TSTP Solution File: SYN465-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN465-1 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 23:55:38 EDT 2022
% Result : Unsatisfiable 0.92s 0.86s
% Output : Proof 1.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN465-1 : TPTP v8.1.0. Released v2.1.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Sep 5 04:19:07 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.
% 0.92/0.86 % SZS status Unsatisfiable
% 0.92/0.86 % SZS output start Proof
% 0.92/0.86 tff(c0_1_type, type, (
% 0.92/0.86 c0_1: $i > $o)).
% 0.92/0.86 tff(a20_type, type, (
% 0.92/0.86 a20: $i)).
% 0.92/0.86 tff(hskp30_type, type, (
% 0.92/0.86 hskp30: $o)).
% 0.92/0.86 tff(c3_1_type, type, (
% 0.92/0.86 c3_1: $i > $o)).
% 0.92/0.86 tff(a15_type, type, (
% 0.92/0.86 a15: $i)).
% 0.92/0.86 tff(hskp9_type, type, (
% 0.92/0.86 hskp9: $o)).
% 0.92/0.86 tff(c2_1_type, type, (
% 0.92/0.86 c2_1: $i > $o)).
% 0.92/0.86 tff(c1_1_type, type, (
% 0.92/0.86 c1_1: $i > $o)).
% 0.92/0.86 tff(ndr1_0_type, type, (
% 0.92/0.86 ndr1_0: $o)).
% 0.92/0.86 tff(hskp25_type, type, (
% 0.92/0.86 hskp25: $o)).
% 0.92/0.86 tff(a8_type, type, (
% 0.92/0.86 a8: $i)).
% 0.92/0.86 tff(hskp29_type, type, (
% 0.92/0.86 hskp29: $o)).
% 0.92/0.86 tff(a6_type, type, (
% 0.92/0.86 a6: $i)).
% 0.92/0.86 tff(hskp8_type, type, (
% 0.92/0.86 hskp8: $o)).
% 0.92/0.86 tff(hskp21_type, type, (
% 0.92/0.86 hskp21: $o)).
% 0.92/0.86 tff(hskp3_type, type, (
% 0.92/0.86 hskp3: $o)).
% 0.92/0.86 tff(a21_type, type, (
% 0.92/0.86 a21: $i)).
% 0.92/0.86 tff(hskp11_type, type, (
% 0.92/0.86 hskp11: $o)).
% 0.92/0.86 tff(a9_type, type, (
% 0.92/0.86 a9: $i)).
% 0.92/0.86 tff(hskp5_type, type, (
% 0.92/0.86 hskp5: $o)).
% 0.92/0.86 tff(a30_type, type, (
% 0.92/0.86 a30: $i)).
% 0.92/0.86 tff(hskp16_type, type, (
% 0.92/0.86 hskp16: $o)).
% 0.92/0.86 tff(a29_type, type, (
% 0.92/0.86 a29: $i)).
% 0.92/0.86 tff(hskp15_type, type, (
% 0.92/0.86 hskp15: $o)).
% 0.92/0.86 tff(a39_type, type, (
% 0.92/0.86 a39: $i)).
% 0.92/0.86 tff(hskp24_type, type, (
% 0.92/0.86 hskp24: $o)).
% 0.92/0.86 tff(hskp31_type, type, (
% 0.92/0.86 hskp31: $o)).
% 0.92/0.86 tff(hskp12_type, type, (
% 0.92/0.86 hskp12: $o)).
% 0.92/0.86 tff(a24_type, type, (
% 0.92/0.86 a24: $i)).
% 0.92/0.86 tff(a13_type, type, (
% 0.92/0.86 a13: $i)).
% 0.92/0.86 tff(a10_type, type, (
% 0.92/0.86 a10: $i)).
% 0.92/0.86 tff(hskp6_type, type, (
% 0.92/0.86 hskp6: $o)).
% 0.92/0.86 tff(a52_type, type, (
% 0.92/0.86 a52: $i)).
% 0.92/0.86 tff(hskp2_type, type, (
% 0.92/0.86 hskp2: $o)).
% 0.92/0.86 tff(a5_type, type, (
% 0.92/0.86 a5: $i)).
% 0.92/0.86 tff(a42_type, type, (
% 0.92/0.86 a42: $i)).
% 0.92/0.86 tff(hskp10_type, type, (
% 0.92/0.86 hskp10: $o)).
% 0.92/0.86 tff(a17_type, type, (
% 0.92/0.86 a17: $i)).
% 0.92/0.86 tff(hskp13_type, type, (
% 0.92/0.86 hskp13: $o)).
% 0.92/0.86 tff(a26_type, type, (
% 0.92/0.86 a26: $i)).
% 0.92/0.86 tff(hskp23_type, type, (
% 0.92/0.86 hskp23: $o)).
% 0.92/0.86 tff(a1_type, type, (
% 0.92/0.86 a1: $i)).
% 0.92/0.86 tff(hskp0_type, type, (
% 0.92/0.86 hskp0: $o)).
% 0.92/0.86 tff(a54_type, type, (
% 0.92/0.86 a54: $i)).
% 0.92/0.86 tff(a28_type, type, (
% 0.92/0.86 a28: $i)).
% 0.92/0.86 tff(hskp14_type, type, (
% 0.92/0.86 hskp14: $o)).
% 0.92/0.86 tff(hskp19_type, type, (
% 0.92/0.86 hskp19: $o)).
% 0.92/0.86 tff(a35_type, type, (
% 0.92/0.86 a35: $i)).
% 0.92/0.86 tff(a12_type, type, (
% 0.92/0.86 a12: $i)).
% 0.92/0.86 tff(hskp7_type, type, (
% 0.92/0.86 hskp7: $o)).
% 0.92/0.86 tff(a40_type, type, (
% 0.92/0.86 a40: $i)).
% 0.92/0.86 tff(hskp22_type, type, (
% 0.92/0.86 hskp22: $o)).
% 0.92/0.86 tff(a76_type, type, (
% 0.92/0.86 a76: $i)).
% 0.92/0.86 tff(1,assumption,(~hskp30), introduced(assumption)).
% 0.92/0.86 tff(2,plain,
% 0.92/0.86 (^[U: $i] : refl((hskp25 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp25 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))),
% 0.92/0.86 inference(bind,[status(th)],[])).
% 0.92/0.86 tff(3,plain,
% 0.92/0.86 (![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.92/0.86 inference(quant_intro,[status(thm)],[2])).
% 0.92/0.86 tff(4,plain,
% 0.92/0.86 (![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.92/0.86 inference(rewrite,[status(thm)],[])).
% 0.92/0.86 tff(5,plain,
% 0.92/0.86 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp25) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp25))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp25) <=> (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp25) <=> (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp25) | hskp9) <=> ((hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp9))), rewrite(((hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp9) <=> (hskp25 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp25) | hskp9) <=> (hskp25 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))))),
% 0.92/0.86 inference(bind,[status(th)],[])).
% 0.92/0.86 tff(6,plain,
% 0.92/0.86 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp25) | hskp9) <=> ![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.92/0.86 inference(quant_intro,[status(thm)],[5])).
% 0.92/0.86 tff(7,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp25) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause163')).
% 0.92/0.86 tff(8,plain,
% 0.92/0.86 (![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.92/0.86 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.92/0.86 tff(9,plain,
% 0.92/0.86 (![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.92/0.86 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.92/0.86 tff(10,plain,(
% 0.92/0.86 ![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.92/0.86 inference(skolemize,[status(sab)],[9])).
% 0.92/0.86 tff(11,plain,
% 0.92/0.86 (![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.92/0.86 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.92/0.86 tff(12,plain,
% 0.92/0.86 (^[U: $i] : refl((hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 0.92/0.86 inference(bind,[status(th)],[])).
% 0.92/0.86 tff(13,plain,
% 0.92/0.86 (![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.92/0.86 inference(quant_intro,[status(thm)],[12])).
% 0.92/0.86 tff(14,plain,
% 0.92/0.86 (![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.92/0.86 inference(rewrite,[status(thm)],[])).
% 0.92/0.86 tff(15,plain,
% 0.92/0.86 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp8) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp8))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp8) | hskp21) <=> ((hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp21))), rewrite(((hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp21) <=> (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp8) | hskp21) <=> (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.92/0.86 inference(bind,[status(th)],[])).
% 0.92/0.86 tff(16,plain,
% 0.92/0.86 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp8) | hskp21) <=> ![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.92/0.86 inference(quant_intro,[status(thm)],[15])).
% 0.92/0.86 tff(17,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp8) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause152')).
% 0.92/0.86 tff(18,plain,
% 0.92/0.86 (![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.92/0.86 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.92/0.86 tff(19,plain,
% 0.92/0.86 (![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.92/0.86 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.92/0.86 tff(20,plain,(
% 0.92/0.86 ![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.92/0.86 inference(skolemize,[status(sab)],[19])).
% 0.92/0.86 tff(21,plain,
% 0.92/0.86 (![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.92/0.86 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.92/0.86 tff(22,plain,
% 0.92/0.86 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))),
% 0.92/0.86 inference(bind,[status(th)],[])).
% 0.92/0.86 tff(23,plain,
% 0.92/0.86 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.92/0.86 inference(quant_intro,[status(thm)],[22])).
% 0.92/0.86 tff(24,plain,
% 0.92/0.86 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.92/0.86 inference(rewrite,[status(thm)],[])).
% 0.92/0.86 tff(25,plain,
% 0.92/0.86 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp8) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp8))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))))),
% 0.92/0.86 inference(bind,[status(th)],[])).
% 0.92/0.86 tff(26,plain,
% 0.92/0.86 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.92/0.86 inference(quant_intro,[status(thm)],[25])).
% 0.92/0.86 tff(27,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause173')).
% 0.92/0.86 tff(28,plain,
% 0.92/0.86 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.92/0.86 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.98/0.86 tff(29,plain,
% 0.98/0.86 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.98/0.86 tff(30,plain,(
% 0.98/0.86 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.98/0.86 inference(skolemize,[status(sab)],[29])).
% 0.98/0.86 tff(31,plain,
% 0.98/0.86 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.98/0.86 tff(32,plain,
% 0.98/0.86 (^[U: $i] : refl((hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))),
% 0.98/0.86 inference(bind,[status(th)],[])).
% 0.98/0.86 tff(33,plain,
% 0.98/0.86 (![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.98/0.86 inference(quant_intro,[status(thm)],[32])).
% 0.98/0.86 tff(34,plain,
% 0.98/0.86 (![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(35,plain,
% 0.98/0.86 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp30) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp30))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp30) <=> (hskp30 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp30) <=> (hskp30 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp30) | hskp11) <=> ((hskp30 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp11))), rewrite(((hskp30 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp11) <=> (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp30) | hskp11) <=> (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))))),
% 0.98/0.86 inference(bind,[status(th)],[])).
% 0.98/0.86 tff(36,plain,
% 0.98/0.86 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp30) | hskp11) <=> ![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.98/0.86 inference(quant_intro,[status(thm)],[35])).
% 0.98/0.86 tff(37,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp30) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause140')).
% 0.98/0.86 tff(38,plain,
% 0.98/0.86 (![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.98/0.86 tff(39,plain,
% 0.98/0.86 (![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.98/0.86 tff(40,plain,(
% 0.98/0.86 ![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.98/0.86 inference(skolemize,[status(sab)],[39])).
% 0.98/0.86 tff(41,plain,
% 0.98/0.86 (![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.98/0.86 tff(42,assumption,(hskp21), introduced(assumption)).
% 0.98/0.86 tff(43,assumption,(~hskp16), introduced(assumption)).
% 0.98/0.86 tff(44,plain,
% 0.98/0.86 (^[U: $i] : refl((hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))),
% 0.98/0.86 inference(bind,[status(th)],[])).
% 0.98/0.86 tff(45,plain,
% 0.98/0.86 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.98/0.86 inference(quant_intro,[status(thm)],[44])).
% 0.98/0.86 tff(46,plain,
% 0.98/0.86 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(47,plain,
% 0.98/0.86 (^[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)) | hskp15) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp15))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) | hskp16) <=> ((hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp16))), rewrite(((hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp16) <=> (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) | hskp16) <=> (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))))),
% 0.98/0.86 inference(bind,[status(th)],[])).
% 0.98/0.86 tff(48,plain,
% 0.98/0.86 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) | hskp16) <=> ![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.98/0.86 inference(quant_intro,[status(thm)],[47])).
% 0.98/0.86 tff(49,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause143')).
% 0.98/0.86 tff(50,plain,
% 0.98/0.86 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.98/0.86 tff(51,plain,
% 0.98/0.86 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.98/0.86 tff(52,plain,(
% 0.98/0.86 ![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.98/0.86 inference(skolemize,[status(sab)],[51])).
% 0.98/0.86 tff(53,plain,
% 0.98/0.86 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.98/0.86 tff(54,plain,
% 0.98/0.86 (((~hskp21) | (~c3_1(a39))) <=> ((~hskp21) | (~c3_1(a39)))),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(55,plain,
% 0.98/0.86 (((~c3_1(a39)) | (~hskp21)) <=> ((~hskp21) | (~c3_1(a39)))),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(56,axiom,((~c3_1(a39)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause101')).
% 0.98/0.86 tff(57,plain,
% 0.98/0.86 ((~hskp21) | (~c3_1(a39))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.98/0.86 tff(58,plain,
% 0.98/0.86 ((~hskp21) | (~c3_1(a39))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[57, 54])).
% 0.98/0.86 tff(59,plain,
% 0.98/0.86 (~c3_1(a39)),
% 0.98/0.86 inference(unit_resolution,[status(thm)],[58, 42])).
% 0.98/0.86 tff(60,plain,
% 0.98/0.86 (((~hskp21) | (~c0_1(a39))) <=> ((~hskp21) | (~c0_1(a39)))),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(61,plain,
% 0.98/0.86 (((~c0_1(a39)) | (~hskp21)) <=> ((~hskp21) | (~c0_1(a39)))),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(62,axiom,((~c0_1(a39)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause100')).
% 0.98/0.86 tff(63,plain,
% 0.98/0.86 ((~hskp21) | (~c0_1(a39))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.98/0.86 tff(64,plain,
% 0.98/0.86 ((~hskp21) | (~c0_1(a39))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[63, 60])).
% 0.98/0.86 tff(65,plain,
% 0.98/0.86 (~c0_1(a39)),
% 0.98/0.86 inference(unit_resolution,[status(thm)],[64, 42])).
% 0.98/0.86 tff(66,plain,
% 0.98/0.86 (((~hskp21) | c2_1(a39)) <=> ((~hskp21) | c2_1(a39))),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(67,axiom,((~hskp21) | c2_1(a39)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause56')).
% 0.98/0.86 tff(68,plain,
% 0.98/0.86 ((~hskp21) | c2_1(a39)),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.98/0.86 tff(69,plain,
% 0.98/0.86 ((~hskp21) | c2_1(a39)),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[68, 66])).
% 0.98/0.86 tff(70,plain,
% 0.98/0.86 ((~hskp21) | c2_1(a39)),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[69, 66])).
% 0.98/0.86 tff(71,plain,
% 0.98/0.86 ((~hskp21) | c2_1(a39)),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.98/0.86 tff(72,plain,
% 0.98/0.86 ((~hskp21) | c2_1(a39)),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[71, 66])).
% 0.98/0.86 tff(73,plain,
% 0.98/0.86 ((~hskp21) | c2_1(a39)),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[72, 66])).
% 0.98/0.86 tff(74,plain,
% 0.98/0.86 ((~hskp21) | c2_1(a39)),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.98/0.86 tff(75,plain,
% 0.98/0.86 ((~hskp21) | c2_1(a39)),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[74, 66])).
% 0.98/0.86 tff(76,plain,
% 0.98/0.86 (c2_1(a39)),
% 0.98/0.86 inference(unit_resolution,[status(thm)],[75, 42])).
% 0.98/0.86 tff(77,assumption,(~hskp15), introduced(assumption)).
% 0.98/0.86 tff(78,assumption,(~ndr1_0), introduced(assumption)).
% 0.98/0.86 tff(79,plain,
% 0.98/0.86 ((ndr1_0 | (~hskp24)) <=> (ndr1_0 | (~hskp24))),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(80,plain,
% 0.98/0.86 (((~hskp24) | ndr1_0) <=> (ndr1_0 | (~hskp24))),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(81,axiom,((~hskp24) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause8')).
% 0.98/0.86 tff(82,plain,
% 0.98/0.86 (ndr1_0 | (~hskp24)),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.98/0.86 tff(83,plain,
% 0.98/0.86 (ndr1_0 | (~hskp24)),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[82, 79])).
% 0.98/0.86 tff(84,plain,
% 0.98/0.86 (~hskp24),
% 0.98/0.86 inference(unit_resolution,[status(thm)],[83, 78])).
% 0.98/0.86 tff(85,plain,
% 0.98/0.86 (((~hskp31) | ndr1_0) <=> ((~hskp31) | ndr1_0)),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(86,axiom,((~hskp31) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 0.98/0.86 tff(87,plain,
% 0.98/0.86 ((~hskp31) | ndr1_0),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.98/0.86 tff(88,plain,
% 0.98/0.86 ((~hskp31) | ndr1_0),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[87, 85])).
% 0.98/0.86 tff(89,plain,
% 0.98/0.86 ((~hskp31) | ndr1_0),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[88, 85])).
% 0.98/0.86 tff(90,plain,
% 0.98/0.86 ((~hskp31) | ndr1_0),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.98/0.86 tff(91,plain,
% 0.98/0.86 ((~hskp31) | ndr1_0),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[90, 85])).
% 0.98/0.86 tff(92,plain,
% 0.98/0.86 ((~hskp31) | ndr1_0),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[91, 85])).
% 0.98/0.86 tff(93,plain,
% 0.98/0.86 ((~hskp31) | ndr1_0),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[92, 85])).
% 0.98/0.86 tff(94,plain,
% 0.98/0.86 ((~hskp31) | ndr1_0),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[93, 85])).
% 0.98/0.86 tff(95,plain,
% 0.98/0.86 (~hskp31),
% 0.98/0.86 inference(unit_resolution,[status(thm)],[94, 78])).
% 0.98/0.86 tff(96,plain,
% 0.98/0.86 ((ndr1_0 | (~hskp12)) <=> (ndr1_0 | (~hskp12))),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(97,plain,
% 0.98/0.86 (((~hskp12) | ndr1_0) <=> (ndr1_0 | (~hskp12))),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(98,axiom,((~hskp12) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause20')).
% 0.98/0.86 tff(99,plain,
% 0.98/0.86 (ndr1_0 | (~hskp12)),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.98/0.86 tff(100,plain,
% 0.98/0.86 (ndr1_0 | (~hskp12)),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[99, 96])).
% 0.98/0.86 tff(101,plain,
% 0.98/0.86 (~hskp12),
% 0.98/0.86 inference(unit_resolution,[status(thm)],[100, 78])).
% 0.98/0.86 tff(102,plain,
% 0.98/0.86 ((hskp31 | hskp24 | hskp12) <=> (hskp31 | hskp24 | hskp12)),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(103,plain,
% 0.98/0.86 (((hskp31 | hskp12) | hskp24) <=> (hskp31 | hskp24 | hskp12)),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(104,plain,
% 0.98/0.86 ((hskp31 | hskp12) <=> (hskp31 | hskp12)),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(105,plain,
% 0.98/0.86 (((hskp31 | hskp12) | hskp24) <=> ((hskp31 | hskp12) | hskp24)),
% 0.98/0.86 inference(monotonicity,[status(thm)],[104])).
% 0.98/0.86 tff(106,plain,
% 0.98/0.86 (((hskp31 | hskp12) | hskp24) <=> (hskp31 | hskp24 | hskp12)),
% 0.98/0.86 inference(transitivity,[status(thm)],[105, 103])).
% 0.98/0.86 tff(107,axiom,((hskp31 | hskp12) | hskp24), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause33')).
% 0.98/0.86 tff(108,plain,
% 0.98/0.86 (hskp31 | hskp24 | hskp12),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.98/0.86 tff(109,plain,
% 0.98/0.86 (hskp31 | hskp24 | hskp12),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[108, 102])).
% 0.98/0.86 tff(110,plain,
% 0.98/0.86 (hskp31 | hskp24 | hskp12),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[109, 102])).
% 0.98/0.86 tff(111,plain,
% 0.98/0.86 (hskp31 | hskp24 | hskp12),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[110, 102])).
% 0.98/0.86 tff(112,plain,
% 0.98/0.86 (hskp31 | hskp24 | hskp12),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[111, 102])).
% 0.98/0.86 tff(113,plain,
% 0.98/0.86 (hskp31 | hskp24 | hskp12),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[112, 102])).
% 0.98/0.86 tff(114,plain,
% 0.98/0.86 (hskp31 | hskp24 | hskp12),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[113, 102])).
% 0.98/0.86 tff(115,plain,
% 0.98/0.86 (hskp31 | hskp24 | hskp12),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[114, 102])).
% 0.98/0.86 tff(116,plain,
% 0.98/0.86 ($false),
% 0.98/0.86 inference(unit_resolution,[status(thm)],[115, 101, 95, 84])).
% 0.98/0.86 tff(117,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.98/0.86 tff(118,plain,
% 0.98/0.86 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp15 | c0_1(a39) | c3_1(a39) | (~ndr1_0) | (~c2_1(a39)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp15 | c0_1(a39) | c3_1(a39) | (~ndr1_0) | (~c2_1(a39)))),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(119,plain,
% 0.98/0.86 ((hskp16 | hskp15 | (~ndr1_0) | c0_1(a39) | c3_1(a39) | (~c2_1(a39))) <=> (hskp16 | hskp15 | c0_1(a39) | c3_1(a39) | (~ndr1_0) | (~c2_1(a39)))),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(120,plain,
% 0.98/0.86 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c0_1(a39) | c3_1(a39) | (~c2_1(a39)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp15 | c0_1(a39) | c3_1(a39) | (~ndr1_0) | (~c2_1(a39))))),
% 0.98/0.86 inference(monotonicity,[status(thm)],[119])).
% 0.98/0.86 tff(121,plain,
% 0.98/0.86 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c0_1(a39) | c3_1(a39) | (~c2_1(a39)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp15 | c0_1(a39) | c3_1(a39) | (~ndr1_0) | (~c2_1(a39)))),
% 0.98/0.86 inference(transitivity,[status(thm)],[120, 118])).
% 0.98/0.86 tff(122,plain,
% 0.98/0.86 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c0_1(a39) | c3_1(a39) | (~c2_1(a39)))),
% 0.98/0.86 inference(quant_inst,[status(thm)],[])).
% 0.98/0.86 tff(123,plain,
% 0.98/0.86 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp15 | c0_1(a39) | c3_1(a39) | (~ndr1_0) | (~c2_1(a39))),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.98/0.86 tff(124,plain,
% 0.98/0.86 ($false),
% 0.98/0.86 inference(unit_resolution,[status(thm)],[123, 117, 43, 77, 76, 65, 59, 53])).
% 0.98/0.86 tff(125,plain,((~hskp21) | hskp16 | hskp15), inference(lemma,lemma(discharge,[]))).
% 0.98/0.86 tff(126,plain,
% 0.98/0.86 (hskp15),
% 0.98/0.86 inference(unit_resolution,[status(thm)],[125, 43, 42])).
% 0.98/0.86 tff(127,plain,
% 0.98/0.86 (((~hskp15) | c1_1(a29)) <=> ((~hskp15) | c1_1(a29))),
% 0.98/0.86 inference(rewrite,[status(thm)],[])).
% 0.98/0.86 tff(128,axiom,((~hskp15) | c1_1(a29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause66')).
% 0.98/0.86 tff(129,plain,
% 0.98/0.86 ((~hskp15) | c1_1(a29)),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.98/0.86 tff(130,plain,
% 0.98/0.86 ((~hskp15) | c1_1(a29)),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[129, 127])).
% 0.98/0.86 tff(131,plain,
% 0.98/0.86 ((~hskp15) | c1_1(a29)),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[130, 127])).
% 0.98/0.86 tff(132,plain,
% 0.98/0.86 ((~hskp15) | c1_1(a29)),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[131, 127])).
% 0.98/0.86 tff(133,plain,
% 0.98/0.86 ((~hskp15) | c1_1(a29)),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[132, 127])).
% 0.98/0.86 tff(134,plain,
% 0.98/0.86 ((~hskp15) | c1_1(a29)),
% 0.98/0.86 inference(modus_ponens,[status(thm)],[133, 127])).
% 0.98/0.86 tff(135,plain,
% 0.98/0.86 ((~hskp15) | c1_1(a29)),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[134, 127])).
% 0.98/0.87 tff(136,plain,
% 0.98/0.87 ((~hskp15) | c1_1(a29)),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[135, 127])).
% 0.98/0.87 tff(137,plain,
% 0.98/0.87 (c1_1(a29)),
% 0.98/0.87 inference(unit_resolution,[status(thm)],[136, 126])).
% 0.98/0.87 tff(138,plain,
% 0.98/0.87 (((~hskp15) | (~c3_1(a29))) <=> ((~hskp15) | (~c3_1(a29)))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(139,plain,
% 0.98/0.87 (((~c3_1(a29)) | (~hskp15)) <=> ((~hskp15) | (~c3_1(a29)))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(140,axiom,((~c3_1(a29)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause109')).
% 0.98/0.87 tff(141,plain,
% 0.98/0.87 ((~hskp15) | (~c3_1(a29))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.98/0.87 tff(142,plain,
% 0.98/0.87 ((~hskp15) | (~c3_1(a29))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[141, 138])).
% 0.98/0.87 tff(143,plain,
% 0.98/0.87 (~c3_1(a29)),
% 0.98/0.87 inference(unit_resolution,[status(thm)],[142, 126])).
% 0.98/0.87 tff(144,plain,
% 0.98/0.87 (((~hskp15) | (~c2_1(a29))) <=> ((~hskp15) | (~c2_1(a29)))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(145,plain,
% 0.98/0.87 (((~c2_1(a29)) | (~hskp15)) <=> ((~hskp15) | (~c2_1(a29)))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(146,axiom,((~c2_1(a29)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause108')).
% 0.98/0.87 tff(147,plain,
% 0.98/0.87 ((~hskp15) | (~c2_1(a29))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.98/0.87 tff(148,plain,
% 0.98/0.87 ((~hskp15) | (~c2_1(a29))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[147, 144])).
% 0.98/0.87 tff(149,plain,
% 0.98/0.87 (~c2_1(a29)),
% 0.98/0.87 inference(unit_resolution,[status(thm)],[148, 126])).
% 0.98/0.87 tff(150,assumption,(c0_1(a29)), introduced(assumption)).
% 0.98/0.87 tff(151,plain,
% 0.98/0.87 (^[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)) | c0_1(W) | (~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)) | c0_1(W) | (~c2_1(W)) | c3_1(W)))),
% 0.98/0.87 inference(bind,[status(th)],[])).
% 0.98/0.87 tff(152,plain,
% 0.98/0.87 (![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)) | c0_1(W) | (~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)) | c0_1(W) | (~c2_1(W)) | c3_1(W))),
% 0.98/0.87 inference(quant_intro,[status(thm)],[151])).
% 0.98/0.87 tff(153,plain,
% 0.98/0.87 (![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)) | c0_1(W) | (~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)) | c0_1(W) | (~c2_1(W)) | c3_1(W))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(154,plain,
% 0.98/0.87 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~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(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | 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)) | (~c2_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_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)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | 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)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c0_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))) | c0_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))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c0_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)) | c0_1(W) | (~c2_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)) | c0_1(W) | (~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)) | c0_1(W) | (~c2_1(W)) | c3_1(W))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c0_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)) | c0_1(W) | (~c2_1(W)) | c3_1(W))))),
% 0.98/0.87 inference(bind,[status(th)],[])).
% 0.98/0.87 tff(155,plain,
% 0.98/0.87 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c0_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)) | c0_1(W) | (~c2_1(W)) | c3_1(W))),
% 0.98/0.87 inference(quant_intro,[status(thm)],[154])).
% 0.98/0.87 tff(156,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause191')).
% 0.98/0.87 tff(157,plain,
% 0.98/0.87 (![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)) | c0_1(W) | (~c2_1(W)) | c3_1(W))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.98/0.87 tff(158,plain,
% 0.98/0.87 (![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)) | c0_1(W) | (~c2_1(W)) | c3_1(W))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[157, 153])).
% 0.98/0.87 tff(159,plain,(
% 0.98/0.87 ![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)) | c0_1(W) | (~c2_1(W)) | c3_1(W))),
% 0.98/0.87 inference(skolemize,[status(sab)],[158])).
% 0.98/0.87 tff(160,plain,
% 0.98/0.87 (![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)) | c0_1(W) | (~c2_1(W)) | c3_1(W))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[159, 152])).
% 0.98/0.87 tff(161,assumption,(~c3_1(a29)), introduced(assumption)).
% 0.98/0.87 tff(162,assumption,(~c2_1(a29)), introduced(assumption)).
% 0.98/0.87 tff(163,assumption,(c1_1(a29)), introduced(assumption)).
% 0.98/0.87 tff(164,plain,
% 0.98/0.87 (((~![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)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | (c0_1(a39) | c3_1(a39) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | (~c0_1(a29)) | (~c2_1(a39)))) <=> ((~![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)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | c0_1(a39) | c3_1(a39) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | (~c0_1(a29)) | (~c2_1(a39)))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(165,plain,
% 0.98/0.87 (((~ndr1_0) | c3_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c3_1(a29) | c2_1(a29) | (~c0_1(a29)) | c0_1(a39) | (~c2_1(a39)) | c3_1(a39)) <=> (c0_1(a39) | c3_1(a39) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | (~c0_1(a29)) | (~c2_1(a39)))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(166,plain,
% 0.98/0.87 (((~![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)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c3_1(a29) | c2_1(a29) | (~c0_1(a29)) | c0_1(a39) | (~c2_1(a39)) | c3_1(a39))) <=> ((~![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)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | (c0_1(a39) | c3_1(a39) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | (~c0_1(a29)) | (~c2_1(a39))))),
% 0.98/0.87 inference(monotonicity,[status(thm)],[165])).
% 0.98/0.87 tff(167,plain,
% 0.98/0.87 (((~![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)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c3_1(a29) | c2_1(a29) | (~c0_1(a29)) | c0_1(a39) | (~c2_1(a39)) | c3_1(a39))) <=> ((~![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)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | c0_1(a39) | c3_1(a39) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | (~c0_1(a29)) | (~c2_1(a39)))),
% 0.98/0.87 inference(transitivity,[status(thm)],[166, 164])).
% 0.98/0.87 tff(168,plain,
% 0.98/0.87 ((~![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)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c3_1(a29) | c2_1(a29) | (~c0_1(a29)) | c0_1(a39) | (~c2_1(a39)) | c3_1(a39))),
% 0.98/0.87 inference(quant_inst,[status(thm)],[])).
% 0.98/0.87 tff(169,plain,
% 0.98/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | c0_1(a39) | c3_1(a39) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | (~c0_1(a29)) | (~c2_1(a39))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.98/0.87 tff(170,plain,
% 0.98/0.87 ($false),
% 0.98/0.87 inference(unit_resolution,[status(thm)],[169, 117, 76, 163, 65, 59, 162, 161, 160, 150])).
% 0.98/0.87 tff(171,plain,((~hskp21) | (~c1_1(a29)) | c2_1(a29) | c3_1(a29) | (~c0_1(a29))), inference(lemma,lemma(discharge,[]))).
% 0.98/0.87 tff(172,plain,
% 0.98/0.87 (~c0_1(a29)),
% 0.98/0.87 inference(unit_resolution,[status(thm)],[171, 149, 42, 143, 137])).
% 0.98/0.87 tff(173,plain,
% 0.98/0.87 (^[U: $i] : refl((hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))),
% 0.98/0.87 inference(bind,[status(th)],[])).
% 0.98/0.87 tff(174,plain,
% 0.98/0.87 (![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.98/0.87 inference(quant_intro,[status(thm)],[173])).
% 0.98/0.87 tff(175,plain,
% 0.98/0.87 (![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(176,plain,
% 0.98/0.87 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp12) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp12))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp12) <=> (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp12) <=> (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))))),
% 0.98/0.87 inference(bind,[status(th)],[])).
% 0.98/0.87 tff(177,plain,
% 0.98/0.87 (![U: $i] : (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp12) <=> ![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.98/0.87 inference(quant_intro,[status(thm)],[176])).
% 0.98/0.87 tff(178,axiom,(![U: $i] : (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause137')).
% 0.98/0.87 tff(179,plain,
% 0.98/0.87 (![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.98/0.87 tff(180,plain,
% 0.98/0.87 (![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[179, 175])).
% 0.98/0.87 tff(181,plain,(
% 0.98/0.87 ![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.98/0.87 inference(skolemize,[status(sab)],[180])).
% 0.98/0.87 tff(182,plain,
% 0.98/0.87 (![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[181, 174])).
% 0.98/0.87 tff(183,plain,
% 0.98/0.87 (^[U: $i] : refl((hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))))),
% 0.98/0.87 inference(bind,[status(th)],[])).
% 0.98/0.87 tff(184,plain,
% 0.98/0.87 (![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.98/0.87 inference(quant_intro,[status(thm)],[183])).
% 0.98/0.87 tff(185,plain,
% 0.98/0.87 (![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(186,plain,
% 0.98/0.87 (^[U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | 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)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp16) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp16))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp16) <=> (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp16) <=> (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))))),
% 0.98/0.87 inference(bind,[status(th)],[])).
% 0.98/0.87 tff(187,plain,
% 0.98/0.87 (![U: $i] : (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp16) <=> ![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.98/0.87 inference(quant_intro,[status(thm)],[186])).
% 0.98/0.87 tff(188,axiom,(![U: $i] : (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause148')).
% 0.98/0.87 tff(189,plain,
% 0.98/0.87 (![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.98/0.87 tff(190,plain,
% 0.98/0.87 (![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[189, 185])).
% 0.98/0.87 tff(191,plain,(
% 0.98/0.87 ![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.98/0.87 inference(skolemize,[status(sab)],[190])).
% 0.98/0.87 tff(192,plain,
% 0.98/0.87 (![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[191, 184])).
% 0.98/0.87 tff(193,assumption,(hskp12), introduced(assumption)).
% 0.98/0.87 tff(194,plain,
% 0.98/0.87 (((~hskp12) | (~c2_1(a24))) <=> ((~hskp12) | (~c2_1(a24)))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(195,plain,
% 0.98/0.87 (((~c2_1(a24)) | (~hskp12)) <=> ((~hskp12) | (~c2_1(a24)))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(196,axiom,((~c2_1(a24)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause113')).
% 0.98/0.87 tff(197,plain,
% 0.98/0.87 ((~hskp12) | (~c2_1(a24))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.98/0.87 tff(198,plain,
% 0.98/0.87 ((~hskp12) | (~c2_1(a24))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[197, 194])).
% 0.98/0.87 tff(199,plain,
% 0.98/0.87 (~c2_1(a24)),
% 0.98/0.87 inference(unit_resolution,[status(thm)],[198, 193])).
% 0.98/0.87 tff(200,plain,
% 0.98/0.87 (((~hskp12) | c3_1(a24)) <=> ((~hskp12) | c3_1(a24))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(201,axiom,((~hskp12) | c3_1(a24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause71')).
% 0.98/0.87 tff(202,plain,
% 0.98/0.87 ((~hskp12) | c3_1(a24)),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.98/0.87 tff(203,plain,
% 0.98/0.87 ((~hskp12) | c3_1(a24)),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[202, 200])).
% 0.98/0.87 tff(204,plain,
% 0.98/0.87 ((~hskp12) | c3_1(a24)),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[203, 200])).
% 0.98/0.87 tff(205,plain,
% 0.98/0.87 ((~hskp12) | c3_1(a24)),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[204, 200])).
% 0.98/0.87 tff(206,plain,
% 0.98/0.87 ((~hskp12) | c3_1(a24)),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[205, 200])).
% 0.98/0.87 tff(207,plain,
% 0.98/0.87 ((~hskp12) | c3_1(a24)),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[206, 200])).
% 0.98/0.87 tff(208,plain,
% 0.98/0.87 ((~hskp12) | c3_1(a24)),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[207, 200])).
% 0.98/0.87 tff(209,plain,
% 0.98/0.87 ((~hskp12) | c3_1(a24)),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[208, 200])).
% 0.98/0.87 tff(210,plain,
% 0.98/0.87 (c3_1(a24)),
% 0.98/0.87 inference(unit_resolution,[status(thm)],[209, 193])).
% 0.98/0.87 tff(211,plain,
% 0.98/0.87 (((~hskp12) | c1_1(a24)) <=> ((~hskp12) | c1_1(a24))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(212,axiom,((~hskp12) | c1_1(a24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause70')).
% 0.98/0.87 tff(213,plain,
% 0.98/0.87 ((~hskp12) | c1_1(a24)),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.98/0.87 tff(214,plain,
% 0.98/0.87 ((~hskp12) | c1_1(a24)),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[213, 211])).
% 0.98/0.87 tff(215,plain,
% 0.98/0.87 ((~hskp12) | c1_1(a24)),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[214, 211])).
% 0.98/0.87 tff(216,plain,
% 0.98/0.87 ((~hskp12) | c1_1(a24)),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[215, 211])).
% 0.98/0.87 tff(217,plain,
% 0.98/0.87 ((~hskp12) | c1_1(a24)),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[216, 211])).
% 0.98/0.87 tff(218,plain,
% 0.98/0.87 ((~hskp12) | c1_1(a24)),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[217, 211])).
% 0.98/0.87 tff(219,plain,
% 0.98/0.87 ((~hskp12) | c1_1(a24)),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[218, 211])).
% 0.98/0.87 tff(220,plain,
% 0.98/0.87 ((~hskp12) | c1_1(a24)),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[219, 211])).
% 0.98/0.87 tff(221,plain,
% 0.98/0.87 (c1_1(a24)),
% 0.98/0.87 inference(unit_resolution,[status(thm)],[220, 193])).
% 0.98/0.87 tff(222,plain,
% 0.98/0.87 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | c2_1(a24) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | c2_1(a24) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(223,plain,
% 0.98/0.87 ((hskp16 | (~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c3_1(a24))) <=> (hskp16 | c2_1(a24) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(224,plain,
% 0.98/0.87 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c3_1(a24)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | c2_1(a24) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24))))),
% 0.98/0.87 inference(monotonicity,[status(thm)],[223])).
% 0.98/0.87 tff(225,plain,
% 0.98/0.87 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c3_1(a24)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | c2_1(a24) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)))),
% 0.98/0.87 inference(transitivity,[status(thm)],[224, 222])).
% 0.98/0.87 tff(226,plain,
% 0.98/0.87 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c3_1(a24)))),
% 0.98/0.87 inference(quant_inst,[status(thm)],[])).
% 0.98/0.87 tff(227,plain,
% 0.98/0.87 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | c2_1(a24) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.98/0.87 tff(228,plain,
% 0.98/0.87 ($false),
% 0.98/0.87 inference(unit_resolution,[status(thm)],[227, 117, 43, 221, 210, 199, 192])).
% 0.98/0.87 tff(229,plain,((~hskp12) | hskp16), inference(lemma,lemma(discharge,[]))).
% 0.98/0.87 tff(230,plain,
% 0.98/0.87 (~hskp12),
% 0.98/0.87 inference(unit_resolution,[status(thm)],[229, 43])).
% 0.98/0.87 tff(231,plain,
% 0.98/0.87 (((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp12 | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c0_1(a29))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp12 | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c0_1(a29))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(232,plain,
% 0.98/0.87 ((hskp12 | (~ndr1_0) | c0_1(a29) | c3_1(a29) | (~c1_1(a29))) <=> (hskp12 | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c0_1(a29))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(233,plain,
% 0.98/0.87 (((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp12 | (~ndr1_0) | c0_1(a29) | c3_1(a29) | (~c1_1(a29)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp12 | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c0_1(a29)))),
% 0.98/0.87 inference(monotonicity,[status(thm)],[232])).
% 0.98/0.87 tff(234,plain,
% 0.98/0.87 (((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp12 | (~ndr1_0) | c0_1(a29) | c3_1(a29) | (~c1_1(a29)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp12 | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c0_1(a29))),
% 0.98/0.87 inference(transitivity,[status(thm)],[233, 231])).
% 0.98/0.87 tff(235,plain,
% 0.98/0.87 ((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp12 | (~ndr1_0) | c0_1(a29) | c3_1(a29) | (~c1_1(a29)))),
% 0.98/0.87 inference(quant_inst,[status(thm)],[])).
% 0.98/0.87 tff(236,plain,
% 0.98/0.87 ((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp12 | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c0_1(a29)),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.98/0.87 tff(237,plain,
% 0.98/0.87 ($false),
% 0.98/0.87 inference(unit_resolution,[status(thm)],[236, 117, 230, 137, 143, 182, 172])).
% 0.98/0.87 tff(238,plain,(hskp16 | (~hskp21)), inference(lemma,lemma(discharge,[]))).
% 0.98/0.87 tff(239,plain,
% 0.98/0.87 (hskp16),
% 0.98/0.87 inference(unit_resolution,[status(thm)],[238, 42])).
% 0.98/0.87 tff(240,plain,
% 0.98/0.87 (((~hskp16) | (~c1_1(a30))) <=> ((~hskp16) | (~c1_1(a30)))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(241,plain,
% 0.98/0.87 (((~c1_1(a30)) | (~hskp16)) <=> ((~hskp16) | (~c1_1(a30)))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(242,axiom,((~c1_1(a30)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause107')).
% 0.98/0.87 tff(243,plain,
% 0.98/0.87 ((~hskp16) | (~c1_1(a30))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.98/0.87 tff(244,plain,
% 0.98/0.87 ((~hskp16) | (~c1_1(a30))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[243, 240])).
% 0.98/0.87 tff(245,plain,
% 0.98/0.87 (~c1_1(a30)),
% 0.98/0.87 inference(unit_resolution,[status(thm)],[244, 239])).
% 0.98/0.87 tff(246,plain,
% 0.98/0.87 (((~hskp16) | c2_1(a30)) <=> ((~hskp16) | c2_1(a30))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(247,axiom,((~hskp16) | c2_1(a30)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause64')).
% 0.98/0.87 tff(248,plain,
% 0.98/0.87 ((~hskp16) | c2_1(a30)),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[247, 246])).
% 0.98/0.87 tff(249,plain,
% 0.98/0.87 ((~hskp16) | c2_1(a30)),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[248, 246])).
% 0.98/0.87 tff(250,plain,
% 0.98/0.87 ((~hskp16) | c2_1(a30)),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[249, 246])).
% 0.98/0.87 tff(251,plain,
% 0.98/0.87 ((~hskp16) | c2_1(a30)),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[250, 246])).
% 0.98/0.87 tff(252,plain,
% 0.98/0.87 ((~hskp16) | c2_1(a30)),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[251, 246])).
% 0.98/0.87 tff(253,plain,
% 0.98/0.87 ((~hskp16) | c2_1(a30)),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[252, 246])).
% 0.98/0.87 tff(254,plain,
% 0.98/0.87 ((~hskp16) | c2_1(a30)),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[253, 246])).
% 0.98/0.87 tff(255,plain,
% 0.98/0.87 ((~hskp16) | c2_1(a30)),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[254, 246])).
% 0.98/0.87 tff(256,plain,
% 0.98/0.87 (c2_1(a30)),
% 0.98/0.87 inference(unit_resolution,[status(thm)],[255, 239])).
% 0.98/0.87 tff(257,plain,
% 0.98/0.87 (((~hskp16) | c3_1(a30)) <=> ((~hskp16) | c3_1(a30))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(258,axiom,((~hskp16) | c3_1(a30)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause65')).
% 0.98/0.87 tff(259,plain,
% 0.98/0.87 ((~hskp16) | c3_1(a30)),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[258, 257])).
% 0.98/0.87 tff(260,plain,
% 0.98/0.87 ((~hskp16) | c3_1(a30)),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[259, 257])).
% 0.98/0.87 tff(261,plain,
% 0.98/0.87 ((~hskp16) | c3_1(a30)),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[260, 257])).
% 0.98/0.87 tff(262,plain,
% 0.98/0.87 ((~hskp16) | c3_1(a30)),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[261, 257])).
% 0.98/0.87 tff(263,plain,
% 0.98/0.87 ((~hskp16) | c3_1(a30)),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[262, 257])).
% 0.98/0.87 tff(264,plain,
% 0.98/0.87 ((~hskp16) | c3_1(a30)),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[263, 257])).
% 0.98/0.87 tff(265,plain,
% 0.98/0.87 ((~hskp16) | c3_1(a30)),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[264, 257])).
% 0.98/0.87 tff(266,plain,
% 0.98/0.87 ((~hskp16) | c3_1(a30)),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[265, 257])).
% 0.98/0.87 tff(267,plain,
% 0.98/0.87 (c3_1(a30)),
% 0.98/0.87 inference(unit_resolution,[status(thm)],[266, 239])).
% 0.98/0.87 tff(268,assumption,(~c0_1(a13)), introduced(assumption)).
% 0.98/0.87 tff(269,assumption,(~c0_1(a24)), introduced(assumption)).
% 0.98/0.87 tff(270,plain,
% 0.98/0.87 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))))),
% 0.98/0.87 inference(bind,[status(th)],[])).
% 0.98/0.87 tff(271,plain,
% 0.98/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.98/0.87 inference(quant_intro,[status(thm)],[270])).
% 0.98/0.87 tff(272,plain,
% 0.98/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(273,plain,
% 0.98/0.87 (^[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))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))))),
% 0.98/0.87 inference(bind,[status(th)],[])).
% 0.98/0.87 tff(274,plain,
% 0.98/0.87 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.98/0.87 inference(quant_intro,[status(thm)],[273])).
% 0.98/0.87 tff(275,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause192')).
% 0.98/0.87 tff(276,plain,
% 0.98/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[275, 274])).
% 0.98/0.87 tff(277,plain,
% 0.98/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[276, 272])).
% 0.98/0.87 tff(278,plain,(
% 0.98/0.87 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.98/0.87 inference(skolemize,[status(sab)],[277])).
% 0.98/0.87 tff(279,plain,
% 0.98/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[278, 271])).
% 0.98/0.87 tff(280,plain,
% 0.98/0.87 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))))),
% 0.98/0.87 inference(bind,[status(th)],[])).
% 0.98/0.87 tff(281,plain,
% 0.98/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.98/0.87 inference(quant_intro,[status(thm)],[280])).
% 0.98/0.87 tff(282,plain,
% 0.98/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.98/0.87 inference(rewrite,[status(thm)],[])).
% 0.98/0.87 tff(283,plain,
% 0.98/0.87 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))))),
% 0.98/0.87 inference(bind,[status(th)],[])).
% 0.98/0.87 tff(284,plain,
% 0.98/0.87 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.98/0.87 inference(quant_intro,[status(thm)],[283])).
% 0.98/0.87 tff(285,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c0_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause195')).
% 0.98/0.87 tff(286,plain,
% 0.98/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[285, 284])).
% 0.98/0.87 tff(287,plain,
% 0.98/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[286, 282])).
% 0.98/0.87 tff(288,plain,(
% 0.98/0.87 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.98/0.87 inference(skolemize,[status(sab)],[287])).
% 0.98/0.87 tff(289,plain,
% 0.98/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.98/0.87 inference(modus_ponens,[status(thm)],[288, 281])).
% 0.98/0.87 tff(290,plain,
% 0.98/0.87 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))))),
% 0.98/0.87 inference(bind,[status(th)],[])).
% 0.98/0.87 tff(291,plain,
% 0.98/0.87 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.98/0.87 inference(quant_intro,[status(thm)],[290])).
% 0.98/0.88 tff(292,plain,
% 0.98/0.88 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(293,plain,
% 0.98/0.88 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) | hskp12) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) | hskp12))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))))),
% 0.98/0.88 inference(bind,[status(th)],[])).
% 0.98/0.88 tff(294,plain,
% 0.98/0.88 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.98/0.88 inference(quant_intro,[status(thm)],[293])).
% 0.98/0.88 tff(295,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause186')).
% 0.98/0.88 tff(296,plain,
% 0.98/0.88 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[295, 294])).
% 0.98/0.88 tff(297,plain,
% 0.98/0.88 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[296, 292])).
% 0.98/0.88 tff(298,plain,(
% 0.98/0.88 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.98/0.88 inference(skolemize,[status(sab)],[297])).
% 0.98/0.88 tff(299,plain,
% 0.98/0.88 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[298, 291])).
% 0.98/0.88 tff(300,plain,
% 0.98/0.88 (^[V: $i, U: $i] : refl((hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 0.98/0.88 inference(bind,[status(th)],[])).
% 0.98/0.88 tff(301,plain,
% 0.98/0.88 (![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.98/0.88 inference(quant_intro,[status(thm)],[300])).
% 0.98/0.88 tff(302,plain,
% 0.98/0.88 (![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(303,plain,
% 0.98/0.88 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | hskp30) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp30))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp30) <=> (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | hskp30) <=> (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 0.98/0.88 inference(bind,[status(th)],[])).
% 0.98/0.88 tff(304,plain,
% 0.98/0.88 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | hskp30) <=> ![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.98/0.88 inference(quant_intro,[status(thm)],[303])).
% 0.98/0.88 tff(305,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | hskp30)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause182')).
% 0.98/0.88 tff(306,plain,
% 0.98/0.88 (![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[305, 304])).
% 0.98/0.88 tff(307,plain,
% 0.98/0.88 (![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[306, 302])).
% 0.98/0.88 tff(308,plain,(
% 0.98/0.88 ![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.98/0.88 inference(skolemize,[status(sab)],[307])).
% 0.98/0.88 tff(309,plain,
% 0.98/0.88 (![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[308, 301])).
% 0.98/0.88 tff(310,assumption,(~c1_1(a13)), introduced(assumption)).
% 0.98/0.88 tff(311,plain,
% 0.98/0.88 (((~hskp8) | c1_1(a13)) <=> ((~hskp8) | c1_1(a13))),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(312,axiom,((~hskp8) | c1_1(a13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause74')).
% 0.98/0.88 tff(313,plain,
% 0.98/0.88 ((~hskp8) | c1_1(a13)),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[312, 311])).
% 0.98/0.88 tff(314,plain,
% 0.98/0.88 ((~hskp8) | c1_1(a13)),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[313, 311])).
% 0.98/0.88 tff(315,plain,
% 0.98/0.88 ((~hskp8) | c1_1(a13)),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[314, 311])).
% 0.98/0.88 tff(316,plain,
% 0.98/0.88 ((~hskp8) | c1_1(a13)),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[315, 311])).
% 0.98/0.88 tff(317,plain,
% 0.98/0.88 ((~hskp8) | c1_1(a13)),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[316, 311])).
% 0.98/0.88 tff(318,plain,
% 0.98/0.88 ((~hskp8) | c1_1(a13)),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[317, 311])).
% 0.98/0.88 tff(319,plain,
% 0.98/0.88 ((~hskp8) | c1_1(a13)),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[318, 311])).
% 0.98/0.88 tff(320,plain,
% 0.98/0.88 ((~hskp8) | c1_1(a13)),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[319, 311])).
% 0.98/0.88 tff(321,plain,
% 0.98/0.88 (~hskp8),
% 0.98/0.88 inference(unit_resolution,[status(thm)],[320, 310])).
% 0.98/0.88 tff(322,assumption,(~c2_1(a13)), introduced(assumption)).
% 0.98/0.88 tff(323,assumption,(hskp16), introduced(assumption)).
% 0.98/0.88 tff(324,plain,
% 0.98/0.88 (~c1_1(a30)),
% 0.98/0.88 inference(unit_resolution,[status(thm)],[244, 323])).
% 0.98/0.88 tff(325,plain,
% 0.98/0.88 (c2_1(a30)),
% 0.98/0.88 inference(unit_resolution,[status(thm)],[255, 323])).
% 0.98/0.88 tff(326,plain,
% 0.98/0.88 (c3_1(a30)),
% 0.98/0.88 inference(unit_resolution,[status(thm)],[266, 323])).
% 0.98/0.88 tff(327,assumption,(~c3_1(a13)), introduced(assumption)).
% 0.98/0.88 tff(328,assumption,(~c1_1(a30)), introduced(assumption)).
% 0.98/0.88 tff(329,assumption,(c3_1(a30)), introduced(assumption)).
% 0.98/0.88 tff(330,assumption,(c2_1(a30)), introduced(assumption)).
% 0.98/0.88 tff(331,plain,
% 0.98/0.88 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a13) | c2_1(a13) | c1_1(a30) | (~ndr1_0) | c3_1(a13) | (~c2_1(a30)) | (~c3_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a13) | c2_1(a13) | c1_1(a30) | (~ndr1_0) | c3_1(a13) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(332,plain,
% 0.98/0.88 ((hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a13) | c1_1(a13) | c2_1(a13)) <=> (hskp8 | c1_1(a13) | c2_1(a13) | c1_1(a30) | (~ndr1_0) | c3_1(a13) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(333,plain,
% 0.98/0.88 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a13) | c1_1(a13) | c2_1(a13))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a13) | c2_1(a13) | c1_1(a30) | (~ndr1_0) | c3_1(a13) | (~c2_1(a30)) | (~c3_1(a30))))),
% 0.98/0.88 inference(monotonicity,[status(thm)],[332])).
% 0.98/0.88 tff(334,plain,
% 0.98/0.88 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a13) | c1_1(a13) | c2_1(a13))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a13) | c2_1(a13) | c1_1(a30) | (~ndr1_0) | c3_1(a13) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.98/0.88 inference(transitivity,[status(thm)],[333, 331])).
% 0.98/0.88 tff(335,plain,
% 0.98/0.88 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a13) | c1_1(a13) | c2_1(a13))),
% 0.98/0.88 inference(quant_inst,[status(thm)],[])).
% 0.98/0.88 tff(336,plain,
% 0.98/0.88 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a13) | c2_1(a13) | c1_1(a30) | (~ndr1_0) | c3_1(a13) | (~c2_1(a30)) | (~c3_1(a30))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[335, 334])).
% 0.98/0.88 tff(337,plain,
% 0.98/0.88 ($false),
% 0.98/0.88 inference(unit_resolution,[status(thm)],[336, 117, 321, 330, 329, 310, 322, 328, 31, 327])).
% 0.98/0.88 tff(338,plain,(c3_1(a13) | (~c2_1(a30)) | (~c3_1(a30)) | c1_1(a13) | c2_1(a13) | c1_1(a30)), inference(lemma,lemma(discharge,[]))).
% 0.98/0.88 tff(339,plain,
% 0.98/0.88 (c3_1(a13)),
% 0.98/0.88 inference(unit_resolution,[status(thm)],[338, 326, 325, 310, 322, 324])).
% 0.98/0.88 tff(340,plain,
% 0.98/0.88 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | c2_1(a13) | c0_1(a13) | (~ndr1_0) | (~c3_1(a13)))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c2_1(a13) | c0_1(a13) | (~ndr1_0) | (~c3_1(a13)))),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(341,plain,
% 0.98/0.88 ((hskp30 | hskp11 | (~ndr1_0) | c2_1(a13) | c0_1(a13) | (~c3_1(a13))) <=> (hskp30 | hskp11 | c2_1(a13) | c0_1(a13) | (~ndr1_0) | (~c3_1(a13)))),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(342,plain,
% 0.98/0.88 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a13) | c0_1(a13) | (~c3_1(a13)))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | c2_1(a13) | c0_1(a13) | (~ndr1_0) | (~c3_1(a13))))),
% 0.98/0.88 inference(monotonicity,[status(thm)],[341])).
% 0.98/0.88 tff(343,plain,
% 0.98/0.88 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a13) | c0_1(a13) | (~c3_1(a13)))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c2_1(a13) | c0_1(a13) | (~ndr1_0) | (~c3_1(a13)))),
% 0.98/0.88 inference(transitivity,[status(thm)],[342, 340])).
% 0.98/0.88 tff(344,plain,
% 0.98/0.88 ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a13) | c0_1(a13) | (~c3_1(a13)))),
% 0.98/0.88 inference(quant_inst,[status(thm)],[])).
% 0.98/0.88 tff(345,plain,
% 0.98/0.88 ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c2_1(a13) | c0_1(a13) | (~ndr1_0) | (~c3_1(a13))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[344, 343])).
% 0.98/0.88 tff(346,plain,
% 0.98/0.88 (hskp30 | hskp11 | c2_1(a13) | (~c3_1(a13))),
% 0.98/0.88 inference(unit_resolution,[status(thm)],[345, 117, 268, 41])).
% 0.98/0.88 tff(347,plain,
% 0.98/0.88 (hskp11),
% 0.98/0.88 inference(unit_resolution,[status(thm)],[346, 339, 1, 322])).
% 0.98/0.88 tff(348,plain,
% 0.98/0.88 (((~hskp11) | (~c3_1(a21))) <=> ((~hskp11) | (~c3_1(a21)))),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(349,plain,
% 0.98/0.88 (((~c3_1(a21)) | (~hskp11)) <=> ((~hskp11) | (~c3_1(a21)))),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(350,axiom,((~c3_1(a21)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause115')).
% 0.98/0.88 tff(351,plain,
% 0.98/0.88 ((~hskp11) | (~c3_1(a21))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[350, 349])).
% 0.98/0.88 tff(352,plain,
% 0.98/0.88 ((~hskp11) | (~c3_1(a21))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[351, 348])).
% 0.98/0.88 tff(353,plain,
% 0.98/0.88 (~c3_1(a21)),
% 0.98/0.88 inference(unit_resolution,[status(thm)],[352, 347])).
% 0.98/0.88 tff(354,plain,
% 0.98/0.88 (((~hskp11) | (~c2_1(a21))) <=> ((~hskp11) | (~c2_1(a21)))),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(355,plain,
% 0.98/0.88 (((~c2_1(a21)) | (~hskp11)) <=> ((~hskp11) | (~c2_1(a21)))),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(356,axiom,((~c2_1(a21)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause114')).
% 0.98/0.88 tff(357,plain,
% 0.98/0.88 ((~hskp11) | (~c2_1(a21))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[356, 355])).
% 0.98/0.88 tff(358,plain,
% 0.98/0.88 ((~hskp11) | (~c2_1(a21))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[357, 354])).
% 0.98/0.88 tff(359,plain,
% 0.98/0.88 (~c2_1(a21)),
% 0.98/0.88 inference(unit_resolution,[status(thm)],[358, 347])).
% 0.98/0.88 tff(360,plain,
% 0.98/0.88 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a30) | c2_1(a21) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a30)) | (~c3_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a30) | c2_1(a21) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(361,plain,
% 0.98/0.88 ((hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a21) | c1_1(a21) | c2_1(a21)) <=> (hskp8 | c1_1(a30) | c2_1(a21) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(362,plain,
% 0.98/0.88 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a21) | c1_1(a21) | c2_1(a21))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a30) | c2_1(a21) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a30)) | (~c3_1(a30))))),
% 0.98/0.88 inference(monotonicity,[status(thm)],[361])).
% 0.98/0.88 tff(363,plain,
% 0.98/0.88 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a21) | c1_1(a21) | c2_1(a21))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a30) | c2_1(a21) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.98/0.88 inference(transitivity,[status(thm)],[362, 360])).
% 0.98/0.88 tff(364,plain,
% 0.98/0.88 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a21) | c1_1(a21) | c2_1(a21))),
% 0.98/0.88 inference(quant_inst,[status(thm)],[])).
% 0.98/0.88 tff(365,plain,
% 0.98/0.88 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a30) | c2_1(a21) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a30)) | (~c3_1(a30))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[364, 363])).
% 0.98/0.88 tff(366,plain,
% 0.98/0.88 (c1_1(a21)),
% 0.98/0.88 inference(unit_resolution,[status(thm)],[365, 117, 321, 325, 326, 324, 359, 353, 31])).
% 0.98/0.88 tff(367,plain,
% 0.98/0.88 (^[V: $i, U: $i] : refl((hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 0.98/0.88 inference(bind,[status(th)],[])).
% 0.98/0.88 tff(368,plain,
% 0.98/0.88 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.98/0.88 inference(quant_intro,[status(thm)],[367])).
% 0.98/0.88 tff(369,plain,
% 0.98/0.88 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(370,plain,
% 0.98/0.88 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp15) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp15))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 0.98/0.88 inference(bind,[status(th)],[])).
% 0.98/0.88 tff(371,plain,
% 0.98/0.88 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp15) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.98/0.88 inference(quant_intro,[status(thm)],[370])).
% 0.98/0.88 tff(372,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause185')).
% 0.98/0.88 tff(373,plain,
% 0.98/0.88 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[372, 371])).
% 0.98/0.88 tff(374,plain,
% 0.98/0.88 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[373, 369])).
% 0.98/0.88 tff(375,plain,(
% 0.98/0.88 ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.98/0.88 inference(skolemize,[status(sab)],[374])).
% 0.98/0.88 tff(376,plain,
% 0.98/0.88 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[375, 368])).
% 0.98/0.88 tff(377,plain,
% 0.98/0.88 (((~hskp11) | c0_1(a21)) <=> ((~hskp11) | c0_1(a21))),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(378,axiom,((~hskp11) | c0_1(a21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause72')).
% 0.98/0.88 tff(379,plain,
% 0.98/0.88 ((~hskp11) | c0_1(a21)),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[378, 377])).
% 0.98/0.88 tff(380,plain,
% 0.98/0.88 ((~hskp11) | c0_1(a21)),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[379, 377])).
