_1(a910)) | c3_1(a912) | c2_1(a912) | (~c1_1(a912)))),
% 2.08/1.65 inference(quant_inst,[status(thm)],[])).
% 2.08/1.65 tff(2864,plain,
% 2.08/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a912) | c3_1(a910) | (~ndr1_0) | (~c2_1(a910)) | (~c0_1(a910)) | (~c1_1(a912)) | c3_1(a912) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900))),
% 2.08/1.65 inference(modus_ponens,[status(thm)],[2863, 2862])).
% 2.08/1.65 tff(2865,plain,
% 2.08/1.65 ($false),
% 2.08/1.65 inference(unit_resolution,[status(thm)],[2864, 124, 2824, 2823, 690, 1124, 2844, 2843, 31, 2760, 2858, 2851])).
% 2.08/1.65 tff(2866,plain,((~c0_1(a900)) | (~c1_1(a912)) | c2_1(a912) | (~c0_1(a906)) | c3_1(a906) | c0_1(a912) | (~c2_1(a906))), inference(lemma,lemma(discharge,[]))).
% 2.08/1.65 tff(2867,plain,
% 2.08/1.65 (~c0_1(a900)),
% 2.08/1.65 inference(unit_resolution,[status(thm)],[2866, 1124, 2821, 2556, 2554, 665, 2555])).
% 2.08/1.65 tff(2868,plain,
% 2.08/1.65 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> (hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))),
% 2.08/1.65 inference(bind,[status(th)],[])).
% 2.08/1.65 tff(2869,plain,
% 2.08/1.65 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 2.08/1.65 inference(quant_intro,[status(thm)],[2868])).
% 2.08/1.65 tff(2870,plain,
% 2.08/1.65 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 2.08/1.65 inference(rewrite,[status(thm)],[])).
% 2.08/1.65 tff(2871,plain,
% 2.08/1.65 (^[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(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp8) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp8))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))))),
% 2.08/1.65 inference(bind,[status(th)],[])).
% 2.08/1.65 tff(2872,plain,
% 2.08/1.65 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 2.08/1.65 inference(quant_intro,[status(thm)],[2871])).
% 2.08/1.65 tff(2873,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause162')).
% 2.08/1.65 tff(2874,plain,
% 2.08/1.65 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 2.08/1.65 inference(modus_ponens,[status(thm)],[2873, 2872])).
% 2.08/1.65 tff(2875,plain,
% 2.08/1.65 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 2.08/1.65 inference(modus_ponens,[status(thm)],[2874, 2870])).
% 2.08/1.65 tff(2876,plain,(
% 2.08/1.65 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 2.08/1.65 inference(skolemize,[status(sab)],[2875])).
% 2.08/1.65 tff(2877,plain,
% 2.08/1.65 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 2.08/1.65 inference(modus_ponens,[status(thm)],[2876, 2869])).
% 2.08/1.65 tff(2878,plain,
% 2.08/1.65 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp8 | c0_1(a946) | c2_1(a946) | c3_1(a946) | (~ndr1_0) | (~c1_1(a900)) | (~c3_1(a900)) | c0_1(a900))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp8 | c0_1(a946) | c2_1(a946) | c3_1(a946) | (~ndr1_0) | (~c1_1(a900)) | (~c3_1(a900)) | c0_1(a900))),
% 2.08/1.65 inference(rewrite,[status(thm)],[])).
% 2.08/1.65 tff(2879,plain,
% 2.08/1.65 ((hskp8 | (~ndr1_0) | c0_1(a900) | (~c3_1(a900)) | (~c1_1(a900)) | c3_1(a946) | c2_1(a946) | c0_1(a946)) <=> (hskp8 | c0_1(a946) | c2_1(a946) | c3_1(a946) | (~ndr1_0) | (~c1_1(a900)) | (~c3_1(a900)) | c0_1(a900))),
% 2.08/1.65 inference(rewrite,[status(thm)],[])).
% 2.08/1.65 tff(2880,plain,
% 2.08/1.65 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a900) | (~c3_1(a900)) | (~c1_1(a900)) | c3_1(a946) | c2_1(a946) | c0_1(a946))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp8 | c0_1(a946) | c2_1(a946) | c3_1(a946) | (~ndr1_0) | (~c1_1(a900)) | (~c3_1(a900)) | c0_1(a900)))),
% 2.08/1.66 inference(monotonicity,[status(thm)],[2879])).
% 2.08/1.66 tff(2881,plain,
% 2.08/1.66 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a900) | (~c3_1(a900)) | (~c1_1(a900)) | c3_1(a946) | c2_1(a946) | c0_1(a946))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp8 | c0_1(a946) | c2_1(a946) | c3_1(a946) | (~ndr1_0) | (~c1_1(a900)) | (~c3_1(a900)) | c0_1(a900))),
% 2.08/1.66 inference(transitivity,[status(thm)],[2880, 2878])).
% 2.08/1.66 tff(2882,plain,
% 2.08/1.66 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp8 | (~ndr1_0) | c0_1(a900) | (~c3_1(a900)) | (~c1_1(a900)) | c3_1(a946) | c2_1(a946) | c0_1(a946))),
% 2.08/1.66 inference(quant_inst,[status(thm)],[])).
% 2.08/1.66 tff(2883,plain,
% 2.08/1.66 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp8 | c0_1(a946) | c2_1(a946) | c3_1(a946) | (~ndr1_0) | (~c1_1(a900)) | (~c3_1(a900)) | c0_1(a900)),
% 2.08/1.66 inference(modus_ponens,[status(thm)],[2882, 2881])).
% 2.08/1.66 tff(2884,plain,
% 2.08/1.66 (hskp8),
% 2.08/1.66 inference(unit_resolution,[status(thm)],[2883, 124, 2824, 2823, 2263, 2257, 2251, 2877, 2867])).
% 2.08/1.66 tff(2885,plain,
% 2.08/1.66 (((~hskp8) | (~c3_1(a909))) <=> ((~hskp8) | (~c3_1(a909)))),
% 2.08/1.66 inference(rewrite,[status(thm)],[])).
% 2.08/1.66 tff(2886,plain,
% 2.08/1.66 (((~c3_1(a909)) | (~hskp8)) <=> ((~hskp8) | (~c3_1(a909)))),
% 2.08/1.66 inference(rewrite,[status(thm)],[])).
% 2.08/1.66 tff(2887,axiom,((~c3_1(a909)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause113')).
% 2.08/1.66 tff(2888,plain,
% 2.08/1.66 ((~hskp8) | (~c3_1(a909))),
% 2.08/1.66 inference(modus_ponens,[status(thm)],[2887, 2886])).
% 2.08/1.66 tff(2889,plain,
% 2.08/1.66 ((~hskp8) | (~c3_1(a909))),
% 2.08/1.66 inference(modus_ponens,[status(thm)],[2888, 2885])).
% 2.08/1.66 tff(2890,plain,
% 2.08/1.66 (~c3_1(a909)),
% 2.08/1.66 inference(unit_resolution,[status(thm)],[2889, 2884])).
% 2.08/1.66 tff(2891,plain,
% 2.08/1.66 (((~hskp8) | c1_1(a909)) <=> ((~hskp8) | c1_1(a909))),
% 2.08/1.66 inference(rewrite,[status(thm)],[])).
% 2.08/1.66 tff(2892,axiom,((~hskp8) | c1_1(a909)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause71')).
% 2.08/1.66 tff(2893,plain,
% 2.08/1.66 ((~hskp8) | c1_1(a909)),
% 2.08/1.66 inference(modus_ponens,[status(thm)],[2892, 2891])).
% 2.08/1.66 tff(2894,plain,
% 2.08/1.66 ((~hskp8) | c1_1(a909)),
% 2.08/1.66 inference(modus_ponens,[status(thm)],[2893, 2891])).
% 2.08/1.66 tff(2895,plain,
% 2.08/1.66 ((~hskp8) | c1_1(a909)),
% 2.08/1.66 inference(modus_ponens,[status(thm)],[2894, 2891])).
% 2.08/1.66 tff(2896,plain,
% 2.08/1.66 ((~hskp8) | c1_1(a909)),
% 2.08/1.66 inference(modus_ponens,[status(thm)],[2895, 2891])).
% 2.08/1.66 tff(2897,plain,
% 2.08/1.66 ((~hskp8) | c1_1(a909)),
% 2.08/1.66 inference(modus_ponens,[status(thm)],[2896, 2891])).
% 2.08/1.66 tff(2898,plain,
% 2.08/1.66 ((~hskp8) | c1_1(a909)),
% 2.08/1.66 inference(modus_ponens,[status(thm)],[2897, 2891])).
% 2.08/1.66 tff(2899,plain,
% 2.08/1.66 ((~hskp8) | c1_1(a909)),
% 2.08/1.66 inference(modus_ponens,[status(thm)],[2898, 2891])).
% 2.08/1.66 tff(2900,plain,
% 2.08/1.66 ((~hskp8) | c1_1(a909)),
% 2.08/1.66 inference(modus_ponens,[status(thm)],[2899, 2891])).
% 2.08/1.66 tff(2901,plain,
% 2.08/1.66 (c1_1(a909)),
% 2.08/1.66 inference(unit_resolution,[status(thm)],[2900, 2884])).
% 2.08/1.66 tff(2902,plain,
% 2.08/1.66 (hskp13 | c0_1(a900)),
% 2.08/1.66 inference(unit_resolution,[status(thm)],[2595, 124, 21, 2834, 2823, 20])).
% 2.08/1.66 tff(2903,plain,
% 2.08/1.66 (hskp13),
% 2.08/1.66 inference(unit_resolution,[status(thm)],[2902, 2867])).
% 2.08/1.66 tff(2904,plain,
% 2.08/1.66 (~c3_1(a921)),
% 2.08/1.66 inference(unit_resolution,[status(thm)],[225, 2903])).
% 2.08/1.66 tff(2905,plain,
% 2.08/1.66 (~c0_1(a921)),
% 2.08/1.66 inference(unit_resolution,[status(thm)],[231, 2903])).
% 2.08/1.66 tff(2906,plain,
% 2.08/1.66 (c2_1(a921)),
% 2.08/1.66 inference(unit_resolution,[status(thm)],[242, 2903])).
% 2.08/1.66 tff(2907,plain,
% 2.08/1.66 (hskp28),
% 2.08/1.66 inference(unit_resolution,[status(thm)],[249, 124, 32, 2906, 2905, 2904, 208])).