% 0.98/0.88 tff(381,plain,
% 0.98/0.88 ((~hskp11) | c0_1(a21)),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[380, 377])).
% 0.98/0.88 tff(382,plain,
% 0.98/0.88 ((~hskp11) | c0_1(a21)),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[381, 377])).
% 0.98/0.88 tff(383,plain,
% 0.98/0.88 ((~hskp11) | c0_1(a21)),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[382, 377])).
% 0.98/0.88 tff(384,plain,
% 0.98/0.88 ((~hskp11) | c0_1(a21)),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[383, 377])).
% 0.98/0.88 tff(385,plain,
% 0.98/0.88 ((~hskp11) | c0_1(a21)),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[384, 377])).
% 0.98/0.88 tff(386,plain,
% 0.98/0.88 ((~hskp11) | c0_1(a21)),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[385, 377])).
% 0.98/0.88 tff(387,plain,
% 0.98/0.88 (c0_1(a21)),
% 0.98/0.88 inference(unit_resolution,[status(thm)],[386, 347])).
% 0.98/0.88 tff(388,plain,
% 0.98/0.88 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c1_1(a30) | c2_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c2_1(a30)) | (~c3_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a30) | c2_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(389,plain,
% 0.98/0.88 ((hskp15 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30))) <=> (hskp15 | c1_1(a30) | c2_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(390,plain,
% 0.98/0.88 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c1_1(a30) | c2_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c2_1(a30)) | (~c3_1(a30))))),
% 0.98/0.88 inference(monotonicity,[status(thm)],[389])).
% 0.98/0.88 tff(391,plain,
% 0.98/0.88 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a30) | c2_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.98/0.88 inference(transitivity,[status(thm)],[390, 388])).
% 0.98/0.88 tff(392,plain,
% 0.98/0.88 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)))),
% 0.98/0.88 inference(quant_inst,[status(thm)],[])).
% 0.98/0.88 tff(393,plain,
% 0.98/0.88 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a30) | c2_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c2_1(a30)) | (~c3_1(a30))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[392, 391])).
% 0.98/0.88 tff(394,plain,
% 0.98/0.88 (hskp15 | (~c1_1(a21))),
% 0.98/0.88 inference(unit_resolution,[status(thm)],[393, 117, 325, 326, 387, 324, 359, 376])).
% 0.98/0.88 tff(395,plain,
% 0.98/0.88 (hskp15),
% 0.98/0.88 inference(unit_resolution,[status(thm)],[394, 366])).
% 0.98/0.88 tff(396,plain,
% 0.98/0.88 (c1_1(a29)),
% 0.98/0.88 inference(unit_resolution,[status(thm)],[136, 395])).
% 0.98/0.88 tff(397,plain,
% 0.98/0.88 (~c3_1(a29)),
% 0.98/0.88 inference(unit_resolution,[status(thm)],[142, 395])).
% 0.98/0.88 tff(398,plain,
% 0.98/0.88 (~c2_1(a29)),
% 0.98/0.88 inference(unit_resolution,[status(thm)],[148, 395])).
% 0.98/0.88 tff(399,plain,
% 0.98/0.88 (^[U: $i] : refl((hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))),
% 0.98/0.88 inference(bind,[status(th)],[])).
% 0.98/0.88 tff(400,plain,
% 0.98/0.88 (![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.98/0.88 inference(quant_intro,[status(thm)],[399])).
% 0.98/0.88 tff(401,plain,
% 0.98/0.88 (![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(402,plain,
% 0.98/0.88 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp30) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp30))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp30) <=> (hskp30 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp30) <=> (hskp30 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp30) | hskp8) <=> ((hskp30 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp8))), rewrite(((hskp30 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp8) <=> (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp30) | hskp8) <=> (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))))),
% 0.98/0.88 inference(bind,[status(th)],[])).
% 0.98/0.88 tff(403,plain,
% 0.98/0.88 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp30) | hskp8) <=> ![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.98/0.88 inference(quant_intro,[status(thm)],[402])).
% 0.98/0.88 tff(404,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp30) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause141')).
% 0.98/0.88 tff(405,plain,
% 0.98/0.88 (![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[404, 403])).
% 0.98/0.88 tff(406,plain,
% 0.98/0.88 (![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[405, 401])).
% 0.98/0.88 tff(407,plain,(
% 0.98/0.88 ![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.98/0.88 inference(skolemize,[status(sab)],[406])).
% 0.98/0.88 tff(408,plain,
% 0.98/0.88 (![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.98/0.88 inference(modus_ponens,[status(thm)],[407, 400])).
% 0.98/0.88 tff(409,plain,
% 0.98/0.88 (((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c0_1(a29))) <=> ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp30 | hskp8 | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c0_1(a29))),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(410,plain,
% 0.98/0.88 ((hskp30 | hskp8 | (~ndr1_0) | c0_1(a29) | c3_1(a29) | (~c1_1(a29))) <=> (hskp30 | hskp8 | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c0_1(a29))),
% 0.98/0.88 inference(rewrite,[status(thm)],[])).
% 0.98/0.88 tff(411,plain,
% 0.98/0.88 (((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | (~ndr1_0) | c0_1(a29) | c3_1(a29) | (~c1_1(a29)))) <=> ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c0_1(a29)))),
% 0.98/0.88 inference(monotonicity,[status(thm)],[410])).
% 0.98/0.88 tff(412,plain,
% 0.98/0.88 (((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | (~ndr1_0) | c0_1(a29) | c3_1(a29) | (~c1_1(a29)))) <=> ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp30 | hskp8 | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c0_1(a29))),
% 0.98/0.88 inference(transitivity,[status(thm)],[411, 409])).
% 0.98/0.88 tff(413,plain,
% 0.98/0.88 ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | (~ndr1_0) | c0_1(a29) | c3_1(a29) | (~c1_1(a29)))),
% 0.98/0.89 inference(quant_inst,[status(thm)],[])).
% 0.98/0.89 tff(414,plain,
% 0.98/0.89 ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp30 | hskp8 | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c0_1(a29)),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[413, 412])).
% 0.98/0.89 tff(415,plain,
% 0.98/0.89 (c0_1(a29)),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[414, 117, 1, 321, 396, 397, 408])).
% 0.98/0.89 tff(416,plain,
% 0.98/0.89 (~hskp21),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[171, 415, 398, 397, 396])).
% 0.98/0.89 tff(417,plain,
% 0.98/0.89 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 0.98/0.89 inference(bind,[status(th)],[])).
% 0.98/0.89 tff(418,plain,
% 0.98/0.89 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.98/0.89 inference(quant_intro,[status(thm)],[417])).
% 0.98/0.89 tff(419,plain,
% 0.98/0.89 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(420,plain,
% 0.98/0.89 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp3) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp3))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 0.98/0.89 inference(bind,[status(th)],[])).
% 0.98/0.89 tff(421,plain,
% 0.98/0.89 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.98/0.89 inference(quant_intro,[status(thm)],[420])).
% 0.98/0.89 tff(422,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause176')).
% 0.98/0.89 tff(423,plain,
% 0.98/0.89 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[422, 421])).
% 0.98/0.89 tff(424,plain,
% 0.98/0.89 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[423, 419])).
% 0.98/0.89 tff(425,plain,(
% 0.98/0.89 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.98/0.89 inference(skolemize,[status(sab)],[424])).
% 0.98/0.89 tff(426,plain,
% 0.98/0.89 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[425, 418])).
% 0.98/0.89 tff(427,plain,
% 0.98/0.89 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | c1_1(a13) | c2_1(a21) | c0_1(a13) | (~ndr1_0) | (~c3_1(a13)) | (~c1_1(a21)) | (~c0_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c1_1(a13) | c2_1(a21) | c0_1(a13) | (~ndr1_0) | (~c3_1(a13)) | (~c1_1(a21)) | (~c0_1(a21)))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(428,plain,
% 0.98/0.89 ((hskp3 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a13) | c0_1(a13) | (~c3_1(a13))) <=> (hskp3 | c1_1(a13) | c2_1(a21) | c0_1(a13) | (~ndr1_0) | (~c3_1(a13)) | (~c1_1(a21)) | (~c0_1(a21)))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(429,plain,
% 0.98/0.89 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a13) | c0_1(a13) | (~c3_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | c1_1(a13) | c2_1(a21) | c0_1(a13) | (~ndr1_0) | (~c3_1(a13)) | (~c1_1(a21)) | (~c0_1(a21))))),
% 0.98/0.89 inference(monotonicity,[status(thm)],[428])).
% 0.98/0.89 tff(430,plain,
% 0.98/0.89 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a13) | c0_1(a13) | (~c3_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c1_1(a13) | c2_1(a21) | c0_1(a13) | (~ndr1_0) | (~c3_1(a13)) | (~c1_1(a21)) | (~c0_1(a21)))),
% 0.98/0.89 inference(transitivity,[status(thm)],[429, 427])).
% 0.98/0.89 tff(431,plain,
% 0.98/0.89 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a13) | c0_1(a13) | (~c3_1(a13)))),
% 0.98/0.89 inference(quant_inst,[status(thm)],[])).
% 0.98/0.89 tff(432,plain,
% 0.98/0.89 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c1_1(a13) | c2_1(a21) | c0_1(a13) | (~ndr1_0) | (~c3_1(a13)) | (~c1_1(a21)) | (~c0_1(a21))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[431, 430])).
% 0.98/0.89 tff(433,plain,
% 0.98/0.89 (hskp3 | (~c1_1(a21))),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[432, 117, 387, 310, 359, 268, 426, 339])).
% 0.98/0.89 tff(434,plain,
% 0.98/0.89 (hskp3),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[433, 366])).
% 0.98/0.89 tff(435,plain,
% 0.98/0.89 (((~hskp3) | c3_1(a6)) <=> ((~hskp3) | c3_1(a6))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(436,axiom,((~hskp3) | c3_1(a6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause82')).
% 0.98/0.89 tff(437,plain,
% 0.98/0.89 ((~hskp3) | c3_1(a6)),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[436, 435])).
% 0.98/0.89 tff(438,plain,
% 0.98/0.89 ((~hskp3) | c3_1(a6)),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[437, 435])).
% 0.98/0.89 tff(439,plain,
% 0.98/0.89 ((~hskp3) | c3_1(a6)),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[438, 435])).
% 0.98/0.89 tff(440,plain,
% 0.98/0.89 ((~hskp3) | c3_1(a6)),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[439, 435])).
% 0.98/0.89 tff(441,plain,
% 0.98/0.89 ((~hskp3) | c3_1(a6)),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[440, 435])).
% 0.98/0.89 tff(442,plain,
% 0.98/0.89 ((~hskp3) | c3_1(a6)),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[441, 435])).
% 0.98/0.89 tff(443,plain,
% 0.98/0.89 ((~hskp3) | c3_1(a6)),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[442, 435])).
% 0.98/0.89 tff(444,plain,
% 0.98/0.89 ((~hskp3) | c3_1(a6)),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[443, 435])).
% 0.98/0.89 tff(445,plain,
% 0.98/0.89 (c3_1(a6)),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[444, 434])).
% 0.98/0.89 tff(446,plain,
% 0.98/0.89 (((~hskp3) | c0_1(a6)) <=> ((~hskp3) | c0_1(a6))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(447,axiom,((~hskp3) | c0_1(a6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause81')).
% 0.98/0.89 tff(448,plain,
% 0.98/0.89 ((~hskp3) | c0_1(a6)),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[447, 446])).
% 0.98/0.89 tff(449,plain,
% 0.98/0.89 ((~hskp3) | c0_1(a6)),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[448, 446])).
% 0.98/0.89 tff(450,plain,
% 0.98/0.89 ((~hskp3) | c0_1(a6)),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[449, 446])).
% 0.98/0.89 tff(451,plain,
% 0.98/0.89 ((~hskp3) | c0_1(a6)),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[450, 446])).
% 0.98/0.89 tff(452,plain,
% 0.98/0.89 ((~hskp3) | c0_1(a6)),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[451, 446])).
% 0.98/0.89 tff(453,plain,
% 0.98/0.89 ((~hskp3) | c0_1(a6)),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[452, 446])).
% 0.98/0.89 tff(454,plain,
% 0.98/0.89 ((~hskp3) | c0_1(a6)),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[453, 446])).
% 0.98/0.89 tff(455,plain,
% 0.98/0.89 ((~hskp3) | c0_1(a6)),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[454, 446])).
% 0.98/0.89 tff(456,plain,
% 0.98/0.89 (c0_1(a6)),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[455, 434])).
% 0.98/0.89 tff(457,plain,
% 0.98/0.89 (((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | (~ndr1_0) | c1_1(a6) | (~c3_1(a6)) | (~c0_1(a6)))) <=> ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp8 | (~ndr1_0) | c1_1(a6) | (~c3_1(a6)) | (~c0_1(a6)))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(458,plain,
% 0.98/0.89 ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | (~ndr1_0) | c1_1(a6) | (~c3_1(a6)) | (~c0_1(a6)))),
% 0.98/0.89 inference(quant_inst,[status(thm)],[])).
% 0.98/0.89 tff(459,plain,
% 0.98/0.89 ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp8 | (~ndr1_0) | c1_1(a6) | (~c3_1(a6)) | (~c0_1(a6))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[458, 457])).
% 0.98/0.89 tff(460,plain,
% 0.98/0.89 (hskp21 | c1_1(a6)),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[459, 117, 321, 456, 445, 21])).
% 0.98/0.89 tff(461,plain,
% 0.98/0.89 (c1_1(a6)),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[460, 416])).
% 0.98/0.89 tff(462,plain,
% 0.98/0.89 (((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | c1_1(a30) | (~ndr1_0) | (~c0_1(a30)) | (~c3_1(a30)))) <=> ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp8 | c1_1(a30) | (~ndr1_0) | (~c0_1(a30)) | (~c3_1(a30)))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(463,plain,
% 0.98/0.89 ((hskp21 | hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c0_1(a30))) <=> (hskp21 | hskp8 | c1_1(a30) | (~ndr1_0) | (~c0_1(a30)) | (~c3_1(a30)))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(464,plain,
% 0.98/0.89 (((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c0_1(a30)))) <=> ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | c1_1(a30) | (~ndr1_0) | (~c0_1(a30)) | (~c3_1(a30))))),
% 0.98/0.89 inference(monotonicity,[status(thm)],[463])).
% 0.98/0.89 tff(465,plain,
% 0.98/0.89 (((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c0_1(a30)))) <=> ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp8 | c1_1(a30) | (~ndr1_0) | (~c0_1(a30)) | (~c3_1(a30)))),
% 0.98/0.89 inference(transitivity,[status(thm)],[464, 462])).
% 0.98/0.89 tff(466,plain,
% 0.98/0.89 ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c0_1(a30)))),
% 0.98/0.89 inference(quant_inst,[status(thm)],[])).
% 0.98/0.89 tff(467,plain,
% 0.98/0.89 ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp8 | c1_1(a30) | (~ndr1_0) | (~c0_1(a30)) | (~c3_1(a30))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[466, 465])).
% 0.98/0.89 tff(468,plain,
% 0.98/0.89 (hskp21 | (~c0_1(a30))),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[467, 117, 321, 326, 324, 21])).
% 0.98/0.89 tff(469,plain,
% 0.98/0.89 (~c0_1(a30)),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[468, 416])).
% 0.98/0.89 tff(470,plain,
% 0.98/0.89 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)))),
% 0.98/0.89 inference(bind,[status(th)],[])).
% 0.98/0.89 tff(471,plain,
% 0.98/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.98/0.89 inference(quant_intro,[status(thm)],[470])).
% 0.98/0.89 tff(472,plain,
% 0.98/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(473,plain,
% 0.98/0.89 (^[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) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))))),
% 0.98/0.89 inference(bind,[status(th)],[])).
% 0.98/0.89 tff(474,plain,
% 0.98/0.89 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.98/0.89 inference(quant_intro,[status(thm)],[473])).
% 0.98/0.89 tff(475,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause190')).
% 0.98/0.89 tff(476,plain,
% 0.98/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[475, 474])).
% 0.98/0.89 tff(477,plain,
% 0.98/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[476, 472])).
% 0.98/0.89 tff(478,plain,(
% 0.98/0.89 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.98/0.89 inference(skolemize,[status(sab)],[477])).
% 0.98/0.89 tff(479,plain,
% 0.98/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[478, 471])).
% 0.98/0.89 tff(480,plain,
% 0.98/0.89 (((~hskp3) | (~c2_1(a6))) <=> ((~hskp3) | (~c2_1(a6)))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(481,plain,
% 0.98/0.89 (((~c2_1(a6)) | (~hskp3)) <=> ((~hskp3) | (~c2_1(a6)))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(482,axiom,((~c2_1(a6)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 0.98/0.89 tff(483,plain,
% 0.98/0.89 ((~hskp3) | (~c2_1(a6))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[482, 481])).
% 0.98/0.89 tff(484,plain,
% 0.98/0.89 ((~hskp3) | (~c2_1(a6))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[483, 480])).
% 0.98/0.89 tff(485,plain,
% 0.98/0.89 (~c2_1(a6)),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[484, 434])).
% 0.98/0.89 tff(486,plain,
% 0.98/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a13) | c2_1(a13) | c0_1(a13) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a13) | c2_1(a13) | c0_1(a13) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(487,plain,
% 0.98/0.89 (((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c1_1(a13) | c0_1(a13) | c2_1(a13)) <=> (c1_1(a13) | c2_1(a13) | c0_1(a13) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(488,plain,
% 0.98/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c1_1(a13) | c0_1(a13) | c2_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a13) | c2_1(a13) | c0_1(a13) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30))))),
% 0.98/0.89 inference(monotonicity,[status(thm)],[487])).
% 0.98/0.89 tff(489,plain,
% 0.98/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c1_1(a13) | c0_1(a13) | c2_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a13) | c2_1(a13) | c0_1(a13) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.98/0.89 inference(transitivity,[status(thm)],[488, 486])).
% 0.98/0.89 tff(490,plain,
% 0.98/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c1_1(a13) | c0_1(a13) | c2_1(a13))),
% 0.98/0.89 inference(quant_inst,[status(thm)],[])).
% 0.98/0.89 tff(491,plain,
% 0.98/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a13) | c2_1(a13) | c0_1(a13) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[490, 489])).
% 0.98/0.89 tff(492,plain,
% 0.98/0.89 ($false),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[491, 117, 325, 326, 310, 322, 445, 268, 485, 479, 469, 461])).
% 0.98/0.89 tff(493,plain,((~hskp16) | c1_1(a13) | c2_1(a13) | c0_1(a13) | hskp30), inference(lemma,lemma(discharge,[]))).
% 0.98/0.89 tff(494,plain,
% 0.98/0.89 (~hskp16),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[493, 322, 310, 268, 1])).
% 0.98/0.89 tff(495,assumption,(hskp9), introduced(assumption)).
% 0.98/0.89 tff(496,plain,
% 0.98/0.89 (((~hskp9) | (~c1_1(a15))) <=> ((~hskp9) | (~c1_1(a15)))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(497,plain,
% 0.98/0.89 (((~c1_1(a15)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a15)))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(498,axiom,((~c1_1(a15)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause118')).
% 0.98/0.89 tff(499,plain,
% 0.98/0.89 ((~hskp9) | (~c1_1(a15))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[498, 497])).
% 0.98/0.89 tff(500,plain,
% 0.98/0.89 ((~hskp9) | (~c1_1(a15))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[499, 496])).
% 0.98/0.89 tff(501,plain,
% 0.98/0.89 (~c1_1(a15)),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[500, 495])).
% 0.98/0.89 tff(502,plain,
% 0.98/0.89 (((~hskp9) | (~c2_1(a15))) <=> ((~hskp9) | (~c2_1(a15)))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(503,plain,
% 0.98/0.89 (((~c2_1(a15)) | (~hskp9)) <=> ((~hskp9) | (~c2_1(a15)))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(504,axiom,((~c2_1(a15)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause119')).
% 0.98/0.89 tff(505,plain,
% 0.98/0.89 ((~hskp9) | (~c2_1(a15))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[504, 503])).
% 0.98/0.89 tff(506,plain,
% 0.98/0.89 ((~hskp9) | (~c2_1(a15))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[505, 502])).
% 0.98/0.89 tff(507,plain,
% 0.98/0.89 (~c2_1(a15)),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[506, 495])).
% 0.98/0.89 tff(508,assumption,(~c1_1(a15)), introduced(assumption)).
% 0.98/0.89 tff(509,assumption,(~c2_1(a15)), introduced(assumption)).
% 0.98/0.89 tff(510,plain,
% 0.98/0.89 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))),
% 0.98/0.89 inference(bind,[status(th)],[])).
% 0.98/0.89 tff(511,plain,
% 0.98/0.89 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.98/0.89 inference(quant_intro,[status(thm)],[510])).
% 0.98/0.89 tff(512,plain,
% 0.98/0.89 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(513,plain,
% 0.98/0.89 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~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))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~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))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_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))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_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)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_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))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp9) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp9))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))))),
% 0.98/0.89 inference(bind,[status(th)],[])).
% 0.98/0.89 tff(514,plain,
% 0.98/0.89 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.98/0.89 inference(quant_intro,[status(thm)],[513])).
% 0.98/0.89 tff(515,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause175')).
% 0.98/0.89 tff(516,plain,
% 0.98/0.89 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[515, 514])).
% 0.98/0.89 tff(517,plain,
% 0.98/0.89 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[516, 512])).
% 0.98/0.89 tff(518,plain,(
% 0.98/0.89 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.98/0.89 inference(skolemize,[status(sab)],[517])).
% 0.98/0.89 tff(519,plain,
% 0.98/0.89 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[518, 511])).
% 0.98/0.89 tff(520,assumption,(~c0_1(a5)), introduced(assumption)).
% 0.98/0.89 tff(521,assumption,(~c1_1(a5)), introduced(assumption)).
% 0.98/0.89 tff(522,assumption,(~hskp3), introduced(assumption)).
% 0.98/0.89 tff(523,assumption,(~hskp8), introduced(assumption)).
% 0.98/0.89 tff(524,assumption,(~c3_1(a15)), introduced(assumption)).
% 0.98/0.89 tff(525,plain,
% 0.98/0.89 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a30) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a30) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(526,plain,
% 0.98/0.89 ((hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a15) | c1_1(a15) | c2_1(a15)) <=> (hskp8 | c1_1(a30) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.98/0.89 inference(rewrite,[status(thm)],[])).
% 0.98/0.89 tff(527,plain,
% 0.98/0.89 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a15) | c1_1(a15) | c2_1(a15))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a30) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30))))),
% 0.98/0.89 inference(monotonicity,[status(thm)],[526])).
% 0.98/0.89 tff(528,plain,
% 0.98/0.89 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a15) | c1_1(a15) | c2_1(a15))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a30) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.98/0.89 inference(transitivity,[status(thm)],[527, 525])).
% 0.98/0.89 tff(529,plain,
% 0.98/0.89 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a15) | c1_1(a15) | c2_1(a15))),
% 0.98/0.89 inference(quant_inst,[status(thm)],[])).
% 0.98/0.89 tff(530,plain,
% 0.98/0.89 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a30) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30))),
% 0.98/0.89 inference(modus_ponens,[status(thm)],[529, 528])).
% 0.98/0.89 tff(531,plain,
% 0.98/0.89 ((~c2_1(a30)) | (~c3_1(a30))),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[530, 117, 523, 328, 508, 509, 524, 31])).
% 0.98/0.89 tff(532,plain,
% 0.98/0.89 ($false),
% 0.98/0.89 inference(unit_resolution,[status(thm)],[531, 326, 325])).
% 0.98/0.89 tff(533,plain,((~hskp16) | hskp8 | c1_1(a30) | c1_1(a15) | c2_1(a15) | c3_1(a15)), inference(lemma,lemma(discharge,[]))).
% 0.98/0.89 tff(534,plain,
% 0.98/0.90 (~hskp16),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[533, 328, 523, 508, 509, 524])).
% 0.98/0.90 tff(535,assumption,(hskp10), introduced(assumption)).
% 0.98/0.90 tff(536,plain,
% 0.98/0.90 (((~hskp10) | (~c2_1(a17))) <=> ((~hskp10) | (~c2_1(a17)))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(537,plain,
% 0.98/0.90 (((~c2_1(a17)) | (~hskp10)) <=> ((~hskp10) | (~c2_1(a17)))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(538,axiom,((~c2_1(a17)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause117')).
% 0.98/0.90 tff(539,plain,
% 0.98/0.90 ((~hskp10) | (~c2_1(a17))),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[538, 537])).
% 0.98/0.90 tff(540,plain,
% 0.98/0.90 ((~hskp10) | (~c2_1(a17))),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[539, 536])).
% 0.98/0.90 tff(541,plain,
% 0.98/0.90 (~c2_1(a17)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[540, 535])).
% 0.98/0.90 tff(542,plain,
% 0.98/0.90 (((~hskp10) | c1_1(a17)) <=> ((~hskp10) | c1_1(a17))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(543,axiom,((~hskp10) | c1_1(a17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 0.98/0.90 tff(544,plain,
% 0.98/0.90 ((~hskp10) | c1_1(a17)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[543, 542])).
% 0.98/0.90 tff(545,plain,
% 0.98/0.90 ((~hskp10) | c1_1(a17)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[544, 542])).
% 0.98/0.90 tff(546,plain,
% 0.98/0.90 ((~hskp10) | c1_1(a17)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[545, 542])).
% 0.98/0.90 tff(547,plain,
% 0.98/0.90 ((~hskp10) | c1_1(a17)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[546, 542])).
% 0.98/0.90 tff(548,plain,
% 0.98/0.90 ((~hskp10) | c1_1(a17)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[547, 542])).
% 0.98/0.90 tff(549,plain,
% 0.98/0.90 ((~hskp10) | c1_1(a17)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[548, 542])).
% 0.98/0.90 tff(550,plain,
% 0.98/0.90 ((~hskp10) | c1_1(a17)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[549, 542])).
% 0.98/0.90 tff(551,plain,
% 0.98/0.90 ((~hskp10) | c1_1(a17)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[550, 542])).
% 0.98/0.90 tff(552,plain,
% 0.98/0.90 (c1_1(a17)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[551, 535])).
% 0.98/0.90 tff(553,plain,
% 0.98/0.90 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | c2_1(a17) | (~ndr1_0) | (~c1_1(a17)) | (~c3_1(a17)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | c2_1(a17) | (~ndr1_0) | (~c1_1(a17)) | (~c3_1(a17)))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(554,plain,
% 0.98/0.90 ((hskp16 | (~ndr1_0) | c2_1(a17) | (~c1_1(a17)) | (~c3_1(a17))) <=> (hskp16 | c2_1(a17) | (~ndr1_0) | (~c1_1(a17)) | (~c3_1(a17)))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(555,plain,
% 0.98/0.90 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a17) | (~c1_1(a17)) | (~c3_1(a17)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | c2_1(a17) | (~ndr1_0) | (~c1_1(a17)) | (~c3_1(a17))))),
% 0.98/0.90 inference(monotonicity,[status(thm)],[554])).
% 0.98/0.90 tff(556,plain,
% 0.98/0.90 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a17) | (~c1_1(a17)) | (~c3_1(a17)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | c2_1(a17) | (~ndr1_0) | (~c1_1(a17)) | (~c3_1(a17)))),
% 0.98/0.90 inference(transitivity,[status(thm)],[555, 553])).
% 0.98/0.90 tff(557,plain,
% 0.98/0.90 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a17) | (~c1_1(a17)) | (~c3_1(a17)))),
% 0.98/0.90 inference(quant_inst,[status(thm)],[])).
% 0.98/0.90 tff(558,plain,
% 0.98/0.90 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | c2_1(a17) | (~ndr1_0) | (~c1_1(a17)) | (~c3_1(a17))),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[557, 556])).
% 0.98/0.90 tff(559,plain,
% 0.98/0.90 (~c3_1(a17)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[558, 117, 43, 552, 541, 192])).
% 0.98/0.90 tff(560,plain,
% 0.98/0.90 (((~hskp10) | (~c0_1(a17))) <=> ((~hskp10) | (~c0_1(a17)))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(561,plain,
% 0.98/0.90 (((~c0_1(a17)) | (~hskp10)) <=> ((~hskp10) | (~c0_1(a17)))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(562,axiom,((~c0_1(a17)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause116')).
% 0.98/0.90 tff(563,plain,
% 0.98/0.90 ((~hskp10) | (~c0_1(a17))),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[562, 561])).
% 0.98/0.90 tff(564,plain,
% 0.98/0.90 ((~hskp10) | (~c0_1(a17))),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[563, 560])).
% 0.98/0.90 tff(565,plain,
% 0.98/0.90 (~c0_1(a17)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[564, 535])).
% 0.98/0.90 tff(566,plain,
% 0.98/0.90 (((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | c0_1(a17) | (~ndr1_0) | (~c1_1(a17)) | c3_1(a17))) <=> ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp30 | hskp8 | c0_1(a17) | (~ndr1_0) | (~c1_1(a17)) | c3_1(a17))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(567,plain,
% 0.98/0.90 ((hskp30 | hskp8 | (~ndr1_0) | c0_1(a17) | c3_1(a17) | (~c1_1(a17))) <=> (hskp30 | hskp8 | c0_1(a17) | (~ndr1_0) | (~c1_1(a17)) | c3_1(a17))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(568,plain,
% 0.98/0.90 (((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | (~ndr1_0) | c0_1(a17) | c3_1(a17) | (~c1_1(a17)))) <=> ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | c0_1(a17) | (~ndr1_0) | (~c1_1(a17)) | c3_1(a17)))),
% 0.98/0.90 inference(monotonicity,[status(thm)],[567])).
% 0.98/0.90 tff(569,plain,
% 0.98/0.90 (((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | (~ndr1_0) | c0_1(a17) | c3_1(a17) | (~c1_1(a17)))) <=> ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp30 | hskp8 | c0_1(a17) | (~ndr1_0) | (~c1_1(a17)) | c3_1(a17))),
% 0.98/0.90 inference(transitivity,[status(thm)],[568, 566])).
% 0.98/0.90 tff(570,plain,
% 0.98/0.90 ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | (~ndr1_0) | c0_1(a17) | c3_1(a17) | (~c1_1(a17)))),
% 0.98/0.90 inference(quant_inst,[status(thm)],[])).
% 0.98/0.90 tff(571,plain,
% 0.98/0.90 ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp30 | hskp8 | c0_1(a17) | (~ndr1_0) | (~c1_1(a17)) | c3_1(a17)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[570, 569])).
% 0.98/0.90 tff(572,plain,
% 0.98/0.90 ($false),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[571, 117, 1, 523, 552, 565, 408, 559])).
% 0.98/0.90 tff(573,plain,((~hskp10) | hskp30 | hskp8 | hskp16), inference(lemma,lemma(discharge,[]))).
% 0.98/0.90 tff(574,plain,
% 0.98/0.90 (~hskp10),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[573, 534, 523, 1])).
% 0.98/0.90 tff(575,assumption,(c2_1(a5)), introduced(assumption)).
% 0.98/0.90 tff(576,plain,
% 0.98/0.90 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a15) | c2_1(a15) | c3_1(a15) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a15) | c2_1(a15) | c3_1(a15) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(577,plain,
% 0.98/0.90 ((hskp8 | (~ndr1_0) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)) | c3_1(a15) | c1_1(a15) | c2_1(a15)) <=> (hskp8 | c1_1(a15) | c2_1(a15) | c3_1(a15) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(578,plain,
% 0.98/0.90 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)) | c3_1(a15) | c1_1(a15) | c2_1(a15))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a15) | c2_1(a15) | c3_1(a15) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5))))),
% 0.98/0.90 inference(monotonicity,[status(thm)],[577])).
% 0.98/0.90 tff(579,plain,
% 0.98/0.90 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)) | c3_1(a15) | c1_1(a15) | c2_1(a15))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a15) | c2_1(a15) | c3_1(a15) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)))),
% 0.98/0.90 inference(transitivity,[status(thm)],[578, 576])).
% 0.98/0.90 tff(580,plain,
% 0.98/0.90 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)) | c3_1(a15) | c1_1(a15) | c2_1(a15))),
% 0.98/0.90 inference(quant_inst,[status(thm)],[])).
% 0.98/0.90 tff(581,plain,
% 0.98/0.90 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a15) | c2_1(a15) | c3_1(a15) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5))),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[580, 579])).
% 0.98/0.90 tff(582,plain,
% 0.98/0.90 ((~c2_1(a5)) | (~c3_1(a5))),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[581, 117, 523, 508, 509, 524, 521, 31])).
% 0.98/0.90 tff(583,plain,
% 0.98/0.90 (~c3_1(a5)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[582, 575])).
% 0.98/0.90 tff(584,plain,
% 0.98/0.90 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp15 | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp15 | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(585,plain,
% 0.98/0.90 ((hskp16 | hskp15 | (~ndr1_0) | c0_1(a5) | c3_1(a5) | (~c2_1(a5))) <=> (hskp16 | hskp15 | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(586,plain,
% 0.98/0.90 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c0_1(a5) | c3_1(a5) | (~c2_1(a5)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp15 | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5)))),
% 0.98/0.90 inference(monotonicity,[status(thm)],[585])).
% 0.98/0.90 tff(587,plain,
% 0.98/0.90 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c0_1(a5) | c3_1(a5) | (~c2_1(a5)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp15 | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5))),
% 0.98/0.90 inference(transitivity,[status(thm)],[586, 584])).
% 0.98/0.90 tff(588,plain,
% 0.98/0.90 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c0_1(a5) | c3_1(a5) | (~c2_1(a5)))),
% 0.98/0.90 inference(quant_inst,[status(thm)],[])).
% 0.98/0.90 tff(589,plain,
% 0.98/0.90 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp15 | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[588, 587])).
% 0.98/0.90 tff(590,plain,
% 0.98/0.90 (hskp16 | hskp15 | (~c2_1(a5)) | c3_1(a5)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[589, 117, 520, 53])).
% 0.98/0.90 tff(591,plain,
% 0.98/0.90 (hskp15),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[590, 575, 534, 583])).
% 0.98/0.90 tff(592,plain,
% 0.98/0.90 (~c2_1(a29)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[148, 591])).
% 0.98/0.90 tff(593,plain,
% 0.98/0.90 (~c3_1(a29)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[142, 591])).
% 0.98/0.90 tff(594,assumption,(ndr1_0), introduced(assumption)).
% 0.98/0.90 tff(595,plain,
% 0.98/0.90 (hskp8 | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5))),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[581, 524, 521, 31])).
% 0.98/0.90 tff(596,plain,
% 0.98/0.90 (~c3_1(a5)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[595, 523, 594, 508, 509, 575])).
% 0.98/0.90 tff(597,assumption,(~c0_1(a29)), introduced(assumption)).
% 0.98/0.90 tff(598,plain,
% 0.98/0.90 (hskp8 | (~ndr1_0) | (~c1_1(a29)) | c0_1(a29)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[414, 1, 161, 408])).
% 0.98/0.90 tff(599,plain,
% 0.98/0.90 (~c1_1(a29)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[598, 523, 594, 597])).
% 0.98/0.90 tff(600,plain,
% 0.98/0.90 (~hskp15),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[136, 599])).
% 0.98/0.90 tff(601,plain,
% 0.98/0.90 (hskp16 | hskp15 | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[589, 520, 53])).
% 0.98/0.90 tff(602,plain,
% 0.98/0.90 (hskp16),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[601, 600, 594, 575, 596])).
% 0.98/0.90 tff(603,plain,
% 0.98/0.90 (c2_1(a30)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[255, 602])).
% 0.98/0.90 tff(604,plain,
% 0.98/0.90 (c3_1(a30)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[266, 602])).
% 0.98/0.90 tff(605,plain,
% 0.98/0.90 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a29) | c1_1(a30) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a29) | c1_1(a30) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(606,plain,
% 0.98/0.90 ((hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a29) | c1_1(a29) | c2_1(a29)) <=> (hskp8 | c1_1(a29) | c1_1(a30) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(607,plain,
% 0.98/0.90 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a29) | c1_1(a29) | c2_1(a29))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a29) | c1_1(a30) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30))))),
% 0.98/0.90 inference(monotonicity,[status(thm)],[606])).
% 0.98/0.90 tff(608,plain,
% 0.98/0.90 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a29) | c1_1(a29) | c2_1(a29))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a29) | c1_1(a30) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.98/0.90 inference(transitivity,[status(thm)],[607, 605])).
% 0.98/0.90 tff(609,plain,
% 0.98/0.90 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a29) | c1_1(a29) | c2_1(a29))),
% 0.98/0.90 inference(quant_inst,[status(thm)],[])).
% 0.98/0.90 tff(610,plain,
% 0.98/0.90 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a29) | c1_1(a30) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30))),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[609, 608])).
% 0.98/0.90 tff(611,plain,
% 0.98/0.90 (hskp8 | c1_1(a29) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30))),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[610, 328, 162, 161, 31])).
% 0.98/0.90 tff(612,plain,
% 0.98/0.90 ($false),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[611, 604, 603, 594, 523, 599])).
% 0.98/0.90 tff(613,plain,(hskp8 | (~ndr1_0) | c1_1(a30) | c2_1(a29) | c3_1(a29) | (~c2_1(a5)) | c0_1(a5) | c0_1(a29) | hskp30 | c1_1(a15) | c2_1(a15) | c3_1(a15) | c1_1(a5)), inference(lemma,lemma(discharge,[]))).
% 0.98/0.90 tff(614,plain,
% 0.98/0.90 (c0_1(a29)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[613, 523, 328, 162, 161, 575, 520, 594, 1, 508, 509, 524, 521])).
% 0.98/0.90 tff(615,plain,
% 0.98/0.90 (((~![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)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | (c2_1(a29) | c3_1(a29) | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c1_1(a29)) | (~c0_1(a29)))) <=> ((~![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)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | c2_1(a29) | c3_1(a29) | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c1_1(a29)) | (~c0_1(a29)))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(616,plain,
% 0.98/0.90 (((~ndr1_0) | c3_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c3_1(a29) | c2_1(a29) | (~c0_1(a29)) | c0_1(a5) | (~c2_1(a5)) | c3_1(a5)) <=> (c2_1(a29) | c3_1(a29) | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c1_1(a29)) | (~c0_1(a29)))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(617,plain,
% 0.98/0.90 (((~![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)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c3_1(a29) | c2_1(a29) | (~c0_1(a29)) | c0_1(a5) | (~c2_1(a5)) | c3_1(a5))) <=> ((~![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)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | (c2_1(a29) | c3_1(a29) | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c1_1(a29)) | (~c0_1(a29))))),
% 0.98/0.90 inference(monotonicity,[status(thm)],[616])).
% 0.98/0.90 tff(618,plain,
% 0.98/0.90 (((~![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)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c3_1(a29) | c2_1(a29) | (~c0_1(a29)) | c0_1(a5) | (~c2_1(a5)) | c3_1(a5))) <=> ((~![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)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | c2_1(a29) | c3_1(a29) | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c1_1(a29)) | (~c0_1(a29)))),
% 0.98/0.90 inference(transitivity,[status(thm)],[617, 615])).
% 0.98/0.90 tff(619,plain,
% 0.98/0.90 ((~![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)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c3_1(a29) | c2_1(a29) | (~c0_1(a29)) | c0_1(a5) | (~c2_1(a5)) | c3_1(a5))),
% 0.98/0.90 inference(quant_inst,[status(thm)],[])).
% 0.98/0.90 tff(620,plain,
% 0.98/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | c2_1(a29) | c3_1(a29) | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c1_1(a29)) | (~c0_1(a29))),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[619, 618])).
% 0.98/0.90 tff(621,plain,
% 0.98/0.90 (c2_1(a29) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c1_1(a29)) | (~c0_1(a29))),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[620, 161, 520, 160])).
% 0.98/0.90 tff(622,plain,
% 0.98/0.90 (~c1_1(a29)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[621, 614, 594, 162, 575, 596])).
% 0.98/0.90 tff(623,plain,
% 0.98/0.90 (~hskp15),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[136, 622])).
% 0.98/0.90 tff(624,plain,
% 0.98/0.90 (hskp16),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[601, 623, 594, 575, 596])).
% 0.98/0.90 tff(625,plain,
% 0.98/0.90 (c2_1(a30)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[255, 624])).
% 0.98/0.90 tff(626,plain,
% 0.98/0.90 (c3_1(a30)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[266, 624])).
% 0.98/0.90 tff(627,plain,
% 0.98/0.90 ($false),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[611, 626, 625, 594, 523, 622])).
% 0.98/0.90 tff(628,plain,(hskp8 | (~ndr1_0) | c1_1(a30) | c2_1(a29) | c3_1(a29) | (~c2_1(a5)) | c0_1(a5) | hskp30 | c1_1(a15) | c2_1(a15) | c3_1(a15) | c1_1(a5)), inference(lemma,lemma(discharge,[]))).
% 0.98/0.90 tff(629,plain,
% 0.98/0.90 (hskp8 | c1_1(a30) | c2_1(a29) | c3_1(a29) | (~c2_1(a5)) | c0_1(a5) | hskp30 | c1_1(a15) | c2_1(a15) | c3_1(a15) | c1_1(a5)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[628, 117])).
% 0.98/0.90 tff(630,plain,
% 0.98/0.90 ($false),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[629, 593, 592, 523, 328, 575, 520, 1, 508, 509, 524, 521])).
% 0.98/0.90 tff(631,plain,((~c2_1(a5)) | hskp8 | c1_1(a30) | c0_1(a5) | hskp30 | c1_1(a15) | c2_1(a15) | c3_1(a15) | c1_1(a5)), inference(lemma,lemma(discharge,[]))).
% 0.98/0.90 tff(632,plain,
% 0.98/0.90 (~c2_1(a5)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[631, 328, 523, 520, 1, 508, 509, 524, 521])).
% 0.98/0.90 tff(633,plain,
% 0.98/0.90 (((~hskp2) | c2_1(a5)) <=> ((~hskp2) | c2_1(a5))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(634,axiom,((~hskp2) | c2_1(a5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 0.98/0.90 tff(635,plain,
% 0.98/0.90 ((~hskp2) | c2_1(a5)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[634, 633])).
% 0.98/0.90 tff(636,plain,
% 0.98/0.90 ((~hskp2) | c2_1(a5)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[635, 633])).
% 0.98/0.90 tff(637,plain,
% 0.98/0.90 ((~hskp2) | c2_1(a5)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[636, 633])).
% 0.98/0.90 tff(638,plain,
% 0.98/0.90 ((~hskp2) | c2_1(a5)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[637, 633])).
% 0.98/0.90 tff(639,plain,
% 0.98/0.90 ((~hskp2) | c2_1(a5)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[638, 633])).
% 0.98/0.90 tff(640,plain,
% 0.98/0.90 ((~hskp2) | c2_1(a5)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[639, 633])).
% 0.98/0.90 tff(641,plain,
% 0.98/0.90 ((~hskp2) | c2_1(a5)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[640, 633])).
% 0.98/0.90 tff(642,plain,
% 0.98/0.90 ((~hskp2) | c2_1(a5)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[641, 633])).
% 0.98/0.90 tff(643,plain,
% 0.98/0.90 (~hskp2),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[642, 632])).
% 0.98/0.90 tff(644,assumption,(~hskp2), introduced(assumption)).
% 0.98/0.90 tff(645,assumption,(~hskp10), introduced(assumption)).
% 0.98/0.90 tff(646,assumption,(hskp13), introduced(assumption)).
% 0.98/0.90 tff(647,plain,
% 0.98/0.90 (((~hskp13) | (~c1_1(a26))) <=> ((~hskp13) | (~c1_1(a26)))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(648,plain,
% 0.98/0.90 (((~c1_1(a26)) | (~hskp13)) <=> ((~hskp13) | (~c1_1(a26)))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(649,axiom,((~c1_1(a26)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause112')).
% 0.98/0.90 tff(650,plain,
% 0.98/0.90 ((~hskp13) | (~c1_1(a26))),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[649, 648])).
% 0.98/0.90 tff(651,plain,
% 0.98/0.90 ((~hskp13) | (~c1_1(a26))),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[650, 647])).
% 0.98/0.90 tff(652,plain,
% 0.98/0.90 (~c1_1(a26)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[651, 646])).
% 0.98/0.90 tff(653,plain,
% 0.98/0.90 (((~hskp13) | c3_1(a26)) <=> ((~hskp13) | c3_1(a26))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(654,axiom,((~hskp13) | c3_1(a26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause69')).
% 0.98/0.90 tff(655,plain,
% 0.98/0.90 ((~hskp13) | c3_1(a26)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[654, 653])).
% 0.98/0.90 tff(656,plain,
% 0.98/0.90 ((~hskp13) | c3_1(a26)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[655, 653])).
% 0.98/0.90 tff(657,plain,
% 0.98/0.90 ((~hskp13) | c3_1(a26)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[656, 653])).
% 0.98/0.90 tff(658,plain,
% 0.98/0.90 ((~hskp13) | c3_1(a26)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[657, 653])).
% 0.98/0.90 tff(659,plain,
% 0.98/0.90 ((~hskp13) | c3_1(a26)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[658, 653])).
% 0.98/0.90 tff(660,plain,
% 0.98/0.90 ((~hskp13) | c3_1(a26)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[659, 653])).
% 0.98/0.90 tff(661,plain,
% 0.98/0.90 ((~hskp13) | c3_1(a26)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[660, 653])).
% 0.98/0.90 tff(662,plain,
% 0.98/0.90 ((~hskp13) | c3_1(a26)),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[661, 653])).
% 0.98/0.90 tff(663,plain,
% 0.98/0.90 (c3_1(a26)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[662, 646])).
% 0.98/0.90 tff(664,plain,
% 0.98/0.90 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a26) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c2_1(a26)) | (~c3_1(a26)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a26) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c2_1(a26)) | (~c3_1(a26)))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(665,plain,
% 0.98/0.90 ((hskp8 | (~ndr1_0) | c1_1(a26) | (~c3_1(a26)) | (~c2_1(a26)) | c3_1(a15) | c1_1(a15) | c2_1(a15)) <=> (hskp8 | c1_1(a26) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c2_1(a26)) | (~c3_1(a26)))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(666,plain,
% 0.98/0.90 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a26) | (~c3_1(a26)) | (~c2_1(a26)) | c3_1(a15) | c1_1(a15) | c2_1(a15))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a26) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c2_1(a26)) | (~c3_1(a26))))),
% 0.98/0.90 inference(monotonicity,[status(thm)],[665])).
% 0.98/0.90 tff(667,plain,
% 0.98/0.90 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a26) | (~c3_1(a26)) | (~c2_1(a26)) | c3_1(a15) | c1_1(a15) | c2_1(a15))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a26) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c2_1(a26)) | (~c3_1(a26)))),
% 0.98/0.90 inference(transitivity,[status(thm)],[666, 664])).
% 0.98/0.90 tff(668,plain,
% 0.98/0.90 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a26) | (~c3_1(a26)) | (~c2_1(a26)) | c3_1(a15) | c1_1(a15) | c2_1(a15))),
% 0.98/0.90 inference(quant_inst,[status(thm)],[])).
% 0.98/0.90 tff(669,plain,
% 0.98/0.90 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a26) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c2_1(a26)) | (~c3_1(a26))),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[668, 667])).
% 0.98/0.90 tff(670,plain,
% 0.98/0.90 (~c2_1(a26)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[669, 117, 523, 663, 652, 508, 509, 524, 31])).
% 0.98/0.90 tff(671,plain,
% 0.98/0.90 (((~hskp13) | (~c0_1(a26))) <=> ((~hskp13) | (~c0_1(a26)))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(672,plain,
% 0.98/0.90 (((~c0_1(a26)) | (~hskp13)) <=> ((~hskp13) | (~c0_1(a26)))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(673,axiom,((~c0_1(a26)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause111')).
% 0.98/0.90 tff(674,plain,
% 0.98/0.90 ((~hskp13) | (~c0_1(a26))),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[673, 672])).
% 0.98/0.90 tff(675,plain,
% 0.98/0.90 ((~hskp13) | (~c0_1(a26))),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[674, 671])).
% 0.98/0.90 tff(676,plain,
% 0.98/0.90 (~c0_1(a26)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[675, 646])).
% 0.98/0.90 tff(677,plain,
% 0.98/0.90 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | c0_1(a26) | (~ndr1_0) | c2_1(a26) | (~c3_1(a26)))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c0_1(a26) | (~ndr1_0) | c2_1(a26) | (~c3_1(a26)))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(678,plain,
% 0.98/0.90 ((hskp30 | hskp11 | (~ndr1_0) | c2_1(a26) | c0_1(a26) | (~c3_1(a26))) <=> (hskp30 | hskp11 | c0_1(a26) | (~ndr1_0) | c2_1(a26) | (~c3_1(a26)))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(679,plain,
% 0.98/0.90 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a26) | c0_1(a26) | (~c3_1(a26)))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | c0_1(a26) | (~ndr1_0) | c2_1(a26) | (~c3_1(a26))))),
% 0.98/0.90 inference(monotonicity,[status(thm)],[678])).
% 0.98/0.90 tff(680,plain,
% 0.98/0.90 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a26) | c0_1(a26) | (~c3_1(a26)))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c0_1(a26) | (~ndr1_0) | c2_1(a26) | (~c3_1(a26)))),
% 0.98/0.90 inference(transitivity,[status(thm)],[679, 677])).
% 0.98/0.90 tff(681,plain,
% 0.98/0.90 ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a26) | c0_1(a26) | (~c3_1(a26)))),
% 0.98/0.90 inference(quant_inst,[status(thm)],[])).
% 0.98/0.90 tff(682,plain,
% 0.98/0.90 ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c0_1(a26) | (~ndr1_0) | c2_1(a26) | (~c3_1(a26))),
% 0.98/0.90 inference(modus_ponens,[status(thm)],[681, 680])).
% 0.98/0.90 tff(683,plain,
% 0.98/0.90 (hskp11 | c2_1(a26)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[682, 117, 1, 663, 676, 41])).
% 0.98/0.90 tff(684,plain,
% 0.98/0.90 (hskp11),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[683, 670])).
% 0.98/0.90 tff(685,plain,
% 0.98/0.90 (~c2_1(a21)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[358, 684])).
% 0.98/0.90 tff(686,plain,
% 0.98/0.90 (c0_1(a21)),
% 0.98/0.90 inference(unit_resolution,[status(thm)],[386, 684])).
% 0.98/0.90 tff(687,plain,
% 0.98/0.90 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | c0_1(a26) | c1_1(a26) | c2_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c3_1(a26)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a26) | c1_1(a26) | c2_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c3_1(a26)))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(688,plain,
% 0.98/0.90 ((hskp3 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a26) | c0_1(a26) | (~c3_1(a26))) <=> (hskp3 | c0_1(a26) | c1_1(a26) | c2_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c3_1(a26)))),
% 0.98/0.90 inference(rewrite,[status(thm)],[])).
% 0.98/0.90 tff(689,plain,
% 0.98/0.90 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a26) | c0_1(a26) | (~c3_1(a26)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | c0_1(a26) | c1_1(a26) | c2_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c3_1(a26))))),
% 0.98/0.91 inference(monotonicity,[status(thm)],[688])).
% 0.98/0.91 tff(690,plain,
% 0.98/0.91 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a26) | c0_1(a26) | (~c3_1(a26)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a26) | c1_1(a26) | c2_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c3_1(a26)))),
% 0.98/0.91 inference(transitivity,[status(thm)],[689, 687])).
% 0.98/0.91 tff(691,plain,
% 0.98/0.91 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a26) | c0_1(a26) | (~c3_1(a26)))),
% 0.98/0.91 inference(quant_inst,[status(thm)],[])).
% 0.98/0.91 tff(692,plain,
% 0.98/0.91 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a26) | c1_1(a26) | c2_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c3_1(a26))),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[691, 690])).
% 0.98/0.91 tff(693,plain,
% 0.98/0.91 (~c1_1(a21)),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[692, 117, 522, 663, 686, 676, 652, 685, 426])).
% 0.98/0.91 tff(694,plain,
% 0.98/0.91 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))),
% 0.98/0.91 inference(bind,[status(th)],[])).
% 0.98/0.91 tff(695,plain,
% 0.98/0.91 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.98/0.91 inference(quant_intro,[status(thm)],[694])).
% 0.98/0.91 tff(696,plain,
% 0.98/0.91 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(697,plain,
% 0.98/0.91 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp10) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp10))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))))),
% 0.98/0.91 inference(bind,[status(th)],[])).
% 0.98/0.91 tff(698,plain,
% 0.98/0.91 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.98/0.91 inference(quant_intro,[status(thm)],[697])).
% 0.98/0.91 tff(699,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause171')).
% 0.98/0.91 tff(700,plain,
% 0.98/0.91 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[699, 698])).
% 0.98/0.91 tff(701,plain,
% 0.98/0.91 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[700, 696])).
% 0.98/0.91 tff(702,plain,(
% 0.98/0.91 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.98/0.91 inference(skolemize,[status(sab)],[701])).
% 0.98/0.91 tff(703,plain,
% 0.98/0.91 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[702, 695])).
% 0.98/0.91 tff(704,plain,
% 0.98/0.91 (~c3_1(a21)),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[352, 684])).
% 0.98/0.91 tff(705,plain,
% 0.98/0.91 (^[U: $i] : refl((hskp24 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> (hskp24 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))),
% 0.98/0.91 inference(bind,[status(th)],[])).
% 0.98/0.91 tff(706,plain,
% 0.98/0.91 (![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.98/0.91 inference(quant_intro,[status(thm)],[705])).
% 0.98/0.91 tff(707,plain,
% 0.98/0.91 (![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(708,plain,
% 0.98/0.91 (^[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)) | hskp3) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp3))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp3) | hskp24) <=> ((hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp24))), rewrite(((hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp24) <=> (hskp24 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp3) | hskp24) <=> (hskp24 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))))),
% 0.98/0.91 inference(bind,[status(th)],[])).
% 0.98/0.91 tff(709,plain,
% 0.98/0.91 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp3) | hskp24) <=> ![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.98/0.91 inference(quant_intro,[status(thm)],[708])).
% 0.98/0.91 tff(710,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp3) | hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause146')).
% 0.98/0.91 tff(711,plain,
% 0.98/0.91 (![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[710, 709])).
% 0.98/0.91 tff(712,plain,
% 0.98/0.91 (![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[711, 707])).
% 0.98/0.91 tff(713,plain,(
% 0.98/0.91 ![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.98/0.91 inference(skolemize,[status(sab)],[712])).
% 0.98/0.91 tff(714,plain,
% 0.98/0.91 (![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[713, 706])).
% 0.98/0.91 tff(715,plain,
% 0.98/0.91 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp24 | hskp3 | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c0_1(a21)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp24 | hskp3 | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c0_1(a21)))),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(716,plain,
% 0.98/0.91 ((hskp24 | hskp3 | (~ndr1_0) | c2_1(a21) | c3_1(a21) | (~c0_1(a21))) <=> (hskp24 | hskp3 | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c0_1(a21)))),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(717,plain,
% 0.98/0.91 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | c2_1(a21) | c3_1(a21) | (~c0_1(a21)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp24 | hskp3 | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c0_1(a21))))),
% 0.98/0.91 inference(monotonicity,[status(thm)],[716])).
% 0.98/0.91 tff(718,plain,
% 0.98/0.91 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | c2_1(a21) | c3_1(a21) | (~c0_1(a21)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp24 | hskp3 | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c0_1(a21)))),
% 0.98/0.91 inference(transitivity,[status(thm)],[717, 715])).
% 0.98/0.91 tff(719,plain,
% 0.98/0.91 ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | c2_1(a21) | c3_1(a21) | (~c0_1(a21)))),
% 0.98/0.91 inference(quant_inst,[status(thm)],[])).
% 0.98/0.91 tff(720,plain,
% 0.98/0.91 ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp24 | hskp3 | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c0_1(a21))),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[719, 718])).
% 0.98/0.91 tff(721,plain,
% 0.98/0.91 (hskp24),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[720, 117, 522, 686, 685, 704, 714])).
% 0.98/0.91 tff(722,plain,
% 0.98/0.91 (((~hskp24) | (~c2_1(a52))) <=> ((~hskp24) | (~c2_1(a52)))),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(723,plain,
% 0.98/0.91 (((~c2_1(a52)) | (~hskp24)) <=> ((~hskp24) | (~c2_1(a52)))),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(724,axiom,((~c2_1(a52)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause94')).
% 0.98/0.91 tff(725,plain,
% 0.98/0.91 ((~hskp24) | (~c2_1(a52))),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[724, 723])).
% 0.98/0.91 tff(726,plain,
% 0.98/0.91 ((~hskp24) | (~c2_1(a52))),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[725, 722])).
% 0.98/0.91 tff(727,plain,
% 0.98/0.91 (~c2_1(a52)),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[726, 721])).
% 0.98/0.91 tff(728,plain,
% 0.98/0.91 (((~hskp24) | (~c0_1(a52))) <=> ((~hskp24) | (~c0_1(a52)))),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(729,plain,
% 0.98/0.91 (((~c0_1(a52)) | (~hskp24)) <=> ((~hskp24) | (~c0_1(a52)))),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(730,axiom,((~c0_1(a52)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause93')).
% 0.98/0.91 tff(731,plain,
% 0.98/0.91 ((~hskp24) | (~c0_1(a52))),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[730, 729])).
% 0.98/0.91 tff(732,plain,
% 0.98/0.91 ((~hskp24) | (~c0_1(a52))),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[731, 728])).
% 0.98/0.91 tff(733,plain,
% 0.98/0.91 (~c0_1(a52)),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[732, 721])).
% 0.98/0.91 tff(734,plain,
% 0.98/0.91 (((~hskp24) | c3_1(a52)) <=> ((~hskp24) | c3_1(a52))),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(735,axiom,((~hskp24) | c3_1(a52)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause54')).
% 0.98/0.91 tff(736,plain,
% 0.98/0.91 ((~hskp24) | c3_1(a52)),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[735, 734])).
% 0.98/0.91 tff(737,plain,
% 0.98/0.91 ((~hskp24) | c3_1(a52)),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[736, 734])).
% 0.98/0.91 tff(738,plain,
% 0.98/0.91 ((~hskp24) | c3_1(a52)),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[737, 734])).
% 0.98/0.91 tff(739,plain,
% 0.98/0.91 ((~hskp24) | c3_1(a52)),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[738, 734])).
% 0.98/0.91 tff(740,plain,
% 0.98/0.91 ((~hskp24) | c3_1(a52)),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[739, 734])).
% 0.98/0.91 tff(741,plain,
% 0.98/0.91 ((~hskp24) | c3_1(a52)),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[740, 734])).
% 0.98/0.91 tff(742,plain,
% 0.98/0.91 ((~hskp24) | c3_1(a52)),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[741, 734])).
% 0.98/0.91 tff(743,plain,
% 0.98/0.91 ((~hskp24) | c3_1(a52)),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[742, 734])).
% 0.98/0.91 tff(744,plain,
% 0.98/0.91 (c3_1(a52)),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[743, 721])).
% 0.98/0.91 tff(745,plain,
% 0.98/0.91 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a52) | c2_1(a52) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c3_1(a52)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a52) | c2_1(a52) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c3_1(a52)))),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(746,plain,
% 0.98/0.91 ((hskp10 | (~ndr1_0) | c1_1(a21) | c3_1(a21) | (~c0_1(a21)) | c0_1(a52) | c2_1(a52) | (~c3_1(a52))) <=> (hskp10 | c0_1(a52) | c2_1(a52) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c3_1(a52)))),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(747,plain,
% 0.98/0.91 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a21) | c3_1(a21) | (~c0_1(a21)) | c0_1(a52) | c2_1(a52) | (~c3_1(a52)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a52) | c2_1(a52) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c3_1(a52))))),
% 0.98/0.91 inference(monotonicity,[status(thm)],[746])).
% 0.98/0.91 tff(748,plain,
% 0.98/0.91 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a21) | c3_1(a21) | (~c0_1(a21)) | c0_1(a52) | c2_1(a52) | (~c3_1(a52)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a52) | c2_1(a52) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c3_1(a52)))),
% 0.98/0.91 inference(transitivity,[status(thm)],[747, 745])).
% 0.98/0.91 tff(749,plain,
% 0.98/0.91 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a21) | c3_1(a21) | (~c0_1(a21)) | c0_1(a52) | c2_1(a52) | (~c3_1(a52)))),
% 0.98/0.91 inference(quant_inst,[status(thm)],[])).
% 0.98/0.91 tff(750,plain,
% 0.98/0.91 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a52) | c2_1(a52) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c3_1(a52))),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[749, 748])).
% 0.98/0.91 tff(751,plain,
% 0.98/0.91 ($false),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[750, 117, 645, 744, 686, 733, 727, 704, 703, 693])).
% 0.98/0.91 tff(752,plain,((~hskp13) | hskp10 | hskp3 | hskp30 | hskp8 | c1_1(a15) | c2_1(a15) | c3_1(a15)), inference(lemma,lemma(discharge,[]))).
% 0.98/0.91 tff(753,plain,
% 0.98/0.91 (~hskp13),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[752, 522, 645, 1, 523, 508, 509, 524])).
% 0.98/0.91 tff(754,plain,
% 0.98/0.91 ((hskp13 | hskp3 | hskp2) <=> (hskp13 | hskp3 | hskp2)),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(755,plain,
% 0.98/0.91 (((hskp3 | hskp2) | hskp13) <=> (hskp13 | hskp3 | hskp2)),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(756,plain,
% 0.98/0.91 ((hskp3 | hskp2) <=> (hskp3 | hskp2)),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(757,plain,
% 0.98/0.91 (((hskp3 | hskp2) | hskp13) <=> ((hskp3 | hskp2) | hskp13)),
% 0.98/0.91 inference(monotonicity,[status(thm)],[756])).
% 0.98/0.91 tff(758,plain,
% 0.98/0.91 (((hskp3 | hskp2) | hskp13) <=> (hskp13 | hskp3 | hskp2)),
% 0.98/0.91 inference(transitivity,[status(thm)],[757, 755])).
% 0.98/0.91 tff(759,axiom,((hskp3 | hskp2) | hskp13), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause35')).
% 0.98/0.91 tff(760,plain,
% 0.98/0.91 (hskp13 | hskp3 | hskp2),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[759, 758])).
% 0.98/0.91 tff(761,plain,
% 0.98/0.91 (hskp13 | hskp3 | hskp2),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[760, 754])).
% 0.98/0.91 tff(762,plain,
% 0.98/0.91 (hskp13 | hskp3 | hskp2),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[761, 754])).
% 0.98/0.91 tff(763,plain,
% 0.98/0.91 (hskp13 | hskp3 | hskp2),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[762, 754])).
% 0.98/0.91 tff(764,plain,
% 0.98/0.91 (hskp13 | hskp3 | hskp2),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[763, 754])).
% 0.98/0.91 tff(765,plain,
% 0.98/0.91 (hskp13 | hskp3 | hskp2),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[764, 754])).
% 0.98/0.91 tff(766,plain,
% 0.98/0.91 (hskp13 | hskp3 | hskp2),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[765, 754])).
% 0.98/0.91 tff(767,plain,
% 0.98/0.91 (hskp13 | hskp3 | hskp2),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[766, 754])).
% 0.98/0.91 tff(768,plain,
% 0.98/0.91 ($false),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[767, 753, 522, 644])).
% 0.98/0.91 tff(769,plain,(hskp3 | hskp2 | hskp10 | hskp30 | hskp8 | c1_1(a15) | c2_1(a15) | c3_1(a15)), inference(lemma,lemma(discharge,[]))).
% 0.98/0.91 tff(770,plain,
% 0.98/0.91 (hskp3),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[769, 643, 574, 1, 523, 508, 509, 524])).
% 0.98/0.91 tff(771,plain,
% 0.98/0.91 (~c2_1(a6)),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[484, 770])).
% 0.98/0.91 tff(772,plain,
% 0.98/0.91 (c3_1(a6)),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[444, 770])).
% 0.98/0.91 tff(773,plain,
% 0.98/0.91 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)))),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(774,plain,
% 0.98/0.91 ((hskp16 | (~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6))) <=> (hskp16 | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)))),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(775,plain,
% 0.98/0.91 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6))))),
% 0.98/0.91 inference(monotonicity,[status(thm)],[774])).
% 0.98/0.91 tff(776,plain,
% 0.98/0.91 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)))),
% 0.98/0.91 inference(transitivity,[status(thm)],[775, 773])).
% 0.98/0.91 tff(777,plain,
% 0.98/0.91 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)))),
% 0.98/0.91 inference(quant_inst,[status(thm)],[])).
% 0.98/0.91 tff(778,plain,
% 0.98/0.91 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6))),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[777, 776])).
% 0.98/0.91 tff(779,plain,
% 0.98/0.91 (~c1_1(a6)),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[778, 117, 534, 772, 771, 192])).
% 0.98/0.91 tff(780,plain,
% 0.98/0.91 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))),
% 0.98/0.91 inference(bind,[status(th)],[])).
% 0.98/0.91 tff(781,plain,
% 0.98/0.91 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.98/0.91 inference(quant_intro,[status(thm)],[780])).
% 0.98/0.91 tff(782,plain,
% 0.98/0.91 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(783,plain,
% 0.98/0.91 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp2))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))))),
% 0.98/0.91 inference(bind,[status(th)],[])).
% 0.98/0.91 tff(784,plain,
% 0.98/0.91 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.98/0.91 inference(quant_intro,[status(thm)],[783])).
% 0.98/0.91 tff(785,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause179')).
% 0.98/0.91 tff(786,plain,
% 0.98/0.91 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[785, 784])).
% 0.98/0.91 tff(787,plain,
% 0.98/0.91 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[786, 782])).
% 0.98/0.91 tff(788,plain,(
% 0.98/0.91 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.98/0.91 inference(skolemize,[status(sab)],[787])).
% 0.98/0.91 tff(789,plain,
% 0.98/0.91 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[788, 781])).
% 0.98/0.91 tff(790,plain,
% 0.98/0.91 (^[U: $i] : refl((hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))),
% 0.98/0.91 inference(bind,[status(th)],[])).
% 0.98/0.91 tff(791,plain,
% 0.98/0.91 (![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.98/0.91 inference(quant_intro,[status(thm)],[790])).
% 0.98/0.91 tff(792,plain,
% 0.98/0.91 (![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(793,plain,
% 0.98/0.91 (^[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)) | hskp30) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp30))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp30) <=> (hskp30 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp30) <=> (hskp30 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp30) | hskp23) <=> ((hskp30 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp23))), rewrite(((hskp30 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp23) <=> (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp30) | hskp23) <=> (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))))),
% 0.98/0.91 inference(bind,[status(th)],[])).
% 0.98/0.91 tff(794,plain,
% 0.98/0.91 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp30) | hskp23) <=> ![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.98/0.91 inference(quant_intro,[status(thm)],[793])).
% 0.98/0.91 tff(795,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp30) | hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause144')).
% 0.98/0.91 tff(796,plain,
% 0.98/0.91 (![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[795, 794])).
% 0.98/0.91 tff(797,plain,
% 0.98/0.91 (![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[796, 792])).
% 0.98/0.91 tff(798,plain,(
% 0.98/0.91 ![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.98/0.91 inference(skolemize,[status(sab)],[797])).
% 0.98/0.91 tff(799,plain,
% 0.98/0.91 (![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.98/0.91 inference(modus_ponens,[status(thm)],[798, 791])).
% 0.98/0.91 tff(800,plain,
% 0.98/0.91 (c0_1(a6)),
% 0.98/0.91 inference(unit_resolution,[status(thm)],[455, 770])).
% 0.98/0.91 tff(801,plain,
% 0.98/0.91 (((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp23 | c2_1(a6) | (~ndr1_0) | c1_1(a6) | (~c0_1(a6)))) <=> ((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp30 | hskp23 | c2_1(a6) | (~ndr1_0) | c1_1(a6) | (~c0_1(a6)))),
% 0.98/0.91 inference(rewrite,[status(thm)],[])).
% 0.98/0.91 tff(802,plain,
% 0.98/0.91 ((hskp30 | hskp23 | (~ndr1_0) | c2_1(a6) | c1_1(a6) | (~c0_1(a6))) <=> (hskp30 | hskp23 | c2_1(a6) | (~ndr1_0) | c1_1(a6) | (~c0_1(a6)))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(803,plain,
% 0.98/0.92 (((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp23 | (~ndr1_0) | c2_1(a6) | c1_1(a6) | (~c0_1(a6)))) <=> ((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp23 | c2_1(a6) | (~ndr1_0) | c1_1(a6) | (~c0_1(a6))))),
% 0.98/0.92 inference(monotonicity,[status(thm)],[802])).
% 0.98/0.92 tff(804,plain,
% 0.98/0.92 (((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp23 | (~ndr1_0) | c2_1(a6) | c1_1(a6) | (~c0_1(a6)))) <=> ((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp30 | hskp23 | c2_1(a6) | (~ndr1_0) | c1_1(a6) | (~c0_1(a6)))),
% 0.98/0.92 inference(transitivity,[status(thm)],[803, 801])).
% 0.98/0.92 tff(805,plain,
% 0.98/0.92 ((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp23 | (~ndr1_0) | c2_1(a6) | c1_1(a6) | (~c0_1(a6)))),
% 0.98/0.92 inference(quant_inst,[status(thm)],[])).
% 0.98/0.92 tff(806,plain,
% 0.98/0.92 ((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp30 | hskp23 | c2_1(a6) | (~ndr1_0) | c1_1(a6) | (~c0_1(a6))),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[805, 804])).
% 0.98/0.92 tff(807,plain,
% 0.98/0.92 (hskp23 | c1_1(a6)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[806, 117, 1, 800, 771, 799])).
% 0.98/0.92 tff(808,plain,
% 0.98/0.92 (hskp23),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[807, 779])).
% 0.98/0.92 tff(809,plain,
% 0.98/0.92 (((~hskp23) | (~c3_1(a42))) <=> ((~hskp23) | (~c3_1(a42)))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(810,plain,
% 0.98/0.92 (((~c3_1(a42)) | (~hskp23)) <=> ((~hskp23) | (~c3_1(a42)))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(811,axiom,((~c3_1(a42)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause96')).
% 0.98/0.92 tff(812,plain,
% 0.98/0.92 ((~hskp23) | (~c3_1(a42))),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[811, 810])).
% 0.98/0.92 tff(813,plain,
% 0.98/0.92 ((~hskp23) | (~c3_1(a42))),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[812, 809])).
% 0.98/0.92 tff(814,plain,
% 0.98/0.92 (~c3_1(a42)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[813, 808])).
% 0.98/0.92 tff(815,plain,
% 0.98/0.92 (((~hskp23) | (~c1_1(a42))) <=> ((~hskp23) | (~c1_1(a42)))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(816,plain,
% 0.98/0.92 (((~c1_1(a42)) | (~hskp23)) <=> ((~hskp23) | (~c1_1(a42)))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(817,axiom,((~c1_1(a42)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause95')).
% 0.98/0.92 tff(818,plain,
% 0.98/0.92 ((~hskp23) | (~c1_1(a42))),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[817, 816])).
% 0.98/0.92 tff(819,plain,
% 0.98/0.92 ((~hskp23) | (~c1_1(a42))),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[818, 815])).
% 0.98/0.92 tff(820,plain,
% 0.98/0.92 (~c1_1(a42)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[819, 808])).
% 0.98/0.92 tff(821,plain,
% 0.98/0.92 (((~hskp23) | c0_1(a42)) <=> ((~hskp23) | c0_1(a42))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(822,axiom,((~hskp23) | c0_1(a42)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause55')).
% 0.98/0.92 tff(823,plain,
% 0.98/0.92 ((~hskp23) | c0_1(a42)),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[822, 821])).
% 0.98/0.92 tff(824,plain,
% 0.98/0.92 ((~hskp23) | c0_1(a42)),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[823, 821])).
% 0.98/0.92 tff(825,plain,
% 0.98/0.92 ((~hskp23) | c0_1(a42)),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[824, 821])).
% 0.98/0.92 tff(826,plain,
% 0.98/0.92 ((~hskp23) | c0_1(a42)),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[825, 821])).
% 0.98/0.92 tff(827,plain,
% 0.98/0.92 ((~hskp23) | c0_1(a42)),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[826, 821])).
% 0.98/0.92 tff(828,plain,
% 0.98/0.92 ((~hskp23) | c0_1(a42)),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[827, 821])).
% 0.98/0.92 tff(829,plain,
% 0.98/0.92 ((~hskp23) | c0_1(a42)),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[828, 821])).
% 0.98/0.92 tff(830,plain,
% 0.98/0.92 ((~hskp23) | c0_1(a42)),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[829, 821])).
% 0.98/0.92 tff(831,plain,
% 0.98/0.92 (c0_1(a42)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[830, 808])).
% 0.98/0.92 tff(832,plain,
% 0.98/0.92 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | c1_1(a42) | c3_1(a42) | (~ndr1_0) | c1_1(a6) | (~c3_1(a6)) | (~c0_1(a6)) | (~c0_1(a42)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a42) | c3_1(a42) | (~ndr1_0) | c1_1(a6) | (~c3_1(a6)) | (~c0_1(a6)) | (~c0_1(a42)))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(833,plain,
% 0.98/0.92 ((hskp2 | (~ndr1_0) | c1_1(a6) | (~c3_1(a6)) | (~c0_1(a6)) | c3_1(a42) | c1_1(a42) | (~c0_1(a42))) <=> (hskp2 | c1_1(a42) | c3_1(a42) | (~ndr1_0) | c1_1(a6) | (~c3_1(a6)) | (~c0_1(a6)) | (~c0_1(a42)))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(834,plain,
% 0.98/0.92 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a6) | (~c3_1(a6)) | (~c0_1(a6)) | c3_1(a42) | c1_1(a42) | (~c0_1(a42)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | c1_1(a42) | c3_1(a42) | (~ndr1_0) | c1_1(a6) | (~c3_1(a6)) | (~c0_1(a6)) | (~c0_1(a42))))),
% 0.98/0.92 inference(monotonicity,[status(thm)],[833])).
% 0.98/0.92 tff(835,plain,
% 0.98/0.92 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a6) | (~c3_1(a6)) | (~c0_1(a6)) | c3_1(a42) | c1_1(a42) | (~c0_1(a42)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a42) | c3_1(a42) | (~ndr1_0) | c1_1(a6) | (~c3_1(a6)) | (~c0_1(a6)) | (~c0_1(a42)))),
% 0.98/0.92 inference(transitivity,[status(thm)],[834, 832])).
% 0.98/0.92 tff(836,plain,
% 0.98/0.92 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a6) | (~c3_1(a6)) | (~c0_1(a6)) | c3_1(a42) | c1_1(a42) | (~c0_1(a42)))),
% 0.98/0.92 inference(quant_inst,[status(thm)],[])).
% 0.98/0.92 tff(837,plain,
% 0.98/0.92 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a42) | c3_1(a42) | (~ndr1_0) | c1_1(a6) | (~c3_1(a6)) | (~c0_1(a6)) | (~c0_1(a42))),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[836, 835])).
% 0.98/0.92 tff(838,plain,
% 0.98/0.92 ($false),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[837, 117, 643, 831, 800, 772, 820, 814, 789, 779])).
% 0.98/0.92 tff(839,plain,(c1_1(a30) | hskp30 | hskp8 | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a5) | c1_1(a5)), inference(lemma,lemma(discharge,[]))).
% 0.98/0.92 tff(840,plain,
% 0.98/0.92 (c1_1(a30)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[839, 524, 523, 508, 509, 1, 520, 521])).
% 0.98/0.92 tff(841,plain,
% 0.98/0.92 (~hskp16),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[244, 840])).
% 0.98/0.92 tff(842,plain,
% 0.98/0.92 (~hskp10),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[573, 841, 523, 1])).
% 0.98/0.92 tff(843,plain,
% 0.98/0.92 (hskp2),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[769, 522, 842, 1, 523, 508, 509, 524])).
% 0.98/0.92 tff(844,plain,
% 0.98/0.92 (c2_1(a5)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[642, 843])).
% 0.98/0.92 tff(845,plain,
% 0.98/0.92 (~c3_1(a5)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[582, 844])).
% 0.98/0.92 tff(846,plain,
% 0.98/0.92 (^[V: $i, U: $i] : refl((hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.98/0.92 inference(bind,[status(th)],[])).
% 0.98/0.92 tff(847,plain,
% 0.98/0.92 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.98/0.92 inference(quant_intro,[status(thm)],[846])).
% 0.98/0.92 tff(848,plain,
% 0.98/0.92 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(849,plain,
% 0.98/0.92 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp13) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp13))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp13) <=> (hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.98/0.92 inference(bind,[status(th)],[])).
% 0.98/0.92 tff(850,plain,
% 0.98/0.92 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp13) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.98/0.92 inference(quant_intro,[status(thm)],[849])).
% 0.98/0.92 tff(851,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause172')).
% 0.98/0.92 tff(852,plain,
% 0.98/0.92 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[851, 850])).
% 0.98/0.92 tff(853,plain,
% 0.98/0.92 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[852, 848])).
% 0.98/0.92 tff(854,plain,(
% 0.98/0.92 ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.98/0.92 inference(skolemize,[status(sab)],[853])).
% 0.98/0.92 tff(855,plain,
% 0.98/0.92 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[854, 847])).
% 0.98/0.92 tff(856,plain,
% 0.98/0.92 (hskp15),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[590, 844, 841, 845])).
% 0.98/0.92 tff(857,plain,
% 0.98/0.92 (~c3_1(a29)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[142, 856])).
% 0.98/0.92 tff(858,plain,
% 0.98/0.92 (~c2_1(a29)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[148, 856])).
% 0.98/0.92 tff(859,plain,
% 0.98/0.92 (c1_1(a29)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[136, 856])).
% 0.98/0.92 tff(860,plain,
% 0.98/0.92 (~hskp13),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[752, 522, 842, 1, 523, 508, 509, 524])).
% 0.98/0.92 tff(861,plain,
% 0.98/0.92 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp13 | c2_1(a29) | c3_1(a29) | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c1_1(a29)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp13 | c2_1(a29) | c3_1(a29) | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c1_1(a29)))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(862,plain,
% 0.98/0.92 ((hskp13 | (~ndr1_0) | c2_1(a29) | c3_1(a29) | (~c1_1(a29)) | c3_1(a5) | c0_1(a5) | (~c2_1(a5))) <=> (hskp13 | c2_1(a29) | c3_1(a29) | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c1_1(a29)))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(863,plain,
% 0.98/0.92 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c2_1(a29) | c3_1(a29) | (~c1_1(a29)) | c3_1(a5) | c0_1(a5) | (~c2_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp13 | c2_1(a29) | c3_1(a29) | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c1_1(a29))))),
% 0.98/0.92 inference(monotonicity,[status(thm)],[862])).
% 0.98/0.92 tff(864,plain,
% 0.98/0.92 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c2_1(a29) | c3_1(a29) | (~c1_1(a29)) | c3_1(a5) | c0_1(a5) | (~c2_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp13 | c2_1(a29) | c3_1(a29) | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c1_1(a29)))),
% 0.98/0.92 inference(transitivity,[status(thm)],[863, 861])).
% 0.98/0.92 tff(865,plain,
% 0.98/0.92 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c2_1(a29) | c3_1(a29) | (~c1_1(a29)) | c3_1(a5) | c0_1(a5) | (~c2_1(a5)))),
% 0.98/0.92 inference(quant_inst,[status(thm)],[])).
% 0.98/0.92 tff(866,plain,
% 0.98/0.92 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp13 | c2_1(a29) | c3_1(a29) | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c1_1(a29))),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[865, 864])).
% 0.98/0.92 tff(867,plain,
% 0.98/0.92 ($false),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[866, 117, 860, 859, 844, 858, 857, 520, 855, 845])).
% 0.98/0.92 tff(868,plain,(hskp3 | c0_1(a5) | hskp8 | c1_1(a15) | c2_1(a15) | c3_1(a15) | c1_1(a5) | hskp30), inference(lemma,lemma(discharge,[]))).
% 0.98/0.92 tff(869,plain,
% 0.98/0.92 (hskp3),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[868, 524, 523, 508, 509, 520, 521, 1])).
% 0.98/0.92 tff(870,plain,
% 0.98/0.92 (~c2_1(a6)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[484, 869])).
% 0.98/0.92 tff(871,plain,
% 0.98/0.92 (c3_1(a6)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[444, 869])).
% 0.98/0.92 tff(872,plain,
% 0.98/0.92 (~c1_1(a6)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[778, 117, 841, 871, 870, 192])).
% 0.98/0.92 tff(873,plain,
% 0.98/0.92 (c0_1(a6)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[455, 869])).
% 0.98/0.92 tff(874,plain,
% 0.98/0.92 (hskp21 | c1_1(a6)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[459, 117, 523, 873, 871, 21])).
% 0.98/0.92 tff(875,plain,
% 0.98/0.92 (hskp21),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[874, 872])).
% 0.98/0.92 tff(876,plain,
% 0.98/0.92 (~c3_1(a39)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[58, 875])).
% 0.98/0.92 tff(877,plain,
% 0.98/0.92 (~c0_1(a39)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[64, 875])).
% 0.98/0.92 tff(878,plain,
% 0.98/0.92 (c2_1(a39)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[75, 875])).
% 0.98/0.92 tff(879,plain,
% 0.98/0.92 (hskp15),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[123, 117, 841, 878, 877, 876, 53])).
% 0.98/0.92 tff(880,plain,
% 0.98/0.92 (~c3_1(a29)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[142, 879])).
% 0.98/0.92 tff(881,plain,
% 0.98/0.92 (~c2_1(a29)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[148, 879])).
% 0.98/0.92 tff(882,plain,
% 0.98/0.92 (c1_1(a29)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[136, 879])).
% 0.98/0.92 tff(883,plain,
% 0.98/0.92 (~c0_1(a29)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[169, 117, 878, 882, 877, 876, 881, 880, 160])).
% 0.98/0.92 tff(884,plain,
% 0.98/0.92 ($false),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[414, 117, 1, 523, 882, 880, 408, 883])).
% 0.98/0.92 tff(885,plain,(c3_1(a15) | hskp30 | hskp8 | c1_1(a15) | c2_1(a15) | c0_1(a5) | c1_1(a5)), inference(lemma,lemma(discharge,[]))).
% 0.98/0.92 tff(886,plain,
% 0.98/0.92 (c3_1(a15)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[885, 521, 321, 508, 509, 520, 1])).
% 0.98/0.92 tff(887,plain,
% 0.98/0.92 (~hskp10),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[573, 43, 321, 1])).
% 0.98/0.92 tff(888,plain,
% 0.98/0.92 (hskp13),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[767, 644, 522])).
% 0.98/0.92 tff(889,plain,
% 0.98/0.92 (~c0_1(a26)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[675, 888])).
% 0.98/0.92 tff(890,plain,
% 0.98/0.92 (c3_1(a26)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[662, 888])).
% 0.98/0.92 tff(891,assumption,(c3_1(a15)), introduced(assumption)).
% 0.98/0.92 tff(892,assumption,(hskp11), introduced(assumption)).
% 0.98/0.92 tff(893,plain,
% 0.98/0.92 (~c2_1(a21)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[358, 892])).
% 0.98/0.92 tff(894,plain,
% 0.98/0.92 (~c1_1(a26)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[651, 888])).
% 0.98/0.92 tff(895,plain,
% 0.98/0.92 (c0_1(a21)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[386, 892])).
% 0.98/0.92 tff(896,plain,
% 0.98/0.92 (~c1_1(a21)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[692, 117, 522, 890, 895, 889, 894, 893, 426])).
% 0.98/0.92 tff(897,plain,
% 0.98/0.92 (~c3_1(a21)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[352, 892])).
% 0.98/0.92 tff(898,plain,
% 0.98/0.92 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | c3_1(a21) | c1_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c0_1(a15)) | c1_1(a21) | (~c0_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c3_1(a21) | c1_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c0_1(a15)) | c1_1(a21) | (~c0_1(a21)))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(899,plain,
% 0.98/0.92 ((hskp2 | (~ndr1_0) | c1_1(a15) | (~c3_1(a15)) | (~c0_1(a15)) | c3_1(a21) | c1_1(a21) | (~c0_1(a21))) <=> (hskp2 | c3_1(a21) | c1_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c0_1(a15)) | c1_1(a21) | (~c0_1(a21)))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(900,plain,
% 0.98/0.92 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a15) | (~c3_1(a15)) | (~c0_1(a15)) | c3_1(a21) | c1_1(a21) | (~c0_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | c3_1(a21) | c1_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c0_1(a15)) | c1_1(a21) | (~c0_1(a21))))),
% 0.98/0.92 inference(monotonicity,[status(thm)],[899])).
% 0.98/0.92 tff(901,plain,
% 0.98/0.92 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a15) | (~c3_1(a15)) | (~c0_1(a15)) | c3_1(a21) | c1_1(a21) | (~c0_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c3_1(a21) | c1_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c0_1(a15)) | c1_1(a21) | (~c0_1(a21)))),
% 0.98/0.92 inference(transitivity,[status(thm)],[900, 898])).
% 0.98/0.92 tff(902,plain,
% 0.98/0.92 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a15) | (~c3_1(a15)) | (~c0_1(a15)) | c3_1(a21) | c1_1(a21) | (~c0_1(a21)))),
% 0.98/0.92 inference(quant_inst,[status(thm)],[])).
% 0.98/0.92 tff(903,plain,
% 0.98/0.92 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c3_1(a21) | c1_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c0_1(a15)) | c1_1(a21) | (~c0_1(a21))),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[902, 901])).
% 0.98/0.92 tff(904,plain,
% 0.98/0.92 (~c0_1(a15)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[903, 117, 644, 895, 897, 508, 891, 789, 896])).
% 0.98/0.92 tff(905,plain,
% 0.98/0.92 (((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp23 | c2_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)))) <=> ((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp30 | hskp23 | c2_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(906,plain,
% 0.98/0.92 ((hskp30 | hskp23 | (~ndr1_0) | c2_1(a21) | c1_1(a21) | (~c0_1(a21))) <=> (hskp30 | hskp23 | c2_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(907,plain,
% 0.98/0.92 (((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp23 | (~ndr1_0) | c2_1(a21) | c1_1(a21) | (~c0_1(a21)))) <=> ((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp23 | c2_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21))))),
% 0.98/0.92 inference(monotonicity,[status(thm)],[906])).
% 0.98/0.92 tff(908,plain,
% 0.98/0.92 (((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp23 | (~ndr1_0) | c2_1(a21) | c1_1(a21) | (~c0_1(a21)))) <=> ((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp30 | hskp23 | c2_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)))),
% 0.98/0.92 inference(transitivity,[status(thm)],[907, 905])).
% 0.98/0.92 tff(909,plain,
% 0.98/0.92 ((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp23 | (~ndr1_0) | c2_1(a21) | c1_1(a21) | (~c0_1(a21)))),
% 0.98/0.92 inference(quant_inst,[status(thm)],[])).
% 0.98/0.92 tff(910,plain,
% 0.98/0.92 ((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp30 | hskp23 | c2_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21))),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[909, 908])).
% 0.98/0.92 tff(911,plain,
% 0.98/0.92 (hskp23 | c1_1(a21)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[910, 117, 1, 895, 893, 799])).
% 0.98/0.92 tff(912,plain,
% 0.98/0.92 (hskp23),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[911, 896])).
% 0.98/0.92 tff(913,plain,
% 0.98/0.92 (~c3_1(a42)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[813, 912])).
% 0.98/0.92 tff(914,plain,
% 0.98/0.92 (~c1_1(a42)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[819, 912])).
% 0.98/0.92 tff(915,plain,
% 0.98/0.92 (c0_1(a42)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[830, 912])).
% 0.98/0.92 tff(916,plain,
% 0.98/0.92 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | c1_1(a42) | c3_1(a42) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a15) | (~c0_1(a42)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp10 | c1_1(a42) | c3_1(a42) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a15) | (~c0_1(a42)))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(917,plain,
% 0.98/0.92 ((hskp10 | (~ndr1_0) | c1_1(a42) | c3_1(a42) | (~c0_1(a42)) | c0_1(a15) | c2_1(a15) | (~c3_1(a15))) <=> (hskp10 | c1_1(a42) | c3_1(a42) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a15) | (~c0_1(a42)))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(918,plain,
% 0.98/0.92 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a42) | c3_1(a42) | (~c0_1(a42)) | c0_1(a15) | c2_1(a15) | (~c3_1(a15)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | c1_1(a42) | c3_1(a42) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a15) | (~c0_1(a42))))),
% 0.98/0.92 inference(monotonicity,[status(thm)],[917])).
% 0.98/0.92 tff(919,plain,
% 0.98/0.92 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a42) | c3_1(a42) | (~c0_1(a42)) | c0_1(a15) | c2_1(a15) | (~c3_1(a15)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp10 | c1_1(a42) | c3_1(a42) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a15) | (~c0_1(a42)))),
% 0.98/0.92 inference(transitivity,[status(thm)],[918, 916])).
% 0.98/0.92 tff(920,plain,
% 0.98/0.92 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a42) | c3_1(a42) | (~c0_1(a42)) | c0_1(a15) | c2_1(a15) | (~c3_1(a15)))),
% 0.98/0.92 inference(quant_inst,[status(thm)],[])).
% 0.98/0.92 tff(921,plain,
% 0.98/0.92 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp10 | c1_1(a42) | c3_1(a42) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a15) | (~c0_1(a42))),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[920, 919])).
% 0.98/0.92 tff(922,plain,
% 0.98/0.92 ($false),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[921, 117, 645, 915, 914, 913, 509, 891, 703, 904])).
% 0.98/0.92 tff(923,plain,((~hskp11) | hskp10 | c2_1(a15) | (~c3_1(a15)) | hskp30 | hskp2 | c1_1(a15) | hskp3), inference(lemma,lemma(discharge,[]))).
% 0.98/0.92 tff(924,plain,
% 0.98/0.92 (~hskp11),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[923, 644, 509, 891, 1, 645, 508, 522])).
% 0.98/0.92 tff(925,plain,
% 0.98/0.92 (c2_1(a26)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[682, 117, 1, 924, 890, 889, 41])).
% 0.98/0.92 tff(926,plain,
% 0.98/0.92 (~c3_1(a13)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[346, 924, 1, 322])).
% 0.98/0.92 tff(927,plain,
% 0.98/0.92 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a13) | c2_1(a13) | c1_1(a26) | (~ndr1_0) | c3_1(a13) | (~c2_1(a26)) | (~c3_1(a26)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a13) | c2_1(a13) | c1_1(a26) | (~ndr1_0) | c3_1(a13) | (~c2_1(a26)) | (~c3_1(a26)))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(928,plain,
% 0.98/0.92 ((hskp8 | (~ndr1_0) | c1_1(a26) | (~c3_1(a26)) | (~c2_1(a26)) | c3_1(a13) | c1_1(a13) | c2_1(a13)) <=> (hskp8 | c1_1(a13) | c2_1(a13) | c1_1(a26) | (~ndr1_0) | c3_1(a13) | (~c2_1(a26)) | (~c3_1(a26)))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(929,plain,
% 0.98/0.92 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a26) | (~c3_1(a26)) | (~c2_1(a26)) | c3_1(a13) | c1_1(a13) | c2_1(a13))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a13) | c2_1(a13) | c1_1(a26) | (~ndr1_0) | c3_1(a13) | (~c2_1(a26)) | (~c3_1(a26))))),
% 0.98/0.92 inference(monotonicity,[status(thm)],[928])).
% 0.98/0.92 tff(930,plain,
% 0.98/0.92 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a26) | (~c3_1(a26)) | (~c2_1(a26)) | c3_1(a13) | c1_1(a13) | c2_1(a13))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a13) | c2_1(a13) | c1_1(a26) | (~ndr1_0) | c3_1(a13) | (~c2_1(a26)) | (~c3_1(a26)))),
% 0.98/0.92 inference(transitivity,[status(thm)],[929, 927])).
% 0.98/0.92 tff(931,plain,
% 0.98/0.92 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a26) | (~c3_1(a26)) | (~c2_1(a26)) | c3_1(a13) | c1_1(a13) | c2_1(a13))),
% 0.98/0.92 inference(quant_inst,[status(thm)],[])).
% 0.98/0.92 tff(932,plain,
% 0.98/0.92 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a13) | c2_1(a13) | c1_1(a26) | (~ndr1_0) | c3_1(a13) | (~c2_1(a26)) | (~c3_1(a26))),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[931, 930])).
% 0.98/0.92 tff(933,plain,
% 0.98/0.92 ($false),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[932, 117, 321, 890, 310, 322, 894, 31, 926, 925])).
% 0.98/0.92 tff(934,plain,(hskp2 | c1_1(a13) | c2_1(a13) | hskp30 | c0_1(a13) | c2_1(a15) | (~c3_1(a15)) | hskp10 | c1_1(a15) | hskp3), inference(lemma,lemma(discharge,[]))).
% 0.98/0.92 tff(935,plain,
% 0.98/0.92 (hskp2),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[934, 887, 322, 1, 268, 509, 886, 310, 508, 522])).
% 0.98/0.92 tff(936,plain,
% 0.98/0.92 (c2_1(a5)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[642, 935])).
% 0.98/0.92 tff(937,plain,
% 0.98/0.92 (c3_1(a5)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[590, 77, 43, 575])).
% 0.98/0.92 tff(938,plain,
% 0.98/0.92 (c3_1(a15)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[885, 521, 523, 508, 509, 520, 1])).
% 0.98/0.92 tff(939,plain,
% 0.98/0.92 (~hskp21),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[125, 77, 43])).
% 0.98/0.92 tff(940,plain,
% 0.98/0.92 (((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | c1_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c0_1(a15)))) <=> ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp8 | c1_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c0_1(a15)))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(941,plain,
% 0.98/0.92 ((hskp21 | hskp8 | (~ndr1_0) | c1_1(a15) | (~c3_1(a15)) | (~c0_1(a15))) <=> (hskp21 | hskp8 | c1_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c0_1(a15)))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(942,plain,
% 0.98/0.92 (((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | (~ndr1_0) | c1_1(a15) | (~c3_1(a15)) | (~c0_1(a15)))) <=> ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | c1_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c0_1(a15))))),
% 0.98/0.92 inference(monotonicity,[status(thm)],[941])).
% 0.98/0.92 tff(943,plain,
% 0.98/0.92 (((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | (~ndr1_0) | c1_1(a15) | (~c3_1(a15)) | (~c0_1(a15)))) <=> ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp8 | c1_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c0_1(a15)))),
% 0.98/0.92 inference(transitivity,[status(thm)],[942, 940])).
% 0.98/0.92 tff(944,plain,
% 0.98/0.92 ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | (~ndr1_0) | c1_1(a15) | (~c3_1(a15)) | (~c0_1(a15)))),
% 0.98/0.92 inference(quant_inst,[status(thm)],[])).
% 0.98/0.92 tff(945,plain,
% 0.98/0.92 ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp8 | c1_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c0_1(a15))),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[944, 943])).
% 0.98/0.92 tff(946,plain,
% 0.98/0.92 (hskp21 | (~c3_1(a15)) | (~c0_1(a15))),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[945, 117, 523, 508, 21])).
% 0.98/0.92 tff(947,plain,
% 0.98/0.92 (~c0_1(a15)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[946, 939, 938])).
% 0.98/0.92 tff(948,plain,
% 0.98/0.92 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a15))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a15))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(949,plain,
% 0.98/0.92 ((hskp30 | hskp11 | (~ndr1_0) | c2_1(a15) | c0_1(a15) | (~c3_1(a15))) <=> (hskp30 | hskp11 | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a15))),
% 0.98/0.92 inference(rewrite,[status(thm)],[])).
% 0.98/0.92 tff(950,plain,
% 0.98/0.92 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a15) | c0_1(a15) | (~c3_1(a15)))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a15)))),
% 0.98/0.92 inference(monotonicity,[status(thm)],[949])).
% 0.98/0.92 tff(951,plain,
% 0.98/0.92 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a15) | c0_1(a15) | (~c3_1(a15)))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a15))),
% 0.98/0.92 inference(transitivity,[status(thm)],[950, 948])).
% 0.98/0.92 tff(952,plain,
% 0.98/0.92 ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a15) | c0_1(a15) | (~c3_1(a15)))),
% 0.98/0.92 inference(quant_inst,[status(thm)],[])).
% 0.98/0.92 tff(953,plain,
% 0.98/0.92 ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a15)),
% 0.98/0.92 inference(modus_ponens,[status(thm)],[952, 951])).
% 0.98/0.92 tff(954,plain,
% 0.98/0.92 (hskp11 | (~c3_1(a15)) | c0_1(a15)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[953, 117, 1, 509, 41])).
% 0.98/0.92 tff(955,plain,
% 0.98/0.92 (hskp11),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[954, 947, 938])).
% 0.98/0.92 tff(956,plain,
% 0.98/0.92 (~c2_1(a21)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[358, 955])).
% 0.98/0.92 tff(957,plain,
% 0.98/0.92 (c0_1(a21)),
% 0.98/0.92 inference(unit_resolution,[status(thm)],[386, 955])).
% 0.98/0.92 tff(958,plain,
% 0.98/0.92 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c2_1(a21) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a21)) | (~c0_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c2_1(a21) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a21)) | (~c0_1(a21)))),
% 0.98/0.93 inference(rewrite,[status(thm)],[])).
% 0.98/0.93 tff(959,plain,
% 0.98/0.93 ((hskp15 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5))) <=> (hskp15 | c2_1(a21) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a21)) | (~c0_1(a21)))),
% 0.98/0.93 inference(rewrite,[status(thm)],[])).
% 0.98/0.93 tff(960,plain,
% 0.98/0.93 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c2_1(a21) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a21)) | (~c0_1(a21))))),
% 0.98/0.93 inference(monotonicity,[status(thm)],[959])).
% 0.98/0.93 tff(961,plain,
% 0.98/0.93 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c2_1(a21) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a21)) | (~c0_1(a21)))),
% 0.98/0.93 inference(transitivity,[status(thm)],[960, 958])).
% 0.98/0.93 tff(962,plain,
% 0.98/0.93 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)))),
% 0.98/0.93 inference(quant_inst,[status(thm)],[])).
% 0.98/0.93 tff(963,plain,
% 0.98/0.93 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c2_1(a21) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a21)) | (~c0_1(a21))),
% 0.98/0.93 inference(modus_ponens,[status(thm)],[962, 961])).
% 0.98/0.93 tff(964,plain,
% 0.98/0.93 (~c1_1(a21)),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[963, 117, 77, 957, 575, 956, 521, 376, 937])).
% 0.98/0.93 tff(965,plain,
% 0.98/0.93 (~c3_1(a21)),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[352, 955])).
% 0.98/0.93 tff(966,plain,
% 0.98/0.93 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c2_1(a21) | c3_1(a21) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | c1_1(a21))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c2_1(a21) | c3_1(a21) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | c1_1(a21))),
% 0.98/0.93 inference(rewrite,[status(thm)],[])).
% 0.98/0.93 tff(967,plain,
% 0.98/0.93 ((hskp8 | (~ndr1_0) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)) | c3_1(a21) | c1_1(a21) | c2_1(a21)) <=> (hskp8 | c2_1(a21) | c3_1(a21) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | c1_1(a21))),
% 0.98/0.93 inference(rewrite,[status(thm)],[])).
% 0.98/0.93 tff(968,plain,
% 0.98/0.93 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)) | c3_1(a21) | c1_1(a21) | c2_1(a21))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c2_1(a21) | c3_1(a21) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | c1_1(a21)))),
% 0.98/0.93 inference(monotonicity,[status(thm)],[967])).
% 0.98/0.93 tff(969,plain,
% 0.98/0.93 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)) | c3_1(a21) | c1_1(a21) | c2_1(a21))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c2_1(a21) | c3_1(a21) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | c1_1(a21))),
% 0.98/0.93 inference(transitivity,[status(thm)],[968, 966])).
% 0.98/0.93 tff(970,plain,
% 0.98/0.93 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)) | c3_1(a21) | c1_1(a21) | c2_1(a21))),
% 0.98/0.93 inference(quant_inst,[status(thm)],[])).
% 0.98/0.93 tff(971,plain,
% 0.98/0.93 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c2_1(a21) | c3_1(a21) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | c1_1(a21)),
% 0.98/0.93 inference(modus_ponens,[status(thm)],[970, 969])).
% 0.98/0.93 tff(972,plain,
% 0.98/0.93 ($false),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[971, 117, 523, 575, 956, 965, 521, 31, 937, 964])).
% 0.98/0.93 tff(973,plain,(hskp15 | hskp8 | (~c2_1(a5)) | c1_1(a5) | hskp30 | c2_1(a15) | c1_1(a15) | hskp16 | c0_1(a5)), inference(lemma,lemma(discharge,[]))).
% 0.98/0.93 tff(974,plain,
% 0.98/0.93 (hskp15),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[973, 936, 321, 521, 1, 509, 508, 43, 520])).
% 0.98/0.93 tff(975,plain,
% 0.98/0.93 (~c2_1(a29)),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[148, 974])).
% 0.98/0.93 tff(976,plain,
% 0.98/0.93 (~c3_1(a29)),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[142, 974])).
% 0.98/0.93 tff(977,plain,
% 0.98/0.93 (~hskp10),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[573, 43, 523, 1])).
% 0.98/0.93 tff(978,plain,
% 0.98/0.93 (hskp11 | c2_1(a26)),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[682, 117, 1, 890, 889, 41])).
% 0.98/0.93 tff(979,plain,
% 0.98/0.93 (c2_1(a26)),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[978, 924])).
% 0.98/0.93 tff(980,plain,
% 0.98/0.93 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a29) | c2_1(a29) | c3_1(a29) | c1_1(a26) | (~ndr1_0) | (~c2_1(a26)) | (~c3_1(a26)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a29) | c2_1(a29) | c3_1(a29) | c1_1(a26) | (~ndr1_0) | (~c2_1(a26)) | (~c3_1(a26)))),
% 0.98/0.93 inference(rewrite,[status(thm)],[])).
% 0.98/0.93 tff(981,plain,
% 0.98/0.93 ((hskp8 | (~ndr1_0) | c1_1(a26) | (~c3_1(a26)) | (~c2_1(a26)) | c3_1(a29) | c1_1(a29) | c2_1(a29)) <=> (hskp8 | c1_1(a29) | c2_1(a29) | c3_1(a29) | c1_1(a26) | (~ndr1_0) | (~c2_1(a26)) | (~c3_1(a26)))),
% 0.98/0.93 inference(rewrite,[status(thm)],[])).
% 0.98/0.93 tff(982,plain,
% 0.98/0.93 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a26) | (~c3_1(a26)) | (~c2_1(a26)) | c3_1(a29) | c1_1(a29) | c2_1(a29))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a29) | c2_1(a29) | c3_1(a29) | c1_1(a26) | (~ndr1_0) | (~c2_1(a26)) | (~c3_1(a26))))),
% 0.98/0.93 inference(monotonicity,[status(thm)],[981])).
% 0.98/0.93 tff(983,plain,
% 0.98/0.93 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a26) | (~c3_1(a26)) | (~c2_1(a26)) | c3_1(a29) | c1_1(a29) | c2_1(a29))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a29) | c2_1(a29) | c3_1(a29) | c1_1(a26) | (~ndr1_0) | (~c2_1(a26)) | (~c3_1(a26)))),
% 0.98/0.93 inference(transitivity,[status(thm)],[982, 980])).
% 0.98/0.93 tff(984,plain,
% 0.98/0.93 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a26) | (~c3_1(a26)) | (~c2_1(a26)) | c3_1(a29) | c1_1(a29) | c2_1(a29))),
% 0.98/0.93 inference(quant_inst,[status(thm)],[])).
% 0.98/0.93 tff(985,plain,
% 0.98/0.93 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a29) | c2_1(a29) | c3_1(a29) | c1_1(a26) | (~ndr1_0) | (~c2_1(a26)) | (~c3_1(a26))),
% 0.98/0.93 inference(modus_ponens,[status(thm)],[984, 983])).
% 0.98/0.93 tff(986,plain,
% 0.98/0.93 (c1_1(a29) | (~c2_1(a26))),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[985, 117, 523, 890, 162, 161, 894, 31])).
% 0.98/0.93 tff(987,plain,
% 0.98/0.93 (c1_1(a29)),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[986, 979])).
% 0.98/0.93 tff(988,plain,
% 0.98/0.93 ((~c1_1(a29)) | c0_1(a29)),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[414, 117, 1, 523, 161, 408])).
% 0.98/0.93 tff(989,plain,
% 0.98/0.93 (c0_1(a29)),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[988, 987])).
% 0.98/0.93 tff(990,plain,
% 0.98/0.93 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | c2_1(a29) | c0_1(a26) | c1_1(a26) | (~ndr1_0) | (~c3_1(a26)) | (~c1_1(a29)) | (~c0_1(a29)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a29) | c0_1(a26) | c1_1(a26) | (~ndr1_0) | (~c3_1(a26)) | (~c1_1(a29)) | (~c0_1(a29)))),
% 0.98/0.93 inference(rewrite,[status(thm)],[])).
% 0.98/0.93 tff(991,plain,
% 0.98/0.93 ((hskp3 | (~ndr1_0) | c2_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c1_1(a26) | c0_1(a26) | (~c3_1(a26))) <=> (hskp3 | c2_1(a29) | c0_1(a26) | c1_1(a26) | (~ndr1_0) | (~c3_1(a26)) | (~c1_1(a29)) | (~c0_1(a29)))),
% 0.98/0.93 inference(rewrite,[status(thm)],[])).
% 0.98/0.93 tff(992,plain,
% 0.98/0.93 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c1_1(a26) | c0_1(a26) | (~c3_1(a26)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | c2_1(a29) | c0_1(a26) | c1_1(a26) | (~ndr1_0) | (~c3_1(a26)) | (~c1_1(a29)) | (~c0_1(a29))))),
% 0.98/0.93 inference(monotonicity,[status(thm)],[991])).
% 0.98/0.93 tff(993,plain,
% 0.98/0.93 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c1_1(a26) | c0_1(a26) | (~c3_1(a26)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a29) | c0_1(a26) | c1_1(a26) | (~ndr1_0) | (~c3_1(a26)) | (~c1_1(a29)) | (~c0_1(a29)))),
% 0.98/0.93 inference(transitivity,[status(thm)],[992, 990])).
% 0.98/0.93 tff(994,plain,
% 0.98/0.93 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c1_1(a26) | c0_1(a26) | (~c3_1(a26)))),
% 0.98/0.93 inference(quant_inst,[status(thm)],[])).
% 0.98/0.93 tff(995,plain,
% 0.98/0.93 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a29) | c0_1(a26) | c1_1(a26) | (~ndr1_0) | (~c3_1(a26)) | (~c1_1(a29)) | (~c0_1(a29))),
% 0.98/0.93 inference(modus_ponens,[status(thm)],[994, 993])).
% 0.98/0.93 tff(996,plain,
% 0.98/0.93 ((~c1_1(a29)) | (~c0_1(a29))),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[995, 117, 522, 890, 162, 889, 894, 426])).
% 0.98/0.93 tff(997,plain,
% 0.98/0.93 ($false),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[996, 989, 987])).
% 0.98/0.93 tff(998,plain,(hskp2 | hskp3 | c2_1(a29) | hskp30 | hskp8 | c3_1(a29) | c2_1(a15) | (~c3_1(a15)) | hskp10 | c1_1(a15)), inference(lemma,lemma(discharge,[]))).
% 0.98/0.93 tff(999,plain,
% 0.98/0.93 (hskp2),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[998, 161, 162, 1, 523, 522, 509, 938, 977, 508])).
% 0.98/0.93 tff(1000,plain,
% 0.98/0.93 (c2_1(a5)),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[642, 999])).
% 0.98/0.93 tff(1001,assumption,(~c1_1(a29)), introduced(assumption)).
% 0.98/0.93 tff(1002,plain,
% 0.98/0.93 (~hskp15),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[136, 1001])).
% 0.98/0.93 tff(1003,plain,
% 0.98/0.93 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a29) | c2_1(a29) | c3_1(a29) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a29) | c2_1(a29) | c3_1(a29) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)))),
% 0.98/0.93 inference(rewrite,[status(thm)],[])).
% 0.98/0.93 tff(1004,plain,
% 0.98/0.93 ((hskp8 | (~ndr1_0) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)) | c3_1(a29) | c1_1(a29) | c2_1(a29)) <=> (hskp8 | c1_1(a29) | c2_1(a29) | c3_1(a29) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)))),
% 0.98/0.93 inference(rewrite,[status(thm)],[])).
% 0.98/0.93 tff(1005,plain,
% 0.98/0.93 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)) | c3_1(a29) | c1_1(a29) | c2_1(a29))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a29) | c2_1(a29) | c3_1(a29) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5))))),
% 0.98/0.93 inference(monotonicity,[status(thm)],[1004])).
% 0.98/0.93 tff(1006,plain,
% 0.98/0.93 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)) | c3_1(a29) | c1_1(a29) | c2_1(a29))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a29) | c2_1(a29) | c3_1(a29) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)))),
% 0.98/0.93 inference(transitivity,[status(thm)],[1005, 1003])).
% 0.98/0.93 tff(1007,plain,
% 0.98/0.93 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)) | c3_1(a29) | c1_1(a29) | c2_1(a29))),
% 0.98/0.93 inference(quant_inst,[status(thm)],[])).
% 0.98/0.93 tff(1008,plain,
% 0.98/0.93 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a29) | c2_1(a29) | c3_1(a29) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5))),
% 0.98/0.93 inference(modus_ponens,[status(thm)],[1007, 1006])).
% 0.98/0.93 tff(1009,plain,
% 0.98/0.93 (c1_1(a29) | (~c2_1(a5)) | (~c3_1(a5))),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[1008, 117, 523, 162, 161, 521, 31])).
% 0.98/0.93 tff(1010,plain,
% 0.98/0.93 (~c3_1(a5)),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[1009, 1001, 575])).
% 0.98/0.93 tff(1011,plain,
% 0.98/0.93 ($false),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[590, 1010, 1002, 43, 575])).
% 0.98/0.93 tff(1012,plain,(c1_1(a29) | hskp16 | (~c2_1(a5)) | c0_1(a5) | hskp8 | c2_1(a29) | c3_1(a29) | c1_1(a5)), inference(lemma,lemma(discharge,[]))).
% 0.98/0.93 tff(1013,plain,
% 0.98/0.93 (c1_1(a29)),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[1012, 1000, 43, 520, 523, 162, 161, 521])).
% 0.98/0.93 tff(1014,plain,
% 0.98/0.93 (c0_1(a29)),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[988, 1013])).
% 0.98/0.93 tff(1015,plain,
% 0.98/0.93 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | c2_1(a29) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c3_1(a5)) | (~c1_1(a29)) | (~c0_1(a29)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a29) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c3_1(a5)) | (~c1_1(a29)) | (~c0_1(a29)))),
% 0.98/0.93 inference(rewrite,[status(thm)],[])).
% 0.98/0.93 tff(1016,plain,
% 0.98/0.93 ((hskp3 | (~ndr1_0) | c2_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c1_1(a5) | c0_1(a5) | (~c3_1(a5))) <=> (hskp3 | c2_1(a29) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c3_1(a5)) | (~c1_1(a29)) | (~c0_1(a29)))),
% 0.98/0.93 inference(rewrite,[status(thm)],[])).
% 0.98/0.93 tff(1017,plain,
% 0.98/0.93 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c1_1(a5) | c0_1(a5) | (~c3_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | c2_1(a29) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c3_1(a5)) | (~c1_1(a29)) | (~c0_1(a29))))),
% 0.98/0.93 inference(monotonicity,[status(thm)],[1016])).
% 0.98/0.93 tff(1018,plain,
% 0.98/0.93 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c1_1(a5) | c0_1(a5) | (~c3_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a29) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c3_1(a5)) | (~c1_1(a29)) | (~c0_1(a29)))),
% 0.98/0.93 inference(transitivity,[status(thm)],[1017, 1015])).
% 0.98/0.93 tff(1019,plain,
% 0.98/0.93 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c1_1(a5) | c0_1(a5) | (~c3_1(a5)))),
% 0.98/0.93 inference(quant_inst,[status(thm)],[])).
% 0.98/0.93 tff(1020,plain,
% 0.98/0.93 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a29) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c3_1(a5)) | (~c1_1(a29)) | (~c0_1(a29))),
% 0.98/0.93 inference(modus_ponens,[status(thm)],[1019, 1018])).
% 0.98/0.93 tff(1021,plain,
% 0.98/0.93 ((~c3_1(a5)) | (~c1_1(a29)) | (~c0_1(a29))),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[1020, 117, 522, 162, 520, 521, 426])).
% 0.98/0.93 tff(1022,plain,
% 0.98/0.93 (~c3_1(a5)),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[1021, 1014, 1013])).
% 0.98/0.93 tff(1023,plain,
% 0.98/0.93 ((~c2_1(a5)) | c3_1(a5) | (~c1_1(a29)) | (~c0_1(a29))),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[620, 117, 162, 161, 520, 160])).
% 0.98/0.93 tff(1024,plain,
% 0.98/0.93 ($false),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[1023, 1022, 1014, 1000, 1013])).
% 0.98/0.93 tff(1025,plain,(c3_1(a29) | c2_1(a29) | c0_1(a5) | hskp3 | c1_1(a5) | hskp30 | hskp8 | hskp16 | c2_1(a15) | c1_1(a15)), inference(lemma,lemma(discharge,[]))).
% 0.98/0.93 tff(1026,plain,
% 0.98/0.93 ($false),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[1025, 976, 975, 520, 522, 521, 1, 321, 43, 509, 508])).
% 0.98/0.93 tff(1027,plain,(hskp16 | c0_1(a5) | hskp3 | c1_1(a5) | hskp30 | c2_1(a15) | c1_1(a15) | c2_1(a13) | c0_1(a13) | c1_1(a13)), inference(lemma,lemma(discharge,[]))).
% 0.98/0.93 tff(1028,plain,
% 0.98/0.93 (hskp16),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[1027, 522, 520, 521, 1, 509, 508, 322, 268, 310])).
% 0.98/0.93 tff(1029,plain,
% 0.98/0.93 (~c1_1(a30)),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[244, 1028])).
% 0.98/0.93 tff(1030,plain,
% 0.98/0.93 (c3_1(a30)),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[266, 1028])).
% 0.98/0.93 tff(1031,plain,
% 0.98/0.93 (c2_1(a30)),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[255, 1028])).
% 0.98/0.93 tff(1032,plain,
% 0.98/0.93 (c3_1(a13)),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[338, 1031, 1030, 310, 322, 1029])).
% 0.98/0.93 tff(1033,plain,
% 0.98/0.93 (hskp11),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[346, 1032, 1, 322])).
% 0.98/0.93 tff(1034,plain,
% 0.98/0.93 (~c3_1(a21)),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[352, 1033])).
% 0.98/0.93 tff(1035,plain,
% 0.98/0.93 (~c2_1(a21)),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[358, 1033])).
% 0.98/0.93 tff(1036,plain,
% 0.98/0.93 (c1_1(a21)),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[365, 117, 321, 1031, 1030, 1029, 1035, 1034, 31])).
% 0.98/0.93 tff(1037,plain,
% 0.98/0.93 (c0_1(a21)),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[386, 1033])).
% 0.98/0.93 tff(1038,plain,
% 0.98/0.93 ($false),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[432, 117, 522, 1037, 310, 1035, 268, 426, 1032, 1036])).
% 0.98/0.93 tff(1039,plain,(hskp3 | c1_1(a13) | c0_1(a13) | hskp30 | c2_1(a13) | c0_1(a5) | c1_1(a5) | c2_1(a15) | c1_1(a15)), inference(lemma,lemma(discharge,[]))).
% 0.98/0.93 tff(1040,plain,
% 0.98/0.93 (hskp3),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[1039, 521, 268, 1, 322, 520, 310, 509, 508])).
% 0.98/0.93 tff(1041,plain,
% 0.98/0.93 (~c2_1(a6)),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[484, 1040])).
% 0.98/0.93 tff(1042,plain,
% 0.98/0.93 (c3_1(a6)),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[444, 1040])).
% 0.98/0.93 tff(1043,plain,
% 0.98/0.93 (c0_1(a6)),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[455, 1040])).
% 0.98/0.93 tff(1044,plain,
% 0.98/0.93 (((~hskp9) | (~c3_1(a15))) <=> ((~hskp9) | (~c3_1(a15)))),
% 0.98/0.93 inference(rewrite,[status(thm)],[])).
% 0.98/0.93 tff(1045,plain,
% 0.98/0.93 (((~c3_1(a15)) | (~hskp9)) <=> ((~hskp9) | (~c3_1(a15)))),
% 0.98/0.93 inference(rewrite,[status(thm)],[])).
% 0.98/0.93 tff(1046,axiom,((~c3_1(a15)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause120')).
% 0.98/0.93 tff(1047,plain,
% 0.98/0.93 ((~hskp9) | (~c3_1(a15))),
% 0.98/0.93 inference(modus_ponens,[status(thm)],[1046, 1045])).
% 0.98/0.93 tff(1048,plain,
% 0.98/0.93 ((~hskp9) | (~c3_1(a15))),
% 0.98/0.93 inference(modus_ponens,[status(thm)],[1047, 1044])).
% 0.98/0.93 tff(1049,plain,
% 0.98/0.93 (~hskp9),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[1048, 886])).
% 0.98/0.93 tff(1050,assumption,(~c2_1(a6)), introduced(assumption)).
% 0.98/0.93 tff(1051,assumption,(c3_1(a6)), introduced(assumption)).
% 0.98/0.93 tff(1052,plain,
% 0.98/0.93 (hskp16 | (~c1_1(a6))),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[778, 117, 1051, 1050, 192])).
% 0.98/0.93 tff(1053,plain,
% 0.98/0.93 (~c1_1(a6)),
% 0.98/0.93 inference(unit_resolution,[status(thm)],[1052, 43])).
% 1.05/0.93 tff(1054,assumption,(c0_1(a6)), introduced(assumption)).
% 1.05/0.93 tff(1055,plain,
% 1.05/0.93 (hskp21 | c1_1(a6)),
% 1.05/0.93 inference(unit_resolution,[status(thm)],[459, 117, 523, 1054, 1051, 21])).
% 1.05/0.93 tff(1056,plain,
% 1.05/0.93 (hskp21),
% 1.05/0.93 inference(unit_resolution,[status(thm)],[1055, 1053])).
% 1.05/0.93 tff(1057,plain,
% 1.05/0.93 (hskp15),
% 1.05/0.93 inference(unit_resolution,[status(thm)],[125, 1056, 43])).
% 1.05/0.93 tff(1058,plain,
% 1.05/0.93 (~c3_1(a29)),
% 1.05/0.93 inference(unit_resolution,[status(thm)],[142, 1057])).
% 1.05/0.93 tff(1059,plain,
% 1.05/0.93 (~c2_1(a29)),
% 1.05/0.93 inference(unit_resolution,[status(thm)],[148, 1057])).
% 1.05/0.93 tff(1060,plain,
% 1.05/0.93 (~c3_1(a39)),
% 1.05/0.93 inference(unit_resolution,[status(thm)],[58, 1056])).
% 1.05/0.93 tff(1061,plain,
% 1.05/0.93 (c1_1(a29)),
% 1.05/0.93 inference(unit_resolution,[status(thm)],[136, 1057])).
% 1.05/0.93 tff(1062,plain,
% 1.05/0.93 (c2_1(a39)),
% 1.05/0.93 inference(unit_resolution,[status(thm)],[75, 1056])).
% 1.05/0.93 tff(1063,assumption,(~hskp9), introduced(assumption)).
% 1.05/0.93 tff(1064,plain,
% 1.05/0.93 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp9 | c3_1(a39) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c1_1(a39) | (~c2_1(a39)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp9 | c3_1(a39) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c1_1(a39) | (~c2_1(a39)))),
% 1.05/0.93 inference(rewrite,[status(thm)],[])).
% 1.05/0.93 tff(1065,plain,
% 1.05/0.93 ((hskp9 | (~ndr1_0) | c2_1(a29) | c3_1(a29) | (~c1_1(a29)) | c3_1(a39) | c1_1(a39) | (~c2_1(a39))) <=> (hskp9 | c3_1(a39) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c1_1(a39) | (~c2_1(a39)))),
% 1.05/0.93 inference(rewrite,[status(thm)],[])).
% 1.05/0.93 tff(1066,plain,
% 1.05/0.93 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a29) | c3_1(a29) | (~c1_1(a29)) | c3_1(a39) | c1_1(a39) | (~c2_1(a39)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp9 | c3_1(a39) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c1_1(a39) | (~c2_1(a39))))),
% 1.05/0.93 inference(monotonicity,[status(thm)],[1065])).
% 1.05/0.93 tff(1067,plain,
% 1.05/0.93 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a29) | c3_1(a29) | (~c1_1(a29)) | c3_1(a39) | c1_1(a39) | (~c2_1(a39)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp9 | c3_1(a39) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c1_1(a39) | (~c2_1(a39)))),
% 1.05/0.93 inference(transitivity,[status(thm)],[1066, 1064])).
% 1.05/0.93 tff(1068,plain,
% 1.05/0.93 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a29) | c3_1(a29) | (~c1_1(a29)) | c3_1(a39) | c1_1(a39) | (~c2_1(a39)))),
% 1.05/0.93 inference(quant_inst,[status(thm)],[])).
% 1.05/0.93 tff(1069,plain,
% 1.05/0.93 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp9 | c3_1(a39) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c1_1(a39) | (~c2_1(a39))),
% 1.05/0.93 inference(modus_ponens,[status(thm)],[1068, 1067])).
% 1.05/0.93 tff(1070,plain,
% 1.05/0.93 (c1_1(a39)),
% 1.05/0.93 inference(unit_resolution,[status(thm)],[1069, 117, 1063, 1062, 1061, 1060, 1059, 1058, 519])).
% 1.05/0.93 tff(1071,plain,
% 1.05/0.93 (~c0_1(a39)),
% 1.05/0.93 inference(unit_resolution,[status(thm)],[64, 1056])).
% 1.05/0.93 tff(1072,plain,
% 1.05/0.93 (((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | c0_1(a39) | c3_1(a39) | (~ndr1_0) | (~c1_1(a39)))) <=> ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp30 | hskp8 | c0_1(a39) | c3_1(a39) | (~ndr1_0) | (~c1_1(a39)))),
% 1.05/0.93 inference(rewrite,[status(thm)],[])).