% 2.08/1.66 tff(2908,plain,
% 2.08/1.66 (c3_1(a916)),
% 2.08/1.66 inference(unit_resolution,[status(thm)],[271, 2907])).
% 2.08/1.66 tff(2909,plain,
% 2.08/1.66 (c1_1(a916)),
% 2.08/1.66 inference(unit_resolution,[status(thm)],[282, 2907])).
% 2.08/1.66 tff(2910,plain,
% 2.08/1.66 (c0_1(a916)),
% 2.08/1.66 inference(unit_resolution,[status(thm)],[260, 2907])).
% 2.08/1.66 tff(2911,plain,
% 2.08/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c3_1(a909) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | c2_1(a909) | (~c1_1(a909)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a909) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | c2_1(a909) | (~c1_1(a909)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 2.08/1.66 inference(rewrite,[status(thm)],[])).
% 2.08/1.66 tff(2912,plain,
% 2.08/1.66 (((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a909) | c2_1(a909) | (~c1_1(a909))) <=> (c3_1(a909) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | c2_1(a909) | (~c1_1(a909)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 2.08/1.66 inference(rewrite,[status(thm)],[])).
% 2.08/1.66 tff(2913,plain,
% 2.08/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a909) | c2_1(a909) | (~c1_1(a909)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c3_1(a909) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | c2_1(a909) | (~c1_1(a909)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916))))),
% 2.08/1.66 inference(monotonicity,[status(thm)],[2912])).
% 2.08/1.66 tff(2914,plain,
% 2.08/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a909) | c2_1(a909) | (~c1_1(a909)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a909) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | c2_1(a909) | (~c1_1(a909)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916)))),
% 2.08/1.66 inference(transitivity,[status(thm)],[2913, 2911])).
% 2.08/1.66 tff(2915,plain,
% 2.08/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a916)) | (~c1_1(a916)) | (~c0_1(a916)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c3_1(a909) | c2_1(a909) | (~c1_1(a909)))),
% 2.08/1.66 inference(quant_inst,[status(thm)],[])).
% 2.08/1.66 tff(2916,plain,
% 2.08/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c3_1(a909) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | c2_1(a909) | (~c1_1(a909)) | (~c3_1(a916)) | (~c0_1(a916)) | (~c1_1(a916))),
% 2.08/1.66 inference(modus_ponens,[status(thm)],[2915, 2914])).
% 2.08/1.66 tff(2917,plain,
% 2.08/1.66 (c2_1(a909)),
% 2.08/1.66 inference(unit_resolution,[status(thm)],[2916, 124, 2910, 2909, 2908, 2901, 2556, 2555, 2890, 2554, 31])).
% 2.08/1.66 tff(2918,plain,
% 2.08/1.66 (^[U: $i] : refl((hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 2.08/1.66 inference(bind,[status(th)],[])).
% 2.08/1.66 tff(2919,plain,
% 2.08/1.66 (![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.08/1.66 inference(quant_intro,[status(thm)],[2918])).
% 2.08/1.66 tff(2920,plain,
% 2.08/1.66 (![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.08/1.66 inference(rewrite,[status(thm)],[])).
% 2.08/1.66 tff(2921,plain,
% 2.08/1.66 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp1))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) | hskp10) <=> ((hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp10))), rewrite(((hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp10) <=> (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) | hskp10) <=> (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 2.08/1.66 inference(bind,[status(th)],[])).
% 2.08/1.66 tff(2922,plain,
% 2.08/1.66 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) | hskp10) <=> ![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.08/1.66 inference(quant_intro,[status(thm)],[2921])).
% 2.08/1.66 tff(2923,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause150')).
% 2.08/1.66 tff(2924,plain,
% 2.08/1.66 (![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.08/1.66 inference(modus_ponens,[status(thm)],[2923, 2922])).
% 2.08/1.66 tff(2925,plain,
% 2.08/1.66 (![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.08/1.66 inference(modus_ponens,[status(thm)],[2924, 2920])).
% 2.08/1.66 tff(2926,plain,(
% 2.08/1.66 ![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.08/1.66 inference(skolemize,[status(sab)],[2925])).
% 2.08/1.66 tff(2927,plain,
% 2.08/1.66 (![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.08/1.66 inference(modus_ponens,[status(thm)],[2926, 2919])).
% 2.08/1.66 tff(2928,plain,
% 2.08/1.66 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | hskp1 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914)))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp10 | hskp1 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914)))),
% 2.08/1.66 inference(rewrite,[status(thm)],[])).
% 2.08/1.66 tff(2929,plain,
% 2.08/1.66 ((hskp10 | hskp1 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c0_1(a914))) <=> (hskp10 | hskp1 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914)))),
% 2.08/1.66 inference(rewrite,[status(thm)],[])).
% 2.08/1.66 tff(2930,plain,
% 2.08/1.66 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c0_1(a914)))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | hskp1 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914))))),
% 2.08/1.66 inference(monotonicity,[status(thm)],[2929])).
% 2.08/1.66 tff(2931,plain,
% 2.08/1.66 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c0_1(a914)))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp10 | hskp1 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914)))),
% 2.08/1.66 inference(transitivity,[status(thm)],[2930, 2928])).
% 2.08/1.66 tff(2932,plain,
% 2.08/1.66 ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c2_1(a914) | (~c3_1(a914)) | (~c0_1(a914)))),
% 2.08/1.66 inference(quant_inst,[status(thm)],[])).
% 2.08/1.66 tff(2933,plain,
% 2.08/1.66 ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp10 | hskp1 | c2_1(a914) | (~ndr1_0) | (~c3_1(a914)) | (~c0_1(a914))),
% 2.08/1.66 inference(modus_ponens,[status(thm)],[2932, 2931])).
% 2.08/1.66 tff(2934,plain,
% 2.08/1.66 (hskp10 | hskp1),
% 2.08/1.66 inference(unit_resolution,[status(thm)],[2933, 124, 2563, 2562, 2561, 2927])).
% 2.08/1.66 tff(2935,plain,
% 2.08/1.66 (hskp1),
% 2.08/1.66 inference(unit_resolution,[status(thm)],[2934, 1184])).
% 2.08/1.66 tff(2936,plain,
% 2.08/1.66 (~c1_1(a902)),
% 2.08/1.66 inference(unit_resolution,[status(thm)],[1986, 2935])).
% 2.08/1.66 tff(2937,plain,
% 2.08/1.66 (hskp14 | c0_1(a900)),
% 2.08/1.66 inference(unit_resolution,[status(thm)],[2749, 124, 21, 2824, 2834, 700])).
% 2.08/1.66 tff(2938,plain,
% 2.08/1.66 (hskp14),
% 2.08/1.66 inference(unit_resolution,[status(thm)],[2937, 2867])).
% 2.08/1.66 tff(2939,plain,
% 2.08/1.66 (hskp6),
% 2.08/1.66 inference(unit_resolution,[status(thm)],[596, 2938, 21])).
% 2.08/1.66 tff(2940,plain,
% 2.08/1.66 (~c2_1(a907)),
% 2.08/1.66 inference(unit_resolution,[status(thm)],[407, 2939])).
% 2.08/1.66 tff(2941,plain,
% 2.08/1.66 (c2_1(a902)),
% 2.08/1.66 inference(unit_resolution,[status(thm)],[1596, 2935])).
% 2.08/1.66 tff(2942,plain,
% 2.08/1.66 (c0_1(a902)),
% 2.08/1.66 inference(unit_resolution,[status(thm)],[1607, 2935])).
% 2.08/1.66 tff(2943,plain,
% 2.08/1.66 (c1_1(a907)),
% 2.08/1.66 inference(unit_resolution,[status(thm)],[418, 2939])).
% 2.08/1.66 tff(2944,plain,
% 2.08/1.66 (c0_1(a907)),
% 2.08/1.66 inference(unit_resolution,[status(thm)],[725, 2939])).
% 2.08/1.66 tff(2945,plain,
% 2.08/1.66 (hskp0),
% 2.08/1.66 inference(unit_resolution,[status(thm)],[1624, 124, 2944, 2943, 2942, 2941, 2940, 2936, 1618])).
% 2.08/1.66 tff(2946,plain,
% 2.08/1.66 (~c3_1(a901)),
% 2.08/1.66 inference(unit_resolution,[status(thm)],[651, 2945])).
% 2.08/1.66 tff(2947,plain,
% 2.08/1.66 (~c1_1(a901)),
% 2.08/1.66 inference(unit_resolution,[status(thm)],[657, 2945])).
% 2.08/1.66 tff(2948,plain,
% 2.08/1.66 (~c0_1(a901)),
% 2.08/1.66 inference(unit_resolution,[status(thm)],[663, 2945])).
% 2.08/1.66 tff(2949,plain,
% 2.08/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a907) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a907) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900))),
% 2.08/1.66 inference(rewrite,[status(thm)],[])).
% 2.08/1.66 tff(2950,plain,
% 2.08/1.66 (((~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c0_1(a907)) | c0_1(a900) | (~c1_1(a900)) | (~c2_1(a900)) | c3_1(a901) | c1_1(a901) | c0_1(a901)) <=> (c2_1(a907) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900))),
% 2.08/1.66 inference(rewrite,[status(thm)],[])).
% 2.08/1.66 tff(2951,plain,
% 2.08/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c0_1(a907)) | c0_1(a900) | (~c1_1(a900)) | (~c2_1(a900)) | c3_1(a901) | c1_1(a901) | c0_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a907) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900)))),
% 2.08/1.66 inference(monotonicity,[status(thm)],[2950])).
% 2.08/1.66 tff(2952,plain,
% 2.08/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c0_1(a907)) | c0_1(a900) | (~c1_1(a900)) | (~c2_1(a900)) | c3_1(a901) | c1_1(a901) | c0_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a907) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900))),
% 2.08/1.66 inference(transitivity,[status(thm)],[2951, 2949])).
% 2.08/1.66 tff(2953,plain,
% 2.08/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c0_1(a907)) | c0_1(a900) | (~c1_1(a900)) | (~c2_1(a900)) | c3_1(a901) | c1_1(a901) | c0_1(a901))),
% 2.08/1.66 inference(quant_inst,[status(thm)],[])).
% 2.08/1.66 tff(2954,plain,
% 2.08/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a907) | c0_1(a901) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900)),
% 2.08/1.66 inference(modus_ponens,[status(thm)],[2953, 2952])).
% 2.08/1.66 tff(2955,plain,
% 2.08/1.66 (c3_1(a907)),
% 2.08/1.66 inference(unit_resolution,[status(thm)],[2954, 124, 2824, 2834, 2944, 2940, 2948, 2947, 2946, 322, 2867])).