% 1.05/0.93 tff(1073,plain,
% 1.05/0.93 ((hskp30 | hskp8 | (~ndr1_0) | c0_1(a39) | c3_1(a39) | (~c1_1(a39))) <=> (hskp30 | hskp8 | c0_1(a39) | c3_1(a39) | (~ndr1_0) | (~c1_1(a39)))),
% 1.05/0.93 inference(rewrite,[status(thm)],[])).
% 1.05/0.93 tff(1074,plain,
% 1.05/0.93 (((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | (~ndr1_0) | c0_1(a39) | c3_1(a39) | (~c1_1(a39)))) <=> ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | c0_1(a39) | c3_1(a39) | (~ndr1_0) | (~c1_1(a39))))),
% 1.05/0.93 inference(monotonicity,[status(thm)],[1073])).
% 1.05/0.93 tff(1075,plain,
% 1.05/0.93 (((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | (~ndr1_0) | c0_1(a39) | c3_1(a39) | (~c1_1(a39)))) <=> ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp30 | hskp8 | c0_1(a39) | c3_1(a39) | (~ndr1_0) | (~c1_1(a39)))),
% 1.05/0.93 inference(transitivity,[status(thm)],[1074, 1072])).
% 1.05/0.93 tff(1076,plain,
% 1.05/0.93 ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | (~ndr1_0) | c0_1(a39) | c3_1(a39) | (~c1_1(a39)))),
% 1.05/0.93 inference(quant_inst,[status(thm)],[])).
% 1.05/0.93 tff(1077,plain,
% 1.05/0.93 ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp30 | hskp8 | c0_1(a39) | c3_1(a39) | (~ndr1_0) | (~c1_1(a39))),
% 1.05/0.93 inference(modus_ponens,[status(thm)],[1076, 1075])).
% 1.05/0.93 tff(1078,plain,
% 1.05/0.93 ($false),
% 1.05/0.93 inference(unit_resolution,[status(thm)],[1077, 117, 1, 523, 1071, 1060, 408, 1070])).
% 1.05/0.93 tff(1079,plain,(hskp16 | hskp30 | hskp8 | hskp9 | (~c0_1(a6)) | (~c3_1(a6)) | c2_1(a6)), inference(lemma,lemma(discharge,[]))).
% 1.05/0.93 tff(1080,plain,
% 1.05/0.93 (hskp16),
% 1.05/0.93 inference(unit_resolution,[status(thm)],[1079, 1049, 321, 1, 1043, 1042, 1041])).
% 1.05/0.93 tff(1081,plain,
% 1.05/0.93 (~c1_1(a30)),
% 1.05/0.93 inference(unit_resolution,[status(thm)],[244, 1080])).
% 1.05/0.93 tff(1082,plain,
% 1.05/0.93 (c3_1(a30)),
% 1.05/0.93 inference(unit_resolution,[status(thm)],[266, 1080])).
% 1.05/0.93 tff(1083,plain,
% 1.05/0.93 (c2_1(a30)),
% 1.05/0.93 inference(unit_resolution,[status(thm)],[255, 1080])).
% 1.05/0.93 tff(1084,plain,
% 1.05/0.93 (c3_1(a13)),
% 1.05/0.93 inference(unit_resolution,[status(thm)],[338, 1083, 1082, 310, 322, 1081])).
% 1.05/0.93 tff(1085,plain,
% 1.05/0.93 (hskp11),
% 1.05/0.93 inference(unit_resolution,[status(thm)],[346, 1084, 1, 322])).
% 1.05/0.93 tff(1086,plain,
% 1.05/0.93 (~c3_1(a21)),
% 1.05/0.93 inference(unit_resolution,[status(thm)],[352, 1085])).
% 1.05/0.93 tff(1087,plain,
% 1.05/0.93 (~c2_1(a21)),
% 1.05/0.93 inference(unit_resolution,[status(thm)],[358, 1085])).
% 1.05/0.93 tff(1088,plain,
% 1.05/0.93 (c1_1(a21)),
% 1.05/0.93 inference(unit_resolution,[status(thm)],[365, 117, 321, 1083, 1082, 1081, 1087, 1086, 31])).
% 1.05/0.93 tff(1089,plain,
% 1.05/0.93 (c0_1(a21)),
% 1.05/0.93 inference(unit_resolution,[status(thm)],[386, 1085])).
% 1.05/0.93 tff(1090,plain,
% 1.05/0.93 (hskp15 | (~c1_1(a21))),
% 1.05/0.93 inference(unit_resolution,[status(thm)],[393, 117, 1083, 1082, 1089, 1081, 1087, 376])).
% 1.05/0.93 tff(1091,plain,
% 1.05/0.93 (hskp15),
% 1.05/0.93 inference(unit_resolution,[status(thm)],[1090, 1088])).
% 1.05/0.93 tff(1092,plain,
% 1.05/0.93 (~c3_1(a29)),
% 1.05/0.93 inference(unit_resolution,[status(thm)],[142, 1091])).
% 1.05/0.93 tff(1093,plain,
% 1.05/0.93 (c1_1(a29)),
% 1.05/0.93 inference(unit_resolution,[status(thm)],[136, 1091])).
% 1.05/0.93 tff(1094,plain,
% 1.05/0.93 (c0_1(a29)),
% 1.05/0.93 inference(unit_resolution,[status(thm)],[414, 117, 1, 321, 1093, 1092, 408])).
% 1.05/0.93 tff(1095,plain,
% 1.05/0.93 (~c2_1(a29)),
% 1.05/0.93 inference(unit_resolution,[status(thm)],[148, 1091])).
% 1.05/0.93 tff(1096,plain,
% 1.05/0.93 (~hskp21),
% 1.05/0.93 inference(unit_resolution,[status(thm)],[171, 1093, 1095, 1092, 1094])).
% 1.05/0.94 tff(1097,plain,
% 1.05/0.94 (hskp21 | (~c0_1(a30))),
% 1.05/0.94 inference(unit_resolution,[status(thm)],[467, 117, 321, 1082, 1081, 21])).
% 1.05/0.94 tff(1098,plain,
% 1.05/0.94 (~c0_1(a30)),
% 1.05/0.94 inference(unit_resolution,[status(thm)],[1097, 1096])).
% 1.05/0.94 tff(1099,plain,
% 1.05/0.94 (hskp21 | c1_1(a6)),
% 1.05/0.94 inference(unit_resolution,[status(thm)],[459, 117, 321, 1043, 1042, 21])).
% 1.05/0.94 tff(1100,plain,
% 1.05/0.94 (c1_1(a6)),
% 1.05/0.94 inference(unit_resolution,[status(thm)],[1099, 1096])).
% 1.05/0.94 tff(1101,plain,
% 1.05/0.94 ($false),
% 1.05/0.94 inference(unit_resolution,[status(thm)],[491, 117, 1083, 1082, 310, 322, 1042, 268, 1041, 479, 1100, 1098])).
% 1.05/0.94 tff(1102,plain,(c1_1(a5) | c1_1(a13) | c2_1(a13) | c0_1(a13) | hskp30 | c0_1(a5) | c2_1(a15) | c1_1(a15)), inference(lemma,lemma(discharge,[]))).
% 1.05/0.94 tff(1103,plain,
% 1.05/0.94 (c1_1(a5)),
% 1.05/0.94 inference(unit_resolution,[status(thm)],[1102, 520, 322, 268, 1, 310, 509, 508])).
% 1.05/0.94 tff(1104,plain,
% 1.05/0.94 (((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | c0_1(a5) | (~c1_1(a5)) | (~ndr1_0) | c3_1(a5))) <=> ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp30 | hskp8 | c0_1(a5) | (~c1_1(a5)) | (~ndr1_0) | c3_1(a5))),
% 1.05/0.94 inference(rewrite,[status(thm)],[])).
% 1.05/0.94 tff(1105,plain,
% 1.05/0.94 ((hskp30 | hskp8 | (~ndr1_0) | c0_1(a5) | c3_1(a5) | (~c1_1(a5))) <=> (hskp30 | hskp8 | c0_1(a5) | (~c1_1(a5)) | (~ndr1_0) | c3_1(a5))),
% 1.05/0.94 inference(rewrite,[status(thm)],[])).
% 1.05/0.94 tff(1106,plain,
% 1.05/0.94 (((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | (~ndr1_0) | c0_1(a5) | c3_1(a5) | (~c1_1(a5)))) <=> ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | c0_1(a5) | (~c1_1(a5)) | (~ndr1_0) | c3_1(a5)))),
% 1.05/0.94 inference(monotonicity,[status(thm)],[1105])).
% 1.05/0.94 tff(1107,plain,
% 1.05/0.94 (((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | (~ndr1_0) | c0_1(a5) | c3_1(a5) | (~c1_1(a5)))) <=> ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp30 | hskp8 | c0_1(a5) | (~c1_1(a5)) | (~ndr1_0) | c3_1(a5))),
% 1.05/0.94 inference(transitivity,[status(thm)],[1106, 1104])).
% 1.05/0.94 tff(1108,plain,
% 1.05/0.94 ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | (~ndr1_0) | c0_1(a5) | c3_1(a5) | (~c1_1(a5)))),
% 1.05/0.94 inference(quant_inst,[status(thm)],[])).
% 1.05/0.94 tff(1109,plain,
% 1.05/0.94 ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp30 | hskp8 | c0_1(a5) | (~c1_1(a5)) | (~ndr1_0) | c3_1(a5)),
% 1.05/0.94 inference(modus_ponens,[status(thm)],[1108, 1107])).
% 1.05/0.94 tff(1110,plain,
% 1.05/0.94 ((~c1_1(a5)) | c3_1(a5)),
% 1.05/0.94 inference(unit_resolution,[status(thm)],[1109, 117, 1, 321, 520, 408])).
% 1.05/0.94 tff(1111,plain,
% 1.05/0.94 (c3_1(a5)),
% 1.05/0.94 inference(unit_resolution,[status(thm)],[1110, 1103])).
% 1.05/0.94 tff(1112,assumption,(c3_1(a5)), introduced(assumption)).
% 1.05/0.94 tff(1113,plain,
% 1.05/0.94 (^[U: $i] : refl((hskp12 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp12 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))),
% 1.05/0.94 inference(bind,[status(th)],[])).
% 1.05/0.94 tff(1114,plain,
% 1.05/0.94 (![U: $i] : (hskp12 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp12 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 1.05/0.94 inference(quant_intro,[status(thm)],[1113])).
% 1.05/0.94 tff(1115,plain,
% 1.05/0.94 (![U: $i] : (hskp12 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp12 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 1.05/0.94 inference(rewrite,[status(thm)],[])).
% 1.05/0.94 tff(1116,plain,
% 1.05/0.94 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp12) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp12))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp12) <=> (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp12) <=> (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp12) | hskp2) <=> ((hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp2))), rewrite(((hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp2) <=> (hskp12 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp12) | hskp2) <=> (hskp12 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))))),
% 1.05/0.94 inference(bind,[status(th)],[])).
% 1.05/0.94 tff(1117,plain,
% 1.05/0.94 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp12) | hskp2) <=> ![U: $i] : (hskp12 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 1.05/0.94 inference(quant_intro,[status(thm)],[1116])).
% 1.05/0.94 tff(1118,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp12) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause164')).
% 1.05/0.94 tff(1119,plain,
% 1.05/0.94 (![U: $i] : (hskp12 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 1.05/0.94 inference(modus_ponens,[status(thm)],[1118, 1117])).
% 1.05/0.94 tff(1120,plain,
% 1.05/0.94 (![U: $i] : (hskp12 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 1.05/0.94 inference(modus_ponens,[status(thm)],[1119, 1115])).
% 1.05/0.94 tff(1121,plain,(
% 1.05/0.94 ![U: $i] : (hskp12 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 1.05/0.94 inference(skolemize,[status(sab)],[1120])).
% 1.05/0.94 tff(1122,plain,
% 1.05/0.94 (![U: $i] : (hskp12 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 1.05/0.94 inference(modus_ponens,[status(thm)],[1121, 1114])).
% 1.05/0.94 tff(1123,assumption,(c1_1(a5)), introduced(assumption)).
% 1.05/0.94 tff(1124,plain,
% 1.05/0.94 (((~hskp2) | (~c1_1(a5))) <=> ((~hskp2) | (~c1_1(a5)))),
% 1.05/0.94 inference(rewrite,[status(thm)],[])).
% 1.05/0.94 tff(1125,plain,
% 1.05/0.94 (((~c1_1(a5)) | (~hskp2)) <=> ((~hskp2) | (~c1_1(a5)))),
% 1.05/0.94 inference(rewrite,[status(thm)],[])).
% 1.05/0.94 tff(1126,axiom,((~c1_1(a5)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause131')).
% 1.05/0.94 tff(1127,plain,
% 1.05/0.94 ((~hskp2) | (~c1_1(a5))),
% 1.05/0.94 inference(modus_ponens,[status(thm)],[1126, 1125])).
% 1.05/0.94 tff(1128,plain,
% 1.05/0.94 ((~hskp2) | (~c1_1(a5))),
% 1.05/0.94 inference(modus_ponens,[status(thm)],[1127, 1124])).
% 1.05/0.94 tff(1129,plain,
% 1.05/0.94 (~hskp2),
% 1.05/0.94 inference(unit_resolution,[status(thm)],[1128, 1123])).
% 1.05/0.94 tff(1130,plain,
% 1.05/0.94 (((~![U: $i] : (hskp12 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp12 | hskp2 | (~c1_1(a5)) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)))) <=> ((~![U: $i] : (hskp12 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp12 | hskp2 | (~c1_1(a5)) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)))),
% 1.05/0.94 inference(rewrite,[status(thm)],[])).
% 1.05/0.94 tff(1131,plain,
% 1.05/0.94 ((hskp12 | hskp2 | (~ndr1_0) | (~c1_1(a5)) | (~c3_1(a5)) | (~c2_1(a5))) <=> (hskp12 | hskp2 | (~c1_1(a5)) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)))),
% 1.05/0.94 inference(rewrite,[status(thm)],[])).
% 1.05/0.94 tff(1132,plain,
% 1.05/0.94 (((~![U: $i] : (hskp12 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp12 | hskp2 | (~ndr1_0) | (~c1_1(a5)) | (~c3_1(a5)) | (~c2_1(a5)))) <=> ((~![U: $i] : (hskp12 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp12 | hskp2 | (~c1_1(a5)) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5))))),
% 1.05/0.94 inference(monotonicity,[status(thm)],[1131])).
% 1.05/0.94 tff(1133,plain,
% 1.05/0.94 (((~![U: $i] : (hskp12 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp12 | hskp2 | (~ndr1_0) | (~c1_1(a5)) | (~c3_1(a5)) | (~c2_1(a5)))) <=> ((~![U: $i] : (hskp12 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp12 | hskp2 | (~c1_1(a5)) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)))),
% 1.05/0.94 inference(transitivity,[status(thm)],[1132, 1130])).
% 1.05/0.94 tff(1134,plain,
% 1.05/0.94 ((~![U: $i] : (hskp12 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp12 | hskp2 | (~ndr1_0) | (~c1_1(a5)) | (~c3_1(a5)) | (~c2_1(a5)))),
% 1.05/0.94 inference(quant_inst,[status(thm)],[])).
% 1.05/0.94 tff(1135,plain,
% 1.05/0.94 ((~![U: $i] : (hskp12 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp12 | hskp2 | (~c1_1(a5)) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5))),
% 1.05/0.94 inference(modus_ponens,[status(thm)],[1134, 1133])).
% 1.05/0.94 tff(1136,plain,
% 1.05/0.94 (hskp12 | (~c2_1(a5))),
% 1.05/0.94 inference(unit_resolution,[status(thm)],[1135, 117, 1129, 1123, 1122, 1112])).
% 1.05/0.94 tff(1137,plain,
% 1.05/0.94 (hskp12),
% 1.05/0.94 inference(unit_resolution,[status(thm)],[1136, 575])).
% 1.05/0.94 tff(1138,plain,
% 1.05/0.94 (~c2_1(a24)),
% 1.05/0.94 inference(unit_resolution,[status(thm)],[198, 1137])).
% 1.05/0.94 tff(1139,plain,
% 1.05/0.94 (c3_1(a24)),
% 1.05/0.94 inference(unit_resolution,[status(thm)],[209, 1137])).
% 1.05/0.94 tff(1140,plain,
% 1.05/0.94 (c1_1(a24)),
% 1.05/0.94 inference(unit_resolution,[status(thm)],[220, 1137])).
% 1.05/0.94 tff(1141,plain,
% 1.05/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a13) | c2_1(a13) | c2_1(a24) | c0_1(a13) | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a24)) | (~c3_1(a24)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a13) | c2_1(a13) | c2_1(a24) | c0_1(a13) | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a24)) | (~c3_1(a24)))),
% 1.05/0.94 inference(rewrite,[status(thm)],[])).
% 1.05/0.94 tff(1142,plain,
% 1.05/0.94 (((~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a5) | (~c3_1(a5)) | (~c2_1(a5)) | c1_1(a13) | c0_1(a13) | c2_1(a13)) <=> (c1_1(a13) | c2_1(a13) | c2_1(a24) | c0_1(a13) | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a24)) | (~c3_1(a24)))),
% 1.05/0.94 inference(rewrite,[status(thm)],[])).
% 1.05/0.94 tff(1143,plain,
% 1.05/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a5) | (~c3_1(a5)) | (~c2_1(a5)) | c1_1(a13) | c0_1(a13) | c2_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a13) | c2_1(a13) | c2_1(a24) | c0_1(a13) | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a24)) | (~c3_1(a24))))),
% 1.05/0.94 inference(monotonicity,[status(thm)],[1142])).
% 1.05/0.94 tff(1144,plain,
% 1.05/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a5) | (~c3_1(a5)) | (~c2_1(a5)) | c1_1(a13) | c0_1(a13) | c2_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a13) | c2_1(a13) | c2_1(a24) | c0_1(a13) | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a24)) | (~c3_1(a24)))),
% 1.05/0.94 inference(transitivity,[status(thm)],[1143, 1141])).
% 1.05/0.94 tff(1145,plain,
% 1.05/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a5) | (~c3_1(a5)) | (~c2_1(a5)) | c1_1(a13) | c0_1(a13) | c2_1(a13))),
% 1.05/0.94 inference(quant_inst,[status(thm)],[])).
% 1.05/0.94 tff(1146,plain,
% 1.05/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a13) | c2_1(a13) | c2_1(a24) | c0_1(a13) | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a24)) | (~c3_1(a24))),
% 1.05/0.94 inference(modus_ponens,[status(thm)],[1145, 1144])).
% 1.05/0.94 tff(1147,plain,
% 1.05/0.94 ($false),
% 1.05/0.94 inference(unit_resolution,[status(thm)],[1146, 117, 1140, 1139, 310, 322, 575, 1138, 268, 520, 479, 1112])).
% 1.05/0.94 tff(1148,plain,((~c2_1(a5)) | c1_1(a13) | c2_1(a13) | c0_1(a13) | c0_1(a5) | (~c3_1(a5)) | (~c1_1(a5))), inference(lemma,lemma(discharge,[]))).
% 1.05/0.94 tff(1149,plain,
% 1.05/0.94 (~c2_1(a5)),
% 1.05/0.94 inference(unit_resolution,[status(thm)],[1148, 520, 322, 268, 310, 1111, 1103])).
% 1.05/0.94 tff(1150,plain,
% 1.05/0.94 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | c2_1(a5) | c0_1(a5) | (~ndr1_0) | (~c3_1(a5)))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c2_1(a5) | c0_1(a5) | (~ndr1_0) | (~c3_1(a5)))),
% 1.05/0.94 inference(rewrite,[status(thm)],[])).
% 1.05/0.94 tff(1151,plain,
% 1.05/0.94 ((hskp30 | hskp11 | (~ndr1_0) | c2_1(a5) | c0_1(a5) | (~c3_1(a5))) <=> (hskp30 | hskp11 | c2_1(a5) | c0_1(a5) | (~ndr1_0) | (~c3_1(a5)))),
% 1.05/0.94 inference(rewrite,[status(thm)],[])).
% 1.05/0.94 tff(1152,plain,
% 1.05/0.94 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a5) | c0_1(a5) | (~c3_1(a5)))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | c2_1(a5) | c0_1(a5) | (~ndr1_0) | (~c3_1(a5))))),
% 1.05/0.94 inference(monotonicity,[status(thm)],[1151])).
% 1.05/0.94 tff(1153,plain,
% 1.05/0.94 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a5) | c0_1(a5) | (~c3_1(a5)))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c2_1(a5) | c0_1(a5) | (~ndr1_0) | (~c3_1(a5)))),
% 1.05/0.94 inference(transitivity,[status(thm)],[1152, 1150])).
% 1.05/0.94 tff(1154,plain,
% 1.05/0.94 ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a5) | c0_1(a5) | (~c3_1(a5)))),
% 1.05/0.94 inference(quant_inst,[status(thm)],[])).
% 1.05/0.94 tff(1155,plain,
% 1.05/0.94 ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c2_1(a5) | c0_1(a5) | (~ndr1_0) | (~c3_1(a5))),
% 1.05/0.94 inference(modus_ponens,[status(thm)],[1154, 1153])).
% 1.05/0.94 tff(1156,plain,
% 1.05/0.94 (hskp11 | c2_1(a5) | (~c3_1(a5))),
% 1.05/0.94 inference(unit_resolution,[status(thm)],[1155, 117, 1, 520, 41])).
% 1.05/0.94 tff(1157,plain,
% 1.05/0.94 (hskp11),
% 1.05/0.94 inference(unit_resolution,[status(thm)],[1156, 1149, 1111])).
% 1.05/0.94 tff(1158,plain,
% 1.05/0.94 (~c3_1(a21)),
% 1.05/0.94 inference(unit_resolution,[status(thm)],[352, 1157])).
% 1.05/0.94 tff(1159,plain,
% 1.05/0.94 (~c2_1(a21)),
% 1.05/0.94 inference(unit_resolution,[status(thm)],[358, 1157])).
% 1.05/0.94 tff(1160,plain,
% 1.05/0.94 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | c2_1(a5) | (~c1_1(a5)) | (~ndr1_0) | (~c3_1(a5)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | c2_1(a5) | (~c1_1(a5)) | (~ndr1_0) | (~c3_1(a5)))),
% 1.05/0.94 inference(rewrite,[status(thm)],[])).
% 1.05/0.94 tff(1161,plain,
% 1.05/0.94 ((hskp16 | (~ndr1_0) | c2_1(a5) | (~c1_1(a5)) | (~c3_1(a5))) <=> (hskp16 | c2_1(a5) | (~c1_1(a5)) | (~ndr1_0) | (~c3_1(a5)))),
% 1.05/0.94 inference(rewrite,[status(thm)],[])).
% 1.05/0.94 tff(1162,plain,
% 1.05/0.94 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a5) | (~c1_1(a5)) | (~c3_1(a5)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | c2_1(a5) | (~c1_1(a5)) | (~ndr1_0) | (~c3_1(a5))))),
% 1.05/0.94 inference(monotonicity,[status(thm)],[1161])).
% 1.05/0.94 tff(1163,plain,
% 1.05/0.94 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a5) | (~c1_1(a5)) | (~c3_1(a5)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | c2_1(a5) | (~c1_1(a5)) | (~ndr1_0) | (~c3_1(a5)))),
% 1.05/0.94 inference(transitivity,[status(thm)],[1162, 1160])).
% 1.05/0.94 tff(1164,plain,
% 1.05/0.94 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a5) | (~c1_1(a5)) | (~c3_1(a5)))),
% 1.05/0.94 inference(quant_inst,[status(thm)],[])).
% 1.05/0.94 tff(1165,plain,
% 1.05/0.94 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | c2_1(a5) | (~c1_1(a5)) | (~ndr1_0) | (~c3_1(a5))),
% 1.05/0.94 inference(modus_ponens,[status(thm)],[1164, 1163])).
% 1.05/0.94 tff(1166,plain,
% 1.05/0.94 (hskp16 | c2_1(a5)),
% 1.05/0.94 inference(unit_resolution,[status(thm)],[1165, 117, 1103, 192, 1111])).
% 1.05/0.94 tff(1167,plain,
% 1.05/0.94 (hskp16),
% 1.05/0.94 inference(unit_resolution,[status(thm)],[1166, 1149])).
% 1.05/0.94 tff(1168,plain,
% 1.05/0.94 (~c1_1(a30)),
% 1.05/0.94 inference(unit_resolution,[status(thm)],[244, 1167])).
% 1.05/0.94 tff(1169,plain,
% 1.05/0.94 (c3_1(a30)),
% 1.05/0.94 inference(unit_resolution,[status(thm)],[266, 1167])).
% 1.05/0.94 tff(1170,plain,
% 1.05/0.94 (c2_1(a30)),
% 1.05/0.94 inference(unit_resolution,[status(thm)],[255, 1167])).
% 1.05/0.94 tff(1171,plain,
% 1.05/0.94 (c1_1(a21)),
% 1.05/0.94 inference(unit_resolution,[status(thm)],[365, 117, 321, 1170, 1169, 1168, 1159, 1158, 31])).
% 1.05/0.94 tff(1172,plain,
% 1.05/0.94 (c0_1(a21)),
% 1.05/0.94 inference(unit_resolution,[status(thm)],[386, 1157])).
% 1.05/0.94 tff(1173,plain,
% 1.05/0.94 (hskp15 | (~c1_1(a21))),
% 1.05/0.94 inference(unit_resolution,[status(thm)],[393, 117, 1170, 1169, 1172, 1168, 1159, 376])).
% 1.05/0.94 tff(1174,plain,
% 1.05/0.94 (hskp15),
% 1.05/0.94 inference(unit_resolution,[status(thm)],[1173, 1171])).
% 1.05/0.94 tff(1175,plain,
% 1.05/0.94 (~c3_1(a29)),
% 1.05/0.94 inference(unit_resolution,[status(thm)],[142, 1174])).
% 1.05/0.94 tff(1176,plain,
% 1.05/0.94 (~c2_1(a29)),
% 1.05/0.94 inference(unit_resolution,[status(thm)],[148, 1174])).
% 1.05/0.94 tff(1177,plain,
% 1.05/0.94 (c3_1(a15)),
% 1.05/0.94 inference(unit_resolution,[status(thm)],[533, 1168, 321, 508, 509, 1167])).
% 1.05/0.94 tff(1178,plain,
% 1.05/0.94 (~hskp9),
% 1.05/0.94 inference(unit_resolution,[status(thm)],[1048, 1177])).
% 1.05/0.94 tff(1179,plain,
% 1.05/0.94 (^[U: $i] : refl((hskp9 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> (hskp9 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))),
% 1.05/0.94 inference(bind,[status(th)],[])).
% 1.05/0.94 tff(1180,plain,
% 1.05/0.94 (![U: $i] : (hskp9 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp9 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.05/0.94 inference(quant_intro,[status(thm)],[1179])).
% 1.05/0.94 tff(1181,plain,
% 1.05/0.94 (![U: $i] : (hskp9 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp9 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.05/0.94 inference(rewrite,[status(thm)],[])).
% 1.05/0.94 tff(1182,plain,
% 1.05/0.94 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp0) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp0))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp0) | hskp9) <=> ((hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp9))), rewrite(((hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp9) <=> (hskp9 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp0) | hskp9) <=> (hskp9 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))))),
% 1.05/0.94 inference(bind,[status(th)],[])).
% 1.05/0.94 tff(1183,plain,
% 1.05/0.94 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp0) | hskp9) <=> ![U: $i] : (hskp9 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.05/0.94 inference(quant_intro,[status(thm)],[1182])).
% 1.05/0.94 tff(1184,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp0) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause139')).
% 1.05/0.94 tff(1185,plain,
% 1.05/0.94 (![U: $i] : (hskp9 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.05/0.94 inference(modus_ponens,[status(thm)],[1184, 1183])).
% 1.05/0.94 tff(1186,plain,
% 1.05/0.94 (![U: $i] : (hskp9 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.05/0.94 inference(modus_ponens,[status(thm)],[1185, 1181])).
% 1.05/0.94 tff(1187,plain,(
% 1.05/0.94 ![U: $i] : (hskp9 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.05/0.94 inference(skolemize,[status(sab)],[1186])).
% 1.05/0.94 tff(1188,plain,
% 1.05/0.94 (![U: $i] : (hskp9 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.05/0.94 inference(modus_ponens,[status(thm)],[1187, 1180])).
% 1.05/0.94 tff(1189,plain,
% 1.05/0.94 (((~![U: $i] : (hskp9 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp0 | c2_1(a5) | c0_1(a5) | (~c1_1(a5)) | (~ndr1_0))) <=> ((~![U: $i] : (hskp9 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp9 | hskp0 | c2_1(a5) | c0_1(a5) | (~c1_1(a5)) | (~ndr1_0))),
% 1.05/0.94 inference(rewrite,[status(thm)],[])).
% 1.05/0.94 tff(1190,plain,
% 1.05/0.94 ((hskp9 | hskp0 | (~ndr1_0) | c2_1(a5) | c0_1(a5) | (~c1_1(a5))) <=> (hskp9 | hskp0 | c2_1(a5) | c0_1(a5) | (~c1_1(a5)) | (~ndr1_0))),
% 1.05/0.94 inference(rewrite,[status(thm)],[])).
% 1.05/0.94 tff(1191,plain,
% 1.05/0.94 (((~![U: $i] : (hskp9 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp0 | (~ndr1_0) | c2_1(a5) | c0_1(a5) | (~c1_1(a5)))) <=> ((~![U: $i] : (hskp9 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp0 | c2_1(a5) | c0_1(a5) | (~c1_1(a5)) | (~ndr1_0)))),
% 1.05/0.94 inference(monotonicity,[status(thm)],[1190])).
% 1.05/0.94 tff(1192,plain,
% 1.05/0.94 (((~![U: $i] : (hskp9 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp0 | (~ndr1_0) | c2_1(a5) | c0_1(a5) | (~c1_1(a5)))) <=> ((~![U: $i] : (hskp9 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp9 | hskp0 | c2_1(a5) | c0_1(a5) | (~c1_1(a5)) | (~ndr1_0))),
% 1.05/0.94 inference(transitivity,[status(thm)],[1191, 1189])).
% 1.05/0.94 tff(1193,plain,
% 1.05/0.94 ((~![U: $i] : (hskp9 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp0 | (~ndr1_0) | c2_1(a5) | c0_1(a5) | (~c1_1(a5)))),
% 1.05/0.94 inference(quant_inst,[status(thm)],[])).
% 1.05/0.94 tff(1194,plain,
% 1.05/0.94 ((~![U: $i] : (hskp9 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp9 | hskp0 | c2_1(a5) | c0_1(a5) | (~c1_1(a5)) | (~ndr1_0)),
% 1.05/0.94 inference(modus_ponens,[status(thm)],[1193, 1192])).
% 1.05/0.94 tff(1195,plain,
% 1.05/0.94 (hskp9 | hskp0 | c2_1(a5) | (~c1_1(a5))),
% 1.05/0.94 inference(unit_resolution,[status(thm)],[1194, 117, 520, 1188])).
% 1.05/0.94 tff(1196,plain,
% 1.05/0.94 (hskp0),
% 1.05/0.94 inference(unit_resolution,[status(thm)],[1195, 1178, 1103, 1149])).
% 1.05/0.94 tff(1197,plain,
% 1.05/0.94 (((~hskp0) | (~c2_1(a1))) <=> ((~hskp0) | (~c2_1(a1)))),
% 1.05/0.94 inference(rewrite,[status(thm)],[])).
% 1.05/0.94 tff(1198,plain,
% 1.05/0.94 (((~c2_1(a1)) | (~hskp0)) <=> ((~hskp0) | (~c2_1(a1)))),
% 1.05/0.94 inference(rewrite,[status(thm)],[])).
% 1.05/0.94 tff(1199,axiom,((~c2_1(a1)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause134')).
% 1.05/0.94 tff(1200,plain,
% 1.05/0.94 ((~hskp0) | (~c2_1(a1))),
% 1.05/0.94 inference(modus_ponens,[status(thm)],[1199, 1198])).
% 1.05/0.94 tff(1201,plain,
% 1.05/0.94 ((~hskp0) | (~c2_1(a1))),
% 1.05/0.94 inference(modus_ponens,[status(thm)],[1200, 1197])).
% 1.05/0.94 tff(1202,plain,
% 1.05/0.94 (~c2_1(a1)),
% 1.05/0.94 inference(unit_resolution,[status(thm)],[1201, 1196])).
% 1.05/0.94 tff(1203,plain,
% 1.05/0.94 (((~hskp0) | (~c1_1(a1))) <=> ((~hskp0) | (~c1_1(a1)))),
% 1.05/0.94 inference(rewrite,[status(thm)],[])).
% 1.05/0.94 tff(1204,plain,
% 1.05/0.94 (((~c1_1(a1)) | (~hskp0)) <=> ((~hskp0) | (~c1_1(a1)))),
% 1.05/0.94 inference(rewrite,[status(thm)],[])).
% 1.05/0.94 tff(1205,axiom,((~c1_1(a1)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause133')).
% 1.05/0.94 tff(1206,plain,
% 1.05/0.94 ((~hskp0) | (~c1_1(a1))),
% 1.05/0.94 inference(modus_ponens,[status(thm)],[1205, 1204])).
% 1.05/0.94 tff(1207,plain,
% 1.05/0.94 ((~hskp0) | (~c1_1(a1))),
% 1.05/0.94 inference(modus_ponens,[status(thm)],[1206, 1203])).
% 1.05/0.94 tff(1208,plain,
% 1.05/0.94 (~c1_1(a1)),
% 1.05/0.94 inference(unit_resolution,[status(thm)],[1207, 1196])).
% 1.05/0.94 tff(1209,plain,
% 1.05/0.94 (((~hskp0) | c0_1(a1)) <=> ((~hskp0) | c0_1(a1))),
% 1.05/0.94 inference(rewrite,[status(thm)],[])).
% 1.05/0.94 tff(1210,axiom,((~hskp0) | c0_1(a1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause86')).
% 1.05/0.94 tff(1211,plain,
% 1.05/0.94 ((~hskp0) | c0_1(a1)),
% 1.05/0.94 inference(modus_ponens,[status(thm)],[1210, 1209])).
% 1.05/0.94 tff(1212,plain,
% 1.05/0.94 ((~hskp0) | c0_1(a1)),
% 1.05/0.94 inference(modus_ponens,[status(thm)],[1211, 1209])).
% 1.05/0.94 tff(1213,plain,
% 1.05/0.94 ((~hskp0) | c0_1(a1)),
% 1.05/0.94 inference(modus_ponens,[status(thm)],[1212, 1209])).
% 1.05/0.94 tff(1214,plain,
% 1.05/0.94 ((~hskp0) | c0_1(a1)),
% 1.05/0.94 inference(modus_ponens,[status(thm)],[1213, 1209])).
% 1.05/0.94 tff(1215,plain,
% 1.05/0.94 ((~hskp0) | c0_1(a1)),
% 1.05/0.94 inference(modus_ponens,[status(thm)],[1214, 1209])).
% 1.05/0.94 tff(1216,plain,
% 1.05/0.94 ((~hskp0) | c0_1(a1)),
% 1.05/0.94 inference(modus_ponens,[status(thm)],[1215, 1209])).
% 1.05/0.94 tff(1217,plain,
% 1.05/0.94 ((~hskp0) | c0_1(a1)),
% 1.05/0.94 inference(modus_ponens,[status(thm)],[1216, 1209])).
% 1.05/0.94 tff(1218,plain,
% 1.05/0.94 ((~hskp0) | c0_1(a1)),
% 1.05/0.94 inference(modus_ponens,[status(thm)],[1217, 1209])).
% 1.05/0.94 tff(1219,plain,
% 1.05/0.94 (c0_1(a1)),
% 1.05/0.94 inference(unit_resolution,[status(thm)],[1218, 1196])).
% 1.05/0.94 tff(1220,plain,
% 1.05/0.94 (((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp23 | c1_1(a1) | c2_1(a1) | (~ndr1_0) | (~c0_1(a1)))) <=> ((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp30 | hskp23 | c1_1(a1) | c2_1(a1) | (~ndr1_0) | (~c0_1(a1)))),
% 1.05/0.94 inference(rewrite,[status(thm)],[])).
% 1.05/0.94 tff(1221,plain,
% 1.05/0.94 ((hskp30 | hskp23 | (~ndr1_0) | c2_1(a1) | c1_1(a1) | (~c0_1(a1))) <=> (hskp30 | hskp23 | c1_1(a1) | c2_1(a1) | (~ndr1_0) | (~c0_1(a1)))),
% 1.05/0.94 inference(rewrite,[status(thm)],[])).
% 1.05/0.94 tff(1222,plain,
% 1.05/0.94 (((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp23 | (~ndr1_0) | c2_1(a1) | c1_1(a1) | (~c0_1(a1)))) <=> ((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp23 | c1_1(a1) | c2_1(a1) | (~ndr1_0) | (~c0_1(a1))))),
% 1.05/0.94 inference(monotonicity,[status(thm)],[1221])).
% 1.05/0.94 tff(1223,plain,
% 1.05/0.94 (((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp23 | (~ndr1_0) | c2_1(a1) | c1_1(a1) | (~c0_1(a1)))) <=> ((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp30 | hskp23 | c1_1(a1) | c2_1(a1) | (~ndr1_0) | (~c0_1(a1)))),
% 1.05/0.94 inference(transitivity,[status(thm)],[1222, 1220])).
% 1.05/0.94 tff(1224,plain,
% 1.05/0.94 ((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp23 | (~ndr1_0) | c2_1(a1) | c1_1(a1) | (~c0_1(a1)))),
% 1.05/0.94 inference(quant_inst,[status(thm)],[])).
% 1.05/0.94 tff(1225,plain,
% 1.05/0.94 ((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp30 | hskp23 | c1_1(a1) | c2_1(a1) | (~ndr1_0) | (~c0_1(a1))),
% 1.05/0.94 inference(modus_ponens,[status(thm)],[1224, 1223])).
% 1.05/0.94 tff(1226,plain,
% 1.05/0.94 (hskp23),
% 1.05/0.94 inference(unit_resolution,[status(thm)],[1225, 117, 1, 1219, 1208, 1202, 799])).
% 1.05/0.94 tff(1227,plain,
% 1.05/0.94 (~c3_1(a42)),
% 1.05/0.94 inference(unit_resolution,[status(thm)],[813, 1226])).
% 1.05/0.94 tff(1228,plain,
% 1.05/0.94 (~c1_1(a42)),
% 1.05/0.94 inference(unit_resolution,[status(thm)],[819, 1226])).
% 1.05/0.94 tff(1229,plain,
% 1.05/0.94 (c1_1(a29)),
% 1.05/0.94 inference(unit_resolution,[status(thm)],[136, 1174])).
% 1.05/0.94 tff(1230,plain,
% 1.05/0.94 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp9 | c1_1(a42) | c3_1(a42) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | (~c2_1(a42)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp9 | c1_1(a42) | c3_1(a42) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | (~c2_1(a42)))),
% 1.05/0.94 inference(rewrite,[status(thm)],[])).
% 1.05/0.94 tff(1231,plain,
% 1.05/0.94 ((hskp9 | (~ndr1_0) | c2_1(a29) | c3_1(a29) | (~c1_1(a29)) | c3_1(a42) | c1_1(a42) | (~c2_1(a42))) <=> (hskp9 | c1_1(a42) | c3_1(a42) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | (~c2_1(a42)))),
% 1.05/0.94 inference(rewrite,[status(thm)],[])).
% 1.05/0.94 tff(1232,plain,
% 1.05/0.94 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a29) | c3_1(a29) | (~c1_1(a29)) | c3_1(a42) | c1_1(a42) | (~c2_1(a42)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp9 | c1_1(a42) | c3_1(a42) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | (~c2_1(a42))))),
% 1.05/0.94 inference(monotonicity,[status(thm)],[1231])).
% 1.05/0.94 tff(1233,plain,
% 1.05/0.94 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a29) | c3_1(a29) | (~c1_1(a29)) | c3_1(a42) | c1_1(a42) | (~c2_1(a42)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp9 | c1_1(a42) | c3_1(a42) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | (~c2_1(a42)))),
% 1.05/0.94 inference(transitivity,[status(thm)],[1232, 1230])).
% 1.05/0.94 tff(1234,plain,
% 1.05/0.94 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a29) | c3_1(a29) | (~c1_1(a29)) | c3_1(a42) | c1_1(a42) | (~c2_1(a42)))),
% 1.05/0.94 inference(quant_inst,[status(thm)],[])).
% 1.05/0.94 tff(1235,plain,
% 1.05/0.94 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp9 | c1_1(a42) | c3_1(a42) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | (~c2_1(a42))),
% 1.05/0.94 inference(modus_ponens,[status(thm)],[1234, 1233])).
% 1.05/0.94 tff(1236,plain,
% 1.05/0.94 (~c2_1(a42)),
% 1.05/0.94 inference(unit_resolution,[status(thm)],[1235, 117, 1178, 1229, 1228, 1227, 1176, 1175, 519])).
% 1.05/0.94 tff(1237,plain,
% 1.05/0.94 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a42) | c3_1(a42) | c1_1(a30) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30)) | c2_1(a42))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a42) | c3_1(a42) | c1_1(a30) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30)) | c2_1(a42))),
% 1.05/0.95 inference(rewrite,[status(thm)],[])).
% 1.05/0.95 tff(1238,plain,
% 1.05/0.95 ((hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a42) | c1_1(a42) | c2_1(a42)) <=> (hskp8 | c1_1(a42) | c3_1(a42) | c1_1(a30) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30)) | c2_1(a42))),
% 1.05/0.95 inference(rewrite,[status(thm)],[])).
% 1.05/0.95 tff(1239,plain,
% 1.05/0.95 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a42) | c1_1(a42) | c2_1(a42))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a42) | c3_1(a42) | c1_1(a30) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30)) | c2_1(a42)))),
% 1.05/0.95 inference(monotonicity,[status(thm)],[1238])).
% 1.05/0.95 tff(1240,plain,
% 1.05/0.95 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a42) | c1_1(a42) | c2_1(a42))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a42) | c3_1(a42) | c1_1(a30) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30)) | c2_1(a42))),
% 1.05/0.95 inference(transitivity,[status(thm)],[1239, 1237])).
% 1.05/0.95 tff(1241,plain,
% 1.05/0.95 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a42) | c1_1(a42) | c2_1(a42))),
% 1.05/0.95 inference(quant_inst,[status(thm)],[])).
% 1.05/0.95 tff(1242,plain,
% 1.05/0.95 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a42) | c3_1(a42) | c1_1(a30) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30)) | c2_1(a42)),
% 1.05/0.95 inference(modus_ponens,[status(thm)],[1241, 1240])).
% 1.05/0.95 tff(1243,plain,
% 1.05/0.95 ($false),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[1242, 117, 321, 1170, 1169, 1228, 1227, 1168, 31, 1236])).
% 1.05/0.95 tff(1244,plain,(c0_1(a5) | hskp30 | c1_1(a15) | c2_1(a15) | c2_1(a13) | c0_1(a13) | c1_1(a13)), inference(lemma,lemma(discharge,[]))).
% 1.05/0.95 tff(1245,plain,
% 1.05/0.95 (c0_1(a5)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[1244, 508, 1, 509, 322, 268, 310])).
% 1.05/0.95 tff(1246,plain,
% 1.05/0.95 (((~hskp2) | (~c0_1(a5))) <=> ((~hskp2) | (~c0_1(a5)))),
% 1.05/0.95 inference(rewrite,[status(thm)],[])).
% 1.05/0.95 tff(1247,plain,
% 1.05/0.95 (((~c0_1(a5)) | (~hskp2)) <=> ((~hskp2) | (~c0_1(a5)))),
% 1.05/0.95 inference(rewrite,[status(thm)],[])).
% 1.05/0.95 tff(1248,axiom,((~c0_1(a5)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause130')).
% 1.05/0.95 tff(1249,plain,
% 1.05/0.95 ((~hskp2) | (~c0_1(a5))),
% 1.05/0.95 inference(modus_ponens,[status(thm)],[1248, 1247])).
% 1.05/0.95 tff(1250,plain,
% 1.05/0.95 ((~hskp2) | (~c0_1(a5))),
% 1.05/0.95 inference(modus_ponens,[status(thm)],[1249, 1246])).
% 1.05/0.95 tff(1251,plain,
% 1.05/0.95 (~hskp2),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[1250, 1245])).
% 1.05/0.95 tff(1252,plain,
% 1.05/0.95 (hskp13),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[767, 522, 644])).
% 1.05/0.95 tff(1253,plain,
% 1.05/0.95 (hskp10),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[752, 524, 522, 1, 523, 508, 509, 646])).
% 1.05/0.95 tff(1254,plain,
% 1.05/0.95 (hskp16),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[573, 1253, 523, 1])).
% 1.05/0.95 tff(1255,plain,
% 1.05/0.95 (~c1_1(a30)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[244, 1254])).
% 1.05/0.95 tff(1256,plain,
% 1.05/0.95 ($false),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[533, 1255, 1254, 523, 508, 509, 524])).
% 1.05/0.95 tff(1257,plain,(c3_1(a15) | hskp8 | c1_1(a15) | c2_1(a15) | hskp30 | hskp3 | (~hskp13)), inference(lemma,lemma(discharge,[]))).
% 1.05/0.95 tff(1258,plain,
% 1.05/0.95 (c3_1(a15)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[1257, 522, 508, 509, 1, 321, 1252])).
% 1.05/0.95 tff(1259,plain,
% 1.05/0.95 (hskp10),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[934, 1258, 322, 1, 268, 509, 644, 310, 508, 522])).
% 1.05/0.95 tff(1260,plain,
% 1.05/0.95 (hskp16),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[573, 1259, 321, 1])).
% 1.05/0.95 tff(1261,plain,
% 1.05/0.95 (~c1_1(a30)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[244, 1260])).
% 1.05/0.95 tff(1262,plain,
% 1.05/0.95 (c2_1(a30)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[255, 1260])).
% 1.05/0.95 tff(1263,plain,
% 1.05/0.95 (c3_1(a30)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[266, 1260])).
% 1.05/0.95 tff(1264,plain,
% 1.05/0.95 (hskp10),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[934, 644, 322, 1, 268, 509, 891, 310, 508, 522])).
% 1.05/0.95 tff(1265,plain,
% 1.05/0.95 (~c0_1(a17)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[564, 1264])).
% 1.05/0.95 tff(1266,plain,
% 1.05/0.95 (c1_1(a17)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[551, 1264])).
% 1.05/0.95 tff(1267,plain,
% 1.05/0.95 (c3_1(a17)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[571, 117, 1, 321, 1266, 1265, 408])).
% 1.05/0.95 tff(1268,plain,
% 1.05/0.95 (~c2_1(a17)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[540, 1264])).
% 1.05/0.95 tff(1269,plain,
% 1.05/0.95 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | c0_1(a17) | c2_1(a17) | (~ndr1_0) | (~c3_1(a17)))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c0_1(a17) | c2_1(a17) | (~ndr1_0) | (~c3_1(a17)))),
% 1.05/0.95 inference(rewrite,[status(thm)],[])).
% 1.05/0.95 tff(1270,plain,
% 1.05/0.95 ((hskp30 | hskp11 | (~ndr1_0) | c2_1(a17) | c0_1(a17) | (~c3_1(a17))) <=> (hskp30 | hskp11 | c0_1(a17) | c2_1(a17) | (~ndr1_0) | (~c3_1(a17)))),
% 1.05/0.95 inference(rewrite,[status(thm)],[])).
% 1.05/0.95 tff(1271,plain,
% 1.05/0.95 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a17) | c0_1(a17) | (~c3_1(a17)))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | c0_1(a17) | c2_1(a17) | (~ndr1_0) | (~c3_1(a17))))),
% 1.05/0.95 inference(monotonicity,[status(thm)],[1270])).
% 1.05/0.95 tff(1272,plain,
% 1.05/0.95 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a17) | c0_1(a17) | (~c3_1(a17)))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c0_1(a17) | c2_1(a17) | (~ndr1_0) | (~c3_1(a17)))),
% 1.05/0.95 inference(transitivity,[status(thm)],[1271, 1269])).
% 1.05/0.95 tff(1273,plain,
% 1.05/0.95 ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a17) | c0_1(a17) | (~c3_1(a17)))),
% 1.05/0.95 inference(quant_inst,[status(thm)],[])).
% 1.05/0.95 tff(1274,plain,
% 1.05/0.95 ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c0_1(a17) | c2_1(a17) | (~ndr1_0) | (~c3_1(a17))),
% 1.05/0.95 inference(modus_ponens,[status(thm)],[1273, 1272])).
% 1.05/0.95 tff(1275,plain,
% 1.05/0.95 (hskp11),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[1274, 117, 1, 1265, 1268, 41, 1267])).
% 1.05/0.95 tff(1276,plain,
% 1.05/0.95 (~c3_1(a21)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[352, 1275])).
% 1.05/0.95 tff(1277,plain,
% 1.05/0.95 (~c2_1(a21)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[358, 1275])).
% 1.05/0.95 tff(1278,plain,
% 1.05/0.95 (c1_1(a21)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[365, 117, 321, 330, 329, 328, 1277, 1276, 31])).
% 1.05/0.95 tff(1279,plain,
% 1.05/0.95 (c0_1(a21)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[386, 1275])).
% 1.05/0.95 tff(1280,plain,
% 1.05/0.95 ($false),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[692, 117, 522, 890, 1279, 889, 894, 1277, 426, 1278])).
% 1.05/0.95 tff(1281,plain,(hskp2 | hskp3 | (~c2_1(a30)) | (~c3_1(a30)) | c1_1(a30) | hskp30 | c2_1(a13) | c0_1(a13) | c2_1(a15) | (~c3_1(a15)) | c1_1(a13) | c1_1(a15)), inference(lemma,lemma(discharge,[]))).
% 1.05/0.95 tff(1282,plain,
% 1.05/0.95 ($false),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[1281, 1263, 1262, 644, 522, 1261, 1, 322, 268, 509, 1258, 310, 508])).
% 1.05/0.95 tff(1283,plain,(hskp3 | hskp2 | hskp30 | c2_1(a13) | c0_1(a13) | c2_1(a15) | c1_1(a13) | c1_1(a15)), inference(lemma,lemma(discharge,[]))).
% 1.05/0.95 tff(1284,plain,
% 1.05/0.95 (hskp3),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[1283, 1251, 1, 322, 268, 509, 310, 508])).
% 1.05/0.95 tff(1285,plain,
% 1.05/0.95 (~c2_1(a6)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[484, 1284])).
% 1.05/0.95 tff(1286,plain,
% 1.05/0.95 (c3_1(a6)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[444, 1284])).
% 1.05/0.95 tff(1287,plain,
% 1.05/0.95 (c0_1(a6)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[455, 1284])).
% 1.05/0.95 tff(1288,plain,
% 1.05/0.95 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 1.05/0.95 inference(bind,[status(th)],[])).
% 1.05/0.95 tff(1289,plain,
% 1.05/0.95 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.05/0.95 inference(quant_intro,[status(thm)],[1288])).
% 1.05/0.95 tff(1290,plain,
% 1.05/0.95 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.05/0.95 inference(rewrite,[status(thm)],[])).
% 1.05/0.95 tff(1291,plain,
% 1.05/0.95 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp2))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), (((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 1.05/0.95 inference(bind,[status(th)],[])).
% 1.05/0.95 tff(1292,plain,
% 1.05/0.95 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.05/0.95 inference(quant_intro,[status(thm)],[1291])).
% 1.05/0.95 tff(1293,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause166')).
% 1.05/0.95 tff(1294,plain,
% 1.05/0.95 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.05/0.95 inference(modus_ponens,[status(thm)],[1293, 1292])).
% 1.05/0.95 tff(1295,plain,
% 1.05/0.95 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.05/0.95 inference(modus_ponens,[status(thm)],[1294, 1290])).
% 1.05/0.95 tff(1296,plain,(
% 1.05/0.95 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.05/0.95 inference(skolemize,[status(sab)],[1295])).
% 1.05/0.95 tff(1297,plain,
% 1.05/0.95 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 1.05/0.95 inference(modus_ponens,[status(thm)],[1296, 1289])).
% 1.05/0.95 tff(1298,plain,
% 1.05/0.95 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a39) | c3_1(a39) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c1_1(a39))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a39) | c3_1(a39) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c1_1(a39))),
% 1.05/0.95 inference(rewrite,[status(thm)],[])).
% 1.05/0.95 tff(1299,plain,
% 1.05/0.95 ((hskp2 | (~ndr1_0) | c2_1(a29) | c3_1(a29) | (~c1_1(a29)) | c3_1(a39) | c1_1(a39) | c0_1(a39)) <=> (hskp2 | c0_1(a39) | c3_1(a39) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c1_1(a39))),
% 1.05/0.95 inference(rewrite,[status(thm)],[])).
% 1.05/0.95 tff(1300,plain,
% 1.05/0.95 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a29) | c3_1(a29) | (~c1_1(a29)) | c3_1(a39) | c1_1(a39) | c0_1(a39))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a39) | c3_1(a39) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c1_1(a39)))),
% 1.05/0.95 inference(monotonicity,[status(thm)],[1299])).
% 1.05/0.95 tff(1301,plain,
% 1.05/0.95 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a29) | c3_1(a29) | (~c1_1(a29)) | c3_1(a39) | c1_1(a39) | c0_1(a39))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a39) | c3_1(a39) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c1_1(a39))),
% 1.05/0.95 inference(transitivity,[status(thm)],[1300, 1298])).
% 1.05/0.95 tff(1302,plain,
% 1.05/0.95 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a29) | c3_1(a29) | (~c1_1(a29)) | c3_1(a39) | c1_1(a39) | c0_1(a39))),
% 1.05/0.95 inference(quant_inst,[status(thm)],[])).
% 1.05/0.95 tff(1303,plain,
% 1.05/0.95 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a39) | c3_1(a39) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c1_1(a39)),
% 1.05/0.95 inference(modus_ponens,[status(thm)],[1302, 1301])).
% 1.05/0.95 tff(1304,plain,
% 1.05/0.95 (c1_1(a39)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[1303, 117, 644, 1061, 1071, 1060, 1059, 1058, 1297])).
% 1.05/0.95 tff(1305,plain,
% 1.05/0.95 ($false),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[1077, 117, 1, 523, 1071, 1060, 408, 1304])).
% 1.05/0.95 tff(1306,plain,(hskp16 | hskp30 | hskp8 | hskp2 | (~c0_1(a6)) | (~c3_1(a6)) | c2_1(a6)), inference(lemma,lemma(discharge,[]))).
% 1.05/0.95 tff(1307,plain,
% 1.05/0.95 (hskp16),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[1306, 1251, 321, 1, 1287, 1286, 1285])).
% 1.05/0.95 tff(1308,plain,
% 1.05/0.95 (~c1_1(a30)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[244, 1307])).
% 1.05/0.95 tff(1309,plain,
% 1.05/0.95 (c2_1(a30)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[255, 1307])).
% 1.05/0.95 tff(1310,plain,
% 1.05/0.95 (c3_1(a30)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[266, 1307])).
% 1.05/0.95 tff(1311,plain,
% 1.05/0.95 (c3_1(a13)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[338, 1310, 1309, 310, 322, 1308])).
% 1.05/0.95 tff(1312,plain,
% 1.05/0.95 (hskp11),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[346, 1311, 1, 322])).
% 1.05/0.95 tff(1313,plain,
% 1.05/0.95 (~c3_1(a21)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[352, 1312])).
% 1.05/0.95 tff(1314,plain,
% 1.05/0.95 (~c2_1(a21)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[358, 1312])).
% 1.05/0.95 tff(1315,plain,
% 1.05/0.95 (c1_1(a21)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[365, 117, 321, 1309, 1310, 1308, 1314, 1313, 31])).
% 1.05/0.95 tff(1316,plain,
% 1.05/0.95 (c0_1(a21)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[386, 1312])).
% 1.05/0.95 tff(1317,plain,
% 1.05/0.95 (hskp15 | (~c1_1(a21))),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[393, 117, 1309, 1310, 1316, 1308, 1314, 376])).
% 1.05/0.95 tff(1318,plain,
% 1.05/0.95 (hskp15),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[1317, 1315])).
% 1.05/0.95 tff(1319,plain,
% 1.05/0.95 (c1_1(a29)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[136, 1318])).
% 1.05/0.95 tff(1320,plain,
% 1.05/0.95 (~c3_1(a29)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[142, 1318])).
% 1.05/0.95 tff(1321,plain,
% 1.05/0.95 (~c2_1(a29)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[148, 1318])).
% 1.05/0.95 tff(1322,plain,
% 1.05/0.95 (c0_1(a29)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[414, 117, 1, 321, 1319, 1320, 408])).
% 1.05/0.95 tff(1323,plain,
% 1.05/0.95 (~hskp21),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[171, 1322, 1321, 1320, 1319])).
% 1.05/0.95 tff(1324,plain,
% 1.05/0.95 (hskp21 | (~c0_1(a30))),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[467, 117, 321, 1310, 1308, 21])).
% 1.05/0.95 tff(1325,plain,
% 1.05/0.95 (~c0_1(a30)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[1324, 1323])).
% 1.05/0.95 tff(1326,plain,
% 1.05/0.95 (hskp21 | c1_1(a6)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[459, 117, 321, 1287, 1286, 21])).
% 1.05/0.95 tff(1327,plain,
% 1.05/0.95 (c1_1(a6)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[1326, 1323])).
% 1.05/0.95 tff(1328,plain,
% 1.05/0.95 ($false),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[491, 117, 1309, 1310, 310, 322, 1286, 268, 1285, 479, 1327, 1325])).
% 1.05/0.95 tff(1329,plain,(c1_1(a15) | c1_1(a13) | c2_1(a13) | c0_1(a13) | hskp30 | c2_1(a15)), inference(lemma,lemma(discharge,[]))).
% 1.05/0.95 tff(1330,plain,
% 1.05/0.95 ($false),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[1329, 507, 501, 322, 268, 1, 310])).
% 1.05/0.95 tff(1331,plain,((~hskp9) | c2_1(a13) | c0_1(a13) | hskp30 | c1_1(a13)), inference(lemma,lemma(discharge,[]))).
% 1.05/0.95 tff(1332,plain,
% 1.05/0.95 (~hskp9),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[1331, 322, 268, 1, 310])).
% 1.05/0.95 tff(1333,assumption,(hskp3), introduced(assumption)).
% 1.05/0.95 tff(1334,plain,
% 1.05/0.95 (~c2_1(a6)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[484, 1333])).
% 1.05/0.95 tff(1335,plain,
% 1.05/0.95 (c0_1(a6)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[455, 1333])).
% 1.05/0.95 tff(1336,plain,
% 1.05/0.95 (c3_1(a6)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[444, 1333])).
% 1.05/0.95 tff(1337,plain,
% 1.05/0.95 ($false),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[1079, 1336, 1335, 523, 1, 1063, 43, 1334])).
% 1.05/0.95 tff(1338,plain,((~hskp3) | hskp8 | hskp30 | hskp9 | hskp16), inference(lemma,lemma(discharge,[]))).
% 1.05/0.95 tff(1339,plain,
% 1.05/0.95 (~hskp3),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[1338, 1332, 1, 494, 321])).
% 1.05/0.95 tff(1340,assumption,(~hskp11), introduced(assumption)).
% 1.05/0.95 tff(1341,assumption,(~c0_1(a26)), introduced(assumption)).
% 1.05/0.95 tff(1342,assumption,(c3_1(a26)), introduced(assumption)).
% 1.05/0.95 tff(1343,plain,
% 1.05/0.95 (hskp11 | c2_1(a26)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[682, 117, 1, 1342, 1341, 41])).
% 1.05/0.95 tff(1344,plain,
% 1.05/0.95 (c2_1(a26)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[1343, 1340])).
% 1.05/0.95 tff(1345,plain,
% 1.05/0.95 (~c3_1(a13)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[346, 1340, 1, 322])).
% 1.05/0.95 tff(1346,assumption,(~c1_1(a26)), introduced(assumption)).
% 1.05/0.95 tff(1347,plain,
% 1.05/0.95 ($false),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[932, 117, 321, 1342, 310, 322, 1346, 31, 1345, 1344])).
% 1.05/0.95 tff(1348,plain,(hskp11 | (~c3_1(a26)) | c1_1(a13) | c2_1(a13) | c1_1(a26) | hskp30 | c0_1(a26) | c0_1(a13)), inference(lemma,lemma(discharge,[]))).
% 1.05/0.95 tff(1349,plain,
% 1.05/0.95 (hskp11),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[1348, 663, 310, 322, 652, 1, 676, 268])).
% 1.05/0.95 tff(1350,plain,
% 1.05/0.95 (~c2_1(a21)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[358, 1349])).
% 1.05/0.95 tff(1351,plain,
% 1.05/0.95 (c0_1(a21)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[386, 1349])).
% 1.05/0.95 tff(1352,plain,
% 1.05/0.95 (~c1_1(a21)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[692, 117, 1339, 663, 1351, 676, 652, 1350, 426])).
% 1.05/0.95 tff(1353,plain,
% 1.05/0.95 (~c3_1(a21)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[352, 1349])).
% 1.05/0.95 tff(1354,plain,
% 1.05/0.95 (hskp24),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[720, 117, 1339, 1351, 1350, 1353, 714])).
% 1.05/0.95 tff(1355,plain,
% 1.05/0.95 (~c2_1(a52)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[726, 1354])).