% 2.08/1.66 tff(2956,plain,
% 2.08/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a909) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a909)) | (~c1_1(a909)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c3_1(a909) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a909)) | (~c1_1(a909)))),
% 2.08/1.66 inference(rewrite,[status(thm)],[])).
% 2.08/1.66 tff(2957,plain,
% 2.08/1.66 (((~ndr1_0) | c3_1(a909) | (~c2_1(a909)) | (~c1_1(a909)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a901) | c0_1(a901) | c2_1(a901)) <=> (c3_1(a909) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a909)) | (~c1_1(a909)))),
% 2.08/1.66 inference(rewrite,[status(thm)],[])).
% 2.08/1.66 tff(2958,plain,
% 2.08/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a909) | (~c2_1(a909)) | (~c1_1(a909)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a901) | c0_1(a901) | c2_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c3_1(a909) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a909)) | (~c1_1(a909))))),
% 2.08/1.66 inference(monotonicity,[status(thm)],[2957])).
% 2.08/1.66 tff(2959,plain,
% 2.08/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a909) | (~c2_1(a909)) | (~c1_1(a909)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a901) | c0_1(a901) | c2_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c3_1(a909) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a909)) | (~c1_1(a909)))),
% 2.08/1.66 inference(transitivity,[status(thm)],[2958, 2956])).
% 2.08/1.66 tff(2960,plain,
% 2.08/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a909) | (~c2_1(a909)) | (~c1_1(a909)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a901) | c0_1(a901) | c2_1(a901))),
% 2.08/1.66 inference(quant_inst,[status(thm)],[])).
% 2.08/1.66 tff(2961,plain,
% 2.08/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c3_1(a909) | c3_1(a906) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a909)) | (~c1_1(a909))),
% 2.08/1.66 inference(modus_ponens,[status(thm)],[2960, 2959])).
% 2.08/1.66 tff(2962,plain,
% 2.08/1.66 (c2_1(a901) | (~c2_1(a909))),
% 2.08/1.66 inference(unit_resolution,[status(thm)],[2961, 124, 2901, 2556, 2555, 2890, 2554, 2948, 2947, 520])).
% 2.08/1.66 tff(2963,plain,
% 2.08/1.66 (c2_1(a901)),
% 2.08/1.66 inference(unit_resolution,[status(thm)],[2962, 2917])).
% 2.08/1.66 tff(2964,plain,
% 2.08/1.66 (((~hskp8) | (~c0_1(a909))) <=> ((~hskp8) | (~c0_1(a909)))),
% 2.08/1.66 inference(rewrite,[status(thm)],[])).
% 2.08/1.66 tff(2965,plain,
% 2.08/1.66 (((~c0_1(a909)) | (~hskp8)) <=> ((~hskp8) | (~c0_1(a909)))),
% 2.08/1.66 inference(rewrite,[status(thm)],[])).
% 2.08/1.66 tff(2966,axiom,((~c0_1(a909)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause112')).
% 2.08/1.66 tff(2967,plain,
% 2.08/1.66 ((~hskp8) | (~c0_1(a909))),
% 2.08/1.66 inference(modus_ponens,[status(thm)],[2966, 2965])).
% 2.08/1.66 tff(2968,plain,
% 2.08/1.66 ((~hskp8) | (~c0_1(a909))),
% 2.08/1.66 inference(modus_ponens,[status(thm)],[2967, 2964])).
% 2.08/1.66 tff(2969,plain,
% 2.08/1.66 (~c0_1(a909)),
% 2.08/1.66 inference(unit_resolution,[status(thm)],[2968, 2884])).
% 2.08/1.66 tff(2970,plain,
% 2.08/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a909) | c2_1(a907) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a909)) | (~c1_1(a909)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a909) | c2_1(a907) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a909)) | (~c1_1(a909)))),
% 2.08/1.66 inference(rewrite,[status(thm)],[])).
% 2.08/1.66 tff(2971,plain,
% 2.08/1.66 (((~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907)) | c3_1(a901) | c1_1(a901) | (~c2_1(a901)) | c0_1(a909) | (~c2_1(a909)) | (~c1_1(a909))) <=> (c0_1(a909) | c2_1(a907) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a909)) | (~c1_1(a909)))),
% 2.08/1.66 inference(rewrite,[status(thm)],[])).
% 2.08/1.66 tff(2972,plain,
% 2.08/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907)) | c3_1(a901) | c1_1(a901) | (~c2_1(a901)) | c0_1(a909) | (~c2_1(a909)) | (~c1_1(a909)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a909) | c2_1(a907) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a909)) | (~c1_1(a909))))),
% 2.08/1.66 inference(monotonicity,[status(thm)],[2971])).
% 2.08/1.66 tff(2973,plain,
% 2.08/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907)) | c3_1(a901) | c1_1(a901) | (~c2_1(a901)) | c0_1(a909) | (~c2_1(a909)) | (~c1_1(a909)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a909) | c2_1(a907) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a909)) | (~c1_1(a909)))),
% 2.08/1.66 inference(transitivity,[status(thm)],[2972, 2970])).
% 2.08/1.66 tff(2974,plain,
% 2.08/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907)) | c3_1(a901) | c1_1(a901) | (~c2_1(a901)) | c0_1(a909) | (~c2_1(a909)) | (~c1_1(a909)))),
% 2.08/1.66 inference(quant_inst,[status(thm)],[])).
% 2.08/1.66 tff(2975,plain,
% 2.08/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a909) | c2_1(a907) | c1_1(a901) | c3_1(a901) | (~ndr1_0) | (~c2_1(a901)) | (~c3_1(a907)) | (~c1_1(a907)) | (~c2_1(a909)) | (~c1_1(a909))),
% 2.08/1.66 inference(modus_ponens,[status(thm)],[2974, 2973])).
% 2.08/1.66 tff(2976,plain,
% 2.08/1.66 ((~c2_1(a901)) | (~c3_1(a907)) | (~c2_1(a909))),
% 2.08/1.66 inference(unit_resolution,[status(thm)],[2975, 124, 2901, 2943, 2969, 2940, 2947, 2946, 743])).
% 2.08/1.66 tff(2977,plain,
% 2.08/1.66 ($false),
% 2.08/1.66 inference(unit_resolution,[status(thm)],[2976, 2963, 2955, 2917])).
% 2.08/1.66 tff(2978,plain,(c2_1(a912) | hskp12 | hskp7 | c0_1(a912)), inference(lemma,lemma(discharge,[]))).
% 2.08/1.66 tff(2979,plain,
% 2.08/1.66 (c2_1(a912)),
% 2.08/1.66 inference(unit_resolution,[status(thm)],[2978, 21, 32, 665])).
% 2.08/1.66 tff(2980,plain,
% 2.08/1.66 (hskp14),
% 2.08/1.66 inference(unit_resolution,[status(thm)],[707, 2979, 21, 2821])).
% 2.08/1.66 tff(2981,plain,
% 2.08/1.66 (c3_1(a923)),
% 2.08/1.66 inference(unit_resolution,[status(thm)],[587, 2980])).
% 2.08/1.66 tff(2982,plain,
% 2.08/1.66 (~c1_1(a923)),
% 2.08/1.66 inference(unit_resolution,[status(thm)],[570, 2980])).
% 2.08/1.66 tff(2983,plain,
% 2.08/1.66 (~c0_1(a923)),
% 2.08/1.66 inference(unit_resolution,[status(thm)],[576, 2980])).
% 2.08/1.66 tff(2984,assumption,(~c0_1(a923)), introduced(assumption)).
% 2.08/1.66 tff(2985,assumption,(c3_1(a923)), introduced(assumption)).
% 2.08/1.66 tff(2986,plain,
% 2.08/1.66 (hskp13 | (~c2_1(a923))),
% 2.08/1.66 inference(unit_resolution,[status(thm)],[1370, 124, 21, 2985, 2984, 20])).
% 2.08/1.66 tff(2987,plain,
% 2.08/1.66 (~c2_1(a923)),
% 2.08/1.66 inference(unit_resolution,[status(thm)],[2986, 1323])).
% 2.08/1.66 tff(2988,plain,
% 2.08/1.66 (~c3_1(a912)),
% 2.08/1.66 inference(unit_resolution,[status(thm)],[2668, 1323, 21, 689])).
% 2.08/1.66 tff(2989,assumption,(~c1_1(a923)), introduced(assumption)).
% 2.08/1.66 tff(2990,plain,
% 2.08/1.66 ((~c1_1(a906)) | c2_1(a923)),
% 2.08/1.66 inference(unit_resolution,[status(thm)],[1961, 124, 323, 324, 2984, 2989, 325, 520])).
% 2.08/1.66 tff(2991,plain,
% 2.08/1.66 (~c1_1(a906)),
% 2.08/1.66 inference(unit_resolution,[status(thm)],[2990, 2987])).
% 2.08/1.66 tff(2992,plain,
% 2.08/1.66 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a923) | c1_1(a923) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912) | c2_1(a923))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a923) | c1_1(a923) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912) | c2_1(a923))),
% 2.08/1.66 inference(rewrite,[status(thm)],[])).
% 2.08/1.66 tff(2993,plain,
% 2.08/1.66 (((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a923) | c0_1(a923) | c2_1(a923)) <=> (c0_1(a923) | c1_1(a923) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912) | c2_1(a923))),
% 2.08/1.66 inference(rewrite,[status(thm)],[])).
% 2.08/1.66 tff(2994,plain,
% 2.08/1.66 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a923) | c0_1(a923) | c2_1(a923))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a923) | c1_1(a923) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912) | c2_1(a923)))),
% 2.08/1.66 inference(monotonicity,[status(thm)],[2993])).
% 2.08/1.66 tff(2995,plain,
% 2.08/1.66 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a923) | c0_1(a923) | c2_1(a923))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a923) | c1_1(a923) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912) | c2_1(a923))),
% 2.08/1.66 inference(transitivity,[status(thm)],[2994, 2992])).
% 2.08/1.66 tff(2996,plain,
% 2.08/1.66 ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a923) | c0_1(a923) | c2_1(a923))),
% 2.08/1.66 inference(quant_inst,[status(thm)],[])).
% 2.08/1.66 tff(2997,plain,
% 2.08/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a923) | c1_1(a923) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912) | c2_1(a923)),
% 2.08/1.66 inference(modus_ponens,[status(thm)],[2996, 2995])).