% 1.05/0.95 tff(1356,plain,
% 1.05/0.95 (~c0_1(a52)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[732, 1354])).
% 1.05/0.95 tff(1357,plain,
% 1.05/0.95 (c3_1(a52)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[743, 1354])).
% 1.05/0.95 tff(1358,plain,
% 1.05/0.95 (~hskp10),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[573, 494, 321, 1])).
% 1.05/0.95 tff(1359,plain,
% 1.05/0.95 ($false),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[750, 117, 1358, 1357, 1351, 1356, 1355, 1353, 703, 1352])).
% 1.05/0.95 tff(1360,plain,((~hskp13) | c1_1(a13) | c2_1(a13) | hskp30 | c0_1(a13)), inference(lemma,lemma(discharge,[]))).
% 1.05/0.95 tff(1361,plain,
% 1.05/0.95 (~hskp13),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[1360, 322, 310, 1, 268])).
% 1.05/0.95 tff(1362,plain,
% 1.05/0.95 (hskp2),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[767, 1361, 1339])).
% 1.05/0.95 tff(1363,plain,
% 1.05/0.95 (~c0_1(a5)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[1250, 1362])).
% 1.05/0.95 tff(1364,plain,
% 1.05/0.95 (c2_1(a5)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[642, 1362])).
% 1.05/0.95 tff(1365,plain,
% 1.05/0.95 (hskp15 | c3_1(a5)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[589, 117, 494, 1364, 1363, 53])).
% 1.05/0.95 tff(1366,plain,
% 1.05/0.95 (c3_1(a5)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[1365, 77])).
% 1.05/0.95 tff(1367,plain,
% 1.05/0.95 (~c1_1(a5)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[1128, 1362])).
% 1.05/0.95 tff(1368,plain,
% 1.05/0.95 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a13) | c2_1(a13) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | c3_1(a13))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a13) | c2_1(a13) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | c3_1(a13))),
% 1.05/0.95 inference(rewrite,[status(thm)],[])).
% 1.05/0.95 tff(1369,plain,
% 1.05/0.95 ((hskp8 | (~ndr1_0) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)) | c3_1(a13) | c1_1(a13) | c2_1(a13)) <=> (hskp8 | c1_1(a13) | c2_1(a13) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | c3_1(a13))),
% 1.05/0.95 inference(rewrite,[status(thm)],[])).
% 1.05/0.95 tff(1370,plain,
% 1.05/0.95 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)) | c3_1(a13) | c1_1(a13) | c2_1(a13))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a13) | c2_1(a13) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | c3_1(a13)))),
% 1.05/0.95 inference(monotonicity,[status(thm)],[1369])).
% 1.05/0.95 tff(1371,plain,
% 1.05/0.95 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)) | c3_1(a13) | c1_1(a13) | c2_1(a13))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a13) | c2_1(a13) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | c3_1(a13))),
% 1.05/0.95 inference(transitivity,[status(thm)],[1370, 1368])).
% 1.05/0.95 tff(1372,plain,
% 1.05/0.95 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)) | c3_1(a13) | c1_1(a13) | c2_1(a13))),
% 1.05/0.95 inference(quant_inst,[status(thm)],[])).
% 1.05/0.95 tff(1373,plain,
% 1.05/0.95 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a13) | c2_1(a13) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | c3_1(a13)),
% 1.05/0.95 inference(modus_ponens,[status(thm)],[1372, 1371])).
% 1.05/0.95 tff(1374,plain,
% 1.05/0.95 ($false),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[1373, 117, 321, 310, 322, 575, 521, 31, 327, 1112])).
% 1.05/0.95 tff(1375,plain,(c3_1(a13) | c1_1(a13) | c2_1(a13) | (~c2_1(a5)) | c1_1(a5) | (~c3_1(a5))), inference(lemma,lemma(discharge,[]))).
% 1.05/0.95 tff(1376,plain,
% 1.05/0.95 (c3_1(a13)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[1375, 1366, 322, 1364, 1367, 310])).
% 1.05/0.95 tff(1377,plain,
% 1.05/0.95 (hskp11),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[346, 1376, 1, 322])).
% 1.05/0.95 tff(1378,plain,
% 1.05/0.95 (~c3_1(a21)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[352, 1377])).
% 1.05/0.95 tff(1379,plain,
% 1.05/0.95 (~c2_1(a21)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[358, 1377])).
% 1.05/0.95 tff(1380,plain,
% 1.05/0.95 (c1_1(a21)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[971, 117, 321, 1364, 1379, 1378, 1367, 31, 1366])).
% 1.05/0.95 tff(1381,plain,
% 1.05/0.95 (^[U: $i] : refl((hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))),
% 1.05/0.95 inference(bind,[status(th)],[])).
% 1.05/0.95 tff(1382,plain,
% 1.05/0.95 (![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.05/0.95 inference(quant_intro,[status(thm)],[1381])).
% 1.05/0.95 tff(1383,plain,
% 1.05/0.95 (![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.05/0.95 inference(rewrite,[status(thm)],[])).
% 1.05/0.95 tff(1384,plain,
% 1.05/0.95 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | 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)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp25) <=> (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp25) | hskp3) <=> ((hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp3))), rewrite(((hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp3) <=> (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp25) | hskp3) <=> (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))))),
% 1.05/0.95 inference(bind,[status(th)],[])).
% 1.05/0.95 tff(1385,plain,
% 1.05/0.95 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp25) | hskp3) <=> ![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.05/0.95 inference(quant_intro,[status(thm)],[1384])).
% 1.05/0.95 tff(1386,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp25) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause147')).
% 1.05/0.95 tff(1387,plain,
% 1.05/0.95 (![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.05/0.95 inference(modus_ponens,[status(thm)],[1386, 1385])).
% 1.05/0.95 tff(1388,plain,
% 1.05/0.95 (![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.05/0.95 inference(modus_ponens,[status(thm)],[1387, 1383])).
% 1.05/0.95 tff(1389,plain,(
% 1.05/0.95 ![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.05/0.95 inference(skolemize,[status(sab)],[1388])).
% 1.05/0.95 tff(1390,plain,
% 1.05/0.95 (![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.05/0.95 inference(modus_ponens,[status(thm)],[1389, 1382])).
% 1.05/0.95 tff(1391,plain,
% 1.05/0.95 (~hskp21),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[125, 77, 494])).
% 1.05/0.95 tff(1392,assumption,(hskp25), introduced(assumption)).
% 1.05/0.95 tff(1393,plain,
% 1.05/0.95 (((~hskp25) | (~c1_1(a54))) <=> ((~hskp25) | (~c1_1(a54)))),
% 1.05/0.95 inference(rewrite,[status(thm)],[])).
% 1.05/0.95 tff(1394,plain,
% 1.05/0.95 (((~c1_1(a54)) | (~hskp25)) <=> ((~hskp25) | (~c1_1(a54)))),
% 1.05/0.95 inference(rewrite,[status(thm)],[])).
% 1.05/0.95 tff(1395,axiom,((~c1_1(a54)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause92')).
% 1.05/0.95 tff(1396,plain,
% 1.05/0.95 ((~hskp25) | (~c1_1(a54))),
% 1.05/0.95 inference(modus_ponens,[status(thm)],[1395, 1394])).
% 1.05/0.95 tff(1397,plain,
% 1.05/0.95 ((~hskp25) | (~c1_1(a54))),
% 1.05/0.95 inference(modus_ponens,[status(thm)],[1396, 1393])).
% 1.05/0.95 tff(1398,plain,
% 1.05/0.95 (~c1_1(a54)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[1397, 1392])).
% 1.05/0.95 tff(1399,plain,
% 1.05/0.95 (((~hskp25) | c3_1(a54)) <=> ((~hskp25) | c3_1(a54))),
% 1.05/0.95 inference(rewrite,[status(thm)],[])).
% 1.05/0.95 tff(1400,axiom,((~hskp25) | c3_1(a54)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause53')).
% 1.05/0.95 tff(1401,plain,
% 1.05/0.95 ((~hskp25) | c3_1(a54)),
% 1.05/0.95 inference(modus_ponens,[status(thm)],[1400, 1399])).
% 1.05/0.95 tff(1402,plain,
% 1.05/0.95 ((~hskp25) | c3_1(a54)),
% 1.05/0.95 inference(modus_ponens,[status(thm)],[1401, 1399])).
% 1.05/0.95 tff(1403,plain,
% 1.05/0.95 ((~hskp25) | c3_1(a54)),
% 1.05/0.95 inference(modus_ponens,[status(thm)],[1402, 1399])).
% 1.05/0.95 tff(1404,plain,
% 1.05/0.95 ((~hskp25) | c3_1(a54)),
% 1.05/0.95 inference(modus_ponens,[status(thm)],[1403, 1399])).
% 1.05/0.95 tff(1405,plain,
% 1.05/0.95 ((~hskp25) | c3_1(a54)),
% 1.05/0.95 inference(modus_ponens,[status(thm)],[1404, 1399])).
% 1.05/0.95 tff(1406,plain,
% 1.05/0.95 ((~hskp25) | c3_1(a54)),
% 1.05/0.95 inference(modus_ponens,[status(thm)],[1405, 1399])).
% 1.05/0.95 tff(1407,plain,
% 1.05/0.95 ((~hskp25) | c3_1(a54)),
% 1.05/0.95 inference(modus_ponens,[status(thm)],[1406, 1399])).
% 1.05/0.95 tff(1408,plain,
% 1.05/0.95 ((~hskp25) | c3_1(a54)),
% 1.05/0.95 inference(modus_ponens,[status(thm)],[1407, 1399])).
% 1.05/0.95 tff(1409,plain,
% 1.05/0.95 (c3_1(a54)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[1408, 1392])).
% 1.05/0.95 tff(1410,plain,
% 1.05/0.95 (((~hskp25) | c0_1(a54)) <=> ((~hskp25) | c0_1(a54))),
% 1.05/0.95 inference(rewrite,[status(thm)],[])).
% 1.05/0.95 tff(1411,axiom,((~hskp25) | c0_1(a54)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause52')).
% 1.05/0.95 tff(1412,plain,
% 1.05/0.95 ((~hskp25) | c0_1(a54)),
% 1.05/0.95 inference(modus_ponens,[status(thm)],[1411, 1410])).
% 1.05/0.95 tff(1413,plain,
% 1.05/0.95 ((~hskp25) | c0_1(a54)),
% 1.05/0.95 inference(modus_ponens,[status(thm)],[1412, 1410])).
% 1.05/0.95 tff(1414,plain,
% 1.05/0.95 ((~hskp25) | c0_1(a54)),
% 1.05/0.95 inference(modus_ponens,[status(thm)],[1413, 1410])).
% 1.05/0.95 tff(1415,plain,
% 1.05/0.95 ((~hskp25) | c0_1(a54)),
% 1.05/0.95 inference(modus_ponens,[status(thm)],[1414, 1410])).
% 1.05/0.95 tff(1416,plain,
% 1.05/0.95 ((~hskp25) | c0_1(a54)),
% 1.05/0.95 inference(modus_ponens,[status(thm)],[1415, 1410])).
% 1.05/0.95 tff(1417,plain,
% 1.05/0.95 ((~hskp25) | c0_1(a54)),
% 1.05/0.95 inference(modus_ponens,[status(thm)],[1416, 1410])).
% 1.05/0.95 tff(1418,plain,
% 1.05/0.95 ((~hskp25) | c0_1(a54)),
% 1.05/0.95 inference(modus_ponens,[status(thm)],[1417, 1410])).
% 1.05/0.95 tff(1419,plain,
% 1.05/0.95 ((~hskp25) | c0_1(a54)),
% 1.05/0.95 inference(modus_ponens,[status(thm)],[1418, 1410])).
% 1.05/0.95 tff(1420,plain,
% 1.05/0.95 (c0_1(a54)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[1419, 1392])).
% 1.05/0.95 tff(1421,assumption,(~hskp21), introduced(assumption)).
% 1.05/0.95 tff(1422,plain,
% 1.05/0.95 (((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | c1_1(a54) | (~ndr1_0) | (~c0_1(a54)) | (~c3_1(a54)))) <=> ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp8 | c1_1(a54) | (~ndr1_0) | (~c0_1(a54)) | (~c3_1(a54)))),
% 1.05/0.95 inference(rewrite,[status(thm)],[])).
% 1.05/0.95 tff(1423,plain,
% 1.05/0.95 ((hskp21 | hskp8 | (~ndr1_0) | c1_1(a54) | (~c3_1(a54)) | (~c0_1(a54))) <=> (hskp21 | hskp8 | c1_1(a54) | (~ndr1_0) | (~c0_1(a54)) | (~c3_1(a54)))),
% 1.05/0.95 inference(rewrite,[status(thm)],[])).
% 1.05/0.95 tff(1424,plain,
% 1.05/0.95 (((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | (~ndr1_0) | c1_1(a54) | (~c3_1(a54)) | (~c0_1(a54)))) <=> ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | c1_1(a54) | (~ndr1_0) | (~c0_1(a54)) | (~c3_1(a54))))),
% 1.05/0.95 inference(monotonicity,[status(thm)],[1423])).
% 1.05/0.95 tff(1425,plain,
% 1.05/0.95 (((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | (~ndr1_0) | c1_1(a54) | (~c3_1(a54)) | (~c0_1(a54)))) <=> ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp8 | c1_1(a54) | (~ndr1_0) | (~c0_1(a54)) | (~c3_1(a54)))),
% 1.05/0.95 inference(transitivity,[status(thm)],[1424, 1422])).
% 1.05/0.95 tff(1426,plain,
% 1.05/0.95 ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | (~ndr1_0) | c1_1(a54) | (~c3_1(a54)) | (~c0_1(a54)))),
% 1.05/0.95 inference(quant_inst,[status(thm)],[])).
% 1.05/0.95 tff(1427,plain,
% 1.05/0.95 ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp8 | c1_1(a54) | (~ndr1_0) | (~c0_1(a54)) | (~c3_1(a54))),
% 1.05/0.95 inference(modus_ponens,[status(thm)],[1426, 1425])).
% 1.05/0.95 tff(1428,plain,
% 1.05/0.95 ($false),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[1427, 117, 1421, 523, 1420, 1409, 1398, 21])).
% 1.05/0.95 tff(1429,plain,((~hskp25) | hskp21 | hskp8), inference(lemma,lemma(discharge,[]))).
% 1.05/0.95 tff(1430,plain,
% 1.05/0.95 (~hskp25),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[1429, 1391, 321])).
% 1.05/0.95 tff(1431,plain,
% 1.05/0.95 (((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | hskp3 | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c1_1(a21)))) <=> ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp25 | hskp3 | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c1_1(a21)))),
% 1.05/0.95 inference(rewrite,[status(thm)],[])).
% 1.05/0.95 tff(1432,plain,
% 1.05/0.95 ((hskp25 | hskp3 | (~ndr1_0) | c2_1(a21) | c3_1(a21) | (~c1_1(a21))) <=> (hskp25 | hskp3 | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c1_1(a21)))),
% 1.05/0.95 inference(rewrite,[status(thm)],[])).
% 1.05/0.95 tff(1433,plain,
% 1.05/0.95 (((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | hskp3 | (~ndr1_0) | c2_1(a21) | c3_1(a21) | (~c1_1(a21)))) <=> ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | hskp3 | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c1_1(a21))))),
% 1.05/0.95 inference(monotonicity,[status(thm)],[1432])).
% 1.05/0.95 tff(1434,plain,
% 1.05/0.95 (((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | hskp3 | (~ndr1_0) | c2_1(a21) | c3_1(a21) | (~c1_1(a21)))) <=> ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp25 | hskp3 | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c1_1(a21)))),
% 1.05/0.95 inference(transitivity,[status(thm)],[1433, 1431])).
% 1.05/0.95 tff(1435,plain,
% 1.05/0.95 ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | hskp3 | (~ndr1_0) | c2_1(a21) | c3_1(a21) | (~c1_1(a21)))),
% 1.05/0.95 inference(quant_inst,[status(thm)],[])).
% 1.05/0.95 tff(1436,plain,
% 1.05/0.95 ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp25 | hskp3 | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c1_1(a21))),
% 1.05/0.95 inference(modus_ponens,[status(thm)],[1435, 1434])).
% 1.05/0.95 tff(1437,plain,
% 1.05/0.95 ($false),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[1436, 117, 1430, 1339, 1379, 1378, 1390, 1380])).
% 1.05/0.95 tff(1438,plain,(hskp15 | hskp30 | c2_1(a13) | c0_1(a13) | c1_1(a13)), inference(lemma,lemma(discharge,[]))).
% 1.05/0.95 tff(1439,plain,
% 1.05/0.95 (hskp15),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[1438, 322, 1, 268, 310])).
% 1.05/0.95 tff(1440,plain,
% 1.05/0.95 (~c2_1(a29)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[148, 1439])).
% 1.05/0.95 tff(1441,plain,
% 1.05/0.95 (~c3_1(a29)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[142, 1439])).
% 1.05/0.95 tff(1442,plain,
% 1.05/0.95 (hskp15),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[125, 42, 43])).
% 1.05/0.95 tff(1443,plain,
% 1.05/0.95 (c1_1(a29)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[136, 1442])).
% 1.05/0.95 tff(1444,plain,
% 1.05/0.95 (c0_1(a29)),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[988, 1443])).
% 1.05/0.95 tff(1445,plain,
% 1.05/0.95 ($false),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[171, 1444, 1443, 162, 161, 42])).
% 1.05/0.95 tff(1446,plain,((~hskp21) | c2_1(a29) | c3_1(a29) | hskp30 | hskp8 | hskp16), inference(lemma,lemma(discharge,[]))).
% 1.05/0.95 tff(1447,plain,
% 1.05/0.95 (~hskp21),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[1446, 161, 43, 1, 523, 162])).
% 1.05/0.95 tff(1448,plain,
% 1.05/0.95 (~hskp25),
% 1.05/0.95 inference(unit_resolution,[status(thm)],[1429, 1447, 523])).
% 1.05/0.95 tff(1449,plain,
% 1.05/0.95 (((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | hskp3 | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)))) <=> ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp25 | hskp3 | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)))),
% 1.05/0.95 inference(rewrite,[status(thm)],[])).
% 1.05/0.95 tff(1450,plain,
% 1.05/0.95 ((hskp25 | hskp3 | (~ndr1_0) | c2_1(a29) | c3_1(a29) | (~c1_1(a29))) <=> (hskp25 | hskp3 | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)))),
% 1.05/0.96 inference(rewrite,[status(thm)],[])).
% 1.05/0.96 tff(1451,plain,
% 1.05/0.96 (((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | hskp3 | (~ndr1_0) | c2_1(a29) | c3_1(a29) | (~c1_1(a29)))) <=> ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | hskp3 | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29))))),
% 1.05/0.96 inference(monotonicity,[status(thm)],[1450])).
% 1.05/0.96 tff(1452,plain,
% 1.05/0.96 (((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | hskp3 | (~ndr1_0) | c2_1(a29) | c3_1(a29) | (~c1_1(a29)))) <=> ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp25 | hskp3 | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)))),
% 1.05/0.96 inference(transitivity,[status(thm)],[1451, 1449])).
% 1.05/0.96 tff(1453,plain,
% 1.05/0.96 ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | hskp3 | (~ndr1_0) | c2_1(a29) | c3_1(a29) | (~c1_1(a29)))),
% 1.05/0.96 inference(quant_inst,[status(thm)],[])).
% 1.05/0.96 tff(1454,plain,
% 1.05/0.96 ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp25 | hskp3 | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29))),
% 1.05/0.96 inference(modus_ponens,[status(thm)],[1453, 1452])).
% 1.05/0.96 tff(1455,plain,
% 1.05/0.96 (hskp25 | hskp3 | c3_1(a29) | (~c1_1(a29))),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[1454, 117, 162, 1390])).
% 1.05/0.96 tff(1456,plain,
% 1.05/0.96 (~c1_1(a29)),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[1455, 522, 1448, 161])).
% 1.05/0.96 tff(1457,plain,
% 1.05/0.96 (~c2_1(a26)),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[985, 117, 523, 1001, 663, 162, 161, 652, 31])).
% 1.05/0.96 tff(1458,plain,
% 1.05/0.96 (hskp11),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[683, 1457])).
% 1.05/0.96 tff(1459,plain,
% 1.05/0.96 (~c2_1(a21)),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[358, 1458])).
% 1.05/0.96 tff(1460,plain,
% 1.05/0.96 (c0_1(a21)),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[386, 1458])).
% 1.05/0.96 tff(1461,plain,
% 1.05/0.96 (~c1_1(a21)),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[692, 117, 522, 663, 1460, 676, 652, 1459, 426])).
% 1.05/0.96 tff(1462,plain,
% 1.05/0.96 (~c3_1(a21)),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[352, 1458])).
% 1.05/0.96 tff(1463,plain,
% 1.05/0.96 (hskp24),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[720, 117, 522, 1460, 1459, 1462, 714])).
% 1.05/0.96 tff(1464,plain,
% 1.05/0.96 (~c2_1(a52)),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[726, 1463])).
% 1.05/0.96 tff(1465,plain,
% 1.05/0.96 (~c0_1(a52)),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[732, 1463])).
% 1.05/0.96 tff(1466,plain,
% 1.05/0.96 (c3_1(a52)),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[743, 1463])).
% 1.05/0.96 tff(1467,plain,
% 1.05/0.96 ($false),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[750, 117, 645, 1466, 1460, 1465, 1464, 1462, 703, 1461])).
% 1.05/0.96 tff(1468,plain,((~hskp13) | hskp10 | hskp3 | hskp30 | hskp8 | c1_1(a29) | c2_1(a29) | c3_1(a29)), inference(lemma,lemma(discharge,[]))).
% 1.05/0.96 tff(1469,plain,
% 1.05/0.96 (~hskp13),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[1468, 522, 977, 1, 523, 1456, 162, 161])).
% 1.05/0.96 tff(1470,plain,
% 1.05/0.96 (hskp2),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[767, 1469, 522])).
% 1.05/0.96 tff(1471,plain,
% 1.05/0.96 (~c0_1(a5)),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[1250, 1470])).
% 1.05/0.96 tff(1472,plain,
% 1.05/0.96 (c2_1(a5)),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[642, 1470])).
% 1.05/0.96 tff(1473,plain,
% 1.05/0.96 (~c1_1(a5)),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[1128, 1470])).
% 1.05/0.96 tff(1474,plain,
% 1.05/0.96 ($false),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[1012, 1473, 1472, 43, 162, 523, 1456, 161, 1471])).
% 1.05/0.96 tff(1475,plain,(hskp3 | hskp16 | c2_1(a29) | hskp8 | c3_1(a29) | hskp30), inference(lemma,lemma(discharge,[]))).
% 1.05/0.96 tff(1476,plain,
% 1.05/0.96 ($false),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[1475, 1441, 1440, 1339, 321, 494, 1])).
% 1.05/0.96 tff(1477,plain,(c2_1(a13) | hskp30 | c0_1(a13) | c1_1(a13)), inference(lemma,lemma(discharge,[]))).
% 1.05/0.96 tff(1478,plain,
% 1.05/0.96 (c2_1(a13)),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[1477, 310, 268, 1])).
% 1.05/0.96 tff(1479,plain,
% 1.05/0.96 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp15 | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp15 | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)))),
% 1.05/0.96 inference(rewrite,[status(thm)],[])).
% 1.05/0.96 tff(1480,plain,
% 1.05/0.96 ((hskp16 | hskp15 | (~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c2_1(a13))) <=> (hskp16 | hskp15 | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)))),
% 1.05/0.96 inference(rewrite,[status(thm)],[])).
% 1.05/0.96 tff(1481,plain,
% 1.05/0.96 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c2_1(a13)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp15 | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13))))),
% 1.05/0.96 inference(monotonicity,[status(thm)],[1480])).
% 1.05/0.96 tff(1482,plain,
% 1.05/0.96 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c2_1(a13)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp15 | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)))),
% 1.05/0.96 inference(transitivity,[status(thm)],[1481, 1479])).
% 1.05/0.96 tff(1483,plain,
% 1.05/0.96 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c2_1(a13)))),
% 1.05/0.96 inference(quant_inst,[status(thm)],[])).
% 1.05/0.96 tff(1484,plain,
% 1.05/0.96 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp15 | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13))),
% 1.05/0.96 inference(modus_ponens,[status(thm)],[1483, 1482])).
% 1.05/0.96 tff(1485,plain,
% 1.05/0.96 (hskp16 | hskp15 | c3_1(a13) | (~c2_1(a13))),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[1484, 117, 268, 53])).
% 1.05/0.96 tff(1486,plain,
% 1.05/0.96 (c3_1(a13)),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[1485, 77, 1478, 43])).
% 1.05/0.96 tff(1487,assumption,(hskp24), introduced(assumption)).
% 1.05/0.96 tff(1488,plain,
% 1.05/0.96 (~c2_1(a52)),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[726, 1487])).
% 1.05/0.96 tff(1489,plain,
% 1.05/0.96 (~c0_1(a52)),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[732, 1487])).
% 1.05/0.96 tff(1490,plain,
% 1.05/0.96 (c3_1(a52)),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[743, 1487])).
% 1.05/0.96 tff(1491,plain,
% 1.05/0.96 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | c0_1(a52) | c2_1(a52) | (~ndr1_0) | (~c3_1(a52)))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c0_1(a52) | c2_1(a52) | (~ndr1_0) | (~c3_1(a52)))),
% 1.05/0.96 inference(rewrite,[status(thm)],[])).
% 1.05/0.96 tff(1492,plain,
% 1.05/0.96 ((hskp30 | hskp11 | (~ndr1_0) | c2_1(a52) | c0_1(a52) | (~c3_1(a52))) <=> (hskp30 | hskp11 | c0_1(a52) | c2_1(a52) | (~ndr1_0) | (~c3_1(a52)))),
% 1.05/0.96 inference(rewrite,[status(thm)],[])).
% 1.05/0.96 tff(1493,plain,
% 1.05/0.96 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a52) | c0_1(a52) | (~c3_1(a52)))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | c0_1(a52) | c2_1(a52) | (~ndr1_0) | (~c3_1(a52))))),
% 1.05/0.96 inference(monotonicity,[status(thm)],[1492])).
% 1.05/0.96 tff(1494,plain,
% 1.05/0.96 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a52) | c0_1(a52) | (~c3_1(a52)))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c0_1(a52) | c2_1(a52) | (~ndr1_0) | (~c3_1(a52)))),
% 1.05/0.96 inference(transitivity,[status(thm)],[1493, 1491])).
% 1.05/0.96 tff(1495,plain,
% 1.05/0.96 ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a52) | c0_1(a52) | (~c3_1(a52)))),
% 1.05/0.96 inference(quant_inst,[status(thm)],[])).
% 1.05/0.96 tff(1496,plain,
% 1.05/0.96 ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c0_1(a52) | c2_1(a52) | (~ndr1_0) | (~c3_1(a52))),
% 1.05/0.96 inference(modus_ponens,[status(thm)],[1495, 1494])).
% 1.05/0.96 tff(1497,plain,
% 1.05/0.96 ($false),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[1496, 117, 1, 1340, 1490, 1489, 1488, 41])).
% 1.05/0.96 tff(1498,plain,((~hskp24) | hskp30 | hskp11), inference(lemma,lemma(discharge,[]))).
% 1.05/0.96 tff(1499,plain,
% 1.05/0.96 (~hskp24),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[1498, 1340, 1])).
% 1.05/0.96 tff(1500,plain,
% 1.05/0.96 ((hskp24 | hskp21 | hskp5) <=> (hskp24 | hskp21 | hskp5)),
% 1.05/0.96 inference(rewrite,[status(thm)],[])).
% 1.05/0.96 tff(1501,plain,
% 1.05/0.96 (((hskp21 | hskp24) | hskp5) <=> (hskp24 | hskp21 | hskp5)),
% 1.05/0.96 inference(rewrite,[status(thm)],[])).
% 1.05/0.96 tff(1502,axiom,((hskp21 | hskp24) | hskp5), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause38')).
% 1.05/0.96 tff(1503,plain,
% 1.05/0.96 (hskp24 | hskp21 | hskp5),
% 1.05/0.96 inference(modus_ponens,[status(thm)],[1502, 1501])).
% 1.05/0.96 tff(1504,plain,
% 1.05/0.96 (hskp24 | hskp21 | hskp5),
% 1.05/0.96 inference(modus_ponens,[status(thm)],[1503, 1500])).
% 1.05/0.96 tff(1505,plain,
% 1.05/0.96 (hskp24 | hskp21 | hskp5),
% 1.05/0.96 inference(modus_ponens,[status(thm)],[1504, 1500])).
% 1.05/0.96 tff(1506,plain,
% 1.05/0.96 (hskp24 | hskp21 | hskp5),
% 1.05/0.96 inference(modus_ponens,[status(thm)],[1505, 1500])).
% 1.05/0.96 tff(1507,plain,
% 1.05/0.96 (hskp24 | hskp21 | hskp5),
% 1.05/0.96 inference(modus_ponens,[status(thm)],[1506, 1500])).
% 1.05/0.96 tff(1508,plain,
% 1.05/0.96 (hskp24 | hskp21 | hskp5),
% 1.05/0.96 inference(modus_ponens,[status(thm)],[1507, 1500])).
% 1.05/0.96 tff(1509,plain,
% 1.05/0.96 (hskp24 | hskp21 | hskp5),
% 1.05/0.96 inference(modus_ponens,[status(thm)],[1508, 1500])).
% 1.05/0.96 tff(1510,plain,
% 1.05/0.96 (hskp24 | hskp21 | hskp5),
% 1.05/0.96 inference(modus_ponens,[status(thm)],[1509, 1500])).
% 1.05/0.96 tff(1511,plain,
% 1.05/0.96 (hskp5),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[1510, 1499, 1421])).
% 1.05/0.96 tff(1512,plain,
% 1.05/0.96 (((~hskp5) | (~c2_1(a9))) <=> ((~hskp5) | (~c2_1(a9)))),
% 1.05/0.96 inference(rewrite,[status(thm)],[])).
% 1.05/0.96 tff(1513,plain,
% 1.05/0.96 (((~c2_1(a9)) | (~hskp5)) <=> ((~hskp5) | (~c2_1(a9)))),
% 1.05/0.96 inference(rewrite,[status(thm)],[])).
% 1.05/0.96 tff(1514,axiom,((~c2_1(a9)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause127')).
% 1.05/0.96 tff(1515,plain,
% 1.05/0.96 ((~hskp5) | (~c2_1(a9))),
% 1.05/0.96 inference(modus_ponens,[status(thm)],[1514, 1513])).
% 1.05/0.96 tff(1516,plain,
% 1.05/0.96 ((~hskp5) | (~c2_1(a9))),
% 1.05/0.96 inference(modus_ponens,[status(thm)],[1515, 1512])).
% 1.05/0.96 tff(1517,plain,
% 1.05/0.96 (~c2_1(a9)),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[1516, 1511])).
% 1.05/0.96 tff(1518,plain,
% 1.05/0.96 (((~hskp5) | (~c0_1(a9))) <=> ((~hskp5) | (~c0_1(a9)))),
% 1.05/0.96 inference(rewrite,[status(thm)],[])).
% 1.05/0.96 tff(1519,plain,
% 1.05/0.96 (((~c0_1(a9)) | (~hskp5)) <=> ((~hskp5) | (~c0_1(a9)))),
% 1.05/0.96 inference(rewrite,[status(thm)],[])).
% 1.05/0.96 tff(1520,axiom,((~c0_1(a9)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause125')).
% 1.05/0.96 tff(1521,plain,
% 1.05/0.96 ((~hskp5) | (~c0_1(a9))),
% 1.05/0.96 inference(modus_ponens,[status(thm)],[1520, 1519])).
% 1.05/0.96 tff(1522,plain,
% 1.05/0.96 ((~hskp5) | (~c0_1(a9))),
% 1.05/0.96 inference(modus_ponens,[status(thm)],[1521, 1518])).
% 1.05/0.96 tff(1523,plain,
% 1.05/0.96 (~c0_1(a9)),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[1522, 1511])).
% 1.05/0.96 tff(1524,plain,
% 1.05/0.96 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | c0_1(a9) | c2_1(a9) | (~ndr1_0) | (~c3_1(a9)))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c0_1(a9) | c2_1(a9) | (~ndr1_0) | (~c3_1(a9)))),
% 1.05/0.96 inference(rewrite,[status(thm)],[])).
% 1.05/0.96 tff(1525,plain,
% 1.05/0.96 ((hskp30 | hskp11 | (~ndr1_0) | c2_1(a9) | c0_1(a9) | (~c3_1(a9))) <=> (hskp30 | hskp11 | c0_1(a9) | c2_1(a9) | (~ndr1_0) | (~c3_1(a9)))),
% 1.05/0.96 inference(rewrite,[status(thm)],[])).
% 1.05/0.96 tff(1526,plain,
% 1.05/0.96 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a9) | c0_1(a9) | (~c3_1(a9)))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | c0_1(a9) | c2_1(a9) | (~ndr1_0) | (~c3_1(a9))))),
% 1.05/0.96 inference(monotonicity,[status(thm)],[1525])).
% 1.05/0.96 tff(1527,plain,
% 1.05/0.96 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a9) | c0_1(a9) | (~c3_1(a9)))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c0_1(a9) | c2_1(a9) | (~ndr1_0) | (~c3_1(a9)))),
% 1.05/0.96 inference(transitivity,[status(thm)],[1526, 1524])).
% 1.05/0.96 tff(1528,plain,
% 1.05/0.96 ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a9) | c0_1(a9) | (~c3_1(a9)))),
% 1.05/0.96 inference(quant_inst,[status(thm)],[])).
% 1.05/0.96 tff(1529,plain,
% 1.05/0.96 ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c0_1(a9) | c2_1(a9) | (~ndr1_0) | (~c3_1(a9))),
% 1.05/0.96 inference(modus_ponens,[status(thm)],[1528, 1527])).
% 1.05/0.96 tff(1530,plain,
% 1.05/0.96 (~c3_1(a9)),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[1529, 117, 1, 1340, 1523, 1517, 41])).
% 1.05/0.96 tff(1531,assumption,(c3_1(a13)), introduced(assumption)).
% 1.05/0.96 tff(1532,plain,
% 1.05/0.96 (((~hskp5) | (~c1_1(a9))) <=> ((~hskp5) | (~c1_1(a9)))),
% 1.05/0.96 inference(rewrite,[status(thm)],[])).
% 1.05/0.96 tff(1533,plain,
% 1.05/0.96 (((~c1_1(a9)) | (~hskp5)) <=> ((~hskp5) | (~c1_1(a9)))),
% 1.05/0.96 inference(rewrite,[status(thm)],[])).
% 1.05/0.96 tff(1534,axiom,((~c1_1(a9)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause126')).
% 1.05/0.96 tff(1535,plain,
% 1.05/0.96 ((~hskp5) | (~c1_1(a9))),
% 1.05/0.96 inference(modus_ponens,[status(thm)],[1534, 1533])).
% 1.05/0.96 tff(1536,plain,
% 1.05/0.96 ((~hskp5) | (~c1_1(a9))),
% 1.05/0.96 inference(modus_ponens,[status(thm)],[1535, 1532])).
% 1.05/0.96 tff(1537,plain,
% 1.05/0.96 (~c1_1(a9)),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[1536, 1511])).
% 1.05/0.96 tff(1538,assumption,(c2_1(a13)), introduced(assumption)).
% 1.05/0.96 tff(1539,plain,
% 1.05/0.96 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a13) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | c3_1(a9) | (~c3_1(a13)) | (~c2_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a13) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | c3_1(a9) | (~c3_1(a13)) | (~c2_1(a13)))),
% 1.05/0.96 inference(rewrite,[status(thm)],[])).
% 1.05/0.96 tff(1540,plain,
% 1.05/0.96 ((hskp8 | (~ndr1_0) | c1_1(a13) | (~c3_1(a13)) | (~c2_1(a13)) | c3_1(a9) | c1_1(a9) | c2_1(a9)) <=> (hskp8 | c1_1(a13) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | c3_1(a9) | (~c3_1(a13)) | (~c2_1(a13)))),
% 1.05/0.96 inference(rewrite,[status(thm)],[])).
% 1.05/0.96 tff(1541,plain,
% 1.05/0.96 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a13) | (~c3_1(a13)) | (~c2_1(a13)) | c3_1(a9) | c1_1(a9) | c2_1(a9))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a13) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | c3_1(a9) | (~c3_1(a13)) | (~c2_1(a13))))),
% 1.05/0.96 inference(monotonicity,[status(thm)],[1540])).
% 1.05/0.96 tff(1542,plain,
% 1.05/0.96 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a13) | (~c3_1(a13)) | (~c2_1(a13)) | c3_1(a9) | c1_1(a9) | c2_1(a9))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a13) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | c3_1(a9) | (~c3_1(a13)) | (~c2_1(a13)))),
% 1.05/0.96 inference(transitivity,[status(thm)],[1541, 1539])).
% 1.05/0.96 tff(1543,plain,
% 1.05/0.96 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a13) | (~c3_1(a13)) | (~c2_1(a13)) | c3_1(a9) | c1_1(a9) | c2_1(a9))),
% 1.05/0.96 inference(quant_inst,[status(thm)],[])).
% 1.05/0.96 tff(1544,plain,
% 1.05/0.96 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a13) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | c3_1(a9) | (~c3_1(a13)) | (~c2_1(a13))),
% 1.05/0.96 inference(modus_ponens,[status(thm)],[1543, 1542])).
% 1.05/0.96 tff(1545,plain,
% 1.05/0.96 ($false),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[1544, 117, 321, 310, 1538, 1537, 1517, 31, 1531, 1530])).
% 1.05/0.96 tff(1546,plain,(hskp11 | c1_1(a13) | (~c2_1(a13)) | (~c3_1(a13)) | hskp30 | hskp21), inference(lemma,lemma(discharge,[]))).
% 1.05/0.96 tff(1547,plain,
% 1.05/0.96 (hskp11),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[1546, 1486, 1478, 310, 1, 939])).
% 1.05/0.96 tff(1548,plain,
% 1.05/0.96 (~c2_1(a21)),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[358, 1547])).
% 1.05/0.96 tff(1549,plain,
% 1.05/0.96 (c0_1(a21)),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[386, 1547])).
% 1.05/0.96 tff(1550,plain,
% 1.05/0.96 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c1_1(a13) | c2_1(a21) | (~ndr1_0) | (~c3_1(a13)) | (~c2_1(a13)) | (~c1_1(a21)) | (~c0_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a13) | c2_1(a21) | (~ndr1_0) | (~c3_1(a13)) | (~c2_1(a13)) | (~c1_1(a21)) | (~c0_1(a21)))),
% 1.05/0.96 inference(rewrite,[status(thm)],[])).
% 1.05/0.96 tff(1551,plain,
% 1.05/0.96 ((hskp15 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a13) | (~c3_1(a13)) | (~c2_1(a13))) <=> (hskp15 | c1_1(a13) | c2_1(a21) | (~ndr1_0) | (~c3_1(a13)) | (~c2_1(a13)) | (~c1_1(a21)) | (~c0_1(a21)))),
% 1.05/0.96 inference(rewrite,[status(thm)],[])).
% 1.05/0.96 tff(1552,plain,
% 1.05/0.96 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a13) | (~c3_1(a13)) | (~c2_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c1_1(a13) | c2_1(a21) | (~ndr1_0) | (~c3_1(a13)) | (~c2_1(a13)) | (~c1_1(a21)) | (~c0_1(a21))))),
% 1.05/0.96 inference(monotonicity,[status(thm)],[1551])).
% 1.05/0.96 tff(1553,plain,
% 1.05/0.96 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a13) | (~c3_1(a13)) | (~c2_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a13) | c2_1(a21) | (~ndr1_0) | (~c3_1(a13)) | (~c2_1(a13)) | (~c1_1(a21)) | (~c0_1(a21)))),
% 1.05/0.96 inference(transitivity,[status(thm)],[1552, 1550])).
% 1.05/0.96 tff(1554,plain,
% 1.05/0.96 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a13) | (~c3_1(a13)) | (~c2_1(a13)))),
% 1.05/0.96 inference(quant_inst,[status(thm)],[])).
% 1.05/0.96 tff(1555,plain,
% 1.05/0.96 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a13) | c2_1(a21) | (~ndr1_0) | (~c3_1(a13)) | (~c2_1(a13)) | (~c1_1(a21)) | (~c0_1(a21))),
% 1.05/0.96 inference(modus_ponens,[status(thm)],[1554, 1553])).
% 1.05/0.96 tff(1556,plain,
% 1.05/0.96 (~c1_1(a21)),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[1555, 117, 77, 1549, 310, 1478, 1548, 376, 1486])).
% 1.05/0.96 tff(1557,plain,
% 1.05/0.96 (~c3_1(a21)),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[352, 1547])).
% 1.05/0.96 tff(1558,plain,
% 1.05/0.96 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a13) | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c3_1(a13)) | (~c2_1(a13)) | c1_1(a21))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a13) | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c3_1(a13)) | (~c2_1(a13)) | c1_1(a21))),
% 1.05/0.96 inference(rewrite,[status(thm)],[])).
% 1.05/0.96 tff(1559,plain,
% 1.05/0.96 ((hskp8 | (~ndr1_0) | c1_1(a13) | (~c3_1(a13)) | (~c2_1(a13)) | c3_1(a21) | c1_1(a21) | c2_1(a21)) <=> (hskp8 | c1_1(a13) | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c3_1(a13)) | (~c2_1(a13)) | c1_1(a21))),
% 1.05/0.96 inference(rewrite,[status(thm)],[])).
% 1.05/0.96 tff(1560,plain,
% 1.05/0.96 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a13) | (~c3_1(a13)) | (~c2_1(a13)) | c3_1(a21) | c1_1(a21) | c2_1(a21))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a13) | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c3_1(a13)) | (~c2_1(a13)) | c1_1(a21)))),
% 1.05/0.96 inference(monotonicity,[status(thm)],[1559])).
% 1.05/0.96 tff(1561,plain,
% 1.05/0.96 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a13) | (~c3_1(a13)) | (~c2_1(a13)) | c3_1(a21) | c1_1(a21) | c2_1(a21))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a13) | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c3_1(a13)) | (~c2_1(a13)) | c1_1(a21))),
% 1.05/0.96 inference(transitivity,[status(thm)],[1560, 1558])).
% 1.05/0.96 tff(1562,plain,
% 1.05/0.96 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a13) | (~c3_1(a13)) | (~c2_1(a13)) | c3_1(a21) | c1_1(a21) | c2_1(a21))),
% 1.05/0.96 inference(quant_inst,[status(thm)],[])).
% 1.05/0.96 tff(1563,plain,
% 1.05/0.96 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a13) | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c3_1(a13)) | (~c2_1(a13)) | c1_1(a21)),
% 1.05/0.96 inference(modus_ponens,[status(thm)],[1562, 1561])).
% 1.05/0.96 tff(1564,plain,
% 1.05/0.96 ($false),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[1563, 117, 321, 310, 1478, 1548, 1557, 31, 1486, 1556])).
% 1.05/0.96 tff(1565,plain,(hskp15 | c1_1(a13) | hskp30 | hskp16 | c0_1(a13)), inference(lemma,lemma(discharge,[]))).
% 1.05/0.96 tff(1566,plain,
% 1.05/0.96 (hskp15),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[1565, 43, 1, 310, 268])).
% 1.05/0.96 tff(1567,plain,
% 1.05/0.96 (~c2_1(a29)),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[148, 1566])).
% 1.05/0.96 tff(1568,plain,
% 1.05/0.96 (~c3_1(a29)),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[142, 1566])).
% 1.05/0.96 tff(1569,plain,
% 1.05/0.96 (hskp3),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[1475, 1568, 1567, 321, 43, 1])).
% 1.05/0.96 tff(1570,plain,
% 1.05/0.96 (hskp9),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[1338, 1569, 1, 43, 321])).
% 1.05/0.96 tff(1571,plain,
% 1.05/0.96 (~c3_1(a15)),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[1048, 1570])).
% 1.05/0.96 tff(1572,plain,
% 1.05/0.96 (~c2_1(a6)),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[484, 1569])).
% 1.05/0.96 tff(1573,plain,
% 1.05/0.96 (c0_1(a6)),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[455, 1569])).
% 1.05/0.96 tff(1574,plain,
% 1.05/0.96 (c3_1(a6)),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[444, 1569])).
% 1.05/0.96 tff(1575,plain,
% 1.05/0.96 (hskp2),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[1306, 1574, 321, 1, 43, 1573, 1572])).
% 1.05/0.96 tff(1576,plain,
% 1.05/0.96 (~c1_1(a5)),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[1128, 1575])).
% 1.05/0.96 tff(1577,plain,
% 1.05/0.96 (~c1_1(a15)),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[500, 1570])).
% 1.05/0.96 tff(1578,plain,
% 1.05/0.96 (~c2_1(a15)),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[506, 1570])).
% 1.05/0.96 tff(1579,plain,
% 1.05/0.96 (~c0_1(a5)),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[1250, 1575])).
% 1.05/0.96 tff(1580,plain,
% 1.05/0.96 ($false),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[885, 1579, 1578, 321, 1577, 1576, 1571, 1])).
% 1.05/0.96 tff(1581,plain,(hskp16 | hskp30 | c1_1(a13) | c0_1(a13)), inference(lemma,lemma(discharge,[]))).
% 1.05/0.96 tff(1582,plain,
% 1.05/0.96 (hskp16),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[1581, 310, 1, 268])).
% 1.05/0.96 tff(1583,plain,
% 1.05/0.96 (~c1_1(a30)),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[244, 1582])).
% 1.05/0.96 tff(1584,plain,
% 1.05/0.96 (c3_1(a30)),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[266, 1582])).
% 1.05/0.96 tff(1585,plain,
% 1.05/0.96 (c2_1(a30)),
% 1.05/0.96 inference(unit_resolution,[status(thm)],[255, 1582])).
% 1.05/0.96 tff(1586,plain,
% 1.05/0.96 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))),
% 1.05/0.96 inference(bind,[status(th)],[])).
% 1.05/0.96 tff(1587,plain,
% 1.05/0.96 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.05/0.96 inference(quant_intro,[status(thm)],[1586])).
% 1.05/0.96 tff(1588,plain,
% 1.05/0.96 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.05/0.96 inference(rewrite,[status(thm)],[])).
% 1.05/0.96 tff(1589,plain,
% 1.05/0.96 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp8) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp8))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))))),
% 1.05/0.96 inference(bind,[status(th)],[])).
% 1.05/0.96 tff(1590,plain,
% 1.05/0.96 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.05/0.96 inference(quant_intro,[status(thm)],[1589])).
% 1.05/0.96 tff(1591,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause178')).
% 1.05/0.96 tff(1592,plain,
% 1.05/0.96 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.05/0.96 inference(modus_ponens,[status(thm)],[1591, 1590])).
% 1.05/0.96 tff(1593,plain,
% 1.05/0.96 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.05/0.96 inference(modus_ponens,[status(thm)],[1592, 1588])).
% 1.05/0.96 tff(1594,plain,(
% 1.05/0.96 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.05/0.96 inference(skolemize,[status(sab)],[1593])).
% 1.05/0.96 tff(1595,plain,
% 1.05/0.96 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.05/0.96 inference(modus_ponens,[status(thm)],[1594, 1587])).
% 1.05/0.96 tff(1596,plain,
% 1.05/0.96 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | c1_1(a30) | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)) | (~c2_1(a30)) | (~c3_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c1_1(a30) | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)) | (~c2_1(a30)) | (~c3_1(a30)))),
% 1.05/0.96 inference(rewrite,[status(thm)],[])).
% 1.05/0.96 tff(1597,plain,
% 1.05/0.96 ((hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13))) <=> (hskp8 | c1_1(a30) | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)) | (~c2_1(a30)) | (~c3_1(a30)))),
% 1.05/0.97 inference(rewrite,[status(thm)],[])).
% 1.05/0.97 tff(1598,plain,
% 1.05/0.97 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | c1_1(a30) | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)) | (~c2_1(a30)) | (~c3_1(a30))))),
% 1.05/0.97 inference(monotonicity,[status(thm)],[1597])).
% 1.05/0.97 tff(1599,plain,
% 1.05/0.97 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c1_1(a30) | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)) | (~c2_1(a30)) | (~c3_1(a30)))),
% 1.05/0.97 inference(transitivity,[status(thm)],[1598, 1596])).
% 1.05/0.97 tff(1600,plain,
% 1.05/0.97 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13)))),
% 1.05/0.97 inference(quant_inst,[status(thm)],[])).
% 1.05/0.97 tff(1601,plain,
% 1.05/0.97 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c1_1(a30) | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)) | (~c2_1(a30)) | (~c3_1(a30))),
% 1.05/0.97 inference(modus_ponens,[status(thm)],[1600, 1599])).
% 1.05/0.97 tff(1602,plain,
% 1.05/0.97 ($false),
% 1.05/0.97 inference(unit_resolution,[status(thm)],[1601, 117, 523, 330, 329, 1538, 328, 268, 1595, 327])).
% 1.05/0.97 tff(1603,plain,(c3_1(a13) | hskp8 | (~c2_1(a30)) | (~c3_1(a30)) | (~c2_1(a13)) | c1_1(a30) | c0_1(a13)), inference(lemma,lemma(discharge,[]))).
% 1.05/0.97 tff(1604,plain,
% 1.05/0.97 (c3_1(a13)),
% 1.05/0.97 inference(unit_resolution,[status(thm)],[1603, 321, 1585, 1584, 1478, 1583, 268])).
% 1.05/0.97 tff(1605,plain,
% 1.05/0.97 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | c0_1(a39) | c3_1(a39) | c1_1(a30) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30)) | (~c2_1(a39)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c0_1(a39) | c3_1(a39) | c1_1(a30) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30)) | (~c2_1(a39)))),
% 1.05/0.97 inference(rewrite,[status(thm)],[])).
% 1.05/0.97 tff(1606,plain,
% 1.05/0.97 ((hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a39) | c0_1(a39) | (~c2_1(a39))) <=> (hskp8 | c0_1(a39) | c3_1(a39) | c1_1(a30) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30)) | (~c2_1(a39)))),
% 1.05/0.97 inference(rewrite,[status(thm)],[])).
% 1.05/0.97 tff(1607,plain,
% 1.05/0.97 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a39) | c0_1(a39) | (~c2_1(a39)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | c0_1(a39) | c3_1(a39) | c1_1(a30) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30)) | (~c2_1(a39))))),
% 1.05/0.97 inference(monotonicity,[status(thm)],[1606])).
% 1.05/0.97 tff(1608,plain,
% 1.05/0.97 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a39) | c0_1(a39) | (~c2_1(a39)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c0_1(a39) | c3_1(a39) | c1_1(a30) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30)) | (~c2_1(a39)))),
% 1.05/0.97 inference(transitivity,[status(thm)],[1607, 1605])).
% 1.05/0.97 tff(1609,plain,
% 1.05/0.97 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a39) | c0_1(a39) | (~c2_1(a39)))),
% 1.05/0.97 inference(quant_inst,[status(thm)],[])).
% 1.05/0.97 tff(1610,plain,
% 1.05/0.97 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c0_1(a39) | c3_1(a39) | c1_1(a30) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30)) | (~c2_1(a39))),
% 1.05/0.97 inference(modus_ponens,[status(thm)],[1609, 1608])).
% 1.05/0.97 tff(1611,plain,
% 1.05/0.97 ($false),
% 1.05/0.97 inference(unit_resolution,[status(thm)],[1610, 117, 523, 76, 330, 329, 65, 59, 328, 1595])).
% 1.05/0.97 tff(1612,plain,((~hskp21) | hskp8 | (~c2_1(a30)) | (~c3_1(a30)) | c1_1(a30)), inference(lemma,lemma(discharge,[]))).
% 1.05/0.97 tff(1613,plain,
% 1.05/0.97 (~hskp21),
% 1.05/0.97 inference(unit_resolution,[status(thm)],[1612, 321, 1585, 1584, 1583])).
% 1.05/0.97 tff(1614,plain,
% 1.05/0.97 (hskp11),
% 1.05/0.97 inference(unit_resolution,[status(thm)],[1546, 1604, 1478, 310, 1, 1613])).
% 1.05/0.97 tff(1615,plain,
% 1.05/0.97 (~c3_1(a21)),
% 1.05/0.97 inference(unit_resolution,[status(thm)],[352, 1614])).
% 1.05/0.97 tff(1616,plain,
% 1.05/0.97 (~c2_1(a21)),
% 1.05/0.97 inference(unit_resolution,[status(thm)],[358, 1614])).
% 1.05/0.97 tff(1617,plain,
% 1.05/0.97 (c1_1(a21)),
% 1.05/0.97 inference(unit_resolution,[status(thm)],[1563, 117, 321, 310, 1478, 1616, 1615, 31, 1604])).
% 1.05/0.97 tff(1618,plain,
% 1.05/0.97 (~hskp25),
% 1.05/0.97 inference(unit_resolution,[status(thm)],[1429, 1613, 321])).
% 1.05/0.97 tff(1619,plain,
% 1.05/0.97 (hskp3),
% 1.05/0.97 inference(unit_resolution,[status(thm)],[1436, 117, 1618, 1616, 1615, 1390, 1617])).
% 1.05/0.97 tff(1620,plain,
% 1.05/0.97 (c3_1(a6)),
% 1.05/0.97 inference(unit_resolution,[status(thm)],[444, 1619])).
% 1.05/0.97 tff(1621,plain,
% 1.05/0.97 (c0_1(a6)),
% 1.05/0.97 inference(unit_resolution,[status(thm)],[455, 1619])).
% 1.05/0.97 tff(1622,plain,
% 1.05/0.97 (c1_1(a6)),
% 1.05/0.97 inference(unit_resolution,[status(thm)],[459, 117, 1613, 321, 1621, 1620, 21])).
% 1.05/0.97 tff(1623,plain,
% 1.05/0.97 (c0_1(a21)),
% 1.05/0.97 inference(unit_resolution,[status(thm)],[386, 1614])).
% 1.05/0.97 tff(1624,plain,
% 1.05/0.97 (hskp15),
% 1.05/0.97 inference(unit_resolution,[status(thm)],[1555, 117, 1623, 310, 1478, 1616, 376, 1604, 1617])).
% 1.05/0.97 tff(1625,plain,
% 1.05/0.97 (~c3_1(a29)),
% 1.05/0.97 inference(unit_resolution,[status(thm)],[142, 1624])).
% 1.05/0.97 tff(1626,plain,
% 1.05/0.97 (c1_1(a29)),
% 1.05/0.97 inference(unit_resolution,[status(thm)],[136, 1624])).
% 1.05/0.97 tff(1627,plain,
% 1.05/0.97 (c0_1(a29)),
% 1.05/0.97 inference(unit_resolution,[status(thm)],[414, 117, 1, 321, 1626, 1625, 408])).
% 1.05/0.97 tff(1628,plain,
% 1.05/0.97 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))))),
% 1.05/0.97 inference(bind,[status(th)],[])).
% 1.05/0.97 tff(1629,plain,
% 1.05/0.97 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.05/0.97 inference(quant_intro,[status(thm)],[1628])).
% 1.05/0.97 tff(1630,plain,
% 1.05/0.97 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.05/0.97 inference(rewrite,[status(thm)],[])).
% 1.05/0.97 tff(1631,plain,
% 1.05/0.97 (^[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))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_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) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_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) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))))),
% 1.05/0.97 inference(bind,[status(th)],[])).
% 1.05/0.97 tff(1632,plain,
% 1.05/0.97 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(V)) | 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) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.05/0.97 inference(quant_intro,[status(thm)],[1631])).
% 1.05/0.97 tff(1633,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause194')).
% 1.09/0.97 tff(1634,plain,
% 1.09/0.97 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.09/0.97 inference(modus_ponens,[status(thm)],[1633, 1632])).
% 1.09/0.97 tff(1635,plain,
% 1.09/0.97 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.09/0.97 inference(modus_ponens,[status(thm)],[1634, 1630])).
% 1.09/0.97 tff(1636,plain,(
% 1.09/0.97 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.09/0.97 inference(skolemize,[status(sab)],[1635])).
% 1.09/0.97 tff(1637,plain,
% 1.09/0.97 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.09/0.97 inference(modus_ponens,[status(thm)],[1636, 1629])).
% 1.09/0.97 tff(1638,plain,
% 1.09/0.97 (~c2_1(a6)),
% 1.09/0.97 inference(unit_resolution,[status(thm)],[484, 1619])).
% 1.09/0.97 tff(1639,assumption,(c1_1(a6)), introduced(assumption)).
% 1.09/0.97 tff(1640,assumption,(~hskp24), introduced(assumption)).
% 1.09/0.97 tff(1641,plain,
% 1.09/0.97 (hskp5),
% 1.09/0.97 inference(unit_resolution,[status(thm)],[1510, 1640, 1421])).
% 1.09/0.97 tff(1642,plain,
% 1.09/0.97 (~c2_1(a9)),
% 1.09/0.97 inference(unit_resolution,[status(thm)],[1516, 1641])).
% 1.09/0.97 tff(1643,plain,
% 1.09/0.97 (~c1_1(a9)),
% 1.09/0.97 inference(unit_resolution,[status(thm)],[1536, 1641])).
% 1.09/0.97 tff(1644,plain,
% 1.09/0.97 (~c0_1(a9)),
% 1.09/0.97 inference(unit_resolution,[status(thm)],[1522, 1641])).
% 1.09/0.97 tff(1645,plain,
% 1.09/0.97 (^[U: $i] : refl((hskp24 | hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp24 | hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))),
% 1.09/0.97 inference(bind,[status(th)],[])).
% 1.09/0.97 tff(1646,plain,
% 1.09/0.97 (![U: $i] : (hskp24 | hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.09/0.97 inference(quant_intro,[status(thm)],[1645])).
% 1.09/0.97 tff(1647,plain,
% 1.09/0.97 (![U: $i] : (hskp24 | hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.09/0.97 inference(rewrite,[status(thm)],[])).
% 1.09/0.97 tff(1648,plain,
% 1.09/0.97 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp14) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp14))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp14) <=> (hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp14) | hskp24) <=> ((hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp24))), rewrite(((hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp24) <=> (hskp24 | hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp14) | hskp24) <=> (hskp24 | hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))))),
% 1.09/0.97 inference(bind,[status(th)],[])).
% 1.09/0.97 tff(1649,plain,
% 1.09/0.97 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp14) | hskp24) <=> ![U: $i] : (hskp24 | hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.09/0.97 inference(quant_intro,[status(thm)],[1648])).
% 1.09/0.97 tff(1650,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp14) | hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause160')).
% 1.09/0.97 tff(1651,plain,
% 1.09/0.97 (![U: $i] : (hskp24 | hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.09/0.97 inference(modus_ponens,[status(thm)],[1650, 1649])).
% 1.09/0.97 tff(1652,plain,
% 1.09/0.97 (![U: $i] : (hskp24 | hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.09/0.97 inference(modus_ponens,[status(thm)],[1651, 1647])).
% 1.09/0.97 tff(1653,plain,(
% 1.09/0.97 ![U: $i] : (hskp24 | hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.09/0.97 inference(skolemize,[status(sab)],[1652])).
% 1.09/0.97 tff(1654,plain,
% 1.09/0.97 (![U: $i] : (hskp24 | hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.09/0.97 inference(modus_ponens,[status(thm)],[1653, 1646])).
% 1.09/0.97 tff(1655,plain,
% 1.09/0.97 (((~![U: $i] : (hskp24 | hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp14 | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a6)))) <=> ((~![U: $i] : (hskp24 | hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp24 | hskp14 | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a6)))),
% 1.09/0.97 inference(rewrite,[status(thm)],[])).
% 1.09/0.97 tff(1656,plain,
% 1.09/0.97 ((~![U: $i] : (hskp24 | hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp14 | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a6)))),
% 1.09/0.97 inference(quant_inst,[status(thm)],[])).
% 1.09/0.97 tff(1657,plain,
% 1.09/0.97 ((~![U: $i] : (hskp24 | hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp24 | hskp14 | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a6))),
% 1.09/0.97 inference(modus_ponens,[status(thm)],[1656, 1655])).
% 1.09/0.97 tff(1658,plain,
% 1.09/0.97 (hskp24 | hskp14 | (~c1_1(a6))),
% 1.09/0.97 inference(unit_resolution,[status(thm)],[1657, 117, 1054, 1051, 1654])).
% 1.09/0.97 tff(1659,plain,
% 1.09/0.97 (hskp14),
% 1.09/0.97 inference(unit_resolution,[status(thm)],[1658, 1640, 1639])).
% 1.09/0.97 tff(1660,plain,
% 1.09/0.97 (((~hskp14) | (~c0_1(a28))) <=> ((~hskp14) | (~c0_1(a28)))),
% 1.09/0.97 inference(rewrite,[status(thm)],[])).
% 1.09/0.97 tff(1661,plain,
% 1.09/0.97 (((~c0_1(a28)) | (~hskp14)) <=> ((~hskp14) | (~c0_1(a28)))),
% 1.09/0.97 inference(rewrite,[status(thm)],[])).
% 1.09/0.97 tff(1662,axiom,((~c0_1(a28)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause110')).
% 1.09/0.97 tff(1663,plain,
% 1.09/0.97 ((~hskp14) | (~c0_1(a28))),
% 1.09/0.97 inference(modus_ponens,[status(thm)],[1662, 1661])).