% 2.08/1.66 tff(2998,plain,
% 2.08/1.66 ($false),
% 2.08/1.66 inference(unit_resolution,[status(thm)],[2997, 124, 689, 323, 2984, 2989, 665, 325, 540, 2991, 2988, 2987])).
% 2.08/1.66 tff(2999,plain,(hskp13 | (~c2_1(a912)) | (~c0_1(a906)) | c0_1(a923) | c1_1(a923) | c0_1(a912) | c3_1(a906) | (~c2_1(a906)) | hskp7 | (~c3_1(a923))), inference(lemma,lemma(discharge,[]))).
% 2.08/1.66 tff(3000,plain,
% 2.08/1.66 (hskp13),
% 2.08/1.66 inference(unit_resolution,[status(thm)],[2999, 2979, 2556, 2983, 2982, 665, 2554, 2555, 21, 2981])).
% 2.08/1.67 tff(3001,plain,
% 2.08/1.67 (~c3_1(a921)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[225, 3000])).
% 2.08/1.67 tff(3002,plain,
% 2.08/1.67 (~c0_1(a921)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[231, 3000])).
% 2.08/1.67 tff(3003,plain,
% 2.08/1.67 (c2_1(a921)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[242, 3000])).
% 2.08/1.67 tff(3004,plain,
% 2.08/1.67 (hskp28),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[249, 124, 32, 3003, 3002, 3001, 208])).
% 2.08/1.67 tff(3005,plain,
% 2.08/1.67 (c3_1(a916)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[271, 3004])).
% 2.08/1.67 tff(3006,plain,
% 2.08/1.67 (c1_1(a916)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[282, 3004])).
% 2.08/1.67 tff(3007,plain,
% 2.08/1.67 (c0_1(a916)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[260, 3004])).
% 2.08/1.67 tff(3008,plain,
% 2.08/1.67 (~c1_1(a946)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[2684, 124, 3007, 3006, 3005, 2556, 2555, 2257, 2251, 2554, 31])).
% 2.08/1.67 tff(3009,plain,
% 2.08/1.67 (hskp6),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[713, 2979, 21, 2821, 665])).
% 2.08/1.67 tff(3010,plain,
% 2.08/1.67 (~c2_1(a907)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[407, 3009])).
% 2.08/1.67 tff(3011,plain,
% 2.08/1.67 (c0_1(a907)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[725, 3009])).
% 2.08/1.67 tff(3012,plain,
% 2.08/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a946) | c3_1(a946) | c0_1(a912) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a946) | c3_1(a946) | c0_1(a912) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a946))),
% 2.08/1.67 inference(rewrite,[status(thm)],[])).
% 2.08/1.67 tff(3013,plain,
% 2.08/1.67 (((~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c0_1(a907)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a946) | c1_1(a946) | c0_1(a946)) <=> (c0_1(a946) | c3_1(a946) | c0_1(a912) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a946))),
% 2.08/1.67 inference(rewrite,[status(thm)],[])).
% 2.08/1.67 tff(3014,plain,
% 2.08/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c0_1(a907)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a946) | c1_1(a946) | c0_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a946) | c3_1(a946) | c0_1(a912) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a946)))),
% 2.08/1.67 inference(monotonicity,[status(thm)],[3013])).
% 2.08/1.67 tff(3015,plain,
% 2.08/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c0_1(a907)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a946) | c1_1(a946) | c0_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a946) | c3_1(a946) | c0_1(a912) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a946))),
% 2.08/1.67 inference(transitivity,[status(thm)],[3014, 3012])).
% 2.08/1.67 tff(3016,plain,
% 2.08/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c0_1(a907)) | c0_1(a912) | (~c1_1(a912)) | (~c2_1(a912)) | c3_1(a946) | c1_1(a946) | c0_1(a946))),
% 2.08/1.67 inference(quant_inst,[status(thm)],[])).
% 2.08/1.67 tff(3017,plain,
% 2.08/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a946) | c3_1(a946) | c0_1(a912) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c2_1(a912)) | (~c1_1(a912)) | c1_1(a946)),
% 2.08/1.67 inference(modus_ponens,[status(thm)],[3016, 3015])).
% 2.08/1.67 tff(3018,plain,
% 2.08/1.67 (c3_1(a907) | c1_1(a946)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[3017, 124, 2821, 2979, 3011, 2263, 2251, 665, 3010, 322])).
% 2.08/1.67 tff(3019,plain,
% 2.08/1.67 (c3_1(a907)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[3018, 3008])).
% 2.08/1.67 tff(3020,plain,
% 2.08/1.67 (c1_1(a907)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[418, 3009])).
% 2.08/1.67 tff(3021,plain,
% 2.08/1.67 ((~c3_1(a907)) | c1_1(a921)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[750, 124, 3003, 2821, 2979, 3020, 3001, 665, 3010, 743])).
% 2.08/1.67 tff(3022,plain,
% 2.08/1.67 (c1_1(a921)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[3021, 3019])).
% 2.08/1.67 tff(3023,plain,
% 2.08/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a946) | c2_1(a946) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921)) | c1_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a946) | c2_1(a946) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921)) | c1_1(a946))),
% 2.08/1.67 inference(rewrite,[status(thm)],[])).
% 2.08/1.67 tff(3024,plain,
% 2.08/1.67 (((~ndr1_0) | c3_1(a921) | (~c2_1(a921)) | (~c1_1(a921)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a946) | c0_1(a946) | c2_1(a946)) <=> (c0_1(a946) | c2_1(a946) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921)) | c1_1(a946))),
% 2.08/1.67 inference(rewrite,[status(thm)],[])).
% 2.08/1.67 tff(3025,plain,
% 2.08/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a921) | (~c2_1(a921)) | (~c1_1(a921)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a946) | c0_1(a946) | c2_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a946) | c2_1(a946) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921)) | c1_1(a946)))),
% 2.08/1.67 inference(monotonicity,[status(thm)],[3024])).
% 2.08/1.67 tff(3026,plain,
% 2.08/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a921) | (~c2_1(a921)) | (~c1_1(a921)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a946) | c0_1(a946) | c2_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a946) | c2_1(a946) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921)) | c1_1(a946))),
% 2.08/1.67 inference(transitivity,[status(thm)],[3025, 3023])).
% 2.08/1.67 tff(3027,plain,
% 2.08/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c3_1(a921) | (~c2_1(a921)) | (~c1_1(a921)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a906)) | c1_1(a946) | c0_1(a946) | c2_1(a946))),
% 2.08/1.67 inference(quant_inst,[status(thm)],[])).
% 2.08/1.67 tff(3028,plain,
% 2.08/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a946) | c2_1(a946) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | (~c0_1(a906)) | (~c2_1(a921)) | (~c1_1(a921)) | c1_1(a946)),
% 2.08/1.67 inference(modus_ponens,[status(thm)],[3027, 3026])).
% 2.08/1.67 tff(3029,plain,
% 2.08/1.67 ($false),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[3028, 124, 3003, 2556, 2555, 2263, 2257, 3001, 2554, 520, 3008, 3022])).
% 2.08/1.67 tff(3030,plain,(hskp7 | c0_1(a912) | hskp12), inference(lemma,lemma(discharge,[]))).
% 2.08/1.67 tff(3031,plain,
% 2.08/1.67 (c0_1(a912)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[3030, 2578, 32])).
% 2.08/1.67 tff(3032,plain,
% 2.08/1.67 (~hskp10),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[627, 3031])).
% 2.08/1.67 tff(3033,plain,
% 2.08/1.67 (hskp27),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[2270, 3032])).
% 2.08/1.67 tff(3034,plain,
% 2.08/1.67 (c1_1(a900)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[166, 3033])).
% 2.08/1.67 tff(3035,plain,
% 2.08/1.67 (c3_1(a900)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[144, 3033])).
% 2.08/1.67 tff(3036,plain,
% 2.08/1.67 (c2_1(a900)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[155, 3033])).
% 2.08/1.67 tff(3037,plain,
% 2.08/1.67 (~hskp7),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[2577, 323, 324, 325, 429, 428])).
% 2.08/1.67 tff(3038,plain,
% 2.08/1.67 (hskp13 | c0_1(a900)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[2595, 124, 3037, 2439, 2438, 20])).
% 2.08/1.67 tff(3039,plain,
% 2.08/1.67 (c0_1(a900)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[3038, 1323])).
% 2.08/1.67 tff(3040,plain,
% 2.08/1.67 ((~c0_1(a900)) | (~c1_1(a946))),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[2830, 124, 2440, 2438, 323, 324, 2257, 2251, 325, 31])).
% 2.08/1.67 tff(3041,plain,
% 2.08/1.67 (~c1_1(a946)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[3040, 3039])).
% 2.08/1.67 tff(3042,plain,
% 2.08/1.67 (~c1_1(a906)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[2691, 124, 323, 324, 2263, 2257, 325, 520, 3041])).
% 2.08/1.67 tff(3043,plain,
% 2.08/1.67 (hskp0 | c1_1(a946)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[2708, 124, 429, 428, 2263, 2257, 1193, 2702])).
% 2.08/1.67 tff(3044,plain,
% 2.08/1.67 (hskp0),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[3043, 3041])).
% 2.08/1.67 tff(3045,plain,
% 2.08/1.67 (~c3_1(a901)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[651, 3044])).
% 2.08/1.67 tff(3046,plain,
% 2.08/1.67 (~c0_1(a901)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[663, 3044])).
% 2.08/1.67 tff(3047,plain,
% 2.08/1.67 (~c2_1(a901)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[2718, 124, 323, 2263, 2257, 325, 3046, 3045, 540, 3041, 3042])).
% 2.08/1.67 tff(3048,plain,
% 2.08/1.67 (~c1_1(a901)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[657, 3044])).
% 2.08/1.67 tff(3049,plain,
% 2.08/1.67 (~c2_1(a954)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[2654, 124, 1323, 21, 2752, 2725, 20])).
% 2.08/1.67 tff(3050,plain,
% 2.08/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a954) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c2_1(a954) | (~c3_1(a954)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a954) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c2_1(a954) | (~c3_1(a954)))),
% 2.08/1.67 inference(rewrite,[status(thm)],[])).
% 2.08/1.67 tff(3051,plain,
% 2.08/1.67 (((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a954) | c0_1(a954) | (~c3_1(a954)) | c1_1(a901) | c0_1(a901) | c2_1(a901)) <=> (c0_1(a954) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c2_1(a954) | (~c3_1(a954)))),
% 2.08/1.67 inference(rewrite,[status(thm)],[])).
% 2.08/1.67 tff(3052,plain,
% 2.08/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a954) | c0_1(a954) | (~c3_1(a954)) | c1_1(a901) | c0_1(a901) | c2_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a954) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c2_1(a954) | (~c3_1(a954))))),
% 2.08/1.67 inference(monotonicity,[status(thm)],[3051])).
% 2.08/1.67 tff(3053,plain,
% 2.08/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a954) | c0_1(a954) | (~c3_1(a954)) | c1_1(a901) | c0_1(a901) | c2_1(a901))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a954) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c2_1(a954) | (~c3_1(a954)))),
% 2.08/1.67 inference(transitivity,[status(thm)],[3052, 3050])).
% 2.08/1.67 tff(3054,plain,
% 2.08/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a954) | c0_1(a954) | (~c3_1(a954)) | c1_1(a901) | c0_1(a901) | c2_1(a901))),
% 2.08/1.67 inference(quant_inst,[status(thm)],[])).
% 2.08/1.67 tff(3055,plain,
% 2.08/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a954) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c2_1(a954) | (~c3_1(a954))),
% 2.08/1.67 inference(modus_ponens,[status(thm)],[3054, 3053])).
% 2.08/1.67 tff(3056,plain,
% 2.08/1.67 ($false),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[3055, 124, 2440, 2438, 2752, 2725, 2799, 2798, 1665, 2760, 2795, 3049])).
% 2.08/1.67 tff(3057,plain,((~hskp23) | (~c1_1(a900)) | (~c3_1(a900)) | c0_1(a901) | c1_1(a901) | (~c0_1(a900)) | c2_1(a901) | hskp13 | hskp7), inference(lemma,lemma(discharge,[]))).
% 2.08/1.67 tff(3058,plain,
% 2.08/1.67 (~hskp23),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[3057, 3046, 2438, 2440, 3048, 3039, 3047, 1323, 3037])).
% 2.08/1.67 tff(3059,plain,
% 2.08/1.67 (hskp23 | hskp15 | (~c0_1(a900))),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[2629, 124, 2439, 2438, 2626])).
% 2.08/1.67 tff(3060,plain,
% 2.08/1.67 (hskp15),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[3059, 3058, 3039])).
% 2.08/1.67 tff(3061,plain,
% 2.08/1.67 (~c0_1(a924)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[1267, 3060])).
% 2.08/1.67 tff(3062,plain,
% 2.08/1.67 (c2_1(a924)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[1280, 3060])).
% 2.08/1.67 tff(3063,plain,
% 2.08/1.67 (~c3_1(a924)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[2606, 124, 1323, 3037, 3062, 3061, 20])).
% 2.08/1.67 tff(3064,plain,
% 2.08/1.67 (hskp9 | c1_1(a906) | (~c0_1(a900))),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[2840, 124, 2439, 2438, 323, 325, 882])).
% 2.08/1.67 tff(3065,plain,
% 2.08/1.67 (hskp9),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[3064, 3042, 3039])).
% 2.08/1.67 tff(3066,plain,
% 2.08/1.67 (~c3_1(a910)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[959, 3065])).
% 2.08/1.67 tff(3067,plain,
% 2.08/1.67 (c2_1(a910)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[1009, 3065])).
% 2.08/1.67 tff(3068,plain,
% 2.08/1.67 (c0_1(a910)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[2850, 124, 3067, 323, 2263, 2257, 3066, 325, 540, 3041, 3042])).
% 2.08/1.67 tff(3069,plain,
% 2.08/1.67 (~c1_1(a910)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[965, 3065])).
% 2.08/1.67 tff(3070,plain,
% 2.08/1.67 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a924) | c1_1(a910) | c3_1(a910) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c0_1(a910)) | c3_1(a924) | (~c2_1(a924)))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a924) | c1_1(a910) | c3_1(a910) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c0_1(a910)) | c3_1(a924) | (~c2_1(a924)))),
% 2.08/1.67 inference(rewrite,[status(thm)],[])).
% 2.08/1.67 tff(3071,plain,
% 2.08/1.67 (((~ndr1_0) | c1_1(a910) | c3_1(a910) | (~c0_1(a910)) | c3_1(a924) | c0_1(a924) | (~c2_1(a924)) | c1_1(a901) | c0_1(a901) | c2_1(a901)) <=> (c0_1(a924) | c1_1(a910) | c3_1(a910) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c0_1(a910)) | c3_1(a924) | (~c2_1(a924)))),
% 2.08/1.67 inference(rewrite,[status(thm)],[])).
% 2.08/1.67 tff(3072,plain,
% 2.08/1.67 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a910) | c3_1(a910) | (~c0_1(a910)) | c3_1(a924) | c0_1(a924) | (~c2_1(a924)) | c1_1(a901) | c0_1(a901) | c2_1(a901))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a924) | c1_1(a910) | c3_1(a910) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c0_1(a910)) | c3_1(a924) | (~c2_1(a924))))),
% 2.08/1.67 inference(monotonicity,[status(thm)],[3071])).
% 2.08/1.67 tff(3073,plain,
% 2.08/1.67 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a910) | c3_1(a910) | (~c0_1(a910)) | c3_1(a924) | c0_1(a924) | (~c2_1(a924)) | c1_1(a901) | c0_1(a901) | c2_1(a901))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a924) | c1_1(a910) | c3_1(a910) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c0_1(a910)) | c3_1(a924) | (~c2_1(a924)))),
% 2.08/1.67 inference(transitivity,[status(thm)],[3072, 3070])).
% 2.08/1.67 tff(3074,plain,
% 2.08/1.67 ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a910) | c3_1(a910) | (~c0_1(a910)) | c3_1(a924) | c0_1(a924) | (~c2_1(a924)) | c1_1(a901) | c0_1(a901) | c2_1(a901))),
% 2.08/1.67 inference(quant_inst,[status(thm)],[])).
% 2.08/1.67 tff(3075,plain,
% 2.08/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a924) | c1_1(a910) | c3_1(a910) | c0_1(a901) | c1_1(a901) | (~ndr1_0) | c2_1(a901) | (~c0_1(a910)) | c3_1(a924) | (~c2_1(a924))),
% 2.08/1.67 inference(modus_ponens,[status(thm)],[3074, 3073])).
% 2.08/1.67 tff(3076,plain,
% 2.08/1.67 ($false),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[3075, 124, 3062, 3061, 3069, 3066, 3046, 3048, 540, 3047, 3068, 3063])).
% 2.08/1.67 tff(3077,plain,(hskp13 | (~c2_1(a900)) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a906)) | c3_1(a906) | (~c2_1(a906)) | (~c0_1(a914)) | (~c3_1(a914)) | c2_1(a914)), inference(lemma,lemma(discharge,[]))).
% 2.08/1.67 tff(3078,plain,
% 2.08/1.67 (hskp13),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[3077, 3036, 3035, 3034, 2556, 2554, 2555, 2563, 2562, 2561])).
% 2.08/1.67 tff(3079,plain,
% 2.08/1.67 (~c3_1(a921)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[225, 3078])).
% 2.08/1.67 tff(3080,plain,
% 2.08/1.67 (~c0_1(a921)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[231, 3078])).
% 2.08/1.67 tff(3081,plain,
% 2.08/1.67 (c2_1(a921)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[242, 3078])).
% 2.08/1.67 tff(3082,plain,
% 2.08/1.67 (hskp28),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[249, 124, 32, 3081, 3080, 3079, 208])).
% 2.08/1.67 tff(3083,plain,
% 2.08/1.67 (c3_1(a916)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[271, 3082])).
% 2.08/1.67 tff(3084,plain,
% 2.08/1.67 (c1_1(a916)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[282, 3082])).
% 2.08/1.67 tff(3085,plain,
% 2.08/1.67 (c0_1(a916)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[260, 3082])).
% 2.08/1.67 tff(3086,plain,
% 2.08/1.67 (~c1_1(a946)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[2684, 124, 3085, 3084, 3083, 2556, 2555, 2257, 2251, 2554, 31])).
% 2.08/1.67 tff(3087,plain,
% 2.08/1.67 (~c1_1(a906)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[2691, 124, 2556, 2555, 2263, 2257, 2554, 520, 3086])).
% 2.08/1.67 tff(3088,plain,
% 2.08/1.67 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a946) | c2_1(a946) | c0_1(a921) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921)) | c1_1(a946))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a946) | c2_1(a946) | c0_1(a921) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921)) | c1_1(a946))),
% 2.08/1.67 inference(rewrite,[status(thm)],[])).
% 2.08/1.67 tff(3089,plain,
% 2.08/1.67 (((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a946) | c0_1(a946) | c2_1(a946)) <=> (c0_1(a946) | c2_1(a946) | c0_1(a921) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921)) | c1_1(a946))),
% 2.08/1.67 inference(rewrite,[status(thm)],[])).
% 2.08/1.67 tff(3090,plain,
% 2.08/1.67 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a946) | c0_1(a946) | c2_1(a946))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a946) | c2_1(a946) | c0_1(a921) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921)) | c1_1(a946)))),
% 2.08/1.67 inference(monotonicity,[status(thm)],[3089])).
% 2.08/1.67 tff(3091,plain,
% 2.08/1.67 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a946) | c0_1(a946) | c2_1(a946))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a946) | c2_1(a946) | c0_1(a921) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921)) | c1_1(a946))),
% 2.08/1.67 inference(transitivity,[status(thm)],[3090, 3088])).
% 2.08/1.67 tff(3092,plain,
% 2.08/1.67 ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a921) | c0_1(a921) | (~c2_1(a921)) | c1_1(a946) | c0_1(a946) | c2_1(a946))),
% 2.08/1.67 inference(quant_inst,[status(thm)],[])).
% 2.08/1.67 tff(3093,plain,
% 2.08/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a946) | c2_1(a946) | c0_1(a921) | c3_1(a921) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a921)) | c1_1(a946)),
% 2.08/1.67 inference(modus_ponens,[status(thm)],[3092, 3091])).
% 2.08/1.67 tff(3094,plain,
% 2.08/1.67 ($false),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[3093, 124, 3081, 2556, 2263, 2257, 3080, 3079, 2554, 540, 3086, 3087])).
% 2.08/1.67 tff(3095,plain,(hskp12), inference(lemma,lemma(discharge,[]))).
% 2.08/1.67 tff(3096,plain,
% 2.08/1.67 (~c2_1(a917)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[332, 3095])).