% 1.09/0.97 tff(1664,plain,
% 1.09/0.97 ((~hskp14) | (~c0_1(a28))),
% 1.09/0.97 inference(modus_ponens,[status(thm)],[1663, 1660])).
% 1.09/0.97 tff(1665,plain,
% 1.09/0.97 (~c0_1(a28)),
% 1.09/0.97 inference(unit_resolution,[status(thm)],[1664, 1659])).
% 1.09/0.97 tff(1666,plain,
% 1.09/0.97 (((~hskp14) | c3_1(a28)) <=> ((~hskp14) | c3_1(a28))),
% 1.09/0.97 inference(rewrite,[status(thm)],[])).
% 1.09/0.97 tff(1667,axiom,((~hskp14) | c3_1(a28)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause68')).
% 1.09/0.97 tff(1668,plain,
% 1.09/0.97 ((~hskp14) | c3_1(a28)),
% 1.09/0.97 inference(modus_ponens,[status(thm)],[1667, 1666])).
% 1.09/0.97 tff(1669,plain,
% 1.09/0.97 ((~hskp14) | c3_1(a28)),
% 1.09/0.97 inference(modus_ponens,[status(thm)],[1668, 1666])).
% 1.09/0.97 tff(1670,plain,
% 1.09/0.97 ((~hskp14) | c3_1(a28)),
% 1.09/0.97 inference(modus_ponens,[status(thm)],[1669, 1666])).
% 1.09/0.97 tff(1671,plain,
% 1.09/0.97 ((~hskp14) | c3_1(a28)),
% 1.09/0.97 inference(modus_ponens,[status(thm)],[1670, 1666])).
% 1.09/0.97 tff(1672,plain,
% 1.09/0.97 ((~hskp14) | c3_1(a28)),
% 1.09/0.97 inference(modus_ponens,[status(thm)],[1671, 1666])).
% 1.09/0.97 tff(1673,plain,
% 1.09/0.97 ((~hskp14) | c3_1(a28)),
% 1.09/0.97 inference(modus_ponens,[status(thm)],[1672, 1666])).
% 1.09/0.97 tff(1674,plain,
% 1.09/0.97 ((~hskp14) | c3_1(a28)),
% 1.09/0.97 inference(modus_ponens,[status(thm)],[1673, 1666])).
% 1.09/0.97 tff(1675,plain,
% 1.09/0.97 ((~hskp14) | c3_1(a28)),
% 1.09/0.97 inference(modus_ponens,[status(thm)],[1674, 1666])).
% 1.09/0.97 tff(1676,plain,
% 1.09/0.97 (c3_1(a28)),
% 1.09/0.97 inference(unit_resolution,[status(thm)],[1675, 1659])).
% 1.09/0.97 tff(1677,plain,
% 1.09/0.97 (((~hskp14) | c2_1(a28)) <=> ((~hskp14) | c2_1(a28))),
% 1.09/0.97 inference(rewrite,[status(thm)],[])).
% 1.09/0.97 tff(1678,axiom,((~hskp14) | c2_1(a28)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause67')).
% 1.09/0.97 tff(1679,plain,
% 1.09/0.97 ((~hskp14) | c2_1(a28)),
% 1.09/0.97 inference(modus_ponens,[status(thm)],[1678, 1677])).
% 1.09/0.97 tff(1680,plain,
% 1.09/0.97 ((~hskp14) | c2_1(a28)),
% 1.09/0.97 inference(modus_ponens,[status(thm)],[1679, 1677])).
% 1.09/0.97 tff(1681,plain,
% 1.09/0.97 ((~hskp14) | c2_1(a28)),
% 1.09/0.97 inference(modus_ponens,[status(thm)],[1680, 1677])).
% 1.09/0.97 tff(1682,plain,
% 1.09/0.97 ((~hskp14) | c2_1(a28)),
% 1.09/0.97 inference(modus_ponens,[status(thm)],[1681, 1677])).
% 1.09/0.97 tff(1683,plain,
% 1.09/0.97 ((~hskp14) | c2_1(a28)),
% 1.09/0.97 inference(modus_ponens,[status(thm)],[1682, 1677])).
% 1.09/0.97 tff(1684,plain,
% 1.09/0.97 ((~hskp14) | c2_1(a28)),
% 1.09/0.97 inference(modus_ponens,[status(thm)],[1683, 1677])).
% 1.09/0.97 tff(1685,plain,
% 1.09/0.97 ((~hskp14) | c2_1(a28)),
% 1.09/0.97 inference(modus_ponens,[status(thm)],[1684, 1677])).
% 1.09/0.97 tff(1686,plain,
% 1.09/0.97 ((~hskp14) | c2_1(a28)),
% 1.09/0.97 inference(modus_ponens,[status(thm)],[1685, 1677])).
% 1.09/0.97 tff(1687,plain,
% 1.09/0.97 (c2_1(a28)),
% 1.09/0.97 inference(unit_resolution,[status(thm)],[1686, 1659])).
% 1.09/0.97 tff(1688,plain,
% 1.09/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a28) | c0_1(a9) | c1_1(a9) | c2_1(a9) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c3_1(a28)) | (~c2_1(a28)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a28) | c0_1(a9) | c1_1(a9) | c2_1(a9) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c3_1(a28)) | (~c2_1(a28)))),
% 1.09/0.97 inference(rewrite,[status(thm)],[])).
% 1.09/0.97 tff(1689,plain,
% 1.09/0.97 (((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a28) | (~c3_1(a28)) | (~c2_1(a28)) | c1_1(a9) | c0_1(a9) | c2_1(a9)) <=> (c0_1(a28) | c0_1(a9) | c1_1(a9) | c2_1(a9) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c3_1(a28)) | (~c2_1(a28)))),
% 1.09/0.97 inference(rewrite,[status(thm)],[])).
% 1.09/0.97 tff(1690,plain,
% 1.09/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a28) | (~c3_1(a28)) | (~c2_1(a28)) | c1_1(a9) | c0_1(a9) | c2_1(a9))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a28) | c0_1(a9) | c1_1(a9) | c2_1(a9) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c3_1(a28)) | (~c2_1(a28))))),
% 1.09/0.97 inference(monotonicity,[status(thm)],[1689])).
% 1.09/0.97 tff(1691,plain,
% 1.09/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a28) | (~c3_1(a28)) | (~c2_1(a28)) | c1_1(a9) | c0_1(a9) | c2_1(a9))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a28) | c0_1(a9) | c1_1(a9) | c2_1(a9) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c3_1(a28)) | (~c2_1(a28)))),
% 1.09/0.97 inference(transitivity,[status(thm)],[1690, 1688])).
% 1.09/0.97 tff(1692,plain,
% 1.09/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a28) | (~c3_1(a28)) | (~c2_1(a28)) | c1_1(a9) | c0_1(a9) | c2_1(a9))),
% 1.09/0.97 inference(quant_inst,[status(thm)],[])).
% 1.09/0.97 tff(1693,plain,
% 1.09/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a28) | c0_1(a9) | c1_1(a9) | c2_1(a9) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c3_1(a28)) | (~c2_1(a28))),
% 1.09/0.97 inference(modus_ponens,[status(thm)],[1692, 1691])).
% 1.09/0.97 tff(1694,plain,
% 1.09/0.97 ($false),
% 1.09/0.97 inference(unit_resolution,[status(thm)],[1693, 117, 1687, 1676, 1051, 1665, 1644, 1643, 1642, 1050, 479, 1639])).
% 1.09/0.97 tff(1695,plain,(hskp24 | (~c3_1(a6)) | c2_1(a6) | (~c1_1(a6)) | (~c0_1(a6)) | hskp21), inference(lemma,lemma(discharge,[]))).
% 1.09/0.97 tff(1696,plain,
% 1.09/0.97 (hskp24),
% 1.09/0.97 inference(unit_resolution,[status(thm)],[1695, 1620, 1638, 1622, 1621, 1613])).
% 1.09/0.97 tff(1697,plain,
% 1.09/0.97 (~c2_1(a52)),
% 1.09/0.97 inference(unit_resolution,[status(thm)],[726, 1696])).
% 1.09/0.97 tff(1698,plain,
% 1.09/0.97 (~c0_1(a52)),
% 1.09/0.97 inference(unit_resolution,[status(thm)],[732, 1696])).
% 1.09/0.97 tff(1699,plain,
% 1.09/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a52) | c2_1(a52) | c3_1(a29) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a6)) | (~c1_1(a29)) | (~c0_1(a29)) | (~c1_1(a52)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a52) | c2_1(a52) | c3_1(a29) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a6)) | (~c1_1(a29)) | (~c0_1(a29)) | (~c1_1(a52)))),
% 1.09/0.97 inference(rewrite,[status(thm)],[])).
% 1.09/0.97 tff(1700,plain,
% 1.09/0.97 (((~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a6)) | c3_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c0_1(a52) | c2_1(a52) | (~c1_1(a52))) <=> (c0_1(a52) | c2_1(a52) | c3_1(a29) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a6)) | (~c1_1(a29)) | (~c0_1(a29)) | (~c1_1(a52)))),
% 1.09/0.97 inference(rewrite,[status(thm)],[])).
% 1.09/0.97 tff(1701,plain,
% 1.09/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a6)) | c3_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c0_1(a52) | c2_1(a52) | (~c1_1(a52)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a52) | c2_1(a52) | c3_1(a29) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a6)) | (~c1_1(a29)) | (~c0_1(a29)) | (~c1_1(a52))))),
% 1.09/0.97 inference(monotonicity,[status(thm)],[1700])).
% 1.09/0.97 tff(1702,plain,
% 1.09/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a6)) | c3_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c0_1(a52) | c2_1(a52) | (~c1_1(a52)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a52) | c2_1(a52) | c3_1(a29) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a6)) | (~c1_1(a29)) | (~c0_1(a29)) | (~c1_1(a52)))),
% 1.09/0.97 inference(transitivity,[status(thm)],[1701, 1699])).
% 1.09/0.97 tff(1703,plain,
% 1.09/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a6)) | c3_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c0_1(a52) | c2_1(a52) | (~c1_1(a52)))),
% 1.09/0.97 inference(quant_inst,[status(thm)],[])).
% 1.09/0.97 tff(1704,plain,
% 1.09/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a52) | c2_1(a52) | c3_1(a29) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a6)) | (~c1_1(a29)) | (~c0_1(a29)) | (~c1_1(a52))),
% 1.09/0.97 inference(modus_ponens,[status(thm)],[1703, 1702])).
% 1.09/0.97 tff(1705,plain,
% 1.09/0.97 (~c1_1(a52)),
% 1.09/0.97 inference(unit_resolution,[status(thm)],[1704, 117, 1626, 1621, 1620, 1698, 1697, 1625, 1637, 1627, 1622])).
% 1.09/0.97 tff(1706,plain,
% 1.09/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a52) | c2_1(a52) | c0_1(a13) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c3_1(a13)) | (~c2_1(a13)) | c1_1(a52))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a52) | c2_1(a52) | c0_1(a13) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c3_1(a13)) | (~c2_1(a13)) | c1_1(a52))),
% 1.09/0.97 inference(rewrite,[status(thm)],[])).
% 1.09/0.97 tff(1707,plain,
% 1.09/0.97 (((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a13) | (~c3_1(a13)) | (~c2_1(a13)) | c1_1(a52) | c0_1(a52) | c2_1(a52)) <=> (c0_1(a52) | c2_1(a52) | c0_1(a13) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c3_1(a13)) | (~c2_1(a13)) | c1_1(a52))),
% 1.09/0.97 inference(rewrite,[status(thm)],[])).
% 1.09/0.97 tff(1708,plain,
% 1.09/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a13) | (~c3_1(a13)) | (~c2_1(a13)) | c1_1(a52) | c0_1(a52) | c2_1(a52))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a52) | c2_1(a52) | c0_1(a13) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c3_1(a13)) | (~c2_1(a13)) | c1_1(a52)))),
% 1.09/0.97 inference(monotonicity,[status(thm)],[1707])).
% 1.09/0.97 tff(1709,plain,
% 1.09/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a13) | (~c3_1(a13)) | (~c2_1(a13)) | c1_1(a52) | c0_1(a52) | c2_1(a52))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a52) | c2_1(a52) | c0_1(a13) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c3_1(a13)) | (~c2_1(a13)) | c1_1(a52))),
% 1.09/0.97 inference(transitivity,[status(thm)],[1708, 1706])).
% 1.09/0.97 tff(1710,plain,
% 1.09/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a13) | (~c3_1(a13)) | (~c2_1(a13)) | c1_1(a52) | c0_1(a52) | c2_1(a52))),
% 1.09/0.97 inference(quant_inst,[status(thm)],[])).
% 1.09/0.97 tff(1711,plain,
% 1.09/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a52) | c2_1(a52) | c0_1(a13) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c3_1(a13)) | (~c2_1(a13)) | c1_1(a52)),
% 1.09/0.97 inference(modus_ponens,[status(thm)],[1710, 1709])).
% 1.09/0.97 tff(1712,plain,
% 1.09/0.97 ($false),
% 1.09/0.97 inference(unit_resolution,[status(thm)],[1711, 117, 1478, 1620, 1698, 1697, 268, 1638, 479, 1604, 1622, 1705])).
% 1.09/0.97 tff(1713,plain,(c1_1(a13) | c0_1(a13) | hskp30), inference(lemma,lemma(discharge,[]))).
% 1.09/0.97 tff(1714,plain,
% 1.09/0.97 (c1_1(a13)),
% 1.09/0.97 inference(unit_resolution,[status(thm)],[1713, 1, 268])).
% 1.09/0.97 tff(1715,assumption,(~hskp12), introduced(assumption)).
% 1.09/0.97 tff(1716,plain,
% 1.09/0.97 (((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp12 | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | c3_1(a13))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp12 | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | c3_1(a13))),
% 1.09/0.97 inference(rewrite,[status(thm)],[])).
% 1.09/0.97 tff(1717,plain,
% 1.09/0.97 ((hskp12 | (~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c1_1(a13))) <=> (hskp12 | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | c3_1(a13))),
% 1.09/0.97 inference(rewrite,[status(thm)],[])).
% 1.09/0.97 tff(1718,plain,
% 1.09/0.97 (((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp12 | (~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c1_1(a13)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp12 | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | c3_1(a13)))),
% 1.09/0.97 inference(monotonicity,[status(thm)],[1717])).
% 1.09/0.97 tff(1719,plain,
% 1.09/0.97 (((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp12 | (~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c1_1(a13)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp12 | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | c3_1(a13))),
% 1.09/0.97 inference(transitivity,[status(thm)],[1718, 1716])).
% 1.09/0.97 tff(1720,plain,
% 1.09/0.97 ((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp12 | (~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c1_1(a13)))),
% 1.09/0.97 inference(quant_inst,[status(thm)],[])).
% 1.09/0.97 tff(1721,plain,
% 1.09/0.97 ((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp12 | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | c3_1(a13)),
% 1.09/0.97 inference(modus_ponens,[status(thm)],[1720, 1719])).
% 1.09/0.97 tff(1722,plain,
% 1.09/0.97 (hskp12 | (~c1_1(a13)) | c3_1(a13)),
% 1.09/0.97 inference(unit_resolution,[status(thm)],[1721, 117, 268, 182])).
% 1.09/0.97 tff(1723,plain,
% 1.09/0.97 (c3_1(a13)),
% 1.09/0.97 inference(unit_resolution,[status(thm)],[1722, 1715, 1714])).
% 1.09/0.97 tff(1724,assumption,(hskp19), introduced(assumption)).
% 1.09/0.97 tff(1725,plain,
% 1.09/0.97 (((~hskp19) | (~c3_1(a35))) <=> ((~hskp19) | (~c3_1(a35)))),
% 1.09/0.97 inference(rewrite,[status(thm)],[])).
% 1.09/0.97 tff(1726,plain,
% 1.09/0.97 (((~c3_1(a35)) | (~hskp19)) <=> ((~hskp19) | (~c3_1(a35)))),
% 1.09/0.97 inference(rewrite,[status(thm)],[])).
% 1.09/0.97 tff(1727,axiom,((~c3_1(a35)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause104')).
% 1.09/0.97 tff(1728,plain,
% 1.09/0.97 ((~hskp19) | (~c3_1(a35))),
% 1.09/0.97 inference(modus_ponens,[status(thm)],[1727, 1726])).
% 1.09/0.97 tff(1729,plain,
% 1.09/0.97 ((~hskp19) | (~c3_1(a35))),
% 1.09/0.97 inference(modus_ponens,[status(thm)],[1728, 1725])).
% 1.09/0.97 tff(1730,plain,
% 1.09/0.97 (~c3_1(a35)),
% 1.09/0.97 inference(unit_resolution,[status(thm)],[1729, 1724])).
% 1.09/0.97 tff(1731,plain,
% 1.09/0.97 (((~hskp19) | (~c0_1(a35))) <=> ((~hskp19) | (~c0_1(a35)))),
% 1.09/0.97 inference(rewrite,[status(thm)],[])).
% 1.09/0.97 tff(1732,plain,
% 1.09/0.97 (((~c0_1(a35)) | (~hskp19)) <=> ((~hskp19) | (~c0_1(a35)))),
% 1.09/0.97 inference(rewrite,[status(thm)],[])).
% 1.09/0.97 tff(1733,axiom,((~c0_1(a35)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause103')).
% 1.09/0.97 tff(1734,plain,
% 1.09/0.97 ((~hskp19) | (~c0_1(a35))),
% 1.09/0.97 inference(modus_ponens,[status(thm)],[1733, 1732])).
% 1.09/0.97 tff(1735,plain,
% 1.09/0.97 ((~hskp19) | (~c0_1(a35))),
% 1.09/0.97 inference(modus_ponens,[status(thm)],[1734, 1731])).
% 1.09/0.97 tff(1736,plain,
% 1.09/0.97 (~c0_1(a35)),
% 1.09/0.97 inference(unit_resolution,[status(thm)],[1735, 1724])).
% 1.09/0.97 tff(1737,plain,
% 1.09/0.97 (((~hskp19) | c1_1(a35)) <=> ((~hskp19) | c1_1(a35))),
% 1.09/0.97 inference(rewrite,[status(thm)],[])).
% 1.09/0.97 tff(1738,axiom,((~hskp19) | c1_1(a35)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause59')).
% 1.09/0.97 tff(1739,plain,
% 1.09/0.97 ((~hskp19) | c1_1(a35)),
% 1.09/0.97 inference(modus_ponens,[status(thm)],[1738, 1737])).
% 1.09/0.97 tff(1740,plain,
% 1.09/0.97 ((~hskp19) | c1_1(a35)),
% 1.09/0.97 inference(modus_ponens,[status(thm)],[1739, 1737])).
% 1.09/0.97 tff(1741,plain,
% 1.09/0.97 ((~hskp19) | c1_1(a35)),
% 1.09/0.97 inference(modus_ponens,[status(thm)],[1740, 1737])).
% 1.09/0.97 tff(1742,plain,
% 1.09/0.97 ((~hskp19) | c1_1(a35)),
% 1.09/0.97 inference(modus_ponens,[status(thm)],[1741, 1737])).
% 1.09/0.97 tff(1743,plain,
% 1.09/0.97 ((~hskp19) | c1_1(a35)),
% 1.09/0.97 inference(modus_ponens,[status(thm)],[1742, 1737])).
% 1.09/0.97 tff(1744,plain,
% 1.09/0.97 ((~hskp19) | c1_1(a35)),
% 1.09/0.97 inference(modus_ponens,[status(thm)],[1743, 1737])).
% 1.09/0.97 tff(1745,plain,
% 1.09/0.97 ((~hskp19) | c1_1(a35)),
% 1.09/0.97 inference(modus_ponens,[status(thm)],[1744, 1737])).
% 1.09/0.97 tff(1746,plain,
% 1.09/0.97 ((~hskp19) | c1_1(a35)),
% 1.09/0.97 inference(modus_ponens,[status(thm)],[1745, 1737])).
% 1.09/0.97 tff(1747,plain,
% 1.09/0.97 (c1_1(a35)),
% 1.09/0.97 inference(unit_resolution,[status(thm)],[1746, 1724])).
% 1.09/0.97 tff(1748,plain,
% 1.09/0.97 (((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp12 | c0_1(a35) | c3_1(a35) | (~ndr1_0) | (~c1_1(a35)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp12 | c0_1(a35) | c3_1(a35) | (~ndr1_0) | (~c1_1(a35)))),
% 1.09/0.97 inference(rewrite,[status(thm)],[])).
% 1.09/0.97 tff(1749,plain,
% 1.09/0.97 ((hskp12 | (~ndr1_0) | c0_1(a35) | c3_1(a35) | (~c1_1(a35))) <=> (hskp12 | c0_1(a35) | c3_1(a35) | (~ndr1_0) | (~c1_1(a35)))),
% 1.09/0.98 inference(rewrite,[status(thm)],[])).
% 1.09/0.98 tff(1750,plain,
% 1.09/0.98 (((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp12 | (~ndr1_0) | c0_1(a35) | c3_1(a35) | (~c1_1(a35)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp12 | c0_1(a35) | c3_1(a35) | (~ndr1_0) | (~c1_1(a35))))),
% 1.09/0.98 inference(monotonicity,[status(thm)],[1749])).
% 1.09/0.98 tff(1751,plain,
% 1.09/0.98 (((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp12 | (~ndr1_0) | c0_1(a35) | c3_1(a35) | (~c1_1(a35)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp12 | c0_1(a35) | c3_1(a35) | (~ndr1_0) | (~c1_1(a35)))),
% 1.09/0.98 inference(transitivity,[status(thm)],[1750, 1748])).
% 1.09/0.98 tff(1752,plain,
% 1.09/0.98 ((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp12 | (~ndr1_0) | c0_1(a35) | c3_1(a35) | (~c1_1(a35)))),
% 1.09/0.98 inference(quant_inst,[status(thm)],[])).
% 1.09/0.98 tff(1753,plain,
% 1.09/0.98 ((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp12 | c0_1(a35) | c3_1(a35) | (~ndr1_0) | (~c1_1(a35))),
% 1.09/0.98 inference(modus_ponens,[status(thm)],[1752, 1751])).
% 1.09/0.98 tff(1754,plain,
% 1.09/0.98 ($false),
% 1.09/0.98 inference(unit_resolution,[status(thm)],[1753, 117, 1715, 1747, 1736, 1730, 182])).
% 1.09/0.98 tff(1755,plain,((~hskp19) | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.09/0.98 tff(1756,plain,
% 1.09/0.98 (~hskp19),
% 1.09/0.98 inference(unit_resolution,[status(thm)],[1755, 1715])).
% 1.09/0.98 tff(1757,plain,
% 1.09/0.98 (^[U: $i] : refl((hskp19 | hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> (hskp19 | hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))))),
% 1.09/0.98 inference(bind,[status(th)],[])).
% 1.09/0.98 tff(1758,plain,
% 1.09/0.98 (![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.09/0.98 inference(quant_intro,[status(thm)],[1757])).
% 1.09/0.98 tff(1759,plain,
% 1.09/0.98 (![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.09/0.98 inference(rewrite,[status(thm)],[])).
% 1.09/0.98 tff(1760,plain,
% 1.09/0.98 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp11) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp11))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp11) <=> (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp11) <=> (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp11) | hskp19) <=> ((hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp19))), rewrite(((hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp19) <=> (hskp19 | hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp11) | hskp19) <=> (hskp19 | hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))))),
% 1.09/0.98 inference(bind,[status(th)],[])).
% 1.09/0.98 tff(1761,plain,
% 1.09/0.98 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp11) | hskp19) <=> ![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.09/0.98 inference(quant_intro,[status(thm)],[1760])).
% 1.09/0.98 tff(1762,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp11) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause150')).
% 1.09/0.98 tff(1763,plain,
% 1.09/0.98 (![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.09/0.98 inference(modus_ponens,[status(thm)],[1762, 1761])).
% 1.09/0.98 tff(1764,plain,
% 1.09/0.98 (![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.09/0.98 inference(modus_ponens,[status(thm)],[1763, 1759])).
% 1.09/0.98 tff(1765,plain,(
% 1.09/0.98 ![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.09/0.98 inference(skolemize,[status(sab)],[1764])).
% 1.09/0.98 tff(1766,plain,
% 1.09/0.98 (![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.09/0.98 inference(modus_ponens,[status(thm)],[1765, 1758])).
% 1.09/0.98 tff(1767,plain,
% 1.09/0.98 (((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp19 | hskp11 | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)))) <=> ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp19 | hskp11 | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)))),
% 1.09/0.98 inference(rewrite,[status(thm)],[])).
% 1.09/0.98 tff(1768,plain,
% 1.09/0.98 ((hskp19 | hskp11 | (~ndr1_0) | c0_1(a13) | (~c1_1(a13)) | (~c3_1(a13))) <=> (hskp19 | hskp11 | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)))),
% 1.09/0.98 inference(rewrite,[status(thm)],[])).
% 1.09/0.98 tff(1769,plain,
% 1.09/0.98 (((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp19 | hskp11 | (~ndr1_0) | c0_1(a13) | (~c1_1(a13)) | (~c3_1(a13)))) <=> ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp19 | hskp11 | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13))))),
% 1.09/0.98 inference(monotonicity,[status(thm)],[1768])).
% 1.09/0.98 tff(1770,plain,
% 1.09/0.98 (((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp19 | hskp11 | (~ndr1_0) | c0_1(a13) | (~c1_1(a13)) | (~c3_1(a13)))) <=> ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp19 | hskp11 | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)))),
% 1.09/0.98 inference(transitivity,[status(thm)],[1769, 1767])).
% 1.09/0.98 tff(1771,plain,
% 1.09/0.98 ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp19 | hskp11 | (~ndr1_0) | c0_1(a13) | (~c1_1(a13)) | (~c3_1(a13)))),
% 1.09/0.98 inference(quant_inst,[status(thm)],[])).
% 1.09/0.98 tff(1772,plain,
% 1.09/0.98 ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp19 | hskp11 | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13))),
% 1.09/0.98 inference(modus_ponens,[status(thm)],[1771, 1770])).
% 1.09/0.98 tff(1773,plain,
% 1.09/0.98 (hskp19 | hskp11 | (~c1_1(a13)) | (~c3_1(a13))),
% 1.09/0.98 inference(unit_resolution,[status(thm)],[1772, 117, 268, 1766])).
% 1.09/0.98 tff(1774,plain,
% 1.09/0.98 (hskp11),
% 1.09/0.98 inference(unit_resolution,[status(thm)],[1773, 1756, 1714, 1723])).
% 1.09/0.98 tff(1775,plain,
% 1.09/0.98 (~c3_1(a21)),
% 1.09/0.98 inference(unit_resolution,[status(thm)],[352, 1774])).
% 1.09/0.98 tff(1776,plain,
% 1.09/0.98 (((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | c3_1(a13))) <=> ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp30 | hskp8 | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | c3_1(a13))),
% 1.09/0.98 inference(rewrite,[status(thm)],[])).
% 1.09/0.98 tff(1777,plain,
% 1.09/0.98 ((hskp30 | hskp8 | (~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c1_1(a13))) <=> (hskp30 | hskp8 | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | c3_1(a13))),
% 1.09/0.98 inference(rewrite,[status(thm)],[])).
% 1.09/0.98 tff(1778,plain,
% 1.09/0.98 (((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | (~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c1_1(a13)))) <=> ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | c3_1(a13)))),
% 1.09/0.98 inference(monotonicity,[status(thm)],[1777])).
% 1.09/0.98 tff(1779,plain,
% 1.09/0.98 (((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | (~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c1_1(a13)))) <=> ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp30 | hskp8 | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | c3_1(a13))),
% 1.09/0.98 inference(transitivity,[status(thm)],[1778, 1776])).
% 1.09/0.98 tff(1780,plain,
% 1.09/0.98 ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | (~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c1_1(a13)))),
% 1.09/0.98 inference(quant_inst,[status(thm)],[])).
% 1.09/0.98 tff(1781,plain,
% 1.09/0.98 ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp30 | hskp8 | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | c3_1(a13)),
% 1.09/0.98 inference(modus_ponens,[status(thm)],[1780, 1779])).
% 1.09/0.98 tff(1782,plain,
% 1.09/0.98 (hskp30 | hskp8 | (~c1_1(a13)) | c3_1(a13)),
% 1.09/0.98 inference(unit_resolution,[status(thm)],[1781, 117, 268, 408])).
% 1.09/0.98 tff(1783,plain,
% 1.09/0.98 (c3_1(a13)),
% 1.09/0.98 inference(unit_resolution,[status(thm)],[1782, 523, 1, 1714])).
% 1.09/0.98 tff(1784,plain,
% 1.09/0.98 (((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | c0_1(a35) | c3_1(a35) | (~ndr1_0) | (~c1_1(a35)))) <=> ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp30 | hskp8 | c0_1(a35) | c3_1(a35) | (~ndr1_0) | (~c1_1(a35)))),
% 1.09/0.98 inference(rewrite,[status(thm)],[])).
% 1.09/0.98 tff(1785,plain,
% 1.09/0.98 ((hskp30 | hskp8 | (~ndr1_0) | c0_1(a35) | c3_1(a35) | (~c1_1(a35))) <=> (hskp30 | hskp8 | c0_1(a35) | c3_1(a35) | (~ndr1_0) | (~c1_1(a35)))),
% 1.09/0.98 inference(rewrite,[status(thm)],[])).
% 1.09/0.98 tff(1786,plain,
% 1.09/0.98 (((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | (~ndr1_0) | c0_1(a35) | c3_1(a35) | (~c1_1(a35)))) <=> ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | c0_1(a35) | c3_1(a35) | (~ndr1_0) | (~c1_1(a35))))),
% 1.09/0.98 inference(monotonicity,[status(thm)],[1785])).
% 1.09/0.98 tff(1787,plain,
% 1.09/0.98 (((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | (~ndr1_0) | c0_1(a35) | c3_1(a35) | (~c1_1(a35)))) <=> ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp30 | hskp8 | c0_1(a35) | c3_1(a35) | (~ndr1_0) | (~c1_1(a35)))),
% 1.09/0.98 inference(transitivity,[status(thm)],[1786, 1784])).
% 1.09/0.98 tff(1788,plain,
% 1.09/0.98 ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | (~ndr1_0) | c0_1(a35) | c3_1(a35) | (~c1_1(a35)))),
% 1.09/0.98 inference(quant_inst,[status(thm)],[])).
% 1.09/0.98 tff(1789,plain,
% 1.09/0.98 ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp30 | hskp8 | c0_1(a35) | c3_1(a35) | (~ndr1_0) | (~c1_1(a35))),
% 1.09/0.98 inference(modus_ponens,[status(thm)],[1788, 1787])).
% 1.09/0.98 tff(1790,plain,
% 1.09/0.98 ($false),
% 1.09/0.98 inference(unit_resolution,[status(thm)],[1789, 117, 1, 523, 1747, 1736, 1730, 408])).
% 1.09/0.98 tff(1791,plain,((~hskp19) | hskp30 | hskp8), inference(lemma,lemma(discharge,[]))).
% 1.09/0.98 tff(1792,plain,
% 1.09/0.98 (~hskp19),
% 1.09/0.98 inference(unit_resolution,[status(thm)],[1791, 523, 1])).
% 1.09/0.98 tff(1793,plain,
% 1.09/0.98 (hskp11),
% 1.09/0.98 inference(unit_resolution,[status(thm)],[1773, 1792, 1714, 1783])).
% 1.09/0.98 tff(1794,plain,
% 1.09/0.98 (~c3_1(a21)),
% 1.09/0.98 inference(unit_resolution,[status(thm)],[352, 1793])).
% 1.09/0.98 tff(1795,assumption,(c1_1(a13)), introduced(assumption)).
% 1.09/0.98 tff(1796,plain,
% 1.09/0.98 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | c2_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | c2_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)))),
% 1.09/0.98 inference(rewrite,[status(thm)],[])).
% 1.09/0.98 tff(1797,plain,
% 1.09/0.98 ((hskp16 | (~ndr1_0) | c2_1(a13) | (~c1_1(a13)) | (~c3_1(a13))) <=> (hskp16 | c2_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)))),
% 1.09/0.98 inference(rewrite,[status(thm)],[])).
% 1.09/0.98 tff(1798,plain,
% 1.09/0.98 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a13) | (~c1_1(a13)) | (~c3_1(a13)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | c2_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13))))),
% 1.09/0.98 inference(monotonicity,[status(thm)],[1797])).
% 1.09/0.98 tff(1799,plain,
% 1.09/0.98 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a13) | (~c1_1(a13)) | (~c3_1(a13)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | c2_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)))),
% 1.09/0.98 inference(transitivity,[status(thm)],[1798, 1796])).
% 1.09/0.98 tff(1800,plain,
% 1.09/0.98 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a13) | (~c1_1(a13)) | (~c3_1(a13)))),
% 1.09/0.98 inference(quant_inst,[status(thm)],[])).
% 1.09/0.98 tff(1801,plain,
% 1.09/0.98 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | c2_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13))),
% 1.09/0.98 inference(modus_ponens,[status(thm)],[1800, 1799])).
% 1.09/0.98 tff(1802,plain,
% 1.09/0.98 (hskp16 | c2_1(a13) | (~c3_1(a13))),
% 1.09/0.98 inference(unit_resolution,[status(thm)],[1801, 117, 1795, 192])).
% 1.09/0.98 tff(1803,plain,
% 1.09/0.98 (hskp16),
% 1.09/0.98 inference(unit_resolution,[status(thm)],[1802, 322, 1531])).
% 1.09/0.98 tff(1804,plain,
% 1.09/0.98 (~c1_1(a30)),
% 1.09/0.98 inference(unit_resolution,[status(thm)],[244, 1803])).
% 1.09/0.98 tff(1805,plain,
% 1.09/0.98 (c3_1(a30)),
% 1.09/0.98 inference(unit_resolution,[status(thm)],[266, 1803])).
% 1.09/0.98 tff(1806,plain,
% 1.09/0.98 (c2_1(a30)),
% 1.09/0.98 inference(unit_resolution,[status(thm)],[255, 1803])).
% 1.09/0.98 tff(1807,plain,
% 1.09/0.98 (~hskp21),
% 1.09/0.98 inference(unit_resolution,[status(thm)],[1612, 1806, 523, 1805, 1804])).
% 1.09/0.98 tff(1808,plain,
% 1.09/0.98 (~c0_1(a30)),
% 1.09/0.98 inference(unit_resolution,[status(thm)],[467, 117, 1807, 523, 1805, 1804, 21])).
% 1.09/0.98 tff(1809,plain,
% 1.09/0.98 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))),
% 1.09/0.98 inference(bind,[status(th)],[])).
% 1.09/0.98 tff(1810,plain,
% 1.09/0.98 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.09/0.98 inference(quant_intro,[status(thm)],[1809])).
% 1.09/0.98 tff(1811,plain,
% 1.09/0.98 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.09/0.98 inference(rewrite,[status(thm)],[])).
% 1.09/0.98 tff(1812,plain,
% 1.09/0.98 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | 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))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | 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))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~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)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp5) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp5))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))))),
% 1.09/0.98 inference(bind,[status(th)],[])).
% 1.09/0.98 tff(1813,plain,
% 1.09/0.98 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.09/0.98 inference(quant_intro,[status(thm)],[1812])).
% 1.09/0.98 tff(1814,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause177')).
% 1.09/0.98 tff(1815,plain,
% 1.09/0.98 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.09/0.98 inference(modus_ponens,[status(thm)],[1814, 1813])).
% 1.09/0.98 tff(1816,plain,
% 1.09/0.98 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.09/0.98 inference(modus_ponens,[status(thm)],[1815, 1811])).
% 1.09/0.98 tff(1817,plain,(
% 1.09/0.98 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.09/0.98 inference(skolemize,[status(sab)],[1816])).
% 1.09/0.98 tff(1818,plain,
% 1.09/0.98 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 1.09/0.98 inference(modus_ponens,[status(thm)],[1817, 1810])).
% 1.09/0.98 tff(1819,plain,
% 1.09/0.98 (^[U: $i] : refl((hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))),
% 1.09/0.98 inference(bind,[status(th)],[])).
% 1.09/0.98 tff(1820,plain,
% 1.09/0.98 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.09/0.98 inference(quant_intro,[status(thm)],[1819])).
% 1.09/0.98 tff(1821,plain,
% 1.09/0.98 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.09/0.98 inference(rewrite,[status(thm)],[])).
% 1.09/0.98 tff(1822,plain,
% 1.09/0.98 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp7) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp7))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp7) | hskp8) <=> ((hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp8))), rewrite(((hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp8) <=> (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp7) | hskp8) <=> (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))))),
% 1.09/0.98 inference(bind,[status(th)],[])).
% 1.09/0.98 tff(1823,plain,
% 1.09/0.98 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp7) | hskp8) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.09/0.98 inference(quant_intro,[status(thm)],[1822])).
% 1.09/0.98 tff(1824,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp7) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause138')).
% 1.09/0.98 tff(1825,plain,
% 1.09/0.98 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.09/0.98 inference(modus_ponens,[status(thm)],[1824, 1823])).
% 1.09/0.98 tff(1826,plain,
% 1.09/0.98 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.09/0.98 inference(modus_ponens,[status(thm)],[1825, 1821])).
% 1.09/0.98 tff(1827,plain,(
% 1.09/0.98 ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.09/0.98 inference(skolemize,[status(sab)],[1826])).
% 1.09/0.98 tff(1828,plain,
% 1.09/0.98 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.09/0.98 inference(modus_ponens,[status(thm)],[1827, 1820])).
% 1.09/0.98 tff(1829,plain,
% 1.09/0.98 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp8 | hskp7 | c2_1(a13) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp8 | hskp7 | c2_1(a13) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)))),
% 1.09/0.98 inference(rewrite,[status(thm)],[])).
% 1.09/0.98 tff(1830,plain,
% 1.09/0.98 ((hskp8 | hskp7 | (~ndr1_0) | c2_1(a13) | c0_1(a13) | (~c1_1(a13))) <=> (hskp8 | hskp7 | c2_1(a13) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)))),
% 1.09/0.98 inference(rewrite,[status(thm)],[])).
% 1.09/0.98 tff(1831,plain,
% 1.09/0.98 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a13) | c0_1(a13) | (~c1_1(a13)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp8 | hskp7 | c2_1(a13) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13))))),
% 1.09/0.98 inference(monotonicity,[status(thm)],[1830])).
% 1.09/0.98 tff(1832,plain,
% 1.09/0.98 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a13) | c0_1(a13) | (~c1_1(a13)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp8 | hskp7 | c2_1(a13) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)))),
% 1.09/0.98 inference(transitivity,[status(thm)],[1831, 1829])).
% 1.09/0.98 tff(1833,plain,
% 1.09/0.98 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a13) | c0_1(a13) | (~c1_1(a13)))),
% 1.09/0.98 inference(quant_inst,[status(thm)],[])).
% 1.09/0.98 tff(1834,plain,
% 1.09/0.98 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp8 | hskp7 | c2_1(a13) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13))),
% 1.09/0.98 inference(modus_ponens,[status(thm)],[1833, 1832])).
% 1.09/0.98 tff(1835,plain,
% 1.09/0.98 (hskp8 | hskp7 | c2_1(a13) | (~c1_1(a13))),
% 1.09/0.98 inference(unit_resolution,[status(thm)],[1834, 117, 268, 1828])).
% 1.09/0.98 tff(1836,plain,
% 1.09/0.98 (hskp7),
% 1.09/0.98 inference(unit_resolution,[status(thm)],[1835, 322, 1795, 523])).
% 1.09/0.98 tff(1837,plain,
% 1.09/0.98 (((~hskp7) | (~c3_1(a12))) <=> ((~hskp7) | (~c3_1(a12)))),
% 1.09/0.98 inference(rewrite,[status(thm)],[])).
% 1.09/0.98 tff(1838,plain,
% 1.09/0.98 (((~c3_1(a12)) | (~hskp7)) <=> ((~hskp7) | (~c3_1(a12)))),
% 1.09/0.98 inference(rewrite,[status(thm)],[])).
% 1.09/0.98 tff(1839,axiom,((~c3_1(a12)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause122')).
% 1.09/0.98 tff(1840,plain,
% 1.09/0.98 ((~hskp7) | (~c3_1(a12))),
% 1.09/0.98 inference(modus_ponens,[status(thm)],[1839, 1838])).
% 1.09/0.98 tff(1841,plain,
% 1.09/0.98 ((~hskp7) | (~c3_1(a12))),
% 1.09/0.98 inference(modus_ponens,[status(thm)],[1840, 1837])).
% 1.09/0.98 tff(1842,plain,
% 1.09/0.98 (~c3_1(a12)),
% 1.09/0.98 inference(unit_resolution,[status(thm)],[1841, 1836])).
% 1.09/0.98 tff(1843,plain,
% 1.09/0.98 (((~hskp7) | c1_1(a12)) <=> ((~hskp7) | c1_1(a12))),
% 1.09/0.98 inference(rewrite,[status(thm)],[])).
% 1.09/0.98 tff(1844,axiom,((~hskp7) | c1_1(a12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause77')).
% 1.09/0.98 tff(1845,plain,
% 1.09/0.98 ((~hskp7) | c1_1(a12)),
% 1.09/0.98 inference(modus_ponens,[status(thm)],[1844, 1843])).
% 1.09/0.98 tff(1846,plain,
% 1.09/0.98 ((~hskp7) | c1_1(a12)),
% 1.09/0.98 inference(modus_ponens,[status(thm)],[1845, 1843])).
% 1.09/0.98 tff(1847,plain,
% 1.09/0.98 ((~hskp7) | c1_1(a12)),
% 1.09/0.98 inference(modus_ponens,[status(thm)],[1846, 1843])).
% 1.09/0.98 tff(1848,plain,
% 1.09/0.98 ((~hskp7) | c1_1(a12)),
% 1.09/0.98 inference(modus_ponens,[status(thm)],[1847, 1843])).
% 1.09/0.98 tff(1849,plain,
% 1.09/0.98 ((~hskp7) | c1_1(a12)),
% 1.09/0.98 inference(modus_ponens,[status(thm)],[1848, 1843])).
% 1.09/0.98 tff(1850,plain,
% 1.09/0.98 ((~hskp7) | c1_1(a12)),
% 1.09/0.98 inference(modus_ponens,[status(thm)],[1849, 1843])).
% 1.09/0.98 tff(1851,plain,
% 1.09/0.98 ((~hskp7) | c1_1(a12)),
% 1.09/0.98 inference(modus_ponens,[status(thm)],[1850, 1843])).
% 1.09/0.98 tff(1852,plain,
% 1.09/0.98 ((~hskp7) | c1_1(a12)),
% 1.09/0.98 inference(modus_ponens,[status(thm)],[1851, 1843])).
% 1.09/0.98 tff(1853,plain,
% 1.09/0.98 (c1_1(a12)),
% 1.09/0.98 inference(unit_resolution,[status(thm)],[1852, 1836])).
% 1.09/0.98 tff(1854,plain,
% 1.09/0.98 (((~hskp7) | c0_1(a12)) <=> ((~hskp7) | c0_1(a12))),
% 1.09/0.98 inference(rewrite,[status(thm)],[])).
% 1.09/0.98 tff(1855,axiom,((~hskp7) | c0_1(a12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause76')).
% 1.09/0.98 tff(1856,plain,
% 1.09/0.98 ((~hskp7) | c0_1(a12)),
% 1.09/0.98 inference(modus_ponens,[status(thm)],[1855, 1854])).
% 1.09/0.98 tff(1857,plain,
% 1.09/0.98 ((~hskp7) | c0_1(a12)),
% 1.09/0.98 inference(modus_ponens,[status(thm)],[1856, 1854])).
% 1.09/0.98 tff(1858,plain,
% 1.09/0.98 ((~hskp7) | c0_1(a12)),
% 1.09/0.98 inference(modus_ponens,[status(thm)],[1857, 1854])).
% 1.09/0.98 tff(1859,plain,
% 1.09/0.98 ((~hskp7) | c0_1(a12)),
% 1.09/0.98 inference(modus_ponens,[status(thm)],[1858, 1854])).
% 1.09/0.98 tff(1860,plain,
% 1.09/0.98 ((~hskp7) | c0_1(a12)),
% 1.09/0.98 inference(modus_ponens,[status(thm)],[1859, 1854])).
% 1.09/0.98 tff(1861,plain,
% 1.09/0.98 ((~hskp7) | c0_1(a12)),
% 1.09/0.98 inference(modus_ponens,[status(thm)],[1860, 1854])).
% 1.09/0.98 tff(1862,plain,
% 1.09/0.98 ((~hskp7) | c0_1(a12)),
% 1.09/0.98 inference(modus_ponens,[status(thm)],[1861, 1854])).
% 1.09/0.98 tff(1863,plain,
% 1.09/0.98 ((~hskp7) | c0_1(a12)),
% 1.09/0.98 inference(modus_ponens,[status(thm)],[1862, 1854])).
% 1.09/0.98 tff(1864,plain,
% 1.09/0.98 (c0_1(a12)),
% 1.09/0.98 inference(unit_resolution,[status(thm)],[1863, 1836])).
% 1.09/0.98 tff(1865,plain,
% 1.09/0.98 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | c2_1(a13) | c0_1(a13) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c0_1(a12)) | (~c3_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp5 | c2_1(a13) | c0_1(a13) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c0_1(a12)) | (~c3_1(a13)))),
% 1.09/0.98 inference(rewrite,[status(thm)],[])).
% 1.09/0.98 tff(1866,plain,
% 1.09/0.98 ((hskp5 | (~ndr1_0) | c3_1(a12) | (~c1_1(a12)) | (~c0_1(a12)) | c0_1(a13) | c2_1(a13) | (~c3_1(a13))) <=> (hskp5 | c2_1(a13) | c0_1(a13) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c0_1(a12)) | (~c3_1(a13)))),
% 1.09/0.98 inference(rewrite,[status(thm)],[])).
% 1.09/0.98 tff(1867,plain,
% 1.09/0.98 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a12) | (~c1_1(a12)) | (~c0_1(a12)) | c0_1(a13) | c2_1(a13) | (~c3_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | c2_1(a13) | c0_1(a13) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c0_1(a12)) | (~c3_1(a13))))),
% 1.09/0.98 inference(monotonicity,[status(thm)],[1866])).
% 1.09/0.98 tff(1868,plain,
% 1.09/0.98 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a12) | (~c1_1(a12)) | (~c0_1(a12)) | c0_1(a13) | c2_1(a13) | (~c3_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp5 | c2_1(a13) | c0_1(a13) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c0_1(a12)) | (~c3_1(a13)))),
% 1.09/0.98 inference(transitivity,[status(thm)],[1867, 1865])).
% 1.09/0.98 tff(1869,plain,
% 1.09/0.98 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a12) | (~c1_1(a12)) | (~c0_1(a12)) | c0_1(a13) | c2_1(a13) | (~c3_1(a13)))),
% 1.09/0.98 inference(quant_inst,[status(thm)],[])).
% 1.09/0.98 tff(1870,plain,
% 1.09/0.98 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp5 | c2_1(a13) | c0_1(a13) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c0_1(a12)) | (~c3_1(a13))),
% 1.09/0.98 inference(modus_ponens,[status(thm)],[1869, 1868])).
% 1.09/0.98 tff(1871,plain,
% 1.09/0.98 (hskp5),
% 1.09/0.98 inference(unit_resolution,[status(thm)],[1870, 117, 322, 1864, 1853, 268, 1842, 1818, 1531])).
% 1.09/0.98 tff(1872,plain,
% 1.09/0.98 (~c2_1(a9)),
% 1.09/0.98 inference(unit_resolution,[status(thm)],[1516, 1871])).
% 1.09/0.98 tff(1873,plain,
% 1.09/0.98 (~c1_1(a9)),
% 1.09/0.98 inference(unit_resolution,[status(thm)],[1536, 1871])).
% 1.09/0.98 tff(1874,plain,
% 1.09/0.98 (~c0_1(a9)),
% 1.09/0.98 inference(unit_resolution,[status(thm)],[1522, 1871])).
% 1.09/0.98 tff(1875,plain,
% 1.09/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a13) | c0_1(a9) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c2_1(a13) | c0_1(a9) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30)))),
% 1.09/0.98 inference(rewrite,[status(thm)],[])).
% 1.09/0.98 tff(1876,plain,
% 1.09/0.98 (((~ndr1_0) | c2_1(a13) | (~c1_1(a13)) | (~c3_1(a13)) | c0_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c1_1(a9) | c0_1(a9) | c2_1(a9)) <=> (c2_1(a13) | c0_1(a9) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30)))),
% 1.09/0.99 inference(rewrite,[status(thm)],[])).
% 1.09/0.99 tff(1877,plain,
% 1.09/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a13) | (~c1_1(a13)) | (~c3_1(a13)) | c0_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c1_1(a9) | c0_1(a9) | c2_1(a9))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a13) | c0_1(a9) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30))))),
% 1.09/0.99 inference(monotonicity,[status(thm)],[1876])).
% 1.09/0.99 tff(1878,plain,
% 1.09/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a13) | (~c1_1(a13)) | (~c3_1(a13)) | c0_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c1_1(a9) | c0_1(a9) | c2_1(a9))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c2_1(a13) | c0_1(a9) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30)))),
% 1.09/0.99 inference(transitivity,[status(thm)],[1877, 1875])).
% 1.09/0.99 tff(1879,plain,
% 1.09/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a13) | (~c1_1(a13)) | (~c3_1(a13)) | c0_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c1_1(a9) | c0_1(a9) | c2_1(a9))),
% 1.09/0.99 inference(quant_inst,[status(thm)],[])).
% 1.09/0.99 tff(1880,plain,
% 1.09/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c2_1(a13) | c0_1(a9) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30))),
% 1.09/0.99 inference(modus_ponens,[status(thm)],[1879, 1878])).
% 1.09/0.99 tff(1881,plain,
% 1.09/0.99 ($false),
% 1.09/0.99 inference(unit_resolution,[status(thm)],[1880, 117, 1806, 1805, 1795, 322, 1874, 1873, 1872, 479, 1531, 1808])).
% 1.09/0.99 tff(1882,plain,(c2_1(a13) | (~c1_1(a13)) | (~c3_1(a13)) | c0_1(a13) | hskp8), inference(lemma,lemma(discharge,[]))).
% 1.09/0.99 tff(1883,plain,
% 1.09/0.99 (c2_1(a13)),
% 1.09/0.99 inference(unit_resolution,[status(thm)],[1882, 1783, 1714, 268, 523])).
% 1.09/0.99 tff(1884,plain,
% 1.09/0.99 (c0_1(a21)),
% 1.09/0.99 inference(unit_resolution,[status(thm)],[386, 1793])).
% 1.09/0.99 tff(1885,plain,
% 1.09/0.99 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp30 | c3_1(a21) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c1_1(a21)) | (~c0_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp30 | c3_1(a21) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c1_1(a21)) | (~c0_1(a21)))),
% 1.09/0.99 inference(rewrite,[status(thm)],[])).
% 1.09/0.99 tff(1886,plain,
% 1.09/0.99 ((hskp30 | (~ndr1_0) | c3_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c0_1(a13) | (~c1_1(a13)) | (~c2_1(a13))) <=> (hskp30 | c3_1(a21) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c1_1(a21)) | (~c0_1(a21)))),
% 1.09/0.99 inference(rewrite,[status(thm)],[])).
% 1.09/0.99 tff(1887,plain,
% 1.09/0.99 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp30 | (~ndr1_0) | c3_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c0_1(a13) | (~c1_1(a13)) | (~c2_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp30 | c3_1(a21) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c1_1(a21)) | (~c0_1(a21))))),
% 1.09/0.99 inference(monotonicity,[status(thm)],[1886])).
% 1.09/0.99 tff(1888,plain,
% 1.09/0.99 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp30 | (~ndr1_0) | c3_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c0_1(a13) | (~c1_1(a13)) | (~c2_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp30 | c3_1(a21) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c1_1(a21)) | (~c0_1(a21)))),
% 1.09/0.99 inference(transitivity,[status(thm)],[1887, 1885])).
% 1.09/0.99 tff(1889,plain,
% 1.09/0.99 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp30 | (~ndr1_0) | c3_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c0_1(a13) | (~c1_1(a13)) | (~c2_1(a13)))),
% 1.09/0.99 inference(quant_inst,[status(thm)],[])).
% 1.09/0.99 tff(1890,plain,
% 1.09/0.99 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp30 | c3_1(a21) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c1_1(a21)) | (~c0_1(a21))),
% 1.09/0.99 inference(modus_ponens,[status(thm)],[1889, 1888])).
% 1.09/0.99 tff(1891,plain,
% 1.09/0.99 (~c1_1(a21)),
% 1.09/0.99 inference(unit_resolution,[status(thm)],[1890, 117, 1, 1884, 1714, 1883, 1794, 268, 309])).
% 1.09/0.99 tff(1892,plain,
% 1.09/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a21) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | (~c2_1(a13)) | c1_1(a21) | (~c0_1(a21)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a21) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | (~c2_1(a13)) | c1_1(a21) | (~c0_1(a21)))),
% 1.09/0.99 inference(rewrite,[status(thm)],[])).
% 1.09/0.99 tff(1893,plain,
% 1.09/0.99 (((~ndr1_0) | c1_1(a21) | c3_1(a21) | (~c0_1(a21)) | c0_1(a13) | (~c1_1(a13)) | (~c3_1(a13)) | c0_1(a13) | (~c2_1(a13)) | (~c1_1(a13))) <=> (c3_1(a21) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | (~c2_1(a13)) | c1_1(a21) | (~c0_1(a21)))),
% 1.09/0.99 inference(rewrite,[status(thm)],[])).
% 1.09/0.99 tff(1894,plain,
% 1.09/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a21) | c3_1(a21) | (~c0_1(a21)) | c0_1(a13) | (~c1_1(a13)) | (~c3_1(a13)) | c0_1(a13) | (~c2_1(a13)) | (~c1_1(a13)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a21) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | (~c2_1(a13)) | c1_1(a21) | (~c0_1(a21))))),
% 1.09/0.99 inference(monotonicity,[status(thm)],[1893])).
% 1.09/0.99 tff(1895,plain,
% 1.09/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a21) | c3_1(a21) | (~c0_1(a21)) | c0_1(a13) | (~c1_1(a13)) | (~c3_1(a13)) | c0_1(a13) | (~c2_1(a13)) | (~c1_1(a13)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a21) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | (~c2_1(a13)) | c1_1(a21) | (~c0_1(a21)))),
% 1.09/0.99 inference(transitivity,[status(thm)],[1894, 1892])).
% 1.09/0.99 tff(1896,plain,
% 1.09/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a21) | c3_1(a21) | (~c0_1(a21)) | c0_1(a13) | (~c1_1(a13)) | (~c3_1(a13)) | c0_1(a13) | (~c2_1(a13)) | (~c1_1(a13)))),
% 1.09/0.99 inference(quant_inst,[status(thm)],[])).
% 1.09/0.99 tff(1897,plain,
% 1.09/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a21) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | (~c2_1(a13)) | c1_1(a21) | (~c0_1(a21))),
% 1.09/0.99 inference(modus_ponens,[status(thm)],[1896, 1895])).
% 1.09/0.99 tff(1898,plain,
% 1.09/0.99 ($false),
% 1.09/0.99 inference(unit_resolution,[status(thm)],[1897, 117, 1884, 1714, 1883, 1794, 268, 279, 1783, 1891])).
% 1.09/0.99 tff(1899,plain,(hskp8 | c0_1(a13) | hskp30), inference(lemma,lemma(discharge,[]))).
% 1.09/0.99 tff(1900,plain,
% 1.09/0.99 (hskp8),
% 1.09/0.99 inference(unit_resolution,[status(thm)],[1899, 1, 268])).
% 1.09/0.99 tff(1901,plain,
% 1.09/0.99 (((~hskp8) | c2_1(a13)) <=> ((~hskp8) | c2_1(a13))),
% 1.09/0.99 inference(rewrite,[status(thm)],[])).
% 1.09/0.99 tff(1902,axiom,((~hskp8) | c2_1(a13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause75')).
% 1.09/0.99 tff(1903,plain,
% 1.09/0.99 ((~hskp8) | c2_1(a13)),
% 1.09/0.99 inference(modus_ponens,[status(thm)],[1902, 1901])).
% 1.09/0.99 tff(1904,plain,
% 1.09/0.99 ((~hskp8) | c2_1(a13)),
% 1.09/0.99 inference(modus_ponens,[status(thm)],[1903, 1901])).
% 1.09/0.99 tff(1905,plain,
% 1.09/0.99 ((~hskp8) | c2_1(a13)),
% 1.09/0.99 inference(modus_ponens,[status(thm)],[1904, 1901])).
% 1.09/0.99 tff(1906,plain,
% 1.09/0.99 ((~hskp8) | c2_1(a13)),
% 1.09/0.99 inference(modus_ponens,[status(thm)],[1905, 1901])).
% 1.09/0.99 tff(1907,plain,
% 1.09/0.99 ((~hskp8) | c2_1(a13)),
% 1.09/0.99 inference(modus_ponens,[status(thm)],[1906, 1901])).
% 1.09/0.99 tff(1908,plain,
% 1.09/0.99 ((~hskp8) | c2_1(a13)),
% 1.09/0.99 inference(modus_ponens,[status(thm)],[1907, 1901])).
% 1.09/0.99 tff(1909,plain,
% 1.09/0.99 ((~hskp8) | c2_1(a13)),
% 1.09/0.99 inference(modus_ponens,[status(thm)],[1908, 1901])).
% 1.09/0.99 tff(1910,plain,
% 1.09/0.99 ((~hskp8) | c2_1(a13)),
% 1.09/0.99 inference(modus_ponens,[status(thm)],[1909, 1901])).
% 1.09/0.99 tff(1911,plain,
% 1.09/0.99 (c2_1(a13)),
% 1.09/0.99 inference(unit_resolution,[status(thm)],[1910, 1900])).
% 1.09/0.99 tff(1912,plain,
% 1.09/0.99 (c0_1(a21)),
% 1.09/0.99 inference(unit_resolution,[status(thm)],[386, 1774])).
% 1.09/0.99 tff(1913,plain,
% 1.09/0.99 (~c1_1(a21)),
% 1.09/0.99 inference(unit_resolution,[status(thm)],[1890, 117, 1, 1912, 1714, 1911, 1775, 268, 309])).
% 1.09/0.99 tff(1914,plain,
% 1.09/0.99 ($false),
% 1.09/0.99 inference(unit_resolution,[status(thm)],[1897, 117, 1912, 1714, 1911, 1775, 268, 279, 1723, 1913])).
% 1.09/0.99 tff(1915,plain,(hskp12 | c0_1(a13) | hskp30), inference(lemma,lemma(discharge,[]))).
% 1.09/0.99 tff(1916,plain,
% 1.09/0.99 (hskp12),
% 1.09/0.99 inference(unit_resolution,[status(thm)],[1915, 1, 268])).
% 1.09/0.99 tff(1917,plain,
% 1.09/0.99 (c3_1(a24)),
% 1.09/0.99 inference(unit_resolution,[status(thm)],[209, 1916])).
% 1.09/0.99 tff(1918,plain,
% 1.09/0.99 (~c2_1(a24)),
% 1.09/0.99 inference(unit_resolution,[status(thm)],[198, 1916])).
% 1.09/0.99 tff(1919,plain,
% 1.09/0.99 (c1_1(a24)),
% 1.09/0.99 inference(unit_resolution,[status(thm)],[220, 1916])).
% 1.09/0.99 tff(1920,plain,
% 1.09/0.99 (hskp16),
% 1.09/0.99 inference(unit_resolution,[status(thm)],[229, 1916])).
% 1.09/0.99 tff(1921,plain,
% 1.09/0.99 (c3_1(a30)),
% 1.09/0.99 inference(unit_resolution,[status(thm)],[266, 1920])).
% 1.09/0.99 tff(1922,plain,
% 1.09/0.99 (~c1_1(a30)),
% 1.09/0.99 inference(unit_resolution,[status(thm)],[244, 1920])).
% 1.09/0.99 tff(1923,plain,
% 1.09/0.99 (c2_1(a30)),
% 1.09/0.99 inference(unit_resolution,[status(thm)],[255, 1920])).
% 1.09/0.99 tff(1924,assumption,(~c2_1(a24)), introduced(assumption)).
% 1.09/0.99 tff(1925,assumption,(c3_1(a24)), introduced(assumption)).
% 1.09/0.99 tff(1926,plain,
% 1.09/0.99 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | c2_1(a24) | (~ndr1_0) | (~c3_1(a24)) | c0_1(a24))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c2_1(a24) | (~ndr1_0) | (~c3_1(a24)) | c0_1(a24))),
% 1.09/0.99 inference(rewrite,[status(thm)],[])).
% 1.09/0.99 tff(1927,plain,
% 1.09/0.99 ((hskp30 | hskp11 | (~ndr1_0) | c2_1(a24) | c0_1(a24) | (~c3_1(a24))) <=> (hskp30 | hskp11 | c2_1(a24) | (~ndr1_0) | (~c3_1(a24)) | c0_1(a24))),
% 1.09/0.99 inference(rewrite,[status(thm)],[])).
% 1.09/0.99 tff(1928,plain,
% 1.09/0.99 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a24) | c0_1(a24) | (~c3_1(a24)))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | c2_1(a24) | (~ndr1_0) | (~c3_1(a24)) | c0_1(a24)))),
% 1.09/0.99 inference(monotonicity,[status(thm)],[1927])).