% 2.08/1.67 tff(3097,plain,
% 2.08/1.67 (c3_1(a917)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[354, 3095])).
% 2.08/1.67 tff(3098,plain,
% 2.08/1.67 (c1_1(a917)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[343, 3095])).
% 2.08/1.67 tff(3099,plain,
% 2.08/1.67 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (c2_1(a946) | c3_1(a946) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917)) | (~c1_1(a946)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | c2_1(a946) | c3_1(a946) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917)) | (~c1_1(a946)))),
% 2.08/1.67 inference(rewrite,[status(thm)],[])).
% 2.08/1.67 tff(3100,plain,
% 2.08/1.67 (((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a946) | c2_1(a946) | (~c1_1(a946))) <=> (c2_1(a946) | c3_1(a946) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917)) | (~c1_1(a946)))),
% 2.08/1.67 inference(rewrite,[status(thm)],[])).
% 2.08/1.67 tff(3101,plain,
% 2.08/1.67 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a946) | c2_1(a946) | (~c1_1(a946)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (c2_1(a946) | c3_1(a946) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917)) | (~c1_1(a946))))),
% 2.08/1.67 inference(monotonicity,[status(thm)],[3100])).
% 2.08/1.67 tff(3102,plain,
% 2.08/1.67 (((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a946) | c2_1(a946) | (~c1_1(a946)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | c2_1(a946) | c3_1(a946) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917)) | (~c1_1(a946)))),
% 2.08/1.67 inference(transitivity,[status(thm)],[3101, 3099])).
% 2.08/1.67 tff(3103,plain,
% 2.08/1.67 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | ((~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c1_1(a917)) | c3_1(a946) | c2_1(a946) | (~c1_1(a946)))),
% 2.08/1.67 inference(quant_inst,[status(thm)],[])).
% 2.08/1.67 tff(3104,plain,
% 2.08/1.67 ((~![V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | c2_1(a946) | c3_1(a946) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c1_1(a917)) | (~c1_1(a946))),
% 2.08/1.67 inference(modus_ponens,[status(thm)],[3103, 3102])).
% 2.08/1.67 tff(3105,plain,
% 2.08/1.67 (~c1_1(a946)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[3104, 124, 3098, 3097, 2257, 2251, 3096, 10])).
% 2.08/1.67 tff(3106,plain,
% 2.08/1.67 (~hskp11),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[132, 43, 21])).
% 2.08/1.67 tff(3107,plain,
% 2.08/1.67 (hskp27 | hskp11),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[2521, 3105])).
% 2.08/1.67 tff(3108,plain,
% 2.08/1.67 (hskp27),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[3107, 3106])).
% 2.08/1.67 tff(3109,plain,
% 2.08/1.67 (c2_1(a900)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[155, 3108])).
% 2.08/1.67 tff(3110,plain,
% 2.08/1.67 (c1_1(a900)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[166, 3108])).
% 2.08/1.67 tff(3111,plain,
% 2.08/1.67 (c3_1(a900)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[144, 3108])).
% 2.08/1.67 tff(3112,plain,
% 2.08/1.67 (~hskp14),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[2474, 3110, 43, 3109, 3111])).
% 2.08/1.67 tff(3113,plain,
% 2.08/1.67 (c0_1(a900)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[2749, 124, 3112, 21, 3110, 3109, 700])).
% 2.08/1.67 tff(3114,plain,
% 2.08/1.67 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp5 | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c0_1(a917)))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp7 | hskp5 | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c0_1(a917)))),
% 2.08/1.67 inference(rewrite,[status(thm)],[])).
% 2.08/1.67 tff(3115,plain,
% 2.08/1.67 ((hskp7 | hskp5 | (~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c0_1(a917))) <=> (hskp7 | hskp5 | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c0_1(a917)))),
% 2.08/1.67 inference(rewrite,[status(thm)],[])).
% 2.08/1.67 tff(3116,plain,
% 2.08/1.67 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp5 | (~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c0_1(a917)))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp5 | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c0_1(a917))))),
% 2.08/1.67 inference(monotonicity,[status(thm)],[3115])).
% 2.08/1.67 tff(3117,plain,
% 2.08/1.67 (((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp5 | (~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c0_1(a917)))) <=> ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp7 | hskp5 | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c0_1(a917)))),
% 2.08/1.67 inference(transitivity,[status(thm)],[3116, 3114])).
% 2.08/1.67 tff(3118,plain,
% 2.08/1.67 ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp7 | hskp5 | (~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c0_1(a917)))),
% 2.08/1.67 inference(quant_inst,[status(thm)],[])).
% 2.08/1.67 tff(3119,plain,
% 2.08/1.67 ((~![U: $i] : (hskp7 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp7 | hskp5 | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c0_1(a917))),
% 2.08/1.67 inference(modus_ponens,[status(thm)],[3118, 3117])).
% 2.08/1.67 tff(3120,plain,
% 2.08/1.67 (hskp7 | hskp5 | (~c0_1(a917))),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[3119, 124, 3097, 3096, 63])).
% 2.08/1.67 tff(3121,plain,
% 2.08/1.67 (~c0_1(a917)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[3120, 43, 21])).
% 2.08/1.67 tff(3122,plain,
% 2.08/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a946) | c2_1(a946) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | c0_1(a917) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c1_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a946) | c2_1(a946) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | c0_1(a917) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c1_1(a946))),
% 2.08/1.67 inference(rewrite,[status(thm)],[])).
% 2.08/1.67 tff(3123,plain,
% 2.08/1.67 (((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a917) | c0_1(a917) | (~c3_1(a917)) | c1_1(a946) | c0_1(a946) | c2_1(a946)) <=> (c0_1(a946) | c2_1(a946) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | c0_1(a917) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c1_1(a946))),
% 2.08/1.67 inference(rewrite,[status(thm)],[])).
% 2.08/1.67 tff(3124,plain,
% 2.08/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a917) | c0_1(a917) | (~c3_1(a917)) | c1_1(a946) | c0_1(a946) | c2_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a946) | c2_1(a946) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | c0_1(a917) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c1_1(a946)))),
% 2.08/1.67 inference(monotonicity,[status(thm)],[3123])).
% 2.08/1.67 tff(3125,plain,
% 2.08/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a917) | c0_1(a917) | (~c3_1(a917)) | c1_1(a946) | c0_1(a946) | c2_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a946) | c2_1(a946) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | c0_1(a917) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c1_1(a946))),
% 2.08/1.67 inference(transitivity,[status(thm)],[3124, 3122])).
% 2.08/1.67 tff(3126,plain,
% 2.08/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a917) | c0_1(a917) | (~c3_1(a917)) | c1_1(a946) | c0_1(a946) | c2_1(a946))),
% 2.08/1.67 inference(quant_inst,[status(thm)],[])).
% 2.08/1.67 tff(3127,plain,
% 2.08/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a946) | c2_1(a946) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | c0_1(a917) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)) | c1_1(a946)),
% 2.08/1.67 inference(modus_ponens,[status(thm)],[3126, 3125])).
% 2.08/1.67 tff(3128,plain,
% 2.08/1.67 ($false),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[3127, 124, 3110, 3111, 3097, 2263, 2257, 3096, 1665, 3121, 3105, 3113])).
% 2.08/1.67 tff(3129,plain,(hskp5 | hskp7), inference(lemma,lemma(discharge,[]))).
% 2.08/1.67 tff(3130,plain,
% 2.08/1.67 (hskp5),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[3129, 21])).
% 2.08/1.67 tff(3131,plain,
% 2.08/1.67 (~c3_1(a906)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[300, 3130])).
% 2.08/1.67 tff(3132,plain,
% 2.08/1.67 (c2_1(a906)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[294, 3130])).
% 2.08/1.67 tff(3133,plain,
% 2.08/1.67 (c0_1(a906)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[311, 3130])).
% 2.08/1.67 tff(3134,plain,
% 2.08/1.67 (~c1_1(a906)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[2691, 124, 3133, 3132, 2263, 2257, 3131, 520, 3105])).
% 2.08/1.67 tff(3135,plain,
% 2.08/1.67 (c0_1(a900)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[2902, 1323])).
% 2.08/1.67 tff(3136,plain,
% 2.08/1.67 (~c1_1(a912)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[2866, 3135, 1124, 3133, 3131, 665, 3132])).
% 2.08/1.67 tff(3137,plain,
% 2.08/1.67 (hskp14),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[2781, 3136, 665, 1124, 1323, 21])).
% 2.08/1.67 tff(3138,plain,
% 2.08/1.67 (~c0_1(a923)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[576, 3137])).
% 2.08/1.67 tff(3139,plain,
% 2.08/1.67 (c3_1(a923)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[587, 3137])).
% 2.08/1.67 tff(3140,plain,
% 2.08/1.67 (~c2_1(a923)),
% 2.08/1.67 inference(unit_resolution,[status(thm)],[1370, 124, 1323, 21, 3139, 3138, 20])).
% 2.08/1.67 tff(3141,plain,
% 2.08/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a912) | c2_1(a912) | c0_1(a923) | c0_1(a912) | (~ndr1_0) | c2_1(a923) | (~c3_1(a923)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c0_1(a923) | c0_1(a912) | (~ndr1_0) | c2_1(a923) | (~c3_1(a923)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)))),
% 2.08/1.67 inference(rewrite,[status(thm)],[])).
% 2.08/1.67 tff(3142,plain,
% 2.08/1.67 (((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a923) | c0_1(a923) | (~c3_1(a923)) | c1_1(a912) | c0_1(a912) | c2_1(a912)) <=> (c1_1(a912) | c2_1(a912) | c0_1(a923) | c0_1(a912) | (~ndr1_0) | c2_1(a923) | (~c3_1(a923)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)))),
% 2.08/1.68 inference(rewrite,[status(thm)],[])).
% 2.08/1.68 tff(3143,plain,
% 2.08/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a923) | c0_1(a923) | (~c3_1(a923)) | c1_1(a912) | c0_1(a912) | c2_1(a912))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a912) | c2_1(a912) | c0_1(a923) | c0_1(a912) | (~ndr1_0) | c2_1(a923) | (~c3_1(a923)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900))))),
% 2.08/1.68 inference(monotonicity,[status(thm)],[3142])).
% 2.08/1.68 tff(3144,plain,
% 2.08/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a923) | c0_1(a923) | (~c3_1(a923)) | c1_1(a912) | c0_1(a912) | c2_1(a912))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c0_1(a923) | c0_1(a912) | (~ndr1_0) | c2_1(a923) | (~c3_1(a923)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900)))),
% 2.08/1.68 inference(transitivity,[status(thm)],[3143, 3141])).
% 2.08/1.68 tff(3145,plain,
% 2.08/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c3_1(a900)) | (~c1_1(a900)) | (~c0_1(a900)) | c2_1(a923) | c0_1(a923) | (~c3_1(a923)) | c1_1(a912) | c0_1(a912) | c2_1(a912))),
% 2.08/1.68 inference(quant_inst,[status(thm)],[])).
% 2.08/1.68 tff(3146,plain,
% 2.08/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a912) | c2_1(a912) | c0_1(a923) | c0_1(a912) | (~ndr1_0) | c2_1(a923) | (~c3_1(a923)) | (~c1_1(a900)) | (~c3_1(a900)) | (~c0_1(a900))),
% 2.08/1.68 inference(modus_ponens,[status(thm)],[3145, 3144])).
% 2.08/1.68 tff(3147,plain,
% 2.08/1.68 ($false),
% 2.08/1.68 inference(unit_resolution,[status(thm)],[3146, 124, 2824, 2823, 3139, 3136, 1124, 3138, 665, 1665, 3135, 3140])).
% 2.08/1.68 tff(3148,plain,(hskp13 | c2_1(a912) | c0_1(a912) | hskp7), inference(lemma,lemma(discharge,[]))).
% 2.08/1.68 tff(3149,plain,
% 2.08/1.68 (hskp13),
% 2.08/1.68 inference(unit_resolution,[status(thm)],[3148, 1124, 665, 21])).
% 2.08/1.68 tff(3150,plain,
% 2.08/1.68 (c1_1(a912)),
% 2.08/1.68 inference(unit_resolution,[status(thm)],[2585, 3149, 665, 1124, 3133, 3131, 3132])).
% 2.08/1.68 tff(3151,plain,
% 2.08/1.68 (~c0_1(a900)),
% 2.08/1.68 inference(unit_resolution,[status(thm)],[2866, 3150, 1124, 3133, 3131, 665, 3132])).
% 2.08/1.68 tff(3152,plain,
% 2.08/1.68 (hskp14),
% 2.08/1.68 inference(unit_resolution,[status(thm)],[2937, 3151])).
% 2.08/1.68 tff(3153,plain,
% 2.08/1.68 (hskp6),
% 2.08/1.68 inference(unit_resolution,[status(thm)],[596, 3152, 21])).
% 2.08/1.68 tff(3154,plain,
% 2.08/1.68 (~c2_1(a907)),
% 2.08/1.68 inference(unit_resolution,[status(thm)],[407, 3153])).
% 2.08/1.68 tff(3155,plain,
% 2.08/1.68 (c1_1(a907)),
% 2.08/1.68 inference(unit_resolution,[status(thm)],[418, 3153])).
% 2.08/1.68 tff(3156,plain,
% 2.08/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a907) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | c1_1(a906) | (~c3_1(a907)) | (~c1_1(a907)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a907) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | c1_1(a906) | (~c3_1(a907)) | (~c1_1(a907)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900))),
% 2.08/1.68 inference(rewrite,[status(thm)],[])).
% 2.08/1.68 tff(3157,plain,
% 2.08/1.68 (((~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907)) | c3_1(a906) | c1_1(a906) | (~c2_1(a906)) | c0_1(a900) | (~c2_1(a900)) | (~c1_1(a900))) <=> (c2_1(a907) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | c1_1(a906) | (~c3_1(a907)) | (~c1_1(a907)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900))),
% 2.08/1.68 inference(rewrite,[status(thm)],[])).
% 2.08/1.68 tff(3158,plain,
% 2.08/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907)) | c3_1(a906) | c1_1(a906) | (~c2_1(a906)) | c0_1(a900) | (~c2_1(a900)) | (~c1_1(a900)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a907) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | c1_1(a906) | (~c3_1(a907)) | (~c1_1(a907)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900)))),
% 2.08/1.68 inference(monotonicity,[status(thm)],[3157])).
% 2.08/1.68 tff(3159,plain,
% 2.08/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907)) | c3_1(a906) | c1_1(a906) | (~c2_1(a906)) | c0_1(a900) | (~c2_1(a900)) | (~c1_1(a900)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a907) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | c1_1(a906) | (~c3_1(a907)) | (~c1_1(a907)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900))),
% 2.08/1.68 inference(transitivity,[status(thm)],[3158, 3156])).
% 2.08/1.68 tff(3160,plain,
% 2.08/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a907) | (~c3_1(a907)) | (~c1_1(a907)) | c3_1(a906) | c1_1(a906) | (~c2_1(a906)) | c0_1(a900) | (~c2_1(a900)) | (~c1_1(a900)))),
% 2.08/1.68 inference(quant_inst,[status(thm)],[])).
% 2.08/1.68 tff(3161,plain,
% 2.08/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a907) | c3_1(a906) | (~ndr1_0) | (~c2_1(a906)) | c1_1(a906) | (~c3_1(a907)) | (~c1_1(a907)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900)),
% 2.08/1.68 inference(modus_ponens,[status(thm)],[3160, 3159])).
% 2.08/1.68 tff(3162,plain,
% 2.08/1.68 (~c3_1(a907)),
% 2.08/1.68 inference(unit_resolution,[status(thm)],[3161, 124, 2824, 2834, 3155, 3132, 3154, 3131, 743, 3151, 3134])).
% 2.08/1.68 tff(3163,plain,
% 2.08/1.68 (c0_1(a907)),
% 2.08/1.68 inference(unit_resolution,[status(thm)],[725, 3153])).
% 2.08/1.68 tff(3164,plain,
% 2.08/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a946) | c3_1(a946) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900) | c1_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a946) | c3_1(a946) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900) | c1_1(a946))),
% 2.08/1.68 inference(rewrite,[status(thm)],[])).
% 2.08/1.68 tff(3165,plain,
% 2.08/1.68 (((~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c0_1(a907)) | c0_1(a900) | (~c1_1(a900)) | (~c2_1(a900)) | c3_1(a946) | c1_1(a946) | c0_1(a946)) <=> (c0_1(a946) | c3_1(a946) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900) | c1_1(a946))),
% 2.08/1.68 inference(rewrite,[status(thm)],[])).
% 2.08/1.68 tff(3166,plain,
% 2.08/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c0_1(a907)) | c0_1(a900) | (~c1_1(a900)) | (~c2_1(a900)) | c3_1(a946) | c1_1(a946) | c0_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a946) | c3_1(a946) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900) | c1_1(a946)))),
% 2.08/1.68 inference(monotonicity,[status(thm)],[3165])).
% 2.08/1.68 tff(3167,plain,
% 2.08/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c0_1(a907)) | c0_1(a900) | (~c1_1(a900)) | (~c2_1(a900)) | c3_1(a946) | c1_1(a946) | c0_1(a946))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a946) | c3_1(a946) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900) | c1_1(a946))),
% 2.08/1.68 inference(transitivity,[status(thm)],[3166, 3164])).
% 2.08/1.68 tff(3168,plain,
% 2.08/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a907) | c3_1(a907) | (~c0_1(a907)) | c0_1(a900) | (~c1_1(a900)) | (~c2_1(a900)) | c3_1(a946) | c1_1(a946) | c0_1(a946))),
% 2.08/1.68 inference(quant_inst,[status(thm)],[])).
% 2.08/1.68 tff(3169,plain,
% 2.08/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a946) | c3_1(a946) | c2_1(a907) | (~ndr1_0) | c3_1(a907) | (~c0_1(a907)) | (~c1_1(a900)) | (~c2_1(a900)) | c0_1(a900) | c1_1(a946)),
% 2.08/1.68 inference(modus_ponens,[status(thm)],[3168, 3167])).
% 2.08/1.68 tff(3170,plain,
% 2.08/1.68 ($false),
% 2.08/1.68 inference(unit_resolution,[status(thm)],[3169, 124, 2824, 2834, 3163, 2263, 2251, 3154, 322, 3105, 3151, 3162])).
% 2.08/1.68 tff(3171,plain,(c2_1(a912) | hskp7 | c0_1(a912)), inference(lemma,lemma(discharge,[]))).
% 2.08/1.68 tff(3172,plain,
% 2.08/1.68 (c2_1(a912)),
% 2.08/1.68 inference(unit_resolution,[status(thm)],[3171, 665, 21])).
% 2.08/1.68 tff(3173,plain,
% 2.08/1.68 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a946) | c2_1(a946) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912) | c1_1(a946))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a946) | c2_1(a946) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912) | c1_1(a946))),
% 2.08/1.68 inference(rewrite,[status(thm)],[])).
% 2.08/1.68 tff(3174,plain,
% 2.08/1.68 (((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a946) | c0_1(a946) | c2_1(a946)) <=> (c0_1(a946) | c2_1(a946) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912) | c1_1(a946))),
% 2.08/1.68 inference(rewrite,[status(thm)],[])).
% 2.08/1.68 tff(3175,plain,
% 2.08/1.68 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a946) | c0_1(a946) | c2_1(a946))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a946) | c2_1(a946) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912) | c1_1(a946)))),
% 2.08/1.68 inference(monotonicity,[status(thm)],[3174])).
% 2.08/1.68 tff(3176,plain,
% 2.08/1.68 (((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a946) | c0_1(a946) | c2_1(a946))) <=> ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a946) | c2_1(a946) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912) | c1_1(a946))),
% 2.08/1.68 inference(transitivity,[status(thm)],[3175, 3173])).
% 2.08/1.68 tff(3177,plain,
% 2.08/1.68 ((~![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)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c1_1(a906) | c3_1(a906) | (~c0_1(a906)) | c3_1(a912) | c0_1(a912) | (~c2_1(a912)) | c1_1(a946) | c0_1(a946) | c2_1(a946))),
% 2.12/1.68 inference(quant_inst,[status(thm)],[])).
% 2.12/1.68 tff(3178,plain,
% 2.12/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a946) | c2_1(a946) | c0_1(a912) | c3_1(a906) | (~ndr1_0) | c1_1(a906) | (~c0_1(a906)) | (~c2_1(a912)) | c3_1(a912) | c1_1(a946)),
% 2.12/1.68 inference(modus_ponens,[status(thm)],[3177, 3176])).
% 2.12/1.68 tff(3179,plain,
% 2.12/1.68 ($false),
% 2.12/1.68 inference(unit_resolution,[status(thm)],[3178, 124, 689, 323, 2263, 2257, 665, 325, 540, 3105, 2796, 2797])).