% 1.09/0.99 tff(1929,plain,
% 1.09/0.99 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a24) | c0_1(a24) | (~c3_1(a24)))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c2_1(a24) | (~ndr1_0) | (~c3_1(a24)) | c0_1(a24))),
% 1.09/0.99 inference(transitivity,[status(thm)],[1928, 1926])).
% 1.09/0.99 tff(1930,plain,
% 1.09/0.99 ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a24) | c0_1(a24) | (~c3_1(a24)))),
% 1.09/0.99 inference(quant_inst,[status(thm)],[])).
% 1.09/0.99 tff(1931,plain,
% 1.09/0.99 ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c2_1(a24) | (~ndr1_0) | (~c3_1(a24)) | c0_1(a24)),
% 1.09/0.99 inference(modus_ponens,[status(thm)],[1930, 1929])).
% 1.09/0.99 tff(1932,plain,
% 1.09/0.99 (hskp11 | c0_1(a24)),
% 1.09/0.99 inference(unit_resolution,[status(thm)],[1931, 117, 1, 1925, 1924, 41])).
% 1.09/0.99 tff(1933,plain,
% 1.09/0.99 (c0_1(a24)),
% 1.09/0.99 inference(unit_resolution,[status(thm)],[1932, 1340])).
% 1.09/0.99 tff(1934,plain,
% 1.09/0.99 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W))))),
% 1.09/0.99 inference(bind,[status(th)],[])).
% 1.09/0.99 tff(1935,plain,
% 1.09/0.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 1.09/0.99 inference(quant_intro,[status(thm)],[1934])).
% 1.09/0.99 tff(1936,plain,
% 1.09/0.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 1.09/0.99 inference(rewrite,[status(thm)],[])).
% 1.09/0.99 tff(1937,plain,
% 1.09/0.99 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_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) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_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) | (~c3_1(U)) | (~c2_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) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_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) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c1_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))))),
% 1.09/0.99 inference(bind,[status(th)],[])).
% 1.09/0.99 tff(1938,plain,
% 1.09/0.99 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 1.09/0.99 inference(quant_intro,[status(thm)],[1937])).
% 1.09/0.99 tff(1939,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause196')).
% 1.09/0.99 tff(1940,plain,
% 1.09/0.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 1.09/0.99 inference(modus_ponens,[status(thm)],[1939, 1938])).
% 1.09/0.99 tff(1941,plain,
% 1.09/0.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 1.09/0.99 inference(modus_ponens,[status(thm)],[1940, 1936])).
% 1.09/0.99 tff(1942,plain,(
% 1.09/0.99 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 1.09/0.99 inference(skolemize,[status(sab)],[1941])).
% 1.09/0.99 tff(1943,plain,
% 1.09/0.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 1.09/0.99 inference(modus_ponens,[status(thm)],[1942, 1935])).
% 1.09/0.99 tff(1944,assumption,(c1_1(a24)), introduced(assumption)).
% 1.09/0.99 tff(1945,plain,
% 1.09/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c1_1(a30) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | (~c0_1(a30)) | (~c2_1(a30)) | (~c3_1(a30)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a30) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | (~c0_1(a30)) | (~c2_1(a30)) | (~c3_1(a30)))),
% 1.09/0.99 inference(rewrite,[status(thm)],[])).
% 1.09/0.99 tff(1946,plain,
% 1.09/0.99 (((~ndr1_0) | (~c3_1(a30)) | (~c2_1(a30)) | (~c0_1(a30)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | c1_1(a30) | (~c3_1(a30)) | (~c0_1(a30))) <=> (c1_1(a30) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | (~c0_1(a30)) | (~c2_1(a30)) | (~c3_1(a30)))),
% 1.09/0.99 inference(rewrite,[status(thm)],[])).
% 1.09/0.99 tff(1947,plain,
% 1.09/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a30)) | (~c2_1(a30)) | (~c0_1(a30)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | c1_1(a30) | (~c3_1(a30)) | (~c0_1(a30)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c1_1(a30) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | (~c0_1(a30)) | (~c2_1(a30)) | (~c3_1(a30))))),
% 1.09/0.99 inference(monotonicity,[status(thm)],[1946])).
% 1.09/0.99 tff(1948,plain,
% 1.09/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a30)) | (~c2_1(a30)) | (~c0_1(a30)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | c1_1(a30) | (~c3_1(a30)) | (~c0_1(a30)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a30) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | (~c0_1(a30)) | (~c2_1(a30)) | (~c3_1(a30)))),
% 1.09/0.99 inference(transitivity,[status(thm)],[1947, 1945])).
% 1.09/0.99 tff(1949,plain,
% 1.09/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a30)) | (~c2_1(a30)) | (~c0_1(a30)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | c1_1(a30) | (~c3_1(a30)) | (~c0_1(a30)))),
% 1.09/0.99 inference(quant_inst,[status(thm)],[])).
% 1.09/0.99 tff(1950,plain,
% 1.09/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a30) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | (~c0_1(a30)) | (~c2_1(a30)) | (~c3_1(a30))),
% 1.09/0.99 inference(modus_ponens,[status(thm)],[1949, 1948])).
% 1.09/0.99 tff(1951,plain,
% 1.09/0.99 ((~c0_1(a24)) | (~c0_1(a30))),
% 1.09/0.99 inference(unit_resolution,[status(thm)],[1950, 117, 330, 329, 1944, 1925, 328, 1943])).
% 1.09/0.99 tff(1952,plain,
% 1.09/0.99 (~c0_1(a30)),
% 1.09/0.99 inference(unit_resolution,[status(thm)],[1951, 1933])).
% 1.09/0.99 tff(1953,plain,
% 1.09/0.99 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c1_1(a30) | c2_1(a24) | (~ndr1_0) | (~c1_1(a24)) | (~c0_1(a24)) | (~c2_1(a30)) | (~c3_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a30) | c2_1(a24) | (~ndr1_0) | (~c1_1(a24)) | (~c0_1(a24)) | (~c2_1(a30)) | (~c3_1(a30)))),
% 1.09/0.99 inference(rewrite,[status(thm)],[])).
% 1.09/0.99 tff(1954,plain,
% 1.09/0.99 ((hskp15 | (~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c0_1(a24)) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30))) <=> (hskp15 | c1_1(a30) | c2_1(a24) | (~ndr1_0) | (~c1_1(a24)) | (~c0_1(a24)) | (~c2_1(a30)) | (~c3_1(a30)))),
% 1.09/0.99 inference(rewrite,[status(thm)],[])).
% 1.09/0.99 tff(1955,plain,
% 1.09/0.99 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c0_1(a24)) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c1_1(a30) | c2_1(a24) | (~ndr1_0) | (~c1_1(a24)) | (~c0_1(a24)) | (~c2_1(a30)) | (~c3_1(a30))))),
% 1.09/0.99 inference(monotonicity,[status(thm)],[1954])).
% 1.09/0.99 tff(1956,plain,
% 1.09/0.99 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c0_1(a24)) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a30) | c2_1(a24) | (~ndr1_0) | (~c1_1(a24)) | (~c0_1(a24)) | (~c2_1(a30)) | (~c3_1(a30)))),
% 1.09/0.99 inference(transitivity,[status(thm)],[1955, 1953])).
% 1.09/0.99 tff(1957,plain,
% 1.09/0.99 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c0_1(a24)) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)))),
% 1.09/0.99 inference(quant_inst,[status(thm)],[])).
% 1.09/0.99 tff(1958,plain,
% 1.09/0.99 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a30) | c2_1(a24) | (~ndr1_0) | (~c1_1(a24)) | (~c0_1(a24)) | (~c2_1(a30)) | (~c3_1(a30))),
% 1.09/0.99 inference(modus_ponens,[status(thm)],[1957, 1956])).
% 1.09/0.99 tff(1959,plain,
% 1.09/0.99 (hskp15 | (~c0_1(a24))),
% 1.09/0.99 inference(unit_resolution,[status(thm)],[1958, 117, 330, 329, 1944, 328, 1924, 376])).
% 1.09/0.99 tff(1960,plain,
% 1.09/0.99 (hskp15),
% 1.09/0.99 inference(unit_resolution,[status(thm)],[1959, 1933])).
% 1.09/0.99 tff(1961,plain,
% 1.09/0.99 (c1_1(a29)),
% 1.09/0.99 inference(unit_resolution,[status(thm)],[136, 1960])).
% 1.09/0.99 tff(1962,plain,
% 1.09/0.99 (~c3_1(a29)),
% 1.09/0.99 inference(unit_resolution,[status(thm)],[142, 1960])).
% 1.09/0.99 tff(1963,plain,
% 1.09/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a24) | c0_1(a9) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c2_1(a24) | c0_1(a9) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30)))),
% 1.09/0.99 inference(rewrite,[status(thm)],[])).
% 1.09/0.99 tff(1964,plain,
% 1.09/0.99 (((~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c1_1(a9) | c0_1(a9) | c2_1(a9)) <=> (c2_1(a24) | c0_1(a9) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30)))),
% 1.09/0.99 inference(rewrite,[status(thm)],[])).
% 1.09/0.99 tff(1965,plain,
% 1.09/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c1_1(a9) | c0_1(a9) | c2_1(a9))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a24) | c0_1(a9) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30))))),
% 1.09/0.99 inference(monotonicity,[status(thm)],[1964])).
% 1.09/0.99 tff(1966,plain,
% 1.09/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c1_1(a9) | c0_1(a9) | c2_1(a9))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c2_1(a24) | c0_1(a9) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30)))),
% 1.09/0.99 inference(transitivity,[status(thm)],[1965, 1963])).
% 1.09/0.99 tff(1967,plain,
% 1.09/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c1_1(a9) | c0_1(a9) | c2_1(a9))),
% 1.09/0.99 inference(quant_inst,[status(thm)],[])).
% 1.09/0.99 tff(1968,plain,
% 1.09/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c2_1(a24) | c0_1(a9) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30))),
% 1.09/0.99 inference(modus_ponens,[status(thm)],[1967, 1966])).
% 1.09/0.99 tff(1969,plain,
% 1.09/0.99 ($false),
% 1.09/0.99 inference(unit_resolution,[status(thm)],[1968, 117, 330, 329, 1944, 1925, 1924, 1523, 1537, 1517, 479, 1952])).
% 1.09/0.99 tff(1970,plain,(hskp11 | (~c2_1(a30)) | (~c3_1(a30)) | (~c1_1(a24)) | (~c3_1(a24)) | c2_1(a24) | c1_1(a30) | hskp21 | hskp30), inference(lemma,lemma(discharge,[]))).
% 1.09/0.99 tff(1971,plain,
% 1.09/0.99 (hskp21),
% 1.09/0.99 inference(unit_resolution,[status(thm)],[1970, 1340, 329, 1944, 1925, 1924, 328, 330, 1])).
% 1.09/0.99 tff(1972,plain,
% 1.09/0.99 (~c2_1(a29)),
% 1.09/0.99 inference(unit_resolution,[status(thm)],[148, 1960])).
% 1.09/0.99 tff(1973,plain,
% 1.09/0.99 (~c0_1(a29)),
% 1.09/0.99 inference(unit_resolution,[status(thm)],[171, 1972, 1971, 1962, 1961])).
% 1.09/0.99 tff(1974,plain,
% 1.09/0.99 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))))),
% 1.09/0.99 inference(bind,[status(th)],[])).
% 1.09/0.99 tff(1975,plain,
% 1.09/0.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.09/0.99 inference(quant_intro,[status(thm)],[1974])).
% 1.09/0.99 tff(1976,plain,
% 1.09/0.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.09/0.99 inference(rewrite,[status(thm)],[])).
% 1.09/0.99 tff(1977,plain,
% 1.09/0.99 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(W)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(W))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(W)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(W))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(W)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(W))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(W)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(W))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | (~c2_1(W)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | (~c2_1(W))))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))))),
% 1.09/0.99 inference(bind,[status(th)],[])).
% 1.09/0.99 tff(1978,plain,
% 1.09/0.99 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.09/0.99 inference(quant_intro,[status(thm)],[1977])).
% 1.09/0.99 tff(1979,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause189')).
% 1.09/0.99 tff(1980,plain,
% 1.09/0.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.09/0.99 inference(modus_ponens,[status(thm)],[1979, 1978])).
% 1.09/0.99 tff(1981,plain,
% 1.09/0.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.09/0.99 inference(modus_ponens,[status(thm)],[1980, 1976])).
% 1.09/0.99 tff(1982,plain,(
% 1.09/0.99 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.09/0.99 inference(skolemize,[status(sab)],[1981])).
% 1.09/0.99 tff(1983,plain,
% 1.09/0.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.09/0.99 inference(modus_ponens,[status(thm)],[1982, 1975])).
% 1.09/0.99 tff(1984,plain,
% 1.09/0.99 (~c3_1(a39)),
% 1.09/0.99 inference(unit_resolution,[status(thm)],[58, 1971])).
% 1.09/0.99 tff(1985,plain,
% 1.09/0.99 (~c0_1(a39)),
% 1.09/0.99 inference(unit_resolution,[status(thm)],[64, 1971])).
% 1.09/0.99 tff(1986,plain,
% 1.09/0.99 (c2_1(a39)),
% 1.09/0.99 inference(unit_resolution,[status(thm)],[75, 1971])).
% 1.09/0.99 tff(1987,plain,
% 1.09/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a39) | c3_1(a39) | c1_1(a30) | c2_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c0_1(a29) | c0_1(a30) | (~c2_1(a30)) | (~c2_1(a39)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a39) | c3_1(a39) | c1_1(a30) | c2_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c0_1(a29) | c0_1(a30) | (~c2_1(a30)) | (~c2_1(a39)))),
% 1.09/1.00 inference(rewrite,[status(thm)],[])).
% 1.09/1.00 tff(1988,plain,
% 1.09/1.00 (((~ndr1_0) | c0_1(a39) | c3_1(a39) | (~c2_1(a39)) | c0_1(a29) | c2_1(a29) | (~c1_1(a29)) | c1_1(a30) | c0_1(a30) | (~c2_1(a30))) <=> (c0_1(a39) | c3_1(a39) | c1_1(a30) | c2_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c0_1(a29) | c0_1(a30) | (~c2_1(a30)) | (~c2_1(a39)))),
% 1.09/1.00 inference(rewrite,[status(thm)],[])).
% 1.09/1.00 tff(1989,plain,
% 1.09/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a39) | c3_1(a39) | (~c2_1(a39)) | c0_1(a29) | c2_1(a29) | (~c1_1(a29)) | c1_1(a30) | c0_1(a30) | (~c2_1(a30)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a39) | c3_1(a39) | c1_1(a30) | c2_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c0_1(a29) | c0_1(a30) | (~c2_1(a30)) | (~c2_1(a39))))),
% 1.09/1.00 inference(monotonicity,[status(thm)],[1988])).
% 1.09/1.00 tff(1990,plain,
% 1.09/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a39) | c3_1(a39) | (~c2_1(a39)) | c0_1(a29) | c2_1(a29) | (~c1_1(a29)) | c1_1(a30) | c0_1(a30) | (~c2_1(a30)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a39) | c3_1(a39) | c1_1(a30) | c2_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c0_1(a29) | c0_1(a30) | (~c2_1(a30)) | (~c2_1(a39)))),
% 1.09/1.00 inference(transitivity,[status(thm)],[1989, 1987])).
% 1.09/1.00 tff(1991,plain,
% 1.09/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a39) | c3_1(a39) | (~c2_1(a39)) | c0_1(a29) | c2_1(a29) | (~c1_1(a29)) | c1_1(a30) | c0_1(a30) | (~c2_1(a30)))),
% 1.09/1.00 inference(quant_inst,[status(thm)],[])).
% 1.09/1.00 tff(1992,plain,
% 1.09/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a39) | c3_1(a39) | c1_1(a30) | c2_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c0_1(a29) | c0_1(a30) | (~c2_1(a30)) | (~c2_1(a39))),
% 1.09/1.00 inference(modus_ponens,[status(thm)],[1991, 1990])).
% 1.09/1.00 tff(1993,plain,
% 1.09/1.00 ($false),
% 1.09/1.00 inference(unit_resolution,[status(thm)],[1992, 117, 1986, 330, 1961, 1985, 1984, 328, 1972, 1983, 1973, 1952])).
% 1.09/1.00 tff(1994,plain,(hskp11 | (~c2_1(a30)) | c1_1(a30) | (~c3_1(a30)) | (~c1_1(a24)) | c2_1(a24) | (~c3_1(a24)) | hskp30), inference(lemma,lemma(discharge,[]))).
% 1.09/1.00 tff(1995,plain,
% 1.09/1.00 (hskp11),
% 1.09/1.00 inference(unit_resolution,[status(thm)],[1994, 1923, 1922, 1921, 1919, 1918, 1917, 1])).
% 1.09/1.00 tff(1996,plain,
% 1.09/1.00 (~c3_1(a21)),
% 1.09/1.00 inference(unit_resolution,[status(thm)],[352, 1995])).
% 1.09/1.00 tff(1997,plain,
% 1.09/1.00 (c0_1(a21)),
% 1.09/1.00 inference(unit_resolution,[status(thm)],[386, 1995])).
% 1.09/1.00 tff(1998,plain,
% 1.09/1.00 (~c1_1(a21)),
% 1.09/1.00 inference(unit_resolution,[status(thm)],[1890, 117, 1, 1997, 1714, 1911, 1996, 268, 309])).
% 1.09/1.00 tff(1999,plain,
% 1.09/1.00 (((~![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)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | (c2_1(a21) | c3_1(a21) | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)) | (~c1_1(a21)) | (~c0_1(a21)))) <=> ((~![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)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | c2_1(a21) | c3_1(a21) | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)) | (~c1_1(a21)) | (~c0_1(a21)))),
% 1.09/1.00 inference(rewrite,[status(thm)],[])).
% 1.09/1.00 tff(2000,plain,
% 1.09/1.00 (((~ndr1_0) | c3_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c3_1(a21) | c2_1(a21) | (~c0_1(a21)) | c0_1(a13) | (~c2_1(a13)) | c3_1(a13)) <=> (c2_1(a21) | c3_1(a21) | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)) | (~c1_1(a21)) | (~c0_1(a21)))),
% 1.09/1.00 inference(rewrite,[status(thm)],[])).
% 1.09/1.00 tff(2001,plain,
% 1.09/1.00 (((~![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)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c3_1(a21) | c2_1(a21) | (~c0_1(a21)) | c0_1(a13) | (~c2_1(a13)) | c3_1(a13))) <=> ((~![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)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | (c2_1(a21) | c3_1(a21) | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)) | (~c1_1(a21)) | (~c0_1(a21))))),
% 1.09/1.00 inference(monotonicity,[status(thm)],[2000])).
% 1.09/1.00 tff(2002,plain,
% 1.09/1.00 (((~![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)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c3_1(a21) | c2_1(a21) | (~c0_1(a21)) | c0_1(a13) | (~c2_1(a13)) | c3_1(a13))) <=> ((~![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)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | c2_1(a21) | c3_1(a21) | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)) | (~c1_1(a21)) | (~c0_1(a21)))),
% 1.09/1.00 inference(transitivity,[status(thm)],[2001, 1999])).
% 1.09/1.00 tff(2003,plain,
% 1.09/1.00 ((~![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)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c3_1(a21) | c2_1(a21) | (~c0_1(a21)) | c0_1(a13) | (~c2_1(a13)) | c3_1(a13))),
% 1.09/1.00 inference(quant_inst,[status(thm)],[])).
% 1.09/1.00 tff(2004,plain,
% 1.09/1.00 ((~![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)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | c2_1(a21) | c3_1(a21) | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)) | (~c1_1(a21)) | (~c0_1(a21))),
% 1.09/1.00 inference(modus_ponens,[status(thm)],[2003, 2002])).
% 1.09/1.00 tff(2005,plain,
% 1.09/1.00 (~c1_1(a21)),
% 1.09/1.00 inference(unit_resolution,[status(thm)],[2004, 117, 895, 1911, 893, 897, 268, 160, 327])).
% 1.09/1.00 tff(2006,plain,
% 1.09/1.00 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | c3_1(W)))),
% 1.09/1.00 inference(bind,[status(th)],[])).
% 1.09/1.00 tff(2007,plain,
% 1.09/1.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | c3_1(W))),
% 1.09/1.00 inference(quant_intro,[status(thm)],[2006])).
% 1.09/1.00 tff(2008,plain,
% 1.09/1.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | c3_1(W))),
% 1.09/1.00 inference(rewrite,[status(thm)],[])).
% 1.09/1.00 tff(2009,plain,
% 1.09/1.00 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | c3_1(W))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | c3_1(W))))),
% 1.09/1.00 inference(bind,[status(th)],[])).
% 1.09/1.00 tff(2010,plain,
% 1.09/1.00 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | c3_1(W))),
% 1.09/1.00 inference(quant_intro,[status(thm)],[2009])).
% 1.09/1.00 tff(2011,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause193')).
% 1.09/1.00 tff(2012,plain,
% 1.09/1.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | c3_1(W))),
% 1.09/1.00 inference(modus_ponens,[status(thm)],[2011, 2010])).
% 1.09/1.00 tff(2013,plain,
% 1.09/1.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | c3_1(W))),
% 1.09/1.00 inference(modus_ponens,[status(thm)],[2012, 2008])).
% 1.09/1.00 tff(2014,plain,(
% 1.09/1.00 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | c3_1(W))),
% 1.09/1.00 inference(skolemize,[status(sab)],[2013])).
% 1.09/1.00 tff(2015,plain,
% 1.09/1.00 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | c3_1(W))),
% 1.09/1.00 inference(modus_ponens,[status(thm)],[2014, 2007])).
% 1.09/1.00 tff(2016,plain,
% 1.09/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | c3_1(W))) | (c1_1(a30) | c2_1(a21) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a30)) | (~c2_1(a30)) | (~c3_1(a30)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | c3_1(W))) | c1_1(a30) | c2_1(a21) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a30)) | (~c2_1(a30)) | (~c3_1(a30)))),
% 1.09/1.00 inference(rewrite,[status(thm)],[])).
% 1.09/1.00 tff(2017,plain,
% 1.09/1.00 (((~ndr1_0) | (~c3_1(a30)) | (~c2_1(a30)) | (~c0_1(a30)) | c1_1(a30) | (~c2_1(a30)) | (~c0_1(a30)) | c1_1(a21) | c2_1(a21) | c3_1(a21)) <=> (c1_1(a30) | c2_1(a21) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a30)) | (~c2_1(a30)) | (~c3_1(a30)))),
% 1.09/1.00 inference(rewrite,[status(thm)],[])).
% 1.09/1.00 tff(2018,plain,
% 1.09/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a30)) | (~c2_1(a30)) | (~c0_1(a30)) | c1_1(a30) | (~c2_1(a30)) | (~c0_1(a30)) | c1_1(a21) | c2_1(a21) | c3_1(a21))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | c3_1(W))) | (c1_1(a30) | c2_1(a21) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a30)) | (~c2_1(a30)) | (~c3_1(a30))))),
% 1.09/1.00 inference(monotonicity,[status(thm)],[2017])).
% 1.09/1.00 tff(2019,plain,
% 1.09/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a30)) | (~c2_1(a30)) | (~c0_1(a30)) | c1_1(a30) | (~c2_1(a30)) | (~c0_1(a30)) | c1_1(a21) | c2_1(a21) | c3_1(a21))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | c3_1(W))) | c1_1(a30) | c2_1(a21) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a30)) | (~c2_1(a30)) | (~c3_1(a30)))),
% 1.09/1.00 inference(transitivity,[status(thm)],[2018, 2016])).
% 1.09/1.00 tff(2020,plain,
% 1.09/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a30)) | (~c2_1(a30)) | (~c0_1(a30)) | c1_1(a30) | (~c2_1(a30)) | (~c0_1(a30)) | c1_1(a21) | c2_1(a21) | c3_1(a21))),
% 1.09/1.00 inference(quant_inst,[status(thm)],[])).
% 1.09/1.00 tff(2021,plain,
% 1.09/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | c3_1(W))) | c1_1(a30) | c2_1(a21) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a30)) | (~c2_1(a30)) | (~c3_1(a30))),
% 1.09/1.00 inference(modus_ponens,[status(thm)],[2020, 2019])).
% 1.09/1.00 tff(2022,plain,
% 1.09/1.00 (~c0_1(a30)),
% 1.09/1.00 inference(unit_resolution,[status(thm)],[2021, 117, 1923, 1921, 1922, 893, 897, 2015, 2005])).
% 1.09/1.00 tff(2023,plain,
% 1.09/1.00 (hskp23),
% 1.09/1.00 inference(unit_resolution,[status(thm)],[911, 2005])).
% 1.09/1.00 tff(2024,plain,
% 1.09/1.00 (~c3_1(a42)),
% 1.09/1.00 inference(unit_resolution,[status(thm)],[813, 2023])).
% 1.09/1.00 tff(2025,plain,
% 1.09/1.00 (~c1_1(a42)),
% 1.09/1.00 inference(unit_resolution,[status(thm)],[819, 2023])).
% 1.09/1.00 tff(2026,plain,
% 1.09/1.00 (c0_1(a42)),
% 1.09/1.00 inference(unit_resolution,[status(thm)],[830, 2023])).
% 1.09/1.00 tff(2027,assumption,(~c3_1(a42)), introduced(assumption)).
% 1.09/1.00 tff(2028,assumption,(~c1_1(a42)), introduced(assumption)).
% 1.09/1.00 tff(2029,assumption,(c0_1(a42)), introduced(assumption)).
% 1.09/1.00 tff(2030,plain,
% 1.09/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a42) | c3_1(a42) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a24) | (~c0_1(a42)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a42) | c3_1(a42) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a24) | (~c0_1(a42)))),
% 1.09/1.00 inference(rewrite,[status(thm)],[])).
% 1.09/1.00 tff(2031,plain,
% 1.09/1.00 (((~ndr1_0) | c1_1(a42) | c3_1(a42) | (~c0_1(a42)) | c0_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a13) | (~c2_1(a13)) | (~c1_1(a13))) <=> (c1_1(a42) | c3_1(a42) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a24) | (~c0_1(a42)))),
% 1.09/1.00 inference(rewrite,[status(thm)],[])).
% 1.09/1.00 tff(2032,plain,
% 1.09/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a42) | c3_1(a42) | (~c0_1(a42)) | c0_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a13) | (~c2_1(a13)) | (~c1_1(a13)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a42) | c3_1(a42) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a24) | (~c0_1(a42))))),
% 1.09/1.00 inference(monotonicity,[status(thm)],[2031])).
% 1.09/1.00 tff(2033,plain,
% 1.09/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a42) | c3_1(a42) | (~c0_1(a42)) | c0_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a13) | (~c2_1(a13)) | (~c1_1(a13)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a42) | c3_1(a42) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a24) | (~c0_1(a42)))),
% 1.09/1.00 inference(transitivity,[status(thm)],[2032, 2030])).
% 1.09/1.00 tff(2034,plain,
% 1.09/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a42) | c3_1(a42) | (~c0_1(a42)) | c0_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a13) | (~c2_1(a13)) | (~c1_1(a13)))),
% 1.09/1.00 inference(quant_inst,[status(thm)],[])).
% 1.09/1.00 tff(2035,plain,
% 1.09/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a42) | c3_1(a42) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a24) | (~c0_1(a42))),
% 1.09/1.00 inference(modus_ponens,[status(thm)],[2034, 2033])).
% 1.09/1.00 tff(2036,plain,
% 1.09/1.00 ($false),
% 1.09/1.00 inference(unit_resolution,[status(thm)],[2035, 117, 2029, 1944, 1925, 1795, 1538, 2028, 2027, 268, 279, 269])).
% 1.09/1.00 tff(2037,plain,(c0_1(a24) | (~c0_1(a42)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c1_1(a13)) | (~c2_1(a13)) | c1_1(a42) | c3_1(a42) | c0_1(a13)), inference(lemma,lemma(discharge,[]))).
% 1.09/1.00 tff(2038,plain,
% 1.09/1.00 (c0_1(a24)),
% 1.09/1.00 inference(unit_resolution,[status(thm)],[2037, 2026, 1919, 1917, 1714, 1911, 2025, 2024, 268])).
% 1.09/1.00 tff(2039,plain,
% 1.09/1.00 (^[V: $i, U: $i] : refl((hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> (hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))))),
% 1.09/1.00 inference(bind,[status(th)],[])).
% 1.09/1.00 tff(2040,plain,
% 1.09/1.00 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.09/1.00 inference(quant_intro,[status(thm)],[2039])).
% 1.09/1.00 tff(2041,plain,
% 1.09/1.00 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.09/1.00 inference(rewrite,[status(thm)],[])).
% 1.09/1.00 tff(2042,plain,
% 1.09/1.00 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_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) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_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) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_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)) | hskp22) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) | hskp22))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) | hskp22) <=> (hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_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)) | hskp22) <=> (hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))))),
% 1.09/1.00 inference(bind,[status(th)],[])).
% 1.09/1.00 tff(2043,plain,
% 1.09/1.00 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp22) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.09/1.00 inference(quant_intro,[status(thm)],[2042])).
% 1.09/1.00 tff(2044,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)) | hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause183')).
% 1.09/1.00 tff(2045,plain,
% 1.09/1.00 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.09/1.00 inference(modus_ponens,[status(thm)],[2044, 2043])).
% 1.09/1.00 tff(2046,plain,
% 1.09/1.00 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.09/1.00 inference(modus_ponens,[status(thm)],[2045, 2041])).
% 1.09/1.00 tff(2047,plain,(
% 1.09/1.00 ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.09/1.00 inference(skolemize,[status(sab)],[2046])).
% 1.09/1.00 tff(2048,plain,
% 1.09/1.00 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.09/1.00 inference(modus_ponens,[status(thm)],[2047, 2040])).
% 1.09/1.00 tff(2049,plain,
% 1.09/1.00 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)))),
% 1.09/1.00 inference(rewrite,[status(thm)],[])).
% 1.09/1.00 tff(2050,plain,
% 1.09/1.00 ((hskp22 | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | c1_1(a21) | c2_1(a21) | (~c0_1(a21))) <=> (hskp22 | c2_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)))),
% 1.09/1.00 inference(rewrite,[status(thm)],[])).
% 1.09/1.00 tff(2051,plain,
% 1.09/1.00 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | c1_1(a21) | c2_1(a21) | (~c0_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24))))),
% 1.09/1.00 inference(monotonicity,[status(thm)],[2050])).
% 1.09/1.00 tff(2052,plain,
% 1.09/1.00 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | c1_1(a21) | c2_1(a21) | (~c0_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)))),
% 1.09/1.00 inference(transitivity,[status(thm)],[2051, 2049])).
% 1.09/1.00 tff(2053,plain,
% 1.09/1.00 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | c1_1(a21) | c2_1(a21) | (~c0_1(a21)))),
% 1.09/1.00 inference(quant_inst,[status(thm)],[])).
% 1.09/1.00 tff(2054,plain,
% 1.09/1.00 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24))),
% 1.09/1.00 inference(modus_ponens,[status(thm)],[2053, 2052])).
% 1.09/1.00 tff(2055,plain,
% 1.09/1.00 (hskp22 | (~c0_1(a24))),
% 1.09/1.00 inference(unit_resolution,[status(thm)],[2054, 117, 1919, 1917, 895, 893, 2048, 2005])).
% 1.09/1.00 tff(2056,plain,
% 1.09/1.00 (hskp22),
% 1.09/1.00 inference(unit_resolution,[status(thm)],[2055, 2038])).
% 1.09/1.00 tff(2057,plain,
% 1.09/1.00 (((~hskp22) | (~c2_1(a40))) <=> ((~hskp22) | (~c2_1(a40)))),
% 1.09/1.00 inference(rewrite,[status(thm)],[])).
% 1.09/1.00 tff(2058,plain,
% 1.09/1.00 (((~c2_1(a40)) | (~hskp22)) <=> ((~hskp22) | (~c2_1(a40)))),
% 1.09/1.00 inference(rewrite,[status(thm)],[])).
% 1.09/1.00 tff(2059,axiom,((~c2_1(a40)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause98')).
% 1.09/1.00 tff(2060,plain,
% 1.09/1.00 ((~hskp22) | (~c2_1(a40))),
% 1.09/1.00 inference(modus_ponens,[status(thm)],[2059, 2058])).
% 1.09/1.00 tff(2061,plain,
% 1.09/1.00 ((~hskp22) | (~c2_1(a40))),
% 1.09/1.00 inference(modus_ponens,[status(thm)],[2060, 2057])).
% 1.09/1.00 tff(2062,plain,
% 1.09/1.00 (~c2_1(a40)),
% 1.09/1.00 inference(unit_resolution,[status(thm)],[2061, 2056])).
% 1.09/1.00 tff(2063,plain,
% 1.09/1.00 (((~hskp22) | (~c0_1(a40))) <=> ((~hskp22) | (~c0_1(a40)))),
% 1.09/1.00 inference(rewrite,[status(thm)],[])).
% 1.09/1.00 tff(2064,plain,
% 1.09/1.00 (((~c0_1(a40)) | (~hskp22)) <=> ((~hskp22) | (~c0_1(a40)))),
% 1.09/1.00 inference(rewrite,[status(thm)],[])).
% 1.09/1.00 tff(2065,axiom,((~c0_1(a40)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause97')).
% 1.09/1.00 tff(2066,plain,
% 1.09/1.00 ((~hskp22) | (~c0_1(a40))),
% 1.09/1.00 inference(modus_ponens,[status(thm)],[2065, 2064])).
% 1.09/1.00 tff(2067,plain,
% 1.09/1.00 ((~hskp22) | (~c0_1(a40))),
% 1.09/1.00 inference(modus_ponens,[status(thm)],[2066, 2063])).
% 1.09/1.00 tff(2068,plain,
% 1.09/1.00 (~c0_1(a40)),
% 1.09/1.00 inference(unit_resolution,[status(thm)],[2067, 2056])).
% 1.09/1.00 tff(2069,plain,
% 1.09/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a40) | c2_1(a40) | c1_1(a30) | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)) | c0_1(a30) | (~c2_1(a30)) | (~c1_1(a40)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a40) | c2_1(a40) | c1_1(a30) | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)) | c0_1(a30) | (~c2_1(a30)) | (~c1_1(a40)))),
% 1.09/1.00 inference(rewrite,[status(thm)],[])).
% 1.09/1.00 tff(2070,plain,
% 1.09/1.00 (((~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c2_1(a13)) | c0_1(a40) | c2_1(a40) | (~c1_1(a40)) | c1_1(a30) | c0_1(a30) | (~c2_1(a30))) <=> (c0_1(a40) | c2_1(a40) | c1_1(a30) | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)) | c0_1(a30) | (~c2_1(a30)) | (~c1_1(a40)))),
% 1.09/1.00 inference(rewrite,[status(thm)],[])).
% 1.09/1.00 tff(2071,plain,
% 1.09/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c2_1(a13)) | c0_1(a40) | c2_1(a40) | (~c1_1(a40)) | c1_1(a30) | c0_1(a30) | (~c2_1(a30)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a40) | c2_1(a40) | c1_1(a30) | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)) | c0_1(a30) | (~c2_1(a30)) | (~c1_1(a40))))),
% 1.09/1.00 inference(monotonicity,[status(thm)],[2070])).
% 1.09/1.00 tff(2072,plain,
% 1.09/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c2_1(a13)) | c0_1(a40) | c2_1(a40) | (~c1_1(a40)) | c1_1(a30) | c0_1(a30) | (~c2_1(a30)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a40) | c2_1(a40) | c1_1(a30) | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)) | c0_1(a30) | (~c2_1(a30)) | (~c1_1(a40)))),
% 1.09/1.00 inference(transitivity,[status(thm)],[2071, 2069])).
% 1.09/1.00 tff(2073,plain,
% 1.09/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c2_1(a13)) | c0_1(a40) | c2_1(a40) | (~c1_1(a40)) | c1_1(a30) | c0_1(a30) | (~c2_1(a30)))),
% 1.09/1.00 inference(quant_inst,[status(thm)],[])).
% 1.09/1.00 tff(2074,plain,
% 1.09/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a40) | c2_1(a40) | c1_1(a30) | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)) | c0_1(a30) | (~c2_1(a30)) | (~c1_1(a40))),
% 1.09/1.00 inference(modus_ponens,[status(thm)],[2073, 2072])).
% 1.09/1.00 tff(2075,plain,
% 1.09/1.00 (~c1_1(a40)),
% 1.09/1.00 inference(unit_resolution,[status(thm)],[2074, 117, 1923, 1911, 2068, 2062, 1922, 268, 1983, 327, 2022])).
% 1.09/1.00 tff(2076,plain,
% 1.09/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a40) | c2_1(a40) | c2_1(a24) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30)) | c1_1(a40))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a40) | c2_1(a40) | c2_1(a24) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30)) | c1_1(a40))),
% 1.09/1.00 inference(rewrite,[status(thm)],[])).
% 1.09/1.00 tff(2077,plain,
% 1.09/1.00 (((~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c1_1(a40) | c0_1(a40) | c2_1(a40)) <=> (c0_1(a40) | c2_1(a40) | c2_1(a24) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30)) | c1_1(a40))),
% 1.09/1.00 inference(rewrite,[status(thm)],[])).
% 1.09/1.00 tff(2078,plain,
% 1.09/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c1_1(a40) | c0_1(a40) | c2_1(a40))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a40) | c2_1(a40) | c2_1(a24) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30)) | c1_1(a40)))),
% 1.09/1.01 inference(monotonicity,[status(thm)],[2077])).
% 1.09/1.01 tff(2079,plain,
% 1.09/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c1_1(a40) | c0_1(a40) | c2_1(a40))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a40) | c2_1(a40) | c2_1(a24) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30)) | c1_1(a40))),
% 1.09/1.01 inference(transitivity,[status(thm)],[2078, 2076])).
% 1.09/1.01 tff(2080,plain,
% 1.09/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c1_1(a40) | c0_1(a40) | c2_1(a40))),
% 1.09/1.01 inference(quant_inst,[status(thm)],[])).
% 1.09/1.01 tff(2081,plain,
% 1.09/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a40) | c2_1(a40) | c2_1(a24) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30)) | c1_1(a40)),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2080, 2079])).
% 1.09/1.01 tff(2082,plain,
% 1.09/1.01 ($false),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2081, 117, 1923, 1921, 1919, 1917, 2068, 2062, 1918, 479, 2022, 2075])).
% 1.09/1.01 tff(2083,plain,((~hskp11) | c0_1(a13) | c3_1(a13) | hskp30), inference(lemma,lemma(discharge,[]))).
% 1.09/1.01 tff(2084,plain,
% 1.09/1.01 (c3_1(a13)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2083, 1995, 268, 1])).
% 1.09/1.01 tff(2085,plain,
% 1.09/1.01 ($false),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[1897, 117, 1997, 1714, 1911, 1996, 268, 279, 2084, 1998])).
% 1.09/1.01 tff(2086,plain,(hskp30 | c0_1(a13)), inference(lemma,lemma(discharge,[]))).
% 1.09/1.01 tff(2087,plain,
% 1.09/1.01 (hskp30),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2086, 268])).
% 1.09/1.01 tff(2088,plain,
% 1.09/1.01 (((~hskp30) | c0_1(a20)) <=> ((~hskp30) | c0_1(a20))),
% 1.09/1.01 inference(rewrite,[status(thm)],[])).
% 1.09/1.01 tff(2089,axiom,((~hskp30) | c0_1(a20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause42')).
% 1.09/1.01 tff(2090,plain,
% 1.09/1.01 ((~hskp30) | c0_1(a20)),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2089, 2088])).
% 1.09/1.01 tff(2091,plain,
% 1.09/1.01 ((~hskp30) | c0_1(a20)),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2090, 2088])).
% 1.09/1.01 tff(2092,plain,
% 1.09/1.01 ((~hskp30) | c0_1(a20)),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2091, 2088])).
% 1.09/1.01 tff(2093,plain,
% 1.09/1.01 ((~hskp30) | c0_1(a20)),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2092, 2088])).
% 1.09/1.01 tff(2094,plain,
% 1.09/1.01 ((~hskp30) | c0_1(a20)),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2093, 2088])).
% 1.09/1.01 tff(2095,plain,
% 1.09/1.01 ((~hskp30) | c0_1(a20)),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2094, 2088])).
% 1.09/1.01 tff(2096,plain,
% 1.09/1.01 ((~hskp30) | c0_1(a20)),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2095, 2088])).
% 1.09/1.01 tff(2097,plain,
% 1.09/1.01 ((~hskp30) | c0_1(a20)),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2096, 2088])).
% 1.09/1.01 tff(2098,plain,
% 1.09/1.01 (c0_1(a20)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2097, 2087])).
% 1.09/1.01 tff(2099,plain,
% 1.09/1.01 (((~hskp30) | c3_1(a20)) <=> ((~hskp30) | c3_1(a20))),
% 1.09/1.01 inference(rewrite,[status(thm)],[])).
% 1.09/1.01 tff(2100,axiom,((~hskp30) | c3_1(a20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause44')).
% 1.09/1.01 tff(2101,plain,
% 1.09/1.01 ((~hskp30) | c3_1(a20)),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2100, 2099])).
% 1.09/1.01 tff(2102,plain,
% 1.09/1.01 ((~hskp30) | c3_1(a20)),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2101, 2099])).
% 1.09/1.01 tff(2103,plain,
% 1.09/1.01 ((~hskp30) | c3_1(a20)),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2102, 2099])).
% 1.09/1.01 tff(2104,plain,
% 1.09/1.01 ((~hskp30) | c3_1(a20)),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2103, 2099])).
% 1.09/1.01 tff(2105,plain,
% 1.09/1.01 ((~hskp30) | c3_1(a20)),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2104, 2099])).
% 1.09/1.01 tff(2106,plain,
% 1.09/1.01 ((~hskp30) | c3_1(a20)),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2105, 2099])).
% 1.09/1.01 tff(2107,plain,
% 1.09/1.01 ((~hskp30) | c3_1(a20)),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2106, 2099])).
% 1.09/1.01 tff(2108,plain,
% 1.09/1.01 ((~hskp30) | c3_1(a20)),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2107, 2099])).
% 1.09/1.01 tff(2109,plain,
% 1.09/1.01 (c3_1(a20)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2108, 2087])).
% 1.09/1.01 tff(2110,plain,
% 1.09/1.01 (((~hskp30) | c2_1(a20)) <=> ((~hskp30) | c2_1(a20))),
% 1.09/1.01 inference(rewrite,[status(thm)],[])).
% 1.09/1.01 tff(2111,axiom,((~hskp30) | c2_1(a20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause43')).
% 1.09/1.01 tff(2112,plain,
% 1.09/1.01 ((~hskp30) | c2_1(a20)),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2111, 2110])).
% 1.09/1.01 tff(2113,plain,
% 1.09/1.01 ((~hskp30) | c2_1(a20)),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2112, 2110])).
% 1.09/1.01 tff(2114,plain,
% 1.09/1.01 ((~hskp30) | c2_1(a20)),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2113, 2110])).
% 1.09/1.01 tff(2115,plain,
% 1.09/1.01 ((~hskp30) | c2_1(a20)),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2114, 2110])).
% 1.09/1.01 tff(2116,plain,
% 1.09/1.01 ((~hskp30) | c2_1(a20)),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2115, 2110])).
% 1.09/1.01 tff(2117,plain,
% 1.09/1.01 ((~hskp30) | c2_1(a20)),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2116, 2110])).
% 1.09/1.01 tff(2118,plain,
% 1.09/1.01 ((~hskp30) | c2_1(a20)),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2117, 2110])).
% 1.09/1.01 tff(2119,plain,
% 1.09/1.01 ((~hskp30) | c2_1(a20)),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2118, 2110])).
% 1.09/1.01 tff(2120,plain,
% 1.09/1.01 (c2_1(a20)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2119, 2087])).
% 1.09/1.01 tff(2121,assumption,(c0_1(a20)), introduced(assumption)).
% 1.09/1.01 tff(2122,assumption,(c3_1(a20)), introduced(assumption)).
% 1.09/1.01 tff(2123,assumption,(c2_1(a20)), introduced(assumption)).
% 1.09/1.01 tff(2124,plain,
% 1.09/1.01 (((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | (~ndr1_0) | (~c0_1(a20)) | (~c3_1(a20)) | c1_1(a20))) <=> ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp8 | (~ndr1_0) | (~c0_1(a20)) | (~c3_1(a20)) | c1_1(a20))),
% 1.09/1.01 inference(rewrite,[status(thm)],[])).
% 1.09/1.01 tff(2125,plain,
% 1.09/1.01 ((hskp21 | hskp8 | (~ndr1_0) | c1_1(a20) | (~c3_1(a20)) | (~c0_1(a20))) <=> (hskp21 | hskp8 | (~ndr1_0) | (~c0_1(a20)) | (~c3_1(a20)) | c1_1(a20))),
% 1.09/1.01 inference(rewrite,[status(thm)],[])).
% 1.09/1.01 tff(2126,plain,
% 1.09/1.01 (((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | (~ndr1_0) | c1_1(a20) | (~c3_1(a20)) | (~c0_1(a20)))) <=> ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | (~ndr1_0) | (~c0_1(a20)) | (~c3_1(a20)) | c1_1(a20)))),
% 1.09/1.01 inference(monotonicity,[status(thm)],[2125])).
% 1.09/1.01 tff(2127,plain,
% 1.09/1.01 (((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | (~ndr1_0) | c1_1(a20) | (~c3_1(a20)) | (~c0_1(a20)))) <=> ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp8 | (~ndr1_0) | (~c0_1(a20)) | (~c3_1(a20)) | c1_1(a20))),
% 1.09/1.01 inference(transitivity,[status(thm)],[2126, 2124])).
% 1.09/1.01 tff(2128,plain,
% 1.09/1.01 ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | (~ndr1_0) | c1_1(a20) | (~c3_1(a20)) | (~c0_1(a20)))),
% 1.09/1.01 inference(quant_inst,[status(thm)],[])).
% 1.09/1.01 tff(2129,plain,
% 1.09/1.01 ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp8 | (~ndr1_0) | (~c0_1(a20)) | (~c3_1(a20)) | c1_1(a20)),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2128, 2127])).
% 1.09/1.01 tff(2130,plain,
% 1.09/1.01 (hskp21 | hskp8 | c1_1(a20)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2129, 117, 2121, 2122, 21])).
% 1.09/1.01 tff(2131,plain,
% 1.09/1.01 (c1_1(a20)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2130, 1421, 523])).
% 1.09/1.01 tff(2132,plain,
% 1.09/1.01 (^[V: $i, U: $i] : refl((hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V))))),
% 1.09/1.01 inference(bind,[status(th)],[])).
% 1.09/1.01 tff(2133,plain,
% 1.09/1.01 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))),
% 1.09/1.01 inference(quant_intro,[status(thm)],[2132])).
% 1.09/1.01 tff(2134,plain,
% 1.09/1.01 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))),
% 1.09/1.01 inference(rewrite,[status(thm)],[])).
% 1.09/1.01 tff(2135,plain,
% 1.09/1.01 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_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) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_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) | (~c3_1(U)) | (~c2_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) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_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) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_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))) | hskp21) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V))) | hskp21))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V))) | hskp21) <=> (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_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))) | hskp21) <=> (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))))),
% 1.09/1.01 inference(bind,[status(th)],[])).
% 1.09/1.01 tff(2136,plain,
% 1.09/1.01 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | hskp21) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))),
% 1.09/1.01 inference(quant_intro,[status(thm)],[2135])).
% 1.09/1.01 tff(2137,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))) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause188')).
% 1.09/1.01 tff(2138,plain,
% 1.09/1.01 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2137, 2136])).
% 1.09/1.01 tff(2139,plain,
% 1.09/1.01 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2138, 2134])).
% 1.09/1.01 tff(2140,plain,(
% 1.09/1.01 ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))),
% 1.09/1.01 inference(skolemize,[status(sab)],[2139])).
% 1.09/1.01 tff(2141,plain,
% 1.09/1.01 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2140, 2133])).
% 1.09/1.01 tff(2142,plain,
% 1.09/1.01 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a20)))),
% 1.09/1.01 inference(rewrite,[status(thm)],[])).
% 1.09/1.01 tff(2143,plain,
% 1.09/1.01 ((hskp21 | (~ndr1_0) | (~c3_1(a20)) | (~c2_1(a20)) | (~c0_1(a20)) | (~c1_1(a20)) | (~c3_1(a20)) | (~c0_1(a20))) <=> (hskp21 | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a20)))),
% 1.09/1.01 inference(rewrite,[status(thm)],[])).
% 1.09/1.01 tff(2144,plain,
% 1.09/1.01 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c3_1(a20)) | (~c2_1(a20)) | (~c0_1(a20)) | (~c1_1(a20)) | (~c3_1(a20)) | (~c0_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a20))))),
% 1.09/1.01 inference(monotonicity,[status(thm)],[2143])).
% 1.09/1.01 tff(2145,plain,
% 1.09/1.01 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c3_1(a20)) | (~c2_1(a20)) | (~c0_1(a20)) | (~c1_1(a20)) | (~c3_1(a20)) | (~c0_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a20)))),
% 1.09/1.01 inference(transitivity,[status(thm)],[2144, 2142])).
% 1.09/1.01 tff(2146,plain,
% 1.09/1.01 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c3_1(a20)) | (~c2_1(a20)) | (~c0_1(a20)) | (~c1_1(a20)) | (~c3_1(a20)) | (~c0_1(a20)))),
% 1.09/1.01 inference(quant_inst,[status(thm)],[])).
% 1.09/1.01 tff(2147,plain,
% 1.09/1.01 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a20))),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2146, 2145])).
% 1.09/1.01 tff(2148,plain,
% 1.09/1.01 ($false),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2147, 117, 1421, 2121, 2123, 2122, 2141, 2131])).
% 1.09/1.01 tff(2149,plain,(hskp21 | (~c0_1(a20)) | (~c2_1(a20)) | (~c3_1(a20)) | hskp8), inference(lemma,lemma(discharge,[]))).
% 1.09/1.01 tff(2150,plain,
% 1.09/1.01 (hskp21),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2149, 523, 2123, 2122, 2121])).
% 1.09/1.01 tff(2151,plain,
% 1.09/1.01 (hskp16),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[238, 2150])).
% 1.09/1.01 tff(2152,plain,
% 1.09/1.01 (~c1_1(a30)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[244, 2151])).
% 1.09/1.01 tff(2153,plain,
% 1.09/1.01 (c2_1(a30)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[255, 2151])).
% 1.09/1.01 tff(2154,plain,
% 1.09/1.01 (c3_1(a30)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[266, 2151])).
% 1.09/1.01 tff(2155,plain,
% 1.09/1.01 ($false),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[1612, 2154, 2153, 523, 2150, 2152])).
% 1.09/1.01 tff(2156,plain,(hskp8 | (~c2_1(a20)) | (~c3_1(a20)) | (~c0_1(a20))), inference(lemma,lemma(discharge,[]))).
% 1.09/1.01 tff(2157,plain,
% 1.09/1.01 (hskp8),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2156, 2120, 2109, 2098])).
% 1.09/1.01 tff(2158,plain,
% 1.09/1.01 (c1_1(a13)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[320, 2157])).
% 1.09/1.01 tff(2159,plain,
% 1.09/1.01 (c3_1(a13)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[1722, 1715, 2158])).
% 1.09/1.01 tff(2160,plain,
% 1.09/1.01 (hskp11),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[1773, 1756, 2158, 2159])).
% 1.09/1.01 tff(2161,plain,
% 1.09/1.01 (~c3_1(a21)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[352, 2160])).
% 1.09/1.01 tff(2162,plain,
% 1.09/1.01 (~c2_1(a21)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[358, 2160])).
% 1.09/1.01 tff(2163,plain,
% 1.09/1.01 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a21)))),
% 1.09/1.01 inference(rewrite,[status(thm)],[])).
% 1.09/1.01 tff(2164,plain,
% 1.09/1.01 ((hskp12 | (~ndr1_0) | (~c3_1(a20)) | (~c2_1(a20)) | (~c0_1(a20)) | c3_1(a21) | c2_1(a21) | (~c1_1(a21))) <=> (hskp12 | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a21)))),
% 1.09/1.01 inference(rewrite,[status(thm)],[])).
% 1.09/1.01 tff(2165,plain,
% 1.09/1.01 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a20)) | (~c2_1(a20)) | (~c0_1(a20)) | c3_1(a21) | c2_1(a21) | (~c1_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a21))))),
% 1.09/1.01 inference(monotonicity,[status(thm)],[2164])).
% 1.09/1.01 tff(2166,plain,
% 1.09/1.01 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a20)) | (~c2_1(a20)) | (~c0_1(a20)) | c3_1(a21) | c2_1(a21) | (~c1_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a21)))),
% 1.09/1.01 inference(transitivity,[status(thm)],[2165, 2163])).
% 1.09/1.01 tff(2167,plain,
% 1.09/1.01 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a20)) | (~c2_1(a20)) | (~c0_1(a20)) | c3_1(a21) | c2_1(a21) | (~c1_1(a21)))),
% 1.09/1.01 inference(quant_inst,[status(thm)],[])).
% 1.09/1.01 tff(2168,plain,
% 1.09/1.01 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a21))),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2167, 2166])).
% 1.09/1.01 tff(2169,plain,
% 1.09/1.01 (~c1_1(a21)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2168, 117, 1715, 2098, 2120, 2109, 2162, 2161, 299])).
% 1.09/1.01 tff(2170,plain,
% 1.09/1.01 (c2_1(a13)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[1910, 2157])).
% 1.09/1.01 tff(2171,plain,
% 1.09/1.01 (c0_1(a21)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[386, 2160])).
% 1.09/1.01 tff(2172,plain,
% 1.09/1.01 ($false),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[1897, 117, 2171, 2158, 2170, 2161, 268, 279, 2159, 2169])).
% 1.09/1.01 tff(2173,plain,(hskp12 | c0_1(a13)), inference(lemma,lemma(discharge,[]))).
% 1.09/1.01 tff(2174,plain,
% 1.09/1.01 (hskp12),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2173, 268])).
% 1.09/1.01 tff(2175,plain,
% 1.09/1.01 (~c2_1(a24)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[198, 2174])).
% 1.09/1.01 tff(2176,plain,
% 1.09/1.01 (c3_1(a24)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[209, 2174])).
% 1.09/1.01 tff(2177,plain,
% 1.09/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a24) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | (~c2_1(a13)) | (~c3_1(a24)) | c0_1(a24))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a24) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | (~c2_1(a13)) | (~c3_1(a24)) | c0_1(a24))),
% 1.09/1.01 inference(rewrite,[status(thm)],[])).
% 1.09/1.01 tff(2178,plain,
% 1.09/1.01 (((~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | (~c2_1(a13)) | c0_1(a13) | (~c1_1(a13)) | (~c2_1(a13)) | c0_1(a24) | c2_1(a24) | (~c3_1(a24))) <=> (c2_1(a24) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | (~c2_1(a13)) | (~c3_1(a24)) | c0_1(a24))),
% 1.09/1.01 inference(rewrite,[status(thm)],[])).
% 1.09/1.01 tff(2179,plain,
% 1.09/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | (~c2_1(a13)) | c0_1(a13) | (~c1_1(a13)) | (~c2_1(a13)) | c0_1(a24) | c2_1(a24) | (~c3_1(a24)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a24) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | (~c2_1(a13)) | (~c3_1(a24)) | c0_1(a24)))),
% 1.09/1.01 inference(monotonicity,[status(thm)],[2178])).
% 1.09/1.01 tff(2180,plain,
% 1.09/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | (~c2_1(a13)) | c0_1(a13) | (~c1_1(a13)) | (~c2_1(a13)) | c0_1(a24) | c2_1(a24) | (~c3_1(a24)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a24) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | (~c2_1(a13)) | (~c3_1(a24)) | c0_1(a24))),
% 1.09/1.01 inference(transitivity,[status(thm)],[2179, 2177])).
% 1.09/1.01 tff(2181,plain,
% 1.09/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | (~c2_1(a13)) | c0_1(a13) | (~c1_1(a13)) | (~c2_1(a13)) | c0_1(a24) | c2_1(a24) | (~c3_1(a24)))),
% 1.09/1.01 inference(quant_inst,[status(thm)],[])).
% 1.09/1.01 tff(2182,plain,
% 1.09/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a24) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | (~c2_1(a13)) | (~c3_1(a24)) | c0_1(a24)),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2181, 2180])).
% 1.09/1.01 tff(2183,plain,
% 1.09/1.01 (~c3_1(a13)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2182, 117, 2176, 2158, 2170, 2175, 268, 289, 269])).
% 1.09/1.01 tff(2184,plain,
% 1.09/1.01 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))),
% 1.09/1.01 inference(bind,[status(th)],[])).
% 1.09/1.01 tff(2185,plain,
% 1.09/1.01 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.09/1.01 inference(quant_intro,[status(thm)],[2184])).
% 1.09/1.01 tff(2186,plain,
% 1.09/1.01 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.09/1.01 inference(rewrite,[status(thm)],[])).
% 1.09/1.01 tff(2187,plain,
% 1.09/1.01 (^[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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_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) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp6) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp6))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp6) <=> (hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))))),
% 1.09/1.01 inference(bind,[status(th)],[])).
% 1.09/1.01 tff(2188,plain,
% 1.09/1.01 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.09/1.01 inference(quant_intro,[status(thm)],[2187])).
% 1.09/1.01 tff(2189,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause169')).
% 1.09/1.01 tff(2190,plain,
% 1.09/1.01 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2189, 2188])).
% 1.09/1.01 tff(2191,plain,
% 1.09/1.01 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2190, 2186])).
% 1.09/1.01 tff(2192,plain,(
% 1.09/1.01 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.09/1.01 inference(skolemize,[status(sab)],[2191])).
% 1.09/1.01 tff(2193,plain,
% 1.09/1.01 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2192, 2185])).
% 1.09/1.01 tff(2194,plain,
% 1.09/1.01 (c1_1(a24)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[220, 2174])).
% 1.09/1.01 tff(2195,plain,
% 1.09/1.01 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp6 | c2_1(a24) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | c3_1(a13) | (~c1_1(a24)) | c0_1(a24))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp6 | c2_1(a24) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | c3_1(a13) | (~c1_1(a24)) | c0_1(a24))),
% 1.09/1.01 inference(rewrite,[status(thm)],[])).
% 1.09/1.01 tff(2196,plain,
% 1.09/1.01 ((hskp6 | (~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c1_1(a13)) | c0_1(a24) | c2_1(a24) | (~c1_1(a24))) <=> (hskp6 | c2_1(a24) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | c3_1(a13) | (~c1_1(a24)) | c0_1(a24))),
% 1.09/1.01 inference(rewrite,[status(thm)],[])).
% 1.09/1.01 tff(2197,plain,
% 1.09/1.01 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c1_1(a13)) | c0_1(a24) | c2_1(a24) | (~c1_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp6 | c2_1(a24) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | c3_1(a13) | (~c1_1(a24)) | c0_1(a24)))),
% 1.09/1.01 inference(monotonicity,[status(thm)],[2196])).
% 1.09/1.01 tff(2198,plain,
% 1.09/1.01 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c1_1(a13)) | c0_1(a24) | c2_1(a24) | (~c1_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp6 | c2_1(a24) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | c3_1(a13) | (~c1_1(a24)) | c0_1(a24))),
% 1.09/1.01 inference(transitivity,[status(thm)],[2197, 2195])).
% 1.09/1.01 tff(2199,plain,
% 1.09/1.01 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c1_1(a13)) | c0_1(a24) | c2_1(a24) | (~c1_1(a24)))),
% 1.09/1.01 inference(quant_inst,[status(thm)],[])).
% 1.09/1.01 tff(2200,plain,
% 1.09/1.01 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp6 | c2_1(a24) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | c3_1(a13) | (~c1_1(a24)) | c0_1(a24)),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2199, 2198])).
% 1.09/1.01 tff(2201,plain,
% 1.09/1.01 (hskp6),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2200, 117, 2194, 2158, 2175, 268, 2193, 2183, 269])).
% 1.09/1.01 tff(2202,plain,
% 1.09/1.01 (((~hskp6) | (~c3_1(a10))) <=> ((~hskp6) | (~c3_1(a10)))),
% 1.09/1.01 inference(rewrite,[status(thm)],[])).
% 1.09/1.01 tff(2203,plain,
% 1.09/1.01 (((~c3_1(a10)) | (~hskp6)) <=> ((~hskp6) | (~c3_1(a10)))),
% 1.09/1.01 inference(rewrite,[status(thm)],[])).
% 1.09/1.01 tff(2204,axiom,((~c3_1(a10)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause124')).
% 1.09/1.01 tff(2205,plain,
% 1.09/1.01 ((~hskp6) | (~c3_1(a10))),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2204, 2203])).
% 1.09/1.01 tff(2206,plain,
% 1.09/1.01 ((~hskp6) | (~c3_1(a10))),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2205, 2202])).
% 1.09/1.01 tff(2207,plain,
% 1.09/1.01 (~c3_1(a10)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2206, 2201])).
% 1.09/1.01 tff(2208,plain,
% 1.09/1.01 (((~hskp6) | (~c1_1(a10))) <=> ((~hskp6) | (~c1_1(a10)))),
% 1.09/1.01 inference(rewrite,[status(thm)],[])).