% 2.12/1.68 tff(3180,plain,(c3_1(a912) | (~c2_1(a912)) | (~c0_1(a906)) | c0_1(a912) | c3_1(a906) | c1_1(a906)), inference(lemma,lemma(discharge,[]))).
% 2.12/1.68 tff(3181,plain,
% 2.12/1.68 (c3_1(a912)),
% 2.12/1.68 inference(unit_resolution,[status(thm)],[3180, 3172, 3133, 665, 3131, 3134])).
% 2.12/1.68 tff(3182,plain,
% 2.12/1.68 ($false),
% 2.12/1.68 inference(unit_resolution,[status(thm)],[3093, 124, 2582, 323, 2263, 2257, 2583, 2581, 325, 540, 3105, 2797])).
% 2.12/1.68 tff(3183,plain,((~hskp13) | (~c0_1(a906)) | c3_1(a906) | c1_1(a906)), inference(lemma,lemma(discharge,[]))).
% 2.12/1.68 tff(3184,plain,
% 2.12/1.68 (~hskp13),
% 2.12/1.68 inference(unit_resolution,[status(thm)],[3183, 3133, 3131, 3134])).
% 2.12/1.68 tff(3185,plain,
% 2.12/1.68 ($false),
% 2.12/1.68 inference(unit_resolution,[status(thm)],[1333, 124, 3184, 21, 3172, 665, 20, 3181])).
% 2.12/1.68 tff(3186,plain,(c0_1(a912) | hskp7), inference(lemma,lemma(discharge,[]))).
% 2.12/1.68 tff(3187,plain,
% 2.12/1.68 (c0_1(a912)),
% 2.12/1.68 inference(unit_resolution,[status(thm)],[3186, 21])).
% 2.12/1.68 tff(3188,plain,
% 2.12/1.68 (~hskp10),
% 2.12/1.68 inference(unit_resolution,[status(thm)],[627, 3187])).
% 2.12/1.68 tff(3189,plain,
% 2.12/1.68 (hskp27),
% 2.12/1.68 inference(unit_resolution,[status(thm)],[2270, 3188])).
% 2.12/1.68 tff(3190,plain,
% 2.12/1.68 (c3_1(a900)),
% 2.12/1.68 inference(unit_resolution,[status(thm)],[144, 3189])).
% 2.12/1.68 tff(3191,plain,
% 2.12/1.68 (c2_1(a900)),
% 2.12/1.68 inference(unit_resolution,[status(thm)],[155, 3189])).
% 2.12/1.68 tff(3192,plain,
% 2.12/1.68 (c0_1(a900)),
% 2.12/1.68 inference(unit_resolution,[status(thm)],[2595, 124, 3184, 21, 3191, 3190, 20])).
% 2.12/1.68 tff(3193,plain,
% 2.12/1.68 (c1_1(a900)),
% 2.12/1.68 inference(unit_resolution,[status(thm)],[166, 3189])).
% 2.12/1.68 tff(3194,plain,
% 2.12/1.68 (c0_1(a917)),
% 2.12/1.68 inference(unit_resolution,[status(thm)],[3127, 124, 3193, 3190, 3097, 2263, 2257, 3096, 1665, 3105, 3192])).
% 2.12/1.68 tff(3195,plain,
% 2.12/1.68 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | c0_1(a946) | c2_1(a946) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c0_1(a917)) | c1_1(a946))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | hskp0 | c0_1(a946) | c2_1(a946) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c0_1(a917)) | c1_1(a946))),
% 2.12/1.68 inference(rewrite,[status(thm)],[])).
% 2.12/1.68 tff(3196,plain,
% 2.12/1.68 ((hskp0 | (~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c0_1(a917)) | c2_1(a946) | c0_1(a946) | c1_1(a946)) <=> (hskp0 | c0_1(a946) | c2_1(a946) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c0_1(a917)) | c1_1(a946))),
% 2.12/1.68 inference(rewrite,[status(thm)],[])).
% 2.12/1.68 tff(3197,plain,
% 2.12/1.68 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c0_1(a917)) | c2_1(a946) | c0_1(a946) | c1_1(a946))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | c0_1(a946) | c2_1(a946) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c0_1(a917)) | c1_1(a946)))),
% 2.12/1.68 inference(monotonicity,[status(thm)],[3196])).
% 2.12/1.68 tff(3198,plain,
% 2.12/1.68 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c0_1(a917)) | c2_1(a946) | c0_1(a946) | c1_1(a946))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | hskp0 | c0_1(a946) | c2_1(a946) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c0_1(a917)) | c1_1(a946))),
% 2.12/1.68 inference(transitivity,[status(thm)],[3197, 3195])).
% 2.12/1.68 tff(3199,plain,
% 2.12/1.68 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a917) | (~c3_1(a917)) | (~c0_1(a917)) | c2_1(a946) | c0_1(a946) | c1_1(a946))),
% 2.12/1.69 inference(quant_inst,[status(thm)],[])).
% 2.12/1.69 tff(3200,plain,
% 2.12/1.69 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c1_1(V))) | hskp0 | c0_1(a946) | c2_1(a946) | c2_1(a917) | (~ndr1_0) | (~c3_1(a917)) | (~c0_1(a917)) | c1_1(a946)),
% 2.12/1.69 inference(modus_ponens,[status(thm)],[3199, 3198])).
% 2.12/1.69 tff(3201,plain,
% 2.12/1.69 (hskp0 | (~c0_1(a917))),
% 2.12/1.69 inference(unit_resolution,[status(thm)],[3200, 124, 3097, 2263, 2257, 3096, 2702, 3105])).
% 2.12/1.69 tff(3202,plain,
% 2.12/1.69 (hskp0),
% 2.12/1.69 inference(unit_resolution,[status(thm)],[3201, 3194])).
% 2.12/1.69 tff(3203,plain,
% 2.12/1.69 (~c0_1(a901)),
% 2.12/1.69 inference(unit_resolution,[status(thm)],[663, 3202])).
% 2.12/1.69 tff(3204,plain,
% 2.12/1.69 (~c1_1(a901)),
% 2.12/1.69 inference(unit_resolution,[status(thm)],[657, 3202])).
% 2.12/1.69 tff(3205,plain,
% 2.12/1.69 (~c3_1(a901)),
% 2.12/1.69 inference(unit_resolution,[status(thm)],[651, 3202])).
% 2.12/1.69 tff(3206,plain,
% 2.12/1.69 (~c2_1(a901)),
% 2.12/1.69 inference(unit_resolution,[status(thm)],[2718, 124, 3133, 2263, 2257, 3131, 3203, 3205, 540, 3105, 3134])).
% 2.12/1.69 tff(3207,plain,
% 2.12/1.69 (~hskp23),
% 2.12/1.69 inference(unit_resolution,[status(thm)],[3057, 3206, 21, 3190, 3204, 3192, 3203, 3184, 3193])).
% 2.12/1.69 tff(3208,plain,
% 2.12/1.69 (hskp23 | hskp15 | (~c0_1(a900))),
% 2.12/1.69 inference(unit_resolution,[status(thm)],[2629, 124, 3191, 3190, 2626])).
% 2.12/1.69 tff(3209,plain,
% 2.12/1.69 (hskp15),
% 2.12/1.69 inference(unit_resolution,[status(thm)],[3208, 3207, 3192])).
% 2.12/1.69 tff(3210,plain,
% 2.12/1.69 (~c0_1(a924)),
% 2.12/1.69 inference(unit_resolution,[status(thm)],[1267, 3209])).
% 2.12/1.69 tff(3211,plain,
% 2.12/1.69 (c2_1(a924)),
% 2.12/1.69 inference(unit_resolution,[status(thm)],[1280, 3209])).
% 2.12/1.69 tff(3212,plain,
% 2.12/1.69 (~c3_1(a924)),
% 2.12/1.69 inference(unit_resolution,[status(thm)],[2606, 124, 3184, 21, 3211, 3210, 20])).
% 2.12/1.69 tff(3213,plain,
% 2.12/1.69 (hskp9 | (~c0_1(a900))),
% 2.12/1.69 inference(unit_resolution,[status(thm)],[2840, 124, 3191, 3190, 3133, 3131, 882, 3134])).
% 2.12/1.69 tff(3214,plain,
% 2.12/1.69 (hskp9),
% 2.12/1.69 inference(unit_resolution,[status(thm)],[3213, 3192])).
% 2.12/1.69 tff(3215,plain,
% 2.12/1.69 (~c3_1(a910)),
% 2.12/1.69 inference(unit_resolution,[status(thm)],[959, 3214])).
% 2.12/1.69 tff(3216,plain,
% 2.12/1.69 (c2_1(a910)),
% 2.12/1.69 inference(unit_resolution,[status(thm)],[1009, 3214])).
% 2.12/1.69 tff(3217,plain,
% 2.12/1.69 (c0_1(a910)),
% 2.12/1.69 inference(unit_resolution,[status(thm)],[2850, 124, 3216, 3133, 2263, 2257, 3215, 3131, 540, 3105, 3134])).
% 2.12/1.69 tff(3218,plain,
% 2.12/1.69 (~c1_1(a910)),
% 2.12/1.69 inference(unit_resolution,[status(thm)],[965, 3214])).
% 2.12/1.69 tff(3219,plain,
% 2.12/1.69 ($false),
% 2.12/1.69 inference(unit_resolution,[status(thm)],[3075, 124, 3211, 3210, 3218, 3215, 3203, 3204, 540, 3206, 3217, 3212])).
% 2.12/1.69 tff(3220,plain,(hskp7), inference(lemma,lemma(discharge,[]))).
% 2.12/1.69 tff(3221,plain,
% 2.12/1.69 (~c3_1(a908)),
% 2.12/1.69 inference(unit_resolution,[status(thm)],[467, 3220])).
% 2.12/1.69 tff(3222,plain,
% 2.12/1.69 (~c2_1(a908)),
% 2.12/1.69 inference(unit_resolution,[status(thm)],[473, 3220])).
% 2.12/1.69 tff(3223,plain,
% 2.12/1.69 (c1_1(a908)),
% 2.12/1.69 inference(unit_resolution,[status(thm)],[484, 3220])).
% 2.12/1.69 tff(3224,plain,
% 2.12/1.69 ($false),
% 2.12/1.69 inference(unit_resolution,[status(thm)],[1043, 124, 3098, 3097, 3223, 3096, 3222, 3221, 10])).
% 2.12/1.69 % SZS output end Proof
%------------------------------------------------------------------------------