% 1.09/1.01 tff(2209,plain,
% 1.09/1.01 (((~c1_1(a10)) | (~hskp6)) <=> ((~hskp6) | (~c1_1(a10)))),
% 1.09/1.01 inference(rewrite,[status(thm)],[])).
% 1.09/1.01 tff(2210,axiom,((~c1_1(a10)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause123')).
% 1.09/1.01 tff(2211,plain,
% 1.09/1.01 ((~hskp6) | (~c1_1(a10))),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2210, 2209])).
% 1.09/1.01 tff(2212,plain,
% 1.09/1.01 ((~hskp6) | (~c1_1(a10))),
% 1.09/1.01 inference(modus_ponens,[status(thm)],[2211, 2208])).
% 1.09/1.01 tff(2213,plain,
% 1.09/1.01 (~c1_1(a10)),
% 1.09/1.01 inference(unit_resolution,[status(thm)],[2212, 2201])).
% 1.09/1.01 tff(2214,plain,
% 1.09/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a13) | c1_1(a10) | c3_1(a10) | (~ndr1_0) | (~c0_1(a10)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a24))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a13) | c1_1(a10) | c3_1(a10) | (~ndr1_0) | (~c0_1(a10)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a24))),
% 1.09/1.01 inference(rewrite,[status(thm)],[])).
% 1.09/1.01 tff(2215,plain,
% 1.09/1.01 (((~ndr1_0) | c1_1(a10) | c3_1(a10) | (~c0_1(a10)) | c0_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a13) | (~c2_1(a13)) | (~c1_1(a13))) <=> (c0_1(a13) | c1_1(a10) | c3_1(a10) | (~ndr1_0) | (~c0_1(a10)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a24))),
% 1.09/1.02 inference(rewrite,[status(thm)],[])).
% 1.09/1.02 tff(2216,plain,
% 1.09/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a10) | c3_1(a10) | (~c0_1(a10)) | c0_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a13) | (~c2_1(a13)) | (~c1_1(a13)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a13) | c1_1(a10) | c3_1(a10) | (~ndr1_0) | (~c0_1(a10)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a24)))),
% 1.09/1.02 inference(monotonicity,[status(thm)],[2215])).
% 1.09/1.02 tff(2217,plain,
% 1.09/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a10) | c3_1(a10) | (~c0_1(a10)) | c0_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a13) | (~c2_1(a13)) | (~c1_1(a13)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a13) | c1_1(a10) | c3_1(a10) | (~ndr1_0) | (~c0_1(a10)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a24))),
% 1.09/1.02 inference(transitivity,[status(thm)],[2216, 2214])).
% 1.09/1.02 tff(2218,plain,
% 1.09/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a10) | c3_1(a10) | (~c0_1(a10)) | c0_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a13) | (~c2_1(a13)) | (~c1_1(a13)))),
% 1.09/1.02 inference(quant_inst,[status(thm)],[])).
% 1.09/1.02 tff(2219,plain,
% 1.09/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a13) | c1_1(a10) | c3_1(a10) | (~ndr1_0) | (~c0_1(a10)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a24)),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2218, 2217])).
% 1.09/1.02 tff(2220,plain,
% 1.09/1.02 (~c0_1(a10)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[2219, 117, 2194, 2176, 2158, 2170, 268, 2213, 2207, 279, 269])).
% 1.09/1.02 tff(2221,plain,
% 1.09/1.02 (((~hskp6) | c2_1(a10)) <=> ((~hskp6) | c2_1(a10))),
% 1.09/1.02 inference(rewrite,[status(thm)],[])).
% 1.09/1.02 tff(2222,axiom,((~hskp6) | c2_1(a10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause78')).
% 1.09/1.02 tff(2223,plain,
% 1.09/1.02 ((~hskp6) | c2_1(a10)),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2222, 2221])).
% 1.09/1.02 tff(2224,plain,
% 1.09/1.02 ((~hskp6) | c2_1(a10)),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2223, 2221])).
% 1.09/1.02 tff(2225,plain,
% 1.09/1.02 ((~hskp6) | c2_1(a10)),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2224, 2221])).
% 1.09/1.02 tff(2226,plain,
% 1.09/1.02 ((~hskp6) | c2_1(a10)),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2225, 2221])).
% 1.09/1.02 tff(2227,plain,
% 1.09/1.02 ((~hskp6) | c2_1(a10)),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2226, 2221])).
% 1.09/1.02 tff(2228,plain,
% 1.09/1.02 ((~hskp6) | c2_1(a10)),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2227, 2221])).
% 1.09/1.02 tff(2229,plain,
% 1.09/1.02 ((~hskp6) | c2_1(a10)),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2228, 2221])).
% 1.09/1.02 tff(2230,plain,
% 1.09/1.02 ((~hskp6) | c2_1(a10)),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2229, 2221])).
% 1.09/1.02 tff(2231,plain,
% 1.09/1.02 (c2_1(a10)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[2230, 2201])).
% 1.09/1.02 tff(2232,plain,
% 1.09/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a24) | c0_1(a13) | c1_1(a10) | (~ndr1_0) | c0_1(a10) | (~c2_1(a10)) | c3_1(a13) | (~c2_1(a13)) | (~c1_1(a24)) | c0_1(a24))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a24) | c0_1(a13) | c1_1(a10) | (~ndr1_0) | c0_1(a10) | (~c2_1(a10)) | c3_1(a13) | (~c2_1(a13)) | (~c1_1(a24)) | c0_1(a24))),
% 1.09/1.02 inference(rewrite,[status(thm)],[])).
% 1.09/1.02 tff(2233,plain,
% 1.09/1.02 (((~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c2_1(a13)) | c0_1(a24) | c2_1(a24) | (~c1_1(a24)) | c1_1(a10) | c0_1(a10) | (~c2_1(a10))) <=> (c2_1(a24) | c0_1(a13) | c1_1(a10) | (~ndr1_0) | c0_1(a10) | (~c2_1(a10)) | c3_1(a13) | (~c2_1(a13)) | (~c1_1(a24)) | c0_1(a24))),
% 1.09/1.02 inference(rewrite,[status(thm)],[])).
% 1.09/1.02 tff(2234,plain,
% 1.09/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c2_1(a13)) | c0_1(a24) | c2_1(a24) | (~c1_1(a24)) | c1_1(a10) | c0_1(a10) | (~c2_1(a10)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a24) | c0_1(a13) | c1_1(a10) | (~ndr1_0) | c0_1(a10) | (~c2_1(a10)) | c3_1(a13) | (~c2_1(a13)) | (~c1_1(a24)) | c0_1(a24)))),
% 1.09/1.02 inference(monotonicity,[status(thm)],[2233])).
% 1.09/1.02 tff(2235,plain,
% 1.09/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c2_1(a13)) | c0_1(a24) | c2_1(a24) | (~c1_1(a24)) | c1_1(a10) | c0_1(a10) | (~c2_1(a10)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a24) | c0_1(a13) | c1_1(a10) | (~ndr1_0) | c0_1(a10) | (~c2_1(a10)) | c3_1(a13) | (~c2_1(a13)) | (~c1_1(a24)) | c0_1(a24))),
% 1.09/1.02 inference(transitivity,[status(thm)],[2234, 2232])).
% 1.09/1.02 tff(2236,plain,
% 1.09/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c2_1(a13)) | c0_1(a24) | c2_1(a24) | (~c1_1(a24)) | c1_1(a10) | c0_1(a10) | (~c2_1(a10)))),
% 1.09/1.02 inference(quant_inst,[status(thm)],[])).
% 1.09/1.02 tff(2237,plain,
% 1.09/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a24) | c0_1(a13) | c1_1(a10) | (~ndr1_0) | c0_1(a10) | (~c2_1(a10)) | c3_1(a13) | (~c2_1(a13)) | (~c1_1(a24)) | c0_1(a24)),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2236, 2235])).
% 1.09/1.02 tff(2238,plain,
% 1.09/1.02 ($false),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[2237, 117, 2194, 2170, 2231, 2175, 268, 2213, 1983, 2183, 269, 2220])).
% 1.09/1.02 tff(2239,plain,(c0_1(a24) | c0_1(a13)), inference(lemma,lemma(discharge,[]))).
% 1.09/1.02 tff(2240,plain,
% 1.09/1.02 (c0_1(a24)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[2239, 268])).
% 1.09/1.02 tff(2241,plain,
% 1.09/1.02 (hskp16),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[229, 2174])).
% 1.09/1.02 tff(2242,plain,
% 1.09/1.02 (~c1_1(a30)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[244, 2241])).
% 1.09/1.02 tff(2243,plain,
% 1.09/1.02 (c3_1(a30)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[266, 2241])).
% 1.09/1.02 tff(2244,plain,
% 1.09/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c1_1(a30) | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | (~c0_1(a30)) | (~c3_1(a30)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a30) | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | (~c0_1(a30)) | (~c3_1(a30)))),
% 1.09/1.02 inference(rewrite,[status(thm)],[])).
% 1.09/1.02 tff(2245,plain,
% 1.09/1.02 (((~ndr1_0) | (~c3_1(a20)) | (~c2_1(a20)) | (~c0_1(a20)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | c1_1(a30) | (~c3_1(a30)) | (~c0_1(a30))) <=> (c1_1(a30) | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | (~c0_1(a30)) | (~c3_1(a30)))),
% 1.09/1.02 inference(rewrite,[status(thm)],[])).
% 1.09/1.02 tff(2246,plain,
% 1.09/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a20)) | (~c2_1(a20)) | (~c0_1(a20)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | c1_1(a30) | (~c3_1(a30)) | (~c0_1(a30)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c1_1(a30) | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | (~c0_1(a30)) | (~c3_1(a30))))),
% 1.09/1.02 inference(monotonicity,[status(thm)],[2245])).
% 1.09/1.02 tff(2247,plain,
% 1.09/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a20)) | (~c2_1(a20)) | (~c0_1(a20)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | c1_1(a30) | (~c3_1(a30)) | (~c0_1(a30)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a30) | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | (~c0_1(a30)) | (~c3_1(a30)))),
% 1.09/1.02 inference(transitivity,[status(thm)],[2246, 2244])).
% 1.09/1.02 tff(2248,plain,
% 1.09/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a20)) | (~c2_1(a20)) | (~c0_1(a20)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | c1_1(a30) | (~c3_1(a30)) | (~c0_1(a30)))),
% 1.09/1.02 inference(quant_inst,[status(thm)],[])).
% 1.09/1.02 tff(2249,plain,
% 1.09/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a30) | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | (~c0_1(a30)) | (~c3_1(a30))),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2248, 2247])).
% 1.09/1.02 tff(2250,plain,
% 1.09/1.02 ((~c0_1(a24)) | (~c0_1(a30))),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[2249, 117, 2098, 2120, 2109, 2243, 2194, 2176, 2242, 1943])).
% 1.09/1.02 tff(2251,plain,
% 1.09/1.02 (~c0_1(a30)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[2250, 2240])).
% 1.09/1.02 tff(2252,plain,
% 1.09/1.02 (c2_1(a30)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[255, 2241])).
% 1.09/1.02 tff(2253,plain,
% 1.09/1.02 (hskp15 | (~c0_1(a24))),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[1958, 117, 2252, 2243, 2194, 2242, 2175, 376])).
% 1.09/1.02 tff(2254,plain,
% 1.09/1.02 (hskp15),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[2253, 2240])).
% 1.09/1.02 tff(2255,plain,
% 1.09/1.02 (c1_1(a29)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[136, 2254])).
% 1.09/1.02 tff(2256,plain,
% 1.09/1.02 (~c3_1(a29)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[142, 2254])).
% 1.09/1.02 tff(2257,plain,
% 1.09/1.02 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)))),
% 1.09/1.02 inference(rewrite,[status(thm)],[])).
% 1.09/1.02 tff(2258,plain,
% 1.09/1.02 ((hskp21 | (~ndr1_0) | (~c3_1(a20)) | (~c2_1(a20)) | (~c0_1(a20)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24))) <=> (hskp21 | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)))),
% 1.09/1.02 inference(rewrite,[status(thm)],[])).
% 1.09/1.02 tff(2259,plain,
% 1.09/1.02 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c3_1(a20)) | (~c2_1(a20)) | (~c0_1(a20)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24))))),
% 1.09/1.02 inference(monotonicity,[status(thm)],[2258])).
% 1.09/1.02 tff(2260,plain,
% 1.09/1.02 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c3_1(a20)) | (~c2_1(a20)) | (~c0_1(a20)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)))),
% 1.09/1.02 inference(transitivity,[status(thm)],[2259, 2257])).
% 1.09/1.02 tff(2261,plain,
% 1.09/1.02 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c3_1(a20)) | (~c2_1(a20)) | (~c0_1(a20)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)))),
% 1.09/1.02 inference(quant_inst,[status(thm)],[])).
% 1.09/1.02 tff(2262,plain,
% 1.09/1.02 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24))),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2261, 2260])).
% 1.09/1.02 tff(2263,plain,
% 1.09/1.02 (hskp21 | (~c0_1(a24))),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[2262, 117, 2098, 2120, 2109, 2194, 2176, 2141])).
% 1.09/1.02 tff(2264,plain,
% 1.09/1.02 (hskp21),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[2263, 2240])).
% 1.09/1.02 tff(2265,plain,
% 1.09/1.02 (~c2_1(a29)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[148, 2254])).
% 1.09/1.02 tff(2266,plain,
% 1.09/1.02 (~c0_1(a29)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[171, 2265, 2264, 2256, 2255])).
% 1.09/1.02 tff(2267,plain,
% 1.09/1.02 (~c3_1(a39)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[58, 2264])).
% 1.09/1.02 tff(2268,plain,
% 1.09/1.02 (~c0_1(a39)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[64, 2264])).
% 1.09/1.02 tff(2269,plain,
% 1.09/1.02 (c2_1(a39)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[75, 2264])).
% 1.09/1.02 tff(2270,plain,
% 1.09/1.02 ($false),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[1992, 117, 2269, 2252, 2255, 2268, 2267, 2242, 2265, 1983, 2266, 2251])).
% 1.09/1.02 tff(2271,plain,(c0_1(a13)), inference(lemma,lemma(discharge,[]))).
% 1.09/1.02 tff(2272,plain,
% 1.09/1.02 (((~hskp8) | (~c0_1(a13))) <=> ((~hskp8) | (~c0_1(a13)))),
% 1.09/1.02 inference(rewrite,[status(thm)],[])).
% 1.09/1.02 tff(2273,plain,
% 1.09/1.02 (((~c0_1(a13)) | (~hskp8)) <=> ((~hskp8) | (~c0_1(a13)))),
% 1.09/1.02 inference(rewrite,[status(thm)],[])).
% 1.09/1.02 tff(2274,axiom,((~c0_1(a13)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause121')).
% 1.09/1.02 tff(2275,plain,
% 1.09/1.02 ((~hskp8) | (~c0_1(a13))),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2274, 2273])).
% 1.09/1.02 tff(2276,plain,
% 1.09/1.02 ((~hskp8) | (~c0_1(a13))),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2275, 2272])).
% 1.09/1.02 tff(2277,plain,
% 1.09/1.02 (~hskp8),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[2276, 2271])).
% 1.09/1.02 tff(2278,plain,
% 1.09/1.02 ((~hskp21) | (~c2_1(a30)) | (~c3_1(a30)) | c1_1(a30)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[1612, 2277])).
% 1.09/1.02 tff(2279,plain,
% 1.09/1.02 ($false),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[2278, 267, 256, 42, 245])).
% 1.09/1.02 tff(2280,plain,(~hskp21), inference(lemma,lemma(discharge,[]))).
% 1.09/1.02 tff(2281,plain,
% 1.09/1.02 (hskp5),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[1510, 1499, 2280])).
% 1.09/1.02 tff(2282,plain,
% 1.09/1.02 (~c2_1(a9)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[1516, 2281])).
% 1.09/1.02 tff(2283,plain,
% 1.09/1.02 (~c0_1(a9)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[1522, 2281])).
% 1.09/1.02 tff(2284,plain,
% 1.09/1.02 (~c3_1(a9)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[1529, 117, 1, 1340, 2283, 2282, 41])).
% 1.09/1.02 tff(2285,plain,
% 1.09/1.02 (~c1_1(a9)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[1536, 2281])).
% 1.09/1.02 tff(2286,assumption,(hskp31), introduced(assumption)).
% 1.09/1.02 tff(2287,plain,
% 1.09/1.02 (((~hskp31) | c3_1(a76)) <=> ((~hskp31) | c3_1(a76))),
% 1.09/1.02 inference(rewrite,[status(thm)],[])).
% 1.09/1.02 tff(2288,axiom,((~hskp31) | c3_1(a76)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause41')).
% 1.09/1.02 tff(2289,plain,
% 1.09/1.02 ((~hskp31) | c3_1(a76)),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2288, 2287])).
% 1.09/1.02 tff(2290,plain,
% 1.09/1.02 ((~hskp31) | c3_1(a76)),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2289, 2287])).
% 1.09/1.02 tff(2291,plain,
% 1.09/1.02 ((~hskp31) | c3_1(a76)),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2290, 2287])).
% 1.09/1.02 tff(2292,plain,
% 1.09/1.02 ((~hskp31) | c3_1(a76)),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2291, 2287])).
% 1.09/1.02 tff(2293,plain,
% 1.09/1.02 ((~hskp31) | c3_1(a76)),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2292, 2287])).
% 1.09/1.02 tff(2294,plain,
% 1.09/1.02 ((~hskp31) | c3_1(a76)),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2293, 2287])).
% 1.09/1.02 tff(2295,plain,
% 1.09/1.02 ((~hskp31) | c3_1(a76)),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2294, 2287])).
% 1.09/1.02 tff(2296,plain,
% 1.09/1.02 ((~hskp31) | c3_1(a76)),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2295, 2287])).
% 1.09/1.02 tff(2297,plain,
% 1.09/1.02 (c3_1(a76)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[2296, 2286])).
% 1.09/1.02 tff(2298,plain,
% 1.09/1.02 (((~hskp31) | c1_1(a76)) <=> ((~hskp31) | c1_1(a76))),
% 1.09/1.02 inference(rewrite,[status(thm)],[])).
% 1.09/1.02 tff(2299,axiom,((~hskp31) | c1_1(a76)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause40')).
% 1.09/1.02 tff(2300,plain,
% 1.09/1.02 ((~hskp31) | c1_1(a76)),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2299, 2298])).
% 1.09/1.02 tff(2301,plain,
% 1.09/1.02 ((~hskp31) | c1_1(a76)),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2300, 2298])).
% 1.09/1.02 tff(2302,plain,
% 1.09/1.02 ((~hskp31) | c1_1(a76)),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2301, 2298])).
% 1.09/1.02 tff(2303,plain,
% 1.09/1.02 ((~hskp31) | c1_1(a76)),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2302, 2298])).
% 1.09/1.02 tff(2304,plain,
% 1.09/1.02 ((~hskp31) | c1_1(a76)),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2303, 2298])).
% 1.09/1.02 tff(2305,plain,
% 1.09/1.02 ((~hskp31) | c1_1(a76)),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2304, 2298])).
% 1.09/1.02 tff(2306,plain,
% 1.09/1.02 ((~hskp31) | c1_1(a76)),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2305, 2298])).
% 1.09/1.02 tff(2307,plain,
% 1.09/1.02 ((~hskp31) | c1_1(a76)),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2306, 2298])).
% 1.09/1.02 tff(2308,plain,
% 1.09/1.02 (c1_1(a76)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[2307, 2286])).
% 1.09/1.02 tff(2309,plain,
% 1.09/1.02 (((~hskp31) | c0_1(a76)) <=> ((~hskp31) | c0_1(a76))),
% 1.09/1.02 inference(rewrite,[status(thm)],[])).
% 1.09/1.02 tff(2310,axiom,((~hskp31) | c0_1(a76)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause39')).
% 1.09/1.02 tff(2311,plain,
% 1.09/1.02 ((~hskp31) | c0_1(a76)),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2310, 2309])).
% 1.09/1.02 tff(2312,plain,
% 1.09/1.02 ((~hskp31) | c0_1(a76)),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2311, 2309])).
% 1.09/1.02 tff(2313,plain,
% 1.09/1.02 ((~hskp31) | c0_1(a76)),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2312, 2309])).
% 1.09/1.02 tff(2314,plain,
% 1.09/1.02 ((~hskp31) | c0_1(a76)),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2313, 2309])).
% 1.09/1.02 tff(2315,plain,
% 1.09/1.02 ((~hskp31) | c0_1(a76)),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2314, 2309])).
% 1.09/1.02 tff(2316,plain,
% 1.09/1.02 ((~hskp31) | c0_1(a76)),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2315, 2309])).
% 1.09/1.02 tff(2317,plain,
% 1.09/1.02 ((~hskp31) | c0_1(a76)),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2316, 2309])).
% 1.09/1.02 tff(2318,plain,
% 1.09/1.02 ((~hskp31) | c0_1(a76)),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2317, 2309])).
% 1.09/1.02 tff(2319,plain,
% 1.09/1.02 (c0_1(a76)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[2318, 2286])).
% 1.09/1.02 tff(2320,plain,
% 1.09/1.02 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c3_1(a76)) | (~c2_1(a76)) | (~c1_1(a76)) | (~c0_1(a76)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | (~ndr1_0) | (~c3_1(a76)) | (~c2_1(a76)) | (~c1_1(a76)) | (~c0_1(a76)))),
% 1.09/1.02 inference(rewrite,[status(thm)],[])).
% 1.09/1.02 tff(2321,plain,
% 1.09/1.02 ((hskp21 | (~ndr1_0) | (~c3_1(a76)) | (~c2_1(a76)) | (~c0_1(a76)) | (~c1_1(a76)) | (~c3_1(a76)) | (~c0_1(a76))) <=> (hskp21 | (~ndr1_0) | (~c3_1(a76)) | (~c2_1(a76)) | (~c1_1(a76)) | (~c0_1(a76)))),
% 1.09/1.02 inference(rewrite,[status(thm)],[])).
% 1.09/1.02 tff(2322,plain,
% 1.09/1.02 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c3_1(a76)) | (~c2_1(a76)) | (~c0_1(a76)) | (~c1_1(a76)) | (~c3_1(a76)) | (~c0_1(a76)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c3_1(a76)) | (~c2_1(a76)) | (~c1_1(a76)) | (~c0_1(a76))))),
% 1.09/1.02 inference(monotonicity,[status(thm)],[2321])).
% 1.09/1.02 tff(2323,plain,
% 1.09/1.02 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c3_1(a76)) | (~c2_1(a76)) | (~c0_1(a76)) | (~c1_1(a76)) | (~c3_1(a76)) | (~c0_1(a76)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | (~ndr1_0) | (~c3_1(a76)) | (~c2_1(a76)) | (~c1_1(a76)) | (~c0_1(a76)))),
% 1.09/1.02 inference(transitivity,[status(thm)],[2322, 2320])).
% 1.09/1.02 tff(2324,plain,
% 1.09/1.02 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c3_1(a76)) | (~c2_1(a76)) | (~c0_1(a76)) | (~c1_1(a76)) | (~c3_1(a76)) | (~c0_1(a76)))),
% 1.09/1.02 inference(quant_inst,[status(thm)],[])).
% 1.09/1.02 tff(2325,plain,
% 1.09/1.02 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | (~ndr1_0) | (~c3_1(a76)) | (~c2_1(a76)) | (~c1_1(a76)) | (~c0_1(a76))),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2324, 2323])).
% 1.09/1.02 tff(2326,plain,
% 1.09/1.02 (~c2_1(a76)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[2325, 117, 2280, 2319, 2308, 2297, 2141])).
% 1.09/1.02 tff(2327,plain,
% 1.09/1.02 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | (~ndr1_0) | (~c3_1(a76)) | c2_1(a76) | (~c1_1(a76)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | (~ndr1_0) | (~c3_1(a76)) | c2_1(a76) | (~c1_1(a76)))),
% 1.09/1.02 inference(rewrite,[status(thm)],[])).
% 1.09/1.02 tff(2328,plain,
% 1.09/1.02 ((hskp16 | (~ndr1_0) | c2_1(a76) | (~c1_1(a76)) | (~c3_1(a76))) <=> (hskp16 | (~ndr1_0) | (~c3_1(a76)) | c2_1(a76) | (~c1_1(a76)))),
% 1.09/1.02 inference(rewrite,[status(thm)],[])).
% 1.09/1.02 tff(2329,plain,
% 1.09/1.02 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a76) | (~c1_1(a76)) | (~c3_1(a76)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | (~ndr1_0) | (~c3_1(a76)) | c2_1(a76) | (~c1_1(a76))))),
% 1.09/1.02 inference(monotonicity,[status(thm)],[2328])).
% 1.09/1.02 tff(2330,plain,
% 1.09/1.02 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a76) | (~c1_1(a76)) | (~c3_1(a76)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | (~ndr1_0) | (~c3_1(a76)) | c2_1(a76) | (~c1_1(a76)))),
% 1.09/1.02 inference(transitivity,[status(thm)],[2329, 2327])).
% 1.09/1.02 tff(2331,plain,
% 1.09/1.02 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a76) | (~c1_1(a76)) | (~c3_1(a76)))),
% 1.09/1.02 inference(quant_inst,[status(thm)],[])).
% 1.09/1.02 tff(2332,plain,
% 1.09/1.02 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | (~ndr1_0) | (~c3_1(a76)) | c2_1(a76) | (~c1_1(a76))),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2331, 2330])).
% 1.09/1.02 tff(2333,plain,
% 1.09/1.02 ($false),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[2332, 117, 43, 2308, 2297, 192, 2326])).
% 1.09/1.02 tff(2334,plain,((~hskp31) | hskp16), inference(lemma,lemma(discharge,[]))).
% 1.09/1.02 tff(2335,plain,
% 1.09/1.02 (~hskp31),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[2334, 43])).
% 1.09/1.02 tff(2336,plain,
% 1.09/1.02 (hskp24),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[115, 2335, 230])).
% 1.09/1.02 tff(2337,plain,
% 1.09/1.02 (hskp11),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[1498, 2336, 1])).
% 1.09/1.02 tff(2338,plain,
% 1.09/1.02 (~c3_1(a21)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[352, 2337])).
% 1.09/1.02 tff(2339,plain,
% 1.09/1.02 (~c2_1(a21)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[358, 2337])).
% 1.09/1.02 tff(2340,plain,
% 1.09/1.02 ((~hskp3) | hskp30 | hskp9 | hskp16),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[1338, 2277])).
% 1.09/1.02 tff(2341,plain,
% 1.09/1.02 (hskp9),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[2340, 1333, 1, 43])).
% 1.09/1.02 tff(2342,plain,
% 1.09/1.02 (~c3_1(a15)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[1048, 2341])).
% 1.09/1.02 tff(2343,plain,
% 1.09/1.02 (~c2_1(a15)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[506, 2341])).
% 1.09/1.02 tff(2344,plain,
% 1.09/1.02 (~c1_1(a15)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[500, 2341])).
% 1.09/1.02 tff(2345,plain,
% 1.09/1.02 (hskp16 | hskp30 | hskp2 | (~c0_1(a6)) | (~c3_1(a6)) | c2_1(a6)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[1306, 2277])).
% 1.09/1.02 tff(2346,plain,
% 1.09/1.02 (hskp2),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[2345, 1336, 1, 43, 1335, 1334])).
% 1.09/1.02 tff(2347,plain,
% 1.09/1.02 (~c0_1(a5)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[1250, 2346])).
% 1.09/1.02 tff(2348,plain,
% 1.09/1.02 (~c1_1(a5)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[1128, 2346])).
% 1.09/1.02 tff(2349,plain,
% 1.09/1.02 (c3_1(a15) | hskp30 | c1_1(a15) | c2_1(a15) | c0_1(a5) | c1_1(a5)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[885, 2277])).
% 1.09/1.02 tff(2350,plain,
% 1.09/1.02 ($false),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[2349, 2348, 2347, 2344, 2343, 2342, 1])).
% 1.09/1.02 tff(2351,plain,((~hskp3) | hskp30 | hskp16), inference(lemma,lemma(discharge,[]))).
% 1.09/1.02 tff(2352,plain,
% 1.09/1.02 (~hskp3),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[2351, 43, 1])).
% 1.09/1.02 tff(2353,plain,
% 1.09/1.02 ((~hskp25) | hskp21),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[1429, 2277])).
% 1.09/1.02 tff(2354,plain,
% 1.09/1.02 (~hskp25),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[2353, 2280])).
% 1.09/1.02 tff(2355,plain,
% 1.09/1.02 (~c1_1(a21)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[1436, 117, 2354, 2352, 2339, 2338, 1390])).
% 1.09/1.02 tff(2356,plain,
% 1.09/1.02 (~c2_1(a52)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[726, 2336])).
% 1.09/1.02 tff(2357,plain,
% 1.09/1.02 (~c0_1(a52)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[732, 2336])).
% 1.09/1.02 tff(2358,plain,
% 1.09/1.02 (c0_1(a21)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[386, 2337])).
% 1.09/1.02 tff(2359,plain,
% 1.09/1.02 (c3_1(a52)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[743, 2336])).
% 1.09/1.02 tff(2360,plain,
% 1.09/1.02 ((~hskp10) | hskp30 | hskp16),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[573, 2277])).
% 1.09/1.02 tff(2361,plain,
% 1.09/1.02 (~hskp10),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[2360, 43, 1])).
% 1.09/1.02 tff(2362,plain,
% 1.09/1.02 ($false),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[750, 117, 2361, 2359, 2358, 2357, 2356, 2338, 703, 2355])).
% 1.09/1.02 tff(2363,plain,(hskp16 | hskp30), inference(lemma,lemma(discharge,[]))).
% 1.09/1.02 tff(2364,plain,
% 1.09/1.02 (hskp16),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[2363, 1])).
% 1.09/1.02 tff(2365,plain,
% 1.09/1.02 (~c1_1(a30)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[244, 2364])).
% 1.09/1.02 tff(2366,plain,
% 1.09/1.02 (c3_1(a30)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[266, 2364])).
% 1.09/1.02 tff(2367,plain,
% 1.09/1.02 (c2_1(a30)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[255, 2364])).
% 1.09/1.02 tff(2368,plain,
% 1.09/1.02 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a30) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | c3_1(a9) | (~c2_1(a30)) | (~c3_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a30) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | c3_1(a9) | (~c2_1(a30)) | (~c3_1(a30)))),
% 1.09/1.02 inference(rewrite,[status(thm)],[])).
% 1.09/1.02 tff(2369,plain,
% 1.09/1.02 ((hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a9) | c1_1(a9) | c2_1(a9)) <=> (hskp8 | c1_1(a30) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | c3_1(a9) | (~c2_1(a30)) | (~c3_1(a30)))),
% 1.09/1.02 inference(rewrite,[status(thm)],[])).
% 1.09/1.02 tff(2370,plain,
% 1.09/1.02 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a9) | c1_1(a9) | c2_1(a9))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a30) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | c3_1(a9) | (~c2_1(a30)) | (~c3_1(a30))))),
% 1.09/1.02 inference(monotonicity,[status(thm)],[2369])).
% 1.09/1.02 tff(2371,plain,
% 1.09/1.02 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a9) | c1_1(a9) | c2_1(a9))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a30) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | c3_1(a9) | (~c2_1(a30)) | (~c3_1(a30)))),
% 1.09/1.02 inference(transitivity,[status(thm)],[2370, 2368])).
% 1.09/1.02 tff(2372,plain,
% 1.09/1.02 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a9) | c1_1(a9) | c2_1(a9))),
% 1.09/1.02 inference(quant_inst,[status(thm)],[])).
% 1.09/1.02 tff(2373,plain,
% 1.09/1.02 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a30) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | c3_1(a9) | (~c2_1(a30)) | (~c3_1(a30))),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2372, 2371])).
% 1.09/1.02 tff(2374,plain,
% 1.09/1.02 ($false),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[2373, 117, 2277, 2367, 2366, 2365, 2285, 2282, 31, 2284])).
% 1.09/1.02 tff(2375,plain,(hskp11 | hskp30), inference(lemma,lemma(discharge,[]))).
% 1.09/1.02 tff(2376,plain,
% 1.09/1.02 (hskp11),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[2375, 1])).
% 1.09/1.02 tff(2377,plain,
% 1.09/1.02 (~c3_1(a21)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[352, 2376])).
% 1.09/1.02 tff(2378,plain,
% 1.09/1.02 (~c2_1(a21)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[358, 2376])).
% 1.09/1.02 tff(2379,plain,
% 1.09/1.02 (c1_1(a21)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[365, 117, 2277, 2367, 2366, 2365, 2378, 2377, 31])).
% 1.09/1.02 tff(2380,plain,
% 1.09/1.02 (~c0_1(a30)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[467, 117, 2280, 2277, 2366, 2365, 21])).
% 1.09/1.02 tff(2381,plain,
% 1.09/1.02 (c0_1(a21)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[386, 2376])).
% 1.09/1.02 tff(2382,plain,
% 1.09/1.02 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | c1_1(a30) | c2_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | c0_1(a30) | (~c3_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c1_1(a30) | c2_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | c0_1(a30) | (~c3_1(a30)))),
% 1.09/1.02 inference(rewrite,[status(thm)],[])).
% 1.09/1.02 tff(2383,plain,
% 1.09/1.02 ((hskp3 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a30) | c0_1(a30) | (~c3_1(a30))) <=> (hskp3 | c1_1(a30) | c2_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | c0_1(a30) | (~c3_1(a30)))),
% 1.09/1.02 inference(rewrite,[status(thm)],[])).
% 1.09/1.02 tff(2384,plain,
% 1.09/1.02 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a30) | c0_1(a30) | (~c3_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | c1_1(a30) | c2_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | c0_1(a30) | (~c3_1(a30))))),
% 1.09/1.02 inference(monotonicity,[status(thm)],[2383])).
% 1.09/1.02 tff(2385,plain,
% 1.09/1.02 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a30) | c0_1(a30) | (~c3_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c1_1(a30) | c2_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | c0_1(a30) | (~c3_1(a30)))),
% 1.09/1.02 inference(transitivity,[status(thm)],[2384, 2382])).
% 1.09/1.02 tff(2386,plain,
% 1.09/1.02 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a30) | c0_1(a30) | (~c3_1(a30)))),
% 1.09/1.02 inference(quant_inst,[status(thm)],[])).
% 1.09/1.02 tff(2387,plain,
% 1.09/1.02 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c1_1(a30) | c2_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | c0_1(a30) | (~c3_1(a30))),
% 1.09/1.02 inference(modus_ponens,[status(thm)],[2386, 2385])).
% 1.09/1.02 tff(2388,plain,
% 1.09/1.02 (hskp3 | (~c1_1(a21))),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[2387, 117, 2366, 2381, 2365, 2378, 426, 2380])).
% 1.09/1.02 tff(2389,plain,
% 1.09/1.02 (hskp3),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[2388, 2379])).
% 1.09/1.02 tff(2390,plain,
% 1.09/1.02 (c3_1(a6)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[444, 2389])).
% 1.09/1.02 tff(2391,plain,
% 1.09/1.02 (c0_1(a6)),
% 1.09/1.02 inference(unit_resolution,[status(thm)],[455, 2389])).
% 1.09/1.03 tff(2392,plain,
% 1.09/1.03 (c1_1(a6)),
% 1.09/1.03 inference(unit_resolution,[status(thm)],[459, 117, 2280, 2277, 2391, 2390, 21])).
% 1.09/1.03 tff(2393,plain,
% 1.09/1.03 (^[U: $i] : refl((hskp29 | hskp19 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp29 | hskp19 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))),
% 1.09/1.03 inference(bind,[status(th)],[])).
% 1.09/1.03 tff(2394,plain,
% 1.09/1.03 (![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.09/1.03 inference(quant_intro,[status(thm)],[2393])).
% 1.09/1.03 tff(2395,plain,
% 1.09/1.03 (![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.09/1.03 inference(rewrite,[status(thm)],[])).
% 1.09/1.03 tff(2396,plain,
% 1.09/1.03 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp29) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp29))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp29) <=> (hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp29) <=> (hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp29) | hskp19) <=> ((hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp19))), rewrite(((hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp19) <=> (hskp29 | hskp19 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp29) | hskp19) <=> (hskp29 | hskp19 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))))),
% 1.09/1.03 inference(bind,[status(th)],[])).
% 1.09/1.03 tff(2397,plain,
% 1.09/1.03 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp29) | hskp19) <=> ![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.09/1.03 inference(quant_intro,[status(thm)],[2396])).
% 1.09/1.03 tff(2398,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp29) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause158')).
% 1.09/1.03 tff(2399,plain,
% 1.09/1.03 (![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.09/1.03 inference(modus_ponens,[status(thm)],[2398, 2397])).
% 1.09/1.03 tff(2400,plain,
% 1.09/1.03 (![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.09/1.03 inference(modus_ponens,[status(thm)],[2399, 2395])).
% 1.09/1.03 tff(2401,plain,(
% 1.09/1.03 ![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.09/1.03 inference(skolemize,[status(sab)],[2400])).
% 1.09/1.03 tff(2402,plain,
% 1.09/1.03 (![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.09/1.03 inference(modus_ponens,[status(thm)],[2401, 2394])).
% 1.09/1.03 tff(2403,plain,
% 1.09/1.03 ((~hskp19) | hskp30),
% 1.09/1.03 inference(unit_resolution,[status(thm)],[1791, 2277])).
% 1.09/1.03 tff(2404,plain,
% 1.09/1.03 (~hskp19),
% 1.09/1.03 inference(unit_resolution,[status(thm)],[2403, 1])).
% 1.09/1.03 tff(2405,plain,
% 1.09/1.03 (((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp29 | hskp19 | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a6)))) <=> ((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp29 | hskp19 | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a6)))),
% 1.09/1.03 inference(rewrite,[status(thm)],[])).
% 1.09/1.03 tff(2406,plain,
% 1.09/1.03 ((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp29 | hskp19 | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a6)))),
% 1.09/1.03 inference(quant_inst,[status(thm)],[])).
% 1.09/1.03 tff(2407,plain,
% 1.09/1.03 ((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp29 | hskp19 | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a6))),
% 1.09/1.03 inference(modus_ponens,[status(thm)],[2406, 2405])).
% 1.09/1.03 tff(2408,plain,
% 1.09/1.03 (hskp29 | (~c1_1(a6))),
% 1.09/1.03 inference(unit_resolution,[status(thm)],[2407, 117, 2404, 2391, 2390, 2402])).
% 1.09/1.03 tff(2409,plain,
% 1.09/1.03 (hskp29),
% 1.09/1.03 inference(unit_resolution,[status(thm)],[2408, 2392])).
% 1.09/1.03 tff(2410,plain,
% 1.09/1.03 (((~hskp29) | c3_1(a8)) <=> ((~hskp29) | c3_1(a8))),
% 1.09/1.03 inference(rewrite,[status(thm)],[])).
% 1.09/1.03 tff(2411,axiom,((~hskp29) | c3_1(a8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause47')).
% 1.09/1.03 tff(2412,plain,
% 1.09/1.03 ((~hskp29) | c3_1(a8)),
% 1.09/1.03 inference(modus_ponens,[status(thm)],[2411, 2410])).
% 1.09/1.03 tff(2413,plain,
% 1.09/1.03 ((~hskp29) | c3_1(a8)),
% 1.09/1.03 inference(modus_ponens,[status(thm)],[2412, 2410])).
% 1.09/1.03 tff(2414,plain,
% 1.09/1.03 ((~hskp29) | c3_1(a8)),
% 1.09/1.03 inference(modus_ponens,[status(thm)],[2413, 2410])).
% 1.09/1.03 tff(2415,plain,
% 1.09/1.03 ((~hskp29) | c3_1(a8)),
% 1.09/1.03 inference(modus_ponens,[status(thm)],[2414, 2410])).
% 1.09/1.03 tff(2416,plain,
% 1.09/1.03 ((~hskp29) | c3_1(a8)),
% 1.09/1.03 inference(modus_ponens,[status(thm)],[2415, 2410])).
% 1.09/1.03 tff(2417,plain,
% 1.09/1.03 ((~hskp29) | c3_1(a8)),
% 1.09/1.03 inference(modus_ponens,[status(thm)],[2416, 2410])).
% 1.09/1.03 tff(2418,plain,
% 1.09/1.03 ((~hskp29) | c3_1(a8)),
% 1.09/1.03 inference(modus_ponens,[status(thm)],[2417, 2410])).
% 1.09/1.03 tff(2419,plain,
% 1.09/1.03 ((~hskp29) | c3_1(a8)),
% 1.09/1.03 inference(modus_ponens,[status(thm)],[2418, 2410])).
% 1.09/1.03 tff(2420,plain,
% 1.09/1.03 (c3_1(a8)),
% 1.09/1.03 inference(unit_resolution,[status(thm)],[2419, 2409])).
% 1.09/1.03 tff(2421,plain,
% 1.09/1.03 (((~hskp29) | c2_1(a8)) <=> ((~hskp29) | c2_1(a8))),
% 1.09/1.03 inference(rewrite,[status(thm)],[])).
% 1.09/1.03 tff(2422,axiom,((~hskp29) | c2_1(a8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause46')).
% 1.09/1.03 tff(2423,plain,
% 1.09/1.03 ((~hskp29) | c2_1(a8)),
% 1.09/1.03 inference(modus_ponens,[status(thm)],[2422, 2421])).
% 1.09/1.03 tff(2424,plain,
% 1.09/1.03 ((~hskp29) | c2_1(a8)),
% 1.09/1.03 inference(modus_ponens,[status(thm)],[2423, 2421])).
% 1.09/1.03 tff(2425,plain,
% 1.09/1.03 ((~hskp29) | c2_1(a8)),
% 1.09/1.03 inference(modus_ponens,[status(thm)],[2424, 2421])).
% 1.09/1.03 tff(2426,plain,
% 1.09/1.03 ((~hskp29) | c2_1(a8)),
% 1.09/1.03 inference(modus_ponens,[status(thm)],[2425, 2421])).
% 1.09/1.03 tff(2427,plain,
% 1.09/1.03 ((~hskp29) | c2_1(a8)),
% 1.09/1.03 inference(modus_ponens,[status(thm)],[2426, 2421])).
% 1.09/1.03 tff(2428,plain,
% 1.09/1.03 ((~hskp29) | c2_1(a8)),
% 1.09/1.03 inference(modus_ponens,[status(thm)],[2427, 2421])).
% 1.09/1.03 tff(2429,plain,
% 1.09/1.03 ((~hskp29) | c2_1(a8)),
% 1.09/1.03 inference(modus_ponens,[status(thm)],[2428, 2421])).
% 1.09/1.03 tff(2430,plain,
% 1.09/1.03 ((~hskp29) | c2_1(a8)),
% 1.09/1.03 inference(modus_ponens,[status(thm)],[2429, 2421])).
% 1.09/1.03 tff(2431,plain,
% 1.09/1.03 (c2_1(a8)),
% 1.09/1.03 inference(unit_resolution,[status(thm)],[2430, 2409])).
% 1.09/1.03 tff(2432,plain,
% 1.09/1.03 (((~hskp29) | c1_1(a8)) <=> ((~hskp29) | c1_1(a8))),
% 1.09/1.03 inference(rewrite,[status(thm)],[])).
% 1.09/1.03 tff(2433,axiom,((~hskp29) | c1_1(a8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause45')).
% 1.09/1.03 tff(2434,plain,
% 1.09/1.03 ((~hskp29) | c1_1(a8)),
% 1.09/1.03 inference(modus_ponens,[status(thm)],[2433, 2432])).
% 1.09/1.03 tff(2435,plain,
% 1.09/1.03 ((~hskp29) | c1_1(a8)),
% 1.09/1.03 inference(modus_ponens,[status(thm)],[2434, 2432])).
% 1.09/1.03 tff(2436,plain,
% 1.09/1.03 ((~hskp29) | c1_1(a8)),
% 1.09/1.03 inference(modus_ponens,[status(thm)],[2435, 2432])).
% 1.09/1.03 tff(2437,plain,
% 1.09/1.03 ((~hskp29) | c1_1(a8)),
% 1.09/1.03 inference(modus_ponens,[status(thm)],[2436, 2432])).
% 1.09/1.03 tff(2438,plain,
% 1.09/1.03 ((~hskp29) | c1_1(a8)),
% 1.09/1.03 inference(modus_ponens,[status(thm)],[2437, 2432])).
% 1.09/1.03 tff(2439,plain,
% 1.09/1.03 ((~hskp29) | c1_1(a8)),
% 1.09/1.03 inference(modus_ponens,[status(thm)],[2438, 2432])).
% 1.09/1.03 tff(2440,plain,
% 1.09/1.03 ((~hskp29) | c1_1(a8)),
% 1.09/1.03 inference(modus_ponens,[status(thm)],[2439, 2432])).
% 1.09/1.03 tff(2441,plain,
% 1.09/1.03 ((~hskp29) | c1_1(a8)),
% 1.09/1.03 inference(modus_ponens,[status(thm)],[2440, 2432])).
% 1.09/1.03 tff(2442,plain,
% 1.09/1.03 (c1_1(a8)),
% 1.09/1.03 inference(unit_resolution,[status(thm)],[2441, 2409])).
% 1.09/1.03 tff(2443,plain,
% 1.09/1.03 (((~![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp25 | hskp9 | (~ndr1_0) | (~c2_1(a8)) | (~c1_1(a8)) | (~c3_1(a8)))) <=> ((~![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp25 | hskp9 | (~ndr1_0) | (~c2_1(a8)) | (~c1_1(a8)) | (~c3_1(a8)))),
% 1.09/1.03 inference(rewrite,[status(thm)],[])).
% 1.09/1.03 tff(2444,plain,
% 1.09/1.03 ((hskp25 | hskp9 | (~ndr1_0) | (~c1_1(a8)) | (~c3_1(a8)) | (~c2_1(a8))) <=> (hskp25 | hskp9 | (~ndr1_0) | (~c2_1(a8)) | (~c1_1(a8)) | (~c3_1(a8)))),
% 1.09/1.03 inference(rewrite,[status(thm)],[])).
% 1.09/1.03 tff(2445,plain,
% 1.09/1.03 (((~![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp25 | hskp9 | (~ndr1_0) | (~c1_1(a8)) | (~c3_1(a8)) | (~c2_1(a8)))) <=> ((~![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp25 | hskp9 | (~ndr1_0) | (~c2_1(a8)) | (~c1_1(a8)) | (~c3_1(a8))))),
% 1.09/1.03 inference(monotonicity,[status(thm)],[2444])).
% 1.09/1.03 tff(2446,plain,
% 1.09/1.03 (((~![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp25 | hskp9 | (~ndr1_0) | (~c1_1(a8)) | (~c3_1(a8)) | (~c2_1(a8)))) <=> ((~![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp25 | hskp9 | (~ndr1_0) | (~c2_1(a8)) | (~c1_1(a8)) | (~c3_1(a8)))),
% 1.09/1.03 inference(transitivity,[status(thm)],[2445, 2443])).
% 1.09/1.03 tff(2447,plain,
% 1.09/1.03 ((~![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp25 | hskp9 | (~ndr1_0) | (~c1_1(a8)) | (~c3_1(a8)) | (~c2_1(a8)))),
% 1.09/1.03 inference(quant_inst,[status(thm)],[])).
% 1.09/1.03 tff(2448,plain,
% 1.09/1.03 ((~![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp25 | hskp9 | (~ndr1_0) | (~c2_1(a8)) | (~c1_1(a8)) | (~c3_1(a8))),
% 1.09/1.03 inference(modus_ponens,[status(thm)],[2447, 2446])).
% 1.09/1.03 tff(2449,plain,
% 1.09/1.03 (hskp9),
% 1.09/1.03 inference(unit_resolution,[status(thm)],[2448, 117, 2354, 2442, 2431, 2420, 11])).
% 1.09/1.03 tff(2450,plain,
% 1.09/1.03 (~c3_1(a15)),
% 1.09/1.03 inference(unit_resolution,[status(thm)],[1048, 2449])).
% 1.09/1.03 tff(2451,plain,
% 1.09/1.03 (hskp15 | (~c1_1(a21))),
% 1.09/1.03 inference(unit_resolution,[status(thm)],[393, 117, 2367, 2366, 2381, 2365, 2378, 376])).
% 1.09/1.03 tff(2452,plain,
% 1.09/1.03 (hskp15),
% 1.09/1.03 inference(unit_resolution,[status(thm)],[2451, 2379])).
% 1.09/1.03 tff(2453,plain,
% 1.09/1.03 (c1_1(a29)),
% 1.09/1.03 inference(unit_resolution,[status(thm)],[136, 2452])).
% 1.09/1.03 tff(2454,plain,
% 1.09/1.03 (~c3_1(a29)),
% 1.09/1.03 inference(unit_resolution,[status(thm)],[142, 2452])).
% 1.09/1.03 tff(2455,plain,
% 1.09/1.03 (c0_1(a29)),
% 1.09/1.03 inference(unit_resolution,[status(thm)],[414, 117, 1, 2277, 2453, 2454, 408])).
% 1.09/1.03 tff(2456,assumption,(hskp0), introduced(assumption)).
% 1.09/1.03 tff(2457,plain,
% 1.09/1.03 (~c1_1(a1)),
% 1.09/1.03 inference(unit_resolution,[status(thm)],[1207, 2456])).
% 1.09/1.03 tff(2458,plain,
% 1.09/1.03 (c0_1(a1)),
% 1.09/1.03 inference(unit_resolution,[status(thm)],[1218, 2456])).
% 1.09/1.03 tff(2459,plain,
% 1.09/1.03 (((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | c1_1(a1) | (~ndr1_0) | (~c3_1(a1)) | (~c0_1(a1)))) <=> ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp8 | c1_1(a1) | (~ndr1_0) | (~c3_1(a1)) | (~c0_1(a1)))),
% 1.09/1.03 inference(rewrite,[status(thm)],[])).
% 1.09/1.03 tff(2460,plain,
% 1.09/1.03 ((hskp21 | hskp8 | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | (~c0_1(a1))) <=> (hskp21 | hskp8 | c1_1(a1) | (~ndr1_0) | (~c3_1(a1)) | (~c0_1(a1)))),
% 1.09/1.03 inference(rewrite,[status(thm)],[])).
% 1.09/1.03 tff(2461,plain,
% 1.09/1.03 (((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | (~c0_1(a1)))) <=> ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | c1_1(a1) | (~ndr1_0) | (~c3_1(a1)) | (~c0_1(a1))))),
% 1.09/1.03 inference(monotonicity,[status(thm)],[2460])).
% 1.09/1.03 tff(2462,plain,
% 1.09/1.03 (((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | (~c0_1(a1)))) <=> ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp8 | c1_1(a1) | (~ndr1_0) | (~c3_1(a1)) | (~c0_1(a1)))),
% 1.09/1.03 inference(transitivity,[status(thm)],[2461, 2459])).
% 1.09/1.03 tff(2463,plain,
% 1.09/1.03 ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | (~c0_1(a1)))),
% 1.09/1.03 inference(quant_inst,[status(thm)],[])).
% 1.09/1.03 tff(2464,plain,
% 1.09/1.03 ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp8 | c1_1(a1) | (~ndr1_0) | (~c3_1(a1)) | (~c0_1(a1))),
% 1.09/1.03 inference(modus_ponens,[status(thm)],[2463, 2462])).
% 1.09/1.03 tff(2465,plain,
% 1.09/1.03 (~c3_1(a1)),
% 1.09/1.03 inference(unit_resolution,[status(thm)],[2464, 117, 1421, 523, 2458, 2457, 21])).
% 1.09/1.03 tff(2466,plain,
% 1.09/1.03 (^[V: $i, U: $i] : refl((hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))),
% 1.09/1.03 inference(bind,[status(th)],[])).
% 1.09/1.03 tff(2467,plain,
% 1.09/1.03 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.09/1.03 inference(quant_intro,[status(thm)],[2466])).
% 1.09/1.03 tff(2468,plain,
% 1.09/1.03 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.09/1.03 inference(rewrite,[status(thm)],[])).
% 1.09/1.03 tff(2469,plain,
% 1.09/1.03 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp21) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp21))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))))),
% 1.09/1.03 inference(bind,[status(th)],[])).
% 1.09/1.03 tff(2470,plain,
% 1.09/1.03 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp21) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.09/1.03 inference(quant_intro,[status(thm)],[2469])).
% 1.09/1.03 tff(2471,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause174')).
% 1.09/1.03 tff(2472,plain,
% 1.09/1.03 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.09/1.03 inference(modus_ponens,[status(thm)],[2471, 2470])).
% 1.09/1.03 tff(2473,plain,
% 1.09/1.03 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.09/1.03 inference(modus_ponens,[status(thm)],[2472, 2468])).
% 1.09/1.03 tff(2474,plain,(
% 1.09/1.03 ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.09/1.03 inference(skolemize,[status(sab)],[2473])).
% 1.09/1.03 tff(2475,plain,
% 1.09/1.03 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 1.09/1.03 inference(modus_ponens,[status(thm)],[2474, 2467])).
% 1.09/1.03 tff(2476,plain,
% 1.09/1.03 (~c2_1(a1)),
% 1.09/1.03 inference(unit_resolution,[status(thm)],[1201, 2456])).
% 1.09/1.03 tff(2477,plain,
% 1.09/1.03 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp21 | c3_1(a29) | c1_1(a1) | c2_1(a1) | (~ndr1_0) | c3_1(a1) | (~c1_1(a29)) | (~c0_1(a29)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp21 | c3_1(a29) | c1_1(a1) | c2_1(a1) | (~ndr1_0) | c3_1(a1) | (~c1_1(a29)) | (~c0_1(a29)))),
% 1.09/1.03 inference(rewrite,[status(thm)],[])).
% 1.09/1.03 tff(2478,plain,
% 1.09/1.03 ((hskp21 | (~ndr1_0) | c3_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c3_1(a1) | c1_1(a1) | c2_1(a1)) <=> (hskp21 | c3_1(a29) | c1_1(a1) | c2_1(a1) | (~ndr1_0) | c3_1(a1) | (~c1_1(a29)) | (~c0_1(a29)))),
% 1.09/1.03 inference(rewrite,[status(thm)],[])).
% 1.09/1.03 tff(2479,plain,
% 1.09/1.03 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp21 | (~ndr1_0) | c3_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c3_1(a1) | c1_1(a1) | c2_1(a1))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp21 | c3_1(a29) | c1_1(a1) | c2_1(a1) | (~ndr1_0) | c3_1(a1) | (~c1_1(a29)) | (~c0_1(a29))))),
% 1.09/1.03 inference(monotonicity,[status(thm)],[2478])).
% 1.09/1.03 tff(2480,plain,
% 1.09/1.03 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp21 | (~ndr1_0) | c3_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c3_1(a1) | c1_1(a1) | c2_1(a1))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp21 | c3_1(a29) | c1_1(a1) | c2_1(a1) | (~ndr1_0) | c3_1(a1) | (~c1_1(a29)) | (~c0_1(a29)))),
% 1.09/1.03 inference(transitivity,[status(thm)],[2479, 2477])).
% 1.09/1.03 tff(2481,plain,
% 1.09/1.03 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp21 | (~ndr1_0) | c3_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c3_1(a1) | c1_1(a1) | c2_1(a1))),
% 1.09/1.03 inference(quant_inst,[status(thm)],[])).
% 1.09/1.03 tff(2482,plain,
% 1.09/1.03 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp21 | c3_1(a29) | c1_1(a1) | c2_1(a1) | (~ndr1_0) | c3_1(a1) | (~c1_1(a29)) | (~c0_1(a29))),
% 1.09/1.03 inference(modus_ponens,[status(thm)],[2481, 2480])).
% 1.09/1.03 tff(2483,plain,
% 1.09/1.03 ($false),
% 1.09/1.03 inference(unit_resolution,[status(thm)],[2482, 117, 1421, 163, 161, 2457, 2476, 2475, 150, 2465])).
% 1.09/1.03 tff(2484,plain,((~hskp0) | hskp21 | (~c1_1(a29)) | c3_1(a29) | (~c0_1(a29)) | hskp8), inference(lemma,lemma(discharge,[]))).
% 1.09/1.03 tff(2485,plain,
% 1.09/1.03 ((~hskp0) | hskp21 | (~c1_1(a29)) | c3_1(a29) | (~c0_1(a29))),
% 1.09/1.03 inference(unit_resolution,[status(thm)],[2484, 2277])).
% 1.09/1.03 tff(2486,plain,
% 1.09/1.03 (~hskp0),
% 1.09/1.03 inference(unit_resolution,[status(thm)],[2485, 2455, 2280, 2454, 2453])).
% 1.09/1.03 tff(2487,plain,
% 1.09/1.03 (^[U: $i] : refl((hskp2 | hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp2 | hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))),
% 1.09/1.03 inference(bind,[status(th)],[])).
% 1.09/1.03 tff(2488,plain,
% 1.09/1.03 (![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.15/1.03 inference(quant_intro,[status(thm)],[2487])).
% 1.15/1.03 tff(2489,plain,
% 1.15/1.03 (![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.15/1.03 inference(rewrite,[status(thm)],[])).
% 1.15/1.03 tff(2490,plain,
% 1.15/1.03 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp0) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp0))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp0) | hskp2) <=> ((hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp2))), rewrite(((hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp2) <=> (hskp2 | hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp0) | hskp2) <=> (hskp2 | hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))))),
% 1.15/1.03 inference(bind,[status(th)],[])).
% 1.15/1.03 tff(2491,plain,
% 1.15/1.03 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp0) | hskp2) <=> ![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.15/1.03 inference(quant_intro,[status(thm)],[2490])).
% 1.15/1.03 tff(2492,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp0) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause157')).
% 1.15/1.03 tff(2493,plain,
% 1.15/1.03 (![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.15/1.03 inference(modus_ponens,[status(thm)],[2492, 2491])).
% 1.15/1.03 tff(2494,plain,
% 1.15/1.03 (![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.15/1.03 inference(modus_ponens,[status(thm)],[2493, 2489])).
% 1.15/1.03 tff(2495,plain,(
% 1.15/1.03 ![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.15/1.03 inference(skolemize,[status(sab)],[2494])).
% 1.15/1.03 tff(2496,plain,
% 1.15/1.03 (![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.15/1.03 inference(modus_ponens,[status(thm)],[2495, 2488])).
% 1.15/1.03 tff(2497,plain,
% 1.15/1.03 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp2 | hskp0 | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a6)))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp2 | hskp0 | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a6)))),
% 1.15/1.03 inference(rewrite,[status(thm)],[])).
% 1.15/1.03 tff(2498,plain,
% 1.15/1.03 ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp2 | hskp0 | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a6)))),
% 1.15/1.03 inference(quant_inst,[status(thm)],[])).
% 1.15/1.03 tff(2499,plain,
% 1.15/1.03 ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp2 | hskp0 | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a6))),
% 1.15/1.03 inference(modus_ponens,[status(thm)],[2498, 2497])).
% 1.15/1.03 tff(2500,plain,
% 1.15/1.03 (hskp2 | hskp0 | (~c1_1(a6))),
% 1.15/1.03 inference(unit_resolution,[status(thm)],[2499, 117, 2391, 2390, 2496])).
% 1.15/1.03 tff(2501,plain,
% 1.15/1.03 (hskp2),
% 1.15/1.03 inference(unit_resolution,[status(thm)],[2500, 2486, 2392])).
% 1.15/1.03 tff(2502,plain,
% 1.15/1.03 (~c1_1(a5)),
% 1.15/1.03 inference(unit_resolution,[status(thm)],[1128, 2501])).
% 1.15/1.03 tff(2503,plain,
% 1.15/1.03 (~c0_1(a5)),
% 1.15/1.03 inference(unit_resolution,[status(thm)],[1250, 2501])).
% 1.15/1.03 tff(2504,plain,
% 1.15/1.03 (~c1_1(a15)),
% 1.15/1.03 inference(unit_resolution,[status(thm)],[500, 2449])).
% 1.15/1.04 tff(2505,plain,
% 1.15/1.04 (~c2_1(a15)),
% 1.15/1.04 inference(unit_resolution,[status(thm)],[506, 2449])).
% 1.15/1.04 tff(2506,plain,
% 1.15/1.04 ($false),
% 1.15/1.04 inference(unit_resolution,[status(thm)],[2349, 2505, 2504, 2503, 2502, 2450, 1])).
% 1.15/1.04 tff(2507,plain,(hskp30), inference(lemma,lemma(discharge,[]))).
% 1.15/1.04 tff(2508,plain,
% 1.15/1.04 (c0_1(a20)),
% 1.15/1.04 inference(unit_resolution,[status(thm)],[2097, 2507])).
% 1.15/1.04 tff(2509,plain,
% 1.15/1.04 (c2_1(a20)),
% 1.15/1.04 inference(unit_resolution,[status(thm)],[2119, 2507])).
% 1.15/1.04 tff(2510,plain,
% 1.15/1.04 (c3_1(a20)),
% 1.15/1.04 inference(unit_resolution,[status(thm)],[2108, 2507])).
% 1.15/1.04 tff(2511,plain,
% 1.15/1.04 ((~c2_1(a20)) | (~c3_1(a20)) | (~c0_1(a20))),
% 1.15/1.04 inference(unit_resolution,[status(thm)],[2156, 2277])).
% 1.15/1.04 tff(2512,plain,
% 1.15/1.04 ($false),
% 1.15/1.04 inference(unit_resolution,[status(thm)],[2511, 2510, 2509, 2508])).
% 1.15/1.04 % SZS output end Proof
%------------------------------------------------------------------------------